Liquid “communal” entropy

The concept of communal entropy has featured within the lattice models of liquids and mixtures. We show in this appendix that this entropy change is due to a combination of assimilation and expansion. 

Originally, Hirschfelder et al. (1937) introduced the concept of communal entropy to explain the entropy of melting of solids. They specifically stated that this communal sharing of volume gives rise to an entropy of fusion. This idea was later criticized by Rice (1938) and by Kirkwood (1950) and now the whole concept of communal entropy in the context of the theory of liquids is considered to be obsolete. 

In a liquid cluster, an atom or molecule is not confined to a particular cell or cage but can wander over the entire volume of the cluster. The communal entropy of a single cluster of size v>v is then given by /ci ln( - l)fJ, where o, is the average configurational volume of a liquidlike... 

The theory now proceeds as developed in Sections V and VI, essentially unchanged. For example, P v) will have the same bimodal structure as shown in Fig. 14, but will now be continuous. Similar smoothing of all artificially introduced discontinuities will not affect the theory in any essential way. The loss of a sharp distinction between liquid- and solidlike cells could vitiate use of the percolation theory. The nonanalyticity in S will certainly be lost, leading to a communal entropy for which 9S/9p is always less than infinity. However, the first-order phase transition should be preserved, just as it was for most of the parameter space even when )3> 1. The discontinuity in p and v would be reduced, as would be the latent heat. One important effect of this smearing will be the appearance of a critical end point for the liquid, a temperature below which the liquid phase is no longer even metastable. The second-order transition, which is only a small region of parameter space for /8> 1, is now wiped out completely by the restoration of analyticity. Our theory thus leads to a first-order phase transition or no transition at all. However, the entropy catastrophe can be resolved within our theory only if a transition occurs. 

At the NI transition, an orientation-dependent term such as AS " " must play a role [26]. In practice, however, the contribution from this source seems to be comparatively small by inference from those of the monomer liquid crystals [112] (cf. Table 4). In treating the transition entropy of real systems, contributions from the so-called communal entropy as well as other residual entropies are often considered by introducing an extra term ASj in Eq. 1 [15,17,34,35,120] ... 

London dispersion forces is the cause of the higher T °. To explain the similar entropies of fusion, one can assume that the entropy of going from positions fixed in the crystal lattice to full access for the motifs to the liquid volume is R, the gas constant of 8.31 J K mol, the communal entropy [38]. An additional 0.7 R was estimated for the two other stages of melting [39]. Assuming that the latter... 

Communal entropy being less than a positive value, no matter how small, cannot be as fundamental an entropy crisis as the requirement Scomm = 0 to argue for an ideal glass transition. For example, liquid helium shows no glass transition when its entropy becomes equal to such a small positive value. Thus, we will adhere to Scomm = 0 as the most fundamental requirement forthe entropy crisis. This also rules out using the excess entropy AS x (T) in (10.16) used by Kauzmann and various other authors, to be used as a signal of an entropy crisis when it vanishes at a positive temperature, since thermodynamics itself does not rule... 

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