vibrational dynamics and heat capacity of polychloroprene

Vibrational Dynamics and Heat Capacity ofPolychloroprene

Archana Gupta,1 Parag Agarwal,1 Neetu Choudhary,1 Poonam Tandon,2 V. D. Gupta2

1Department of Applied Physics, Institute of Engineering and Technology, M. J. P. Rohilkhand University,Bareilly, India2Department of Physics, Lucknow University, Lucknow, India

Received 5 March 2010; accepted 30 September 2010DOI 10.1002/app.33488Published online 17 February 2011 in Wiley Online Library (wileyonlinelibrary.com).

ABSTRACT: Normal modes and their dispersion havebeen obtained for polychloroprene in the trans form usingWilson’s G F matrix method as modified by Higg’s for aninfinite polymeric chain. Urey Bradley force field has beenused. Several new assignments, which are missing inearlier work, are reported. The assignments of lowerfrequency modes have been confirmed using inelastic

neutron scattering data. The characteristic features ofdispersion curves have been explained. Variation of heatcapacity as a function of temperature has been predicted.VC 2011 Wiley Periodicals, Inc. J Appl Polym Sci 121: 186–195, 2011

Key words: polychloroprene; infrared spectroscopy;phonon dispersion; density of states; heat capacity

INTRODUCTION

Polychloroprene is a widely used polymer and hasmany industrial applications.1–4 It is mainly used inrubber industry but it is also important as a rawmaterial for adhesives. Chloroprene rubber hasexcellent resistance to oil, chemicals, and deteriora-tion, in addition to having flame-retarding proper-ties. It is widely used in automobile parts and in avariety of heavy-duty equipment. Despite its cost,its high durability under harsh conditions makesneoprene rubber a much needed material.

Polychloroprenes have a highly regular structure5

(Fig. 1) consisting primarily of a linear sequence ofthe trans-2-chloro-2 butenylene units (ACH2ACCl¼¼CHACH2A), which result from 1,4-addition poly-merization of chloroprene. Crystallization studieshave shown that small proportions of other struc-tural isomers may also be present.6,7 A study ofinfrared absorption spectra of polychloroprene madeat different temperatures5 has shown that the pro-portion of these structures increases with theincreasing polymerization temperature.

Vibrational spectroscopy is an important tool forprobing conformation and conformationally sensitivemodes of a polymer. The physical properties of apolymer are strongly influenced by the conformation

of the polymer. Vibrational spectroscopy, besidesproviding information about different conforma-tional states, plays an important role in understand-ing the dynamical behavior of polymer chain.Normal mode analysis helps in precise assignmentsand identification of spectral features of a moleculeof known structure and force field. However, theproblem in case of polymers is an order of magni-tude more complex than in simple solids mainlybecause of the absence of simple symmetry andpresence of large contents in unit cell. The art ofconformational finger printing of molecules by infra-red and Raman spectroscopy cannot succeed here.In general, the infrared absorption, Raman spectra,and inelastic neutron scattering from the polymericsystems are very complex and cannot be unraveledwithout full knowledge of dispersion curves. Onecannot appreciate without it, the origin of both, sym-metry dependent and independent spectral features.The dispersion curves also facilitate correlation ofthe microscopic behavior of a crystal with its macro-scopic properties such as specific heat, enthalpy, andfree energy.Normal coordinate calculations and assignment of

various vibrational modes for trans 1,4 polychloro-prene (TPCP) have been reported earlier.8–11 Theagreement between the observed and the calculatedfrequencies reported by Tabb and Koenig8 usingvalence force field is good in the high frequencyrange (above 900 cm�1) but not so in the lower fre-quency range. This disagreement has been attributedby the authors themselves to the least reliability ofthe force constants associated with the chlorine atom

Correspondence to: A. Gupta ([email protected]).

Journal of Applied Polymer Science, Vol. 121, 186–195 (2011)VC 2011 Wiley Periodicals, Inc.

that contribute greatest to the spectrum below900 cm�1. Such studies have also been reported byPetcavich et al.9 However, they have also used va-lence force field that does not take into account non-bonded interactions in both gem and tetra positionsand tension terms. One of the infirmities of theirwork is the use of the same force field for both themolecules trans 1,4 polychloroprene and polydi-chlorobutadiene. The difference between the two isthe presence of hydrogen attached to the carbon inone and chlorine in the other. This will cause localperturbations extending at best up to the nearestneighbors. Arjunan et al.10 have also carried out anormal mode analysis using valence force field.They have not made assignments for the frequen-cies, characteristics of crystallinity.11 Further, disper-sion of normal modes has not been reported bythem. Lack of information on dispersive behavior ofnormal modes in many polymeric systems has beenresponsible for incomplete understanding of thepolymeric spectra. Thus, a fuller interpretation of IRand Raman spectra demands a re-look at the vibra-tional dynamics of TPCP. In continuation of ourwork on the vibrational dynamics of polymeric sys-tems of natural and industrial importance,12–15 in thepresent communication we report a complete normalmode analysis using the Urey-Bradley force field(UBFF)16 as it is more comprehensive than thevalence force field. In the UBFF, relatively lessparameters are required to express the potentialenergy and no quadratic cross terms are included inthe potential energy expression. The interactionbetween nonbonded atoms includes these terms andthus the arbitrariness in choosing the force constantsis reduced. The normal mode frequencies obtainedare in better agreement with the observed IR andRaman data than those reported by previous work-ers. The calculations lead to some new assignments.In the low frequency region (below 1000 cm�1) theresults are compared with the neutron inelastic scat-tering measurements.17 We have also reported thepredictive values of heat capacity in the range of 10–400 K. To the best of our knowledge, such detailedstudies leading to correlation between the micro-scopic behavior and macroscopic properties of thispolymer have not yet been reported.

EXPERIMENTAL DETAILS

Polychloroprene sample was obtained from SigmaAldrich Chemicals Pvt Ltd, USA.

Fourier transform infrared spectroscopy

The FTIR spectra of polychloroprene were recordedat Bruker IFS 28 spectrometer with a liquid-cooledmercury cadmium telluride (MCT) detector having aresolution of 4 cm�1 and 128 scans. The spectrawere recorded as thin films cast from carbon disul-phide solution onto potassium bromide plates. Theobserved FTIR spectra are shown in Figure 2(a,b).

Fourier transform Raman spectroscopy

FT Raman spectra of polychloroprene were recordedusing an efficient visible micro Raman setup at roomtemperature. This setup used an excitation laser lineof wavelength 514 nm, emitted from an Argon ionlaser source with a power of 12 mW to record thevibrational spectra. The scattered Raman light wascollected in a back scattering geometry using amicroscope objective (ULW 50�). The scattered lightwas dispersed using a monochromator with 1200grooves/mm diffraction grating, and an entrance slitwidth of 200 lm. The Raman signals were detectedusing liquid nitrogen cooled charged coupled device(CCD) with an optimal sensitivity in the visiblerange. The total exposure time for each sample was

Figure 1 Chain structure of polychloroprene.

Figure 2 (a) FTIR spectrum of polychloroprene; (b) Sec-ond derivative FTIR spectrum of polychloroprene (900–1400 cm�1).

VIBRATIONAL DYNAMICS AND HEAT CAPACITY OF POLYCHLOROPRENE 187

Journal of Applied Polymer Science DOI 10.1002/app

5 s and averaged over five accumulations. The spec-tral resolution obtained was about 3 cm�1. Theobserved FT Raman spectra are shown in Figure 3.

THEORY

Calculation of normal mode frequencies

Normal mode calculation for an isolated polymericchain was performed using Wilson’s GF matrixmethod18 as modified by Higg’s19 for an infinitepolymeric chain. The vibrational secular equation tobe solved is

jGðdÞFðdÞ � kðdÞIj ¼ 0 0 � d � p (1)

where d is the phase difference between the modesof adjacent chemical units, the G(d) matrix is derivedin terms of internal coordinates, with its inversebeing the kinetic energy, and the F(d) matrix isbased on the Urey-Bradley force field.16 The frequen-cies mi in cm�1 are related to eigen values by

kiðdÞ ¼ 4p2c2m2i ðdÞ (2)

A plot of mi (d) versus d gives the dispersion curvefor the ith mode.

Calculation of heat capacity

Dispersion curves can be used to calculate the spe-cific heat of a system. The density of state functionis calculated from the relation

gðmÞ ¼X

½ðdmj=@dÞ�1�mjðdÞ¼mj (3)

The sum is over all the branches j. The constantvolume heat capacity can be calculated usingDebye’s relation

Cv ¼X

gðmjÞkNAðhmj=kTÞ2

½expðhmj=kTÞ=fexpðhmj=kTÞ � 1Þg2� ð4Þ

with $g(mi) dmi ¼ 1

RESULTS AND DISCUSSION

The crystal structure of trans 1,4-polychloroprene(ACaH2ACCl¼¼CHACbH2A)n has been determinedby Bunn20 from X-ray diffraction results of orientedspecimens. The unit cell is orthorhombic with spacegroup P212121. Each unit cell contains four moleculeswith a fiber repeat distance of 4.79 A. The chlorineatom is displaced out of the plane of theACAC¼¼CHA group by 40� because of the repulsionbetween the bulky chlorine and nearby hydrogenatoms. There are 10 atoms in one repeat unit ofTPCP which give rise to 26 optically active vibra-tions of non-zero frequencies. The four modes forwhich x ! 0 as d ! 0 are called acoustic modes.They are due to translation (one parallel and twoperpendiculars to the chain axis) and one due torotation around the chain axis.The vibrational frequencies were calculated from

the secular eq. (1) for values of d varying from 0 to pin steps of 0.05 p. Initially approximate force con-stants were taken from the potential field data ofb-trans 1,4-polyisoprene (b-TPI)21 and those involv-ing chlorine atoms from poly vinylidene chloride.22

The initial force constants were transferred from pol-yisoprene because of its structural similarity withpolychloroprene.20 A replacement of CH3 group bychlorine and vice versa will not significantly perturbthe force field because of the group character ofCH3. Further the chlorine involving force constantswere transferred from poly vinylidene chloride22

because of the localized nature of modes related tochlorine atom. The accuracy was further judged byexamining the effectiveness of force constants inother chlorine containing molecules e.g., poly vinylchloride.23 The set of force constants so composedwas later refined to give the ‘‘best fit’’ to theobserved spectra. We have used the Urey Bradleyforce field, which takes into account the bonded aswell as nonbonded interactions. The assignmentswere made on the basis of potential energy distribu-tion (PED), band shape, band intensity, and appear-ance/disappearance of modes in similar moleculargroups placed in similar environment. The finalforce constants along with the internal coordinatesare given in Table I. There is a wide difference inthe force constants used by earlier workers8,9 andthe present one. This is much too obvious becausethe Urey Bradley force field covers a wide potentialsurface including nonbonded interactions and ten-sion terms. This is widely reflected in the off-diago-nal elements of F-matrix and the profile of thedispersion curves. These comments are relevantbecause Petcavich and Coleman9 have used sameforce constants for both the systems polydichlorobu-tadiene and polychloroprene. That should not bedone because the force constants are tied down with

Figure 3 FT Raman spectrum of polychloroprene.

188 GUPTA ET AL.


the structure. The matched frequencies along withtheir potential energy distribution (PED) are given inTables II and III.

The dispersion curves are plotted in Figures 4(a)and 5(a) from 1000 to 1500 cm�1 and 0 to 1000 cm�1,respectively. Since all the modes above 1500 cm�1

are nondispersive in nature, the dispersion curvesare plotted only for the modes below 1500 cm�1. Forsimplicity modes are discussed in two separatesections.

Nondispersive modes

In general, the nondispersive modes are the onesthat are highly localized in nature. The free stretch-ing modes generally fall in this region. e.g., CAHstretch, CH2 symmetric and asymmetric stretches.The CAH stretching vibrations in the region from2800 to 3100 cm�1 are highly localized and are ingood agreement with the observed bands. Since themolecule contains two CH2 groups, the absorptionbands appear in pairs. They are slightly displacedfrom each other because of their placement in differ-ent environments and proximity to the chlorineatom. The C¼¼C stretch frequency is calculated at1654 cm�1 and is assigned to the peak at 1659 cm�1.These frequencies occur in the region 1640–1670cm�1 in several other polymeric systems also e.g., intrans 1,4-poly dichlorobutadiene,24 poly dimethylbutadiene,25 and trans 1,4 polyisoprene (a and bform).21,26 These have been found to be the charac-teristic of a stable C¼¼C bond (nonoxidative state)

because the presence of any reactive species wouldhave resulted in appearance/shift of a new absorp-tion line. The C¼¼C stretch frequency is used forthe structural diagnosis of dienes. It has a highervalue for trans configuration (1673 cm�1 in trans-1,4-polybutadiene27) as compared to cis configuration(1637 cm�1 in cis-poly 2-methyl 1,3 pentadiene28).The higher value in case of trans configuration isbecause of the lesser steric hindrances betweenatoms at 1 and 4 position making the double bondstress free.

Dispersive modes

The modes, which are nonlocalized in nature andare strongly coupled, electrically, mechanically orboth, show appreciable dispersion e.g., torsionmodes are strongly coupled with the neighboringunit and are dispersive. The actual dispersion ofmodes is discussed in the next section.The scissoring modes of two CH2 groups are cal-

culated at 1443 and 1434 cm�1 and match well withthe observed peaks at 1443 and 1431 cm�1 respec-tively, in IR. As commented earlier the differencebetween these two modes is due to the differentenvironmental placement of two CH2 groups. Themodes reported by Wallen11 at 1316, 1169, 1084, and958 cm�1 and assigned to the crystalline part ofthe sample are observed at 1327, 1144, 1095, and947 cm�1 respectively, in the second derivative FTIRspectra [Fig. 2(b)]. The constant difference of 610wave numbers could easily be accounted for becauseof the scaling factor. The intensity of the correspond-ing modes is different because of the special treat-ment given by Wallen11 to augment the intensity ofcrystalline and amorphous phases. The peakobserved at 1327 cm�1 and attributed to the crystal-linity has been assigned to the CAC stretch andbending vibrations of C¼¼CAH and HACACb. Theseconform to the assignments made by Tabb andKoenig.8 All the bands related to the crystallinity are

TABLE IInternal Coordinates and Urey Bradley Force Constants

Internalcoordinates

Forceconstants

Internalcoordinates

Forceconstants

m[CaAH 4.17 /[CACbAH] 0.56 (0.21)m[CaAC] 4.40 /[HACbAH] 0.34 (0.295)m[CACl] 2.5 /[HACbACa] 0.30 (0.23)m[C¼¼C] 7.1 /[CACbACa] 0.15 (0.18)m[CAH] 4.75 /[CbACaAH] 0.28 (0.27)m[CACb] 4.4 /[CbACaAC] 0.93 (0.50)m[CbAH] 4.24 /[HACaAH] 0.36 (0.287)m[CbACa] 3.8 /[HACaAC] 0.58 (0.21)/[CaAC¼¼C] 0.74 (0.20) x[CACl] 0.42/[CaACACl] 0.93 (0.55) x[CAH] 0.20/[ClAC¼¼C] 0.87 (0.20) s[C¼¼C] 0.045/[C¼¼CAH] 0.40 (0.20) s[CACb] 0.010/[C¼¼CACb] 0.79 (0.50) s[CbACa] 0.025/[HACACb] 0.43 (0.20) s[CaAC] 0.060

m, /, x, and s denote stretch, angle bend, wagging, andtorsion respectively.Stretching force constants between the nonbonded atoms

in each angular triplet (Gem configuration) are given inparentheses.Unit of force constants for stretch is mdyne/A0, for

angle bend is mdyne A rad�2 for wagging & torsion ismdyne A0.

TABLE IINondispersive Modes

Calc.

Obs.

IR Raman Assignment (% PED) at d ¼ 0

3026 3024 3029 m[CAH] (99)2927 2918 – m[CbAH] (95)2908 2918 2920 m[CaAH] (95)2878 2883* 2862 m[CbAH] (96)2861 2858 2845 m[CaAH] (96)1654 1660 1668 m[C¼¼C] (54), m[CACb] (10)

All frequencies are in cm�1.Only dominant PED’s are given.* marked frequency is taken from second derivative

FTIR spectra.



highly coupled normal modes and show a large dis-persion. To make precise comments on the appear-ance/disappearance of absorption bands in a transi-tion from amorphous to crystalline state, a fullknowledge of crystalline structure is essential. It iswell known that the vibrational spectra of a polymerchain, especially a semi crystalline polymer verymuch depend on the history of the polymer chain.The spectra are very much dictated by the amor-phousity of the polymer and distribution and size ofthe amorphous regions. Reproducibility is very poorunless the past history of the polymer is wiped outby treatment such as annealing. This fact should beborne in mind in making assignments. The bandsappearing in the region 1100–900 cm�1 are associ-ated with CAC skeletal stretching modes.

The lower frequency modes (below 1000 cm�1)need special mention, as there is difference in theassignments of these modes made by variousauthors.8,9,17 The technique of inelastic neutron scat-tering29 (INS) that is very useful in studying the lowfrequency vibrations in polymers has been appliedto confirm the assignments of low frequency modes.Neutrons have high scattering cross section for pro-tons (nearly 82 barns). Hence, one can monitor thenormal modes through the motion of protons. Mostof our assignments match with the observations ofthe INS reported by Kanaya et al.17 Because of thesymmetry dependent selection rules, only limited in-formation regarding molecular dynamics can beobtained from infrared absorption and Raman scat-tering whereas neutron scattering being free fromsuch constraints provides, at least in principle, fulladditional information about molecular systems.Also since the low-frequency vibrations are expectedto depend sensitively on the chain conformation,neutron spectra are expected to provide some ofthese conformation sensitive modes more promi-nently, especially those which involve large ampli-tude of proton motion. e.g., the assignment of theband at 825 cm�1 in IR {/ [Cb-Ca-H] (21), / [H-Ca-C] (15), x[C-H] (12)} has been confirmed by inelasticneutron scattering measurements. Intensities in theneutron spectra are weighted by the vibrational am-plitude of the motions of the hydrogen atoms. Thepeaks in the INS frequency distribution spectra canbe identified with the regions of high density ofstates arising at the zone center or within the zone(reduced zone scheme).

The band observed at 825 cm�1 in IR has beenassigned predominantly to CAH out of plane bend-ing by Petcavich and Coleman9 and to CACl stretch-ing (20%) and ClAC¼¼C bending (14%) by Tabb andKoenig.8 Mochel and Hall30 have shown that thisband cannot involve the CACl bond because itoccurs within two wave numbers of the same placein the polybromoprene spectrum. According to them

it should arise from a vibration consisting of ahydrogen deformation. Our calculations show thatthis mode consists mainly of angle bends of hydro-gen /[Cb-Ca-H], /[H-Ca-C] and wagging of CAHwith a small contribution from CACl stretching(12%). Kanaya et al.17 have stated that in the inelas-tic neutron scattering, an intense and broad peakobserved at 790 cm�1 should include the modeobserved at 825 cm�1 in the IR spectrum and shouldnot be due to the motion of chlorine atom. Thisgives further support to our assignment. This modedisperses and reaches at 861 cm�1 at d ¼ p where itis assigned to a new peak observed at 850 cm�1 inIR. It has major contribution from CAH out of planebending at the zone boundary. In our calculations,CACl stretching is present in the modes calculatedat 679 and 569 cm�1. Mochel and Hall30 have alsoidentified the bands at 667 and 578 cm�1 in IR dueto CACl stretching on comparison with the spectrumof polybromoprene. In inelastic neutron scattering,17

no peaks are observed near these frequencies, whichis suggestive of the fact that these modes are con-cerned with the motion of the chlorine atom. How-ever, the PED of the mode calculated at 679 cm�1

contains CAH wagging also. On varying the forceconstant of x [CAH] over a wide range (from 0.19 to0.27 mdyne A) this contribution does not disappearbut on reaching the zone boundary the contributionof CAH wagging decreases and CACl stretchingincreases gradually.The peak at 468 cm�1 in the Raman spectrum is

attributed to CACl wagging. Kanaya et al.17 havestated that in the inelastic neutron scattering, twoweak peaks observed at 453 and 484 cm�1 corre-spond to this peak. One of these (453 cm�1) ismatched with the value calculated at the zone center(458 cm�1) whereas the other one (484 cm�1) ismatched with the value calculated at the zoneboundary (506 cm�1). This assignment agrees withthat of Petcavich and Coleman.9 The CACACl bend-ing vibrations have been calculated at 407 and 321cm�1. The mode at 232 cm�1 is a torsional modehaving contributions from various torsional motionss [CaAC], s [CbACa], and s[C¼¼C].

Characteristic features of the dispersion curves

Dispersion curves provide knowledge of the degreeof coupling and information concerning the depend-ence of the frequency of a given mode on thesequence length of ordered conformations. In addi-tion, the evaluation of dispersion curves for a three-dimensional (3D) system is somewhat involved both,in terms of dimensions and a large number of inter-actions. It is not easy to solve the problem withoutfirst solving it for a linear isolated chain. This alonecan provide the best starting point. It has been

190 GUPTA ET AL.


TABLEIII

Norm

alModesandTheir

Dispersion

Calc.

Obs.

Assignmen

t(%

PED)(d

¼0)

Calc

Obs.

Assignmen

t(%

PED)(d¼p

)IN

SIR

Ram

anIN

SIR

Ram

an

1443

–1443

–/

[H-C

a-H

](44)þ

/[H

-Ca-C

](33)þm

[Ca-C

](12)

1468

–1443

–/

[H-C

a-C

](23)þ

/[H

-Ca-H](17)þm

[Ca-C](15)þ

/[C

-Cb-H

](13)þ

m[C-C

b](10)þ

m[Cb-C

a](9)

/[H

-Cb-H

](6)

1434

–1431

1430

/[H

-Cb-H

](36)þ

/[C

-Cb-H

](33)þm

[C-C

b](14)

1421

–1431

1430

/[H

-Cb-H

](28)þ

/[H

-Ca-H

](26)þ

/[C

-Cb-H

](19)

/[H

-Ca-C

](10)

)þm[C-C

b](5)

1351

–1346

1339

/[H

-Cb-H

](24)þm

[Cb-C

a](22)þ

/[H

-Ca-H

](10)

1363

–1346

1339

/[H

-Cb-H

](27)þm

[Cb-C

a](23)þ

/[H

-Ca-H

](17)þ

/[H

-Cb-C

a](8)þ

/[C

b-C

a-H

](7)þ

m[C¼C

](5)

/[C

b-C

a-H

](8)þ

/[H

-Cb-C

a](6)

1321

–1327*

–/

[C¼C

-H](20)þ

/[H

-C-C

b](16)þ

/[C

b-C

a-H

](13)

1322

–1327*

–/

[C¼C

-H](18)þ

/[H

-Ca-C](14)þ

/[H

-C-C

b](9)þ

m[Cb-C

a](11)þ

/[H

-Ca-H

](10)þ

/[H

-Ca-C

](10)

/[H

-Ca-H

](8)m[Ca-C

](8)þ

/[C

b-C

a-H

](6)þ

m[C¼C

](6)þ

m[C-C

l](6)

1259

–1261*

1253

/[H

-Cb-C

a](20),m[Ca-C

](18),/

[H-C

b-H

](11)

1242

–1261*

1253

/[H

-Cb-C

a](23),/

[C-C

b-H

](15),/

[H-C

b-H

](12)

/[C

-Cb-H

](10)þ

/[C

b-C

a-H

](9)þ

/[H

-Ca-C

](8)

/[H

-C-C

b](10)þ

/[C

b-C

a-H

](10)þ

/[C

¼C-H

](9)þ

/[H

-Ca-H

](7)

/[H

-Ca-C

](8)

1211

–1205

1211

/[C

-Cb-H

](45),/

[H-C

a-C

](21)þ

/[H

-Cb-C

a](8)

1191

–1205

1211

/[C

-Cb-H

](28)þ/

[H-C

a-C

](19)þ/

[Cb-C

a-H](13)

/[C

b-C

a-H

](6)

/[H

-C-C

b](8)þ

m[Ca-C

](7)þ

/[H

-Cb-C

a](7)

1170

–1144*

1180

/[H

-Ca-C

](29)þm

[Ca-C

](20)þ

/[H

-C-C

b](14)

1156

–1144*

1180

/[H

-Ca-C

](46),/

[C-C

b-H

](20),/

[Cb-C

a-H

](18)

/[C

b-C

a-H

](9)þ

/[C

¼C-H

](7)

/[H

-Cb-C

a](6)

1115

–1117

1110

/[C

-Cb-H

](25)þ/

[H-C

a-C

](19)þ/

[Cb-C

a-H

](15)

1127

–1117

1110

m[Ca-C

](33)þ/

[C-C

b-H

](19)þ

/[H

-Cb-C

a](9)þ

/[H

-Cb-C

a](15)þm

[Ca-C

](10)þ

m[C¼C

](5)

/[H

-Cb-C

a](9)

1086

–1095*

1090

m[C-C

b](49)þ/

[C-C

b-H

](12)þ

/[H

-C-C

b](9)

1079

–1095*

1090

m[C-C

b](45)þ/

[C-C

b-H

](13)þ

/[H

-C-C

b](7)þ

/[C

b-C

a-C

](7)þ

m[Cb-C

a](7)þ

m[Ca-C

](5)

1009

–999

1004

m[Cb-C

a](42)þ

/[C

b-C

a-H

](15)þ/

[H-C

b-C

a](14)

1010

–999

1004

m[Cb-C

a](47)þ

/[H

-Cb-C

a](14)þ/

[Cb-C

a-H](13)þ

/[C

b-C

a-C

](6)þ

/[C

-Cb-H

](5)

/[C

-Cb-H

](6)þ

/[C

b-C

a-C](5)

951

–947*

943

/[C

b-C

a-H

](22)þ

x[C

-H](9)þ

x[C

-Cl](9)

935

–947*

943

/[C

b-C

a-H

](39)þ/

[H-C

b-C

a](12)þ

/[H

-Ca-C

](9)þ

/[C

l-C¼C

](7)þ

/[H

-Cb-C

a](6)þ

m[Cb-C

a](5)

s[Ca-C

](9)þ

/[C

a-C

-Cl](6)

s[Ca-C

](5)þ

/[C

b-C

a-C

](5)þ

/[H

-Ca-C

](5)

834

790

825

827

/[C

b-C

a-H

](21),/

[H-C

a-C

](15),x[C

-H](12)

861

790

850

827

x[C

-H](29)þx

[C-C

l](15)þ/

[Cl-C¼C

](13)þ

m[C-C

l](12)þ

/[C

l-C¼C

](10)þ

x[C

-Cl](7)

/[H

-Cb-C

a](11)þ

m[C-C

l](9)

s[Ca-C

](6))þ/

[C-C

b-H

](5)

782

–777

779

/[H

-Cb-C

a](58)þ/

[C-C

b-H

](11)þ

s[Cb-C

a](11)þ

771

–777

779

/[H

-Cb-C

a](45)þ/

[Cb-C

a-H

](11)þs

[Ca-C

](11)þ

/[C

b-C

a-H

](6)

s[Cb-C

a](11)þ

/[C

-Cb-H

](8)

679

–658

671

x[C

-H](51)þ

m[C-C

l](22)þ

s[C¼C

](9)þ

664

–658

671

x[C

-H](41)þm

[C-C

l](27)þ

s[C¼C

](9)

/[C

b-C

a-C

](5)



TABLEIII.Continued

Calc.

Obs.

Assignmen

t(%

PED)(d

¼0)

Calc

Obs.

Assignmen

t(%

PED)(d¼p

)IN

SIR

Ram

anIN

SIR

Ram

an

569

–557*

577

/[C

¼C-C

b](23)þm

[C-C

l](20)þ/

[Cb-C

a-C

](16)

514

–557*

577

m[C-C

l](29)þ/

[Cb-C

a-C

](21)þ

/[C

a-C

-Cl](9)þ

/[C

a-C-C

l](13)þ

s[Cb-C

a](8)

/[C

a-C¼C

](7)þ

/[C

l-C¼C

](7)þ

m[C¼C

](5)

x[C

-Cl](5)

458

453

471

468

x[C

-Cl](33)þ/

[Ca-C

¼C](18)þm

[C-C

l](11)þ

506

484

471

468

/[C

¼C-C

b](30)þ/

[Ca-C¼C

](15)þm

[Ca-C](10)þ

/[C

l-C¼C

](8)

/[C

a-C-C

l](9)þ

m[C-C

b](6)þ

/[C

l-C¼C

](5)þ

/[H

-C-C

b](5)

407

–418

–/[C

a-C-C

l](45)þ

/[C

a-C

¼C](14)þs

[Ca-C

](12)

438

–418

–/[C

a-C-C

l](26)þm

[C-C

l](15)þx

[C-C

l](12)þ

m[C-C

l](10)

/[C

b-C

a-C

](8)þ

/[C

-Cb-C

a](5)

321

314

––

/[C

-Cb-C

a](23)þ/

[Ca-C

¼C](19)þ/

[Cl-C¼C

](11)

334

314

––

/[C

a-C-C

l](18)þ/

[Cb-C

a-C](16)þs

[Ca-C](12)þ

s[C¼C

](11)þ

/[C

b-C

a-C

](8)þ

/[H

-Cb-C

a](6)

s[C¼C

](9)þ

/[C

-Cb-C

a](9)þ

/[C

a-C

¼C](9)þ

/[C

l-C¼C

](8)

232

233

––

s[Ca-C

](28)þs

[Cb-C

a](16)þ

s[C¼C

](14)þ

229

233

––

s[Ca-C

](24)þ/

[Cl-C¼C

](12)þ/

[C¼C

-Cb](12)þ

/[C

b-C

a-C

](12)þ

/[C

¼C-C

b](6)

s[Cb-C

a](11)þ

/[C

a-C

-Cl](11)þ

/[C

a-C

¼C](7)

162

175

––

s[Ca-C

](17)þ/

[Ca-C

-Cl](16)þ/

[Cl-C¼C

](15)

172

175

––

/[C

a-C¼C

](20)þ/

[C-C

b-C

a](20)þ/

[Cb-C

a-C

](18)

/[C

b-C

a-H

](9)þ

s[C¼C

](7)þ

/[C

¼C-C

b](7)

x[C

-Cl](9)

s[Cb-C

a](5)

INSfreq

uen

cies

arefrom

Ref.[17].

Allfreq

uen

cies

arein

cm�1.

Only

dominan

tPED’s

aregiven

.*aremarked

freq

uen

cies

aretaken

from

secondderivativeFTIR

spectra.

192 GUPTA ET AL.


generally observed that, the intramolecular interac-tions (covalent and nonbonded) are generally strongerthan the intermolecular interactions (hydrogen bond-ing and nonbonded). Crystal field only leads to split-ting near the zone center and zone boundary. Thebasic profile of the dispersion curves remains more orless unaltered. Thus, the study of phonon dispersionin polymeric systems is an important study.

The two scissoring modes of CH2 calculated at1443 cm�1 and 1434 cm�1 at zone center diverge andreach 1468 cm�1 and 1421 cm�1 at the zone bound-ary. The mode at 1443 cm�1 consists mainly of/[HACaAH] (44%) and /[HACaAC] (33%). As dincreases, both these contributions decrease in thismode and start appearing in the lower mode that

has contributions mainly from /[HACbAH]. Thepresence of /[HACaAH] in both the modes may beresponsible for the divergence because of the repul-sion in the energy momentum space from the zonecenter onto the zone boundary. The mode calculatedat 1351 cm�1 disperses and reaches 1363 cm�1 at thezone boundary. As phase angle advances, the contri-bution of /[HACbAH] increases in this mode anddecreases in the higher frequency mode (1434 cm�1)until it becomes almost same in both the modes.The mode calculated at 407 cm�1 decreases gradu-

ally until d ¼ 0.5 p where it shows region of highdensity of states and then it increases with increas-ing value of d until zone boundary. The PED of thismode consists of /[CaACACl] (45%), /[CaAC¼¼C](14%), s[CaAC] (12%), and m[CACl] (10%). The per-centage of /[CaACACl], /[CaAC¼¼C], and s[CaAC]decreases continually till the zone boundary.However, the contribution of stretch decreases tilld ¼ 0.5 p and then starts increasing. During its pro-gression, it mixes with /[ClAC¼¼C], /[CbACaAC],and x[CACl] which may be responsible for the riseof dispersion curve.The dispersion curves at 321, 232, and 162 cm�1

have flat regions around d ¼ 0.5 p indicating highdensity of states. The presence of regions of highdensity of states also refers to some internal symme-try points in the energy momentum space and theseare known as van Hove type singularities.31 Nocrossing is present in the dispersion profile of themodes indicating the lack of the mirror plane ofsymmetry.32

The low-frequency vibrations are expected todepend sensitively on the chain conformation hencethe dispersion curves of TPCP in the low-frequencyregion have been compared with those of b-

Figure 4 (a) Dispersion curves of polychloroprene (1000–1500 cm�1). (b) Density-of-states of polychloroprene (1000–1500 cm�1).

Figure 5 (a) Dispersion curves of polychloroprene below 1000 cm�1. (b) Density of states curves of polychloroprenebelow 1000 cm�1. (c) Inelastic neutron scattering of polychloroprene below 1000 cm�1 taken from reference.17



polyisoprene (CH2C(CH3)¼¼CHACH2)n21 (Fig. 6)

which has conformation completely analogous toit.20 A comparison of low-frequency modes in boththe polymers shows that although the PED is notthe same because of the presence of CH3 group inb-polyisoprene21 in place of chlorine atom but theirdispersive behavior is similar. One of the character-istics of the dispersion curves is the similarity inprofile and weak repulsion in the modes calculatedat 232 and 162 cm�1. These modes have contributionfrom torsions and skeletal angle bends. Althoughthe mode at 162 cm�1 has contribution from chlorineangle bends also, these contributions decrease grad-ually and finally vanish at around d ¼ 0.5 p andsome other skeletal modes come in. In both thesesystems, the regions of high density of states arearound the same value of phase factor (in the neigh-borhood of d ¼ 0.45 p to 0.55 p). This is a commonfeature of the similar chain conformation and gener-ally refers to internal symmetry. It is observed thatthe profiles of the acoustic modes in TPCP and b-TPI bear a great deal of resemblance.

Frequency distribution function and heat capacity

From the dispersion curves, frequency distributionfunction has been obtained and plotted in Figures4(b) and 5(b). The peaks in the frequency distribu-tion curves correspond to the regions of high densityof states (van Hove type singularities). For a one-dimensional system, the density of state function orthe frequency distribution function expresses theway energy is distributed among the variousbranches of normal modes in the crystal. On consid-ering a solid as an assembly of harmonic oscillators,the frequency distribution g(m) is equivalent to a par-tition function. The knowledge of density of statescan be used to obtain the thermodynamic propertiessuch as heat capacity, enthalpy, etc. We have calcu-lated the heat capacity of TPCP in the temperaturerange of 10–400 K using Debye’s equation. This isplotted in Figure 7. The heat capacity follows theusual curve that is linear at low temperatures andtends towards nonlinearity at higher temperatures(classical region). Although the heat capacity ispredictive in nature but it may stimulate someworker to carry out measurements at a later date.

CONCLUSIONS

The Wilson’s GF matrix method as modified byHigg’s along with the Urey Bradley force field hassuccessfully explained the spectroscopic data onTPCP. Several unassigned modes have beenassigned and predictive values of heat capacity as afunction of temperature within the range 10–400Khave been given. However, the contribution fromthe lattice modes is bound to make a difference tothe specific heat because of its sensitivity to thesemodes. Despite several limitations involved in thecalculation of specific heat and absence of experi-mental data, this study would provide a goodstarting point for further basic studies on thermody-namical behavior of polymers.

Financial support to one of the authors (PT) from theAlexander von Humboldt Foundation, Germany and theDepartment of Science and Technology, New Delhi underIndo-Russian project is gratefully acknowledged. We arethankful to Prof. H.W. Siesler and Prof. Arnulf Materny fortheir kind help in obtaining FTIR and Raman spectra.

References

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Figure 6 Comparison of low-frequency dispersion curvesof (a) polychloroprene and (b) b-trans 1,4-polyisoprene.

Figure 7 Variation of heat capacity Cv with temperature.

194 GUPTA ET AL.


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vibrational dynamics and heat capacity of polychloroprene

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