The volume requirements of polymer molecules. I. The apparent specific volume of polystyrene in solution

THE VOLUME REQUIREMENTS OF POLYMER MOLECULES. i. THE APPARENT SPECIFIC VOLUME OF POLYSTYRENE IN SOLUTION Wilfried Heller and Arthur C. Thompson Chemistry Department, Wayne University, Detroit, Michigan Received December 18, 1950

INTRODUCTION

The apparent specific volume of polymers in solution is of interest for several reasons. Its probable variation with the nature of the solvent is bound to reflect the respective variation of the empirical interaction constant, #. An isothermal comparison between the apparent specific volume of a polymer in solution and the specific volume of the same polymer in the liquid state should give immediate information on the sign and on the relative magnitude of the heat of mixing. An isothermal comparison between dissolved and solid polymer below the temperature of an apparent second-order transition should yield information on the nature of this transition. An investigation of the apparent specific volume as a function of polymer concentration might provide a criterion for the assumption of configurational changes of polymer molecules during the transition from moderately concentrated to highly dilute solutions (6). In view of this variety of promising aspects, it is surprising that only very few accurate data are available in the literature on the apparent specific volume of polymers in solution. This is particularly true for polystyrene, one of the favored models in polymer research. In connection with their ultracentrifugal studies, Signer and Gross (12) carried out pycnometric density determinations on solutions of polystyrene of varied molecular weight and concentration in chloroform and in six other solvents. The partial specific volume obtained--apparently pertinent to 20 °O.-varied between 0.88 and 0.91 cm.3g.-1. Unfortunately, however, the error varied between -~0.01 and ±0.05 so that no distinct trend can be detected for any one of the variables. The authors give 0.91 cm.Sg. -I as the characteristic value and they conclude that this value is identical with the specific volume of solid polystyrene. In connection with his extensive viscosity measurements on polystyrene solutions in benzene, Danes (4) carried out a large number of measurements on the solution density relaI Present address: Department of Physica| Sciences, University of Idaho, Moscow, Idaho. 57

58

~VILFRIED HELLER AND ARTHUR C. THOMPSON

tire to benzene. No attempt was made, however, to use these data for evaluating the apparent specific volume or the apparent density of the polymer or of the solvent. An analysis of his data from this point of view, together with a comparative analysis of the intrinsic viscosities derived, will be given in a sequence to the present paper. It will be seen that, on varying concentration, temperature, and molecular weight, the apparent specific volume varies between 0.919 and 0.938 in a partially errati6 and a partially systematic manner. In connection with their swelling Studies on polystyrene, Boyer and Spencer (1) compiled data for the partial density of polystyrene in toluene, which, if converted to partial specific volumes (13) yield the values of 0.909, 0.913, and 0.918 at 0, 20, and 40°C:, respectively, omitting the fourth and fifth decimal places. There are, finally, a few interesting dilatometric data by Breitenbach and Franck (3), which we will have occasion to discuss extensively. The present paper gives a few preliminary results on the apparent specific volume of polystyrene in solution as derived from precise density measurements. The main emphasis is placed on their significance with respect to the problem of the apparent second-order transition of polymers and to the problem of solvent-solute interaction. I.

T H E DERIVATION OF APPARENT SPECIFIC VOLUMES FROM DENSITY ~.[EASUREMENTS

The generally favored equation for calculating the apparent specific volume of a solute, ~2, is based upon the statement of fact that 1

-- = P12

¢12 = cl ~1 +

c2 ~2,

[1]

where ¢1 is the specific volume of the pure solvent, ~bl~the specific volume of the solution, p12 its density, and c is the weight fraction. On rearrangement C2

The related statement V12 = V1 + V2,

[2]

where V is the absolute volume, gives on rearrangement ~2 =

[2a]

¢12 -- ~I ._~ (~1, c

which yields Ap ~2 = Pi p12 C~

q_ i p'~i =

Ap ~Pl C2

q_ i p'-~i'

[2b7

APPARENT

SPECIFIC

VOLUME

OF POLYSTYRENE

59

where Ap = @1 - p12) and c2' is the solute concentration in grams per cubic centimeter of solution. E q u a t i o n [2b] is used t h r o u g h o u t the present work. Equations [ l a ] and F2b] have in common t h a t the specific volume of the solvent in solution must be assumed to be identical with t h a t of the pure solvent, a requirement which gives to the derived 42 the character of an apparent quantity. Any change in 42 as a function of an experimental variable is therefore subject to several interpretations: I t m a y be due (a) to a true change in the space requirement of the solute molecules or it m a y be due, instead, (b) to a change in the space requirement of the solvent molecules immediately adjacent to, adsorbed by, or pervading the solute molecules, the latter possibility applying only to nonrigid polymer molecules. Finally, (c) again in the case of nonrigid polymer molecules, one m a y have to deal with a change in the n u m b e r of unoccupied spaces inside the molecule. In contradistinction, a change in the n u m b e r of unoccupied spaces in volume elements containing solvent only, can be discounted as experimentally undetectable except on selecting temperature as the experimental variable. If sufficient data are available on the variation of ¢12 with c~, an alternate solution is possible. As shown b y Lewis and Randall (9), the partial specific volume d ¢12 d ¢12 ,72 = O ¢12 = ¢12 -- cl - ¢12 + c2 {-3] a c2 d c~ d cl It will be seen from our data that, at least for c >0.01, ¢2 is practically identical with the thermodynamically more significant ~:. As regards the interpretation of changes in P-2, the situation is identical with t h a t outlined for ~2. Still another equation, based on the evident fact of weight additivity,

W12 =

W1 +

W2

[4]

v2p2

F4a]

pl,

[-4b]

yielding p12 = v l p l +

or, transformed p2

Ap' =

- -

+

?)2

where v is the volume fraction and Ap' = @12 - pl), is of no particular use for the immediate purpose, b u t is of interest for calculating, from the density data, the apparent volume fraction of the solute v~ = Ap/ ¢1

-

-

¢2"

It is apparent t h a t the type and number of pycnometric density measurements to be carried out depend on the equation to be used. Equation

60

WILFRIED HELLER AND ARTHUR C. THOMPSON

E3] r e q u i r e s o n l y t h e d e t e r m i n a t i o n of ¢12, b u t d e t e r m i n a t i o n s a t v a r i e d c2 a r e n e c e s s a r y in o r d e r t o a r r i v e a t a sufficiently well defined v a l u e of 75 c h a r a c t e r i s t i c for a g i v e n c~. T h e n u m b e r of n e c e s s a r y d e t e r m i n a t i o n s i n c r e a s e s w i t h t h e d e v i a t i o n of ¢12 (c) f r o m a s t r a i g h t line. B y c o n t r a d i s t i n c t i o n , E q . [25 t does n o t r e q u i r e m o r e t h a n one set of d a t a for a g i v e n e~, b u t i t is n e c e s s a r y t o d e t e r m i n e e i t h e r b o t h ¢12 a n d ¢1, or t h e difference (¢1 - ¢12). I n t h e l a t t e r case, it is sufficient t o k n o w ¢1 w i t h a m o d e r a t e d e g r e e of a c c u r a c y , i.e., t h e n u m b e r of s i g n i f i c a n t figures for ¢1 does n o t n e e d t o e x c e e d b y m o r e t h a n one t h e n u m b e r of s i g n i f i c a n t figures w a n t e d for ¢5. T h e p r e s e n t , p r e l i m i n a r y , d a t a were o b t a i n e d b y t h e c o n v e n t i o n a l m e t h o d of i n d i v i d u a l p y c n o m e t r i c d e n s i t y m e a s u r e m e n t s , b u t t h e o b v i o u s a d v a n t a g e s of t h e d i f f e r e n t i a l m e t h o d i n v i t e its s u b s t i t u t i o n in t h e f o r t h c o m i n g e x t e n s i o n of t h e p r e s e n t work.

II.

EXPERIMENTAL

1. Precision Requi~:ements The literature data quoted show that it is desirable to obtain three significant figures for the apparent specific volume; only then is the effect of experimental variables apt to show up clearly. This defines the necessary accuracy of both absolute and differential density determinations. Discussing here in detail only the former, more exacting, method, it is required that the uncertainty in individual density measurements in, say, 1% solutions be limited to the sixth decimal place if the density difference between solvent and solute is 0.1. It is, therefore, necessary to provide a sufficiently large value for (p~ - - p~) if exploration of more dilute solutions is intended. This was done by selecting, for the more precise work, bromobenzene as the solvent. The value of (pl - p~) is here 0.40. This value is so much larger than in the former instance that it is possible, witl~ the exception of highly dilute solutions, to aim for six significant decimal l~laces. It is necessary for this purpose that both the weight and the volume in pyenometers of practical size and capacity (25 cc.) be determined with an individual error not in excess of =i=2.5 X 10-5 g. and cc., respectively.

21 Volume Determinations The pycnometers used held slightly more than 25 cc. of liquid. They were of the bicapillary type (Fig, 1). The main body of the pycnometers was spherical which is preferable to the conventional, more strained fiat-bottom type. The capillaries were calibrated with a traveling microscope by the conventional method of moving a small mercury column stepwise along their entire length. The pycnometers were filled by injection with a medical syringe until each of the two menisci was near a horizontal razor mark on each capillary. After complete thermal equilibrium had been established, the height difference between each meniscus and the respective mark was determined by means of a cathetometer reading to ± 0.01 ram. The error in volume measurements by this technique was defined by ±1.5 X 10-5 cc.

3. Weight Determinations The apparent weight of the pycnometers was determined with a semimicrobalance whose sensitivity at full load amounted to 4-1.5 X 10-~ g. The conversion to true weights followed the well-known conventional procedure (application of the four different buoyancy corrections pertinent in the present instance and equalization of the surface moisture

A P P A R E N T S P E C I F I C VOLUME OF P O L Y S T Y R E N E

61

film on filled a n d t a r e p y c n o m e t e r ) . I t is worthwhile adding t h a t most of the very critical buoyancy corrections would cancel in the case of differential measurements.

4. Temperature Control I n view of the large cubic expansion coefficient of organic liquids, a rigorous temperature control was necessary, an inconvenience which would be largely eliminated by the differential method. A volume of 25 cc. of bromobenzene, for instance, increases b y 2.3 X 10-5 cc. if the temperature increases from 25.000 to 25.001°C. I t was, therefore, necessary to keep the temperature fluctuations in the pycnometers below this value and to reproduce in each experiment the temperature within the limits of accuracy of a Beckman thermometer read with the cathetometer mentioned above. A thermoregulator of sufficiently high sensitivity and sufficiently low inertia was obtained by winding 800

FIG. 1. Pycnometer. cin. of thin-walled glass tubing, with a capacity for approximately 3 kg. of mercury, to a spiral of approximately 40 cm. diameter which terminated in a narrow capillary. The temperature fluctuations in the well-insulated thermostat, heated with a carbon-filament lamp of low heat capacity, were too small to be detectable with the Beckman thermometer. Considering the difference in heat capacity of the mercury in the thermometer and of the polymer solution in the pycnometer and taking into account the mass differences, it followed t h a t the temperature fluctuations inside the pyenometer were well below 0.001 °C., discounting even the additional favorable fact of a pronounced difference in heat conductance. All the following experiments were carried out at 25.00 4- 0.001°C. The omission of a third decimal place means that, while it is a significant relative figure, its absolute value is not known.

62

W I L F R I E D H E L L E R A N D A R T H U R C. THOMPSON

5. Precision Achieved The total error for density measurements with a given pycnometer derives as slightly less than :I: 1 X 10-6. The actual error found, on very careful work, was not in excess of :i:2.5 X 10-6, the difference being due most likely to uncertainites in the buoyancy corrections. The use of a single pycnometer for all measurements introduces a slight systematic error of unknown m£gnitude. All experiments were, therefore, carried out with two or, if advisable, with three pycnometers. The mean values obtained with different pycnometers did, on careful work, not differ by more than 4-4 × 10-6. An example is given in Table I. The limits of.error to be given in the Tables are defined as the mean deviation of the mean results obtained from different pycnometers. III. THE

APPARENT

SPECIFIC

VOLUME

IN C H L O R O B E N Z E N E

OF POLYSTYRENE

SOLUTION

U n f r a c t i o n a t e d D o w p o l y s t y r e n e was purified b y reprecipitation f r o m a solution in dioxane. T o this effect, the solution was e x t r u d e d f r o m a medical syringe into c o n t i n u o u s l y a g i t a t e d water. T h e finely divided precipitate obtained was easy to dry to constant weight. Chlorobenzene,

preferred to benzene because of its lower vapor pressure, was purified by TABLE I

Sample of Actual Density Data Obtained in Bromobenzene Solution / ~ of polystyrene = 356,000; T = 25.00°C.; c = 0.007535 g./g.; c': 0.011165 g./cc. Pycnometer

P12

P12

II

1.481740 1.481735

1.481737

III III

1.481732 1.481735

1.481733

IV IV

1.481730 1.481728

1.481729

• II

1.481733 ::i=0.O00004

fractional crystallization a n d s u b s e q u e n t distillation. T h e d e n s i t y of the final p r o d u c t was 1.101023 (25.00°C.). (This a n d all o t h e r d e n s i t y d a t a are relative t o w a t e r at 4°C.) T h e t h r e e solutions i n v e s t i g a t e d cover a c o n c e n t r a t i o n range f r o m 1.0-5.2 g. of p o l y m e r / 1 0 0 co. of solution. T h e y were m a d e u p b y weighing, t o within 4-0.2 rag., first t h e d r y p o l y m e r a n d s u b s e q u e n t l y t h e solution. T h e weight fractions, c, are, therefore, t h e p r i m a r y c o n c e n t r a t i o n data. T h e a p p a r e n t specific v o l u m e s o b t a i n e d are compiled in T a b l e I I . T h e y are, in a first a p p r o x i m a t i o n , c o n s t a n t w i t h i n the c o n c e n t r a t i o n r a n g e i n v e s t i g a t e d a n d w a r r a n t therefore t h e c o m p i l a t i o n of a m e a n value for this range. H o w e v e r , an e x a m i n a t i o n of t h e individual d a t a clearly indicates a v e r y slight, b u t definite, increase of t h e a p p a r e n t specific v o l u m e w i t h decreasing c o n c e n t r a t i o n , disregarding t h e d a t a p e r t i n e n t t o t h e low-

APPARENT

SPECIFIC

VOLUME

63

OF POLYSTYRENE

TABLE II Apparent Specific Volume of Unfractionated Polystyrene a in Chlorobenzene Solution at 25.00°C. ¢2

Pycnometer

(Individualmean for respective pycnometer)

¢2

(Over-all mean)

0.00972 0.00972

0.01017 0.01017

III IV

0.924 0.92a

0.922 4- 0.002

0.02314 0.02314 0.02314

0.02547 0.02547 0.02547

II III IV

0.9227 0.9237 0.9227

0.9230 4- 0.0005

0.04734 0.04734

0.05208 0.05208

III IV

0.9217 0.920~

0.9213 4- <0.0004 0.922 -4- 0.002

From Dow Chemical Co. est concentration which are inconclusive in this regard because of the wider spread of the limits of error. IV. THE

SPECIFIC VOLUME OF POLYSTYRENE BROMOBENZENE SOLUTION

IN

In order to verify this slight concentration dependence of the apparent specific volume, bromobenzene was used in the subsequent set of experiments. The increase in experimental accuracy associated with the larger (pl -- p2) value warranted the use of a fractionated sample of polystyrene of definite molecular weight. A 5-g. sample of fractionated Dow polystyrene of 21~w -- 356,000 was kindly provided for this purpose by Dr. R. S. Spencer of the Dow Chemical Company, Midland, Michigan. The bromobenzene was the "Eimer and Amend Tested Purity Reagent" certified by the National Bureau of Standards. Its freezing point is given as -31.053 4- 0.002°C. I t was used without further purification. Its density was found to be 1.485909 at 25.00°C. The results, given in Table III, again indicate a slight increase in specific volume with decreasing concentration, which verifies this effect. A comparison between Tables II and I I I shows that the apparent specific volume of the unfractionated polystyrene in ehlorobenzene and of the high molecular weight fraction of it in bromobenzene, though nearly the same, differ by more than can be accounted for by the experimental error. This finding will be discussed somewhat later in connection with Table VI.

64

WILFRIED

HELLER

AND ARTHUR

C. T H O M P S O N

V. THE PROBLEM OF HIGHLY DILUTE SOLUTIONS As a solution of randomly kinked polymer molecules decreases in concentration, it changes from a continuous system to a discontinuous one. In the former case, there are polymer contacts t h r o u g h o u t the solution, in the latter case volume elements containing polymer and solvent alternate with elements containing solvent only. This transition should be expected (6) to occur in or near the range of concentrations investigated above. I t became therefore of particular interest to explore still more dilute solutions. Since the stock solutions prepared from the small sample of polystyrene had been used up during the preceding experiments, it became necessary to use either another fraction of-polystyrene or to re-use the saved contents of pycnometers which had been emptied and carefully rinsed repeatedly in order to avoid as much as possible a loss of polymer. The latter procedure was adopted since, at t h a t time, no sufficiently reliable information was available on the quantitative effect of molecular weight upon the apparent specific volume. The p y c n o m e t e r contents of the c = 0.007535 series were used for two independent secondary stock solutions of c = 0.004334 a n d c = 0.002016, respectively, and the p y c n o m e t e r contents of the c = 0.03207 series were used for two additional independent secondary stock solutions of c = 0.01788 and c = 0.009007, respectively. The concentrations of these secondary stock solutions also were determined by weighing, after proper dilution with bromobenzene. Figure 2 shows t h a t (pl - p12)/c is, in a good approximation, a constant over the whole range of concentrations considered, irrespective of whether the data originated from primary or secondary stock solutions. The apparTABLE III Apparent Specific Volume of Fractionated Polystyrene ~ (8/I~, = 356,000) in Bromobenzene Solution at 25.00°C.

c

c'

Pyenometer

~b3 (Mean for respective pycnometer)

¢: (Over-all mean)

0.007535 0.007535 0.0O7535

0.011165 0.011165 0.011165

II III IV

0.9254 0.923~ 0.9253

0.9247 ± 0.001

0.032067 0.032067 0.032067

0.047087 .0.047087 0.047087

II III IV

0.9230 0.923L 0.923z

0.9231 ::t=0.0001 0.924 ± 0.001

From Dow Chemical Co.

APPARENT SPECIFIC VOLUME OF POLYSTYRENE

POLYSTYRENE

//

,ooo

16.00

65

14.00 f2.00 ~_oIO.O0 i 8,00

c,Z

6.00 4-00 2.00

I

0.01

I

0.02

I

0.05

g~

FIG. 2. Density decrement, as a function of concentration in bromobenzene solutions of polystyrene. Mw: 356,000; T: 25.00°C.

ent specific volume, however, which is sensitive to differences in the higher decimals of the densities, is not a constant, but seems to rise with concentration at concentrations below 1%. This follows from Fig. 3 which gives the reciprocal, i.e., the apparent density of the polymer. This trend is opposite to that observed at concentrations in excess of 1%, and it is much stronger. It is therefore inviting to consider the concentration range characterized by a maximum in the apparent specific volume as the transition range in the sense pointed out above. However, in view of the fact that the data in highly dilute solutions were obtained with secondary stock solutions only, it is necessary to make due reservations and to await confirmation of the results, in this range, by additional experiments. V I . T H E ISOTHERMAL SPECIFIC VOLUMINA OF DISSOLVED AND

VIRTUAL LIQUID POLYSTYRENE >~T 25°C. In order to compare the apparent specific volume of dissolved polystyrene and the specific volume to be expected from bulk polystyrene if it could be obtained as a liquid at room temperature, advantage is taken of the results of Flory and Fox (7) obtained during their recent density studies on sharp polystyrene fractions between room temperature and 217°C. 2 In confirmation and extension of earlier results rsee the literature We are indebted to Professor Flory for making his data available to us prior to their publication.

66

WILFRIED

HELLER

AND

ARTHUR

C. T H O M P S O N

under Ref. (2)], these authors found that the specific volume of liquid polystyrene increases strictly linearly between the transition temperature and 160°C. They found, in addition, that the temperature coefficient of liquid polystyrene is independent of molecular weight, and they established a quantitative relation on the isothermal variation of the specific volume of liquid polystyrene with molecular weight. From the latter relation, it follows that the isothermal specific volume of a polystyrene of 21~r~ = 356,000 ought to differ by not more than 0.02% from that of a polystyrene of 21~r~ = ~. The former two findings allow, in addition, an extrapolation of the ¢(T) curve of liquid polystyrene of ~r~ = 356,000 to 25.00°C. The value obtained can be considered as practically identical

APPARENT DENSITY OF POLYSTYRENE IN BROMBENZENE S O L U T I O N - 2 5 . 0 0 " C

1.120 m • STOCK SOLUTIONS o DILUTIONS '

o,, 1.110 -

\

~1w : 3 5 6 , 0 0 0 1.100 -

,,o

L09C •

•

o

o

'

1.08C

I.O'tC

t

0.o,o

J

0.020

i

0.030

g cm-S

FIo. 3. The apparent density of polystyrene in bromobenzene solution; /~r: 356,000; T: 25.00°C. with the specific volume, at 25.00°C., of the corresponding virtual polystyren e liquid. The specific volume thus obtained for the virtual liquid agrees surprisingly well with the apparent specific volume of polystyrene in a 1-5% bromobenzene solution, the apparent difference being less than 0.5% (Table IV and Fig. 4). The true difference--on extrapolating t o 100% polystyrene--is bound to be somewhat larger due to the fact that the apparent specific Volume decreases slightly with increasing polymer concentration. In order to increase the significance of the comparison in Table IV and Fig. 4, it is important to have some information on the rate of change of the apparent specific volume of dissolved polystyrene with temperature. To this effect the numerous density data of Danes (4) were evaluated in this respect. A brief subsequent paper on this subject will show that these data, in spite of the appreciable scattering

APPARENT SPECIFIC VOLUME OF POLYSTYRENE

67

0.98

I 0,96

~//

o

o

/ /

rA'~PPAR E NT

,

TRANSITION

/ 0.94

--

/

/ /

6,) /

/ 0.92

-

I

/

/ DISSOLVED POLYSTYRENE (H 8, T h )

FULLY DRAWN CURVE: SPECtFIG VOLUME OF ]BULK POLYSTYRENE |ACCORDING TO FLORY

LAnO FOX,

l__

IF

M = ¢f

L

50

I00

A__ 150

T ~°C)

FIG. 4. The specific volume of solid, virtually liquid, and dissolved polystyrene.

of the results, allow the definite conclusion that the slope di~/dT, of polystyrene dissolved in benzene approximates satisfactorily the slope of the extrapolated data of Flory and Fox. It is, therefore, possible to state that, at temperatures below the transition point, the molecular space requirement of dissolved polystyrene, in a solvent of equal or similar cohesive energy density, is at least very similar to the molecular space requirement in a virtual liquid of bulk polystyrene. This agrees with the findings of Spencer and Gilmore (13) to the effect that the expansion coefficient of polystyrene in toluene closely approximates the "instantaneous" expansion coefficient of solid bulk polystyrene. It follows implicitly from the preceding result that the space requirements of polystyrene molecules in a good solvent are, in a first approximation, the same as in actual bulk polystyrene if the temperature of isothermal comparison is above the transition temperature. In order to genTABLE IV

Specific Volume of Polystyrene at 25.00°C. State of polymer

Actual bulk Virtual bulk (No transition on cooling of liquid) Dissolved in chlorobenzene Dissolved in bromobenzene

_~r~ m

-~ 100,000

Specific volume

Authors

100,000

0.957 0.927

Flory and Fox (7) Flory and Fox (7)

356,000 356,000

0.922=t=0.002 0.924=I=0.001

Heller and Thompson Heller and Thompson

68

WILFRIED I-IELLER AND ARTHUR C. THOMPSON

eralize, one may state that the isothermal volume occupied by a nonrigid polymer molecule is, in a first approximation, independent of whether it is surrounded and pervaded by identical molecules or by low-molecularweight solvent molecules provided that the cohesive energy density of the solvent is the same. It is clear that this represents supporting evidence in favor of the basic assumptions made by Flory and by Huggins in their thermodynamic treatment of polymer solutions. V I I . THE ISOTHERMAL SPECIFIC VOLUME OF DISSOLVED. AND SOLID POLYSTYRENE AT 25°C.

Signer and Gross (12) assumed that the partial specific volume of dissolved polystyrene is identical with that of solid polystyrene, Table IV and Fig. 4 show that such a general statement cannot be made. Using again data by Flory and Fox (7), the specific volume of solid polystyrene of ~r~ = 356,000 interpolates to 0.957 at 25.0°C. This value is more than 3% larger than that of isothermal dissolved polystyrene. The real difference is even somewhat larger due to the concentration dependence of the latter value. This result is of significance as regards the controversial nature of the apparent second-order transition. It should be expected that the specific volume of bubble-free, noncrystalline solid polystyrene is, at constant pressure, identical with the apparent specific volume of polystyrene dissolved in a solvent of equal cohesive energy density. The lack of identity suggests that solid polystyrene is not in a state of thermodynamic equilibrium which agrees with the point of view advanced by a few other authors rsee the reviews under Refs. (2) and (7)1. The large excess volume of more than 3% in solid polystyrene at room temperature apparently supports (13) and may be explained by the assumption of extensive cavities, e.g., ~of a network of capillaries across the solid. The second-order transition point would then represent the temperature of inception for these fissures. Possible reasons for their formation will be given presently. Significant, as to the nature of the transition, is the phenomenon oi volume relaxation, above the transition temperature, which is observed on change in temperature a t constant pressure. The rate of this process decreases rapidly as the transition temperature is approached (7). This shows that the system requires time to acquire its most probable state characteristic for the respective temperature, more so the lower the temperature. Since the molecules are mutually entangled, this means that a critical packing density is reached somewhat above the transition temperature, which imposes upon the system a measurable delay in quantatitarive eonfigurational rearrangement. On reducing the temperature further, a rearrangement in the configuration of neighboring chain segments of

A P P A R E N T S P E C I F I C VOLUME OF P O L Y S T Y R E N E

69

different molecules toward a state of higher probability is possible only whenever and wherever the dampened internal Brownian movement of the entire mass leads to local fluctuations in the potential barriers large enough to allow, in a given volume element, the necessary rotation or sequence of rotations about valence bonds. The probability of such an event (and still more that of translation of an entire molecule) will decrease rapidly with decreasing temperature. As a result, volume elements with more probable configurations of neighboring segments (of different molecules) will alternate with volume elements where the configurations are less probable. We propose to consider this quasi-permanent alternation of eonfigurational probability from volume element to volume element as the pertinent and characteristic property of state at and below the temperature of the apparent second-order transition. This alternation of configurational probability contrasts with the fluctuation of configurational probability in a given volume element of a true liquid which consists of the same entangled polymer molecules. Such a local alternation is equivalent to an alternation in density and, implicity, in cohesive energy. On application of a sufficient stress, the solid is therefore bound to shatter randomly along irregular internal areas, in contrast to crystals. A necessary consequence of an alternation in eonfigurational probability is the development of a "mierostrain" near the transition temperature, if a polymer molecule occupies, as it generally will, a sequence of volume elements. This microstrain should obviously decrease with decreasing molecular weight of a given polymer and it should also decrease with increasing molecular rigidity, i.e., with an increase in intramolecular steric hindrance to rotations about valence bonds. In either instance, the limiting case should be--and actually is--a strain-free first-order transition. This microstrain can, in general, lead only to an unsymmetrical strain in the entire system and it can therefore not be expected to produce birefringence. Such an unsymmetrical strain is apt to lead to localized internal ruptures, i,e. cavitation, in the system "frozen in" on a molecular scale. Some preliminary support for the occurrence of such ruptures by strain may be seen in the observation by Schallamach (11) that rapid cooling of rubber below the transition temperature was accompanied by a clicking noise, The simultaneous sharp drop in thermal conductivity (11)--which simulates a ~first-order transition--finds a very simple explanation on this basis. Limiting ourselves to only one additional example, it is clear that t h e concept of mierostrain and of concomitant cavitation allows also a ready explanation of brittleness and of its dependence on molecular weight, temperature, and polymer structure. The lack of symmetry of the strain can be removed partially by partial flow orientation of polymer chains prior to rapid cooling below the tran-

70

WILFRIED HELLER AND ARTHUR C. THOMPSON

sition temperature. This lowers (10), as expected, the transition temperature itself and it leads to an anisotropy of both cohesive energy and strain. The symmetry axis for either phenomenon should be defined by the direction of orientation, and one should expect that the system is uniaxial negative as regards the strain. This seems to be borne out by the well-known phenomenon of anisotropie brittleness of extruded polystyrene which shatters into a multitude of fibers when tested for brittleness. VIII. THE SIGNIFICANCE OF DILATOMETRIC VOLUME CHANGES" OBSERVED ON MIXING OF POLYMER AND SOLVENT

It is apparent from Fig. 4 that a volume contraction will occur whenever solid polystyrene is mixed with a good solvent at a temperature below the transition point. The observation of a volume change will, therefore, not have any thermodynamic significance unless it differs in magnitude or sign from that to be expected. According to Fig. 4, a minimum contraction of 0.037 cc./g, polystyrene is bound to occur on mixing solid polystyrene at room temperature with bromobenzene. A contraction of' this magnitude would indicate a zero heat of mixing rather than a positive heat of mixing. It is worthwhile to emphasize this point since the volume change observed on mixing of solid polymers with solvents has repeatedly been taken as a thermodynamic criterion. There are, obviously, two ways of excluding an ambiguity of dilatometric results: the best one is to study the effect of mixir~g above the transition temperature; the alternate one consists of an interpretation of dilatometric results on the basis of previously established ~(T) relationships ~ueh as given in Fig. 4. The usefulness of the latter procedure will be tested in the subsequent section. IX. THE EFFECT OF SOLVENTS UPON THE APPARENT SPECIFIC VOLUME OF POLYSTYRENE

Although the agreement between ~he apparent specific volume Of polystyrene in bromobenzene and the specific volume of virtually liquid polystyrene at 25°C. is quite close (Table IV), a definite, though small difference exists between the two values. The difference is larger than our experimental error. It would become still larger on extrapolating to a concentration of 100% 'of polystyrene. The difference is therefore significant on the assumption that the extrapolated temperature fur~ction of virtually liquid polystyrene is correct not only in a first, but also in a higher approximation. Granting this, the conclusion would be that either the space requirement (the number of vacant internal sites) of a polymer at equilibrium is slightly reduced in the presence of a good solvent of low molecular weight or that the solvent molecules immediately adjacent to or pervading the polymer molecules assume a slightly higher packing

APPARENT SPECIFIC VOLUME OF POLYSTYRENE

7]

density t h a n in the solute-free volume elements of the solution. The latter explanation is equivalent to assuming a slight solvation of the polymer molecules, and a minor positive heat of mixing even in a solvent of similar cohesive energy density. Since only the London dispersion forces are operative here, such an effect could not be very pronounced. This agrees with the smallness of the effect observed. The probability of such a solvent effect is supported by a p r o p e r e v a l u ation of dilatometric results obtained b y Breitenbach and Franck (3) on studying the volume changes during partial swelling of polystyrene (containing 0.12% p-divinylbenzene) in four solvents at 20°C. On converting their data to dimensions and units to fit those adopted here, one obtains a volume contraction of 0.056 ec./g, polymer for swelling in chloroform. This is 51% more t h a n one would expect on the basis of Fig. 4. Complete dissolution instead of partial swelling would probably lead to a still larger difference. In other words, the apparent specific v o l u m e at c = 0.03 is 2 0 . 9 0 1 which agrees with the direct data of Signer and Gross (j2) on pure polystyrene. There is therefore little doubt that a thermodynamic volume contraction occurs for this solvent-solute combination. It is now interesting t h a t the volume contraction observed in benzene amounts to only 0.008 cc./g, polymer. This is only slightly more than 20% of the n o n t h e r m o d y n a m i c volume contraction expected from Fig. 4 and it is equivalent t o an apparent specific volume of ~ 0.949 at c = 0.046. This value is larger t h a n t h a t for chloroform. The same holds for the direct clara obtained in benzene b y Danes (4). I t seems, therefore, quite definite t h a t the apparent specific volume varies with the nature of a good solvent. The same follows from the compilation in Table V in spite of the considerable uncertainties inherent in some of the data. 3 It is very n o t e w o r t h y t h a t an opposite solvent effect seems to prevail in poor solvents. One of the swelling agents used b y Breitenbach and Franek (3), cyclohexane, is a poor solvent. In this case a volume expansion was found on mixing. The effect is, in our units, 0.0033 cc./g, polymer. This indicates t h a t there are here cavities inside the dissolved polymer molecules and t h a t these cavities are not only equal, but even approximately 10% in excess of those present in bulk polystyrene at 25°C. This, in turn, seems to prove t h a t the molecules of poor solvents do not penetrate and pervade the coil of a polymer molecule as easily and as fully as those of good solvents. This is in perfect agreement with the well-known fact of a reduced intrinsic viscosity in poor solvents since a reduction in free solvent drainage across the polymer molecule brings it closer to the 3According to a private communication by Dr. Boyer, a recent study by D. J. Streeter and R~ F. Boyer has shown that the partial specificvolume of polystyrene actually varies with the nature of a good solvent and exhibits a minimum in a solvent of intermediate goodness. This study will be published in another periodical.

72

WILFRIED HELLER AND ARTHUR C. THOMPSON TABLE V Apparent Specific Volume of Polystyrene in Various Solvents

Solvent Chloroform Chloroform Toluene Benzene Benzene Chlor0benzene Bromobenzene Ethyl methyl ketone Cyclohexane

c > 0.01; T -- 20-25°C. ¢2 Reference 0.895 4- 0.05 (12) ~0.901 Derived from data in.Ref. (3) 0.913 (13) 0.929 4- 0.01 (4) ~0.949 Derived from data in Ref. (3) 0.922 4- 0.002 This paPer 0.924 4- 0.001 This paper ~0.954 ~0.960

Derived from data ~n Ref. (3) Derived from data in Ref. (3)

behavior of an Einstein sphere. This behavior should be approached more the higher the molecular weight and the lesser the steric hindrance to rotations about valence bonds, i.e., the more the molecule exhibiting limited solvent drainage approximates the shape of a sphere. It is clear t h a t all this adds strong support to recent concepts on the viscosity of polymer solutions (5,8). X. THE EFFECT OF MOLECULAR WEIGHT UPON THE APPARENT SPECIFIC VOLUME Contradictory and inconclusive data in the literature on the effect of molecular weight upon the apparent specific volume of dissolved polystyrene make it desirable to clear up this question in order to evaluate the importance of working with sharp polymer fractions in this type of studies. A preliminary solution of the problem is possible b y following again the procedure adopted and justified in Sec. VI: the data obtained b y Flory and Fox for bulk polystyrene of systematically varied molecular weight are extrapolated to 25.0 °. In this manner, both the apparent specific volume of polystyrene dissolved in bromobenzene and the actual densities of these solutions are calculated as a function of molecular weight. The results, computed b y W. J. Pangonis, 4are given in Table VI. I t follows that, even with bromobenzene as the solvent, the effect of molecular weight is too small for weights in excess of 80,000 in order to be detected in accurate densify measurements with 1% solutions. This explains the good agreement of the data obtained with chlorobenzene and bromobenzene, respectively (Tables I I and III). In addition, the small difference between the respective mean values of the apparent specific volume appears now as significant because a complete absence of lowmolecular-weight material in the chlorobenzene solution would, abcording 4A Graduate Student at Wayne University.

APPARENT SPECIFIC VOLUME OF POLYSTYRENE

73

t o Table VI, enhance the difference in the apparent specific volumes obtained in the two solvents. The apparent specific volume of polystyrene is therefore definitely larger in bromobenzene t h a n in chlorobenzene. The essential result is that, in general, sharp fractions appear unnecessary in studies of the apparent specific volume provided t h a t the molecular weights are within the order of magnitude of 106. On the other hand, it is apparent from Table VI that the solution density is very sensitive to molecular weight if the latter is less than 30,000, even if the experimental accuracy, in 10% solutions, is limited to four decimal places. This m a y suggest the use of the densitometric method for rapid molecular weight determinations on material of a low degree of polymerization. TABLE VI The Effect of Molecular Weight upon the Apparent Specific Volume of Polystyrene in Broraobenzene Solution and upon the Solution Densities

T = 25°C. Extrapolation by means of the equation of Flory and Fox (7) M X 10-a

4~2

p12(10%)

PL2(1%)

356 100 80 50 30 20 10 8 6 5 4 3

0.924~ 0.924~ 0.9247 0.9251 0.9258 0.926b 0.929a 0.930s 0.9338 0.934~ 0.9373 0.9416

1.432480 1.432378 1.43233 1.432214 1.432133 1.431947 1.43139~ 1.431148 1.430472 1.430309 1.42977~ 1.42887s

1.480388 1.480377 1.48037~ 1.480359 1.480350 1.480331 1.480271 1.480245 1.48017~ 1.480155 1.48009s 1.480002

The foregoing statements are not affected by the possibility that an experimental check m a y lead to minor revisions of the numerical data in Table VI, since only the trend of the data, i.e., their relative values, are pertinent to the conclusions drawn. As regards the absolute values given, it is n o t e w o r t h y t h a t an extrapolation to the molecular weight of the monomer yields a specific volume, at 25.0°C., of 1.433 , which differs from the mean value of 1.108, obtained b y a minor extrapolation, to the same temperature, of the various data available in the literature on the specific volume of styrene A close examination of the data by Flory and Fox suggests t h a t this discrepancy m a y be due to a nonvMidity of their ¢(/1I) equation below the lowest molecular weight checked, i.e., below 21Iw = 3000.

74

WILFRIED HELLER AND ARTHUR C. THOMPSON SUMMARY

The apparent specific volume of polystyrene was determined at 25.00°C. in chlorobenzene and bromobenzene. The results are compared with and discussed on the basis of recent density measurements of bulk polystyrene by F l o r y and Fox. It follows that at least 3% of the volume of solid bubble-free bulk polystyrene at room temperature consists of cavities and that the specific volume of bulk polystyrene at room temperature would be nearly the same as that of polystyrene dissolved in a good solvent if the apparent second-order transition could be avoided for the former. The results, indicate that care must be taken in interpreting volume changes observed on mixing solid polymers with solvents. It is proposed to characterize the apparent second-order transition by an alternation of configurational probability in neighboring volume elements. The resulting "microstrain" and cavitation allow a simple explanation of phenomena associated with an apparent second-order transition such as brittleness. Slight divergencies between the apparent specific volume observed and expected in solution and an analysis of pertinent literature data show that the apparent specific volume changes appreciably with the nature of the solvent. It follows, in particular, that the number of vacant sites within a polystyrene molecule in solution is small in good solvents--where conceivably a slight solvation exists--and is very large in poor solvents. In the latter case, the free volume may exceed that found in bulk polystyrene at room temperature. The probable effect of molecular weight upon solution densities and the question of density measurements for rapid molecular weight determinations are discussed briefly by means of extrapolations from data obtained by Flory and Fox. REFERENCES 1. BOYER, t~. F., AND SPENCER, I~. S., J. Polymer Sci. 3, 97 (1948). 2. BOYER, R. F., AND SPENCEI~, R. S., High Polymer Physics, pp. 170-185. Chemical Publishing Co., Inc., Brooklyn, 1948; Advances in Colloid Science, II, pp. 1-57. Interscience Publishers, Inc., New York, 1946. 3. BREITENBACH,J. W., AND.FRAI~CK,H. P., Monatsh. 79, 531 (1948). 4. DANES,V. Z., Kolloid-Z. 68, 110 (1934); see also YAMAGUCHI,B., ibid. 72, 54 (1935). 5. DE]~YE, P., J. Chem. Phys. 14, 636 (1946); DESYE, P., AND BUECHE, A" M., ibid. 16, 573 (1948). 6. FLORY, P. J., J. Chem. Phys, 13, 453 (1945). 7. Fox, T. G., fiR., AND FLORr, P. J., J. Applied Phys. 21, 581 (1950). 8. KIRKWOOI),J. G., AND RISEMAN, J., J. Chem. Phys. 16, 565 (1948). 9. LEwIs, G. N., ANn RANDALL, M., Thermodynamics, McGraw-Hill, New York, 1923. 10. MUE~LER, F. H., Kolloid-Z. 95, 138 (1941). 11. SCHAL~MACH,A., Proe. Phys. Soc. (London) 53, 214 (1941). 12. SIGNE~, R., AN~)G~oss, R., Helv. Chim. Acta 17, 65 (1944). ~ 13. SPENCER, R. S., ANr~GILMORE, G. D., J. Applied Phys. 20, 502 (1949).