Fluctuations elastic properties

A good understanding of the structure of the network in filled rubbers is of great importance, because the rubber s elastic properties are determined primarily by the density of chemical and physical network junctions and their ability to fluctuate. The following types of network junctions occur in filled rubbers ... 

The elastic properties of rubbers are primarily governed by the density of netw ork junctions and their ability to fluctuate [35]. Therefore, knowledge of the network structure composed of chemical, adsorption and topological junctions in filled elastomers as well as their relative weight is of a great interest. The H T2 NMR relaxation experiment is a well established method for the quantitative determination of the network structure in the elastomer matrix outside the adsorption layer [14, 36]. The method is especially attractive for the analysis of the network structure in filled elastomers since filler particles are "invisible" in this experiment due to the low fraction of protons at the Aerosil surface as compared with those in the host matrix. 

Recently, Brillouin scattering has proved useful in this area for studying the frequency dependence of hypersonic (GHz zone) absorption and dispersion velocity in liquid sulphur dioxide [91] the effect of isotopes on hydrodynamic fluctuations in self-associated fluids [92] and the elastic properties of polyethylene glycol solutions in water, benzene and toluene [93]. 

In one study, a model for elastin, the main protein that confers elasticity on solid structures in mammals, had its mobility investigated by examining 1H-13C and 1H dipolar couplings extracted from isotropic-anisotropic correlation experiments.29 The elastic properties of elastin are almost certainly conferred by molecular degrees of freedom, so such studies are important in understanding how this material works in Nature. The motional amplitudes determined from these experiments were found to depend upon the degree of hydration, with the mean square fluctuation angles found to be 11-18° in the dry protein and 16-21° in the 20% hydrated protein. 

In Section 5.7.2 we discussed a general problem of stability of one, two- and three-dimensional phases. Here, we shall analyze stability of the smectic A liquid crystal, which is three-dimensional structure with one-dimensional periodicity. The question of stability is tightly related to the elastic properties of the smectic A phase. Consider a stack of smectic layers (each of thickness Z) with their normal along the z-direction. The size of the sample along z is L, along x and y it is L, the volume is V = Lj L. Fluctuations of layer displacement u(r) = u(z, r i) along z and in bofli directions perpendicular to z can be expanded in the Fourier series with wavevec-tors q and q (normal modes) ... 

The SmA phase has the same symmetry and the same dielectric ellipsoid as in nematics, therefore, everything said above about the birefringence and dichroism is valid for the SmA phase. However, due to specific elastic properties of the layered structure, the director fluctuations are strongly quenched, and the SmA preparations are much more transparent than the nematic ones. This is related to specific elastic properties of the lamellar SmA phase [14]. 

Forster D (1986) On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes. Phys Lett A 114(3) 115-120... 

West B, Schmid F (2010) Fluctuations and elastic properties of lipid membranes in the fluid and gel state a coarse-grained Monte Carlo study. Soft Matter 6 1275-1280... 

In the foregoing discussion of stability of the flat surface of a stressed solid, it was assumed that the elastic material is homogeneous. It was also assumed that, prior to formation of fluctuations in surface shape, the material was homogeneously stressed, that is, the equi-biaxial stress acted throughout the material. This assumption on stress is not essential. It will be shown in Section 8.9 that the results are unaffected if the initial mismatch stress acts only to some finite depth, provided only that this depth extends beyond the roots of the valleys in surface fluctuation. Otherwise, a discontinuity in the initial stress across some plane y = constant is immaterial. Discontinuities in elastic properties, however, do have an influence on stability. 

Molecular simulations of ionomer systems that employ classical force fields to describe interactions between atomic and molecular species are more flexible in terms of system size and simulation time but they must fulfill a number of other requirements they should account for sufficient details of the chemical ionomer architecture and accurately represent molecular interactions. Moreover, they should be consistent with basic polymer properties like persistence length, aggregation or phase separation behavior, ion distributions around fibrils or bundles of hydrophobic backbones, polymer elastic properties, and microscopic swelling. They should provide insights on transport properties at relevant time and length scales. Classical all-atom molecular dynamics methods are routinely applied to model equilibrium fluctuations in biological systems and condensed matter on length scales of tens of nanometers and timescales of 100 ns. 

Quantitative predictions of the model are sensitive to the shape of pores, the distribution of fixed-charged groups at pore walls, the reorganization of charged groups at pore walls upon swelling, proton distribution effects in pores, and microscopic elastic properties of the polymer matrix. A consistent model must account for, and properly validate, all of these details. However, there is significant experimental uncertainty related to all of these properties and there are statistical spatial fluctuations in all of them. 

The intense light scattering of nematics is due to thermally induced orientational fluctuations of the nematic director field. These orientational fluctuation modes are related to the viscous and elastic properties of the nematic (see, for example, Litster [27]). 

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