Excess free energy

The validity of mean field theory for N —y oo has striking consequences for the initial stages of phase separation. " In a metastable state slightly inside the coexistence curve, the nucleation free energy barrier is due to spherical droplets with a radius R The free energy excess of a droplet is written in terms of bulk and surface terms " "... 

Excess Free Energy, Excess Enthalpy, and Excess Entropy... 

The rates of the forward and backward transfers with the free-energy excess AG relate to each other according to the detailed balance principle ... 

Density Free energy Excess free energy Enthalpy... 

This relation is plotted in Fig. 3.7. Equilibrium (AGr = 0) corresponds to the point at which Q. = K. Prior to equilibrium, there is a deficit of products versus reactants (Q < K) that corresponds to a negative AGr and the potential to react until Q increases to equal K. If the system is in a state where Q. > K and (AGr > 1)> reaction to the right will only increase Q.and move the reaction system toward an even greater free energy excess versus the reference point of AG°, so this cannot occur. Rather, the reaction is driven to the left until Q.=K... 

In a single component system two phases (e.g. liquid and vapor) coexist in equilibrium only if there is a stable interface present between them. Such an interface is formed only if an increase in the surface area results in an increase in the system free energy, i.e. d JdS>0. One may thus introduce the surface free energy, Fs, as the free energy excess, proportional to the interfacial surface area ... 

Fig. IX-29. Free energy excess as a function of the crack length Equation (IX.3) can also be written as...

A high free energy excess, particularly in systems with a fine degree of dispersion, is the cause of thermodynamic instability, which is the most important feature of a majority of disperse systems. Thermodynamic instability in turn entails various processes aimed at decreasing the surface energy, which results in the saturation of surface forces. Such processes may occur in a number of ways. For example, in a free disperse system partial saturation of the surface forces may take place in the contact zone between the... 

We like to conclude this introduction observing, after Lifshitz, that a free energy excess is involved in each ETT. Thus, it might happen that, in order to avoid the energy cost involved in opening, say, a neck in the FS, the system might prefer to change its i iase. This could be the case of the martensitic transition oteerved in CuPd. 

Fig. 4.5. Free energy excess AGj for a cluster containing i molecules (a) in an ice-like struture, (6) in an energetically unfavourable structure, (c) in a structure giving optimum bonding for a small value of i. In all cases the temperature is below o °C and the curves have meaning only for integral i.

Recently, a new way of studying, analyzing, and interpreting liquid mixtures has been suggested." The traditional approach to mixtures is based on the study of the excess thermodynamic quantities such as excess free energy, excess entropy, and enthalpy volume. These quantities convey macroscopic... 

Using the result of Eq. (2.37), we obtain for the minimal free energy excess per loop of the amorphous fraction... 

On the other hand, tUting gives rise to the formation of an excess surface per chain as illustrated in Fig. 2.8.b). The corresponding free energy excess per chain is given by... 

We identify the measurable change in interfacial tension, dy, with the excess in free energy per unit area due to the adsorption at the interface. This definition is assumed to hold both at equilibrium and out of equilibrium. The free energy excess can be written as a functional of the volume fraction profile of the surfactant, (p x, t), x being the distance from the interface and t the time,... 

Ewing, M. B. Marsh, K. N. Excess Gibbs free energies, excess enthalpies, excess volumes, and isothermal compressibilities of cyclohexane + 2,3-dimethylbutane J. Chem. Thermodyn. 1974, 6, 35-41... 

Oswal, S. L. Deshpande, D. D. Excess free energies excess volumes for chloroform + tetrahydrofuran system Indian J. 

The excess Gibbs free energy, excess enthalpy, and excess volume are defined as... 

It is also worth emphasizing that the interatomic bonds are not fully compensated at the three-phase contact line. This results in a free energy excess and a linear tension, ae, acting along the perimeter of a three-phase boundary. This linear tension can be either positive or negative and does not exceed 10 dyn/cm. While the linear tension can in most cases be neglected, it plays an essential role in the case of very small droplets, particularly in nucleation. 

In nearly all cases fracture is initiated by surface damage. A rather obvious, and yet very general and determining, factor is the fact that nucleation and the development of surface damage serve as a precondition for the initiation of local fracture processes leading to the loss of stability in solids. This, in turn, means that a solid surface is most vulnerable to the action of the ambient medium. In other words, the surface is the source of both the free energy excess due to the presence of uncompensated chemical bonds and the exposure to the active components of the medium [10]. 

By performing a cumbersome integration or by employing dimension analysis, we can come up with the same mean values of the work of elastic indentation as a function of the measured radius, a, of a hole. This free energy excess is proportional to a . The precision of the estimated mean values is within an order of magnitude, or sometimes even within the precision of dimensionless... 

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