Chain extensibility, limited

Characterization of Limited Chain Extensibility. The molecular origin of the unusual properties of bimodal PDMS networks having been elucidated at least to some extent, it is now possible to utilize these materials in a variety of applications. The first involves the interpretation of limited chain extensibility in terms of the configurational characteristics of the PDMS chains making up the network structure (5,12,13). 

The present theoretical approach to rubberlike elasticity is novel in that it utilizes the wealth of information which RiS theory provides on the spatial configurations of chain molecules. Specifically, Monte Carlo calculations based on the RIS approximation are used to simulate spatial configurations, and thus distribution functions for end-to-end separation r of the chains. Results are presented for polyethylene and polydimethylsiloxane chains most of which are quite short, in order to elucidate non-Gaussian effects due to limited chain extensibility. 

In unfilled rubbers, which are not capable of strain-induced crystallization, the upturns on Mooney-Rivlin curves have shown to be absent 92 95). They disappear also in crystallizable rubbers at elevated temperatures and in the presence of solvents. On the other hand, the upturns do not appear for butadiene, nitrile and polyurethane rubbers if the limited chain extensibility function is introduced in the Mooney-Rivlin expression 97). Mark 92) has concluded that in the absence of selfreinforcement due to strain-induced crystallization or domains the rupture of the networks occurs long before the limited chain extensibility can be reached. 

The formula provides good approximation of the average modulus of elasticity of the system at any instant of time. It allows formulation of a closed-form non-linear theory of the molecular orientation accounting for limited chain extensibility, valid in the entire range of the chain extensions between the Gaussian limit, W (h/Na) = 3h/Na, and full chain extension, h/Na 1. 

Stress-strain measurements on bimodal PDMS networks exhibited upturns in modulus that were much less pronounced than those in crystal-lizable polymer networks. The upturns are independent of temperature and are not diminished by incorporation of solvent. These characteristics are expected for the case of limited chain extensibility. -... 

More quantitative characterization of limited chain extensibility requires a non-Gaussian distribution function for the end-to-end separation, r, of the short network chains. The Fixman-Alben distribution was used to calculate stress-strain isotherms in elongation for bimodal PDMS networks. Good agreement was found between theory and experiment. Other non-Gaussian distribution functions have also been successfully used. The experimental isotherms can also be interpreted... 

Andrady, A. L. Llorente, M. A. Mark, J. E., Model Networks of End-Linked Polydimethylsiloxane Chains. VII. Networks Designed to Demonstrate Non-Gaussian Effects Related to Limited Chain Extensibility. J. Chem. Phys. 1980, 72, 2282-2290. 

It is interesting to note that junction fluctuations increase in the direction of stretching but decrease in the direction perpendicular to it. Therefore the modulus decreases in the direction of stretching, but increases in the normal direction since the state of the network probed in this direction tends to be more nearly affine. The curve of [/" ] versus 1/a is sigmoidal. The parameters k and f of poly(dimethylsiloxane) networks are determined in Figure 17 (155) the intercept of the sigmoidal curves is the phantom modulus. This Flory-Erman theory has been compared successfully with such experiments in elongation and compression (155,162,162-166). It has not yet been extended to take account of limited chain extensibility or strain-induced crystallization (167). 

In summary, the anomalous upturn in modulus observed for crystallizable polymers such as natural rubber and cw-1,4-polybutadiene is largely, if not entirely, due to strain-induced crystallization. In the case of the noncrystaUizable PDMS model networks it is clearly due to the limited chain extensibility, and thus the results on this system will be extremely useM for reliable evaluation of the various non-Gaussian theories of rubber-like elasticity. 

The first important characteristic of limited chain extensibility is the elongation Qfu at which the increase in modulus first becomes discernible. Although the deformation is non-affine in the vicinity of the upturn, it is possible to provide at least a semiquantitative interpretation of such results in terms of the dimensions of the network chains [6, 109]. At the beginning of the upturn, the average extension r of a network chain having its end-to-end vector along the direction of stretching is... 

The isocyanate-end capped polybutadiene (PBNCO) was prepared by a condensation reaction of diisocyanate with the hydroxyl terminal groups of rubber chains. In order to limit chain extension of HTPB through coupling reaction with TDI, a small excess of 5% with respect to the stoichiometric quantities of the latter was used. Larger excess are useless, as with an appropriate choice of the (reaction temperature, only the isocyanate group in para position will react [87]. The reaction was followed by DSC and IR spectroscopy. 

Andrady AL, Llorente MA, Mark JE. Model networks of end-linked polydimethylsiloxane chains. VII. Networks designed to demonstrate non-Gaussian effects related to limited chain extensibility. J Chem Phys 1980 72 2282-90. 

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