Non-Gaussian effects

These Monte Carlo distributions can be used in the standard three-chain model for rubber-like elasticity to generate, for example, stress-strain isotherms [5]. Non-Gaussian effects can cause large increases in modulus at high... 

Birefringence measurements have been shown to be very sensitive to bimodality, and have therefore also been used to characterize non-Gaussian effects resulting from it in PDMS bimodal elastomers [5,123]. The freezing points of solvents absorbed into bimodal networks are also of interest since solvent molecules constrained to small volumes form only relatively small crystallites upon crystallization, and therefore exhibit lower crystallization temperatures [124—126]. Some differential scanning calorimetry (DSC) measurements on... 

The incorporation of non-Gaussian effects in the Rouse theory can only be accomplished in an approximate way. For instance, the optimized Rouse-Zimm local dynamics approach has been applied by Guenza et al. [55] for linear and star chains. They were able to obtain correlation times and results related to dynamic light scattering experiments as the dynamic structure factor and its first cumulant [88]. A similar approach has also been applied by Ganazzoli et al. [87] for viscosity calculations. They obtained the generalized ZK results for ratio g already discussed. 

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. 

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. 

Galiatsatos, V Mark, J. E., Non-Gaussian Effects and Intermolecular Correlations in Bimodal Networks of Poly(dimeth siloxane). In Advances in Silicon-Based Polymer Science. A Comprehensive Resource, Zeigler, J. M. Fearon, F. W. 

Birefringence measurements are very sensitive to himodality and have therefore also been used to chararterize non-Gaussian effects resulting from it in PDMS bimodal elastomers. ... 

The experiments show that the increase of the elasticity modulus starts at a lower degree of swelling for suffer and shorter subchains, because thqr approach their maximum extensibility at smaller content of solvent. Thus, in swollen gels the mechanical behavior is largely influenced by chain extension leading to non-Gaussian effects. 

Networks at very high deformations 1.6.1 Non-Gaussian effects... 

It may be noted that eqs (3.52) and (3.53) are identical for chains with r nl Figure 3.19 compares the stress-strain curves derived under the two conditions (eqs (3.50) and (3.51)). The strong upturn in stress experimentally verified can only be obtained by the non-Gaussian equation. X-ray diffraction on natural rubber has shown that the initial upturn in the load-extension curve is a genuine non-Gaussian effect, unrelated to crystallization. At higher extension... 

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. 

W. van Megen and S. M. Underwood. Tracer diffusion in concentrated colloidal dispersions. II. Non-Gaussian effects. J. Chem. Phys., 88 (1988), 7841-7846. 

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