Isothermal compressibility temperature dependence

The Yl/A isotherms of the racemic and enantiomeric forms of DPPC are identical within experimental error under every condition of temperature, humidity, and rate of compression that we have tested. For example, the temperature dependence of the compression/expansion curves for DPPC monolayers spread on pure water are identical for both the racemic mixture and the d- and L-isomers (Fig. 13). Furthermore, the equilibrium spreading pressures of this surfactant are independent of stereochemistry in the same broad temperature range, indicating that both enantiomeric and racemic films of DPPC are at the same energetic state when in equilibrium with their bulk crystals. 

N-Stearoyltyrosine. The case of N-stearoylserine methyl ester illustrates temperature-dependent enantiomeric discrimination in both monolayers spread from solution and in equilibrium with the bulk phase. Although the IIIA isotherms suggested large differences in the intermolecular associations in homochiral and heterochiral films of SSME, there exist chiral systems in which enantiomeric discrimination as exhibited in film compression properties is much more subtle. N-Stearoyltyrosine (STy) is such a system. 

In order to calculate the dilational contribution exactly a considerable quantity of data is needed. The temperature dependence of the volume, the iso-baric expansivity and the isothermal compressibility is seldom available from 0 K to elevated temperatures and approximate equations are needed. The Nernst-Lindeman relationship [7] is one alternative. In this approximation cP,m -Cv,m is given by... 

Here V is the crystal volume, k-p and ks are the isothermal and adiabatic compressibility (i.e., the contraction under pressure), P is the expansivity (expansion/contraction with temperature), Cp and Cv are heat capacities, and 0e,d are the Einstein or Debye Temperatures. Because P is only weakly temperature dependent,... 

Free Volume Versus Configurational Entropy Descriptions of Glass Formation Isothermal Compressibility, Specific Volume, Shear Modulus, and Jamming Influence of Side Group Size on Glass Formation Temperature Dependence of Structural Relaxation Times Influence of Pressure on Glass Formation... 

Knowledge of temperature and pressure dependence of physical-chemical properties is very useful to estimate the values of derived parameters, such as the thermal expansion coefficient, a, and the isothermal compressibility, Kj. 

The value of the molar volume of a solvent at other temperatures and pressures, not too far from the ambient, can be obtained by employing the isobaric thermal expansibility, ap, and the isothermal compressibility, kt. The former of these expresses the relative increase in volume on raising the temperature at a constant pressure and the latter expresses the relative decrease of the volume on raising the pressure at a constant temperature. These quantities are also temperature and pressure dependent, but over a limited range of these variables near ambient conditions they can be taken as being constant. 

Fig. 3.2). This equation is derived from crystal lattice parameters for ice Ih (Petrenko and Whitworth 1999) and is valid over a temperature range of 160 to 273 K. The ice isothermal compressibility shows a significant temperature dependence (Marion and Jakubowski 2004) ... 

The pressure dependence of equilibrium constants in this work are estimated with Eq. 2.29, which requires knowledge of the partial molar volumes and compressibilities for ions, water, and solid phases. For ions and water, molar volumes and compressibilities are known as a function of temperature (Table B.8 Eqs. 3.14 to 3.19). Molar volumes for solid phases are also known (Table B.9) unfortunately, the isothermal compressibilities for many solid phases are lacking (Millero 1983 Krumgalz et al. 1999). 

Some properties are directly connected with mass and packing density (or its reciprocal specific volume), thermal expansibility and isothermal compressibility. Especially the mechanical properties, such as moduli, Poisson ratio, etc., depend on mass and packing. In this chapter we shall discuss the densimetric and volumetric properties of polymers, especially density and its variations as a function of temperature and pressure. Density is defined as a ratio ... 

A wide variety of density- and temperature-dependent input parameters are required. These include p, the number density of the solvent, kj, the isothermal compressibility, f, the correlation length of density fluctuations, y = Cp/Cv, the ratio of specific heats, and 37, the viscosity. Very accurate equations of state for ethane (74,75,99) and CO2 (74) are available that provide the necessary input information. The necessary input parameters for fluoroform were obtained by combining information from a variety of sources (76,100,101). There is somewhat greater uncertainty in the fluoroform parameters. 

Two characteristics of liquid water that are relevant to the present answer are the equation of state characteristics shown in Figs. 8.11 and 8.12. The isothermal compressibilities shown in Fig. 8.11 indicate that water is stiffer than organic solvents, and that the stiffness is only weakly temperature-dependent. We don t propose here a detailed explanation of that stiffness - it is due to intermolecular interactions among solvent molecules, hydrogen bonding in the case of liquid water (Debenedetti, 2003) - but the present empirical theory of hydrophobicity merely exploits those results. This stiffness is the principal determinant of the low solubility of inert gases in liquid water. In the simplest information models this stiffness, and its temperature dependence, is expressed by the experimental n (n — l))o, which is distinctive of liquid water. 

Figure 8.11 Isothermal compressibilities, Kj = — /V) dV/dp)j, for several solvents plotted as a function of temperature along their saturation curves. The results are taken from Rowlinson and Swinfon (1982). Liquid wafer is sfiffer fhan the other solvents here, and that stiffness is less temperature-dependent.

Compression may take place at a filling station, receiving hydrogen from a pipeline. The energy requirement depends on the compression method. The work required for isothermal compression at temperature T from pressure P, to Pj is of the form... 

The close superposition of C02/polymer isotherms at various tempo-atures, when plotted vs. activity, sugg ts that most of the apparent temperature dependence of the isotherms plotted vs. pressure is related to the activity change of CO2 with temperature. At constant activity, die actual mixing of CO2 with PMMA, PC, or PVBz appears to be nearly athermal i.e., the energy of interaction of CO2 with these polymers seems to be essentially that associated with the compression of the gas to its molar volume in the sorbed state. This aspect of polymer interactions with CO2 will also be consicfored further in forthcoming publications. 

The first three terms of equation 4 can be easily calculated from the available data (fi). The fifth term is zero. The temperature and pressure dependency of the coefficient of thermal expansion, Opif and the isothermal compressibility, up to... 

A study has been made of the temperature dependence of the isothermal compressibility of B203.195... 

A united-atom model for [C4mim][PF6] and [C4mim][N03] was developed in the framework of the GROMOS96 force field [71]. The equilibrium properties in the 298-363 K temperature range were validated against known experimental properties, namely, density, self-diffusion, shear viscosity, and isothermal compressibility [71]. The properties obtained from the MD simulations agreed with experimental data and showed the same temperature dependence. 

Such a derivation was originally developed and used by Kirchoff [1858] and Rankine [1849] ( ) to express the temperature dependence of vapor pressure. It was also successfully used by Brostow (O to express the temperature dependence of the isothermal compressibility of a wide variety of organic liquids, some metallic liquids and water. By a similar analogy, we have used it to express the viscosity of liquid mold fluxes. 

Figure 9.9 Exceptional physical properties of liquid water (solid lines) temperature dependences (upper diagrams) of the density d (45) and isothermal compressibility Xt (adapted from Refs. (45 7)) pressure dependences (lower drawings) of the shear viscosity 7] at various temperatures (adapted from Ref. (48)) and of the isothermal diffusion coefficient Z) at 0 (adapted from Ref. (49)). Dashed lines sketch typical dependences displayed by almost all other liquids. Note that at —15 °C no value is given for 17 at/ > 300MPa, because of a phase transition towards ice V (Figure 8.5).

Films of 5-NS and 5-NS(Me) have a remarkable coincidence of isotherms over a 30 °C range a negative expansion temperature dependence only appears in the inflection as the films approach collapse. The inflection seems to be real and can be differentiated clearly from the collapse behavior for 8-NP(Me). Thus the plots of surface pressure vs. area/mole-cule and surface potential vs. area/molecule (not shown) for 5-NS, 5-NS (Me), and 2-NP(Me) differ from each other. Moreover, the inflections for 5-NS and 5-NS (Me) remain invariant with a varying rate of compression whereas the collapse pressure of 8-NP(Me) is slightly pressure sensitive. It appears, therefore, that films of 5-NS and 5-NS (Me) exhibit a zero temperature dependence over most of the pressure range but a negative temperature dependence as they approach collapse. 

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