Frozen entropy

It may be noted that the entropy of the melt is considered as entirely configurational in AG theory. At Tm, it is equal to = dJiJT . The manner of decrease of this quantity is considered as determined by the difference between the heat capacities of melt and the crystalline phases in the supercooled region. At Tg, the frozen entropy, 5 is calculated as... 

Clearly, the sticking coefficient for the direct adsorption process is small since a considerable amount of entropy is lost when the molecule is frozen in on an adsorption site. In fact, adsorption of most molecules occurs via a mobile precursor state. Nevertheless, direct adsorption does occur, but it is usually coupled with the activated dissociation of a highly stable molecule. An example is the dissociative adsorption of CH4, with sticking coefScients of the order 10 -10 . In this case the sticking coefficient not only contains the partition functions but also an exponential... 

Formally, S2 represents a decrease in the autocorrelation function caused by the motion S2=0 corresponds to completely unrestricted motion of a bond (N-H in this case), while S2=0 is expected if the bond reorientations are frozen. It was shown recently that the order parameter may be related to the statistical mechanical properties of a protein molecule [33-35] hence, changes in the NMR-derived order parameters can indicate localized contributions to overall molecular entropy. 

Ulbrich and Waldbaum [14] pointed out that calorimetrically determined third law entropies for many geologically important minerals may be in error because site mixing among cations, magnetic spin disorder, and disorder among water molecules in the crystals is frozen in the samples used for calorimetric measurements. They have calculated corrections based on known crystallographic data for several minerals. 

The processes of life involve both energetic and entropic factors. When we walk, run, climb, fidget, dance, or toss and turn in bed, we are doing work against physical forces. When we ice fish on a frozen lake in Minnesota, we need to generate heat to keep our body temperature constant. That heat is lost to the enviromnent (an ineffective way to heat Minnesota in the winter but it happens nonetheless). In contrast, when we synthesize DNA in the process of cell division with its precisely ordered sequence of bases or synthesize proteins with their precisely ordered sequences of amino acids, it is entropy that we must overcome, not physical forces or heat exchange. The bottom line is that we need a source of energy to five. 

A negative change in entropy associated with the decreased freedom of motion of water molecules in the vicinity of a nonpolar group. As pointed out by Jencks one should not be too literal when interpreting this behavior, because the system is dynamic, and not frozen. The term flickering cluster implies some reduction in libration and rotation without complete loss. 

All the above methods are somehow based on an orbital hypothesis. In fact, in the multipolar model, the core is typically frozen to the isolated atom orbital expansion, taken from Roothan Hartree Fock calculations (or similar [80]). Although the higher multipoles are not constrained to an orbital model, the radial functions are typically taken from best single C exponents used to describe the valence orbitals of a given atom [81]. Even tighter is the link to the orbital approach in XRCW, XAO, or VOM as described above. Obviously, an orbital assumption is not at all mandatory and other methods have been developed, for example those based on the Maximum Entropy Method (MEM) [82-86] where the constraints/ restraints come from statistical considerations. 

Now the assumption is dropped that the chemical reaction is a rate-controlled conversion to an invariant product composition, and the composition is permitted to vary with local thermodynamic state. Zel dovich, Brinkley Si Richardson, and Kirkwood Wood pointed out that since in a chemically reactive wave, pressure is a function not only of density and entropy but also of chemical composition, the sound speed for a reacting material should be defined as the frozen sound speed... 

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