Free energy, additivity

Finally, Newmann and co-workers [30] (see also Ref. 31) have argued that while free energy contributions may not be strictly additive as in Eq. IV-11, there should, in principle, be an equation of state relating the work of adhesion to the separate liquid surface tensions such as... 

In Chapter III, surface free energy and surface stress were treated as equivalent, and both were discussed in terms of the energy to form unit additional surface. It is now desirable to consider an independent, more mechanical definition of surface stress. If a surface is cut by a plane normal to it, then, in order that the atoms on either side of the cut remain in equilibrium, it will be necessary to apply some external force to them. The total such force per unit length is the surface stress, and half the sum of the two surface stresses along mutually perpendicular cuts is equal to the surface tension. (Similarly, one-third of the sum of the three principal stresses in the body of a liquid is equal to its hydrostatic pressure.) In the case of a liquid or isotropic solid the two surface stresses are equal, but for a nonisotropic solid or crystal, this will not be true. In such a case the partial surface stresses or stretching tensions may be denoted as Ti and T2-... 

The small additions to all themiodynamic potentials are the same when expressed in temis of appropriate variables. Thus the first-order correction temi when expressed in temis of Vand P is the correction temi for the Helmlioltz free energy A ... 

As with SCRF-PCM only macroscopic electrostatic contribntions to the Gibbs free energy of solvation are taken into account, short-range effects which are limited predominantly to the first solvation shell have to be considered by adding additional tenns. These correct for the neglect of effects caused by solnte-solvent electron correlation inclnding dispersion forces, hydrophobic interactions, dielectric saturation in the case of... 

Most characteristics of amphiphilic systems are associated with the alteration of the interfacial stnicture by the amphiphile. Addition of amphiphiles might reduce the free-energy costs by a dramatic factor (up to 10 dyn cm in the oil/water/amphiphile mixture). Adding amphiphiles to a solution or a mixture often leads to the fomiation of a microenuilsion or spatially ordered phases. In many aspects these systems can be conceived as an assembly of internal interfaces. The interfaces might separate oil and water in a ternary mixture or they might be amphiphilic bilayers in... 

The ernes of ionic surfactants are usually depressed by tire addition of inert salts. Electrostatic repulsion between headgroups is screened by tire added electrolyte. This screening effectively makes tire surfactants more hydrophobic and tliis increased hydrophobicity induces micellization at lower concentrations. A linear free energy relationship expressing such a salt effect is given by ... 

A linear dependence approximately describes the results in a range of extraction times between 1 ps and 50 ps, and this extrapolates to a value of Ws not far from that observed for the 100 ps extractions. However, for the simulations with extraction times, tg > 50 ps, the work decreases more rapidly with l/tg, which indicates that the 100 ps extractions still have a significant frictional contribution. As additional evidence for this, we cite the statistical error in the set of extractions from different starting points (Fig. 2). As was shown by one of us in the context of free energy calculations[12], and more recently again by others specifically for the extraction process [1], the statistical error in the work and the frictional component of the work, Wp are related. For a simple system obeying the Fokker-Planck equation, both friction and mean square deviation are proportional to the rate, and... 

Additionally, as in all Tl-based approaches, the free energy differences are linear functions of the potential. Thus non-rigorous decompositions may be made into contributions from the different potential energy terms, parts of system and individual coordinates, providing valuable insight into the molecular mechanisms of studied processes [8, 9, 10). 

In Equation (5.58) the outer summation is over the p points q which are used to sample the Brillouin zone, is the fractional weight associated with each point (related to the volume of Brillouin zone space surrounding q) and vi are the phonon frequencies. In addition to the internal energy due to the vibrational modes it is also possible to calculate the vibrational entropy, and hence the free energy. The Helmholtz free energy at a temperature... 

Especially for large values of Aw, there could be an additional entropy effect beyond that calculated in the last section which arises from the interaction of nearest neighbors. That is, reaction (8.A) might be characterized by both a AHp jj. and a ASp jj.. In this case Aw might be viewed as the pairwise contribution to a free energy ACpaj with... 

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