The Adam-Gibbs relation

Here (Tq is a constant associated with the surface tension. If we now follow the standard procedure of finding the size of the critical nucleus, which sets the derivative to zero, we recover the nucleation free barrier proportional to 

The main feature of the above derivation is the assumption that the surface tension of a liquid nucleus decreases with radius as /R. 

It is interesting to note that the two expressions (Rosenfeld and Adam-Gibbs) for diffusion give quite different dependences on the entropy. Both have been used extensively and over a temperature range and seem to provide good agreement with simulation results. 

Therefore, the ability of the entropy of water to provide a measure of diffusion is well established, although the precise reason remains to be understood. 

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B, 109,15068 (2005). Spatially Heterogeneous Dynamics and the Adam-Gibbs Relation in the Dzugutov Liquid. 

Substituting Eq. (2.9) in the Adam-Gibbs relation for relaxation time Xad T) yields an expression for the strength parameter [18,41]... 

The Adam-Gibbs relation, namely, log [D(T, p)] versus (75c)-1, was found to be valid at each density [53]. 

In liquids, one of the most celebrated equations that connects the microscopic dynamics of molecules with thermodynamics is the Adam-Gibbs relation. This relates the translational diffiisivity of the system to configurational entropy as follows ... 

Figure 10.3. Correlations between diffusion coefficient, configurational entropy, and tetrahedral order parameter (/h). Note that the left side of the y-axis represents the logarithm of diffusivity and the right side of ffie y-axis represents (th). The straight line fitting of the data validates the Adam-Gibbs relation between entropy and the diffusion coefficient, as discussed in the text The dashed line shows the correlation between (th) and configurational entropy. Adapted wifli permission from J. Phys. Chem. B, 114 (2010), 3633. Copyright (2010) American Chemical Society.

C. Adam-Gibbs Relation Between the Configurational Entropy Sc and Relaxation in Glass-Forming Liquids... 

As discussed in Section II, the Adam-Gibbs [48] model of relaxation in cooled liquids relates the structural relaxation times x, associated with long wavelength relaxation processes (viscosity, translational diffusion, rates of diffusion-limited... 

The Adam-Gibbs equation for viscous liquid relaxation asserts that the time scale for re-equilibration after some perturbation is related to the excess entropy of liquid over crystal, according to... 

The reversible step may be related to the dynamic crossover in protein hydration water at To 345 5K. NMR self-diffusion results [19] indicate that at this temperature a sudden change in hydration water dynamics occurs and the inverse diffusion constant switches from low-temperature super-Arrhenius behavior to high-temperature Arrhenius behavior. Neutron techniques (QENS) have also been used to study protein hydration water at this high-r crossover. Figure 21 shows the atomic MSD of protein hydration water at the low-r crossover measured using MD simulation. These crossovers can also be shown theoretically. Whenever the slope of an Arrhenius plot of the D T) changes, the specific heat has a peak. The well-known Adam-Gibbs equation (AGE) shows this as... 

Actually, Adam and Gibbs claim to compute the average relaxation time T (T) which is then related to rj T) through tjoctG with G the shear rigidity assumed to have a negligible temperature dependence. 

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