Free energy of liquids

Figure 4.3a shows schematically how the Gibbs free energy of liquid (subscript 1) and crystalline (subscript c) samples of the same material vary with temperature. For constant temperature-constant pressure processes the criterion for spontaneity is a negative value for AG, where the A signifies the difference final minus initial for the property under consideration. Applying this criterion to Fig. 4.3, we conclude immediately that above T , AGf = Gj - G. is negative... 

The phase diagram constructed in this way, with the assumption that the difference in free energy of liquid lead and solid lead, Fo(l) — Fg(c), is a linear function of the temperature, and that the other parameters remain unchanged, is shown as Fig. 8. It is seen that it is qualitatively similar to the phase diagram for the lead-thallium system in the range 0-75 atomic percent thallium. 

This simple theory is unsatisfactory, in that the rate of change of the difference in free energy of liquid and crystalline lead predicted by the Clausius-Clapeyron equation leads to a temperature scale for Fig. 8 four... 

Quirke, N. Jacucci, G., Energy difference functions in Monte Carlo simulations application to the calculation of free energy of liquid nitrogen. II. The calculation of fluctuation in Monte Carlo averages, Mol. Phys. 1982, 45, 823-838... 

Asthagiri, D. Pratt, L. R. Kress, J. D., Free energy of liquid water on the basis of quasichemical theory and ab initio molecular dynamics, Phys. Rev. E 2003, 68, 041505... 

Hermans, J. Pathiaseril, A. Anderson, A., Excess free-energy of liquids from molecular-dynamics simulations — application to water models, J. Am. Chem. Soc. 1988,110, 5982-5986. 

Fig. 14. The Gibbs free energy of liquid water calculated from the Weres-Rice Model (from...

We begin by formulating the free energy of liquid-crystalline polymer solutions using the wormlike hard spherocylinder model, a cylinder with hemispheres at both ends. This model allows the intermolecular excluded volume to be expressed more simply than a hard cylinder. It is characterized by the length of the cylinder part Lc( 3 L - d), the Kuhn segment number N, and the hard-core diameter d. We assume that the interaction potential between them is given by... 

The other thermodynamic functions are also easily found. If we confine ourselves to low pressures, of the order of atmospheric pressure, we can neglect the term PV in the Gibbs free energy of liquid or solid. Then the Helmholtz and Gibbs free energies are approximately equal and are given by... 

Mezei M, Swaminathan S, Beveridge DL (1978) Ab initio calculation of the free energy of liquid water, J Am Chem Soc, 100 3255-3256... 

Computation of the Free Energy of Liquid Water by the Monte Carlo Recursion Method. 

Enthalpy of liquefaction of the probe vapour (kJ/mol). Surface tension or surface free energy of liquid (mN/m). 

London component of surface free energy of liquid (mN/m). 

The two-particle distribution tells us the probability that particles will be found at ri and r2 and will thereby serve as the basis for determining the energy of interaction between different pairs of particles when the best statements we can make about the system are statistical. For example, when describing the energetics of liquids our statements about the structure of that liquid will be couched in the language of distribution functions. In preparation for our later work on the free energy of liquids (see chap. 6), we find it convenient to introduce an auxilliary... 

J. H. Vera, S. G. Sayegh, and G. A. Ratcliff. 1977. A quasi lattice-local composition model for the excess Gibbs free energy of liquid mixtures. Fluid Phase Equilib. 1 113. 

Z. Li and H. A. Scheraga, Chem. Phys. Lett., 154, 516 (1989). Calculation of the Free Energy of Liquid Water by the Monte Carlo Recursion Method. 

N. Quirke and G. Jacucci, Mol. Phys., 45, 823 (1982). Energy Difference Functions in Monte Carlo Simulations. Application to (1) The Calculation of the Free Energy of Liquid Nitrogen, (2) The Fluctuation of Monte Carlo Averages. 

Table 4. Charge Sensitivity of the Helmholtz Free Energy of Liquid Methanol, and Solutions of Glycine (G), Threonine (T), and Serine (S) Dipeptides in MethanoH...

R. H. Henchman, Free energy of liquid water from a computer simulation via cell theory. J. Chem. Phys., 126 (2007), 064504-064508. 

M. G. Sceats, M. Stavola, and S. A. Rice, A zeroth order random network model of liquid water, J. Chem. Phys. 70 (1979), 3927-3938 M. G. Sceats and S. A. Rice, A random network model calculation oF the free energy of liquid water. J. Chem. Phys. 72 (1980), 6183-6192. 

When more than two kinds of liquids are used, a useful technique introduced by Erbil and Meric [22] can be used. The method, based on a parameter identification problem, uses only the total surface free energy of liquids, which can be obtained precisely by experiment. For this method, an equation that shows the interaction between the solid and liquid surfaces is needed. 

The melting-point of 6 is 1808 K and the enthalpy of melting is 1.636 X 10 J mol . The heat capacity of the liquid iron exceeds that of the solid by about 1.3 J mol . Show that the difference of free energy of liquid and solid iron as a function of temperature at constemt pressure is given in J mol by... 

Eqs. (5,66) to (5.68)). The expression for the Gibbs free energy for the solute species remains the same (see Eq, (5.80)), The final expression for Gibbs free energy of liquid phase is... 

The most successful statistical theory of liquids is that derived by Simha and Somcynsky. The model considers liquids to be mixtures of voids dispersed in solid matter, i.e., a lattice of unoccupied and occupied sites. The occupied volume fraction, y (or its counterpart the free volume fraction f = 1 - y), is the principal variable y = P, T). From die configurational partition function the configurational contribution to the Helmholtz molar free energy of liquid i was expressed as [3] ... 

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