Rubber theory

On the basis of the simple rubber theory, Fei has been expressed as [1,24-29]... 

This model is based on classic rubber theory, suggesting that elastin is made up of a network of random chains that are kinetically free and exist in a high entropic state. Stretching orders the chains and limits their conformational freedom, thus decreasing the overall entropy of the system (Hoeve and Flory, 1974). This provides the restoring force to the relaxed state. 

A number of different mechanisms have been proposed to account for the rubberlike properties of materials. In classical rubber theory these properties are attributed to a decrease in conformational entropy on deforming a network of kinetically free random polymer molecules. Stress orders the polymer chains and decreases their entropy by limiting their conformational freedom, thus providing the restoring force to the relaxed state. Such a theory was developed for elastin by Hoeve and Flory... 

The tenet of classical rubber theory has been that the chains are in random networks and the networks comprise a Gaussian distribution of end-to-end chain lengths. However, the mechanisms and molecular bases for the elasticity of proteins are more complex than that of natural rubber. In biological systems elastomeric proteins consist of domains with blocks of repeated sequences that imply the formation of regular stmctures and domains where covalent or noncovalent cross-linking occurs. Although characterised elastomeric proteins differ considerably in their precise amino acid sequences they all contain elastomeric domains comprised of repeated sequences. It has also been suggested that several of these proteins contain p-tums as a structural motif (Tatham and Shewry 2000). 

The values of X calculated from Eq. 26 are given in Table 8. It should be pointed out that the classical rubber theory does not account for a dependence of molecular orientation on the considered length scale, as found for sample C in Fig. 29. Therefore the simplistic approach presented here should in principle be restricted to samples A and B for which the principal directions for the low-q SANS data (I and II) are close to the principal directions for the refractive index. The data in Table 8 actually show a satisfactory agreement between calculated and experimental mean square chain dimensions for samples A and B. For sample C, the agreement is less satisfactory in the direction perpendicular to the chain elongation, but one must be aware that for this sample, the directions in which Rg j and Rg jj measured... 

In this work we used polystyrene-based ionomers.-Since there is no crystallinity in this type of ionomer, only the effect of ionic interactions has been observed. Eisenberg et al. reported that for styrene-methacrylic acid ionomers, the position of the high inflection point in the stress relaxation master curve could be approximately predicted from the classical theory of rubber elasticity, assuming that each ion pah-acts as a crosslink up to ca. 6 mol %. Above 6 mol %, the deviation of data points from the calculated curve is very large. For sulfonated polystyrene ionomers, the inflection point in stress relaxation master curves and the rubbery plateau region in dynamic mechanical data seemed to follow the classical rubber theory at low ion content. Therefore, it is generally concluded that polystyrene-based ionomers with low ion content show a crosslinking effect due to multiplet formation. More... 

Meissner, B., Bound Rubber Theory and Experiment. J. Appl. Polym. Sci. 1993, 50, 285-292. 

The second postulate of the ideal-rubber theory is that, after deformation, the distribution of chain end-to-end vectors is perturbed in exactly the ratio determined by the macroscopic deformation. This assumption is called the principle of affine deformation. The distribution of chain end-to-end vectors is now given by ... 

Still other possibilities exist e.g., a concept revealing a weakness of the Doi-Ed-wards model the modelization of the melt by a temporary rubber leads to the use of the classical rubber theory this is known to encounter considerable discrepancies for actual rubbers (crosshnked melts). A slightly different description of a rubber would lead to greater motion of the crosslinks, and consequently of more extensive rearrangement of the tube constraints in the melt (see Sect. 13). 

Origin of Nonlinear Viscoelasticity in Filled Rubbers Theory and Practice... 

Meissner B. Bound rubber theory and experiment. J Appl Polym Sci 1993 50 285-92. 

Coefficient of friction as function of contact pressure in lubricated sliding on rubber. Theory calculated on basis of deformation losses. 

The starting point is the probability of finding a conformation i (s) for the linear chain. This problem is discussed in detail in the chapter by Edwards and Muthukumar, and we give a brief description in Section 8.3.2 within this chapter, because of use in rubber theory, and we refer the mathematically interested reader to these parts of this series (Volume 2, Chapter 9). Assuming Gaussian conformations, it is given by the Wiener measure " ... 

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