Heat capacity increment, dependence

Hen egg-white lysozyme, lyophilized from aqueous solutions of different pH from pH 2.5 to 10.0 and then dissolved in water and in anhydrous glycerol, exhibits a cooperative conformational transition in both solvents occurring between 10 and 100°C (Burova, 2000). The thermal transition in glycerol is reversible and equilibrium follows the classical two-state mechanism. The transition enthalpies AHm in glycerol are substantially lower than in water, while transition temperatures Tm are similar to values in water, but follow similar pH dependences. The transition heat capacity increment ACp in glycerol does not depend on the pH and is 1.25 0.31 kj (mol K) 1 compared to 6.72 0.23 kj (mol K)-1 in water. Thermodynamic analysis of the calorimetric data reveals that the stability of the folded conformation of lysozyme in glycerol is similar to that in water at 20-80°C but exceeds it at lower and higher temperatures. 

Fig. 4. Temperature dependence of the specific enthalpy of denaturation of myoglobin and ribonuclease A (per mole of amino acid residues) in solutions with pH and buffer providing maximal stability of these proteins and compensation of heat effects of ionization (see Privalov and Khechinashvili, 1974). The broken extension of the solid lines represents a region that is less certain due to uncertainty in the A°CP function (see Fig. 2). The dot-and-dash lines represent the functions calculated with the assumption that the denaturation heat capacity increment is temperature independent.

Applying the established temperature dependence of A, Cp to the substances listed in Tables II and III, one can find that the enthalpy of the transfer of all these substances from the gaseous phase to water decreases to zero within the temperature range 100-180°C (Fig. 10). As is evident, when one linearly extrapolates A%H values determined at 25°C, using the usual assumption that Ag Cp is temperature-independent, one finds a lower value of the temperature TH(g w) at which the hydration enthalpy is zero (see the last column in Table II). It is clear, however, that these values, obtained by linear extrapolation, i.e., assuming constant heat capacity increment, have only a fictitious meaning. Nevertheless, in all cases one can conclude that the heat of solvation becomes zero at an elevated temperature in the range of 410 40 K. 

Molecular Mass Dependence of the Heat Capacity Increment at the Glass Transition... 

Here ACp is the heat capacity increment associated with exploration of the landscape (i.e. the jump in Cp as T > Tg). Of course the relative height Tu/Tk is then greater for liquids with small ACp (i.e. strong liquids), in accord with the higher Tc/Tg found by Rdssler et al (12,13) for the stronger liquids. The value of Tu turns out to depend only weakly on the functional form assumed for ACp. The two simple choices,... 

The transition of a protein or a single cooperative domain from the native to the denatured state is always accompanied by a significant increase of its partial heat capacity (see, for reviews, Sturtevant, 1977 Privalov, 1979). The denaturationaJ increment of heat capacity A JCP = C° Cp amounts to 25-50% of the partial heat capacity of the native protein and does not depend noticeably on the environmental conditions under which denaturation proceeds (Fig. 1) or on the method of denaturation. However, it is different foi different proteins and seems to correlate with the number of contacts between nonpolar groups in native proteins (Table I). On the other hand, the partial specific heat capacities of denatured states of different proteins appear to be rather similar (Tiktopulo et... 

The general thermodynamic properties of proteins reported above give rise to several questions What do the asymptotic (at Tx) values of the denaturation enthalpy and entropy mean and why are they apparently universal for very different proteins Why should the denaturation enthalpy and entropy depend so much on temperature and consequently have negative values at low temperature In other words, why is the denaturation increment of the protein heat capacity so large, with a value such that the specific enthalpies and entropies of various proteins converge to the same values at high temperature ... 

The JANAF Thermochemical Tables consist of thermal functions and formation functions, both of which are temperature dependent. The thermal functions consist of heat capacity, enthalpy increments, entropy, and Gibbs en-... 

Measurement of the heat content. Heat content determinations at high temperatures are generally easier than direct heat capacity measurements. They were widely used in early stages of measurement to obtain Cp data of molten salts. The enthalpy increment of a substance between temperatures T and T2, Hp2 — Hp T2 > T ), is measured in general using a drop calorimeter. Two techniques are employed, depending on the way the measurements are carried out. 

Polymerization entropies can be determined in several ways via the temperature dependence of the equilibrium concentrations of the monomer, via the heat capacity, via the activation constants for polymerization and depolymerization, or via an incremental calculation method. The heat capacity serves to determine the entropy of polymerization because the quotient of specific entropy and specific heat capacity, (A5 /c ) is about unity at 298 K for polymers irrespective of their constitution. False results occur if, for example, monomer association in the vapor phase occurs, or if, with polymers, there is a physical transition in the temperature range between calorimetric measurement and equilibrium measurement. 

In certain cases, the entropy of polymerization can also be calculated using an increment method. A direct determination, for example, of from the heat capacity is possible, but this method can give incorrect values in some circumstances. Incorrect values are observed when a monomer associates in the vapor phase, or when physical transitions occur in polymers in the range of temperatures between calorimetric measurements and equilibrium measurements. If such effects are excluded, then the quotient S%s/Cp 298 is remarkably constant for the most dissimilar monomer-polymer systems (Table 16-10). Determination of the entropy of polymerization from the temperature dependence of the equilibrium concentrations of the monomer is relatively unambiguous. Alternatively, it can be determined from the Arrhenius parameters Ap of polymerization and A p of depolymerization [of equation (16-52)]. 

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