Entropy extended states

Description of the mechanics of elastin requires the understanding of two interlinked but distinct physical processes the development of entropic elastic force and the occurrence of hydrophobic association. Elementary statistical-mechanical analysis of AFM single-chain force-extension data of elastin model molecules identifies damping of internal chain dynamics on extension as a fundamental source of entropic elastic force and eliminates the requirement of random chain networks. For elastin and its models, this simple analysis is substantiated experimentally by the observation of mechanical resonances in the dielectric relaxation and acoustic absorption spectra, and theoretically by the dependence of entropy on frequency of torsion-angle oscillations, and by classical molecular-mechanics and dynamics calculations of relaxed and extended states of the P-spiral description of the elastin repeat, (GVGVP) . The role of hydrophobic hydration in the mechanics of elastin becomes apparent under conditions of isometric contraction. 

Rubber thus frozen in the extended state does not recover elastically upon release of stress it has a permanent set . In other words, retraction is blocked by cohesive forces On warming up, however, retraction occurs at once Under ordinary conditions, at room temperature, however, the lattice forces of the crystallites formed upon extension are not strong enough to prevent the rubber from retraction. The entropy factor then surpasses the work of crystallisation. 

At 130°C, the temperature of the experiment, oxidative scission and cross-linking are both going on all the time. The reactions happen, however, in the condition of the network at the time. This means that the continuous stress relaxation experiment measures only the degradation step, because the new cross-links form in the stretched chains that is, the second network develops in the extended state, at equilibrium. There is no significant change in conformational entropy on formation of these cross-links, and the change in stress is near zero. 

This is an expression of Nernst s postulate which may be stated as the entropy change in a reaction at absolute zero is zero. The above relationships were established on the basis of measurements on reactions involving completely ordered crystalline substances only. Extending Nernst s result, Planck stated that the entropy, S0, of any perfectly ordered crystalline substance at absolute zero should be zero. This is the statement of the third law of thermodynamics. The third law, therefore, provides a means of calculating the absolute value of the entropy of a substance at any temperature. The statement of the third law is confined to pure crystalline solids simply because it has been observed that entropies of solutions and supercooled liquids do not approach a value of zero on being cooled. 

The elastic contribution to Eq. (5) is a restraining force which opposes tendencies to swell. This constraint is entropic in nature the number of configurations which can accommodate a given extension are reduced as the extension is increased the minimum entropy state would be a fully extended chain, which has only a single configuration. While this picture of rubber elasticity is well established, the best model for use with swollen gels is not. Perhaps the most familiar model is still Flory s model for a network of freely jointed, random-walk chains, cross-linked in the bulk state by connecting four chains at a point [47] ... 

The reversible recovery of a deformed elastomer to its original (undeformed) state is due to an entropic driving force. The entropy of polymer chains is minimum in the extended conformation and maximum in the random coil conformation. Cross-linking of an elastomer to form a network structure (IX) is... 

The mathematical basis for the exponential series method is Eq. (5.3), the use of which has recently been criticized by Phillips and Lyke.(19) Based on their analysis of the one-sided Laplace transform of model excited-state distribution functions, it is concluded that a small, finite series of decay constants cannot be used to represent a continuous distribution. Livesey and Brouchon(20) described a method of analysis using pulse fluorometry which determines a distribution using a maximum entropy method. Similarly to Phillips and Lyke, they viewed the determination of the distribution function as a problem related to the inversion of the Laplace transform of the distribution function convoluted with the excitation pulse. Since Laplace transform inversion is very sensitive to errors in experimental data,(21) physically and nonphysically realistic distributions can result from the same data. The latter technique provides for the exclusion of nonrealistic trial solutions and the determination of a physically realistic solution. These authors noted that this technique should be easily extendable to data from phase-modulation fluorometry. 

The question then is how do living organisms keep going for extended periods of time how do they maintain their entropy at reasonably low levels i.e. keep their state of organization at a high level ... 

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