Non-Gaussian Effects and Intermolecular Correlations in Bimodal

Downloaded by CORNELL UNIV on October 24, 2016 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1990-0224.ch011

11 Non-Gaussian Effects and Intermolecular Correlations in Bimodal Networks of Poly(dimethylsiloxane) Vasilios Galiatsatos1 and James E . Mark Department of Chemistry and the Polymer Research Center, University of Cincinnati, Cincinnati, O H 45221

Strain-birefringence measurements were carried out on unswollen networks of poly(dimethylsiloxane) (PDMS) at elongation at 0-90 °C. An increase in the mole percent of short chains in the networks increased the non-Gaussian deviations from linearity of the dependence of birefringence on stress. Birefringence-temperature measurements showed the deviations to be insensitive to temperature, as would be expected for an intramolecular effect. In addition, these measurements yielded values of the optical configuration parameter and its temperature coefficient that are in good agreement with other published results for bimodal PDMS networks. The magnitudes of the intermolecular correlations were estimated from the optical anisotropies and were found to decrease as the mole percent of short chains increased. This observation is also consistent with intermolecular interactions not being the origin of the observed non-Gaussian effects.

STUDIES OF THE MECHANC IAL PROPERTIES

of polymer networks have yielded a great deal of important molecular information on the elasticity of polymer chains (1-3). For many systems, however, this approach is being supplemented increasingly by studies of the optical properties of the same Current address: Goodyear Research Laboratories, Department 410 F, 142 Goodyear Boulevard, Akron, O H 44305

0065-2393/90/0224-0201$06.00/0 © 1990 American Chemical Society

Zeigler and Fearon; Silicon-Based Polymer Science Advances in Chemistry; American Chemical Society: Washington, DC, 1989.

SILICON-BASED POLYMER SCIENCE: A COMPREHENSIVE RESOURCE


202

networks (2, 3). This approach has been used for poly(dimethylsiloxane) (PDMS) [-Si(CH 3 ) 2 0-] n (4-8), in part because of its superb optical prop erties, specifically its transparency that also makes it very attractive for applications such as contact lenses (9). This chapter reports birefringence measurements carried out on PDMS networks that have a bimodal distribution of chain lengths. Such networks are of considerable interest, because their high extensibility permits them to be deformed into ranges of elongation in which both their mechanical (3, 5-7, 10-12) and optical (5-7) properties exhibit markedly non-Gaussian be havior. The desired data were obtained from networks with various shortchain-long-chain compositions in the unswollen state at 0-90 ° C . The results were used to characterize (1) the non-Gaussian behavior in terms of the stress optical coefficient C (2) and (2) intermolecular correlations as repre sented by the nonintrinsic part of the optical anisotropy (6, 13).

Theory The relationship between the measured relative retardation (R) and the stress-induced birefringence (Δη) is given by R = tàn (2), in which t is the sample thickness. The stress optical coefficient C is defined by Δ η = CT (2), in which τ is the true stress (T = f/A; f is the force in newtons per square millimeter, and A is the cross-sectional area of the network sample). This coefficient is thus simply the slope of the line in a plot of Δ η versus τ. Finally, the optical configuration parameter Δα is defined by

(1)

in which k is the Boltzmann constant and η is the refractive index of the network. This parameter may be calculated also by using rotational isomeric state theory (13) and is an important quantity for testing theoretical aspects of the optical behavior of networks. The stress optical coefficient C merits special attention, because it leads directly to the parameter Γ 2 that characterizes the optical anisotropy of the network chain under strain. Γ 2 is defined by (13)

r

= ^ y

, τ

0

Ο

(2)

in which c^ is the anisotropic part of the polarizability tensor contributed by the structural unit indexed by i, r is the end-to-end distance of the chain, and Τ is the temperature in kelvins. The average unperturbed end-to-end


11.

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Bimodal Networks of Poly(dimethylsiloxane)

203

distance of the chain is denoted by 0 . In terms of C, Γ 2 is given by _ 1 2

21nkTC

" 2 7 7 ( n 2 + 2)2

W

in which η is the refractive index.


Experimental Details The PDMS chains used were hydroxyl terminated and were obtained from Petrarch Systems, Inc. (Bristol, PA). Their number-average molecular weights (M „) were 660 and 880 g/mol for the short chains and 21.3 X 103 g/mol for the long chains (7). Their polydispersity indices would be expected to be ~ 2 . Two sets of networks were prepared. In the first network, the M„ of the short chains was 660 g/mol (660-21.3 Χ 103), and in the second network, it was 880 g/ mol (880-21.3 Χ 103). The compositions of the networks are given in Table I. The chains were end linked with tetraethoxysilane, with stannous 2-ethylhexanoate as catalyst. The reactions were carried out for 2 days under a protective atmosphere of nitrogen at room temperature. Additional details are given elsewhere (7, 8, 14). All sample sheets thus prepared were gently extracted to remove the approximately 3 wt % soluble material they contained. Strips (ca. 30 mm by 80 mm by 1 mm) were cut from the extracted sheets. The thicknesses of the strips were determined from their densities by weighing them after their lateral dimensions had been determined by means of a cathetometer. The tensile force and birefringence were simultaneously measured as functions of the strain. In brief, the samples were suspended vertically between two clamps; the lower clamp was fixed, and the upper clamp was connected to a force transducer (Statham "strain" gauge). The output of the transducer was monitored by a Hew lett-Packard chart recorder (7, 8). Values of the birefringence An were determined by using a single-frequency He-Ne laser according to well-established procedures (2, 7, 8). Values were calculated directly from the sample thickness and the relative retardation R, which was measured with a Babinet-type compensator. The meas urements on the 660-21.3 Χ 103 samples were carried out at 0-90 °C, and those on the 880-21.3 Χ 103 samples were carried out at 25 °C.

Table I. Optical Properties of Bimodal PDMS Networks M of Short Chains (g/mol) n

660 880

Mol % of Short Chains in Network 0

90.8 92.0 60.0 70.0 93.4

T (°C)

C ( X 10 )

10

1.37 1.17 1.74 1.52 0.71

25

4

b

Optical Anisotropics T (A ) IV (A ) 2

3

0.21 0.18 0.28 0.25 0.12

"The short chains were combined with long chains with M„ = 21.3 X 103 g/mol. C is the stress optical coefficient in square millimeters per newton. b


3

0.17 0.14 0.24 0.21 0.08

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SILICON-BASED POLYMER SCIENCE: A COMPREHENSIVE RESOURCE


Results and Discussion Typical birefringence-stress results, for the 660-21.3 Χ 103 networks, are shown in Figure 1. The anomalous downward curvature at large a at this composition, 92.0 mol % short chains, is larger than that obtained at 90.8 mol % (7) but much less than that obtained at 93.4 mol % (8), even though the short chains were somewhat larger in this case (M n = 880 g/mol). The curvature does not seem to depend on temperature, as it would if straininduced crystallization was important (5). Values of C calculated from the least-squares representation of these data and from the corresponding data for the other networks are given in Table I. The decrease in C with increase in mole percent of the short chains is characteristic of this type of nonGaussian behavior (8). Some of the birefringence-temperature results for the same networks are given in Figure 2. Again, no changes of birefringence with temperature were observed that would suggest a significant intermolecular contribution to the non-Gaussian behavior. Values of 10 2 5 Δα calculated from equation 1 for one of the 660-21.3 Χ 103 networks are shown as a function of tem-

l—ι—ι—ι—I

f/A

I Γ

2

5

Ν mm"

Figure 1. Dependence of birefringence on true stress of bimodal PDMS network containing 92.0 mol % short chains. The measurements were carried out at elongation in the unswollen state at 20 (O), 40 (€)), and 60(φ)°€. The. slopes of the lines are C , the stress optical coefficient.


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perature in Figure 3. The value at —25 ° C is 3.8 em3, with a temperature coefficient (I0 daa/dt) of 0.038 cm 3 /K. These results are in excellent agree ment with the values of 3.2 cm 3 and 0.037 cm 3 /K obtained during a previous study of bimodal PDMS networks (5) but are somewhat different from the values of 5.2 cm 3 and 0.063 cm 3 /K reported for unimodal PDMS networks 25

30


26 22

c

Non-Gaussian Effects and Intermolecular Correlations in Bimodal

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