Entropy additional contributions

One of the consequences of accepting the presence of multiple magnetic states is an additional contribution to the entropy and, therefore, several authors have considered the inclusion of multiple states in their description of low-temperature phase transformations in Fe and its alloys (Kaufman et al. 1963, Miodownik 1970, Bendick and Pepperhoff 1978). However, most authors have, in the end, preferred to describe the magnetic effects in Fe using more conventional temperature-independent values for the magnetic moments of the relevant phases. This is partly linked to the absence of any provision for the necessary formalism in current... 

Osborne-Lee et al. (12) have accounted for the additional contribution to the excess entropy of mixing and found the following excess free energy of mixing per amphiphile... 

Here Fe(t) and Fg(t) are the time-dependent nonequilibrium Helmholtz free energies of the e and g states, respectively. The energy difference A U(t) can be replaced by a free energy difference due to the fact that the entropy is unchanged in a Franck-Condon transition [51]. Free energies in Eq. (3) can be represented [54] by a sum of an equilibrium value Fcq and an additional contribution related to nonequilibrium orientational polarization in the solvent. Thus for the free energy in the excited state Fe(t) we have... 

The entropy of the adsorbate may be identified with the excess entropy S if this excess is referred to the entropy of gas molecules at rest. It consists of additive contributions due to configurations and vibrations (of the adsorbed molecule) around its rest position ... 

Even if simple expressions for the directional field are not available, it is possible to draw certain conclusions about the other thermodynamic functions from (4.2). The orientational free energy Fi<>0 leads to the following additional contributions to the entropy, internal energy and heat capacity at constant volume... 

In the magnetically ordered materials, the additional contribution f(Cm/T) AT, expressed in eq. (2.7), reflects the amount of the entropy change associated with the ordering. In the case of localized moments this expression should be equal to RlnM where M is the multiplicity of the ground state, but in the itinerant systems strongly reduced values are found. 

The transition entropies under atmospheric pressure can be conventionally determined by DSC. The heats estimated by DSC are often affected by the amount of sample loaded on the pan and also on the scanning speed of the apparatus. They may include some additional contributions due to pretran-sitional and posttransitional phenomena occurring in the immediate vicinity of the transition [113-117]. In addition, some difficulty is inevitably invoked in selecting a baseline to measure the area of the absorption peak. In view of these difficulties involved in the DSC method, the use of the Clapeyron rela-... 

The favorable effect on polyolefin miscibility of statistical segment length asymmetry due to the entropy contributions required for conformational adjustments has also been emphasized by Bates et al. [87]. In a series of papers. Bates and Fredrickson [88] attributed the miscibility of athermal or nearly athermal polymer mixtures mainly to these conformational asymmetries which contribute substantially to a nonlocal conformational excess entropy of mixing. The effect is exemplified for the amorphous polyethylene/poly-(ethylethylene) blend. Due to the fact that unperturbed PE and PEE molecules cannot be randomly interchanged, a positive excess free energy of mixing caused by nonlocal excess entropy contribution is anticipated by the authors. The effect of asymmetry on polymer miscibility is also supported by computer simulations, which suggest additional contributions due to entropy density differences of the pure polymeric phases [89]. 

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