Unperturbed dimensions of polystyrene in mixed solvents at high temperature

Eur Pol.lm. J. Vol. 18. pp. 735 to 739. 1982

0014-3057/82.080735-05503.00/0 Copyright ~'; 1982 Pergamon Press Ltd

Printed in Great Britain. All rights reserved

UNPERTURBED DIMENSIONS OF POLYSTYRENE IN MIXED SOLVENTS AT HIGH TEMPERATURE A.-A. A. ABDEL-AZIM and M. B. HUGLIN Department of Chemistry and Applied Chemistry, University of Salford, Salford M5 4WT. England

(Received 3 February 1982) Abstract--At 371.5 K, which is the 0-temperature for polystyrene (PS) in 3-methyl cyclohexanol (MC), intrinsic viscosities [~] have been measured for PS samples of different relative molar mass M in mixtures of MC with a thermodynamically good solvent 1,2.3,4-tetrahydronaphthalene over the whole range of solvent composition. Eleven graphical procedures have been utilised and assessed in deriving the unperturbed polymer dimensions expressed as Ks (in the relation [rl] = KoM~"2=3 where • is the expansion factor). For those procedures concluded to be the most reliable, there was no influence of binary solvent composition: the value of Ks = 78 ( _-_+1) x 10- 3 dm 3 kg- ~ was the same as that obtained directly under 0-conditions.

INTRODUCTION In a previous communication [13 we reported data on viscosity slope constants and chain expansion factors in solutions comprising 1,2.3.4-tetrahydronaphthalene (TET), polystyrene (PS) and 3-methyl cyclohexanol (MC). The temperature used was 371.5 K. which is the 0-temperature for PS in MC [1, 2]. This allowed binary T E T / M C solvents to be used over the whole range of mixed solvent composition, since T E T is a thermodynamically good solvent for PS. In the present report, the intrinsic viscosities [~l] of PS samples of different relative molar mass M in these solvent media are employed to derive the unperturbed dimensions of the polymer at 371.5 K. In particular, interest is centred on (i) comparing the extrapolation procedures used and (ii) examining whether the unperturbed dimensions obtained in binary solvents differ from those measured directly in MC, i.e. under 0-conditions. EXPERIMENTAL

Materials MC and TET were purified as described before [1]. Five PS samples were obtained from Polymer Laboratories Ltd., Church Stretton, Shropshire, England. The polydispersity indices M,,/M, were quoted as ~<1.09 and the values of M as 1.06 x I0 ~, 2.94 x l0 s, 4.20 x 10 ~, 6.40 x 10s and 9.60 x 10-~. In the same order, these samples are denoted here as PS1, PS2, PS3, PS4 and PS5.

Techniques Preparation of mixed solvents and polymer solutions as well as the mode of determining [~/] have been described elsewhere [ 1]. RESULTS Table 1 shows the values of [r/] for samples PS1-PS5 in TET, MC and nine binary solvents having compositions expressed in terms of the volume fraction ~b,,,c of M C at 371.5 K.

Unperturbed dimensions are defined as [(r2)o/ M] ~'2, where (r2)o is the unperturbed mean square end-to-end distance. Here it suffices to express them simply as Ke in view of the interrelation via the Flory constant q~o in Eqn (1). K0 = q~0 [ ( r2)0/M] 3:2.

(1)

In terms of the measured intrinsic viscosity under 0-conditions, [r/J0, the value of Ko is given by Eqn (2)

[~]~ = KcVtI:-"

(2)

Eqn (21 can be applied directly to only one of the systems [solvent (k) in Table 1]. For the remaining ten [solvents (a)--(j) in Table 1.], it is necessary to exploit various graphical procedures, which yield K0 from the intercept on the ordinate axis in the appropriate linear plot. The full equations relevant to these methods may be obtained via the references quoted in Table 2, where the methods are identified simply as A-J. Since most of these procedures are self-explanatory, clarification is reserved for only methods C, E, G and J. In method C. the abscissa includes a term DM. where the factor /) was found by Dondos and Benoit[5] to be equal to 1.2 x 10 -3 ( v - 0 5 0 ) in which v is the exponent in the K u h n - M a r k Houwink-Sakaurada equation: In] = K,, m~.

(3)

The values of K,. were found to increase from 3.60 x 10 -a to 77 x 1 0 - a d m a k g -~ on going from solvent (a) to solvent (k), whilst there is a decrease from 0.83 to 0.50 in the corresponding values of v. The values of K,, and v were employed to implement method J. In method E, the value of Ko is obtained from the intercept via the solvent dependent factor ¢~e). which is equal to q~0 only under 0-conditions. ¢~e) is given by Eqn 4. in which E is calculated from v via Eqn 5. q~) = ¢0 (1 - 2.63 e + 2.86 e 2) = ( 2 v - 1)/3. 735

(4) (5)

A.-A. A. ABDEL-AZIM and M. B. HUGLIN

736

Table 1. Intrinsic viscosities at 371.5 K for PS samples of different molar mass in TET/MC mixtures Solvent Designation Composition (~,~) a b c d e f g h i j k

0 0.084 0.201 0.293 0.402 0.502 0.602 0.710 0.801 0.917 1.000

[7] (dm3kg - t) PS3 PS4

PSI

PS2

53.9 51.4 50.0 48.5 45.6 44.3 42.2 38.0 34.2 30.0 25.1

124 116 114 109 103 97.6 89.2 79.0 69.0 55.9 42.0

167 154 151 147 136 130 117 103 88.6 70.0 50.0

PS5

237 215 212 206 191 180 162 142 119 92.0 61.7

330 295 291 274 250 235 210 187 160 121 75.3

For molar masses of samples PSI-PS5, see Experimental Section.

In m e t h o d G the factor g(~t) within the abscissa is defined as

then a final corrected Ks by means of iterative procedures [9, 13].

(6)

g(~t)-~-8~t3i(I + 30t2)3/2.

W h e n g(a) is unknown, its value is taken initially to be unity to yield an approximate estimate of Ks. This is then used to obtain 0(:I) [via Eqns 2, 6 and 7] and

-- (F~']/['~'lo) ~''3.

(7)

However, in the present systems the values of D1]s a n d hence g(~t) were available, thus enabling the entire abscissa g(a)M 2/3 I t / I - t/3 to be plotted directly.

Table 2. Co-ordinates and intercept relating to extrapolation procedures used to determine Ks Procedure Designation

Ref.

Ordinate

Abscissa

A B C D

3 4 5 6

Mt/2 Ma/S M 1/2 - DM

E

7

F G H I J

8 9 I0 11 12

[ ~ ] M - t/2 rr/]M- t/2 ['r/]M -t/2 ['t/]M- t/2 [~]M- i/5 [q]I/2 M - t/, [~/]2/3 M - I/3

Intercept on ordinate

Ke Ks Ks Ks

M~/,o M7:2o

[¢(c)/¢o]Ko Ktg:2 K2s/3 0.786 K~/~ K~:3 logKe

M[r/]- t

[~l]'/SM"2Is

0(,,)M2/3 [~]- t/3 M t:3

[r/]Z/~M- 1/3 log [2K~(1 - v)]

MCr/] - 1 v- ~

Table 3. Values of 103 x Ks (in dm 3 kg- t) derived from different extrapolation procedures for PS in different mixed solvents [(a)-(k)']

Solvent

A

B

C

D

Method E F

G

H

I

a b ¢ d e f g h i j k

77 79 79 79 78 78 79 78 78 78 77

45 50 54 56 58 60 65 67 69 72 77

40 42 44 45 48 52 60 63 65 73 77

43 45 46 48 49 51 52 54 57 64 77

77 78 78 78 78 79 79 79 78 79 77

78 79 79 79 78 78 79 78 78 78 77

79 79 79 80 80 80 80 80 80 88 104

11 13 15 17 18 23 41 47 55 73 77

For composition of solvents, see Table 1.

2.5 16 18 21 31 38 46 50 55 73 77

J T

J 78

/

_L

Unperturbed dimensions of polystyrene

737 0

0.4 e

f

~

Ih I

0.3 % 0.2 -

c,

o.i 0

'

~--.- k

I

I

I

I

0.5

1.0

i.5

2.0

g (o)

I" ~ ']'~"SMZ/:Zx I0 -~

Fig. 1, Plots according to method G [for compositions of solvents (a)-.(k), see Table 1]. Plots (Figs 1-4) according to some of these methods have been selected to illustrate specific features to be considered in the Discussion section. The resultant values of K0 for all the methods are given in Table 3. Finally, a method not involving extrapolation is considered. This semi-empirical interpretation of Eqn 3 is due to Munk and Halbrook [14] and utilises Eqn 8. Ke = O3/~,- 2v)

(8)

where Q = [K,,][q~ol-2")"3][N~2M/'L] ~ - 1

(9)

In Eqn 9, (M/L) is the molar mass of polymer per unit length of chain, which was calculated by Munk and Halbrook [14"1 to be 4.14 × 10 9 g m o l - l cm- 1 for PS. These authors postulated that there is no thermodynamic interaction among polymer segments within a short section of a chain with a characteristic number of segments No, where No was estimated to be approx. 9. Invoking ~o = 2.87 x 10 '3 mol-~ Eqn 8

0

b ,

~-

!

0

c

/ //d

b C d

30

e

e ,f

.

/" f

20-

9 ~J

h

T

j

IO

IO ~

0

2O

o

,,,

k

~-----------o

I 5 ( M'/z-

I

I0 ~)M ) X l O -z

Fig. 2. Plots according to method C [designation of solvents as in Fig. 1].

o

I I

f

4o

o---o

t

8o

,o

o- k

i 120

M 7/zo

Fig. 3. Plots according to methods D and E [designation of solvents as in Fig. 1].

738

A.-A. A. ABDEL-AZIMand M. B. HUGLIN -I

DISCUSSION

The plots specified in Table 2 afforded good linearity in general. Where slight curvature was evident, it resulted from the small departure of one datum point from the line and this point was neglected in effecting the extrapolation. Deviations of this nature occurred only for thermodynamically good solvents. Thus, method G (Fig. 1) and method A gave slight downward curvature at the highest M, but only for v/> 0.70. In methods H and I the small downward curvature for v >I 0.75 was yielded at the lowest M. On the other hand, the curvature at high M and at v > 0.80 obtained with method C (Fig. 2) was in an upward direction. Clearly, in method C, the combination of high M and high v reduces the factor /5 within the abscissa M ~ / : - / ) M by too large an amount under these conditions. Of perhaps greater importance is the success of these procedures in yielding a unique intercept (and hence K o) independent of the nature of the solvent medium. Table 3 shows that only methods A and G fulfil this directly and yield K~ = 78 ( + 1) x 10- 3 dm a kg- ~. In methods D (Fig. 3), B, C, F, H and I the plots intersect before the ordinate axis, as a consequence of which the intercepts, and hence K~ values, increase with decreasing solvent power, i.e. with increasing ~,,~. However, this effect is not pronounced for method H, high values of K~ being yielded only for the poor solvents (j) and (k) and constant values of approx. 80 x 10-3dm3kg - t for the remaining solvents [(a)--(i)]. In this respect method H seems to be of wider applicability than indicated by its originators I'10], who suggested its restriction to systems in which •, > 1.4. Here the systems comprising solvents (a)--(i) have ct > 1.29. It should be noted that the actual plots involved in method D (Fig. 3) and method E are identical, the constant values of K0 for the latter in Table 3 arising solely from the application of the correction factor ~ ) / ~ o to the intercepts obtained in the former. We have examined the possibility of applying this correction factor to the results afforded by methods B, C, F and I, but the resultant corrected Ke values still increased with increasing Smo-

M

~-z

0

O.t

O.Z

0.3

=, - 0.5

Fig. 4. Plot according to m e t h o d J.

was used to evaluate Ke separately for each solvent system. A random variation between 62 x 10 -3 and 77 x 10 ° a dm 3 kg- t was obtained, the average value being 68 x 10- a dm a kg- t. Since an extrapolation to give the required intercept is not involved, this method is excluded from Table 2. However, we have recast Eqn 8 into the following graphical form log Q = [(4 - 2v)/3] log Ke.

(10)

According to Eqn 10, a plot of log Q vs (4 - 2v)/3 should be linear, pass through the origin of axes and have a slope of log Ke. This plot is shown in Fig. 5, the slope yielding Ke = 69 x 10- 3 dm a kg- t.

I.I

I.O O

--~ 0 . 9 I

//, 0

I

t

0.8

0.9

{4-2=,1/3

Fig. 5. Plot according to Eqn 10.

I 1.0

Unperturbed dimensions of polystyrene Data (K,, and v) derived from measurements in all the solvent media are embodied in the single plot (Fig. 4) for method J. This plot gives excellent linearity and the resultant Ks = 78 x 10- 3 dm 3 kg- I quoted in Table 3 agrees well with the values obtained via methods A, E, G and H for each solvent medium. Since it also utilises K,, and v values, it is rather surprising that the method of Munk and Halbrook gives rise to a value of Ko which is approx. 110o smaller. With regard to these two procedures, method J appears to be preferable in view of (i) the fact that it obviates the need to invoke No, ¢0 and M,L, the values of which are open to some uncertainty, especially for No, (ii) the value of Ko obtained from it, (iii) less scatter in the plot and (iv) the simpler form of the co-ordinates required for the plot (note, however, that for method J we have re-arranged the long, complicated form of ordinate in the original paper [12] to the simple short form given in Table 2).

739

involves cyclohexane as solvent at 307.6 K, giving Ko ~-84 x 1 0 - 3 d m a k g - l . Taking d l n ( r 2 ) o i d T - i x 10-3 deg -1 [2, 15], the value of K s at 371.5 K thereby is estimated to be 76 x 1 0 - 3 d m a k g -1. which is very close to the value obtained here. It has been proposed 1"16] that, at a particular temperature, the value of Ko in a mixed solvent may deviate from its value in a single solvent by an amount depending on the excess Gibbs free energy of mixing of the solvent components. We have shown[17] that the MC/q'ET mixtures at 371.5 K have a positive excess free energy of mixing. However, there appears to be no difference between the Ko in MC and the values in the binary solvents.

Acknowledgement--One of us (A.A.A.) thanks the Egyptian Government for financial support.

REFERENCES

CONCLUSIONS Extrapolation procedures were conceived originally as a convenient means of deriving unperturbed dimensions from experimental data relating to a variety of conditions of solvent and different molar masses of polymer. Cowie [7] has provided a critical review. As soon as the successful implementation of a particular method is found to be contingent on any restrictions, this method necessarily loses some of its attraction. Such is the situation with regard to certain of the procedures discussed above. For the solutions examined here, there is a wide range of thermodynamic solvent power, the minimum and maximum values of ~t being 1.00 and 1.64 respectively: moreover M also extends over a fairly wide range. Provided several liquids of widely different solvent power are available, method J is seen to be very reliable. If it is desired to use only one solvent, method E (i.e. the corrected form of method D) is recommended. Methods A and G do not require correction factors, but should utilise polymer having 106 > M > 10 s. Most previous work [15] on PS under 0-conditions

I. A. A. Abdel-Azim and M. B. Huglin, Makromolek. Chem. Rapid Commun. 2, 119 (1981!. 2. A. Bazuaye and M. B. Huglin, Polymer 20, 44 (1979) 3. W. H. Stockmayer and M. Fixman, J. Polym. Sci. (C) 1, 137 (1963). 4. M. Ueda and K. Kajitani, Makromolek. Chem. 108, 138 (1967). 5. A. Dondos and H. Benoit, Polymer 19, 523 (1978). 6. M. Bohdaneck~'. J. Polym. Sci. (B) 3, 201 (19651. 7. J. M. G. Cowie, Polymer 7, 487 (19661. 8. G. C. Berry. J. chem. Phys. 46, 1338 (1967). 9. M. Kurata and W. H. Stockmayer, Fortschr. Hoehpolym.--Forsch. 3, 196 (1963). 10. H. lnagaki, H. Suzuki and M. Kurata, ,/. Poiym. Sci (C) 15, 4O9 (1966). 11. P. J. Flory and T. G Fox, J. Am. chem. Soc. 73. 1904 (1951). 12. K. Kamide and W. R. Moore, J. Polym Sci (B) 2, 809 (1964). 13. M. B. Huglin, D. H. Whitehurst and D. Sims J. appl. Pol),m. Sci. 12, 1889 (1968). 14. P. Munk and M. E. Halbrook, Macromolecules 9, 441 (1976). 15. Polymer Handbook, (Edited by J. Brandrup and E. H. Immergut), 2nd Edn. Wiley, New York (1975). 16. A. Dondos and H. Benoit, Eur. Polym. J. 4, 561 (1968). 17. A. A. Abdel-Azim and M. B. Huglin to be published.