1092
J. E. MARK
The Temperature Coefficient of the Polydimethylsiloxane Chain Configuration from Swelling Equilibrium Measurements
by J. E. Mark T h e Department of Chemiatry, Stanford University, Stanford, California
(Received November 9, 1963)
The temperature dependence of the degree of swelling of polydimethylsiloxane (PDMS) networks in equilibrium with an athermal solvent is used to determine the temperature coefficient of the unperturbed dimensions of the polymer chains comprising the network. A moderately large, positive value of d In (r2)0/dT is obtained, in agreement with values determined by other methods.
Introduction The temperature coefficient of the unperturbed mean square end-to-end distance, d In (r2)O/dT,has assumed great importance in the interpretation of the spatial configuration of a polymer chain in terms of basic structural parameters.l-’ It is the purpose of the present investigation to determine this quantity for PDMS chains from the temperature dependence of the equilibrium extent of swelling of PDMS networks in an athermal solvent. Comparison with values of the same quantity obtained from stress-temperature measurements on unswollen networks6 and from intrinsic viscosity-temperature data on athermal PDMS solutions6 can be used to assess the validity of the postulate that the elastic free energies of polymer chains in a network are strictly additive. The elastic response (Le., internal pressure) of a polymer network subject to swelling by a solvent depends on the mean square distention of its chains relative to their unperturbed dimensions in the absence of all constraints. Thus the extent to which a polymer network will imbibe solvent with which it is in contact depends on the unperturbed dimensions of the polymer chains comprising the network, at the temperature of measurement, and the change in equilibrium swelling with temperature must therefore depend on the temperature coefficient of (r2)0. Observation of the temperature dependence of equilibrium swelling should therefore afford a method for determining the temperature coefficient of (r2j0 if the following quantities are also known: specific volumes and thermal expansion coefficients of polymer and solvent, molecular T h e Journal of P h y e k l Chemietry
weight of the solvent, and the free energy of mixing parameterg for the system, XI. The determination of XI can be avoided by choosing an athermal solvent (for which x1 would be small and independent of temperature). Dimethylsiloxane oligomers and networks consisting of PDRIS chains have close structural similarity; a system of these two components can be expected to exhibit an enthalpy of mixing of virtually zero9 and a small value of xl. Initial measurements on PDMS networks swollen by dimethylsiloxane oligomers indicated that the approximation X I = 0 could not be made in this analysis; small deviations of the quantity from zero are sufficient to affect the apparent value of d In (r2)o/dT. In an attempt to correct for this, the apparent temperature coefficient of ( T ~ was ) ~ determined for a series of networks of different degrees of cross-linking swollen by several dimethylsiloxane oligomers differing in molecular weight. From these data it should be pos(1) 0. B. Ptitsyn and I. A. Sharanov, Z h . Tekhn. Fiz., 27, 2744, 2762 (1957). (2) A. Ciferri, C. A. J. Hoeve, and P. J. Flory, J . Am. Chem. S o c . , 83, 1015 (1961).
(3) P. J. Flory, A. Ciferri, and R. Chianp, ibid., 83, 1023 (1961). (4) C. A. J. Hoeve, J . Chem. Phys., 35, 1266 (1961). (5) K . Nagai and T. Ishikawa, ibid., 37, 496 (1962). (6) J. E. Mark and P. J. Flory, J . Am. Chem. Soc., 86, 138 (1964). (7) P. J. Flory, V. Crescenzi. and J. E. Mark, ibid., 86, 146 (1964). (8) P. J. Flory, “Principles of Polymer Chemistry,” Cornel1 University Press, Ithaoa, N. Y., 1953. (9) G. Delmas, D. Patterson, and D. Bohme, Trans. Faraday Soc., 58, 2116 (1962).
TEMPERATURE COEFFICIENT OF THE
POLYDIMETHYLSIILOXANE CHAIN
sible to estimate d In (r2jO/dTfor a PDMS network comprising chains of infinite length between crom links swollen by a dimethylsiloxane oligomer of infinite chain length. Since the effect of end groups of thie solvent and junction points of the network are thus eliminated, x1 for such a system is assuredly zero att all temperatures and the true value of d In (r2)o/dZ' should be obtained.
Experimental Preparation of PDMS Networks. An unfractionated sample of PDMSIO having a molecular weight of 1.1 >< lo6 was used for the preparation of the cross-linked samples. The polymer was pressed between sheets of cellophane to a uniform thickness of approximately 0.10 cm. These sheets were then irradiated with high energy ellectrons from a General Electric resonant transformer t o the desired dose. 'I'o ensure network uniformity, samples were irradiated on opposite sides for equal lengths of time. The cellophane was washed off and the cross-linked samples were extracted with carbon tetraclhloride' at room temperature for a t leatit 12 hr. The soluble portion never exceeded 5% of the sample. Determination of l?egree of Swelling. The solven1,s were commercially available dimethylsiloxane fluids (General Electric, SF-96 series). The molecular weight of each oligoiner was determined from its bulk viscosity a t 40" using the empirical relationship of Warrick, et ai." The specific volumes and cubical thermal expansion coefficients of the solvents (Si-5, 10, 20, 50) and polymer were determined by pycnometry and dilatometry, rlespectively. These data are summarized in Table I. Table I : Characteristicu of Solvents and Polymer Material
Specifio volume 9, X 1021, deg.-l a t 30". cm.a/g. at 6 7 . 5 O
Si-5a 10 20 50 Cross-linked p o1y mer a Xumber designates a t 25".
1.0968 1.0726 1.0561 1.0467
0.990 0.947 0.938 0,909
M , X 10-8
0.716 1.19 2.06 3.71
1.0360 0 .m o approximate bulk viscosity in centistokes
After extraction and drying, the cross-linked samples were cut into the shape shown in Fig. 1. The absence of horizontal faces on the samples minimized drainage errors. During swelling, the strip was totally immerseld in the solvent a t constant temperature. At approxii-
CONFIGURATION
1093
1111D
Figure 1. Swelling equilibrium apparatus: A, adjustable collar; B, constant temperature bath; C, swollen network; D, solvent.
mately 8-hr. intervals, the sample was raised within the cell and allowed to drain a t constant temperature for a fixed length of time (15 min. for the low viscosity fluids, Si-5 and Si-10; 30 min. for the others). The swollen network was then removed and weighed in an aluminum dish. The sample was immersed in the solvent for another 8-hr. period, drained, and reweighed. When the weight of a sample was constant within a few tenths of a milligram, the system was considered to be at equilibrium. Up to 3 weeks was required for equilibration a t the first temperature of measurement, 30'. Once equilibrium was established a t this temperature, however, the swollen network attained constant weight at the other temperatures relatively rapidly (within 2 or 3 days). The volume fraction of polymer v2 was calculated from the weights and specifip volumes of polymer and solvent a t each temperature (30, 55, 80, 105O). It was necessary to assume additivity of volume in this calculation; in view of the structural similarity of solvent and polymer the error introduced is certainly negligible. Measurements on (10) This sample was generously provided by the Silicones Department of the General Electric Co., Waterford, N. Y. (11) E. L. Warrick, W. A. Piccoli, and F. 0. Stark, J . A m . Chem. Soc., 77, 5017 (1965).
Volume 68,Number 6 M a y , 1964
1094
J. E. MARK
the descending temperature cycle reproduced those of the ascending cycle well within the limits of experimental error. In this investigation four networks (A, B, C, D) of varying degrees of cross linking were studied in four solvents varying in molecular weight.
on the left-hand side of eq. 1 is small in comparison with the first; this approximation can therefore be introduced in this term without hesitation. As will be shown, this approximation is rendered completely negligible in the consequent treatment of the data. Rearrangement of eq. 1yields
Results The equilibrium volume fraction of polymer is shown as a function of temperature in Fig. 2 . Data for polymer networks A and B in solvents Si-5, 10, 20, and 50 are presented; similar curves were obtained for the other systems but are not shown here.
Since Vo is directly proportional to ( T ~ ) ~ ~the " fractional change of the right-hand side of eq. 2 with temperature is -d In (r2)o/dT. Values of the tempera) ~ on the assumption ture coefficient of ( T ~ calculated that x1 = 0 a t all temperatures (Table 11) showed a Table I1 : Swelling Equilibrium Results
System
,.
h
026- 2
"
"
v
0
B-5
"
A-IO
"-
A-5 10 20 50 B-5 10 20 50 c-5 10
0.26 0.24 A-5
0.22 0.20
I
30
40
60
Y
v
c v
70
60
I
I
I
80
90
100
-
I
T 'C
Figure 2. Temperature dependence of volume fraction of polymer a t swelling equilibrium; letter and number designate network and solvent, respectively.
According to the theory of swelling of network structures,8 a t equilibrium or maximum swelling
(VVl/V*'/~V;'8)
[21Z1'8
-
(v2/2)(Vo/V*)
- [In (I -
v2)
=
+ + v2
~
1
~
2
(1) ~ 1
where v is the number of chains in the network, VI the molar volume of the solvent, V* the specific volume of the unswollen network, Vo the volume associated with the undistorted chains before the imposition of cross links, v2 the volume fraction of polymer a t swelling equilibrium, and x1 the free energy parameter for mixing of solvent with the polymer network. Since all networks considered here were formed in the absence of diluent, the reference volume Vo g V* a t the temperature of cross linking. The second term The Journal of Physical Chemistry
Dose, mrads
9.0
30.
50.
20 50 50 D-5 10 20
75.
ae a t
30°
0.2158 0.2659 0.3367 0.4138 0,2790 0.3435 0.4198 0.5000 0.5065 0.5630 0.6510 0.7490 0.7201 0.5954 0,6638 0.7469
0.31 0.27 0.23 0.20 0.33 0.27 0.26 0.24 0.32 0.27 0.20 0.21 0.20 0.31 0.26 0.21
0.09 0.10 0.15 0.14 0.00 0.07 0.04 0.02 -0.12 -0.10 0.01 -0.15 -0.09 -0.18 -0.16 -0.10
trend with both the molecular weight of the solvent and the degree of cross linking of the network. This is due to the exceedingly small temperature coefficient of vz; even small contributions to x1 from chain ends of the solvent and junction points 'In the network are sufficient to affect significantly the apparent value of d In (r2)o/dT. To remove the effect of solvent chain ends, the uncorrected value (xl = 0) of d In (r2)o/dT for each network was plotted against the reciprocal of the solvent molecular weight M and extrapolated to M equal infinity (Fig. 3). A linear dependence was observed for each network. The vertical lines in each plot indicate the relative reliability of the measurements; the data for the most highly cross-linked networks are less reliable because the changes in weight of the samples with temperature are smaller than those measured for other networks. Values of the tempera-
TEMPERATURE COEFFICIENT O F THE IPOLYDIMETHYLSILOXANE CHAIN CONFIGURATION
-
0.4
0.2
L
NETWORK A V
Y
&
n
0 -
0.2
-
0-
-
-0.2
0 - 7
--
: -
02 -
-0.2O
-.
c
-
.____
02 -0;
B
1095
Unfortunately, this method cannot claim the accuracy and precision obtained in stress-temperature or intrinsic viscosity-temperature studies. This is due to the exceedingly small temperature dependence of 02 (d In v2/dT E 10-4). In stress-temperature measurements the fractional change in force with temperature is of the order of deg.-l as is also the fractional change in the intrinsic viscosity of an athermal solution with temperature.
Discussion
6
-
This method for evaluating the temperature coefficient of the unperturbed dimensions of PDMS chains gives a value in agreement with those obtained by other techniques.6 The agreement between values for the polymer chains in very different environments consisting of the dilute solution, the swollen network, and the undiluted network is very difficult to reconcile with the claim12 that intermolecular interactions in the undiluted, amorphous state drastically alter the configuration characteristic of the free chain. Indeed these results corroborate previous work2,3y6indicating that the elastic free energies of polymer chains making up a network are additive, and that the configuration of a chain in the amorphous state is not significantly .influenced by intermolecular interactions. These results on networks at swelling equilibrium also give considerable support to the theory8 developed for such systems.
f-r
. L I 0 0,5 10
1.5
-
Figure 3. Extrapolation of uncorrected d In (r2)o/dT for each network to valueEi for infinite molecular weight of solvent.
ture coefficient of (rz)>O corrected to infinite molecular weight for the solvent must then be further cor.rected for the effect of network junctions. Clearly, for an idealized network having infinite chain length between cross links the equilibrium volume fraction of polymer must equa,l zero, but theory does not indicate how this extrapolation should be performed. Extrapolation to v2 = 0 would also imake the approximation in the ,second term of eq. 1 insignificant (since v2 approaches zero much more rapidly than does v;"). Although this extrapolation cannot be made unambiguously, the data do indicate that as the densi1,y of cross links decreases (as indicated, for example, by the relative value of v2 for a network in equilibrium with Si-5, a t ;io"), d In (r2)O/dTaplproaches a moderately large, positive value. This result is in agreement with the value obtained by stress-temperature and intrinsic viscosity-temperature measurements,'! 0.75 f 0.15 X .10-8deg.-1.
Acknowledgment. Support by the United States Air Force under grant AFOSR-62-131 is gratefully acknowledged. The author particularly wishes to thank Prof. P. J. Flory, who gave much invaluable advice and encouragement throughout the course of the work. Grateful acknowledgment is also expressed to Dr. E. Stivers of the Raychem Corporation, Redwood City, Calif., for performing the electron beam irradiation of the polymer samples. (12) M. V. Volkenstein, "Configurational Gtatistics of Polymeric Chains," Interscience Publishers, New York, N. Y . , 1963, Chapter 8.
Volume 68,Number 6 M a y , 1064
