Discrete-exchange model

We have applied the discrete-exchange model to these data. An exchange between Na ion under a particular slow-motion condition and in the extreme narrowing limit is assumed. Transverse relaxation time and diffusion coefficient are written as follows ... 

Figure 3. The transverse relaxation rate constants of 33Na ion in agar gel at 2.34 T (x) and at 8.45 T (o) as a function of the fraction of Na ion. Solid lines are results of fitting data to the discrete- exchange model.

A simple model that takes into account the hydration effects on the self-diffusion is a two-site discrete exchange model with a hydration and a bulk site. Here, we assume that water molecules per AOT hydrate the water-surfactant interface and that these water molecules are free to diffuse laterally within the hydration layer, with a diffusion constant, which... 

Simple Models. The surface chemical properties of clay minerals may often be interpreted in terms of the surface chemistry of the structural components, that is, sheets of tetrahedral silica, octahedral aluminum oxide (gibbsite) or magnesium hydroxide (brucite). In the discrete site model, the cation exchange framework, held together by lattice or interlayer attraction forces, exposes fixed charges as anionic sites. 

If there is no driving term Awix) in these TDHF equations, discrete excitation energies are determined by values of hco for which the determinant of the residual homogeneous equations vanishes. This gives the equations of the random-phase approximation (RPA) for excitation energies, in an exact-exchange model [94,407]. 

Fig. 5.4. The kinetic network model for the discrete NRE model used by Zheng et al. [102] The state labels represent the conformation (letter) and temperature (subscript) for each replica. For example, F2U1 represents the state in which replica 1 is folded and at temperature T2, while replica 2 is unfolded at temperature T. Gray and black arrows correspond to folding and unfolding transitions, respectively, while the temperature at which the transition occurs is indicated by the solid and dashed lines (for T2 and Ti, repectively). The bold arrows correspond to temperature exchange transitions, with the solid and dashed lines denoting transitions with rate parameters a and wa, respectively...

Wihlin P, Schimmelpfennig B, Wahlgren U, Grenthe I, VaUet V. On the combined use of discrete solvent models and continuum descriptions of solvent effects in ligand exchange reactions a case study of the uranyl(VI) aquo ion. Theor Chem Acc. 2009 124 377-384. 

Heterogeneity Adsorbents and ion exchangers can be physically and chemically heterogeneous. Although exceptions exist, solutes generally compete for the same sites. Models for adsorbent heterogeneity have been developed for both discrete and continuous distributions of energies [Ross and Olivier, On Physical Adsorption, Interscience, New York, 1964 Jaroniec and Madey, Rudzinsld and Everett, gen. refs.]. 

Another method that has been applied by our group to the study of enzymatic reactions is the Effective Fragment Potential (EFP) method [19]. The EFP method (developed at Mark Gordon s group at Iowa State University) allows the explicit inclusion of environment effects in quantum chemical calculations. The solvent, which may consist of discrete solvent molecules, protein fragments or other material, is treated explicitly using a model potential that incorporates electrostatics, polarization, and exchange repulsion effects. The solute, which can include some... 

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