Stretched network elasticity

It has been shown in Chapter XI that the force of retraction in a stretched network structure depends also on the degree of cross-linking. It is possible therefore to eliminate the structure parameter ve/Vo) by combining the elasticity and the swelling equations, and thus to arrive at a relationship between the equilibrium swelling ratio and the force of retraction at an extension a (not to be confused with the swelling factor as). In this manner we obtain from Eq. (XI-44) and Eq. (39)... 

This universal result is useful to describe network elasticity, because almost none of the subchains in the network is close to full stretching. But as soon as people started doing single molecule experiments, the stretching of DNA to almost its full contour length became possible and brought interesting unexpected results. 

For uniaxially stretched networks, the molecular deformations are characterised by the radii of gyration R u an respectively parallel and perpendicular to the stretching direction. From the small-angle scattering function, the molecular deformation of a stretched elastic phantom chain has been calculated for three cases 1) Free-fluctuation phantom network... 

The scattering form fator S (q) of an elastic strand in a stretched network is a function of 9 and <() In this study of uniaxial deformation,... 

The rubber s polymer network allows elasticity and flexibility to be combined with crystallization-induced strength and toughness when stretched. The elastic nature of this network also accoimts for the exceptional resilience of cured rubber products. This resilience means less kinetic energy is lost as heat during repeated stress deformation. Products made from natural rubber are less likely than most other elastomers to fail from excessive heat buildup or fatigue when exposed to severe dynamic conditions. This has secured the place of natural rubber as the preferred sidewall elastomer in radial tires. 

Two cytoskeletal proteins, tltln (also known as connectm) and nebulm, account for 15% of the total protein in the myofibril. Together these proteins form a flexible filamentous network that surrounds the myofibrils. Titin is an elastic protein and can stretch under tension. Its discovery and characteriza-... 

The elasticity of a polymer is its ability to return to its original shape after being stretched. Natural rubber has low elasticity and is easily softened by hearing. Flowever, the vulcanization of rubber increases its elasticity. In vulcanization, rubber is heated with sulfur. The sulfur atoms form cross-links between the poly-isoprene chains and produce a three-dimensional network of atoms (Fig. 19.17). Because the chains are covalently linked together, vulcanized rubber does not soften as much as natural rubber when the temperature is raised. Vulcanized rubber is also much more resistant to deformation when stretched, because the cross-... 

Arbabi, S Sahimi, M, Elastic Properties of Three-Dimensional Percolation Networks with Stretching and Bond-Bending Eorces, Physical Review B 38, 7173, 1988. 

The constrained-junction model was formulated in order to explain the decrease of the elastic moduli of networks upon stretching. It was first introduced by Ronca and Allegra [39], and Flory [40]. The model assumes that the fluctuations of junctions are diminished below those of the phantom network because of the presence of entanglements and that stretching increases the range of fluctuations back to those of the phantom network. As indicated by the second part of Equation (26), the fluctuations in a phantom network are substantial. For a tetrafunctional network, the mean-square fluctuations of junctions amount to as much as half of the mean-square end-to-end vector of the network chains. The strength of the constraints on these fluctuations is measured by a parameter k, defined as... 

The size and shape of polymer chains joined in a crosslinked matrix can be measured in a small angle neutron scattering (SANS) experiment. This is a-chieved by labelling a small fraction of the prepolymer with deuterium to contrast strongly with the ordinary hydrogenous substance. The deformation of the polymer chains upon swelling or stretching of the network can also be determined and the results compared with predictions from the theory of rubber elasticity. 

When an elastic polymer network is stretched, the polymer chains are deformed. The verification of the theory has been largely based on measurements of the elastic restoring forces... 

It was noted in Ref. 12b that such important physical characteristic exists as elasticity of the spatial H-bond network, which is usually employed [15, 16, 19] for calculations of water spectra. As is intuitively clear, this elasticity should be somehow related to the R-band spectrum, since the stretching vibration, determined by the H-bond elasticity, is believed [16, 35, 51] to present the origin of this band in water. As a basic mechanism, one could regard an additional power loss due to interaction with the a.c. field of the H-bond vibrations. However in Ref. 7, as well as in Ref. 12b, a physical picture relating the CS well to bending vibrations was not established. 

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