Entropy relaxation

The interpretation of these data becomes clearer when introducing an entropy relaxation by slow cooling before an analysis with a faster heating rate (see Sect. 6.1.3). Figure 7.79 documents that the enthalpy relaxation centers at the glass transitions of the homopolymers with a reduction in peak amplitude on copolymerization that is larger than expected from the reduction in concentration. This is the typical behavior of phase-separated polymers. Even more conclusive is that electron microscopy on the same samples reveals that all these high-molar-mass S/MS block copolymers are microphase-separated. 

Fig. 2. The schematic curves of the entropy, s, and the free volume, Vf, around Tg for polymers. Upper 1 the change of s for the liquid glass frozen partially from the supercooled liquid, shown by the dashed line, 2 the entropy relaxation and 3 the change of s with a jump at Tg upon heating. Lower The dashed line upon cooling is the Vf curve for the same liquid glass, the solid line upon heating after relaxation shows the Vf curve with a jump at Tg and the dashed line shows a reversible jump of Vf between Tg and Te.

As we have seen above, the temporal evolution of Mg is due to the longitudinal relaxation The temporal evolution of Mj (or My), which is described as transverse relaxation, is fundamentally different. It corresponds to the loss of phase coherence between the individual magnetic moments. Transverse relaxation can be described as an entropy relaxation in the sense that the final state (0, 0, Mq) is characterized by a higher entropy than the initial state (M, My, M ). As in the case of the temporal evolution of Mg, the analytical form of the My f(t) function is not predictable without careful analysis. This problem will also be discussed later. 

The mechanisms of deexcitation of stressed chains have been discussed en passant while investigating bond strength and chain loading. These mechanisms are chain slip with respect to a surrounding matrix (enthalpy relaxation), change of chain conformation (entropy relaxation), or chain rupture. 

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

A second type of relaxation mechanism, the spin-spm relaxation, will cause a decay of the phase coherence of the spin motion introduced by the coherent excitation of tire spins by the MW radiation. The mechanism involves slight perturbations of the Lannor frequency by stochastically fluctuating magnetic dipoles, for example those arising from nearby magnetic nuclei. Due to the randomization of spin directions and the concomitant loss of phase coherence, the spin system approaches a state of maximum entropy. The spin-spin relaxation disturbing the phase coherence is characterized by T. ... 

Transient, or time-resolved, techniques measure tire response of a substance after a rapid perturbation. A swift kick can be provided by any means tliat suddenly moves tire system away from equilibrium—a change in reactant concentration, for instance, or tire photodissociation of a chemical bond. Kinetic properties such as rate constants and amplitudes of chemical reactions or transfonnations of physical state taking place in a material are tlien detennined by measuring tire time course of relaxation to some, possibly new, equilibrium state. Detennining how tire kinetic rate constants vary witli temperature can further yield infonnation about tire tliennodynamic properties (activation entlialpies and entropies) of transition states, tire exceedingly ephemeral species tliat he between reactants, intennediates and products in a chemical reaction. 

Figure 4.14 shows the first few iteration steps in the evolution of the spatial measure block-entropy of rule R122 for blocks with size B < 5. Although the irreversibility of this rule predictably leads to a decrease of entropy with time, there nonetheless appears to be a relaxation to equilibrium values. Observe also... 

Entropy is a measure of disorder in materials. Relaxed polymer chains with a random conformation (shape in space), like cooked spaghetti or a box of fishing worms, have a high degree of entropy, which is favored by Mother Nature. If the chains are stretched out (stressed), the number of conformations the chains can have in space is limited, and the entropy is reduced (see Figure B). The ratio of final length to initial length is denoted a. 

The main models are described in a review by Vrhovski and Weiss [8]. For ideal elastomers in the extended mode, all the energy resides on the backbone and can therefore be recovered upon relaxation [18]. Generally, it is believed that the mechanism of elasticity is entropy-driven, thus the stretching decreases the entropy of the system and the recoil is then induced by a spontaneous return to the maximal level of entropy [8]. 

We have seen that the cooperative region, which represents a nominal dynamical unit of liquid, is of rather modest size, resulting in observable fluctuation effects. Xia and Wolynes [45] computed the relaxation barrier distribution. The configurational entropy must fluctuate, with the variance given by the usual expression [77] 5Sc) ) = Cp barrier height for a particular region is directly related to the local density of states, and hence to... 

The earliest and simplest approach in this direction starts from Langevin equations with solutions comprising a spectrum of relaxation modes [1-4], Special features are the incorporation of entropic forces (Rouse model, [6]) which relax fluctuations of reduced entropy, and of hydrodynamic interactions (Zimm model, [7]) which couple segmental motions via long-range backflow fields in polymer solutions, and the inclusion of topological constraints or entanglements (reptation or tube model, [8-10]) which are mutually imposed within a dense ensemble of chains. 

The fact that only intermolecular energies are needed for the binding estimate has often been interpreted in such a way that intramolecular relaxation/strain, entropy, receptor desolvation etc. are neglected. We have tried to illustrate here that, at least formally, this is not the case. Using ion binding to crown ethers as an example one can easily see that these effects are in principle embedded in the linear response approximation. Whether the approximations involved in the LIE type of equation are accurate enough is another matter. However, from the various reports on the method published so far it appears that most systems, irrespective of force fields, simulation... 

Apart from the above mentioned redox type reactions, we like to consider (in connection with work to be published by us elsewhere) another type of relaxations, due to the possible reorganisations of sorption intermediates on the catalyst surface, as suggested by some investigations in our laboratory. This structuring on the catalyst surface is equivalent to a change in the entropy of the system catalyst surface / adsorbed intermediates and seems to be responsible e.g. for the selectivity change under transient conditions in the oxidation of hydrocarbons. Actually this structural organization of the surface intermediates is also a rate process which can be observed under transient conditions. 

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