Entropy inverse temperature transitions

T[ and Tj, are the on-set temperature for the hydrophobic folding and assembly transition, that is, inverse temperature transition, in pbs (0.15 N NaCl, 0.01 M phosphate) as determined by light scattering and in water as determined by DSC, respectively. Both values are linearly extrapolated tofx = 1 and rounded to a number divisible by 5. AH and AS are the values at/x = 0.2 on the curve for a linear fit of the DSC derived endothermic heats and entropies of the transitions for die polymers in water. 

Figure 2.8. Ordered water molecules surround oillike groups, as first shown by Stackelberg and Muller. As oil-like groups associate, this structured water becomes less ordered liquid water this is the large positive change in entropy responsible for the inverse temperature transition, the phase transition that is fundamental to protein function. As shown in the upper left, hydration of a proximal carboxylate...

Inverse Temperature Transitions Provide Negative Entropy to Protein... 

The inverse temperature transition is a specific mechanism whereby thermal energy (heat) provides an increase in order of the protein part of the system. A decrease in entropy of this sort has been termed negative entropy by Schrodinger. ° While the total entropy (disorder) for the complete system of protein and water increases as the temperature is raised, the structural protein component, critical to the conversion of thermal energy to mechanical work, increases in negative entropy. The protein component increases in order by the folding that shortens length and by the assembly of oillike domains that builds structures. 

Inverse Temperature Transitions Extract Order (Negative Entropy) from Energy Sources ... 

Despite the absorption of heat for the transition and the overall increase in entropy of -(-4.0 EU for the water plus protein, the protein component actually increases in order on raising the temperature. As unambiguously demonstrated by crystallization of a cyclic analog (see Figure 2.7), in this case the protein component of the water plus protein system becomes more ordered as the temperature is raised. For this and additional reasons, noted below in section 5.1.3, we call this transition exhibited by our model protein, poly (GVGVP), an inverse temperature transition. 

Formation of hydrophobic hydration is exothermic (Butler, 1937). Accordingly, when the temperatiure of the dissolved protein with its hydrophobic hydration is raised from below to above the inverse temperature transition, an endothermic transition due to the conversion of hydrophobic hydration to bulk water occurs. The transition from hydrophobic hydration to bulk water represents a positive change in entropy. By finding a suitable solvent that allows the transition but reduces the heat of the transition to near zero, it becomes possible to determine whether a decrease in elastic... 

Examples with different repeat compositions of 2,000 polymer preparations. T, T, AQ, AH, and AS are on-set temperature, maximum heat absorption temperature, heat, enthalpy, and entropy of the inverse temperature transition as determined by DSC, respectively. AH and AS are values per mole of repeating peptide. This is true for the DSC data reported in all tables in this article. 

Figure 2.5 shows also the concentration dependence of the inverse Kauzmann temperature T (entropy catastrophe temperature). For the pure metal, T is much higher than the temperature T0 as discussed. The 77-line should also decrease with increasing concentration and end in the triple point(C, 7 )[2.21] as follows from its definition (AS = 0). It is interesting to note that at this point the real Kauzmann temperature and the inverse Kauzmann temperature meet. But in real systems, the amorphous phase has an excess entropy (small fraction of the entropy of fusion) when compared to the corresponding crystal, the exact amount determined from the kinetics and timescale of the glass transformation. Therefore, another glass transition temperature line with finite excess entropy must be considered, which will be parallel to the Tg-line (above it) and cross the T0- and 77-lines not exactly in the triple point. 

Cycloheptane and cyclooctane data on the thermal properties are also given in Table 3.1 They show little change from the cyclopentane and cyclohexane properties. Again, there is no indication of increasing amounts of conformational entropy in the transition entropies. For cyclooctane in solution H and NMR could prove ring-inversions and pseudorotation among the boat-chair conformations through the twist-boat-chair intermediate to very low temperatures (100 K). Only about 6% of the cydooctane could be found at about 300 K in the other three crown-family... 

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