Entropy orientational, rule

The first three members of the series with n = 1-3 illustrate Richards s rule with methane, a close to spherical molecule, and Walden s rule with ethane and propane, two non-spherical, rigid molecules. The threefold increase in the entropy of fusion of ethane and propane is caused by the added orientational motion. The linear increase of mass with the number of C-atoms also increases the interaction-energy and, thus, keeps T almost constant... 

A detailed study of crystals of macromolecules 20,21) and their melting under equilibrium conditions revealed that the entropy of fusion, ASf, is often about 7-12 J/(K mol) per mobile unit or "bead" (22). This entropy is linked mainly to the conformational disorder (A and mobility that is introduced on fusion. Sufficiently below the melting temperature, disorder and thermal motion in crystals is exclusively vibrational. While vibrations are small-amplitude motions that occur about equilibrium positions, conformational, orientational, and translational motions are of large amplittide. These types of large-amplitude motion can be assessed by their contributions to heat capacity (23), entropy (22), and identified by relaxation times of the nuclear magnetization 24), Orientational and positional entropies of fusion ASQ ent trans importance to describe the fusion of small molecules. They can be deriv from the many data on fusion of the appropriate rigid, small molecules of nonspheiical and spherical shapes [nonspheiical molecules Walden s rule (1908), ASf = AS j ent AStrans 20-60 J/(K mol) and spherical molecules Richards rule 0 97), ASf = trans = 2-14 J/(K mol)].. The contributions of ASQ ent melting of... 

A detailed analysis of the entropy data on extensive examples using the empirical fusion rules was given by Xenopoluos et al. [34], The three types of disordering that have been studied by these rules are positional [35], orientational [36], and conformational [37-39], which have typical entropy changes of 7-14, 20-50, and 7-12 J/(mol K), respectively [34], Positional and orientational motions are independent of molecular size, whereas conformational motion is proportional to the number of flexible bonds in the molecule. 

A more detailed empirical rule for the entropy of melting is listed at the bottom of Fig. 3.7. Three types of disorder make up the change on fusion positional (pos), orientational (or), and conformational (conf). The approximate contributions to AS are listed in brackets. The first term represents Richards s rule. It is the only contribution for spherical motifs. Irregular motifs can, in addition, show orientational disorder, and thus gain an extra 20-50 J/(K mol) on fusion. Flexible molecules, finally, have a third contribution to the entropy of fusion of 7 -12 J/(K mol) for each flexible bead within the molecule. 

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