I AD-ft 43 22 6 T NE TR NSFOR NTION OF LIQUID TO AORPHO JS SOLID: THE illF TINE TO VITRIFY FOR..CU) PRINCETON UNIV NJ DEPT OFI CHEMICAL ENGINEERING M T ARONNIME ET AL. JUN 64 TR-l

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OFFICE OF NAVAL RESEARCH

Contract NO0014-84-K-0021

TECHNICAL REPORT NO. 1

THE TRANSFORMATION OF LIQUID TO AMORPHOUS SOLID:

THE TIME TO VITRIFY FOR STYRENE POLYMERIZATION

by

Marc T. Aronhime and John K. Gillham

for publication in

Journal of Applied Polymer Science

PRINCETON UNIVERSITYPolymer Materials Program

Department of Chemical EngineeringPrinceton, New Jersey 08544

June 1984

Reproduction in whole or in part is permitted forany purpose of the United States Government

This document has been approved for public release and sale;its distribution is unlimited

DTICPrincipal Investigator ELECTE

John K. Gillham JUL 1 9 19C(609) 452-4694C-2,

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84 07 13 003

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4. TITLE (and Subtitie) S. TYPE OF REPORT & PERIOD COVERED

The Transformation of Liquid to Amorphous Solid: April 1984 - June 1984The Time to Vitrify for Styrene Polymerization

6. PERFORMING ORG. REPORT NUMBIER

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Marc T. Aronhime and John K. Gillham N00014-84-K-0021

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASKAREA & WORK UNIT NUMBERS

Polymer Materials ProgramDepartment of Chemical EngineeringPrinceton University, Princeton, NJ 08544

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IS. SUPPLEMENTARY NOTES

It. (EY WORDS (Continue on ,ove&e aide iinscea a'y and Identtf by block nmber)Time-Temperature-Transformation Cure DiagramsVitrification KineticsPolymerization ConversionStyrene Glass TransitionR.Polystyrenedot

... ABSTRACT (Continue an revered aide If no ,aae and Identify by block Bmber)

> A model is presented for the calculation of the time to vitrify versustemperature for isothermal polymerization by the chain growth mechanism. Themodel is based on the glass transition temperature (Tg) rising from its initialvalue to the reaction temperature. The relationships between Tg' and the volumffraction of polymer and monomer, the volume fraction of polymer and the extentof reaction, and the extent of reaction and time, are also required. In a ploof temperature versus time the vitrification curve is S-shaped; tt! ttme

DD, FOANI. 1473 EDITION OF I NOV 6S IS OBSOLETES/N 0102 6014-6601 SECURITY CL.ASSIIlCATION OF THiSl PAGE (Whet Date Saterud)

S t-JqIITY CLASSIFICATION OF THIS PAGFeI7(We Data Entered)

passes through a maxlmum just above the glass transition temperature of theunreacted monomer and passes through a minimum just below the maximum glasstransition temperature. The model applies to linear polymerization in whichmonomer and high molecular weight polymer are the dominant species, i.e., tochain reactions. In this communication the model is applied to the bulkpolymerization of styrene by the free radical mechanism.

SICURITY CLASSIPICATION OF THIS PAGEMfU6h1 Data EntereEd)

THE TRANSFORMATION OF LIQUID TO AMORPHOUS SOLID:THE TIME TO VITRIFY FOR STYRENE POLYMERIZATION

M. T. Aronhime and J. K. GilihamPolymer Materials Program

Department of Chemical EngineeringPrinceton University

Princeton, New Jersey 08544

SYNOPSIS

A model is presented for the calculation of the time to vitrify versus tem-

perature for isothermal polymerization by the chain growth mechanism. The model

is based on the glass transition temperature (Tg) rising from its initial value

to the reaction temperature. The relationships between Tgand the volume frac-

tion of polymer and monomer, the volume fraction of polymer and the extent of

reaction, and the extent of reaction and time, are also required. In a plot of

temperature versus time the vitrification curve is S-shaped; the time passes

through a maximum just above the glass transition temperature of the unreacted

monomer and passes through a minimum just below the maximum glass transition

temperature. The model applies to linear polymerization in which monomer and

high molecular weight polymer are the dominant species, i.e., to chain reac-

tions. In this communication the model is applied to the bulk polymerization of

styrene by the free radical mechanism.

INTRODUCTION

The transformation by chemical reaction of low molecular weight liquid into

high molecular weight amorphous solid pol.ymer is a fundamental process in the

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coatings, adhesives and thermoset industries. As the chemical reaction pro-

ceeds, the molecular weight and glass transition temperature (Tg) increase and,

if the reaction is carried out below the maximum glass transition temperature

(Tgp), the Tg will eventually reach the reaction temperature. Vitrification is

defikied to occur when the glass transition temperature becomes equal to the tem-

perature of reaction. A search of the literature for experimental data reveals

that the determination of the time to vitrification has scarcely been studied.

The purpose of this report is to extend a model which has been developed for

thermosetting systems (1,2,3) to calculate the time to vitrify for linear

isothermal polymerizations. Vitrification is important not only because the

material turns to a solid, but because the chemical reaction is quenched and so

limiting conversions are reached when reacting below Tgp. The limiting conver-

sions obtained at vitrification are also computed. (In practice Tg is generally

greater than the cure temperature only because of an inconsistency in the defi-

nition of Tg with respect to the quenching of chemical reactions.)

Previous results have shown that in the context of a time-temperature-

transformation (TTT) cure diagram for thermosetting materials undergoing step-

growth polymerization, the reaction temperature versus time to vitrification is

an S-shaped curve (1,2). The present work will test the generality of the S-

shaped vitrification curve of the TTT diagram by examining a linear system, in

particular, the free radical polymerization of styrene. The linear case for

step-growth polymerization and the non-linear case for chain-growth polymeriza-

tion are under investigation.

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MODEL

In order to calculate the time to vitrify at a given temperature for linear

chain-growth polymerization, several relationships are needed in addition to the

criterion that the glass transition temperature equals the temperature of reac-

tion. These relationships are:

i) Tg versus volume fraction of polymer;

ii) volume fraction of polymer versus extent of reaction; and

iii) extent of reaction versus time.

This model differs from previous work (2,3) in that the relationship be-

tween T and extent of reaction at Tg will be derived from more fundamental con-

cepts, rather than assuming an empirical relationship between Tg and extent of

reaction. The conversion at vitrification can be calculated directly from free

volume concepts for binary mixtures since in chain polymerization monomer and

high molecular weight polymer are the dominant species. Contributions by other

species (e.g., initiator) are neglected in this communication.

From free volume theory (4,5,6), the glass transition temperature,

T = ctPTgp + %0- )T (1)g Op + %(1- p)

where a = difference between the volume coefficients of expansion of liquid and

glass, = volume fraction, and the subscripts p and m refer to polymer and

monomer, respectively. Rearranging Eq. 1, the volume fraction of polymer,

wp a % g (2)

S p(Tg-Tqp) + %(Tgm-Tg)Ig

4-

By considering a simple mass balance of monomer and polymer, *p can be

written in terms of the extent of reaction p:

P/Pp (3)

P , [(1-P)pml + PP

where p = density. This relationship assumes volume additivity for mixtures of

monomer and polymer. Thus, the free volume model allows for the determination

of the extent of reaction at vitrification for any temperature between Tgm and

T gp since

p (4)

= (pM/p)[(11) - 1] + 1

Using values of pm = 0.90 gm/ml, pp = 1.05 gm/ml, 0. = 11.7 x 10-4/0C (7), '=

5.5 x 10- 4/.C (7), Tgp = 100 0C, and Tgm = -100 0C (assumed), a plot of the pre-

dicted values of p at Tg from Eq. 4 and Eq. 2 is shown in Fig. 1. For simpli-

city pm and pp were taken to be independent of temperature.

A reaction mechanism and the appropriate kinetics are required in order to

calculate the time to vitrification. The rate of polymeriation of styrene,

using a free radical initiator and considering termination by combination only,

is (8,9)

Rp - -d[M]/dt = k pM](fk d[1)/kt )1/2 (5)

where 1M] 1 monomer concentration, f - initiator efficiency, (I)= initiator

L

OVA.~

-5-

concentration, and kp, kd, kt = propagation, initiator decomposition, and ter-

mination rate constants, respectively. Considering first order decomposition of

the initiator, and from [M] = [M] 0 (1-p), then from Eq. 5,

-1n(l-p) = 2k p(f[I] /kdkt )/ 2 [l-exp(-kdt/2)] (6)

where [M] o = initial monomer concentration and [I]o = initial initiator con-

centration. The following model parameters are used (8):

[M]o = 8.65 mole/X

[I] o = 0.10 mole/1

f = 0.5

kp = (1.62 x 1010i/mole-hr)exp(-6.21 kcal mole-1/RT)

kt = (2.088 x 1011it/mole-hr)exp(-1.91 kcal mole-I/RT)

kd (benzoyl peroxide) = (2.725 x 1017 hr-1 )exp(-29.71 kcal mole-I/RT).

It is assumed that kp, kt, and kd are independent of extent of reaction, i.e.,

the reactions are not diffusion-controlled until vitrification occurs.

Figure 2 is a plot of reaction temperature versus time to vitrification,

obtained by solving Eq. 6 for t, once p is known. The S-shaped vitrification

curve is evident, although due to the nature of the kinetic mechanism the vitri-

fication times at low temperatures are physically unrealizable.

ACKNOWLEDGMENT

Appreciation for financial support is extended to the Office of Naval

Research and the Paint Research Institute.

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REFERENCES

1 J. K. Gillham, in Developments in Polymer Characterisation-3, J. V.Dawkins, Ed., Applied Science, London, 1982, Ch. 5.

2. J. B. Enns and J. K. Gillham, J. Appl. Polym. Sci., 28, 2567 (1983).

3. H. E. Adabbo and R. J. J. Williams, J. Appl. Polym. Sci., 27, 1327 (1982).

4. F. Bueche, Physical Properties of Polymers, Interscience Publishers, NewYork, 1962, p.116.

5. K. Horie, I. Mita, and H. Kambe, J. Polym. Sci., A-1, 6, 2663 (1968).

6. D. C. Sundberg and D. R. James, J. Polym. Sci.: Polym. Chem. Ed., 16, 523(1978).

7. To G. Fox and S. Loshaek, J. Polym. Sci., 15, 371 (1955).

8. G. Odian, Principles of Polymerization, 2nd. ed., John Wiley and Sons, NewYork, 1981.

9. So L. Rosen, Fundamental Principles of Polymeric Materials for Practicing

Engineers, Barnes & Noble, Inc., New York, 1982.

FIGURE CAPTIONS

Fig. 1 Extent of reaction at vitrification vs. reaction temperature forlinear, free radical polymerization of styrene. See text for modelparameters.

Fig. 2 Reaction temperature vs. time to vitrify for linear, free radicalpolymerization of styrene: Tgp = 100*C, Tgm = -100*C (assumed). Forother model parameters, see text. Equation 6 is solved from-99.999999950C to +99.99950C.

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