solid state polymerization

Solid state polymerization

S.N. Vouyiouka, E.K. Karakatsani, C.D. Papaspyrides*

Laboratory of Polymer Technology, School of Chemical Engineering, National Technical

University of Athens, Zographou, Athens 157 80, Greece

Received 23 November 2004; revised 24 November 2004; accepted 24 November 2004

Available online 7 January 2005

Abstract

Polyesters and polyamides are commercially important polymers prepared by polycondensation. The conventional

solution to melt polymerization techniques stop at a low or medium molecular weight product, due to problems arising

from severe increase of the melt viscosity and operating temperatures. Higher molecular weights may be reached by Solid

State Polymerization (SSP) at temperatures between the glass transition and the onset of melting. Polycondensation

progresses through chain end reactions in the amorphous phase of the semicrystalline polymer, which in most cases is in

the form of flakes (mean diameterO1.0 mm) or powder (mean diameter!100 mm); reaction by-products are removed by

application of vacuum or through convection caused by passing an inert gas. The advantages of SSP include low operating

temperatures, which restrain side reactions and thermal degradation of the product, while requiring inexpensive equipment,

and uncomplicated and environmentally sound procedures. Disadvantages of SSP focus on low reaction rates, compared to

melt phase polymerization, and possible solid particle processability problems arising from sintering. The review begins

with a theoretical background regarding SSP, the fundamentals of techniques and equipment, including the use of inert gas

in reactive systems. Further, it is explained how SSP progress involves both chemical and physical steps, since it is

controlled by reaction kinetics, reactive chain-end mobility in the amorphous phase, and condensate removal through

diffusion. The reaction temperature emerges as the most important parameter of SSP rate variation, due to its interaction

with all aspects of the process. High prepolymer molecular weight affects positively the SSP rate, since it is accompanied

by elevated degrees of crystallinity; this implies more effective confinement of the amorphous phase and, therefore high

concentration and homogeneous distribution of reactive chain ends in the non-crystalline regions. Similarly, refinement in

reacting particle size distribution and morphology, in conjunction with high gas flow rates, increases the interfacial area per

unit volume and the effectiveness of convective by-product elimination. Finally, the SSP rate increases principally by the

use of phosphorous catalysts, which also reduce agglomeration. In the following sections of this review, emphasis is on the

progress in experimentally determining the intrinsic rate constants of principal relevant chemical reactions. The

corresponding kinetic models are either based on the Flory theory, where the rate expressions are in terms of end-group

concentrations, or on a power-law description of the rate with respect to reaction time. Recent advances in modeling and

large scale simulation of the various physical and chemical processes occurring within a SSP reactor are reported. The goal

is to describe the dynamic evolution of all chemical species within the particle and its surroundings, and assess its

dependence on basic process variables. Finally, special focus is given on methods of manipulating the molecular weight

Prog. Polym. Sci. 30 (2005) 10–37

www.elsevier.com/locate/ppolysci

0079-6700/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.progpolymsci.2004.11.001

* Corresponding author. Tel.:C30210 7723179; fax:C30210 7723180.

E-mail address: [email protected] (C.D. Papaspyrides).

http://www.elsevier.com/locate/ppolysci

S.N. Vouyiouka et al. / Prog. Polym. Sci. 30 (2005) 10–37 11

distribution of the SSP product, by varying prepolymer particle size distribution, initial stoichiometry and condensate

content in the surroundings.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: Solid state polymerization; SSP; Polyamides; Polyesters; SSP rate; Kinetics; Simulation; Molecular weight distribution

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2. SSP techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.1. Types of reactor and main characteristics for batch and continuous processes . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2. Use of inert gas in SSP systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3. Parameters affecting the SSP rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.1. Reaction temperature effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2. Initial end group concentration effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3. Particles geometry and gas flow rate effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.4. Crystallinity effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.5. Use of catalysts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4. Kinetics and simulation of SSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1. Reaction kinetics of SSP processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2. Modeling and simulation of SSP processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5. SSP and molecular weight distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

1. Introduction

Polyesters and polyamides (PAs) are important

commercial polycondensation polymers, widely used

in a variety of applications. In addition to their

commanding positions as textile fibers, PAs can be

readily processed through extrusion or injection

molding to yield mechanical and electrical parts,

while polyesters play an important role in the

automotive tire cord and bottle market [1]. Both are

mostly prepared by a stoichiometric stepwise reaction

between difunctional reactants, which is accompanied

by the formation of a lowmolecular weight condensate

[2,3]. In such condensation polymers, there is an

equilibrium such as the one described in Eq. (1) [4]

P1 CP24P3 CB (1)

where P1 and P2 are monomer molecules or polymer

chains which combine to form P3 (a longer chain), and

B is a small molecule by-product, e.g. water in the case

of PAs and glycols and water in the case of polyesters.

The reaction schemes for the formation of typical

polycondensation polymers are presented in Fig. 1.

The prerequisites to obtain a polymer product of

high molecular weight (MW) consist of maintaining

proper end-group stoichiometry, removing the

condensate to prevent depolymerization, thereby

shifting the reaction equilibrium to the right [4–6].

Nomenclature

a0, a1, a2 constants

BPA-PC poly(bisphenol A carbonate)

[C1]t concentration of the stoichiometrically

deficient end groups at any given time

[C1]0 initial concentration of the stoichiometri-

cally deficient end groups

[C2]t concentration of the end groups in excess

at any given time

[C2]0 initial concentration of the end groups in

excess

[C*] concentration of end groups in the non-

crystalline phase of polymer

[C] total end group concentration

[C]t total end group concentration at any given

time

[C]0 initial total end group concentration

[Cai] apparent inactive end group concentration

[Camorphous] concentration of a component in the

amorphous phase of the polymer

Ccondens. concentration of the by-product in the

semicrystalline polymer

CO2 carbon dioxide

KCOOH carboxyl end groups

[COOH] concentration of carboxyl end groups

[COOH]t concentration of carboxyl end groups at

any given time

[COOH]0 initial concentration of carboxyl end

groups

[Coverall] concentration of a component in the total

mass of the polymer

D diffusivity

Dcondens. diffusivity of the by-product in the


D0,condens. diffusivity of the by-product in the

completely amorphous polymer

DEG diffusivity of ethylene glycol in the


DH2O diffusivity of water in the semicrystalline

polymer

dmean mean diameter of the reacting particle

DP degree of polymerization

Ea reaction activation energy

EG ethylene glycol

He helium

k reaction rate constant

ka apparent rate constant

Keq equilibrium constant

k2 2nd order kinetics rate constant

kf forward rate constant

ktransest. transesterification rate constant

kester. esterification rate constant�Mn mean number-average molecular weight�Mn0

initial mean number-average molecular

weight�Mv viscosity average molecular weight at any

given time�Mv0 initial viscosity average molecular weight

MW molecular weight

MWD molecular weight distribution

n reaction order

N2 nitrogen

KNH2 amine end groups

[NH2] concentration of amine end groups

[NH2]t concentration of amine end groups at any

given time

[NH2]0 initial concentration of amine end groups

–OH hydroxyl end groups

[OH] concentration of hydroxyl end groups

pt fractional polymerization conversion at

any given time

p0 initial fractional polymerization

conversion

P product of the concentrations of the end

groups

Pt product of the concentrations of the end

groups at any given time

P0 product of the initial concentrations of the

end groups

PAs polyamides

PA-6,6 polyhexamethyleneadipamide

PA-6 polycaproamide

PA-4,6 polytetramethyleneadipamide

PA-12 polylaurolactam

PBT poly(butylene terephthalate)

PDEs partial differential equations

PDI polydispersity index

PEN poly(ethylene naphthalate)

PET poly(ethylene terephthalate)

S.N. Vouyiouka et al. / Prog. Polym. Sci. 30 (2005) 10–3712

PEPA 2-(2 0pyridyl) ethyl phosphonic acid

RV relative viscosity

R the universal gas constant

Rester. esterification rate expression

Rtransest. transesterification rate expression

SHP sodium hypophospite

SMT solid-melt transition

SSP solid state polymerization

S/V particle surface area per unit volume

scCO2 supercritical carbon dioxide

t reaction time

T absolute temperature

Tm melting point

Tg glass transition point

x the distance in the direction of diffusion

xc the mass fraction crystallinity

Greek letters

D[C] the difference between the total end group

concentration of the prepolymer and final

product

D[COOH] the difference between the carboxyl end

group concentration of the prepolymer and

final product

3 fractional molar excess of end groups

qt migration time of functional end groups


A significant difference between polyamides and

polyesters is that the equilibrium constant for

polyamides is hundreds times larger than that for

polyesters, and thus a much higher by-product

concentration can be tolerated in the first case,

where the removal requirements are much less

severe [1]. For example, in polyamides, the

equilibrium constant varies between 100 and 750

depending on the water content in the reacting

system [2,7–9], meanwhile the relevant values for

transesterification and esterification widely used in

poly(ethylene terephthalate) (PET) melt polycon-

densation models are 0.5–1 and 1.25, respectively

[10–13].

The predominant industrial process for polyhex-

amethyleneadipamide (PA-6,6) production involves

first solution polymerization starting from an

aqueous PA-6,6 salt solution, removal of the

water from the reactor and finally polymerization

in the melt state (250–270 8C) [14]. In the case of

poly(ethylene terephthalate) (PET), the common

commercial practice of production involves melt

polycondensation of the reactants (dimethyl tereph-

thalate–ethylene glycol or terephthalic acid–ethyl-

ene glycol), usually carried out around at 285 8C

[15]. An example of polymerization operating

conditions is presented in Table 1 [1], where a

degree of polymerization (DP) of 80 was reached

for both polymers considered. The high tempera-

tures used in these processes, combined with high

residence times, encourage thermal degradation

and gel formation, which can drastically impair

the quality of the end product [16]. For example, in

the case of PA-6,6, an undesirable reaction is the

dimerization of the diamine to a triamine, which

results in three-dimensional network formation and

finally in gelling [2,17,18]. The problems are

enhanced when dealing with more thermo-sensitive

polymers (i.e. polytetramethyleneadipamide, PA-

4,6), due to the high processing temperatures

required (260–320 8C) [18–21]. In addition, since

the melt viscosity increases very rapidly with the

polymerization progress, various problems arise

regarding the stirring of the reacting system, the

removal of the by-product and the temperature

control. Therefore, melt-based techniques are

usually not carried to high conversion, and result

mainly in the production of resins useful in

applications which do not require a high macro-

molecular chain length, e.g. a typical reached value

of the mean number-average molecular weight is

15,000–25,000 g/mol, suitable for textile appli-

cations, whereas for injection or blow molding

applications, the molecular weight should be more

than 30,000 g/mol [14,15,22–24].

With step-growth polymers, such as polyamides

and polyesters, one route to high molecular weight

products has been through Solid State Polymeriz-

ation (SSP) [25,26]. Accordingly, starting materials

are heated to a temperature higher than the glass

transition temperature (Tg), but lower than the

onset of melting (Tm) so as to make the end groups

mobile enough to react [5,15,27] and the by-

products are removed by passing inert gas through

Table 1

Operating polymerization conditions resulting in DP equal to 80 [1]

Feed line Stages

Esterification Prepolycondensation Finishing stage

PET Terephthalic acid T: 360 8C T: 270 8C T: 290 8C

Ethylene glycol t: 3 h t: 2.2 h t: 1.5 h

P: 4 atm P: 50 Torr P: 5 Torr

Prepolycondensation Melt polycondensation

PA 6,6 Adipic acid T: 254 8C T: 267 8C

Hexamethylenediamine t: 1 h t: 1.1 h

Water P: 18 atm P: 1 atm

Fig. 1. Reaction schemes for the formation of typical polycondensation polymers.


Fig. 2. Scheme of the ‘two-phase model’. o: by-products or

oligomers. Reproduced from Mallon et al. [51] by permission of

John Wiley and Sons, Inc., New York.


the reacting mass or by maintaining reduced

pressure [15,22,28].

SSP has certain advantages which render its

application attractive. SSP polymers often have

improved properties, because monomer cyclization

and other side reactions are limited, or even

avoided, due to the low SSP operating temperatures

[16]. Only linear chains seem to be formed [29],

and usually SSP products show greater heat

stability in the molten state than samples prepared

in the melt [30]; on the other hand, their monomer

and oligomers content is so low, that there is no

essential need for it to be removed [31]. Further-

more, the increase in the molecular weight during

SSP is accompanied by increased crystallinity and

crystal perfection [32] while drying the polymer,

which is important because moisture content may

influence processability in the manufacture of yarns

[33]. In addition, there is practically no environ-

mental pollution, because no solvent is required,

and the process can be a continuous operation [34].

However, at SSP low temperatures, the chain

building reactions are slow compared to polym-

erization in the melt [30,32,35], because of the

reduced mobility of the reacting species, and the

slow diffusion of the by-products. Agglomeration of

the reacting particles has also been reported during

SSP, especially at high reaction temperatures, and

is related to a low softening point of the reacting

mass and to condensate retention in the system

[36–40].

Various aspects of SSP have been reviewed during

the last decade [40–42]. The relevant papers suggest

that two categories of SSP may be considered,

according to whether the starting materials are

crystalline monomers or semicrystalline prepolymers.

In the first case, the monomer is transformed into a

polymer at a temperature lower than the melting

points of either monomer or polymer, by a reaction

which rarely takes place in a real solid state.

Depending on the reaction conditions, SSP is

accompanied, by a distinct transition of the process

from the solid to the melt state, as thoroughly

explained in Section 3.3 [38–40,43–46]. In the

second case, the polymerization is carried out on

low or medium molecular weight semicrystalline

prepolymers at a temperature below their melting

points [4,47,48]; Zimmerman [49,50] suggested

a ‘two-phase model’, according to which polymeriz-

ation proceeds in the amorphous regions, where end

groups and low molecular weight substances (con-

densate, oligomers) are excluded from crystalline

regions (Fig. 2). The equilibrium in the amorphous

regions is the same as for a completely amorphous or

molten polymer at the same temperature. Although

the main interest in SSP of monomers has been

confined up to now to laboratory studies, SSP of

prepolymers is already integrated into industrial

production processes, usually in the finishing stage.

For example, to have PET with DP equal to 145, SSP

of PET prepolymer (DPZ80) is performed at

atmospheric pressure, at 235 8C for 7 h. By compari-

son, for PA-6,6 of the same initial DP, the SSP is

carried out at 200 8C, and the residence time is 2 h to

achieve the same DP increase [1].

The SSP starting materials may take on various

physical shapes or geometry. ‘Preextrusion SSP’ of

prepolymers uses starting materials in the form

of flakes (or chips, mean diameter O1.0 mm) or

powders (mean diameter !100 mm), and has become

a common feature in the production of polymers for

industrial fibers or molded products. If SSP is carried

out after the prepolymer shaping operation, e.g. in

fibers or thin films, it is termed as ‘postextrusion

SSP’. The latter, still at the development stage,

potentially offers several advantages over the tra-

ditional ‘preextrusion SSP’, because the geometries

used in ‘postextrusion SSP’ (fibers or thin films) have

at least one dimension much smaller than chips,

and the condensate can be more effectively removed

[28,32,48,52,53].


2. SSP techniques

2.1. Types of reactor and main characteristics

for batch and continuous processes

SSP may be carried out in glass tubes (Fig. 3a) [33,

34,54,55], fluidized (Fig. 3b) and fixed bed reactors

[36,56,57], rotating flasks [20], tumbler dryers [19,22,

32,58–60], a liquid inert medium (Fig. 3c) [38–40,45,

46,61], vertical reactors with stirring blades [17],

rotating blenders [21], etc. Mechanical agitation is

usually provided in SSP systems, in order to facilitate

good heat and mass transfer, and to prevent

agglomeration, especially for SSP temperatures

above 200 8C [30,36,62]. The use of microwave

energy has been also applied in order to increase the

SSP rate, as a result of exciting and heating the

condensate in the polymer, and increasing diffusion

rates. For example, in the case of PA-6,6 SSP at

Fig. 3. Typical solid state polymerization reactors. (a) Glass tube. Reprodu

New York, (b) fluidized bed reactor [36], (c) in liquid medium [38].

202 8C the diffusion coefficient of water is increased

from 1.09!10K6 to 2.22!10K6 cm2/s when using

microwaves [51,63]. In the past, the progress of an

SSP reaction was often estimated by continuously

weighing the reacting mass [43–45,64] in order to

determine the amount of water formed. In current

technology, progress is often followed by an end

group analysis [65]. In the first case, regarding PAs,

false DP may be assessed because of the separation of

volatile diamine along with water [44].

During SSP procedures, by-products are removed

by application of vacuum or through convection

caused by passing an inert gas, usually at atmospheric

pressure. Oligomers formed during the reaction may

pass by sublimation into the gas phase, along with the

condensate. Therefore, if the inert gas is recycled, the

system should contain apparatus to remove vaporous

reaction by-products and any atmospheric oxygen

(e.g. bag filters, gas washing, catalytic gas cleaning)

ced from Li et al. [34] by permission of John Wiley and Sons, Inc.,


[22]. If a high vacuum is used in an SSP process, the

subsequent return to atmospheric pressure may result

in oxidation and discoloration of the polymer [16,58].

On the other hand, Ma et al. [66] showed that for PET,

SSP proceeds faster in vacuum than under a nitrogen

sweep, as a result of the faster removal of the by-

products and the formation of cyclic oligomers

(primarily trimers), the sublimation of which provides

an additional pathway for the progress of the reaction.

Finally, in the case of polyamide monomers, high

pressure SSP (196–490 MPa) has been also applied to

provide well oriented polymers. However, such a

technique results in low polymerization rates, due to

the slow diffusion of water [67].

Among SSP systems, a fluidized bed consumes a

great deal of energy and is not economically feasible,

vacuum process is preferred for small capacity, and a

fixed bed is ideal for a continuous process. The fixed

bed provides for large capacity, but it is difficult to

minimize the temperature gradient across the reactor,

and the method calls for a large amount of hot

nitrogen, which is an energy consuming process.

However, increased capacity averages out the invest-

ment and energy cost [62].

2.2. Use of inert gas in SSP systems

The use of the inert gas in SSP systems serves three

principal objectives: to remove the condensate, to

inhibit polymer oxidation by excluding oxygen from

the reactor atmosphere, and to heat the reacting mass.

In solid state monomer polyamidation, the use of the

inert gas is also associated with a suggested

mechanism, according to which the volatile com-

ponent of the PA-6,6 salt (i.e. hexamethylenediamine)

partially volatilizes at the reaction temperature,

thereby creating a vacancy defect, proper for the

nucleation of the generated polymer phase. The inert

gas contributes to this volatilization process and as a

result the vacancy defects and the number of

nucleation sites increase and so does the conversion

rate [68].

The inert gases used most often in SSP processes

are nitrogen (N2), carbon dioxide (CO2), helium (He)

[60,69], superheated steam [19] and supercritical

carbon dioxide (scCO2) [23,27,70,71]. In many

cases, the characteristics of the inert gas must be

taken into consideration, since they may influence

the SSP process. For example, the use of ultra dry gas

characterized by a dew point below 30 8C may lead to

a significant increase in the SSP rate [14], whereas it is

observed that steam in the carrier gas reduces the

overall rate, but also suppresses the degradation which

leads to colored products [19,22]. A dependence of

the final molecular weight achieved on the inert gas in

PET prepared by SSP has been reported in some

studies. Devotta and Mashelkar [72] relate the

dependence of this influence to the different rates of

absorption and solubilization of each gas in the

polymer mass, and thus there is a dependence on the

inert gas identity of the free volume available for

diffusion of by-products and reaction of end groups.

For example, due to its smaller molecular size, He has

a relatively higher diffusivity than either N2 and CO2,

resulting in a higher free-volume growth rate and a

higher DP with use of He. Similarly, CO2 can be

advantageously used instead of N2, because of its

higher solubility in the polymer, which can induce a

plasticization effect, and considerably enhance the

local mobility. This is also confirmed in the case in the

use of SSP to prepare poly(bisphenol A carbonate)

(BPA-PC) [23,27,73], where the use of scCO2

resulted in higher reaction rates in comparison to N2

and higher final molecular weights, with a reaction

activation energy about half of the value with N2. This

effect, in conjunction with the positive impact of the

scCO2 pressure on the SSP rate, appears to be a

consequence of the increased end group mobility due

to plasticization of the polymer by dissolved CO2 and

of the easier condensate (phenol, Fig. 1c) removal due

to its solubility in the sweep fluid. By contrast, Mallon

and Ray [69] found that using the right experimental

conditions, the type of inert gas apparently has no

significant effect on the preparation of PET by SSP,

since equivalent molecular weights are achieved with

N2, CO2 and He. Finally, if air is used for the removal

of by-products formed in SSP in the preparation of

PET, degradation offsets polymerization on exposure

to oxygen and moisture at 210 8C and above, resulting

in reduced or negative gains in molecular weight;

moreover, in such case, the carboxyl content in PET

product increases [62].

SSP systems may involve heating under continu-

ous inert gas flow (open system), where the by-

product removal is favored [19,20,27,32,34,55], or

under a stagnant inert gas atmosphere (closed system),


where the loss of monomers and oligomers is hindered

[18,45]—this system was mostly applied in the

previous decades in monomer SSP. Alternatively, a

combination of these two systems may be used, with

heating first carried out in an inert atmosphere,

followed by flow of an inert gas [74,75]. This

combination offers the advantages of both systems,

and provides maintenance of the monomers in the

reactor and satisfactory removal of the by-product in

order to favor the polymerization reaction.

3. Parameters affecting the SSP rate

As it involves both chemical and physical attri-

butes, SSP presents a complex reaction process. Based

on Eq. (1) and on the restrictions set by SSP nature,

one can identify several rate-determining steps [4,5,

19]:

†

Tab

De

Co

Ch

En

Int

sio

The intrinsic kinetics of the chemical reaction

†
The diffusion of the reactive end groups
†
The diffusion of the condensate in the solid
reacting mass (interior diffusion)

†
The diffusion of the condensate from the reacting
mass surface to the inert gas (surface diffusion)

A large number of parameters are reported to affect

the SSP overall rate and define the relevant rate-

determining step. In Section 3.1, an effort is made to

present these parameters and the relevant controlling

mechanisms, beginning with the ones considered to be

the most important. Accordingly, the discussion

presents reaction temperature, initial end group

concentration, particle geometry, gas flow rate and

le 2

pendence of the most important variables on the controlling mechanism

ntrolling mechanism Parameters

Reaction temperature

At low reaction tem-

peratures

At high reaction

peratures

emical reaction Yes (strong influence) Yes (weak influ

d group diffusion Yes (weak influence) Yes (strong influ

erior by-product diffu-

n

Yes (weak influence) Yes (strong influ

crystallinity effects on the SSP rate; the use of

catalysts is also included. The dependence of the

most important operating variables on the controlling

mechanism in the absence of gas phase resistance, i.e.

when the surface by-product diffusion is not a limiting

factor, is presented briefly in Table 2 [15,24].

3.1. Reaction temperature effect

The reaction temperature is probably the most

important factor in SSP, due to its interaction with

almost all other aspects of the process [76]. The role

of the SSP temperature is significant, as it may

influence the limiting step of the process and may

cause changes in the controlling mechanism [5,77,

78], with a resulting change of the reaction activation

energy [24]. Walas has pointed out that when the

effect of the reaction temperature change is intense,

the chemical reaction controls [79].

The dependence of the reaction temperature on the

intrinsic SSP rate constant is indicated by the values

of the SSP activation energy (Ea), reported to be

between 10.5–81.5 kcal/mol in the case of PAs, and

15.0–42.5 kcal/mol for polyesters (Table 3). In

general, the reported SSP values are slightly higher

than those for melt processes [1,7,10,20,80]. With

PET, the polycondensation equilibrium constant (Keq)

used in SSP studies is similar with that for the melt

process [11]. For polyamides, the Keq is a function of

the reaction temperature. More specifically, in the

case of SSP to prepare polycaproamide (PA-6) [31], at

given water content and for reaction temperatures in

the range of 170–210 8C, the amide equilibrium

constant is described by Eq. (2), where the enthalpy

of reaction isK7.6 kcal/mol, revealing an exothermic

in the absence of gas phase resistance [15,24]

Particle size Prepolymer

MW and

crystallinity

Catalyst

concen-

tration

tem-

ence) No No Yes

ence) No Yes No

ence) Yes (strong influence) Yes Yes

Table 3

Reaction kinetic data related to the irreversible SSP of polymers

Starting material Operating conditions Rate constant (k) Activation

energy

(kcal/mol)

Khripkov et al. [44] PA 6,6 salt 180–188 8C,

0–8 h, N2

6.3–32.5!10K3 81.5

Catalytic reaction,

k: (g/mol) minK1

9.2–43.8!10K3 57.8–72.8

Oya et al. [45] 3-Aminocaproic acid 140–185 8C, Two stages vs. reaction time, k: sK1

0–30 h, vacuum First stage: 0.853–6.40!10K5 38.1

in liquid medium Second stage: 2.03–10.1!10K5 32.1

Griskey et al. [47] PA 6,6

(dmeanZ0.18 cm)

90–135 8C,

0K10 h, N2

kZ1.53!1010 exp(K12,960/RT)

k: hK0.51

13.0

Chen et al. [4] PA 6,6

(dmeanZ0.35–0.20 cm)

120–180 8C,

5–20 h, N2

kZ1.39!104 exp(K10,500/RT)

k: hK0.5

10.5

PA 6,10


120–180 8C,

5–20 h, N2

kZ1.68!104 exp(K13,200/RT)

k: hK1

13.2

Fujimoto et al. [33] PA 6,6

(dmeanZ0.3 cm)

160–210 8C,

0–80 h, N2

log kZ13.8–(5.90!103/T),

k: hK1

26.0

Srinivasan et al. [32] PA 6,6 fibers 220–250 8C,

0–4 h, N2

kZ6.29!1040 exp(K76,000/RT)

k: (g/mol)2 sK1

76.0

Srinivasan et al. [48] PA 6,6 fibers 220–250 8C,

0–4 h, N2

2nd order: kZ3.06!1018

exp(K42,000/RT) k: (g/mol) sK1

42.0

3rd order: kZ1.18!1031

exp(K61,000/RT) k: (g/mol)2 sK1

61.0

Gaymans et al. [55] PA 6


110–205 8C,

1–24 h, N2

For conversionsO30%:

kZ0.28

Chen et al. [4] PET


160–200 8C,

5–20 h, N2

kZ6.6!1017

exp(K42,500/RT) k: hK1

42.5

Duh [94] PET

(dmeanZ106–160 mm)

200–230 8C,

0–20 h, N2

kZ1.0287!109 exp(K0.0068[C]0–23,565/RT) k: (kg/meq) hK1

23.56

Duh [88] PET 190–220 8C,

0–30 h, N2

kZ653.044 exp(19,326/RT)

k: (kg/meq) hK1

19.33

Duh [11] PET

(dmeanZ425–600 mm)

230 8C,

7–50 h, N2

ktransest.Z1.03–1.63!10K3

(kg/meq) hK1

kester.Z1.07–1.38!10K3

(kg/meq) hK1

Jabarin et al. [116] Commercial PET (Good-

year VFR-6014, Firestobe

A, Eastman 7328)

200–250 8C,

0–16 h, N2

Catalytic reaction,

k: (g/mol) minK0.5

18.4–23.2

Goodyear VFR-6014

kZ624!1010 exp(K22,800/RT)

Firestobe A kZ828!1010

exp(K23,200/RT)

Eastman 7328 kZ5.70!1010

exp(K18,400/RT)

Kim et al. [24] Commercial PET (dmeanZ0.25–0.28 cm)

160–230 8C,

0–12 h, N2

160–200 8C:

19–35

200–230 8C:

15–16

Ma et al. [66] PET films 250 8C, 6 h, Catalytic reaction

N2, vacuum ktransest.Z0.0111 (kg/meq) hK1

kesterif. Z0.0264 (kg/meq) hK1

(continued on next page)


Fig. 4. Effect of different reaction temperatures on �Mn during PA 6

SSP in a fixed bed reactor: (1) 220, (2) 200 and (3) 190 8C.

Reproduced from Xie [84] by permission of John Wiley and Sons,

Inc., New York.

Table 3 (continued)

Starting material Operating conditions Rate constant (k) Activation

energy

(kcal/mol)

Karayannidis et al.

[115]

PET films 210–240 8C,

0–8 h, vacuum

kZ1.83!1010 exp(K99,600/RT)

k: (g/mol) sK1

23.80

Shi et al. [71] PBA-PC

(dmeanZ75–125 mm)

120–165 8C,

0–10 h, N2

Catalytic reaction kf: hK1

kfZ[C1]0 kZ3.36!1013

exp(K99,600/RT)

23.8

Shi et al. [27] PBA-PC

(dmeanZ75–125 mm)

90–135 8C,

0–4 h, ScCO2,

(138–345 bar)

Catalytic reaction kf: hK1

138 bar: kfZ1.31!109

exp(K64,900/RT)

15.5

207 bar: kfZ1.21!107

exp(K48,400/RT)

11.6

345 bar: kfZ1.15!107

exp(K47,800/RT)

11.4

Sun et al. [100] PEN 200–245 8C,

0–15 h, N2

kZ1.78!106 exp(K7922/RT)

k: (g/mol) minK0.5

7.9


reaction. Another pertinent equation (Eq. (3)) has

been suggested by Kulkarni et al. [81]

log Keq Z1761:4

TK0:6614 (2)

Keq Z exp3:9842C 2:4877!104

T

R(3)

where Keq is the equilibrium constant for polycon-

densation of PA-6, T is the absolute temperature and R

is the universal gas constant.

The temperature of SSP for monomers must be

high enough to facilitate chain growth but not so high

that it leads to partial melting with simultaneous

sticking, cyclization or other side reactions. In

general, nucleation and growth behavior is observed.

Of course, increased temperature, shortens the first

stage of the SSP reaction, beyond which the

polymerization rate increases more intensively [45,

68,82]. In the case of SSP involving aminoacids [43]

and PA salts [68], the rate doubles with every 2 8C

increment of the reaction temperature. It is reported

that this high SSP ‘temperature coefficient’ may be

related to the molecular mobility of the monomer and

to the number of active sites, which increase

significantly with increasing temperature [83]. Fur-

thermore, it is observed that when the melting point

(Tm) of the monomer is high, the temperature range of

SSP becomes larger, the SSP temperature coefficient

decreases and thus the impact of the reaction

temperature on the SSP rate is diminished [43].

Turning to prepolymers, an increase of the SSP

temperature accelerates the overall rate of the process

(Fig. 4) as a result of speeding up the chemical

reaction, the mobility of the functional end groups, the

by-product diffusion and the relevant mass transport

rates [5,32,33,47,48,57,76,84–87]. According to Duh

Fig. 5. Effect of prepolymer intrinsic viscosity (IV) on the progress

of PET SSP at 210 8C. Reproduced from Duh [94] by permission of

John Wiley and Sons, Inc., New York.


[88], increased reaction temperature leads to a

decrease of the inactive end group concentration,

since some of these are rejected into the amorphous

phase as a result of the polymer crystallization at a

higher temperature. Although there are many dis-

crepancies on the optimum SSP temperature, it is

generally accepted that such a temperature should be

not too close to the Tm to prevent particle agglomera-

tion [30]. Proposed SSP temperatures vary between

20 and 160 8C below the final Tm, with the usual

preferred temperature just below Tm [3,19,51,77,84,

89–91].

In many cases, SSP is carried out successively at

different temperatures. By this temperature-staging,

the problem of polymer grains agglomeration during

SSP may be overcome, because the prepolymer

softening temperature is thus increased and sticking

at higher reaction temperature is prevented [34,36,37,

51,62,63]. In addition, problems related to oligomer

formation [22] and to initial moisture and impurities

in the prepolymer [14,21,92] are also diminished.

3.2. Initial end group concentration effect

Based on the aforementioned ‘two-phase model’

proposed by Zimmerman [49,50] (Fig. 2), the rate of

SSP is expected to be higher than the one extrapolated

from melt equations at the same temperature, because

of the increased concentration of the chain end in the

amorphous regions of the polymer. However, this

does not happen, mainly because of end group

diffusion limitations, which do not exist in melt,

where the activation energy for diffusion is much

lower [50]. Thus, in the beginning of SSP, the active

end group distribution in the reacting sites would be

homogenous as in the case of melt process and

consequently the reaction kinetics and mechanisms

will be similar. As SSP proceeds further, the reacting

species close to each other are mostly reacted and

their concentration and distribution change locally

[50,55]. Then, end group diffusion limitations appear

and result, in many cases, in reducing the apparent

reaction rate constant [24,71,93] and reaching an

asymptotic value of molecular weight [27,66,71,89] at

long reaction times.

The diffusion of end groups comprises in many

cases the rate-controlling step, which is often

concluded experimentally by the effect of the initial

end group concentrations on the reaction rate.

Accordingly, it is generally observed that the lower

the concentration of the end groups (higher initial

number-average molecular weight Mn0), the higher is

the mean number-average molecular weight Mn at the

end of the SSP reaction (Fig. 5) [19,55,86,94].

According to Gaymans et al. [55] and regarding SSP

for PA-6, this may be due to a more effective

confinement of the amorphous phase and, therefore

high concentration and homogeneous distribution of

reactive chain end in the non-crystalline regions of the

higher Mn0prepolymers. The same author, in a

previous paper [19], attributes this effect also to the

fact that the higher Mn0prepolymers show less

tendency to crystallize during SSP and thus the end-

group mobility is less inhibited. A similar explanation

is given by Duh [88,94], who indicates that in a lower

Mn0prepolymer it is easier for polymer chains to fit

into the crystal lattices and to form rigid crystals; as a

result, a greater number of end groups will be trapped

and become inactive. However, these researchers

have considered the SSP as a one-stage process and

studied the effect of Mn0on the SSP rate. A different

approach was made by Li et al. [95], who divided SSP

for PA-6 into two stages. In the first reaction stage, the

end groups with the smallest end-to-end distances

react easily without needing to diffuse; thus, in this

initial stage, the lower the Mn0of the prepolymers, the

faster is the rate of the reaction because of the higher

end-group concentration. In the second reaction stage,


the diffusion of the polymer chains (segmental

diffusion) starts to be the limiting step and faster

molecular weight growth is observed for samples with

higher Mn0for the reasons discussed above. On the

other hand, in the case of SSP of BPA-PC, it was

reported that the kinetics are independent of the initial

molecular weight with supercritical CO2 as the sweep

fluid, as long as the reaction temperature is much

higher than Tg [27].

The effect of remelting on the SSP rate is also

associated with the end-group diffusion and may be

explained based on the previous theory: the procedure

of remelting, following some time after starting SSP, is

found to increase the polymerization rate [11,55,81,86,

95,96]. This effect is considered to be a result of the

homogenization/redistribution of the reactive end-

group separation and of the decrease of the prepolymer

water content, which take place during the remelting,

and which facilitate end group diffusion [55,93,95].

Besides the influence of the initial molecular

weight of the prepolymer, the initial ratio of the end

groups also plays an important role. In the case of SSP

for PAs, and especially when the starting material is

salt, the volatile diamine escapes along with the

polycondensation water and therefore the amine end

groups should be in excess in order to compensate for

the loss and to maintain near stoichiometric equival-

ence [43,45]. Proposed ratios of initial amine to

carboxyl end-group concentrations ([NH2]/[COOH])

are in the range of 1.2–2 and 0.6–1.1 [17,58,97]. In the

case of PA prepolymers, the observed autocatalytic

effect of the carboxyl end-group in SSP [55]

implies that polymers with a large excess of

–COOH over –NH2 polymerize much faster than in

the opposite case [50]. In the case of PET, it has been

supported by many researchers that there must be an

optimized ratio of initial carboxyl to hydroxyl end-

group concentrations ([COOH]/[OH]), because the

main reactions of esterification (reaction between

hydroxyl and carboxyl ends) and transesterification

(reaction between two hydroxyl ends) (Fig. 1b) are in

competition and the by-products formed (water and

ethylene glycol (EG), respectively) exhibit different

diffusivities D in the solid polymer, e.g. at 230 8C

DEGZ3.1!10K6 and DH2OZ5.7!10K6 cm2/s

[11,24]. Thus, Chang et al. [62] support that the

optimized ratio [COOH]/[OH] depends on the geo-

metry of the reacting particles and should vary

relatively. In the case of powdered PET, a high

hydroxyl end concentration is preferred, because this

way the diffusion of the main by-product (EG)

becomes easy; in the case of larger chip size, a high

carboxyl concentration is preferred in order to favor

esterification, since water diffusion is easier in

comparison to EG. The same conclusions were

deduced in a recent paper by Duh [11], who analyzed

many detailed data found in patent literature, and set

optimum values for carboxyl end group concen-

trations, depending on the controlling mechanism of

the reaction: in SSP of PET pellets, the lower

diffusivity of EG retards transesterification and, after

a certain reaction time, higher rates are observed in

higher carboxyl content prepolymers. Finally, the

[OH]/[COOH] ratio was found to play a very

important role in the case of the SSP of poly(butylene

terephthalate) (PBT). The higher this ratio (O0.5), the

more Mn increases, while for small ratios, the process

can lead to only minor increases in the Mn [98].

The role of the end group diffusion in the SSP

process has been also emphasized in simulation

models with a molecular basis [34,81,86,96,99],

through the definition of the ‘characteristic migration

time of the functional end groups (qt)’, referred to a

specific reaction. In general, a low value of this

parameter means higher micro-level diffusivity of the

polymer molecule in the reacting mass, thereby

causing an increase in the rate constant of the relevant

reaction [34]. According to Kulkarni and Gupta [81],

three different values of qt must be used during the

modeling of SSP for PA-6, since three major

reversible reactions are involved in its kinetic scheme,

namely ring opening, polycondensation and polyaddi-

tion; the influence of the change of these three qt on

the reaction rate is examined. The same approach was

made by Li et al. [34], in a study on the SSP of PA-6,6.

3.3. Particles geometry and gas flow rate effect

The presence of the polycondensation by-product

in the reacting mass may cause degradation reactions,

which explain the fact that in many SSP cases there is

a maximum value Mn (for long reaction times), after

which the molecular weight reaches an asymptotic

value, or even starts decreasing [72,90,98]. In the case

of polyamides, it is anticipated that the initial moisture

content of the prepolymer pellets will affect SSP: an

Fig. 6. Effect of particle size on SSP rate of PET at 230 8C.

Reproduced from Duh [94] by permission of John Wiley and Sons,

Inc., New York.


increase of moisture content results in a decrease of

the DP, because higher initial water content promotes

the reversible polycondensation reaction towards the

left [99]. On the other hand, it is reported that the rate

is not greatly influenced by a high initial amount of

water, because the latter is decreased to zero at the

first stages of SSP due to the simultaneous drying

[33–35].

Turning to reaction mechanism for melt polyami-

dation, the effect of the by-product concentration in

the reacting mass is also explained through the

reaction scheme presented in Eq. (4) [7]:

-COOHCH2N-4 -COOK/CH3N-

4 -CONH-CH2O(4)

The first step is similar to the ‘salting’ reaction and the

second reaction is the rate-controlling step. The free

water greatly affects the dielectric constant of the

reaction mixture due to its high polarity, and a higher

dielectric constant makes the lefthand side of the

‘salting’ reaction more stable, and reduces the amount

of the intermediate involved in the rate-controlling

step. Therefore, the reaction rate is decreased with

increasing water concentration.

The effect of the by-product diffusion on the SSP rate

is generally more intense at high operating tempera-

tures, where the chemical reaction is no longer the

controlling step [5,24,93]. A by-product diffusion effect

may be detected by varying the reacting particle size

and the flow rate of the inert gas. If SSP is reaction-rate-

controlled, the DP is independent of particle size [27].

By contrast, particle size strongly influences the overall

ratewhendiffusionof the by-productwithin the polymer

particle controls, with this influence weakening when

the process is controlled by both diffusion and reaction

[15,86].

In the case of monomers SSP, the size of the

crystals of the reacting mass is disregarded by most

researchers; its effect is not significant for grain sizes

below 20–25 mesh [41].

In the case of prepolymers, it is generally accepted

that a smaller size of prepolymer particles can lead to

an increased SSP rate (Fig. 6), and consequently to a

decrease of the residence time, due to the shorter

diffusion distance and the larger particle surface area

per unit volume (ratio S/V) [1,94]. Under certain

reaction temperature conditions, the SSP rate is found

to increase when the diameter of polymer particles

decreases, indicating that diffusion of the by-product

through the solid polymer (interior mass transfer) is

rate-controlling [4,5,15,71,86,94,100]. More specifi-

cally, particle size decrease may lead to a change of

the mechanism, as Huang and Walsh [78] observed in

the SSP of PET, where a shift from interior diffusion

control to surface diffusion control occurred on

reducing the polymer size. On the other hand, by-

product diffusion limitations may be totally neglected

when the half thickness (x) of the reacting particle

follows Eq. (5) [66]

x!

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDcondens:

kCcondens:

s(5)

where k is the reaction rate constant, x is the diffusion

distance, and Dcondens. and Ccondens. are the diffusivity

and concentration of the by-product in the semicrys-

talline polymer, respectively.

The effect of particle size on SSP rate is more

intense in the case of polyester prepolymers, while in

polyamides the reaction rate does not increase so


dramatically with decreasing particle size. For

example, in the case of SSP for PET, a decrease of

the particle diameter from 0.266 to 0.14 cm results in

reducing the residence time by 56%, whereas the

relative decrease in SSP for PA-6,6 is only 3%. This is

attributed to the larger equilibrium constant for

polyamidation, which tolerates much higher conden-

sate concentrations in the particle without serious rate

reduction [1].

In addition, the surface by-product diffusion is

influenced by the flow of the inert gas. Acceleration in

the gas flow can increase the mass and heat transfer

rates in the gas-solid system and decrease the

resistance to the diffusion of the by-product from

the particle surface into the bulk of the gas phase

[1,11,27,35,71,101]. It is reported that, at a given

reaction temperature, increasing the gas flow velocity

in the SSP of small-sized PET sample results in

changing the limiting step from surface diffusion

control to chemical reaction control [78]. On the other

hand, the effect of gas flow rate is not very significant

in cases where the diffusion of condensate inside the

particles is the controlling step [27,57,66,84].

The role of the by-product diffusion in the SSP

process has been also emphasized in simulation

models, where three possible geometric situations

are considered. To the extent that polymer flakes

resemble plane sheets or cylinders, and polymer

powders resemble spheres, the main by-product

diffusion equations are expressed by Eqs. (6)–(8) [4,

5,102]

Plane sheets :vCcondens:

vtZDcondens:

v2Ccondens:

vx2(6)

Cylinders :vCcondens:

vt

ZDcondens:

v2Ccondens:

vx2C

1

x

vCcondens:

vx

� �(7)

Spheres :vCcondens:

vt

ZDcondens:

v2Ccondens:

vx2C

2

x

vCcondens:

vx

� �(8)

where x the distance in the direction of diffusion, and

Dcondens. and Ccondens. are the diffusivity and

concentration of the by-product in the semicrystalline

polymer, respectively.

It is important to emphasize that, during SSP, the

effect of the chemical nature of the reactingmass on by-

product diffusion is not greatly considered. However,

Papaspyrides et al. [38–40,46,103] underlined the effect

of the hygroscopic nature of the reacting mass on SSP

for PAs, as derived from the water sorption mechanism

ofpolyamides. Thus, the role of polycondensationwater

becomes very important, since it was suspected that the

water formed had no tendency to diffuse out of the

reacting mass. More specifically, the SSP of different

PAs salts was investigated by dispersing the monomer

particles in an inert non-solvent and using a glassware

assembly, which provided continuousmonitoring of the

physical form of the reacting mass (Fig. 3c). It was

observed that the SSP was accompanied, depending on

the reaction conditions, by a distinct transition of the

process from the solid to the melt state (‘Solid-Melt

Transition’, SMT), where a very fast agglomeration of

the reacting grains took place. The phenomenon was

readily seen macroscopically, since stirring failed to

keep the particles in suspension, while microscopically

the transformation of sharp-edged crystals to nearly

spherical particles was evident. Taking into account

these experimental findings and the hygroscopic nature

of the polyamides, a generalized mechanism for the

effect of polycondensation water on reaction behavior

has been proposed (Fig. 7). The reaction begins at the

defective sites of the monomer crystalline structure,

being the active centers of the reaction (Fig. 7a). For

active centers up to or very near to the grain surface, the

water formed can be easily removed to the surrounding

heating medium, without affecting the reacting mass.

On the contrary, in the inner grain, the water cannot be

easily removed and hydrates the polar hydrophilic

groups of the salt structure. In the case of low reaction

rates (i.e. low rates of water formation) an organized

accommodation of the by-product within the crystal

structure is performed. As the accumulated amount of

water increases, a ‘highly hydrated’ area of monomer

surrounds the active centers. This ‘highly hydrated’ area

has a lower melting point and soon falls into the melt

state (Fig. 7b). After the formation of these melt areas,

the reaction proceedsmainly in themelt state, the rate is

considerably increased, andwater accumulation leads to

an increase of the totalmelt area (Fig. 7c). Eventually an

overlapping of these melt areas occurs, which explains

Fig. 7. Schematic diagram of the solid-melt transition phenomenon

(SMT). ($), Defects of the monomer crystalline structure; Dark area,

Polymer nuclei insoluble in water; Shaded area, ‘Highly hydrated’

and eventually melt area. Reproduced from Kampouris et al. [38] by

permission of Elsevier Science LTD, Oxford, UK.


the observed transition of the reaction from the solid to

the melt state (Fig. 7d). As the reaction proceeds

further, the molecular weight increases, the hygrosco-

picity of the reacting system decreases, and finally the

solid character of the system is restored.At high reaction

rates, it is proposed that the time available for a

controlled accommodation of the water formed is very

limited, resulting in a more rapid breakdown of the salt

structure and subsequently in a faster appearance of the

SMT phenomenon. This proposed model of water

accumulation–hydration-transition to the melt was

found to predominate in PAs salts ofmoderate structural

organization, while deviation from this model may

occur when the network of the coordinating polar

groups becomes more rigid (e.g. ethylenediammonium

fumarate).

3.4. Crystallinity effect

Contradictory opinions have been expressed con-

cerning the change of crystallinity during SSP.

According to Wu et al. [86], crystallinity can be

assumed constant in SSP. By contrast, Li et al. [34]

and Mallon and Ray [51] observed that the crystal

perfection and/or size gradually increase during the

SSP of PA-6,6 and PET. Kim et al. [24] observed that

PET crystallinity increases significantly within the

first few hours of SSP and then stabilizes, showing

only small variations with increased reaction time.

Crystallinity is considered to influence the SSP

rate, because its role is essential in controlling critical

parameters of the reaction, such as the end-group and

the by-product diffusion. It is assumed that the size

and perfection of the crystalline lamellae and their

packing influence the molecular mobility of the chain

end groups. For example, in well-crystallized semi-

crystalline polymers, the motion of chain segments is

restrained by the fact that almost all of them are

anchored in crystals [51,95]. In fact, the effect of

crystallinity on the SSP rate is two-sided. Again,

accepting the ‘two-phase model’ [49,50], in which the

end groups are assumed to be expelled in the

amorphous phase (Fig. 2), an increase of crystallinity

leads to higher concentration of end groups rejected in

the amorphous phase and thus to an increase of the

reaction rate [15,51,86]. On the other hand, as SSP

proceeds, the mobility of the polymer chains is

believed to decrease because of the crystallinity

increase [28], which also hinders the escape of by-

products from the reacting mass; therefore diffusivity

decreases with increasing crystallinity [34]. More-

over, when the degree of crystallinity is high, a

considerable fraction of macrochains are immobilized

and protected against attack of low molecular weight

by-products formed during condensation, while inter-

action between end groups is favored [87]. Summar-

izing the above, the contrary effects of crystallinity

can be understood with respect to the SSP kinetic

mechanisms: in by-product diffusion limited reac-

tions, high crystallinity reduces the SSP rate by

imposing higher resistance to mass transfer, whereas

in chemical reaction-controlled process, high crystal-

linity results in increasing SSP rate because of the

concentration of end groups in the amorphous regions

[24]. It has been suggested that for optimum behavior,

the reacting particles should have a sufficiently high

crystallinity to prohibit particle agglomeration [1,37];

specifically, Wu et al. proposed a value of 40% [86].

The effects of crystallinity are included in the SSP

kinetics models and simulation mainly through

equations based on the concentrations of


the noncrystallizing components (i.e. end-groups, by-

products (Eq. (9)) and the by-product diffusion (Eq.

(10)) [48,51,90,95]

½Camorphous�Z½Coverall�

1Kxc(9)

Dcondens: Z ð1KxcÞD0;condens: (10)

where xc is the mass fraction crystallinity, [Camorphous]

and [Coverall] are the concentrations of a component in

the amorphous phase of polymer and the total mass of

the polymer, respectively, and Dcondens. and D0,condens

are the diffusivities of the by-product in the semi-

crystalline polymer and the completely amorphous

polymer, respectively.

In addition to the effects of the crystallinity of the

prepolymers, the method by which crystallization

develops may also influence the SSP process. Crystal-

lized prepolymers are produced either by solvent

evaporation or by crystallization from the melt [104].

In the second technique, the structures of thermally

crystallized polymers are strongly affected by the

crystallization process and present a memory of the

thermal history, i.e. temperatures and times of

crystallization, cooling rates, etc [105]. Therefore, in

cases of SSP with thermally crystallized prepolymers,

the reaction progress may be influenced by the

crystallization history, which may effect the structure

characteristics of the SSP products.

Turning to the solvent induced crystallization

processes, it seems that the latter are preferable

when particulate characteristics are of highest

importance. Thus, in cases of by-product diffusion-

controlled SSP processes, for which the reacting

particles size plays a significant role, solvent

induced technique seems preferable, since it can

give a specific crystal size distribution, crystal

shapes and structures of the prepolymer. The latter

cannot be fully achieved in crystallizing by cooling

from the melt. Here, the polymer molecules exhibit

strong ‘competition’ with each other and add to a

specific crystal surface simultaneously, rendering the

situation much more chaotic [106]. On the other

hand, when purity of the SSP product is essential,

crystallization from the melt would be preferable, in

order to avoid any contamination of the product

by he solvent. Finally, it should be mentioned that

the environmental benefits of SSP are evident for

thermally crystallized prepolymers, e.g. PET, but the

advantage is lost with solvent induced prepolymers,

like polycarbonates. In fact, the solvents known to

induce crystallinity, e.g. acetone, are difficult to

handle in a large scale commercial plant, and their

removal is very difficult. However, the use of the

proper gas, e.g. scCO2, can compensate the use of

organic solvents, inducing crystallization in the

polycarbonate prepolymer [27,70,71,73].

3.5. Use of catalysts

The presence of catalysts in the preparation of

polyamides and polyesters has an accelerating effect

on the rate of polymerization in both solid and melt

phase reactions. The disadvantages of SSP are mainly

overcome with the use of catalysts, which aim to

increase the reaction rate and avoid particles agglom-

eration [103]. Therefore, acidic, basic and neutral

compounds have been examined for their catalytic

action. In the case of acid catalyzed polyamidation,

the mechanism proposed involves the following

equilibria [2,107]:

-COOHCHC4 -COOHC2 (11)

COOHC2 CH2N-4 -CONH-CHCCH2O (12)

However, there is not a unique proposed mechan-

ism to explain the catalytic action in SSP processes.

For example, Khripkov et al. [108] conclude that

noncatalytic SSP of PA-6,6 salt, involves reactions

between the end-groups of monomers and the

propagating polymer chains, with initiation and

propagation reactions carried out in the defective

parts of small salt crystals. In catalytic processes, the

presence of linear oligomers is reported after a short

time of SSP reaction; thus, they assume that the

growth of polymer chain is achieved not only with the

reaction between the monomer and the propagating

polymer chain, but also between the oligomers

themselves. On the other hand, Papaspyrides et al.

[46,103] correlated the effect of catalysts to the

proposed mechanism of Solid-Melt Transition in the

PAs salts. It was proposed that the presence of a good

catalyst in the reacting structure contributes to an

easier removal of the water formed in the reaction

Fig. 8. Solid state polyamidation of hexamethylenediammonium

adipate at 142 8C. —, pure salt; – – –, salt containing 1.60% w/w

boric acid, (,), conversion; (:), water accumulation parameter.

Drawn after data from Ref. [46].


(Fig. 8). In other words, hydration seems restricted

and the diffusion of the water is favored so that the

right-hand reaction is encouraged. It should be

mentioned that the use of SSP catalysts currently

constitutes a significant research area, since a uniform

catalysis mechanism has not yet been suggested, and

most catalysts are used empirically.

The catalysts most often used in the SSP of

monomers are presented below. For the SSP of

aminoacids, the effectiveness of the catalytic action

of several compounds follows the order: 1% H3BO3,

0.2% MgOO0.5% (COONH4)2O0.5% (CH3COO)2-ZnO0.2% Na2CO3O0.6% CH3COOHO0.5%

(NH4)2SO4O1% SnCl2 [43]. For the SSP of PA-6,6

salt, reported catalysts include: H3BO3O(COOH)2OH3PO4OMgO, and Na2CO3, NaHSO4 and (SiO2)n are

proved to be inactive [44]. For polyoxamidation,

compounds belonging to groups IVb and Vb of the

periodic table of elements were found to act as

catalysts: SbF3wAs2O3[GeO2OSb2O3OBi2O3-

wPbO [30].

In the SSP of prepolymers, the addition of easily

diffusing acidic compounds (e.g. H3PO4, HBO3,

H2SO4) leads to higher reaction rate, while in the

absence of them the reaction rate is limited by the

diffusion of the autocatalyzing acid chain end groups

[55]. In the SSP of PAs, the catalysts used are mainly

phosphorous compounds, such as 2-(2 0pyridyl) ethyl

phosphonic acid (PEPA), sodium (SHP) and manga-

nous hypophosphite [14,37]. Moisture in the pellets is

considered to deactivate the catalyst, therefore

evaporation of water from the surface should be

encouraged by the use of a low dew point inert gas

[14].

The use of thermoplastic polyurethane [109] and of

sterically hindered hydroxylphenylalkylphosphonic

ester or monoester (such as Irganoxw 1222 and

1425) [110] has been also proposed so as to catalyze

SSP reactions.

Reported techniques to incorporate the catalyst in

the SSP starting materials may vary, and their

effectiveness depends on whether the catalyst is

thoroughly dispersed in the SSP reacting mass.

Thus, the catalyst may be added in a PA salt solution

during the prepolymer production [14,58], or alter-

natively into the prepolymer melt, by injection into a

low relative viscosity melt prior to pelletizing [14].

Other techniques suggest impregnation of the pre-

polymer in a catalyst solution [111] or melt-blending

the prepolymer with a masterbatch containing the

catalyst [16] before carrying out SSP. Finally, in the

case of the SSP of PA salts, a nucleation–coprecipi-

tation technique is proposed, in which the catalyst is

introduced in the solution of the reactants and

precipitates together with the PA salt [103,112,113].

4. Kinetics and simulation of SSP

One can roughly classify the literature of SSP

kinetics and simulation into two areas. In the first,

emphasis is given primarily on the determination of

intrinsic or apparent rate constants of the various main

and side reactions, assuming no diffusion limitations.

The second places emphasis on the modeling and

simulation of the various physical processes that

occur simultaneously with chemical reaction in large-

scale reactors. Both areas are rapidly growing, and

future activity is expected, since the major task in the

kinetic study of solid state polymerization is to

determine the optimum operating conditions and

establish a kinetic model useful for reactor design.

4.1. Reaction kinetics of SSP processes

Despite the fact that the chemical kinetics of SSP

in polyesters and polyamides has been the subject of

numerous studies, there is no universal agreement on

the relevant chemical kinetic expressions. In general,

the kinetic models developed to date are classified


into two groups: the Flory theory-based models and

the power-law models. According to Flory’s theory

[114], the kinetics can be described as either second-

(Eq. (13)) or third- (Eq. (14)) order, assuming equal

reactivity of the functional end groups. This principle

is most accurate for the final stages of polymerization,

for which the molecular weight is high. Thus, it

becomes evident that in the SSP of prepolymers,

which excludes the very early stages of polymeriz-

ation, the kinetic expressions can be written in terms

of functional group concentrations [102]. In the case

of polyamides, the rate equations are

2nd order :Kd½COOH�

dtZ k2½COOH�½NH2� (13)

3rd order :Kd½COOH�

dtZ k3½COOH�

2½NH2� (14)

where k2 (kg/meq h) and k3 (kg2/meq2 h) are the 2nd

and 3rd order rate constants, respectively, and

[COOH] and [NH2] are the concentrations (meq/kg)

of carboxyl and amine end groups, respectively.

Obviously, third order kinetics indicate that one of

the functional groups exhibits catalytic behavior, and

thus its effect on polymerization must be included in

the rate equation. The kinetics during the melt

polyesterification, studied by Flory, showed that 2nd

order kinetics refer to polymerizations catalyzed by a

small amount of a strong acid catalyst, the concen-

tration of which is included in the rate constant k2. In

these cases, the 2nd order course continues up to a

degree of polymerization of 90%, while in uncata-

lyzed polymerizations, 3rd order is followed only for

conversions higher than 80% (80–93%) [114].

Many different but almost equivalent sets of

integrated equations have been developed to describe

Flory’s theory, and are presented below for the

irreversible SSP reaction, since the hydrolysis rate

may be assumed negligible due to the low reaction

temperatures (Table 3). In addition, in many studies of

intrinsic SSP kinetics, only data for short reaction

times are used, to exclude limitations regarding end

group diffusion [27,66,71].

In particular, Gaymans et al. [19] studied the SSP

of unbalanced PA-4,6 and they proposed a kinetic

expression in terms of the product of the concen-

trations of the end groups (P) and of the reaction order

(n) (Eq. (15)). In case of a balanced starting material,

the apparent reaction order is assessed by the increase

of the number-average molecular weight versus

reaction time. Under the specific experimental limits,

the SSP reaction did not follow 3rd order kinetics, but

the apparent order varied between 3.5 and 5.2,

revealing that with decreasing reaction temperature,

the apparent order increases

Kd½COOH�

dtZ k

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½COOH�$½NH2�

p� �n

Z kffiffiffiP

p� �n

01ffiffiffiffiffiPt

p

� �nK1

K1ffiffiffiffiffiP0

p

� �nK1

Z ðnK1Þkt (15)

where k is the rate constant (kgnK1/meqnK1 h),

[COOH]t and [NH2]t are the concentrations (meq/kg)

of the end groups at any given time t, [COOH]0 and

[NH2]0 are the initial concentrations (meq/kg) of the

end groups, P0Z[COOH]0$[NH2]0 and PtZ[COOH]t$[NH2]t, (meq/kg)2.

In the study of the SSP of PA-6,6 fibers [48],

assuming a balanced prepolymer and a polydispersity

index (PDI) equal to 2 during SSP, a rate expression in

terms of the reaction order (n), of the viscosity

average molecular weight (Mv) and of the degree of

crystallinity (xc) has been developed (Eq. (16)) based

on the ‘two-phase model’ and Eq. (9). The relevant

data gave equally good fits with 2nd and 3rd order

reaction kinetics

Kd½C��

dtZ k½C��n0 ðMvÞ

nK1 K ðMv0ÞnK1

ZðnK1Þ2nK1

ð1KxcÞnK1

kt (16)

where k is the reaction rate constant (gnK1/molnK1 h),

[C*] is the concentration (mol/g) of end groups in the

noncrystalline phase of polymer, Mv0 is the initial

viscosity average molecular weight, and Mv is the

viscosity average molecular weight at any given time

t, g/mol.

Turning to PET, Duh [11] determined the intrinsic

rate constants for esterification and transesterification

in the case of PET powder SSP. The relevant rate


expressions are

Rtransest: Z 2ktransest:½OH�202ktransest:

ðt

0½OH�2

ZKðD½C�K2D½COOH�Þ (17)

Rester: Z 2kester:½OH�½COOH�02kester:

ðt

0½OH�

!½COOH�

ZK2D½COOH� (18)

where kester. and ktransest. are the esterification and

transesterification rate constants ((kg/meq h), respect-

ively, [OH] and [COOH] are the hydroxyl and

carboxyl end group concentrations (meq/kg), respect-

ively, D[C] and D[COOH] are the differences

between the total and carboxyl end group concen-

trations (meq/kg), respectively, of the prepolymer and

final product.

The product of the end-group concentrations was

expressed as exponential function of reaction time t

(Eq. (19)), and the relevant constants (a0, a1, a2) were

determined by curve fitting. Eq. (19) was used in the

integration of the relevant rate expressions (Eq. (17)

and (18)), to calculate the rate constants

½OH�2 or ½OH�½COOH�Z a0 Ca1 exp Kt

a2

� �(19)

Duh [88,94] also developed a simple semiempi-

rical rate equation (Eq. (20)), assuming that SSP is

reaction-controlled and that only transesterification

occurs. According to his studies, two categories of end

groups exist: active and inactive groups. The inactive

end groups include chemically dead end groups and

functional end groups that are firmly trapped in the

crystalline structure and cannot participate in the

reaction. It was suggested that the overall SSP

followed a 2nd order kinetics. The proposed rate

equation contains two parameters: the apparent

reaction rate constant (ka) and the constant apparent

inactive end group concentration [Cai], found to

decrease linearly with the SSP temperature. Finally, in

the Arrhenius equation of the rate constant (ka), the

frequency factor was found to be an exponential

function of the initial total end group concentration

[C]0.

Kd½C�

dtZ 2kað½C�K ½Cai�Þ

20½C�0 K ½C�t

t

Z 2kað½C�0 K ½Cai�Þ½C�t K2kað½C�0

K ½Cai�Þ½Cai� (20)

where ka is the apparent 2nd order rate constant

(kg/meq h), [C]0 and [C]t are the total end group

concentrations (meq/kg) initially and at time t,

respectively, and [Cai] is the constant apparent

inactive end group concentration (meq/kg).

Karayannidis et al. [115] considered only transes-

terification during the SSP of amorphous and

unoriented PET films and verified the rate equation,

for which Mn increases linearly with time. On the

other hand, during PET SSP, Ma et al. [66] considered

both the transesterification and esterification reactions

and using relevant software, they solved the kinetic

expressions in Eqs. (21)–(23). In the same paper, they

also modified the above equations according to the

aforementioned Duh theory [94] and estimated new

rate constants based on inactive end group concen-

trations

d½OH�

dtZK4ktransest:½OH�

2 Kkester:½COOH�

!½OH� (21)

d½COOH�

dtZKkester:½COOH�½OH� (22)

Mn Z2!106

½COOH�C ½OH�(23)

where ktransest. and kester. are the rate constants

(kg/meq h) for transesterification and esterification,

respectively, [OH] and [COOH] are the concen-

trations of hydroxyl and carboxyl end groups

(meq/kg), and Mn is the mean number-average

molecular weight (g/mol).

Shi et al. [27,71] investigated the kinetics of the

SSP of BPA-PC based on the Flory theory, using only

the data at short reaction times, and assuming that the

rate is controlled by transesterification. They devel-

oped a 2nd order rate expression (Eq. (24)), written in

terms of end group concentrations, fractional conver-

sion (p) of the stoichiometrically deficient end group


and fractional molar excess of the other group (3)

Kd½C1�

dtZ k½C1�½C2�

01

3ln

1C3Kpt

1Kpt

K ln1C3Kp0

1Kp0

� �

Z ½C1�0k2t

(24)

where k2 is the 2nd order kinetics rate constant,

(kg/meq h), [C1]t and [C2]t are the concentrations

(meq/kg) of the stoichiometrically deficient end-

groups and the end groups in excess at time t,

respectively, with initial values [C1]0 and [C2]0,

respectively, p0 the fractional conversion in the

prepolymerization stage, and

3Z½C2�0 K ½C1�0

½C1�0(25)

pt Z½C1�0 K ½C1�t

½C1�0(26)

As far as the power-law models are concerned, a

widely used equation is that of Walas [79], who

pointed out that the rate of a process in a solid

material, which is controlled by the chemical reaction

and diffusion, usually varies as some power of the

time (n) (Eq. (27))

rateZ ktn (27)

Griskey and Lee [47] used a modified form of

Walas equation, which assumes that the number-

average molecular weight (Mn) in solid state polym-

erization varies as a power of the time equal toK0.49

for the SSP of PA-6,6. For the analysis of their kinetic

data on the SSP of PA-6, Gaymans et al. [55]

suggested that the process is limited by the diffusion

rate of the autocatalyzing acid end and that this is not

only dependent on the concentration and the tem-

perature, but also on the changing pair-wise distance

distribution among end-groups. Therefore, they

developed a kinetic expression which associates the

rate of reaction with the concentration of the

catalyzing end groups [COOH], and to a power n of

time (Eq. (28)), combining thus the Flory theory with

the Walas equation. It was found that the SSP kinetics

had more than one region, and for conversions higher

than 30% the reaction rate was 1st order in the

carboxyl end-group concentration, and reciprocal to

the reaction time (nZK1)

Kd½COOH�

dt

Z k COOH½ �tn

0 ln Kd½COOH�

dt=½COOH�t

� �

Z ln k Cn ln t (28)

where k the reaction rate constant (1/hnC1) and

[COOH]t is the carboxyl end group concentration at

time t (meq/g).

Chen and Chen [93] also used both Flory theory-

based rate equations and power-law equations to

determine the effective rate constants of esterification

and ester interchange reaction, which take place

during the SSP of PET. The Flory theory-based rate

equations they used were 2nd and 3rd order for the

esterification and interchange reaction, respectively.

The order of the power-law equations used wasK2 in

both cases. According to Jabarin and Lofgren [116],

who investigated the kinetics of SSP of PET for a

variety of conditions, the mean number-average

molecular weight at any time of SSP (Mn) is related

to the square root of the reaction time (ffiffit

p), and is

given through a simple empirical equation. The same

kinetic approach was also used by Kim at al. [24] in

PET SSP and by Sun at al. [100] in the case of

poly(ethylene naphthalate) (PEN) SSP.

Finally, Fujimoto et al. [33] formulated a power-

law rate equation during their study of the SSP of PA-

6,6 based on the relative viscosity (RV), found

experimentally from the ratio of the viscosity of a

solution of 8.4% (by weight) polymer in a solution of

90% formic acid to the viscosity of the formic acid

solution. It was found that the RV of their samples

increased linearly with heating time during SSP.

However, it should be emphasized that such an

expression serves only as a tool to get some idea of

the rheological behavior of the polymer during SSP.

According to Zimmerman [50], if the course of the

reaction was followed by RV measurements rather

than by end-group concentrations, the results could

become confusing because of the possibility of


branching reactions, since the viscosity will not

usually increase as fast with increasing molecular

weight for a branched chain as for a linear one.

4.2. Modeling and simulation of SSP processes

Because of the industrial importance of SSP,

mathematical modeling and process simulation have

been employed to gain a better understanding of the

relevant mechanisms and to predict the influence of

different parameters on the SSP rate. The majority of

these modeling studies involve the solution of the full

system of partial differential equations (PDEs), which

describe the change with time and position of all

chemical species within the particle. In these models,

each species balance contains the rates of all reactions

in which the species participates, and each condensate

molecule balance contains an additional term for

diffusion of the condensate within the particle. These

models contain a significant number of physicochem-

ical parameters (rate constants, diffusion coefficients,

etc.), one or more of which must be adjusted to fit the

experimental data to the model. Such models have

been developed for SSP of a variety of polymers,

belonging to the families of both polyesters and

polyamides, including PET, PBT, BPA-PC, PA-6 and

PA-6,6.

Regarding PA-6, Kaushik and Gupta [96]

explained some limited experimental data quite well

and predicted qualitative trends observed experimen-

tally in the SSP of PA-6 chips with intermediate

remelting. More specifically, they set critical values

for the water diffusivity inside the reacting particles,

for the particles surface water concentration and for

the particle radius for which no considerable increase

of �Mn occurs. Kulkarni and Gupta [81] later devel-

oped an improved model, using the Vrentas-Duda

theory for diffusion coefficients. The effects of

changing the important operating conditions on SSP,

e.g. intermediate remelting of PA-6 powder, water

concentration in the vapor phase, minimizing the

monomer and water contents before SSP, size and

degree of crystallinity of polymer particles, etc. have

been studied. The same effects are also considered in

the comprehensive model for the SSP of PA-6

developed by Li et al. [95]. Xie [99] also developed

a model for SSP of PA-6, which explores the effect of

different parameters on number-average chain length

and polydispersity index.

Yao et al. [35,117] developed a reactor model to

describe the SSP of PA-6,6 in a moving bed and to

simulate process start-up, shut-down and different

disturbances during operation. A model of the SSP of

PA-6,6 has also been developed by Li et al. [34], in

which the variations of molecular weight and water

content at different positions inside the chip indicated

that the major polymerization occurs in a thin shell

near the periphery of the chip, with the molecular

weight at the core increasing more slowly because of

the limited diffusion of water. Furthermore, in

agreement with experimental data, based on their

simulation, Yao and Ray [1] found that the residence

time in the SSP reactor increases rapidly with a

decrease of the DP in the feed line, and that the size of

PA particles does not have a considerable effect on the

SSP rate.

Turning to PET, a general model to describe

continuous SSP reactors has also been applied to a

moving packed bed reactor case study. Reactor

temperature and the condensate (ethylene glycol and

water) concentration in the inert gas both affected the

final DP, while variable crystallinity and gas phase

mass transfer effects were also studied [51,57]. Wang

and Deng [85] proposed a comprehensive model for

the SSP of PET to account for the influence of reactive

chainmobility on reaction rate, the diffusion of volatile

by-products (ethylene glycol, water and acetaldehyde)

and the effect of crystallinity. The effect of crystallinity

was also brought out by a mathematical model for the

SSP of PET, developed by Devotta and Mashelkar

[72]. This work was a continuation of the work of

Ravindranath and Mashelkar [15], who used a

mathematical model for simulation of industrial SSP

process of PET to predict the influence of particle

shape, size, temperature, etc. on the polycondensation

process for all the operational regimes (reaction rate-,

diffusion- or diffusion and reaction rate-controlled

process). In order to analyze the mechanism of the SSP

process for PET, Gao et al. [101] proposed a semi-

analytical method, which showed that the overall

reaction rate for a single PET pellet can be appro-

priately simulated by a model controlled jointly by

diffusion and reaction rates. The same conclusion was

reached by Tang et al. [118] who proposed a single

dimensional model to seek a solution for the SSP


process and analyze its mechanism. They also found

that from the core to the surface, the SSP rate increases

monotonically due to a gradual reduction of the

concentration of by-products. Another model, devel-

oped by Goodner et al. [77] assumes that diffusion of

the reaction condensate in the solid polymer is the rate-

limiting step in the overall polymerization kinetics.

This equilibrium model provides an upper bound on

molecular weight and its rate of increase, as well as a

useful tool for understanding the effects of temperature

and particle size. A quantitative prediction in the effect

of temperature, particle size, starting molecular weight

and ratio of end-groups on theDP is also possible using

a comprehensive model developed by Wu et al. [86],

based on an analysis of the similarities and differences

between solid state and melt polymerizations. More-

over, the effects of temperature and chain entangle-

ment on chainmobilitywere considered byKang [119]

to estimate the rate constants of nine chemical

reactions occurring during the SSP of PET. Kang

applied the free volume theory to diffusion of the

volatile by-products, and formulated an ordinary

differential equation to calculate the mass transfer

rate of these. Finally, Kim et al. [120], based on Kang

simulation [119], suggested a model, to predict the

concentrations of hydroxyl, carboxyl, vinyl ester

end groups and terephthalic acid monomer in the

resulting PET.

Gostoli et al. [89] modeled the SSP of PBT, taking

into account five chemical reactions, and the diffusion

of three volatile species. They found that the

molecular weight increases and reaches a maximum,

which strongly depends on the water diffusivity. At

longer times an asymptotic value is reached due to the

acidolysis reaction, in competition with thermal

degradation. A few years later, based on the data

obtained through their first model, the same research-

ers [98] reported a quantitative mathematical descrip-

tion for the SSP of PBT, which helped them to analyze

the influence of the initial number-average molecular

weight, the initial ratio between hydroxyl and

carboxyl end group concentrations and the sample

thickness. The models of Wang et al. [85], Devotta et

al. [72], Ravindranath et al. [15] and the model of

Kulkarni et al. [81] can also be used to analyze the

SSP of PBT.

The models developed by Goodner et al. [77] and

by Devotta et al. [72] can be used for analyzing

the SSP process for BPA-PC. In addition, Goodner et

al. [90] developed a model describing the melt phase

polycondensation kinetics of polycarbonate, which

was then applied to the SSP of an individual spherical

particle. The model includes the diffusion of the by-

product (phenol) in the particle, and tracks the

evolution of the molecular weight as a function of

both the process conditions (time, temperature, and

initial crystallinity and molecular weight) and the

properties of the system (rate constants, equilibrium

constant and phenol diffusion coefficient).

5. SSP and molecular weight distribution

Using a statistical method and assuming equal

reactivity of the functional groups, and the absence of

intramolecular reaction or other side reactions, Flory

[114,121] came to the conclusion that during a typical

linear step-polymerization the molecular weight

distribution (MWD) widens and the polydispersity

index (PDI) reaches a value of 2 when the fractional

conversion (p) is close to 1. On the other hand,

Korshak [3] claims narrowing of the MWD due to

degradation reactions, to which the longest molecules

are especially liable. In particular, for SSP reactions,

the interaction between the reaction kinetics and the

MWD should be emphasized. At very low values of

the forward kinetic constant (kf), the reaction is

kinetically limited, the condensate produced quickly

diffuses out of the polymer particle and the overall

polydispersity barely increases. If the forward reac-

tion kinetics is increased, diffusion limitations start to

manifest, causing a radial condensate concentration

gradient in the particle. This gradient causes a

gradient in the local MW, which in turns leads to a

broadened MWD over the particle as a whole, as

evidenced by the drastic increase of the overall

polydispersity [77].

In agreement with the aforementioned approaches,

different polymerization conditions resulting in a

variety of MWD data are presented in the following.

Feldmann and Feinauer [122] investigated the SSP of

polylaurolactam (PA-12) and reported an unstable,

broad MWD. In their study on SSP of PA-4,6 in a

fluidized bed reactor, Gaymans and Schuijer [19]

concluded that the SSP process is not susceptible to

MWD broadening. On the other hand, Fakirov [28]


found that SSP of PA-6 fibers under vacuum resulted

in narrowing of the molecular weight distribution.

Furthermore, Kulkarni and Gupta [81] found that

during the SSP of PA-6 the average PDI rises rapidly

at first, and then increases more gradually to values

above 2.0. In the SSP of PET, Cha [123] found a

broader than most probable MWD. Mallon and Ray

[51] also reported the variability of molecular weight

in a PBT particle after SSP, which causes the overall

polydispersity to increase dramatically, and men-

tioned that similar results should be expected for PET.

It must be emphasized at this point that the shape of a

distribution function usually depends on the polym-

erization conditions as well, which differed in all of

the examples above.

Meyer reported that broadening of the MWD may

be due to the fact that equilibrium is not achieved in a

typical SSP process and, as a result, reactions of

additional polycondensation keep occurring [124].

Zimmerman [49] attributes the same effect to a

microscopic nonuniformity of the solid reagent,

where the polymer chains present a distribution of

crystallite sizes. Furthermore, the observed variation

of Mn with location in the solid pellet of PA-6 leads to

values of PDI above the normal value of 2.0 [81].

Especially for polyesters, Mallon and Ray [51]

mention that the diffusion of the by-product is

sufficiently slow and a particles outer regions have

lower local concentrations of the diffusant than do the

interior points. This feature for reactions close to

equilibrium means that the effective polymerization

rate at the exterior is greater, and the nonuniformity in

average Mn across the particle radius leads to

increased polydispersity. This is also the case for

BPA-PC [73], for which the broadening of MWD is

attributed to the slow diffusion of the by-product

(phenol) inside the polymer particle.

Another explanation for the broadening of MWD,

based on the operating problems of the different kinds

of reactors used during SSP, is given by Mallon and

Ray [57], as follows: In the case of a moving packed

bed reactor, the uneven flow of polymer particles

leading to a variation in residence times, the uneven

flow of purge gas resulting in differing mass transfer

rates, and the uneven radial temperature distribution

across the reactor giving a range of particle reaction/

diffusion rates and gas-solid mass transfer rates, lead

to spread of molecular weights. In the case of

a fluidized bed reactor, the very broad residence

time distribution results in a very broad MWD under

reaction-controlled conditions. However, with appro-

priate operation changes, these problems may be

overcome somewhat. For example, in the case of PET,

one can use a purge gas that contains increased

condensate level, decreasing in this way the variation

on the molecular weight inside a particle, since areas

of high MW will be inhibited from further polym-

erization while areas of low MWwill still polymerize.

An explanation for the reported MWD narrowing

is based on the fact that certain prepolymers contain

relatively large amounts of monomer and oligomers.

During SSP, these volatile residues are eliminated

along with the reaction by-product, leading to

narrowing of the MWD [42,99].

Based on the considerations given above, the more

important parameters mentioned to affect the evol-

ution of MWD during SSP may be highlighted. First

of all is the particles size, a decrease of which leads to

narrowing of the MWD [73,90,99], as a result of

enhanced by-product diffusion. For example, in the

case of BPA-PC SSP [73], the PDI of powder

remained just below 2, meanwhile the value for

polymer beads (dmeanZ3.6 mm) was as high as 2.6.

Secondly, the stoichiometry is a significant factor:

according to Goodner et al. [125], as the rate of

polymerization decreases due to the nonstoichio-

metric ratio of end groups, more time is available

for condensate removal from the polymer particles,

and its concentration gradient inside the particles

becomes less severe. So, if a less polydisperse

material is needed and reducing the particle size is

not an option, stoichiometry may be used to minimize

the adverse effects of slow mass transfer. Xie [99] also

reported that, in the case of PA-6, the PDI decreases

with an increase of the reaction temperature, and/or an

increase of the initial water concentration, and/or a

decrease of the initial polymerization degree of the

polymer, and/or an increase of the concentration of

the monomer.

6. Conclusions

Solid State Polymerization (SSP) may be applied

with polycondensation polymers, e.g. polyamides and

polyesters, in order to increase the degree of


polymerization and to improve the quality of the end

product. The most important commercial advantages

of SSP focus on the use of easy and inexpensive

equipment, and on avoiding some of the drawbacks of

conventional polymerization processes.

A significant amount of literature on SSP has been

accumulated during the last 50 years and may be

classified to experimental and theoretical data includ-

ing simulation aspects: in both cases the scope is to

assess the importance of each possible process factor,

to suggest a relative mechanism, to predict SSP

behavior and finally to optimize the overall procedure.

Because of the complexity of the process, different

experimental conditions lead to different conclusions,

often contradictory, which reveal that the chemical

and physical process involves a variety of reaction

parameters. This article provides a background to

determine the impact of each parameter and to

correlate it to the reaction mechanism. Among these

parameters, the reaction temperature may be high-

lighted as the most important, since the temperature

coefficient of the SSP reaction is rather high. The

particles size, crystallinity, initial molecular weight of

the SSP starting material and the polycondensation

by-product formed greatly influence the reaction rate

and determine the controlling step of the process.

On the other hand, it seems that the central issue

today involves means to overcome the main drawback

of SSP, i.e. the slow rate compared to melt

polymerization. Therefore, the use of catalysts in

SSP comprises an important research topic, with

breakthroughs needed to devise methods to obtain a

uniform catalysis mechanism. This will result in

further industrial application,and boost the use of SSP

based processes. Of course, research concerning all

other aforementioned aspects of SSP should be

continued and enhanced in the future to fully under-

stand and establish this promising technology.

Acknowledgements

The authors wish to thank E. Barabouti and

S. Christou for their significant contribution to the

literature survey and Christos Tsenoglou for his help

and support. We would like to thank also Joe Weber

and David Marks for useful discussions within the

frame of an on-going research interaction between

NTUA and INVISTA, Inc. (former DuPont Textiles

and Intermediates, Inc.).

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