on the polymerization of sulfur and selenium in the liquid ... · equilibrium of liquid sulfur and...
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On the polymerization of sulfur and selenium in the liquid state: an ESR studyCitation for published version (APA):Koningsberger, D. C. (1971). On the polymerization of sulfur and selenium in the liquid state : an ESR study.Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR109059
DOI:10.6100/IR109059
Document status and date:Published: 01/01/1971
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ON THE POL YMERIZATION
OF
SULFUR AND SELENIUM IN THE LIOUID STATE
AN ESR STUDY
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR
IN DE TECHNISCHE WETENSCHAPPEN
AAN DE TECHNISCHE HOGESCHOOL TE EINDHOVEN,
OP GEZAG VAN DE RECTOR MAGNIFICUS PROF. DR. IR. A.A.TH.M. VAN TRIER
VOOR EEN COMMISSIE UIT DE SENAAT
IN HET OPENBAAR TE VERDEDIGEN
OP VRIJDAG 19 MAART 1971 DES NAMIDDAGS TE 4 UUR
DOOR
Dl EDERIK CHRISliAAN KONINGSBERGER
GEBOREN TE DELFT
offsetdrukkerij elke tilburg
DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR
DE PROMOTOR
PROF.DR. P. VAN DER LEEDEN
EN
DE CO-PROMOTOR
PROF.DR. G.G.A. SCHUIT
aan pia ika
11Met al ons weten
aîs de vogel op
wie zoveel- belangr1:jks voorb1:j
gaat, wam• hij niets van begrijpt"
Lauritlard
CO.NTENTS
INJ"RODUCTION
GRAPTER 1. Polymerization theory
1. I. Introduetion
I . 2. Neu! approach in the
I. 3. Ubriwn
when monovalent
CHAPTER 2. Survey of literature on experimental determination
of the polymerization parameters of liquid sulfur
and liquid selenium
Evaluation of a reliability interval for
obtained from viscosity measurements
2. I. Introduetion
2.2. Weight fraction (~}
2.3. Determination the heat oj'
manber average chain
measurements of sutfur and selenium
2.4. interval for the value of ~Hry, obtained ,, from viscosity measurements
2.5. Magnetic measurements
CHAPTER 3. Lineshape analysis
3. I. Intx•oduction
3.2. Mathematical basis
Cl~PTER 4. Reactivity of the chain end spin state
4. 1. Introduetion
4.2. Calaulations of reaction rate constant
ll
16
16
17
20
23
23
24
29
33
36
39
39
40
43
43
43
CHAPTER 5. Experimental te::hniques
5.1. Introduetion
5. 2 .. ESR spectrometer
5.3. High temperature ESR
5.4. The measurement of the
5.5. Sample
CHAPTER 6. Evaluation of th~ polymerization parameters from
the results of the ESR measurements
6. I. Introduc:tion
6.2. ESR measurements
6. 3. Calcuîation of the
process
6.4. Calculation of the kinetic data of the
process
6.5. Discussion
CHAPTER 7. Experiments on the quenched liquid state. "Catena-S~'
allotrope
7. 1. Introduetion
48
60
64
67
67
67
79
96
98
102
102
7. 2. Arguments givert in li terature for the exis tanc:e 1 02
of the
7. 3. ResuLts
7 J,, At tempt at an
Discuss1.:on
CHAPTER 8. Influence of oxygen on the selenium ESR signal.
Electrical conductivity and skin effect
8.1. Introduetion
8.2. of selenium samples, containing
amounts of oxygen
8.3. Electrical and the reZ.a.tion to the
measured ESR
8.4. sk1:n effect
104
109
115
115
J 15
117
119
CHAPTER 9. Final remarks LJ:d conclusions
Swnmary 121
Appendix A 123
Appendix B 124
Appendix 127
Appendix D 127
lieferences 128
List of symboZs 132
Samenvatting 134
DankzJoord 136
Levensbericht 137
I 1
IN:l'RODUCT ION
At a temperature of J60°C the viscosity of liquid sulfur risEs ~
factor 104 within some ten :legrees (see fig. I, curve l). At bi5hsr
temperatures the viscosity decreases with rising temperature. The
viscosity of selenium above its melting point (T ; 220°C) shows the same m
behaviour (see fig. l, curve 2). The mechanism determining the temperature
dependenee of the viscosity of liquid sulfur anè selenium has been the
subject of many investigations. A satisfactory theoretica! model can be based
on a polymerization process invalving an equilibrium between rings and
chains.
Fig. 1. Viscosity n (poise) versus terrr,;;er•atu.re T
Bcceon ei; a;.-.
curve 2: El data ob~ained f:r>om !Jobinsh ec
x data ob~ained f:r•om liu:t:r~eun "' i;J,
12
When the chain ends possess free electron spin states magnetic
measurements are an important tool in investigating the polymerization
process. Determination of the static magnetic susceptibility gives the
number of free spins. With this information and that of the weight
fraction polymer the number average chain length can be calculated. From
the temperature dependenee of the number average chain length the heat of
scission of a bond in a chain can be derived. The measurement of the
dynamic susceptibility using electron spin resonance (ESR) is usually more
sensitive than the static one. Moreover, it has the advantage of discriminating
between paramagnetic contributions of different origin. Apart from the
intensity (number of free spins) one can get information from lineshape and
linewidth of the ESR absorption. If the life-time of the spin state is
determined by one single relaxation mechanism, the lineshape must be
Lorentzian. If this relaxation mechanism is dominated by one type radical
reaction, it is possible to find its reaction rate from the value of the
linewidth. From the temperature dependenee of the linewidth one can calculate
its activatien energy.
Gee (4) was the first to develop a satisfactory model of the polymerizatio
process for sulfur based upon an equilibrium between eight-membered rings and
linear-chain polymers. This model is basic for all the theoretica! work to
be cited. From this concept he was able to calculate numerical values for the
parameters which describe the polymerization equilibrium.
Other authors (5) (6) later developed alternative treatments of the
polymerization equilibrium. The methods used by Gee and the other authors
each have their own specific drawbacks. There remained an opportunity to try
a new method of descrihing the polymerization equilibrium. This will be
developed in chapter I, where the disadvantages of the other treatments will
be discussed. \~en iodine is added, the viscosity of sulfur and its temperature
dependenee shows striking changes (see fig. 2). By extension of the newly
developed description of the polymerization process to the case of iodine
dope it was possible to calculate the number average chain length using the
spin intensity measurements on doped samples and the added dope concentration.
In chapter l the calculation procedure on doped material will be developed.
Assuming values for some equilibrium constants, the number average chain
length and the spin intensity can be evaluated. The number of spins, which is
13
determined experimentally, is compared with the calculated values.
Fig. 2. Viscosity 11
,// ' .
pure sulfur
-------- 'i't "1. J
-· -·- 4 °/o J
versus temperature T
Data were obtained from J.Schenk et ar. (7).
A survey of the literature on experimental determinations of the
polymerization parameters is to be found in chapter 2. The theoretica!
calculations of Gee and those of Eisenberg and Tobolsky on the polymerization
equilibrium of liquid sulfur and selenium (8) are based upon experimental
values of the weight fraction polymer. The reliability of different
measurements of the weight fraction polymer in sulfur and selenium will be
discussed. The most reliable data are chosen to calculate in chapter 6 the
polymerization parameters from the results of our ESR measurements. Several
authors (4) (5) (6) have tried to determine polymerization parameters from
viscosity data. Applying Gee 1 s methad to viscosity data of sulfur and selenium,
we have tried to give a reliability interval for the value of the heat of
scission bonds in chains obtained from viscosity data.
Magnetic measurements (9) (JO) (IJ) on the polymerization of liquid sulfur
and selenium are discussed. We could find no ESR measurements on liquid
pure selenium in the literature.
In chapter 3 the mathematica! lay-out of a computer program is described
to campare the lineshape of the ESR absorption with given analytica! functions
(Lorentzian, Gaussian). This procedure enables one to calculate also the
parameters of the chosen best fit lineshape tagether with their limits of
accuracy.
!4
The reactivity of the chain end spin state will be discussed in
chapter 4. The reaction rate and the activatien energy of different types
of radical reactions are calculated from the theoretica! models involved.
The experimental techniques used are described in chapter 5. The
maximum temperature obtainable with a commercially available ESR cavity
is 350°C. A high ternperature ESR cavity has been developed with a stable
quality factor of 4000, enabling us to measure reliably and accurately
spin concentrations up to 800°C.
The determination of the intensity of an absorption line in spectroscopie
investigation is always a rather difficult problem, For the particular
difficulaties concerning the measurement of the number of free spins with
ESR methods Casteleyn and Ten Bosch (12) have given a very thorough
analysis of systernatic errors. Starting frorn their work, the errors introduced
with the measurement of the spin intensity as a function of the ternperature,
are investigated. The rnethod used for the deterrnination of the spin
intensity is described.
The rather strong decrease of the viscosity of sulfur and selenium due to
srnall amounts of some irnpurities indicated that the purity of the sulfur
and selenium material had to be very high. At the maximum chain length (of the
order of 10 6 atoms) the paramagnetic impurities must be an order of
magnitude lower than I ppm to ensure reliable spin density measurements.
Highly pure commercially available material was used; however, it was necessary
to free the sulfur from carbon and the selenium from oxygen.
In chapter 6 ESR measurements on pure and iodine doped sulfur and pure
selenium are described. The polymerization parameters calculated from the
results of the ESR measurements are discussed and compared with values
obtained by other authors. The reaction rates and activatien energies of the
radical reactions determining the lifetime of the spin state are calculated
from the ESR results.
Determination of the weight fraction polymer in liquid sulfur led to
the discovery of various phenomena, which were explained by the assumption
of the existence of short sulfur chains (13). In chapter 7
the results of ESR measurements on quenched sulfur are described and
compared with the concept of catena-s8
•
15
In addition to th.e cha.i.ned ESR signal other signals have been observed
in selenium which are attri!Juted to oxygen impurities (14). Unlike sulfur,
liquid selenium has a relatcvely high electrical conductivity (cr = JO 1
at T = 300°C) which may make; corrections for skin depth necessary. The
addition of oxygen impurities changes the conductivity. The conductivity
has been previously investigated by many authors with conflicting results.
The conductivity of selenium, purified by different methods has been
measured in our laboratory. The results of the ESR and conductivity
measurements are given and discussed in Chapter 8. At the end of this
thesis final remarks and conclusions about the results of our ESR
measurements are given.
-] cm
16
GRAPTER I
POLYMERIZATION THEORY
1. 1. Introduetion
The theoretica! description of the polymerization equilibrium of
liquid sulfur by Gee (4) has the drawback that it leads to different
expressions for the temperature dependenee of the number average
chain length below and above the temperature of initial polymerization.
This disadvantage has been eliminated by Tobolsky et al. (5), who
derived a closed formula covering both ranges, the chains now
being assumed to contain units of eight atoms. To avoid this somewhat
arbitrary assumption, Poulis et al. (6) proposed another procedure
which, however, lacked somewhat in simplicity. For a detailed
description of these theories the reader is referred to the literature.
By choosing suitable reactions in descrihing the polymerization
equilibrium, it is possible to remove the assumption of the eight atomie
chain units comparatively simple. In all the theoretica! work cited the
equilibrium constant of the polymerization reaction is assumed to be
independent of the length of the reactants. In the new treatment
described bel01J this assumption will also be made. A parameter p
will be introduced, which is also used by Flory (15) to calculate the
number average chain length and the molecular weight distribution of
condensation and addition polymers.
Section 1.2.deals with the new approach in descrihing the polymerization
equilibrium of sulfur and selenium in the liquid state.
Eisenberg et al. (16) calculated theoretically the number average chain
length of selenium as a function of the added iodine dope at a temperature
of T = 300°C. Also in this case the chain length was assumed to contain
units of eight atoms. Moreover, the iodine dope was taken up in the
polymerization equilibrium by reaction with an eight-membered ring.
The newly developed description of .the polymerization equilibrium is
extended to the case of iodine dopeinsection 1.3.
17
I. 2. New approach in descrihing the polymerization equilibrium of
Ziquid sulfur and selenium
From different experiments described in the literature (see
chapter 3) the liquid state can be assumed to consist of a mixture
of eight membered rings and diradical linear chains. In descrihing
the polymerization equilibrium no attention will be paid here to the
way in which this equilibrium is reached. This will be done in
chapters 4 and 6. To avoid the problem mentioned in the introduetion
the following equilibrium reactions were chosen:
where
C .• C./C.+. , 1. J 1. J
R concentratien eight-membered rings,
c. concentratien diradical chains containing 1.
K1,K2
=equilibrium constants.
(1.2.1)
(I .2. 2)
In the following the symbol used to denote a molecule will be equal to the
symbol for a concentration. As unit of concentratien the kmole/kg will
be used. Reaction (1.2.2) describes the equilibrium between chains of
different lengths. Assuming that the equilibrium constant K2 is
independent of i and j, a distribution tunetion for Ci can be derived.
It will then be possible to express in an easy and simple way
the number average chain length Pn in the equilibrium constants K1
and the ring concentratien R. To relate the formal theory to the
experiments, formulae will be derived to express Pn, K2 and K1
in
the spins N, the weight fraction polymer ~ and the total
concentratien atoms M0
present.
The distribution function may be derived from the second equation
chosen.
*(number concentrat ion)
Choosing j in formula (1.2.2):
c. ].
I C I
18
For shortness we wil! introduce the abbrevation:
p
Combining (1.2.3) and (1.2.4) gives the concentratien of chains
containing i-atoms as a function of p and K2
:
i p K2
(1.2.3)
(I. 2. 4)
(1.2.5)
The distribution function for the molefraction chains containing i-atoms
is derived as fellows:
n. ].
i-1 ( 1-p)p • (1.2.6)
The distribution between ring and chain concentratien is given by the first
equation (1.2.1). The ring concentratien R can be expressed in p, K1
and
K2 with the help of (1.2.1):
R
When the condition is fulfilled that all the atoms present M0
are
incorporated in rings or in chains:
M 0 i
+ SR
p can be calculated as a function of K1
, K2
and M0
•
(1.2. 7)
(I. 2. 8)
In this way the concentrations Ci and Rare known as a function of K1
, K2
and M0
•
The number average chain length Pn is given by:
p n
l:in. = -1-i l_ - -p (1.2.9)
19
Using this relation and {1.2.7), Pn can be derived as a function of
K1
, K2
and R:
p n
1- 'fj RK1/K
2
(1.2. JO)
Formulae {1.2.6) and (1.2.9) are analogous to those derived by Flory {17)
for the distribution function of the molefraction n. and the number ~
average chain length Pn. The parameter p is the intermediary connecting
reaction kinetics to molecular distribution. Formula {1.2.10) is valid
in the whole temperature range of the liquid state. The derivation of
the Flory distribution from reaction (1.2.2) makes it possible to avoid
assumptions about the number of atoms in a chain unit.
The formal theory is related to the ESR experiments by the fact
that the total number of chains C = I;Ci is equal to N/2 , where N is l
the number of spins. The total number of atoms incorporated in chains
is equal to 4M0
• The number average chain length is now given by:
q>Mo Pn = NTi
With the help of {1.2. 9) p can be expressed in M0 ,~,N:
p =
K2 can be calculated from formula {1.2.5):
c l:C . • l. l.
Combining (1.2.12) and (1.2.13) gives:
N/2 •
K1 can be evaluated using formula (1.2.7), (1.2.12) and (1.2.14):
M 0
(I - N/2<PM / , 0
{I. 2. 11)
(1.2.12)
(1.2. 13)
(I .2.14)
(1.2.15)
When P »I: n
20
p
Formulae (1.2.15) and (1.2.14) can be simplified if P~1:
(I .2.16)
(1.2.17)
(I. 2. 18)
1.3. Desaription of the polymerization equilibrium when monovalent dope
(iodine) is added
To describe the polymerization equilibrium in this case the following
reactions are chosen:
KI R~ c8 KI c
8/R (I .3. I)
K2 c.+c. K2 c.c./c.+. (I .3.2) ci+j~ ~ J ~ J ~ J '
K'
ei! 2 C.+X K' CiX/Cil (1.3.3) ~ ' ~ 2
ci2 ciJ+x 4Kz = 1X/Ci2 (1.3.4)
where Gil and ci2 mean the concentratien chains with i atoms terminated
by one and two dope atoms, respectively.x denotes the concentration
dope atoms. The equilibrium constant 4K2 ' for reaction (1.3.4) arises
from counting the number of possibilities for breaking and combining
molecules in comparison with reaction (1.3.3). By assuming that all the
21
dope atoms are in equilibrium with chain ends, the presence of 12 molecules is neglected.
To find a distribution function for Cil and ci2
formula (1.2.5) will
be used:
c. ~
'!'he dis tribution funation for 'cil is derived by using formulae (I. 3. 3)
and (1.3.5):
Frem formulae (1.3.4) and (1.3.6) follows for ci2 :
Ci2 = Ci1X/4K2 = piX2K2/4(K2)2.
It is now possible to calculate the number average chain length by:
~ei + ~ei! + ~ ~
Using (1.3.5), (1.3.6) and (1.3.7) gives after summation:
p n -p
where p in principle has another value as in the case of the undoped
material.
(1.3.5)
(1.3.6)
( l. 3. 7)
(1.3.8)
(1.3.9)
A formula for the total number of atoms M0
(S or Se) can be derived by:
M 0
SR+ ~ici + ~ici 1 + ~ici2 • L ~ ~
With the aid of (1.3.5), (1.3.6) and (1.3.7), (1.3.10) is transferred
into:
M 0
K2 . K2 2 (K + -x + ---x )
2 Ki 4(k' )2 2
(1.3.10)
(1.3.11)
The totalconcentration of rlope
x 0
22
atoms (X0
) kmole/kg is:
x+ ~cil + z~ci2' ~ ~
which becomes, after substitution of (1.3.6) and (1.3.7):
K2 K x x + (K' x
+ __ 2_ X2) 0 -p 2 2 (KI) 2
2
The number of spins N is given by:
N z~ci + ~cil ' ~ ~
from which with (1.3.6) and (1.3.7) is derived:
K2 N = _L. (2K
2 + i(' X)
J-p 2
(I. 3. 12)
(I. 3. 13)
(I. 3. 14)
( l. 3. IS)
In the experiments M0
and K0
are known. When K1
and K2 are evaluated
from the ESR measurements on the pure material and the number of spins
in doped samples has been measured, Pn can be calculated.
~1oreover,the model involved can be checkeá by calculating Pn and N and
comparing the evaluated values with those obtained in the first case.
The evaluation of N and
X and M are known. 0 0
can only be carried out when K1
, K2
,
23
CHAPTER 2
SURVEY OF LITERATURE ON EXPERIMENTAL DETERMINATIONS OF THE POLYMERIZATION
PARAMETERS OF LIQUID SULFUR AND SELENIUM. l'.'VALUATION OF A RELIABILITY
INTERVAL FOR ~H2 , OBTAINED FROM VISCOSITY MEASUREMENTS.
2.1. Introduetion
The evaluation of the polymerization parameters P n, K1 and is
only possible when the weight fraction polymer (~) is known. In
section 2.2 the reliability of the determinations of the parameter (~)
by different authors is discussed and the most reliable data are chosen.
Direct and indirect experimental data will typify the reliability interval
of ~. In section 2.3 the determination of the number average chain length
Pn and the heat of reaction ~H2 by different authors from viscosity
measurements are given and discussed. In section 2.4 we will make an attempt
to calculate a reliability interval for the value ~H2 for sulfur and
selenium thus obtained. The data for the weight fraction polymer chosen
in sectien 2.2 will be used. The results of magnetic measurements,
interpreted as caused by a polymerization process and from which
polymerization parameters have been determined, will be given in section
2.5. The discussion of some of these results will be dealt with later
(chapter 6).
24
2.2. Weight fraation polymer (~)
a. Sulfur
Gee's (4) theoretical description (1952) of the "disco1;1tinuity" in
the viscosity of liquid sulfur was based upon the choice of the reaction
between rings and chains:
(2 .2.1)
For Pn >> I and applying Van 't Hoffs law to K3
he derived the following
formula for the temperature dependenee of the weight fraction polymer $
valid above the transition point:
I - exp (2.2.2)
Applying (2.2.2) to data of the weight fraction polymer given by
Hammick et al. (18) (1928) (fig. 3 points 1), he plotted -ln(1-$) versus
1000/T.
Assuming 6H3
to be constant and extrapolating to ~ o he found 0 Gee' s curve fits the data 6H3 4.0 kcal/mole and T$: 423 K (150 C).
of Hammick for 160°C < T < 200°C rather well. See fig. 3 curve I. Gee
suggested (in 1952) that the discrepancies for T > 200°C arose from
experimental errors in the determination of the weight fraction polymer.
Fairbrather et al. (19) analyzing in 1954 the specific heat data from Braun
et al. (20), derived for the temperature dependenee of 6H3
:
-3180 + 9.98(T- T~'), (2.2.3)
where T'$ = 433 K (160°C) is the temperature at which the transition in the
viscosity takes place. Inserting (2.2.3) in (2.2.2) with T$ = T'$, ~ may be
calculated as a function of the temperature (T > T'$) (see fig. 3 curve II).
25
60
50-
IJ)
20
10-
0
~00
Fig. 3. Weight fraction potymer ~ versus temperature T (°C).
points 1: 0 Hammick,
2: 0 P.W.Schenk (gas stream, pure),
J: ® J.Schenk (Ziquid N2, pure),
4: x J.Schenk (water, pure),
5: r8l J.Schenk (water, impure).
curves I: Gee (theoretical}.(~ 1 ), II: Fairbrather et al. ( t;neoretical) ( ~2) •
III: Accepted (experimental) (~m) .
26
The remairring diserepar c:ies led P. H. Schenk (21) (1955) and J. Schenk
(22) (1956) to a c:areful im·estigation of the possible experimental errors
that may occur in the deten,ination of the weight fraction polymer. short
survey of these sourees of '·rror will now be given.
The usual experimental approach to the determination of this fraction
consists in quenchin~ the liquid state from different temperatures and in
assuming that the part which is insoluble in cs2 is the polymer fraction
belauging to the temperature from which it has been quenched.
Hammick et al. (18) quenched draplets of liquid sulfur in water and
the influence of the size of sulfur particles on the rate of
the equilibrium. He obtained the highest fraction polymer by
quenched liquid sulfur dispersed in a salution of H2so
4 and (N~4 ) 2 so4
3 points 1).
P.H. Schenk (21) developed another methad to quench the equilibrium.
A cold gas stream is blown against a thin squirt of viseaus sulfur, issuing
from a narrow opening at the bottorn of a heating vessel. The tiny sulfur
particles were caught on a plate. He did not find his methad suitable
for temperatures between 160°C and 250°C sirree the viscosity of sulfur in
that region is too high. Avoiding carefully the error sourees described
below and using purified sulfur, he obtained the results given in
fig. 3 points 2. To study the influence of the preserree of water he used a
a moistened gas stream. Queuehing from T = 400°C, he found 30% lower
values for ~. He also studied the influence of impurities. Impure sulfur
quenc:hed from the same temperature gave a 50% higher value weight fraction
polymer than the pure materiaL The initial state of sulfur quenched from
above the transition point is an unstable plast~c configt ation.
After about one day this material has hardened. During the harderring
process the rings crystallize ~n the orthorhombic farm (S )· In the Cl.
harderred state the sulfur can be ground and the orthorhombic farm
dissolved. It was found that in the plastic state visible light transfers
the polymers to rings. Polymers irradiated for one hour by sunlight,
changed for the greater part into the orthorhombic configuration.
J. Schenk (22) stuclied the influence of time on the conversion of the
harderred polymers into the stable orthorhombic farm. This process has a
27
relaxation time of the order of some months. By quenching the liquid
state in liquid nitrogen he avoided the harderring process. Below T = -30°C
this amorphous state is stable and can be ground at liquid nitrogen
temperatures. After warming up the material, the dissolving procedure can
be applied immediat~ly. Fig. 3 points 3 shows the weight fraction polymer
obtained by thus queuehing purified sulfur in liquid nitrogen. Points 4
indicate the weight fraction polymer found by queuehing purified sulfur in
water.
Summarizing, the following conclusions may be drawn. The speed of
freezing the equilibrium by quenching in water is lower than with the "gas
stream" and "liquid nitrogen" method. Moreover, water has an unfavourable
influence on the determination of the weight fraction polymer.Consequently
Hammiek's determinations have become rather unreliable. From the described
experiments it is reasonable t6 believe that the "gas stream" and "liquid
nitrogen" methad produce the same "freezing time".
It is seen from fig. 3 that it is possible to draw a curve (III) through
points 3 and 4. It may, however, be possible that the cooling speed in
both methods is not high enough and that the measured weight fractions
polymer are not identical (in fact too low) to those present in the liquid
state. Curve lil will be chosen as the most reliable experimental data
known from the literature. Fairbrother's calculated data, curve II, will
be considered as an alternative. In the following these curves are indicated
by and ~ 2 respectively.
b, Selenium
Briegleb (23) investigated the different allotropie modifications of
selenium in 1929. He quenched the liquid state in finely divided ice
particles, cooled at T = -180°C. Just as in the case of sulfur, a fraction
of the quenched material was insoluble in cs2• Quenching in water gave
irreproducible results. Solving the soluble part of the quenched material
proceeded very slowly. It was necessary to treat the quenched material for
several hours with cs2 . No other quenching experiments need to be taken
into account. Results from infrared spectra (25) on liquid selenium give
support to the idea that the non-polymer weight fraction consists of eight
membered selenium rings. Accepting this idea, we can apply similar methods
28
Fig. 4. Weight f:raction poZyme:r ~ versus tempe:rature ~ (°C)
points 0 Briegleb (selenium).
0 accepted experimental (sulfur),
curves I: accepted experimental (selenium),
II: accepted theo:retical (sulfur),
III: accepted experimental (sulfur).
and procedures to investigate the liquid state of sulfur and selenium.
For the reasons mentioned the weight fractions polymer found by
Briegleb are assumed to be corr·esponding to the polymer fractions in the
liquid state. Fig. 4 points 0 shows the results of Briegleb. As studies on
the determination of ~ are rather scarce, the uncertainties may be more
considerable than in the case of sulfur.
29
2.3. Determination of the heat of reaetion and the number average
ohain length Pn jrom visoosity measurements of liquid sulfur and
selenium
2.3.1. Introduetion
This sectien starts with a survey in adapted forrn of the general ideas
developed by Gee to calculate öH2
and Pn from viscosity measurements of
liquid sulfur. To obtain these data from viscosity measurements it is
necessary to have a description of the dependenee of the viscosity on the
concentratien (c) of a salution of polymers in a solvent.
In this conneetion it is customary to use the so-called "intrinsic"
viscosity
where:
defined by:
[n] lim c+o
n viscosity of the solution,
n0
viscosity of the solvent,
c concentration polymer.
The relationship between viscosity of the solution and polymer
concentration is described by Buggins (25):
where:
k' Huggins' slope constant, value usually between
0.3 and 0.5.
Assuming that q, may take the function of c, (2.3.2) may now be
written:
n/ n = I + ( n] <P + k' [ n] 0
(2.3.1)
(2.3.2)
(2.3.3)
30
The relationship between intrinsic viscosity and number average
chain length can be expressed by:
where:
[n] APa n
A constant, average value 0.9 calculated for the
polymers mentioned in (26),
(2.3.4)
a constant, which generally lies between 0.5 and I (16).
From the formulae (1.2.11) and (1.2.18) the number average chain length
can be expressed in the weight fraction polymer and the equilibrium
constant K2
(Pn>>l):
Taking:
p n /Mo<j>/K2 •
and combining (2.3.6) with (2.3.5) gives:
p n
! tjl 2 exp
[
LIH2 _ LIS2]
2RT 2R
Above the transition point, Pn ~ 105
• So >>1, from which follows
that the third term of (2.3.3) is the dominant one. Substituting
(2.3.7) and (2.3.4) in the thus simplified form of (2.3.3) produces:
[ 2+a• [ 2] ln n/<t j = l.n k'A
Assuming that a plot:
i'lS - a --
2 + ln
R
B + C/T ,
+ a
(2.3.5)
(2.3.6)
(2.3.7)
(2.3.8)
(2.3.9)
31
fits the viscosity of the solvent and that [k'A2
) and ilS 2 are temperature
independent, it is possible to determine öH2 as a function of ~ from
(2.3.8). When k' and A are obtained from other sources, öS2
can be
calculated as a funétion of a from (2.3.8). With the help of formula
(2.3.7) it is then possible to evaluate values for Pn.
2.3.2. Determinations of 8H2 and Pn known from the literature.
a.
With the help of formula (2.3.8) Gee determined ilH2 for sulfur using
viscosity data from Bacon and Fanelli (l). Below the transition point he
fitted the viscosity n0
to the plot:
-9.67 + 29;0
Taking a "typical" value for a =2/3 (27), he found LIH2 = 35 kcal/mole
using ~I as data for the weight fraction polymer. With a value for
(2.3.10)
A = 0.83 and k' = 0.4 he calculated Pn as a function of temperature with
a maximum value of 105 . As we have seen, the value of öH2
obtained from the
viscosity measurements, depends on the choice of the parameter a and of the
relationship between viscosity and polymer concentration. The reliability
of the measurements of Hammick has been discussed insection 2.1.
With every commandation of his pioneering work on the theoretical treatment
of the polymerization process of sulfur, the numerical evaluation of the
polymerization parameters 8H2 and Pn does not explicitly show the
uncertainties involved. On the other hand, a betterapproachwith the help
of experimental data known at that time (1952) was not possible.
Tobolsky and Eisenberg (5) used the polymerization parameters obtained
by Gee to check the validity of their newly developed theoretica! treatment.
The values of the equilibrium constauts K1
and K3
(see formula 2.2.1) were
calculated from the "experimental" data from Gee.
32
Selenium
~·!· Eisenberg and Tobolsky (8) determined data for the equilibrium
constant K3
from the measurements of the weight fraction polymer by Briegleb.
From viscosity measurements of Krebs (28) they "guessed" a value for the
heat of reaction ~H2 •
Taking for ~s 2 the same value as for sulfur, they calculated data for
number average chain length Pn. Their work was the first attempt at
determining the values of K2 and
b.2. Keezer (29) has tried to develop a method for evaluating the
equilibLium constant K2 and Pn in liquid pure selenium from viscosity
measurements of thallium doped selenium. He assumed that the number average
chain length and therefore also the viscosity starts to decrease when the
impurity concentration exceeds the chain end concentration.
JJL --L~~-LuuuiLQ __ _J ____ ~LL~LU~~c._~~JJ~'ffil
thallium concentration I PPM)
Fig. s. Straight Linea through points (e) are isotherme through the
viseosity of different thaLLium eoneentrations. Straight ~ine
through points (&I is the visaosity of pure seLenium. To eaah
point OIV beLongs a thaLLium aonaentration and, aonsequentty,
a number of atoms (z) in a ahain.
33
Following this model it should be possible to estimate Pn in pure Se by
determining the impurity concentration at which the first decrease in
viscosity occurs. His methad is demonstrated in fig. 5. Keezer assumes
that in his model at each given te'mperature, and at a certain dope
concentration all the chain ends are terminated by thallium atoms. The
results of our ESR measurements, however, do not support his model. As a
matter of fact, the chains are in dynamic equilibrium and therefore chain
ends are produced and disappear at each temperature. By adding monovalent
dopes, a certain number of chain ends are terminated by dope atoms, and
the equilibrium concentration free chain ends will be retained. New chain
ends are now produced through which the number average chain length is
shortened. We may therefore, draw the conclusion that Keezer's conception
was based on an inaccurate assumption.
2.4. Reliability interval for the value of ~H2 obtained from viscosity
measurements
a. Sulfur
Substituting (2.3.9) in (2.3.8):
[ ~H2]
C + a -y- I/T (2.4.1)
We have calculated n/~2+a with the help of ~m and ~ 2 and the viscosity
data of fig. I curve 1. In figure 6 curve I (using $m) and curve II
(using ~ 2 ) are displayed against 1000/T. These lines have been drawn through
points calculated with a= 2/3. At 1000/T = 1.813 and 2.070 points are
evaluated with a= I [Ö] and a ! [Ijl]· If straight lines were drawn
through the points corresponding with a = I and a = !, the slope would
hardly be influenced by the value of a (this is explicitly shown for
selenium). In table I data for ~H2 (in kcal/mole) are obtained using $2
and
~ respectively, and three different values for a. (C'=J0-3c) m
Fig. 6 .
34
o sutfu; :;pm) o $u\fur ;~ 2 ) X se\eP,IUn'l
nj~ 2+a (poise) versus 1000/T
aurve I: aalauZated with the of ~m(o: aurve II: aaZauZated with the heZp of~ 2 (o:
r:l: aalaulated with the help of ~
points 9 : aalaulated with the help of </l
0: = 1 0: = 2/3 a = 1/2
!2 22-2C' 44-3C' 59-4C'
~m 25-2C' 38-3C' 51-4C I
= 2/3),
= 2/3),
= 1) >
1;).
Table I. Heat of reaation AH2(kaal/mole) for sulfur, aaZauZated as
a funation of ~2, and a. C is taken unknown .
35
Taking for C the value 2940, we find the föllowing data for öH2
:
a. =; 1 a = 2/3 a. = 1/2
<1>2 23 35 47
q,m 19 29 39
Table 2. Heat of reaation À82 (kcal/mole) for sulfur, calculated -1
as a function of q, 2, <Pm and a.. C is taken 2940 (K ) .
b. Selenium
Analogously to the case of sulfur we have calculated ~;q,z+a. with the
help of formula (2.4.1). Using the viscosity data for selenium from fig.
curve 2 and the values weight fraction polymer <P from fig. 4 curve I, we
obtain the following data for öH2
(kcal/mole)
a. = 1 a. = 2/3 a. = 1/2
18-2C' 26-3C' 35-4C'
Table 3. Heat of reaction 682 (kcal/mole) for selenium, calculated
as a function of a.. C is taken unknown .
As in the case of selenium the"transition point" lies below the melting
point, n0
(T) -data are lacking. Thus C is unknown. In the case of sulfur,
the C~term has an influence of 1\::20%. Some argument a about ring mass, ring
size and interaction might give a more accurate approximation than our
guess that the influence of the C~term will again be ~20%. Co~pared with
36
the other uncertainties involved this guess hardly seems toa rough.
When 6H2
for sulfur is evaluated from the ESR measurements, the best ESR
fit a can be derived. Assuming that this value is suitable for selenium,
an estimation for C can be given when the value for 6H2
for selenium is
known from the ESR measurements.
2.5. Magnetic measurements
2.5.1. Introduetion
The theoretical model descrihing the polymerization equilibrium is
based on the assumption that the chain ends consist of free spin states.
Magnetic measurements can give a direct proof of this assumption. When
the polymer weight fraction is known, determination of the number of
chain ends makes it possible to evaluate directly Pn' K1
and K2
• Magnetic
measurements known from the literature, which are interpreted as caused
by a polymerization process and from which polymerization parameters are
determinated, are discussed in the following sections.
2.5.2. ESR measurements
a. Liguid sulfur
The ESR measurements of Gardner and Fraenkel (19) (1956) were a direct
proof of the chain end spin state model. They obtained interpretable data
for the number of chain ends in a temperature interval 240°C<T<350°C. Using
density data of Kellas (30) and ~ 2 as data for the weight fraction polymer,
they obtained for 6H2
= 33.4 ± 4.8 kcal/male.
They calculated P = (5.0 ± 2.5)xJ04 at T = 300°C. A systematic error in the n
determination of spins was the uncertainty about the lineshape of the ESR
resonance curve. A discussion about the lineshape and the interpretation
37
of the ternperature dependenee of the lineshape is given in chapters 3, 4
and 6. Further ESR rneasurements on liquid sulfur in the literature are
only known frorn Van Aken (31). He deterrnined seven values of the radical
concentratien in a ternperature range of !80°C<T<330°C. These were compared
'"ith the"theoretical"values frorn Eisenberg and Tobolsky. A systernatic
deviation of 50 - 100% was found. The value obtained by Gardner and
Fraenkel at T = 300°C, agrees well with Van Aken's spin calibration at
that temperature.
b. Liquid selenium
ESR rneasurements on liquid pure selenium are not known frorn the literature.
Abdullaev et al. (32) has tried to find ESR signals but he obtained no
results.
2.5.3. Static susceptibility
a. Liquid sulfur
Poulis et al. (JO) determined the paramagnetic susceptibility in
the ternperature range of 320°C<T<520°C. Using ~I and q, 2 as data for the
'"eight fraction polyrner they obtained for IIH2 the values 34,9 and
34.6 kcal/rnole respectively. They calculated Pn from their measurements
and extrapolated to lower temperatures with the help of Gee's theory.
b.
Massen et al. (I I) evaluated frorn the paramagnetic susceptibility
of liquid selenium a value for = 40 kcal/rnole. In the temperature
interval 520°C<T<820°C they calculated P • The contribution of the n
saturated vapour to the total susceptibility was relatively much
higher than in the case of sulfur. The pararnagnetic contribution of
the liquid was on the average 1% of the total susceptibility.
Variatiens of 1:104
in the total force on the sample and sample tube
were detectable.
39
CHAPTER 3
LINESHAPE ANALYSIS
.3. 1 • Int:t>oduction
Gardoer and Fraenkel (1956) di:scussed the reactivity of the chain
end spin state of liquid sulfur. To explain the enlargement of the line
width with ·ri.sing ·temperature they proposed that the lifetime of the
spin state 'iOas determinéd by the rate of a radical reaction. When this
chemica! reaction rate is tlH:: dominant relaxation mechanism, the line
shape is expecied to be Lorentzian.
Gardner a.nd Fraenkel used the analytica! expression of the
Lore1ttzian lineshape to evaluate the intensity of their ESR
measurements. They were not able to give an accurate analysis on
the lineshape of liquid sulfur. This introduced an extra
uucertainty in the number of spins, sine~. they did nat know the
re.al lineshape. To check the model of the re.activity of the chain
end spin state (Lorentzian lineshape is expected) and to av~id
the uncertainties in de.termining the intensity from numerical
integr.a~ion, a computer program has been developed to co~p.are the ESR
absorption line ~ith given analytical fnnctions (differentiated
Lorentzian and Gaussian profiles~ et~.). !he criterion of the least
squares is used to find thé best fitting values for the line parameters
involved. The analytical function leading to the smallest least squares
sum is chosen. A great aàvantage of this me.thod is that intensity,
linewidth and g-value are dete-rmined as line parallléters and, consequently,
they are known, taking into account all data available in the registrogram.
Moreover, the output of the first part of the computer program contains
a set of constauts stating ho~ the sum of squares varies ~ith the values
of all para:naters used in tO.e synthesis of the registrogram. This set of
constauts forms a basic set of data for the secoud part of the program.
which calculates the reliability interval of the line parameters, In
40
the following sectiou the mathematica! basis of the computer program
is given~
3 . 2 . i•Jaf:;hematica 1- bas is
In general~ one may describe the absarptien curve Y(x) by some
analytic.al functions F, depending on a number of parameters ei and on
x;
i = l ••••• , •• m-2
In actual ESR practice the first derivative y{x) of the absarptien
Y(x) is reearcled For that reasen the experimental y(x) bad to be
(3.2. I)
. h èF k' b' . f b . co~pared w~t ~· Ta ~ng the ar Ltrar~ness o the asel1ne a"Way and
allO'JKing for baseline drift, the registrogram may then be described by:
{3.2.2)
A number n of coordinate pairs (x.,y.) is fed into the computer, The 3 3
distance bet~,o;een consecutive points is chosen. camparabie to the recording
speed multiplied by the time constant of the spectrometer. Recordings
y(x) generally do not satisfy (3.2.2) o~ing to noise and disturbances.
The parameters ei are fitted in such way that:
n t: {y. - f(c.,x.)}2,
j ... J J ~ J h (3.2.3)
is minirnized. This minimum value 'ió'ill be called h0 • ln actual practice
we consider Lorentzian and Gaussian lineshapes only. Others might have
been used if the need had arisen. We thus get two h0-values. The analytical
form leading to the smallest h0
was chosen. The corresponding values of
the parameters ei will be denoted as ci0 •
Next, it rnay be tried to ans~er the question whether this best
choice is an adequate one. In our description (x. exact) the residual J
varianee (32) is: h
0
n-m-1 (3.2.4}
41
The residual varianee SN2
of the noise on the empty cavity signalis also
calculated.
lf s2/sN2
does not deviate significantly from l the choice of the
line shape will be considered adequate. +ro
The intensity I = f Y(x)dx, the linewidth AR and the g-valoe fellow from
the c, 's. 10
To cstablish a procedure to find the limits of reliability of the
parameters c10
the function f(c1 ,x) is made linear (Taylor-expansion)
around the minimum value f : 0
f(c. + Ac.Jx.) = f(c 1. 0,xJ.) 1.0 ~ J
"' l ~ f l + E -- Ac. • i=l aci L
(3.2.5)
where higher order terms are neglected. In this linearizing procedure
the parameters c10
are constants. t:.ci has taken over the function of c1
•
Clearly,when the function:
n 2 L (y,- f(c. + Ac.,x.}
j=l J w 1. J h' ::::: (3.2.6)
is minimizcd with respect to Ac i, this minimum W"ill be eqoal to h0
for
all A~. co. The function f(c. + ~c.,x.) is a linear expression in 6c,. l. 1.0 ]. J l.
The variances of ~c. can now be calculated w-ith the methad of linear 1
regression (33). Since óci has taken over tbe function of ei the
variances of ei will be equal to those of Aci. The variances and
covariances are found using a matrix Ms formed from the coefficients
of óci i~ (3.2.5):
n (3. 2.7) 1\.1 j=i
W-7 t .. ~ 11
(3.2.8)
(3.2.9)
42
where ~~-) = the inverse of M~
'i, the t-distributi"n (34).
SZ . the residual varianee calculated earlier·
For Lorentzian and Gaussian lineshapes it is possible to choose
the analytical expression in such a way that each quantity (e.g. ~H~t,g)
is represented by only one parameter (c1). The covariance is then of no
interest.
The EL·-xs computer of our institute was used, with Algol 60 as algorithmic
language.The computer program has been written by T. de Neef. To minimize
h he applied the methods of Taylor (J5) and Fletcher and Powell (36).
43
CHAPTER 4
REACTIVITY OF THE CHAIN END SPIN STATE
4. I. Introduetion
When the lifetime of the spin state of the chain end is determined
by the rate of a radical reaction, the temperature dependenee of the
linewidth of the ESR absorption depends on heat of activation of the
reaction involved.
In the next section three obvious radical reactions will be presented.
It is possible that one reaction or a combination of these reactions
dominates the lifetime of the chain end spin state. To investigate this,
the reaction rate constant is theoretically calculated from the three
alternative reactions.
In Chapter ó the experimental data of the linewidths will be used to
evaluated the reaction rate constants. An attempt is then made to choose
between the reaction(s) which dominate the lifetime of the chain end
spin state.
4.2. Calcu~tions of the reaction rate constant
The mean lifetime (T) of a radical chain end, which will be denoted
by Ce , will be given by the following relation:
dC e
dt
c e
T (4. 2. I)
Equation (4.2.1) will be used in the folowing to relate the reaction rate
constant to the mean lifetime of the spin state.
44
a. Radical-combination reaction
The energy diagram is given in figure 7.
i Ea~_,/_---·,\\ \
\ \
l!H2 I \
I \ . , ___ .._ __
•.• c~ + c• ... ...c - c ...
E' a E~' = -l!H2
Fig. 7. Energy diagram of the :radioal-aombin.ation :reaotion.
The symbol "C-C" denotes a bond in a chain.
The rate of disappearance of the radical chain end is given by:
dC - ___;:, = k' (C ) 2
dt a e '
where k' is the rate constant of the reaction of a chain end with a
another one. Substituting (4.2.1) in (4.2.2) allows the reaction rate
constant k~ to be expressed in the mean lifetime T:
k' a
(4.2.2)
(4.2.3)
The relationship between the relaxation time (in this case the mean lifetime
on the chain ends) and the linewidth (l!H = the distance between points
of extreme slope) for a Lorentzian is given by:
T (4.2.4)
where L 6.47 x 10-8 Oe.sec (T in sec, l!H Ln Oe).
45
Substituting (4.2.4) in (4.2.3) gives:
With the help of Ce N/2, formula (1.2.18), and the relation
the reaction rate constant k' is a
k' a
l'.H exp
evaluated:
[+ l'.H2 - l'.S2]
_ 2RT 2R]
LM lep 0
By using the kinetic equation for k::
k' a k~a exp [- E~/RT],
the logarithm of k~ can be expressed by:
ln k' a [
l'.H 1 l'.H2 1'.82 ln LM lept 2RT - ZR = ln [k~J
0
b. Ring-addition reaction
The energy diagram is given in figure 8:
IE • /".,--,
I ' \t. E 'I I
b: I I I
I I I I 6H 3 I
I I _,
•• • c i+e···
E'/RT a
Fig. 8. Energy diagram of the ring-addition reaotion,
(4.2.5)
(4.2.6)
(4.2.7)
(4.2.8)
46
The rate of disappearance of the chain end with this type of radical
reaction is:
dC e
dt k~ Ce(R-R) ,
where kb is the rate constant of the reaction of a chain end with an
atomie bond (R-R) in an eight-membered ring.
Wi"th the help of (4.2.1) ~ is related to T by:
. I ~ = T(R-R)
Using (R-R) = M0 (1 - ~) and combining formula (4.2.10), (4.2.4) and the
kinetic equation for ~· the logarithm of the reaction rate constant k~
can be given by:
ln ~
c. Radical-displacement reaction
Figure 9 shows the energy diagram
r K -- + ... c:
Fig. 9. Energy diagram of the radiaaZ-dispZaeement reaetion.
(4.2.9)
(4.2.10)
(4.2.11)
47
Calculating in the same way as in ~· and keeping in mind that the number
of honds in ebains equals ( ~4>M0 ), the expression for the logarithm of
the reaction rate constant k~ of the radical-displacement reaction, is
given by:
ln k' c ln [~H$]
0
ln k' - E' /RT oe c
In Chapter 6 it has been tried to fit ln k' into the plot:
ln k' :F + G/T. .
(4.2.12)
(4.2.J3)
lf this fitting~procedure is successful, then data for activation energies
and pre-exponential factors can be evaluated since L, M0
, $, ÀS2 and
liH2
are known.
48
CHAPTER 5
EXPERTMENTAL TECHNIQUES
5.1. Introduetion
This chapter is concerned with the description of experimental
techniques and preparations of ESR samples. A temperature unit inserted
in a dual sample ESR cavity, both constructed in our laboratory, was
combined with a commercial ESR spectrometer for performing sensitive and
reliable spin intensity measurements up to 800°C. In section 5.2.
reference is made to the specifications of the E-15 Varian spectrometer
combine,d with the Varian standard cavity. Sectien 5.3. describes the
construr:,tion of the high temperature ESR outfit and ment i ons the
specifications of the commercial ESR spectrometer combined with this
outfit. The method used for the de terminatien of the nu.'l!ber of free spins
as a function of the temperature is described in sectien 5.4. Sectien
5.5. deals with the methods of sample purification and preparation. At
the end of this section the determination of the spin content of the
calibration material (D.P.P.H.) is to be found.
5.2. ESR spectrometer
The ESR measurements have been carried out on a Varian V 4500 A
and an E IS (new type) spectrometer. According to the specif ications
the sensitivity of the new type is 5 times that of the old apparatus.
The minimum detectable number of spins N (min) of s meter is specifiêd by Varian:
10 N8
(min) = 5 x 10 .6H ,
the E 15 spectra-
where b,H is the signa! linewidth in Oe at half maximum absorption.
This specificatien is obtained by Varian using the weak pitch sample
(part No. 904450-02); 10 13 spins f 25%, placed inside the Varian
(5.2.1)
49
standard single cavity. This sample produces no dielectrical losses in
the cavity. The dimensions of the sample tube are: effective length
~22 mm, inner diameter 2.8 ±0.2 mm. To determine the minimum number of
spins, Varian prescribes the following procedure. The weak pitch sample
is scanned with spectrometer settings:
(I) maximum power (200 mW),
(2) amplitude of magnetic field modulation (frequency 100kHz), chosen
for maximum signal height,
(3) scanning time: 4 minutes,
(4) scanning range: 40 Oe,
(5) integration time: I second.
The peak-to-peak amplitude (A) of the pitch recording, obtained with these
settings of the spectrometer is now determined.To obtain noise data, noise
is recorded for 2 minutes at a constant static magnetic field (setting
1500 Oe, receiver gain unchanged). Next, the maximum amplitude (N) of
the noise pattern of the recording is determined. The signal to noise
ratio (R) is then calculated by the relation:
R = A/N x 2.5 • (5.2.2)
Specifications of base line drift is obtained by scanning from 500 Oe
to 4500 Oe for 2 minutes (cavity empty) with the same sensitivity setting
as for the measurement of weak pitch. The maximum base line drift is allowed
to be 25% of the amplitude of the pitch signal. The manuals contain further
specifications and a description of the microwave circuit. In section
5.3.this test procedure will be applied to the combination of theE 15
spectrometer with the laboratory-made high temperature outfit.
5.3. High temperature ESR outfit
5.3.1. Introduetion
The ESR investigations of the polymerization of liquid sulfur and
selenium described in this thesis were successful, owing to the
properties of the combination of the E 15 spectrometer with the laboratory-
50
made high temperature outfit:
(1) Attainable temperatures up to 800°C, without losses of
sensitivity.
(2) Possibility of measuring reliable spin intensities as a function
of the temperature, with
(a) reproducible baseline at each temperature ,
(b) the same maximum baseline drift as specified by Varian.
The Varian temperature unit V 4540 uses a hot nitrogen gas stream
to heat the ESR sample, placed in a quartz dewar inside the cavity. The
maximum attainable temperature with this unit is 300°C. No other
commercial heating units for temperatures higher than 350°C are available.
Several workers have been trying to make high temperature ESR
heating devices (37). Some of them reached ternperatures of about l300°K
by placing heating wires inside the cavity. Most of the cavities
described in the literature are not adaptable to co=ercial spectro
meters and they are not suitab]e for accurate determination of the spin
concentration.
Investigating the possibilities of neating the sample inside the
cavity two rnethods seerned to be useful. They were the hot gas stream
(H.G.) and the hear.ing wire (H.W.) methods. The advantage of the H.W.
method is the direct heating of the sample. It is a great disadvantage
that the pJ.ace of the wires inside the cavity is very critical, especially
in the TE 102 cavity. It is our experience that fcr sensitive ESR
measurements this metbod is not useful. Lorentz forces cause displacement
of the wires inside the cavity when the static magnetic field is scanned.
This produces short-term changes in the quality factor of the cavity,
which results in irreproducible measurements. The H.G. method was
chosen. Two heating devices have been developed, which are extensions of
the Varian hot gas stream method.
Ta carry out spin intensity measurements as a function of the
temperature, a dual sample TE 104 cavity has been used. The sample to be
rneasured is placed in one channel of the cavity and the standard sample
in the ether. The standard sample is kept at a welldefined temperature
51
(T = 20°C). The sample to be measured is heated by a hot nitrogen gas
stream. Each channel has two opposite "windows", which occupy the
greater part of their walls. Each window is covered by a stainless steel
plate(0.06mm in thickness), which is pressed against the wall by a
frame containing a ~00 kHz field modulation coil embedded in araldite.
The sample is heated and as a consequence the cavity becomes hot. This
in turn causes the quality factor to decrease', the measurements become
irreproducible, and baseline drift occurs. Effective cooling, which is
necessary to do away with all these incompatihilities, is impracticable.
In order to make possible sensitive and reliable spin intensity measurements
at high temperatures (800°C), we have modified a copy of the Varian
TE 104. In fact we have designed a new type of cover of the windows as
described below.
5.3.2. Construction of the TE 104 high temperature cavity
In fig. 10 an exploded view of the modified cavity is shown.
Fig. 10. ExpZoded view of the Zaboratory-made high temperature
TE 104 aavity.
(3) PLATE
(_i) COILHOLDER MAT, PERSPEX
Q2
MAT; NI CHROMIUM
52
COOLER MAT~COPPER
11. CPoaa-aection of a coveP with coating compartment.
Dimenaiona in mm.
53
lts body, made of brass, has the same dimensions as the VarianTE 104.
A layer of approximately 2-5 ~ of silver is applied electrolytically.
To avoid the oxidation of the silver layer, the body is electro
lytically gold plated. This procedure ensures low skindepth (iow
losses) in the cavity walls. No glossing material is added to the baths,
M.a.surenwnts: 1 weak pll:ch Vanan A::192mm 2 nt:IIW
empty ca.v1ty scan rang. ZOOO Ot>
4000 0. • tHi50Ci
Fig. 12. ESR test of the Zabo:ruto:ry-made high temperatu:x>e
TE 104 aavity.
because this decreases the quality (Q) considerably.To ensure sensitive
measurements at high temperatures, direct cooling of the covers was chosen.
It was required, that the frequency and the maximum amplitude of the
magnetic field modulation should be the same as in the original cavity.
The new covers consist of anichromium plate'of 0.2 mm thickness silvered
on the side facing the samples. The nichromium plate is fitted to
a cooling campartment in which the modulation coils are mounted. A cross
section of a cover with cooling campartment is shown in figure 11.
Owing to the use of the nichromium plate of 0.2 mm in thickness, the
amplitude of the 100kHz field modulation is decreased by 1.1, whereas
54
the cooling and the rigidity are satisfactory. The~onfiguration of
the modulation coils is nearly the same as in the original cavity.
V
z n
Fig. 13. Channet indiaation and ahasen aoordinate axes.
The impedance of the modulation coils has to be adapted to the 100 kHz
modulation amplifier. To avoid baseline drift at great sweepranges,
silver gaskets have to be placed between the silvered nichromium plate and
the cavity wall. Also the screws of the cooling compartments and the flange
conneetion between the waveguide and the cavity have to be tightened with
the samemoment (6-14 lb.in.) in diagonal succession. An ESR test and
the specifications of the high temperature ESR cavity are given in fig. 12,
fig. 13 and table 4, respectively.
The original Varian dual sample cavity can be used in combination with
the new type covers, when the four screws holding the two cavity parts
together, are countersunk.
55
Qualitl factor Qloaded 4200 (without dewars)
Qloaded 4000 (with dewars)
Quality factor constant within
5% up to 1300 K.
Sensitivitz test carried out in combination
with varian EJ5 spectrometer
R = A/N x 2. 5 ~ I 00
h.f. power 160 mW (leveled)
Varian weak pitched placed in
dewar channel II. Dewar in
channel I empty.
Offset baseline < 25% of A weak pitch.
Flow cooling water ~I ml/ sec.
Modulation coil. coil holder see Fig. 11
(coi).sist of 5 wires wire diameter 0.15 nnn
wound in parallel) length 5 m
number of turns 90
inner diameter '1 i 11.5 mm
co~
outer 20 mm
Electrical data impediance 40rl at 105Hz (<j>:82°)
of the coil d.c. resistance 0.8 n
Table 4. Speeifieations of the laboratory-made high temperature
TE 104 ESR eavity .
56
5.3.3. Heating devices
In fig. 14 the two designs of hot-gas units are sketched. The
dewar is inserted in channel II of the dual sample cavity. It is a
modification of the Varian dewar (part No. 961-180).
The original dewar consists of a vacuum campartment from which the part
that projects from the cavity, is silvered to reduce radiation losses.
It was found that at sample temperatures above 400°C silver particles
entering the cavity disturbed the ESR measurements. This is avoided
by making two separate vacuum compartments, the lower one of which is
silvered. The quartz material of this dewar has no detectable paramagnetic
impurities.
samplt'! hol.der
s.it~red ;~awum
HG n l'f!9!0"
~~
Fig. 14. The two designs hot-gas wzits.
The hot-gas unit I (H.G.I) consistsof a platinum wire wound around
a care of Al 2o3• This care is placed into the lower campartment of the
insert dewar with the help of a conical stopper. Using the H.G.I unit
at high temperatures, an appreciable temperature gradient appears along
57
the sample placed in the dewar. This is caused by radiation losses in the
unsilvered part of the dewar. The maximum temperature attainable with this
unit is about 750°C. To obtain lower gradients and higher temperatures,
a.second hot-gas unit (H.G.II) has been constructed which can produce more
heating power. When this unit is used, the H.G.II dewar is connected to the
insert dewar. The teehuical specifications of the heating devices are
given in table 5.
H,G, I H.G. II
heating. coil wire platinum Kanthal
diameter (mm) 0.5 0.4
length (m) 11 14
number of turns 70 2000
re si stance (>l) 1 to 3 45
heating data maximum power 200 1200
(electrical) (W)
gas flow 3 -1 (m sec ) 0.25x10 -3 max.10 -3
max. temp. (K) 1000 1300
gradient at max.
temperature (K/mm) 5 1,5
of hot-gas units.
5.3.4. Temperature measurements
The temperature of the ESR sample inside the dewar is calibrated
with a resistance thermometer (type W 85 K, Degussa) about the same length
(20 mm) and diameter (3 mm) of the standard sample tube. In this way
a value is obtained for the average temperature of the sample. In fig. 15
58
700
600
500
400
300
0 20 40 60 BO 100 120 140 160 180 200 220 240
Fig. 15. Temperature T of H.G. I versus eleotrioal power W (Watts).
X oalibration of July 8, 1970,
o oalibration of Aug. 5, 1970.
Fig. 16. TWo thermo-oouples to an empty sample tube .
59
the temperature of the H.G.I unit is shawn against the electrical power
of the heater coil. The temperature gradient for H.G.I along the sample
is determined using an empty sample tube to which two thermocouples
arefittedas sketched in fig. 16. The measured gradient is very
sensitive to rotation around the axis of the empty sample tube. In fact,
the sample bolders inside the dewar (see fig. 14) produce an inhomogeneous
flow resistance, owing to which the heat release along the samplè is not
uniform in the horizontal plane.
Fig. 17. Temperature difference AT(°C) over the sample versus tempGrature
T(°C).
For this reason the measurement of the temperature gradient is somewhat
unreliable. In fig. 17 is given a rough measure for the temperature
difference over the sample. In our work the H.G. II is used to
investigate the influence of the temperature gradient on the ESR
spectrum of liquid sulfur. The temperature gradient is expected
to be proportional to the heating power of the gas stream. We have
changed the temperature gradient by altering the flow keeping the
sample temperature constant.
60
5. 4. The measurement of the ESR spin intensity
5.4. l. Introduetion
In the early fifties ESR research workers were unable to measure
spin intensities with any form of accuracy. In the last few years it has been
possible to reach an accuracy of about 10%, provided the experimental
circumstances are favourable. In our experiments we have .used the dual
sample cavity method. The sample to be measured is placed inside the
insert dewar in channel II. The ESR spectrum can now be measured as a
function of the temperature. For purposes of comparison channel I
contains a cylindrical sample D.P.P • .H.(diphenylpicrylhydrazyl) (0 0.5 mm ,
effective length = 1 mm), which in the following will be considered
as a "point" sample. T.he spincontent of the DPPH material could be
calibrated with an accuracy of about 1% (see section 5.5.5). This
sample is caoled by an airflow to keep its temperature constant
within 5°C (T 20 ~ 5°C) when the sample in channel II is heated
from room temperature to 700°C.
Casteleyn et al. (12) have investigated the errors which can be made at
room temperature when the number of spins is determined with this type
of cavity. Their analysis is presented below in an adapted farm. Errors
that may be introduced by calibration procedures at high temperatures
will be discussed at the end of sectien 5.4.2.
5.4.2. Determination of the number of spins in a TE 104 cavity
If F(H) is the ESR absorption, we define the intensity I:
+oo
I f F(H)dH
It is convenient to represent I by the following formula:
I KQBN gT-I V
(5. 4.1)
(5.4 .2)
where:
K
Q
s N
V
g
T
BI
B2 V s dT
61
parameter independent of the ESR sample ,
quality factor of the loaded cavity ,
amplification factor of the detection system ,
number of spins per volume unit ,
Landé·factor,
absolute temperature
amplitude of the magnetic component of the microwave field
inside the cavity ,
amplitude of the magnetic field modulation ,
volume of the sample
volume element .
Formula (5.4.2) is valid only when the linewidth of the absorption is
small compared with the value of the static magnetic field; microwave
saturation is nat allowed to occur. When the ESR sample and a calibration
sample are bath present in a cavity, the values of K and Q are the
same for bath samples. The ratio of the intensities of the samples with
unknown (Iu) and known number of spins (Ik) is:
with:
I SU (N gT-1) U V U
Ik= Sk (NvgT-I)k• yk
y = f Bl2B2dT vs
The determination of the ratio Yu/yk is difficult.
(5.4.3)
(5.4.4)
As a matter of fact. the sample influences the distribution of the micro-
wave field in the cavity, because the dielectric constant of a sample
causes a Campression of the microwave field. Moreover, this compression
influences the field distribution in the other channel. An additional
difficulaty arises from the fact that the microwave and modulation
fields are inhomogeneously distributed over the sample volume. The
dimensions of the calibration sample D.P.P.H. are small compared with
62
those of the cavity. When tle D.P.P.H. sample is placed in the crigin
(microwave electric field 0) the compression of the microwave field
and therefore the influence on the other channel can be neglected.
In the following we s'hall arrange the expressions in such a way
that a real experiment is compared with an "ideal" one: point samples
placed i'n the origin, dielectric constants being neglected.
The influence of the compression and the inhomogeneitv of the
microwave field on the ESR signal of the sample to be measured can be
described by introducing a compression and a volume factor respectively.
A ,dimensionless parameter b(r) descrihing the spatial distribution of
the field is introduced by the formula:
b(;)
with i:radius vector.
2 (BI B2);
2 + (BI B2 )o
The influenve of the sample on the microwave field distribution is
described by the compression factor
f comp
where the prime indicates the presence of a sample. Q/Q' takes into
account the change in the quality factor of the cavity caused by the
presence of the sample.
(5.4.5)
(5.4.6)
The inhomogeneous distribution of B1 and B2 is taken up in the volume
factor fvol"
f b(;)dT vs
Combination of (5.4.4), (5.4.5), (5.4.6) and (5.4.7):
y
(5.4.7)
(5.4.8)
2 Keeping in mind that the term (B 1 B2 ) need not necessarily be the same
for both channels, a channel correction factor is introduced by:
63
2 (B
1 B2)Ó(II)
fchannel = 2 (Bl B2)Ó(I)
(5.4.9)
The number of spins of the sample to he calihrated can he given hy a
formula, which will, he of direct utility when carrying out spin intensity
measurements.
When the sample to he measured causes a compression of the microwave
field, which shifts the field in the place of the calihration sample,
it is possihle to hring the D.P.P.H. sample to the new (~0) origin.
In that case f (k) l. comp Since the dimensions of the pointsample are very smal! fv
01(k) = l.
Using (5.4.3), (5.4.8) and (5.4.9) with f 1
(k) l and f (k) = 1: vo comp
where N s
(l/B)u
Ns(k) (I/~)k
N .V • V S
In appendix A
into the factors fx'
The influence
the volume factor (fvol) will he further split
f y
of
and fz. Fig. 13 shows the coordinate axes.
the conductivity on the microwave field
(5.4.10)
distrihution inside the sample (skin effect) is neglected in the
considerations mentioned ahove hecause of the low conductivity of
liquid sulfur. From conductivity measurements on liquid selenium
(see Chapter 8) we could show that in the temperature interval of our
ESR measurements neglect of this effect is allowahle.
The qualities of the high temperature ESR cavity permit of
doing spin calibration measurements at high temperatures without
introducing additional error sources •. lf the dielectric constant
of the sample to be calibrated changes as a function of the
temperature, an additional error souree can occur. In Appendix B,
where an attempt is made to estimate a value for the compression
factor of liquid sulfur, this subject will he further treated.
64
5.5. SampLe preparation
5.5.1. Introduetion
Ihe first ESR measurements on liquid sulfur showed the sulfur
signal (g = 2.024) and an additional signal vith g-value g ~ 2.010.
The signa! with g-value g ""_ 2.010 is also mentioned iP the literature
(9) and attributed to sulfur carbon compounds. Just above the
transition temperature of polymerization the impurity signa! was much
grester than the polymerization signa!. To obtain equilibrium data
at these temperatures the sulfur material was purified fram carbon,
which is described in sectien 5.5.2.
Far more serieus problems arose when preparing the selenium
samples, Two different impurity signals proved to be present, the
intensities being dependent on the metbod of sample preparation.
Moreover. the amplitudes of these signals ~ere much higher than tbe
polymerization signa! in the whole temperature range. It is known
from the literature (14) that at room temperature an ESR signal
(l!H ~ !0 Oe and g "" 2.00.36} exists in selenium. The amplitude of this
signal is stroJ.l;ly dependent on the content of oxygen and the heat
treatment of the sample. Our first ESR measurements on solid and
liquid selenium (38) produced the signal referred above. superimposed
on a broad slgnal, the rneasurements giving irreproducible results.
After heating for several hours in the ESR apparatus~ the measurem.ents
became better reproduelbie at each temperature. However. it was not
possible to give an interpretation in terros of a polymerization process.
By applying the methad of Kozyrev (39) for deoxygenizing the selenium
rnaterial, somewhat better results were obtained. 'I'his was described
in an internal report (40). l'he linewidth of the ESR signal was
temperature independent (AH % 400 Oe). From the tentperature dependenee
of the intensity a value for 8H2 ~ Il kcal/mole could be derived. This
value in fact was much too low in comparison with data obtained from
the viscosity and from the magnetic me.asureroents of Massen ct al. (11).
M.oreover. the entropy cha.ng:e (.1S2) was calculated to be negative
(~ 20 cal/mole K). Selenium producing interpretablc results~ was
deoxyg:enized by the methad described in section 5.5.3. The development
65
of this purification method is described in an internal report (41).
During the prepatation of the sulfu~ samples, doped.with iodine,
it was nor possible to avoid the introduetion of impurities. Same
remarks about the preparatien of these samples are given in sectien 5.5.4.
Sectien 5.5.5. deals with the deterruiuation of the spin content
of the DPPH material which was used for the spin ca!loracion measurements.
5.5.2, Prepatation of sulfut samples
The sulfut material was commercially obtained from Johnson and
Hatthey (catalogue No. JM 775, impurity 2 in J06). This material was
further purified from carbon following the metbod of Von Wattenberg (42).
A quartz tube heated to about 700°C was placed in hot sulfur (~400°C}.
After a period of about 30 min carbon precipitated on the quartz tube.
The carbon ~as removed and the process repeated tor a longer time until
the quartz tube stayed clean. The sulfur was subsequently destilled
under ~acuuru into quartz sample tubes without any dateetabie paramagnetic
impurities. In these samples no impurity signal was found~
5.5.3. Preparatien of the seleniucr samples
Samples were made from selenium pellets, commercially obtained
fro~ Johnson and Matthey (catalogue No. JH 781, iropurity) in 105), The
pellets were evacuated at 10-S torr for one hour at 20°C, and then
heated in vacuum at the rate of 15°C/hr antil a temperature of 190°C
was reached. Keeping the temperature at J90°C, the selenium ~terial was flusbed with purified argon gas and evacuated again~ The selenium
was then degassed and distilled at approximately J0-5 torr for two
hours in the liquid state {~350°C), When the purification was
finisheà~ the samples were sealed in quartz ESR saruple tubes without
any detectable paramagnetic impurities.
66
5.5. 4. Preparatien of the s1.üfur samples doped uith iodine
The sulfur material was the same as used for the prepan<tion of
the pure samples. The doping matedal was double-·sublimated iodine~
E.M. Merk A.G. No. 476. Since it was not possible to work in an
environment which was completely free of contamination (for instanee
during the weighing of the doping materiai), impurities (presumably
carbon) were introduced into these samples. In the internal report (41)
the method of preparing these samples was treated extensively.
5.5.5. Calibration samples
The spin content of the DPPH material obtained commercially
from Fluka was investigated by a method developed at the Central
Laberatory of the D. S.M. (43). Following th~.s method, it is possible
to reach an accuracy of about !%. The determinatiou of th0. spin
content was carried out in the inorganic laboratory of the Depart:alen:.
of Chemistry of our institulion. A smal! arr.cant was brought into a
quartz capillary with which the microwave (modulation) field
distribution and the channel correction factor could be measured.
67
CHAPTER 6
EVALUATION OF THE POLYMERIZATION PARAMETERS FOR THE RESULTS OF THE
ESR MEA.SUREMENTS
6. I . Introduetion
Section 6.2 deals with the results of the ESR measurements on the
polymerization equilib-rium of liquid sulfur and selenium both pure and
of liquid iodine-doped sulfur. In section 6.3 the equilibrium and in
section 6.4 the kinetic data of the polymerization process are calculated
from the results of the ESR measurements. A discussion of the equilibrium
and kinetic data is given in section 6.5. These data will be compared
with the results of other authors.
6.2. ESR measurements
6.2.1. Recording of the ESR signals, eliminating of the cavity background
and impurity signals.
6.2.1.1. Liquid sulfur.
Some of the sulfur signals were recorded on the V-4500 A apparatus
(lowest measured point at T = l72°C). The microwave power used in the
measurements was 16 mW. It proved necessary to eliminate cavity background
up to 250°C. Some of the ESR data were printed out on a tape and fed into
the computer. In this way, was obtained the lineshape analysis of liquid
sulfur described in 6.2.2.1.
The high temperature ESR outfit became foolproof around August,
1970. Moreover, the new type ESR (E-15) spectrometer was available from
that time.
With these apparatus new ESR measurements were carried out on liquid
sulfur. It was possible to find interpretable ESR signals from T = 153°C
upwards. In most cases it was not necessary to eliminate cavity background.
The measurements mentioned in 6.2.1.2 and 6.3.1.3 were all performed with
68
these apparatus. The microwave power was 160 mW. No microwave saturation
occured.
6.2.!.2. Liquid selenium
The linewidth (öH) found in selenium is on the average ten times
the linewidth of sulfur in the same temperature interval. Because the
spin concentration (N) is comparable to that in liquid sulfur, it is
found that the signal amplitude (A) is extremely small: A -, N(IIH) -z. For this reason broad cavity signals must be carefully eliminated.
During the measurements of the selenium polymerization data, tape
printing apparatus was not available. Therefore, cavity background
signals were noise-averaged by hand. The background signals were
subtracted from the selenium recordings.
6.2.1.3. Iodine-doped sulfur
In most cases it was not necessary to subtract background signals.
The additional signal (presumably impurities; g-value on the average
g = 2.008, ClH :;>6 5 Oe) \.ias subtracted by making the spectrum symmetiical.
The g-value and the linewidth of the additional signal differed enough
from those of the ESR signal of liquid iodine-doped sulfur for the
subtraction procedure to be carried out. Dwing the relatively large
linewidth for sulfur samples with dopes higher than 5.6 wt %, the
intensity of the ESR signal was too low to make the subtraction procedure
of the impurity signal at low temperatures possible· Consequently, for
these samples ESR data at low temperatures are not available.
It was not possible to perform ESR measurements at temperatures above
500°C ~ith ESR samples of liquid iodine-doped sulfur, since vapor locks
disturbed' the ESR measurements. For this reason ESR data at temperatures
exceeding 500°C are lacking.
69
i~ dH
3300 3400
H \Oel
.. t~ \ dH
H \Oel -3200
Fig. 18. Lineshape adaption of liquid sulfur (a) T = 566°C;
{b) T = 178°C; {a) T = 172.5°C.
(al
(b)
(c)
70
6.2.2. Lineshape analysis
6.2.2. 1. Sulfur
Fig. 18 a, band c show the lineshape adaption of liquid sulfur at
T 566°C, T = 178°C and T = 172°C. The measured points are indicated
by asterisks. The solid curves represent the best fit Lorentzian and
Gaussian lineshapes, respectively: It is seen in Table 6 that the
lineshape is Lorentzian at T 566°C. At T = 178°C a Lorentzian lineshape
T = 556°C T = I78°C T = 172 o,
Lorentz Gauss Lorentz Gauss Lorentz Gauss
SZ 5. I ,-z 4 Z5 43 34 I 36
s; 0.06 0.06 13 13 13 I 13
SZ/SZ N
0.8 70 1.9 3.3 Z.6 I Z.8
Table 6. Lineshape selection for liquid sulfur (44).
~s a better approximation than a Gaussian one. At T
aot possible to choose between the alternatives. In the full temperature
range of the ESR measurements on liquid sulfur the lineshape is taken
Lorentzian for the determination of the spin intensity.
71
6.2.2.2. Selenium
In Fig. 19(a,b) the measured points are indicated by asterisks.
Owing to the background eliminatien by hand the determfnat.ion of the
residual varianee of the noise (s;) became somewhat unreliable. The
spectrum measured at T 410°C gave for s2;s~ the value I in the
case of a Lorent4ian adaption, and 1.7 in the case of a Gaussian
adaption. For the spectrum measured at T = 325°C, these values were 4.8
and 10.2, respectively. In both cases the Lorentzian lineshape is the
best approximation. The lineshape is taken Lorentzian for the
determination of the spin intensity.
(a)
tor~ntzs.n
lSOO 3500 4000 iiSOO
1~ dK
(b)
2800 3000
Fig. 19. Lineshape adaption of ~iquid se~enium (a) T = 410°C;
(bJ T J2E/c.
72
6.2.2.3. Sulfur doped with iodine
A recording of a sulfur sample doped with 0.026 wt iodine is shown
in Fig. 20. There are no reasous to suppose that the lineshape should
be different from that of the signal of pure sul.f\l.r, Owing to the
additional signal no computer analysis of the lineshape was made here.
However, it is possible to perform this if the impurity peak is
subtracted from the sulfur-iodine signal. This is described in the
internal report (~1) .. , .·
1
Fig. 20. t'SR spectrum of
iodine. '1'
-3275
with 0~026% {wt %)
73
6.2.3. Linewidths of the ESR signals
The linewidths of the ESR signalsof liquid pure sulfur and selenium
are displayed against 1000/T in Fig. 21. The linewidths of sulfur samples
doped with different amounts of iodine are given in Fig. 22 as a function
of 1000/T. In Table 7 the numbers 2-8 are related to the weight and
atomie percentages, respectively. It is not possible to give uniform
data for the accuracy of the measured linewidths. For sulfur at high
temperatures an accu~acy of 2% can be èlaimed. At temperatures just
::\h:~um ASUUur :G&FJ
a
Fig. 21. The Unewidth t:.H of the E'SR sf-gnals of liquid sulfur (o)
and Uquid seleniwn ( o) as a funotion of 1000/T (K-l).
Points ( 4) indioates the values of Aff measured by Gardner
and Fraenkel (9).
74
above the temperature of initial polymerization this is 15%. Owing to
the subtraction procedure of the cavity background the uncertainty of
the linewidth of selenium is on the average 15%. The accuracy of the
' 10
9
s ~ I .. ~
' l
3 I
w' u ,, 1.5 1,6 1,7 1.9 1,9 2,0 2,1 2.3
Fig. 22. J.'he lindewidth of the signals (S and SI) as
funation of
Curve 1 indiaates the va~ues for pu:r•e su~fur.
The nwnbers 2 - and the are reLated to the
iodine in Table 7.
75
linewidth of the sulfur-dope ESR signals varied from dope to dope and
can be seen in the simplest way from the deviations of the measured
points from the straight lines.
number 2
symbol • wt %
iodine (I) 0.026
at % 6.6 x
iodine (I) I0-3
Table 7. numbers 2
atomie iodine
3 4
\7 0
i
0.344 2.25
8. 7 x 5.78 x
I0-2 I I
and the
percentages_,
6.2.4. The measured number of spins
6.2.4.1. Liquid sulfur
5 I 6 7 8
• 0 I 0 • 5.60 10.9 17.0 27.5
]. 48 3.00 4.92 8. 75
lated te the and
i
In Fig. 23 the number of spins N (kmole/kg) is given as a function
of 1000/T(K-J) indicated by (0). In Appendix C the spin calibration
measurements are discussed. An absolute spin calibration has been carried
out at three different temperatures. The points (O) in Fig. 23 were
obtained by first doing relative measurements of the spin intensity as
a function of the temperature and then calibrating by the three absolute
measurements. The performance of the relative measurements of the spin
intensity is more accurate than the absolute calibration procedure.
It will be seen in Appendix C that it was not possible to claim
76
] r-........ ~. 10:
ro'
t01
lil'
I
:l 10~
10 12 16 2.2 <Se)
Fig. 23. The number of spins N (kmole/kg) of Liquid suLfur (o} and
Uquid seLenium ( /';) as a funation of 1000/T(K-1). The
temperature intervat of the magnetia measurements on Liquid
suLfur of Poulis et at. (x0
) and Gardner et at. (ESR) are
indiaated by arrows. The sotid and dotted aurves have been
aataulated with the hetp of the poLymerization theory (see
seation 6.3.5).
77
an accuracy of more tltan 25% for the values of the absolute number of
spins. At temperatures right atove the transition point of polymerization
this value must be taken sor~~ewhat greater. G-ardner and Fraenkel gave
relative 2SR intensity ~easurements in the temperaturn range 240°C < T
< 350°C. They calibrated the number of spins at T ~ 300°C. The value
of their calibration was N ~ 3.5 + 1.8 kruole/kg. Our measurements at this
temperature rcsulted in N = 4.8,: 1.3 kmole/kg. This value lies within
th-è limits of accuracy of Cardner and Fraenkel.
6.2.4.2. Liquid selenium
By camparing at a eertaio temperature the relative spin intensity
of liquid selenium with that of liquid sulfur, the ESR measurements of
liquid selenium were calibrated absolutely with the help of spin
calibration measuremcnts of liquid sulfur. The accuracy of the
determination of the number of spins in liquid selenium :ts estimated to
be J0-35%, somewhat greater at the lowest temperature. In Fig. 23 the
number of spins N, ~easured in liquid selenium (8)~ is displayed against
1000/T.
6.2.4.3. Liquid iodine-doped sulfur
Just as in the case of liquid selenium the spin intensîty of the
ESR measure~ents on iodine-doped sulfur samples were determined by
camparing the relative spin intensity with that of liquid pure sulfur.
At two temperatures an absolute calibration was perforrned. The values
obtained by the comparative ml'!thod mentioned above lie withit?- the
linits of accuracy of the results of these calibrations. In Fig. 24
the nun:ilier of spins N for liquid iodine-doped sulfur is given as a
function of 1000/T(K-I).
6. 2.5. g-values
The g-values of liquid pure and iodine-doped sulfur are both
78
:iJ.'
J
Fig. 2t.. The num.her of spins N (kmole/k.g) (S and SI) as a funotion -1 of iOOO/T(K J. Fel' nwnhet>s and symbots see Tab Ze 7. The
soZià and dotted curves have been caleuLated with the help
of t-he polyme:vization theory (tHJe seetion 6. 3, 6.1).
79
g "" 2.024;: 0.005 and nearly temperature independent. Owing to the
braad ESR signal and the subtrac ti on procedure the accuracy of the
tietermination of the g-value of liquid selenium was lo•e.r. The g-value
of liquid pure sel~nium was found to be 2.03 + 0.02.
6.3. EquilibPiu~ data of the polymerization pPocess, oalaulated fz~m
the spin intensities of' the ESR measureme11ts
6.3.i. The equilibrium constants K1
and K2
Frorn the weight frac.tion polymer ç2
(see sectien 2.2 and Fig. 3)
and the number of spins N the equilibrium constants K1 and K2 for sulfur
•ere calculated with formula (J.2.l4) and (!.2.15), The calculated
values of K1 and K2
are represented in Fig. 25 by the symbols ((]) and
{.), respectively.
A somewhat different procedure was used to evaluate K1 and K2
fro~ $0
and the number of spins. Since values for óm are only knmro in the
tentperature interval l95°C < T < 400°C. In this interval K2
was
calculated with the helpuf formula (1.2.!5) from ~mand the number of
spins (see Fig. 25, points (o».Assuming van 't Hoff's law valid~ a
best fit straight curve was obtained and extrapolated tn lower (T 153°C)
and to higher temperator es (T 700°C), Using these extrapolated values
and the nurnber of spins, ~m ~as evaluated with formula (1.2.14) in
these temperature ranges. In Fig. 26 calculated values of Om are
shoW11 in the interval 153°C < T < 195°C. Measured values of $m (see
Chapter 2) are given in the temperature range 195°C < T < 260°C.
With the help of the number of spins N and the measured and calculated
values for '+'m~ K1
was evaluated using formula (1.2.15) (see Fig. 25
points 6).
For selenium K1 and K2 were calculated using the Yeight fraction
polymer op~ obtained, by Brieileh. end the m(',asured nurnber of spins N.
These values of K1 and K2 are iiven in Fig. 25 by the symbols (k) and
(a). respectively.
16' BO .~
ui'
I - 1&'
1(0 lUlt Ko ~,
"~ •
,,
' " • ~ V " ,,
Fig. 25. KJ ar.d x2 (S and Se) -.1 against 1000/T(K ),
KI (S) {points 0 caZculated with N and $2,
points A caiaulated with N and <.r x_ '
(Se) points A calculated with N and Ç,
}(2 (S) {points • aalcu~ted with N and ~z>
points 0 caZculated with N and Çm""
K2
(Se) points 0 calculated with 11 and Ó·
SI
Assuming Van 1 t Hoff's lav tobevalid for K1
and K2 ~ the logarithm of
these equilibrium constants can be expressed by:
(6. 3. I)
and
(6.3.2)
Fitting the logarithms of K1
and K2
(both calculated from $2
and N)
against 1000/T~ gave for the heats of reaction alld entropy changes
the values as in Table 8.
-----
I I KI K2
·---~ (kmole/kg)
~~•H +36.9 :t 0.4 +35-5 ± 0.3
(kcal/mole) öH1
(<P2l 6H2(<P2)
óS +24.2 ± 0.6 +16.6 i 0.5
I (cal/mole K) •s, <<Pzl AS2($2) ~ ..
Table 8. Heats of Peaation (Ah') and entropy changes (t.S) for K1
a:nd
calculated with1N and $ 2 .(FOP sulfur.)
,------····
t-K~ .... K2
(kmole/kg)
AH +36.4 ± 0.2 +35. 7 ± 0.6
(kcal/tDOle) ! AH 1 (<$. m) AH2
(.p )
AS +2'.L6 ± 0.3 +17.8 ± l
(cal/1IlQle K) ~ ...
os 1 (<l>m) AS2 (óm)
Table 9. Heats o.f roeaction (Mi) and entropy ehangea (AS) for K1
and
K2 ~ ealculated IJith N and $m .(Por sulfur.)
82
!n Table 9 these values arn shown obtained with the help of values
K and K bath calculated from ~ and N. tt is seen from Table 8 and I 2 m
9 that the two sets of polymer weight fractions {f2 and ~m) have a very
limited influence on the results of óH 1• 65 1, bH2 and ns2 ~
In tabel 10 the heats of reaction and entropy changes for Kl and
K2
of selenium were calculated.
1 !
KI K2 (kii'Ole{kg)
I IIH ·····-1 +31 ± 2
I +29 ± 2
(kcal/male) AH1 (~) AH2 (~)
as +15 ± 3 + 5 ± 3
(cal/male K) liS I($) 1152(<)
!
'
Table tO. Heats of reaction (aq) and entropy changes (t~} for K1 and
K2
,. catcu.Jated with N and ~.(For selenium.)
The values of the heats of reaction are derived from the slope of
the straight lines and thus obtained from the relative measurecents
only* The uncertainties are small compared with those in the entropy
changes~ whicb involve absolute values. This fact introduces a
systematic error of about 20%, which is oot incorporated in Tables 8,
9 and IQ,
The best fit curves for K1 to (6.3.1) and K2 to (6.3.2) for sulfur,
obtained with data for the weight fractions polymer $2 and ~0 ~ will be
be denoted in the following by K1 (~2 ) and K1 (9m)' and K2 (~ 2 ) and
K2 {~m), respectively. The best fit curves for K1 (6.3.1) and ~ (6.3.2)
for selenium$ will henceforth be denoted by K1
(~) and K2
(t). For
83
sulfur. better residual variances (4J) were obtained when K1
,
calculated vith $" as well as with $ , was fitted to " 0
(6.3.3)
The best fit for Kî (calculated with 92) to (6.3.3) is denoted in the
following by K[ (~ 2 ) and is shown by the dotted curve in Fig. 25
through the pOints ( 0) from !000/T""' 1.9 to loYer, and from 1000/T
= ! .2 to higher temperatures, resp€.ctively. ln the interval
1.2 < 1000/T < 1.9 the solid curve through points(O)indicates the best
fit follo""ing fon:nula (6. 3. l).
K~ ($m) ~ndicates the best fit to formula (6.3.3) for values of K 1 ~
calculated with ~m· This best fit is given in Fig. 25 with a solid
curve through the points(ó)from 1000/T = 1.9 to lower and from
1000/T = 1.2 to higher temperature, respectivcly. In the interval
1.2 < 1000/T < 1.9 the solid curve through points (li) corresponds \.'ith
the best fit to formula (6.3.1). It is seen that in this interval most
of the points (o) and (li) coinc.ide.
6.3.2. Weight fraction polymer
6. 3. 2. 1. l.iquid sulfur
üsing fonnula (1.2.5) </; can be expressed riCi :L_ =
M 0
pK2 --2-(J-p) Mo
(6.3.4)
By the formula (1.2.8) pis given as a function of K1
and K2
- Inserting
pin (6.3.4)t 4> is known as a funcdon of K1
and K2
• Following the methad
roentioned above, the datted curve (---) in Fig. 26 is calculated vith
the help of Kj (~ 2 ) and K2 ($2). In the same way the solid curve in
Fig. 26 is e.valulated using K1' (qim.) and K2
(4m).
,,
' ' '
' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' I
,/ ' '
84
~ .. .h--~L__j~.----'---1 2111 210 un too
Fig. 26. Weight [raction poZymer ~ {S) as a function of T(°C),
Dotted "'-"""" <-----1: aalt;U/.ated with K1 1~2 J ctnd Kicp2!,
Solid CUPVe calc-ulateà with K1 (4>m} a:nd K2(ç,m),•
Dotted c<.Ar".;e {·"'- -·~): Pepvesents lf!2
.,
Poin.ts o If T ::> 195°C: meaaured values of lf!m
(aee Chapter 2)~
If 15J°C < T < 195°: calculal::ed values
of $m (see text}.
85
6.3.2.2. Liquid selenium
In the same way as in tl1e case of liquid sulfur the weight fraction
polymer 4! for selenium is calculated with Kl ($) and K2
(rj:>). In Fig. 27
the solid curve corresponds with the evaluated values for the 'Wei&ht
fraction polymer. 'Ihe results t.'f the measurements by Briegleb are
indicated by points (o).
'!,; 1)J • tWO'Ö;Ihl 1r•ctKr- IWlif""'')
Fig. 27. We·ight j'raetion polymer 4> {Se) es a funoticm of T(°CJ.
SoZid cur-oe aalcul-at6d tJith K/$) and X2
fq.,),
Points 0 : values m2asured by Briegleb (see Chapter· 2).
6.3.3. The number average chainlength Pn
6.3.3:1. Liquid sulfur
'Ihe number average chainlength Pn is calculated from $z and the
number of spins N with the help of formula (l. 2.J 1). The calculated
values are indicated ln :Fig. 28 by points\ o ). In the same way Pn is
calculated from $mand N~ denoted in Fig. 28 by points (o). Since p
,;
...
•rf )
... -
•'
' '
86
...
Fig. 28. Number average ahain'length Pn (SJ as a function of Tf°CJ. Dotted curve oaZcuZated with K1 f~2 J and K2f$2J, Solid curve caLcuZated with K1 t~m) and K2 t~m)~ Points o aa'Lculated with N ar.d ~ 2 .. Points o ca'lculated with N and ~m ..
Points I oal.cu~ated with N(x0
Jand 'a by PouUs et a~ (10!.
is given by formula (1.2.8) as a function of KJ and ~' it is possible
to calculate Pn from K1 and ~ using (1.2,9), In this vay are obtained
the solid and dotted curves in Fig. 2B, using KJ ('m) and K2 ($m)'
and Kj (92) and K2 (~2 ), respectively.
87
To check the accuracy of the extrapolations to lower temperatures of
the sets of best fits Kt ($2 ) and K2 ($ 2), and K; (<Pm) and K2 ($m),
the sharp decline in Pn was also calculated by making use
of the equilibrium constant K3
and the ring fraction R = M0
(J - $)/8.
It eau be easily shown that the equilibrium constant K3 can be related
to KJ and K2 by:
K3 K2
(6.3.5) . KJ
Substituting R M0
average chainlength
( 1 - $)/8 and (6.3.5) in formula (1.2.10) the number
is expressed in K3
and I $:
p (6.3.6) n
If the expression for R = M0
(1 - $)/8 and formula (6.3.5) are used in
(1.2.7), we obtain
(fi .3. 7)
When P >> 1, p8 can betaken ~ 1. By using p8 ~ and formula (6.3.7), n
K3 was evaluated in the temperature interval 160°C < T < 190°C with the
help of, first, ~ 2 and then $m· In this interval it was possible to fit
'K f ln lM31 (fi.3.8)
O'
Assuming Van 't Hoff's law tobevalid at temperatures below T l60°C,
K3
was extrapolated to 130°C. The best fits for K3 calculated with
and ~ 2 are denoted in the following by K3 ($m) and by K3 ($ 2),
respectively. Negleering 9 below T = J60°C, P was calculated with n
K3
($m) and K3 ($ 2), using 6.3.6; the results are shown in Fig. 29 by
curves II and III, respectively.
Above T 160°C, <P 1: 1, and therefore P is calculated as a function . n
of K3 and N. Inserting (1.2.13) and (6.3.5) in (1.2.8) the following
equation for p is obtained:
N 0 • (6.3.9)
88
From (6.3.9) p, and therefore =1/1 - p, is known as a function of
K3
and N. In this way the points (o) and(~)are evaluated with the help
of N and K3 (q,2), and N and K3
(q,m)' respectively (see Fig. 29).
HÎ
w'
10'
10'
I I I I ' I :
' /J) ) n0'/~//' m --- / lll-----
Fig. 29. Number average chaintength Pn (SJ as a function of
curve I catcutated with K1 (q,m) and K2 (~m),
curve II calcutated with K3 (q,m),
curve III catcutated with (q, 2J, curve IV catculated with K1 (~ 2 ; and K2 (q, 2J, points r:. catculated with K3 ( q,m) and N,
points 0 calcu tated wi th ( ~ 2; and N.
89
6.3.3.2. Liquid selenium
The points (o) in Fig. 30 have been calculated with formula (1.2.11)
from N and the weight fraction ~. Using formula (1.2.8) and (1.2.9),
Pn is evaluated as a function of K1 (~) and K2 (~); see curve I in Fig. 30.
10,
10
m'
w'
10 0
P., \number average cha:nla-ngtl-il
' ' \
' \ \
"'~~Se) "'
nts> T(Î:J -
soo 600 700 800
Fig. 30. Nwnber average chainlength Pn (S and Se) as a function of
Sotid curve I (Se) calcutated with K1 (~) and K2 { q;)'
Dotted curve I {St.:) model belCfl.,; 1' , m Solid curve 1I {S) catculated with (qom) and
Points 0 {Se) calculated with q, and N,
Points /':, (Se) catculated with N(x0
) and q, by Massen
et at. { ]1).
900
90
6.3.4. The equilibrium constant K3
6.3.4.1. Liquid sulfur
In Fig. 31 the solid and dotted curves (S) represent K3 (~m) and
K3
($1 )~ respectively. The way in which these curves ~ere obtained is
Fig. 31. -1 X3 (S and Se} ae a funotion of 1000/T{X },
Soli.d euwe (SJ : 1C1 ( ;p J _, " m
Dotted curve
CW'Ve (Se!
IS!: K3
lo2
J, : K
3(1f).
described insection 6.3.3, 1. To check the relation K3 ~ K2/K1 with the
help of the results from the ESR experiments, the values of t..H3
and
t..s3 obtained by the best fits K3 (~2 ) and K3 {'rn) are compared with
those derived from ~ (ç2)/Kl (~2 ) and K2 ($m)/K1 ($ru) respectively.
The results are shown in table IJ and Table 12, respectively.
6.3.4.2. l.iquid selenium
Gsing formula (6,3.7) and p8 ~ J, K3
was calculated from the weight
fraction polymer obta:tne:d by Brie:gle.b. K3
fitte:d formul.a (6.3.8) 1 ~chich
L
l(kcal/rnole)
óS3
(cal/mole K) 1
91
1. 14 ::!: 0.02
Table 1!. Heat of reaction (Mi3 ) and entropy cha11.ge ft:.s3J for K/$
2)
a1".d x2ro2
J!K1
frJJ2J. (For su"Lfu:r.)
K3(t) ___ .. K2(•)l~~
(kmole/kg) (kmoleÎkg) I ~··-/,fl : 3 (kcal/mole) -2.09 ± 0.05 . -2 ~ "l r--------+--~·
. .,s 3---~---~_o_._~ .. " 0.1 ~.-.. ~~i 6J ! (cal/rnole K) .......... _ ..
'rable 12. Heat of reaction (t:,H3J ar-.d entropy change (t:.s,3J for k:/t;.m)
anà X;/ r!Jm)!K1 { 9,,/. (}"or sulfur.)
~-··
: LI.HJ
L(kcal/rnole)
"s3 (cal/mole K).
K3(.rnl
{kmole/kg)
i -5.8,1.3
Table 13. Heat of reaetion (t.H;) ar>..d entropy cha:nge (t:.S3J j'or K/rtJ)
::md KirJ;.J/K1
(J?). (For seZenium.)
is shown in Fig~ 31, curve (Se). in Table 13 the values fo~ ~H3 and
ós3
obtained from the best fit are compaLed with those calculated
from the relation K2/K 1•
6.3.5. lhe number of spins
6.3.5,1. Liquid sulfur
When p is solved as a function of K1 and K2 and then inserted in
fornula (!,2,13), the number of spins N can be calculated as a function
of K1 and K2• ln Fig. 23 tbe solid and dotted curves through points (o)
are evaluated with the help of Kj ($m) and K2 ($m), and Ki {$2) and
K2
($2), respectively.
6.3.5.2. Liquid selenium
!he sameprocedure as described in 6.3.5.1 is applied to liquid
selenium. The curve through points(6)in Fig- 23 was calculated with
K1 (<) and K2
(;ó).
6.3.6. Equilibrium data of the polymerization process of liquid iodine
doped sulfur
Since no data for Ki (=equilibrium constant of reaction 1.).3.)
are available, Ki. was taken equal to JS (!fm). In the internal report {41) it
is e:xplicitely show that in a 1<lÎde range of values Ki scarcely inquences
the calculation of N. Pn and $·
By inserting K2 = K2 in equation (1.3.11) and (1.3.13), it Yas possible
to solve p and X from these equations as a function of M0
, 10
, K2
and
K1, For K2 and K1
the best fits K2 (~m) and Ki (4Jm) weLe taken. In the
sections 6.3.6.i~ 6.3.6.2 and 6.3.6.3 the solution for pand X as a
function of M0
, 10
, K2 {$m) and Kj ($m) will be used and denoted by p'
and X1• respectivel:;.
93
6.3.6.1. The number of spins N in iodine-doped sulfur (SI}
By using K2 "' Ki and inserting p "" p' .and X "' X1 in equatiun
(1.3.15), thc number of spinscan be ealculated as a function of the
iudinc dope (X0
~ I0). Fig. 24 shows the results of these calculations.
ln the ten;perature range 1.2 < 1000/T < 2.1 the c:alculated values of
N lie within 20% of the values of liquid pure sulfur. The calculated
values of the dopes of 0.026 and O.J44 wt k are in good correspondence
with the measured values. For higher dopes, deviations of the measured
num:.ers of spins fron the calculated values occur.
6.3.6.2. Ihe weight fr.action pol~er 4 (SI)
In the case of iodine-doped sulfur thc weight fraction polymer
can be defined by
7ic1 + ~icil + ric12 ,._ ]. :i >I
0
With the aid of (1.3.5)~ (1.3.6) and (!.J.7), formula (6.J.IO) is
transferred into:
1oserting K2
~ K2, p = p' and X~ X' in equation {ó.3.tl) the veight
fraction pol~r can be calculated as a function of the iocline dope.
The results of t.he calculations are given in Fig. 32.
6.3.6.J. The number a":erdge chainlength Pn{SI)
(6.3.!0)
(6 .J. IJ)
The number average c.hainlength P0 'Jas calculated as a function of
the iodine dope by introducing p"" p' in formula (1.3.9), In Fig. 33 the
calculated curves of F0 ~ith different percentages iodine dopes are
shO\JTI.
The reliabilit:y of the developt~d des-cription of the polymeriz.ation
94
Fig. 32. W€igth fraotion polymer 6 (S and SI) as a function of T(°C).
CUI'Ve 1 (S) ca.lcuZated with x:! (if>m) and K2 (tpm)..
cul"ve 2 - 8 (SI) caZ.cu.l-ated ü.lith the po'Lymerization theory
(n~~er 2 - 8 are related to iodine dope in
TaNe ?).
process of liquid iodine-doped sulfur has been tested by the following
method. Ry waking use of the measured number of spins, Nm' and taking
K2 = K2, p can be solved from (1.3.15) as a function of Nm, X and K2 •
This solution is denoted by p11• When p = pn is deserted in (J .3,13)
using ~ ~ Ki, X can be solved as a function of X0
, Nm' K2 the
salution being denoted as X11• Substituting X X'' in p 1r and p p 11
in formula (1.3.9), the mllllber average cha.inglength Pn can be
calculated as a
been calcula ted
function of I~ t X and lC. The points in Fig. 33 have m o -.,
using thé data of Nm• X0 end K2 (~~). Tt is seen that
95
w'
u' '·
.. . ••• ~ 0
'
• • • • 'b • -· • •
Fig. 33. llwnber average chainlength Pn (S ar.d SI) as a fu:·uJtion of
T(°C}.
CUl"Ve 1
CUPVe 2 - 8 {SI)
points (SI}
calcuZated with K1 {Çm) ~~ K2 (~m)~
oalcuZ.ated with po"Lymei'ization theory ~
ca"lcuZated with N aro.d polyme1'ization t/heory
(numbers 2 8 a:n.d syrnbol-s are related to iodine dope in Tab"Le ?).
96
the calculated points of the dope with 0.026 and 0.344 wt % are in good
agreement with the theoretical curves. At higher dopes the calculated
points deviate from the theoretical curves at lower and higher
temperatures.
It seems reasonable to make an attempt to evaluate data for K; from Nm'
X0
, K2
and K1
. In (41) the failure of this evaluation is discussed.
6.4. Kinetic data of the polymerization process, evaluated from the
linewidth of the ESR measurements
6.4. ]. Liquid sulfur
In Appendix D it will be seen, that the reaction rate constant of
the radical-displacement reaction and the ring-addition reaction, as
calculated in Chapter 4, has to be divided by a factor 2. This has also
to be done for the reaction rate constant and the pre-exponential
factors which are shown in Fig. 34 and Tables 14 and 15, respectively.
In Fig. 34 the reaction rate constant for the ring-addition
reaction (0) and the radical-displacement (~) is displayed against
1000/T. The points (O) and (~) were calculated with the help of formula
(4.2.11) and (4.2.12), respectively, using ~m as data for the weight
fraction polymer. Points (e) were obtained from the ring-addition
reaction using ~ 2 as data for the weight fraction polymer. It is seen
that the ring-addition reaction is in excellent agreement with an
Arrhenius-plot. The reaction rate constant as calculated for the radical
combination reaction, gives a negative activatien energy, which is seen
from formula (4.2.8), taking the results of the radical-displacement
reaction [ln(~H/,JM0~)] and the temperature dependenee of the term
+ 6H~/2RT = + 17.500/RT.
The ring-addition reaction is chosen from the three alternatives to
be the reaction, which determines the reactivity of the chain end spin
state.
The heat of activatien and pre-exponential factors of the curves through
points (o) and (•) are given in Table 14
'"'' 1'
" 10
trtL ...... L .. 1.0
97
....!..____l__L ...... 1 ........ ..! .... . 1,4 1,6 1,8 2.0 2,4
Fig. 34. Reaation rate oonstant k 1 for the radioal-displacement
ueing Ijl (points à), and for the ring-addition m ueing q,m and q, 2, respeotiveZy (pointe o ande).
k\(q,m) k'b(q,2)
(kg/kmole.sec) (kg/kmole.sec)
• 4.49 ± 0.06 5.10 ± 0.07
(kcal/mo le)
k' ob (2.4 i 0.2)xlo 12 (4.9 ± 0.3)xlo 12
(kg/kmo le. sec)
Table 14. Heats of aotivation and pre-exponentiaZ faotors of the
reaotion rate constant k'b of the ring-addition reaotione. (For suZfur.)
•
98
6.4.2. Liquid selenium
Since the temperat:ure interval of the measurements of the lin
linwidths was too small, and their accuracy insufficient, it was not
possible to choose between the radical displacement and the ring
addition reaction. For the samereasans as mentioned insection 6.4,1,
the radical-combination reaction was not taken :Lnto account.
On the basis of similarity of properties of liquid sulfur and selenium,
the ring-addition reaction was chosen. In Fig. 34 points(o)correspond
with calculated values for the reaction rate constant of the ring
addition reaction for selenium. The heat of activatien and pre-exponenrial
factor evàluated from the best fit, were 6.3 + 0.7 kcal/mole and
(5 + 3) x 10 14 kg/kmole.sec.
6.4.3. Liquid iodine-doped sulfur
For dopes higher than 5.6 wt % no choice eau be made between the ring-
addition and radical-displacement reactions owing to lack of ESR data
at low and high temperatures. For samples with dopes lower than 5.6%
the radical displacement reaction gives a negative heat of activation
at low temperatures, just as in the case of pure sulfur. Therefore, the
ring-addition reaction was chosen to be the dominant reaction in limiting
the life-time of the chain end spin state for dopes lower than 5.6%. On
the basis of similarity, also this reaction was assumed to determine the
life-time of the spin state for higher dopes. In Table 15 the heats of
activadon and pre-exponenti.al factors are given as a function of the
iodine dope. In section 6.5 the results will be further discussed.
6. 5. Discussion of the x•esults obtained the ESR experiments
By extending the temperature range for which magnetic measurements
for liquid sulfur are known from the literature, it was possible to
99
wt % I ·--,
iodine 0.026 l 0.344 2.25 15.60 10.9 17.0 27.5
i
E' 5.31 4.81 4.4 i 3.24 3.54 2.7 2.4 b
.:: 0.06 : + 0 (kcal/mole) + 0.06 i- .08 .:: 0.07 + 0.1 + 0.1 -k;bx10
12 4.9 3.4 i ~.9
2.6 2.4 3.6
(kg/kmole.sec) + 0.6 .:: 0.4 1- - 0.2 + 0.3 + 0.41 -
Table 15, Heats of activation and pre-exponentia'L factOI's of the
reaction rate constant k 'b of the :r•ing-addition reaction
as a function of the iodine dope.
obtain additional information on kinetic and equilibrium data. Values
of the number average chainlength, calculated with the help of the
measured number of spins and the two ·sets of weight fractions polymer,
were obtained at the low temperature side of the maximum of the chain
length. By extrapolating the best fit curves for the equilibrium
constauts K1
and K2
, obtained in the temperature range 153° T < 700°C
from the ESR measurements, a transition temperature in the chainlength
could be calculated, with the help of the polymerization theory. It is
seen in sectien 6.4 that the polymerization theory and the experiments
are in go~'d agreement with each other. The weight fraction polymer ~m
gives the best results. There is good conformity between the equilibrium
data obtained from the measurements of the static susceptibility by
Poulis et al. (10) and those obtained from our ESR measurements.
The kinetic data evaluated from our measurements indicate the
ring-addition reaction to be dominating the way in which the equilibrium
is reached. It seems worthwhile to draw attention to the fact that the
possibility to effectuate this selection is due to combining intensity
and linewidth data and is thus a special feature of the application of
ESR to polymerization processes. The fact that a break in a chain
sametimes occurs caused by the reaction 1.2.2, ensures the Flory
100
distribution proposed in Chapter 1. The relaxation time for this process,
regulating the details in the chainlength distribution, must be (rather)
langer than that of the ring-addition reaction.
Our re sul ts show that the rad ie al displacement reac ti on, which was
proposed by Gardnor et al. (9) fails to give reliable results.
In Appendix D it is seen that the reaction rate ~onstant kb for the
ring-addition reaction has the same temperature dependenee as the ESR
linewidth. This means that the activatien energy Eb is the temperature
dependent. Since the activatien energy Eb is temperature independent,
the heat of reaction 6H3 = Eb Eb must be a function of the temperature,
which was also found by Fairbrather et al. ( 19) from data of the specific
heat.
The results of our ESR measurements on selenium give support to the
ideas of similarity in properties of liquid sulfur and selenium. Good
correspondence exists between the extrapolated values of the number
average chainlength evaluated from the results of our measurements and
the values obtained from the measurements of the static susceptibility
by Massen et al. ( I I ) •
Especially at high temperatures the number average chainlength of
selenium is somewhat greater than in the case of sulfur. The viscosity
of selenium, however, is on the average JO times lower than that of
liquid sulfur. The uncertainties of the terros k', A en C in formula
(2.4.1) renders a numerical calculation with the help of the equilibrium
data obtained from the ESR re sul ts difficul t. The fact that the reaction
rate constant of the ring-addition reaction of liquid selenium is on the
average 50 times greater than for sulfur, may be correlated to the lower
viscosity of selenium.
A consolidation of the polymerization theory as develope~ for
liquid pure sulfur, is found in the ESR experiments on liquid iodine
doped sulfur. The description of the polymerization process in the case
of icdine dope is consistent with the data obtained from the ESR
experiments on doped samples. It is possible that for higher dopes a
better conformity is obtained when the evaluated kinetic data are
incorporated in the equilibrium constant K1• The systematic decline of
the activatien energy of the ring-addition reaction with increasing dope
101
concentratien can not be fully understood by our description of the
polymerization.
lOL
CHAPTER 7
EXI'FI!JMI!NTS ON 'I"IU•; (]UENCH~;JJ l.lQUJD STATE, 11 CI\TENA-S8
" ALI.IIl'](Ol'J;
Some expe.l."Ün~ntc.tl t'e,'l.ttln..~s~ knm.vn frutrt the: l.it~r(ttur'.r_·~ ücc.uring .lil
the liquid olnd qu~nched 1 iqv~J. state. elf t:iulfur~ r.iu~ üût: be under~t;o,)d with
t.hc he.J.r qf Lhc polymeri~uliun th<•O>:y. l'he.s~ h>C\Lun'E were att:ribuL~d 111
.. ::; r1 ...
" Althougl1 i.u vurious p;_q.lurs th. .. '=!
11 C.:..:J.tena-!)B 11 allotropC'. i.::; aö~umt=o.(i lCJ be. exi~_;t,,i.ug ;J d~:::finit.e expetimE:'nt:~1
pl"'oot i~; qt,>l known.
A ll~-v~.1d I!.SR ~i i.en.;.ll (de.ncd:(:U in the fL1ll(1wing by t..ht~ B·· .si)~n:d) w.:~s rneabtll"(.~d
hy 1,.1~ ~n Lh€. temper.'i.tL.Ll-~ .i.nt ... ~rv:.tl 2.0°(: -:.: 'l' ~: 2ü\/\: ... Thj.:. )~-$igu;.IL Jll"I)V(:-!cl
dl_f[~r·ent fr(tl~l the ~up,:~r.i.rnpüsed polyilll•rization ::;1gw .. d.s mc.:lsllrt"~d ~n llH:::
l.i<juid ~t.•tc· c>[ oulfur l.n.>m T = i'j/'c upward~- l)y r<Olatinp, nur J·~SI!
n•easurem(':nl.!:i on th<~ c.fW.!nched 1 i (!_u.i. cl (T ~.: T ) .:111d on the. qtJ(~~~c.:b-.:~.:1 :::ül iJ 'r
~ti::ltes tu thin !-ligüul~ udditi()~"J.~ll infonnat.1.C:l0 could he o!Jt;tiüed ubout
the -~~u.l[ur a1li')t:r:'up~:::: 11 Cat~~n;l-~~ 8 ". Sol?!:çL.i.on 7.2 d(~.:JJ.s with th(! tll(l::;t impol-ta~~t .:.n:·guments glv(;l~ in th~~ Jitt·~.r.::tr .. l.lf't'
fot· iL~ exist~'~cc. Sectien 7.3 givea tJ1e rt.~~ults C)[ tl1~ r~levant l~SR
e.xperitnents c.r1rried out i11 ovr le:abor:a.tory ... Jn ~'-·ctir . .111 7.4 tht·:=c result:::;
<l.rt~. Ji~cus~a'!d :lnd coJ.npare.d 1NÎ tb the argunh~nl::; m(.:ntloned in 7 ... 2. /\n
•lttempt iR J.Jit.'ll llW.d12 to JL')-L.:lO:::e the nfit.~ll'·e uf 11 C:ät:~~n;~-s 8 " ...
7, 2. !l!i··g'1.tJ~Ic::?nt:.;.J f!ï.:1.l(:.:'1 .. 1. ln Uie lii:er'll-((.J..J:'~! fur· th·? e::clul~ru ... ~e oj" t.h:'! nOQIA:.~ru ... i-~3 8 "
<<!.l-ul-l'U[J•''
.J. Schenk (2?) llW.intaJt"!l.:·c.l u quä.ntjty of l:iUlfur at YOUII\ temperat~ll"""t:!l
C!btdined by l.ir·st quenc.hl.ng the 1 i.']••;d "t<tt<> from 'I' - 220°C (aiHW(> tb~
U',:.nu::>iti;.-,11 point of p~·dyJlll.:!:'izütion),.lO.d ~ubsequt~nt.ly )3.t'üUnding it .:lt
liqL1id nitrl.l(_':en tempt:~r,·llur~. Ev~l::y d~'Y he touk a :..:.:.lwple .:.1ncl of it
he determirh,:..cJ Lhe fLlCLiun whic.h W;J.::!; .in:soluhlt=! 1.!~ c.s 2 ~ it i~ .scon 1n
1;-ig. J~ th.1.t. LhE:!: insc.,lt...lbl.r.:.· fr..s.c.tL""l•~ ri.acs unt:i J lL . .uttains a m.Jx.i.mum
103
aftel: about three d;~.ys, Sim:e th"' qu"nched poly1n<or~ are not stotblc (sloll
convereion into St< , (see also Ch~pter 2) Schenk assun\ed that chere must
be another co.-.figurat:i.0\1 which ~-~ eonverted into polymers.
l5
Fig. 35. Wrdght fi'uation polym••1' ~as a fimatlon of the ;storuge Um<•
ut r'OOm t<mp~1'atUN> (see text).
lUUII~.diately ~fter qu(:!lChing thC liquid StJ.te ftülll T = 130°[; (belaw
the transition point of pclymerizatiou) a fr«ction (I to 27,) of insoluL•h
svlfur was rneagured.
The. ""'"t day the insolvble fraction of the ql.lenchc:d IMoterial, stored <H
T c ~o"c was fol!nd to be 4%. J. Schenk propos.;,d that in the liq1.dd state
in addi.rion to the polymedzation e>quilibrium short chains are present
(ch<li<l) ength <\bout eight atoms), whic;h ar i se from thc opelling of eight
m<lmbered rings. When queuehing th<o liquid SC<'<te, these short ct.ains are
al 50 frooe-Il- When the polymers assume an ordered structure af ter warming
<•P ta room temper<~.ture, thGse $hort ch<liüs might be incorporated in it,
which need~ some time..
As ,~ consequenç.e short Ch.}in:s have to be pre.sc.nt in thc frac:tion
SOlUbl<l Îll CS2
, whO::I\ the disSOlving experimli!tlt is c<trded OUt illiJllediately
after the q",e.nching procedure. p.,w. Schenk ct al. (1•5) hwestigaled t.his
fraction CJ.refully by cooling ie <J.t T = -78°C. At thü cemperatu~c the
rinBs crystallize from the solution, Upon evaporating th~ solution at
roOJII t.;!mperature i t was founrl that a bout 25 grammes sulfur t1ad been
I Oio
Pl"<'Sent i.n 100 grammes r:s2. Whea the sulfur ü dissolved -:.ga.in in cs2 .~
ir.?Ctio,\ of al.>vut f>O% had b~come ~nsol<Jble. Thcy det..:rmine,l the averago;.
numl.H . .'I:" of ;,ltOmfi per mc.decule. for thl'; short ch.ai~~ fraction c.ryosc.opi.cally,
w!iic.l1 lurn(~.d out tu be B. J. From the.ir expo.t"iment...s. the.y dre.w th~
ct .. Hl.CllJ~ion t.hat i.n udditiQn to the ei.ght-merubr::-red rin,gs:l' short cha.in~
uf 8 S-atom .• W~l:-e .-;u lub! e in cs2. whi eh we re converted i.nto polymer~ ~ft""
tt:::mov).ng the ï':lolvent~ S.î.milar result~ we"I:"(! obtained by quen,ching the
liquid st~te frvm t('.I)Jp.,ratur~s heluw and ahove the point of initi.Jl
polymerL>Jtion. In '' later puhÜ<.:<~tiol\ P.W. Schenk ct al. (/16) osing
iodim~t·ric met:hods:l' de~cr.ibed a quantitativc deter-rninat.ion of thc centent
vf rines and •hort chaio (cato;>.ü<l-S8
) fractions i,, cs2
solutions. Aftel."
C'Vi.lpO< atioo> of tiol) sol (ltions and e~tracti_on Of th" BOLÎ-d witb CS2 St
~oom lempe.r;ItU["l~ they f1)und th.;.!t on the avt.~ra,ge .5.5% of l:.:ht: fracr.::ion
!':"ulft.Ll: .Goluhle in t:S:t. at '.l' = -78°C W;Js c.or~verted into polymer.
The ~·:Ul:CHTI-iJly of the. lll-t~1 tiLtg poi.Lll. of pure sulf1.1~· wa.s investi,g.1.tt::d hy
!;rnith (41), who attr·_i_buted lhe phcnomenon to ûx-m."o>bcred 'l:ings. f!.W. Schenk
t.~l alL (116) c.::tlcuL~Hed 5-.SZ 11 c.atcna-s0
" to be present ii'I the 1 i.quid ;u;
T = I 1 '•. 5 °(; whic.h could be r"sponsi hlc for Lhe anomaly uf th<:' melti •lll point.
F"<<brorher et:~!. (19) discuss"d the sh<~rpness of the ons..:t of
polymc•t•ization. l>"th sp(•cifiç heat and vi$cosit:V shoor th" b"gümings of
'-' di~continuity $'-''"" ten desn•cs b<:'lOw the point of iolitial polymerizati<>•1.
They ca 1 cu latec:l that the pr<Jsence of short chains could be rt•sponsible
fo1- lhi!1: $low r~~e. tlowever 7 in their opi(lion thc pheQomenon could
t!qU•>Jly W<>Jl be <'><pl:Üo\(!J by a~sUmll\8 the i'X"sence of la.l'ge ring ••
~;·ur- .:1 dt·t.ailed di~c:ussim1 .c"J[ thlf'! urguments &i"en in the Iite.l"ätur<
(or tht.· ex i ~tenc:t.~ of thlf! .allotrope: .,(;.~tena-s8 n the te-ad.~l.'" is f~J.rther
ref ... ~t·:red t·.o the litera.tlH'e.
7. 'J _I. Sample !»-.-parat \vn
Th.c ald fur md~:r:.r-i.al v:sed for the q~u:·nching experiment$ wü.a si mi lar
l'.o thLll'. ft1r tltt'· measutement~ described if1 Chapl;:e:r 6. hl a gloveboxr
!OS
flushed wlth pucified nierogen gas, th~ sulfur is heated in a beat. At
<> chosen (<omperature the boat w<ls emptied in a dew<Ir, filleu with liquid
ni r.rogen. Tn th~ liquid nierogen s.:>mJ?le tubes were Eilled wi.th tht:
q\1e.nch<:.:.d $1.1l.Îur 111.:1teri~tl a~.-..d se a led off. The samples wer~ stored in t;.he
liqui.d <Ütrol!/"' until the ES!\ lllli!asur"ments wen' pertorl'<"'d. The broad ESH
~i81\al was rneasurcd OCk th.e ~.aale sulfur samples which were uïSed for
obç.üning d;)t.~ for the polymli!rizatiNl equilibrium. (Chapt.:r 6.)
7.3.2. I::SR signal ohtainocl by qu.:nching from T
Wllil.E'! mainudning the tempo<ature of. the s&lllple at 1' = -I60°C it
1.-'J~lt~ tt-.an~ü:rr~d to t.he sp~!.;t;.rometer;p a.nd it~ ESR spectrum ltltasured.
(See Fig. 36 .:>). Thc observ"d signal h.:>s Rome featur"s in common with i'
Jg-"P''~trum(e 1 ~ 2.039, s2
= 2,024 and g3 ~ 2.00 .. )but its i'orm is net
consis cent wi 1: h a 11 pur.~t" )g-sp~ctrumr Wh en th€ ::;~titlp le Wt)$ subsequ.en.t ly
h''" ted up co room ~«Olperatvrf. the pe•>l<" at g 1
- 2. U 39 ''"d g,2
~ 2. 024
d.i "appe<!C(•d irrev<•rÜbly. 'Che Pü<>l< at gJ - 2.00 ... appeareó relatively
otablc, the g-vnlue could nuw be detarmined as g = 2.005.
Since th« circumst<\i\Ces of S;J.mple prep3ration m.:>de it posdble hr
impuritlms to ba built in, a purlty telt had to be carried out. In
.] iquid pc, re samples only the polymer aignill (g = 2. 024) is found sup~r-
impos".:.'d on 11 th1..~ hruc:lll $ignJ..ln~ Since the int.f.p.sity of the :;i.g11al at
g = 2. 005 r-I.E!mu.iw .. ~d inv(J.riant jn the liq~,id st.:..~ te~ the conc.lusion was
Jr,%m th<ll thü signa! was due U> the presence of ~om<: impuritics,
i.tll;roduce,:;d durine, .f;ample r)reparation. Wit.:h a sample from the SC:lmC
tjlH=.mch~ld .-;11ltur ·~••lterial a dis::;c)lving (::Xp\=;.riment w-as c~l)::'l"i.ed out.
At't HSR :;pectrum ~)f the i.,•lrt in~:;vluhle in CS2. wa.s rt.~Corded ~1.t 1' 7:1 20°C.
(Sec ~ig. 36 b) Ihe Yignal at 8 • 2.005 was founcl also bere. Prom the
:>iolublt..~· p.:irl I\•) ~ign~d was obt..-.i:ned. It c:an be supported th.at the
impur-it:y :-=.:pin :_:;,t:ate W~Hi present .)t the; Chain encJe:.
Conclu~tnn;, i\pc•r t i't01\\ the impurity ::;i8jlal C:lt 2.005 thürli' might be
R Jg ~·'V •:tl!H.~ Û(lrldl witb gl = 2-030, 8 = 2.024 c>nd g (J.e,,-;.r 2.00 ... the 2 3
l.Jöt be.ing ob~(.;ur*d by the impuri ty •ignl'l·
106
107
7.3.3. ESR signal obtained by queuehing from T
In Fig. 36 c its spectrum is shwon when measured at T = --160°C.
The ESR signal consistsof a 3 g-value spectrum g1= 2.039, g2 2.024,
g3
= 2.002, this spectrum will in the following be denoted by (3 g-I).
By heating up to T = 20°C the signal disappears irreversibly without
Ieaving any residual signal. For this reason it was supposed that no
paramagnetic impurities were present in this sample.
7.3.4. Samples quenched from 400°C and 145°C, measured after storing
for some weeks at T = 20°C.
Fig. 36 d and 36 e show the ESR spectra measured at room
temperature. It is seen that a 3 g-values signal arises (g1 = 2.05i,
2.024, = 2. 002 which we shall deno te in the f ollowing by (3 g- II)) .
7.3.5. Queuehing the solid stable orthorhombic allotropie farm from
T = 70°C.
The solid state (polycrystalline material) is heated up to 70°C
and then quenched in liquid nitrogen. The spectrum measured at T = l60°C
is given in Fig. 36 f. This spectru~ might bedescribed as a 3 g-Il
spectrum with some admixture of 3 g-I. The signal also disappears when
the sample is heated up to room temperature.
Fig. 36. {a) ESR spectrum of sulfur
(b) ESR signal of the part insoluble
obtained at ( 2),
(c) ESR spectrum of sulfur
(d) and (e) ESR spectra of su"Lfur
m-J - and .T::::
some weeks at room temperature,
(f) ESR spectrum of
auencnea from T
fr•om T
in of the material
from
and stored fo:r
orthorhombic sulfur,
•
108
7.3.6. ESR oeasurements solid and liquid statas between
T 20°C ànd t =
A braad ESR signal was found in the solid and liquid states by carefut
elimination of cavity background signals. Tte polymer signa! of liquid
sulfur is superimposed upon this broad signal from T = l53°C upwards, In
Fig. 37 the num.her of spins conesponding to this bnlad signa! is displayed
against 1000/T. The line'Width is about 800 Oe and the g-value 2.11 .:::_ 0.02.
both temperature independent. Wben the pure sulfur matedal, closed
ju the sample tube,is caoled to room tecrperature from higter temperatures
the amplitude of this hroad signa! was found slowly to decrease in the time.
Af ter about one day a very 'Weak 3-g spectrum is found superimposed on tbe
braad signal. This 3-g spectrum disappears when the sample is heated up to
tiH~ l iquiè state.
lil' • 8
1-'ig. 17. ,"Ju.mber o.f spins o.f '1the 8-signal." as a: funation cf 1000/:l'(K-1).
109
7 .4. Atterr1pt at an in.terpretation. of the measured ESR signale. Discussion
on the "catena-5/' alZotJ'Ope.
Section 7 .4. i deals with the ESR signals obtained frorn the quenched
solid artd quenched liquid states. The 3 g-I and 3 g-II signals are
attributed to a quenched sulfur chain end and a quenched dislocation in an
orthorhombic sulfur envirement, respectively, Section 7.4,'2 treats the
interpretatitm of the braad signal. This signal is attributed to a compound
having properties -which are to a grcat extent similar to those cormected
with the "catena-S3
" allotrope. llo'Wever" the structure of this compopnd is
assumed to be different trom that of an eight-me~bered chain.
7.4. I. Discussion of the ESR signals obtained from the quenched liquid
state
7. 4. I. l. 3 g-I signals
A comparison of the signals shown in Fig. 36 a (described in 7.3.2)
and 36 c (described in 7 .3.3) leads to the suggestion that the quenched
liquid sulfur in both cases contains the saoe species responsible for the
3 g-I spectrum. The spectrum of Fig. 36 a shows an additional signa!~
~hich, however, is attributed to inpurities and therefore, will be further
neglected. Freezing the polymerization equilibrÎUG means logically the
queuehing of polymer chain ends, and these must therefore, be responsible
for the 3 3-1 signal found in material quenched from T = 400°C. At a
temperature of T "" 145°C the polyme:c concentration chain ends in the
liquid state is, ho\on:Wer~ below the detection limit of the ESR spect-rometer.
Since tUe 3 g-I signal is still found present in the material quenched
from this temperature, cbaiu ends must occur, which L1 this case are not
connected to the "normal'! polymer signa Is in the liguid~ state. Later on
"'e will try to establish a relatiou of this 3 g~·I signal to tbat of the
broad signal in the liquid state (section 7.4.2).
The disappearance of the 3 g-I signal by heating the samples to room
llO
temperature is explaim:d by rt~::ombination of chain ends. In the liquid
state, broadening of the ESR signal caused by lifetime shortening of the
chain end spin state, leads to an isotropie signal with a g-value 2,024.
1'his g-value is equal to the central g-value ("" g1) of the 3 g-I spectrum.
Chátelain (48)and Bnttet (49) obtained similar ESR signals by conden~>ing
sulfur vapour on a helium finger. Theit- 3-g value (called 13 signal)
consists of the g-values: gt = 2.0405~ g2 = 2.0259 ar.d g3 ~ 2.0023.
Analogous 3-g signals ~ere also found in frozen amine solutions of sulfur
by Hodgson et al. (50) (g 1 = 2.055, &z = 2.035 and g3 = 2.003), and in
cysteine by Kurita et al. (51) (g 1 = 2.052, g2 = 2.029 and g3 ~ 2.003).
To explain the anisatrapie 3-g value, l<urita et aL assumed tha:t the
unpaired electron of the sulfur radic<;Il is in Q TI~orbital (wi th principal
component the sulfur 3-p orbital). Configuration interaction with non
bonding sp2-hybrid orbita.ls or with a bonding o-orbital can lead to the
anisotropy in the g-factor (52).
7.4.1.2. 3g-Usignals
By irradiationapolycrystalline sample of the orthorhombic allotrope
Sa with fast neutrons (1-2 MeV), Chä:telain et aL (49) found among ethers
a 3-g value !'lÏ_gnal, which was idendcal with the 3 g-Il signa! described
in 7.3.4 and 7. '3.5. The resulcs of section 7.3.5. suggest that the crigin
of tbe 3 g-II signal is a lattice fault, which in the present case might
be supposed to consist of a vacancy.
lt was already mentioned that at room temperaturc the quenched polymer
material is slow"ly converted into 50
: To explain tbe formation of the
signals mentioned in 7.3.4, ve propose~ that eight-membered rings are
slowly formed from the quenctu!!d, pol:ymer chains. Sevcral ma:chanisms of
crystal growth from pol}~rs cart be proposed.
E.g. I) the chain doesnotsplit 11 in time" leading toa '18 1 ~screw-axis 11 ,
2) interaction between the ebains on the gro'"'th surface, etc. We suggest
that due to the normal close packing teudency in crysta1s the orthorhombic
I I I
local symrnetry of such faults will be se much alike that the corresponding
differences in sets of 3 g-fl values can oot be (easily) ~istinguished.
The ring formation is in agreement with the decrease in time of the
polymer weight fraction as measured by J~Schenk.
7.4.2. Discussion of thc braad ESR si.gnal. "Catena-s8
u
The concentratien of the short chain fraction betonging to the
polymerization equilibrium is far too low for this fraction to be
responsible for the "cateua-s8"
T = 220°C the molefraction n8 polymer at T =. 145°C calcnlated
phenomena mentior)ed in 7.2. In fact. at
1/P " I n
frorn the
? and the weight fraction . . . -9
polymer1zat1on 1s 10
Assuming that the braad signal arises from the allotrope "catena-S8
1\
the corn~sponding weight fra.ction can be ca.lculated from the spin intensity
of this sig~al. Tf the spin intensity of the B-signal at T = 145°C is
due to 11 catena-s8
" it would correspond to a Yelght fraction of about 0.03%
YbÎch is about a factor of one hundred toa low.
Wiewioro<Jski et al. (53)~ proposed that "catena-s8
•t a.rises froru an
intermedia te state of the equilibrium R~ c8
. They described this inter
mediate _statè by the following reactions:
(7.4.1)
(7.>1.2}
where c8
is the concentratien eight--membered rings belonging to the basic
polymerization reaction.
Wie-wiorowski et al. thought the energy necessary for the formation of th&.
complex [c8
.nR] to be ruuch lower than the formation of a braken ring. In
reaction 7.4.1 the energy necessary for breaking the ring is to a large
extent campensared by the stabilitat:ion of the chem.ical bond in the
complex [c8
.nR].ln tbis way the formation of the complex becomes thermo
dynamically favourable even at low temperatures.
In a later pnblication of the same research gronp Hiller et al. (54) gave
results of semi-empirical molecular orbital {ru.o.) calculations on the
112
bonding of sulfur compounGs. lhe ground state {highest filled molecular
or"::>ital) of the c.îght-memhered riug is essential composed
orbital~ it::s energy bein& -9,02 eN. TJ.king into account a
of the p -atooic y
d-character of
the excited state (lO"-'E'St empty mo.iecul&r orbit.alL they found a relatively
low lying motecular orbitdl baving an encrgy of: -:1.62 eV. They C3lculated
that the free electroos of u broken ring are localited at each end of a
chain. I11 rhe formation of complexe-s between rings and short chains, the
riligs take up the free electrens of the chain ends and thus facifate a
puiring of these electrons. Actulally. Miller et al. used c:heir calculati•;ms
to exp::_;án absence of any paramdgne-tism in molten sulfur below the poinc
of initia! polymed t.ation.
l<'e assume th<~.t in these complexes a paramagnedc state is present and
propose a structure fot: these co:npounds, which is schematically- given by:
where ------~ indicates u s8-chain anè 0 an eight-:nembered ring. This
co:up;:mnd ... : ll ba de'toteè in the follo>.:ing by che R-c8 polymers. The spins
öf the ebains are pnired in the lewest ernpty Q,O, of the ring. At the ends
of this chainlike con:plex pnramagnetîc states sbould be present. '!he life--10
time of this ~pin state is very short ( ~- 10 sec), which follows fron:
the relatively L::u:-ge lindewidth.
l~ben queuehing molten sulfur from I < T$ the R~c8 polymcrs are frozen.
Heuting up tbe quenched material to roo:n teGJperature, some of the R-c8
poly:ners s~~rt to co:nbîne. This explains the disappearance of the 3 g-I
sig.n.a.:s and the weight frac.tion polymer of about 12: found when the
dissolving experiments are corried out im:nediately after quencbin.g. 1f on
the: .average 120 units of eight llttoms .are pre.sent, the number of spins of
:he B-signal corrcsponds with about 4% weight fraction po:i.yrner, It seer:1s
reasonable to asswne that compounds with a strucc:ure just menticned are
113
also present in the amorphous and polycrystalline orthorhombic states. A
weak indication of the 3 g-I spectrum may be detected in Fig. 36 f.
·n1e i:nfluence of local electric and m11gnetic fields is averaged by the
line-broadeaing of the spin state consequent upon the shortening of the
life-time. QeEmdtir'g this spin state, the influence of the environment on
the paramagnetic centre becomes visible. The signals 3 g-I and 3 g-Il
described in 7.3.3. 7.3.4 and 7.3.5 are generaled in this way.
In principle, all the properties~ previously attributed to 11catèna-s8
"
may be now considered to beloog to the ~-c8 polymers and their interaction
wüh cs2
.
The investigations by 'J.'auro et ai. (55) of the solubility of sulfur iu
carbon disuHide sho\o'S the possibility of forming a weak bounding inter
action between the csz-molecule and an eight-membered ring.
Ti1e measurements of P.W. Schenk et al. (lt6) may tww be tentatively
understood by the following description of their experbnents.
We suppose thnt the process of dissolving the R.-c8 polymer in cs2 consists
of splitting the rings and the chains~ by formation of a new R-cs2 complex.
Jhe R-cs2
complexes and the s8-t:hains are not fro..:en out at T = -78°C.
During or after the evaporation of the CS2
, the s8-chains combine to
$11
-polyrners 011d give rise to the ~ 50% insoluble fraction in CS2 • This
corresponds t,.~/.th the J to J ratio of s8-rings and s
8-chains in the original
R-c8
polymers.
Th:is descript.:ion also agrees \o.'ith cbe cryoscopie deterrnination described
by P.W. Sche:1k of the "mcan" :nolecular weight.
\-le susgest that che sharpness of the onset of the polymerization process
(viscosity and specHic heat) is determined by the R-c8 polymers and that
the beginnî_ng of the polymerizacion st.at'ts with these R-c8
complexes as
an intenieäiated state.
Summarising we may conelude:
(1) Tlle 3 g-1 spectrum, accuring after queuehing the liquid state and
disappearing at heating up to Yoom temperature, is due to chain ends
in a "s table 11 am.orphous environment.
114
(2) The 3 g-Il spectrum is due to dislocations in orthorhombic sulfur.
They show up when a) the quenched liquid state starts crystallising
at room temperature, b) the solid material is tempered at ana
quenched, but disappears on annealing at room temperature,
(3) The suggestion that the braad signal is doe to a R-c8
polymer makes it
possible to relate the polymer weight fractions found by queuehing
from < T<P with the measured number of spins belonging to the B-signal.
(4) These R-C8
polymers might explain the disselving experiments of
P.W. Schenk, assuming that t~e cs2 solvent splits the R-c8 polymers in
s8-rings and s
8-chains, by formation of R-cs 2 complexes.
(5) In this picture the reality of "catena-S8
" would be restricted to
solutions in cs2.
(6) The anomaly of the melting point and th,e sharpness of the orwet of
the viscosity and the anomaly of the specific heat might be duE to thE
R-C8
polymers.
115
CHAPTER 8
INFLUENCE OF OXYGEN ON THE SELENirM ESR SIGNAL. ELECTRICAL CONDUCTIVITY
AND SKIN EFFECT
8. 1 • Introduetion
Section 8.2 describes the ESR measurements on three selenium samples,
each prepared by a different method. In section 8.3 the ESR results of two
of these samples will be Q.iscllssed in view of the rneasurement of the
electrical conductivity on two other samples from the same sources. The
results of this discussion will be used in making an attempt to derive a
relationship between the content of oxygen impurities and the conductivity
and its temperature dependenee in the solid and liquid states of selenium.
Secdon 8.4 deals with the calculation of a measure for the skin depth for
the selenium samples which were used in performing the ESR measurements.
8.2. E'SR signûs of se"lewium samples containing different amour1ts of
oxygen
Our first ESR measurements were carried out on the selenium ~aterial
mentioned in 5.5.3. The pellets were ground at room temperature in the
atmosphere. The powder was brought in the ESR sample tube, which was then
evacuated to 10-2 torr and sealed off. The measurements became reproducible
after heating for several hours in the ESR apparatus. The number of spins
N, measured with these samples is displayed in Fig. 38 against 1000/T(K 1)
and denoted by the symbol (o), In the given temperature range the linewidth
and the g-value varied from L;H ~ 400 Oe and g = 2.08 + 0.02 at lower to
l\H ~ 200 Oe and g = 2.02 + 0.02 at higher temperatures. In these samples an
additional signa! was present (bH~ 10 Oe, g 2.0036), which was also found
by Sampath (14) and Abdulaev (32) (56). After treating for several hours
(T 500°C) this latter signa! disappeared irreversibly.
Selenium material, which was de-oxygenized 5 times following the methad of
Kozyrev (39) (40) (denoted in the following by Method I), gave the number
116
of spins N denoted in Fig. 38 by the symbol (ll). The linewidth (llH ~ 400 Oe)
proved temperature independent. The g-value lay within the range g = 2.03
to g = 2.09. Sectien 5.5.1 describes the polymerization parameters,
calculated with the help of this measured number of spins N.
Selenium samples with which the results were obtained presented in
Chapter 6, were de-oxygenized by the metbod described in sectien 5.5.3
t· lkmole/kgl
'o 19~0 ll 0 0
ll 0 0~0
0 0
0 ll
0
0
0 1000/T o<'l
·• 10 1.1 1,2 1,3 1,4 1,S 1,6 1,7 1,8 1.9 2,0 2,1 2,2 2,3
Fig. 38. Number of spins N (kg)kmole in selenium with different amounts
of oxygen as a function of 1000/T(K-1),
points ( 0 ) : se Z.enium material, ground at T = 20°C in the
atmosphere,
points ( fJ. ) : selenium material., upon which the method of Kozyrev
has been applied 5 times,
points (0): selenium material., which has been purified following
the method described insection 5.5.3.
117
(henceforth denoted by Metbod II). For purposes of comparison the number
of spins N found in these samples is given in Fig. 38, denoted by the
symbol (o), (for linewidth see Fig. 21; g-value 2.11±0.02)
8.3. Electrical and the relation to the measured ESR signals
A literature study (57) on the electrical conductivity of selenium in
the solid and liquid states revealed the conflicting results of several
authors. The measurements of Abdulaev (58) were an indication of the
difference in the conductivity and its temperature dependenee of de~
oxygenized and non-de-oxygenized pure selenium. To obtain information about
the oxygen content and the skin depth of the samples which were used for
the ESR measurements, the conductivity was measured. These measurements
were described in (57). The four-point metbod was used and it was possible
to perfarm the conductivity measurement from the solid to the liquid states
without interruption. The conductivity was measured on selenium de
oxygenized by methods I and II, respectively. The conductivity a of
selenium is displayed in Fig. 39 as a function of 1000/T(K- 1). The points
(L\) and (o) correspond to selenium de-oxygenized by methods 1 and II,
respectively. The lowest dotted cur7e through points (! )corresponds to
measurements in the supercaoled liquid state. The highest dotted curve
( y ) refers to an intermediate state; the supercaoled liquid starts to
crystallize. It is seen from Fig. 39 that no discontinuity occurrs in
selenium which is de-oxygenized by Metbod II. It has already been mentioned
that with this selenium the polymerization data were obtained described in
Chapter 6. The selenium samples de-oxygenized by metbod I, produced at the
melting point a discontinuity of the conductivity of about 1000 times. The
number of spins measured in this selenium has also a different temperature
behaviou.r as in selenium (U). Although we do not pretend to understand how
and why the oxygen impurities influence the conductivity and the spin
intensity of the ESR signals, we feel rather sure (I) that the selenium(II)
data are those for pure selenium, and (2) that some measure of the influence
of oxygen bas been established.
Fig. 39.
118
10.) .
~ <> t4'cm' l
10'
"
làs ~ ' l
0~ ' 10. I
I ~..;'#~
1ti'
------- 'l ---- ------!. ________ !
1Ö.
10'
IO'Ifl 1.4 1.6 1.8 2.0 12 2.4 2.6
Eleatriaal aonduativity o(Q-1am-1)
points (!::.): see aaption Fig. 38,
points ( 0): see aaption Fig. 38.
~
2JI 3.0 n 3.4
-1 as a funation of 1000/T(K ),
119
8.4. Skin effect
The skin depth (ó) was calculated with the help of the following
formula
where:
IJ
\)
(J
6 = 1/ (nvvll) i,
skin depth in m -7 magnetic permeability (ur.:::::; I) 4n x 10 H/m
frequency of the microwave electromagnetic field 10 10 Hz
conductivity Q/m
-3 To estimate the order of the skin depth we may take a 10 at
(8.4.1)
T = 550°C for impure and O= 10-4 at T 420°C for pure liquid selenium,
corresponding to skin depths of Çl:;:; 15 and ç::::; 50 mm, respectively.
The sample is a cylinder with radius r = 1.4 mm. Thus a small correction
may have to be made for the uninteresting impure samples and hardly any
correction for the more interesting pure ones.
Conclusions:
( 1) Abdullaev' s conclusion from two-point measurements that "pure" selenium
has no discontinuity in the electrical conductivity, has been proved
correct by us using a four-point method, and a more rigarous ESR
controlled purification method.
(2) For pure selenium no skin correction was necessary.
120
CHAPTER 9
FINAL REMARKS AND CONCLUSIONS
Confrontation of viscosity data of the liquid states of pure sulfur,
pure selenium and iodine-doped sulfur with the polymerization parameters
obtained from the results of the ESR meàsurements leads to the conclusion
that such data have only qualitative significance.
The advantage of ESR methods is discriminating between contributions
from different origins is demonstrated in this work. As regards sensitivity
the results of the studies of "sulfur and selenium conducted by us (ESR) and
by Poulis and Massen (x0
) show that, depending on the linewidth of the ESR
signal, either methad can be the "more sensitive.
Moreover, ESR methods give information on the kinetic data which can
be used in combination with equilibrium data to obtain insight into the
polymerization processes.
121
SUMMARY
This thesis deals with an ESR study of the polymerization of sulfur
and selenium in the liquid state.
A new attempt at descrihing the polymerization equilibrium of sulfur
and selenium in the liquid state has been developed, and the polymerization
equilibrium of 'iodine-doped sulfur has been studied.
To obtain information on the reaction rate constauts from the linewidth of
the ESR signals, the influence of the linewidth on the reaction rate
constauts of three possible reaction mechanisms were calculated.
It was necessary to develop a lineshape analysis to investigate the kinetic
process. This analysis was helpful in determining of the number of spins
from the ESR measurements.
From the literature theoretical and experimental curves for the weight
fraction polymer of sulfur were obtained, and their validity has been
investigated with the help of the ESR measurements and the polymerization
theory.
The temperature range for which magnetic measurements for liquid sulfur
are known from the literature, has been extended to higher and lower
temperatures.
It would seem that before our investigation no ESR signals from liquid
pure selenium were reported.
The experimental equipment necessary for performing the ESR measurements
as a function of the temperature was a combination of a commercially available
spectrometer and a laboratory-made high ternperature ESR outfit. The qualities
(high sensitivity, wide temperature range, etc) of the combination enabled
us to obtain the ESR results from which the polymerization data mentioned
in this thesis were calculated.
For sulfur and selenium, additional information on equilibrium data of
the polymerization process has been obtained. The combining of these data
with those regarding lineshape and linewidth have affered for the first time
the possibility to obtain data concerning reaction kinetics in the entire
temperature range, the lirnits of accuracy of which have now been deterrnined.
Camparisou of the results mentioned above support the ideas of similarity
in properties of liquid sulfur and liquid selenium. Additional data for the
122
polymerization equilibrium .md new data for the polymerization kinetics of
selenium have been obtained.
Combining the equilibrium and kinetic data obtained from the results
of the ESR experiments, we were able to choose between the three different
reaction mechanisms. It has been concluded that the ring-addition reaction
de termines the way in which the polymerization equilibrium of liquid sulfur
and liquid selenium is reached.
The ESR measurements carried out on sulfur samples doped with different
amounts of iodine, support the polymerization theory as developed for
liquid pure sulfur.
The fact that the viscosity of selenium is on the average ten times
lower than' that of liquid sulfur, may be correlated to the fact that the
reaction rate constant of the ring-addition reaction for selenium is about
50 times greater than for sulfur.
Combination of the intensities and types of ESR signals obtained from
the liquid, quenched-liquid, and quenched-solid states of sulfur with
properties which in the literature are related to the sulfur allotrope
"catena-s8", leads to the introduetion of R-c
8 polymers. The concept
"catena-s8
" is restricted to sulfur solutions in cs2
.
To obtain interpretable polymerization data for selenium, de-oxygenizing
of the selenium material proved extremely important. It was possible, using
ESR methods, to follow the degree of de-oxygenizing. Moreover, the
disappearance of the discontinuity in the conductivity at the melting point
of seleniur~ shows that the oxygen content in the selenium material has
reached an undetectable value. The mechanism by which the oxygen impurities
influence the ESR signals and the conductivity of selenium farm a subject
for further study.
123
APPENDIX A
The volume factor (fv01 ).
Assuming first that B1
is homogeneous, fvol can be taken equal to the
filling factor n (37):
-2 -J B
1 (max)V s
A cylindrical sample (length 1, thickness d), symmetrica11y p1aced in a
rectangu1ar cavity, gives a filling factor (37):
n llr· + 0.92 (I - n1) (I - lld),
where: r a (ll:)l;
"1 I +- sin 1 ..:: a ;cl J
I + Jl ' a J
(A-!)
(A-2)
(A-3)
(A-4)
where J1
is first order Bessel function and a is the cavity height (~22 mm).
lf 1 = a and d « a (d ~ 2. 8 mm):
In our case the inhomogeneity of B1
in the x-direction is the
important factor. By splitting fv01 = f 1 .fd:
+1/2 b(x) = l J b(x)dx 1-1/2
We may take fd~ I, which gives fvol = f 1 .
1 ..;;; a.
In Fig. 40 the 1ength correction f 1 is disp1ayed as a function of the
sample length.
(A-5)
124
Fig. 40. The length aorreation f(l) as a funation of the sample length;
sample is plaaed symmetriaally.
APPE'NDIX B
The compression factor (fcompr)
An attempt at the determination of the compression factor of liquid
sulfur is obtained by measuring the change of the quality factor and
of the resonance frequency of the cavity. Defining w by:
w w = w • ( 0
) 0 + l. 2Q •
the following formula can be derived:
öw ---.,..-w
where V c
V ~s -r Eo,Ho
volume of the cavity,
volume of the sample,
undisturbed electric and magnetic·fields inside the
cavity,
complex.
(B-I)
(B-2)
l25
Formula (B-2) is only valid if S$~ples are s:na:ll and 6@ -- << 1. w
Taking: .Gr"" 1, S = nE0
and Êr = €: 1 - it't we can derive (60) fora
cylindrica:l sample tube:
ÓW 4 4' [< D à - _ _2. " (< l) 2 ) - ( ) j , "' a a
0
and
~ 'è r D 4 d ) '] 2Q c'' ) - (
Q 2 a a ,
where d inside diameter
D outsicte diameter
length taken equal to the height {"" a) of the cavity.
Casteleyn et al. (12) determined the changes of the resonan.ç_e
irequency of the c,avity and the compression factor, ca'Jsed by a number
·ar empty sample tubes of various sizes. {Sec table 16).
Frorn the literature we found for quartz: sr "" t..O and ó
>Jhcrc
Using these values aml tak.ing a "" 0.25~ the calculated values of -
sre in good correspondence l.i'ith the measuced values.
The compression of our ernpty :>ample tube was measure-d to be 1.04.
The compresslon due to tbe sul fur :nacerial alom: 6w0
foll<n>Jing 1.:ay. The measured values of ( W) and
sulfur material is:
óQ Q
- (0.53 + 0.02) x lD-4
-2 = (1.10 + 0.2} X·ID
0'
was estirnated in the
( 6Q) caused by the Q
'dith the help of for~ula (B-3) and (B-4)~ and taking D (2.85 + tL05)mro~
(B-3)
(B-4)
126
a~ (22! 0.\)mm, Q = 4500, we calculated for sulfur
Since Er{sulfur)<
smaller then due
~ (quartz), t~e compression due to sulfur material is r
to the empty sample tube. For safety. we have taken of
f "" !. l * comp For selenium the same compression factor as derived fnr sulfur was used.
Measured by Casteleyn
et al. (12)
x I0-5
f compr
rable J6. Measured mui cakuW.teà vaLues
different sizes.
calculated,taking Er 4?
a ~ 0.25~ ê = J x lo-3
of! óroo -~-"or ' w ''
0
_§Ç_ Q
sampLe P...<.bes of
127
APPENDIX C
Discussion of che accuracy of the spin calibration measurement
rf the dielectric constant is independent of the temperatu:re and na
skin effect occurs (bath checked for sulfur and selenium) the relative
accuracy of the spin intensities is nearly e:qual to the accuracy witb which
A(6H)2
can be deterrnined. (The errors in deLermining the change in quality
factor as a function of the ternperature and the sensitivity settings are
small 1 viz. ~ 2%.)
The determination of the absolute number of spins is more inaccurate.
This arises from tlle errors which wlly be made in the determination of the
terms mentioned in formula (5.4.10). !hese errors are extensively discussed
in (41). The maximurn possible error that can be made in the absolute value
of the nu':llber of spins is + 15%, to be inc.reased with the error in tbe
determination of A(6H)2
•
APPlWDIX D
Reac.tion rate constant kb and k~
We will consider the num'oer of chains of length n as a function of the
time during which their length does not change. The spinstates of the ends
of the ebains may be killed by either a ring-addition or a splitting of a
ring. Since rea.ction constauts do not depend on chainlength and our
measurements have been carried out in equilibrium, the relaxation time of
these processes must be equal, anà give rise to the factor two mentioned
in sectien 6.4.1.
In the same way can be derived that the re.action rate consta:1t k~ has
to be devideà by a factor two as mentioned insection 6.4.1.
128
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SL. D.J. Millerand L.G. Cusachs, Cllem. Phys. Letters, l970, 2~ 501.
55. f. J. Touro and T. K. l4iewiorowski, J. ?hys. Ghe::n. , 1966, J!l, 35 34.
56. G.B. At.dullaev, N.l. lb-ra.gimov, Sh. V. Maoedov and A.Kh. lbadov, Soviet
Phys. Semiconductors, 1970,
57. Int.ernal report: lil, W. Jeuken, 1971, Department of :Physics~ group N.L.,
Uuiversity of Téchnology, Eind~iOVen. Netl1erlands.
58. G.B. Abdullaev e.t aL. Sav. Phys. SoL State, 1964, ~· 786.
131
59. M.W. Brodwin and M.K. Parsons, J. Appl. Phys., 1965, 494.
60. Internal report IV, G. Mulder, 1970. Department of Physics, groep N.L.
University of Technology, Eindhoven, Netherlands.
132
LIST SY/<JBOLS
amplitude of the ESR signal
amplitude of the magnetic component of the microwave field
amplitude of the magnetic field modolation
concentration chains
concentration atomie bonds in chains per unit mass
concentration chain ends
concentration chains contaning i-atoms
concentration ebains terminated by one dope atom
concentrat ion chains terminated by two dope atoms
activation energy of forward .reaction
F ESR absorption curve
first derivative of the ESR absorption curve
f1
length correction factor
g g-value
H magnetic field intensity
fiH linewidth of the ESR signal
6H heat of forward reaction
I intensity of the ESR absorption
K equilibrium constant
k' rate constant of the forward reaction
k~ pre-exponential factor of the forward reaction
k" rate constant of the backward reaction
p
Q
R
R
concentratien atoms per unit mass
number of spins per unit. mass
number of spins in sample tube
number of spins per volume unit
mole-fraction of chains with i-atom
number average chainlength
pararoe ter of F lory ~ 17)
quality factor of the cavity
concentratien eight-membered rings
universal gas constant
(R-R)
133
concentratien atomie bonds in rings per unit mass
residual varianee
s2 residual varianee of the noise
N
~S entropy change
T melting point m
V c
V s
x
!) 0
\)
dr
temperature of initial polymerization
volume of the cavity
volume of the sample tube
dope concentratien
constant in formula of intrinsic viscosity
amplification factor
skin depth
dielectric constant
viscosity
viscosity of the solvent
intrinsic viscosity
magnetic permeability
frequency
electrical conductivity
relaxation time
volume element
weight fraction polymer:
static paramagnetic susceptibility
angular frequency
134
SANENVAT2'IlJG
In dit proefschrift wordt een onderzoek beschreven naar de polymerisatie
van-vloeibaar zwavel en vloeibaar selenium met behulp van elektronenspinreso
nantie.
Een nieuwe methode is ontwikkeld om het polymerisatieproces van vloei
baar zwavel en vloeibaar selenium theoretische te beschrijven. Het is
mogelijk gebleken deze methode ook toe te passen op het polymerisatie-even
wicht van met jodium gedoopt zwavel.
Voor het verkrijgen van informatie over de reaktiesnelheidskonstante
uit de lijnbreedte van het ESR-signaal is de invloed van de lijnbreedte op
de reaktiesnelheidskonstante van drie verschillende reaktiemechanismen bere
kend.
Daarvoor was het noodzakelijk een methode te ontwikkelen voor de analyse
van de lijnvorm van een absorptieverschijnsel. Deze analysemethode bleek ook
nuttig te zijn bij het bepalen van het aantal vrije spins uit de ESR-metingen.
Uit de literatuur werden een theoretische en experimentele kromme ver
kregen voor de gewichtsfraktie polymeer in vloeibaar zwavel. De juistheid
van deze krormnen is met behulp van de SSR-metingen en de polymerisatietheorie
onderzocht.
Het temperatuurgebied waarvoor magnetische metingen aan zwavel bekend
zijn, is naar boven en naar beneden uitgebreid. Voorzover wij uit de literatuur
hebben kunnen nagaan zijn er nog geen ESR-signalen van vloeibaar zuiver
selenium bekend.
De apparatuur die noodzakelijk was om de ESR-metingen als funktie van de
temperatuur te verrichten bestond uit een kombinatie van een kommercicel be
schikbare ESR-spectrometer en een in het laboratorium gebouwde hoge-tempera
tuur-unit. De kwaliteiten (grote gevoeligheid, groot temperatuurinterval, enz.)
van deze kombinatie stelden ons in staat de ESR-metingen te verrichten waarop
de in dit proefschrift vermelde gegevens over het polymerisatie-evenwicht van
zwavel en selenium gebaseerd zijn.
Voor zwavel en selenium zijn aanvullende gegevens verkregen over het
reaktie-evenwicht van het polymerisatieproces. Het kombineren van deze gegevens
met die over lijnvorm en -breedte biedt voor het eerst de mogelijkheid gegevens
over reaktiesnelheden in het gehele temperatuurgebied te verkrijgen, waarvan de
135
betrouwbaarheidsgrenzen nu bepaald zijn.
Vergelijking van bovenvermelde resultaten steunt de veronderstelling dat vloei-
baar zwavel en vloeibaar selenium chemische en fysische eigenschappen
bezitten.
Door gegevens van reaktie-evenwicht en reaktiesnelheid te kombineren,
kon een keuze gemaakt worden uit de drie verschillende reaktiemechanismen.
Het blijkt, dat de ring-additiereaktie de wijze bepaalt waarop het polyme
risatie-evenwicht van vloebaar zwavel en vloeibaar selenium tot stand komt.
ESR-metingen aan jodium-gedoopt zwavel steunen de polymerisatietheo
rieën, zoals die voor vloeibaar zwavel ontwikkeld zijn.
Het feit, dat de viskositeit van selenium gemiddeld tien maal zo laag
is als die· van zwavel, zou gekorreleerd kunnen worden aan het feit, dat de
reaktiesnelheidskonstante van de ring-additiereaktie van selenium 50 maal
zo groot is als die van zwa·.rel.
Het kombineren van de spinintensiteiten en de verschillende soorten
van ESR-signalen van vloeibaar, afgeschrokken vloeibaar en afgeschrokken
vast zwavel met de eigenschappen die in de literatuur toegeschreven worden
aan de zwavelmodifikatie "catena-s8
", heeft geleid tot de introduktie van
een nieuw begrip, namelijk het R-c8
polymeer. Het bestaan van "catena-s8
"
wordt nu beperkt tot in oplossingen van zwavel in zwavelkoolstof.
Voor het verkrijgen van interpreteerbare ESR-signalen van selenium,
bleek het zeer belangrijk te zijn, het selenium materiaal zuurstofvrij te
maken. De mate van zuurstofverontreiniging kon met behulp van ESR getest
worden.
Het verdwijnen van de diskontinuheit in de geleiding bij het smeltpunt
van selenium is een kriterium voor het zuurstofvrij zijn van selenium. Het
mechanisme waarmee zuurstofverontreiniging de ESR-signalen en de geleiding
van selenium beinvloedt, kan een onderwerp van verdere studie vormen.
136
DANKWOORD
Dat mijn ouders mij in de gelegenheid hebben gesteld wetenschappelijk
onderwijs te volgen, stemt mij tot grote dankbaarheid.
Het proefschrift in deze vorm is alleen tot stand gekomen dankzij de
samenwerking met velen. In het bijzonder zou ik willen noemen: W. Jeuken,
G. Mulder, T. de Neef, G. Overbrugge, B. Pelupessy, P. Rieter-en J. van
Wolput.
Voor de technische assistentie dank ik de heer H. van Leeuwen en de
werkplaats van de afdeling der Technische Natuurkunde en voor de hulp bij
het chemische werk mejuffrouw M. Kuyer.
Voor de (meet)gastvrijheid die ik in de laatste jaren in de sectie
Anorganische Chemie onder leiding van Prof. Dr. G.C.A. Schuit van de afde
line der Scheikundige Technologie genoten heb, ben ik bijzonder erkentelijk.
Prof. Dr. D. Heikeus dank ik voor de wijze waarop hij mij in de geheimen
van flory-verdelingen heeft ingewijd.
Ook de gastvrijheid in de groep van Prof. Dr. F. van der Maesen mag
niet onvermeld blijven, met name de steun van de heer Ir. Kipperman bij het
uitvoeren van de geleidingsmeringen aan selenium stel ik zeer op prijs.
Ook hen, die tot de uiteindelijke vorm van dit manuscript hun bijdrage
hebben geleverd, betuig ik mijn dank. Dit zijn mejuffrouw M. Gruyters en
de heo•.r H. van Leeuwen voor het verzorgen van het tekenwerk, mevrouw F ..
Duifhuis-van Tongeren voor het typewerk en de heer H.J.A. van Beekurn voor
de korrektie van de Engelse tekst.
137
LEl'ElVSBERICHT
Op verzoek van de Senaat van de Technische Hogeschool volgen hier enkele
persoonlijke gegevens.
Diederik Christiaan Koningsberger werd geboren op 6 juni 1938 te Delft.
Eindexamen Gymnasium B deed hij in 1958, waarna twee jaar militaire dienst
volgden.
In 1960 begonnnen met de studie voor natuurkundig ingenieur aan deze
hogeschool, behaalde hij in 1966 het ingenieursdiploma met als afstudeer
onderwerp ontwerp en bou-.r van een ESR-spectrometer.
Na zijn afstuderen trad hij als wetenschappelijk medewerker in tijdelijke
dienst van deze hogeschool.
In samenwerking met het Radiotherapeutisch Instituut te Eindhoven is
een onderzoek gedaan naar de toepassingsmogelijkheden van ESR-methoden in
de bestudering van stofwisselingsverschijnselen in maligne en benigne weef
sels. Er zijn ESR-metingen verricht aan verschillende soorten weefsels.
Medio 1967 werd begonnen met het onderzoek dat in dit proefschrift
wordt beschreven.
ln samenwerking met het Medisch Biologisch Laboratorium van RVO-TNO
te Rijswijk is de korrelatie onderzocht tussen de door bestraling ontstane
vrije radikalen in DNA en zijn biologische inaktivering.
Ee,n aantal stagiairs en afstudeerders, van wie enigen in de referen
ties vermeld zijn, heeft ontwerpen verband houdend met het promotie-onder
zoek bestudeerd.
STELLINGEN
Behorende bij het proefschrift van D.C. Koningsberger
19 maart 1971
•'J
STELLINGEN
I
De methode, die Keezer gebruikt om de ketenlengte van vloeibaar
zuiver selenium te bepalen, is gebaseerd op een onjuiste
veronderstelling.
Dit proefschrift 2.
II
Het E.S.R. signaal, dat Pinkus en Piette gevonden hebben in de
in cs2 onoplosbare fractie afgeschrokken vloeibaar zwavel is
naar alle waarschijnlijkheid afkomstig van een verontreiniging.
A.G. Pinkus and L.B. Piette, J. Phys. Chem., 1959, 2086.
lil
De verklaring die Abdullaev c.s. geven voor het verdwijnen van
het ESR signaal van zuurstof-, jodium- en brom1uope in vloeibaar
selenium bij een temperatuur van ongeveer 470°C, is niet in
overeenstemming met de resultaten van dit proefschrift.
G.B. Abdullaev, N.I. s:1, V. Mamedov and A.Kh. Ibadov
So,viet Phys. Semieonduetors, 19?0, 4.
IV
Door met behulp van de ESR-methode een relatie te leggen tussen
de stralingsgevoeligheid en de aanwezigheid van stabiele vrije
radicalen in levende organismen, kan een beter inzicht in de
invloed van ionerende straling op levende organismen verkregen
worden.
V
Tri-aceton-amine-N-oxyl (TAN) maakt levende cellen gevoeliger
voor straling; dit effect verdwijnt na toevoeging van zuur
stof. De hypothese van Jones c.s. dat dit effect wordt veroor
zaakt door een reactie van zuurstof met de radicaalgroep van
TAN is aanvechtbaar.
W.B.G. Jones, T. Brustad and K.F. Nakken, Int. J. Radiat. Biol.,
1970, 591.
VI
De oprichting van een werkgroep ·~agnetische Resonantie in
Biologische op de Technische Hogeschool te Eindhoven
is alleen dan zinvol, wanneer een zeer nauwe samenwerking
bestaat met een Medisch-Biologisch Laboratorium.
VII
Bij het trainen van de jeugd in de tennissport wordt over
het algemeen te weinig aandacht besteed aan het aanleren
van spelinzicht en wedstrijdmentaliteit.
VIII
De bezoldiging van het wetenschappelijk corps aan Univer
siteiten en Hogescholen dient meer in overeenstemming te
zijn met de prestaties welke geleverd worden bij het geven
van onderwijs en het doen van onderzoek dan met het aantal
dienstjaren van de betrokkene.