Hopping events

By their nature, and in contrast with microscopic and scattering techniques that are used to elucidate long-ranged structure, spectroscopic methods interrogate short-range structure such as interactions between fixed ions in side chains and counterions, main chain conformations and conformational dynamics, and the fundamental hopping events of water molecules. The most common methods involve infrared (mid-IR and to a much lesser extent near- and far-IR) and solid-state NMR spectroscopies, although other approaches, such as molecular probes, have been utilized. 

While D issuing from these experiments is not strictly the diffusion coefficient of water per se, but rather that of H throughout the ensemble of environments in the hydration microstructure, these authors rationalized that it could in fact be identified with D at both high and low water contents. It should be appreciated that self-diffusion coefficients measured in this way reflect fundamental hopping events on a molecular scale. 

NMR is the most fundamental molecular specific probe of diffusion. Polymer motions and the spectroscopic signature of a given nucleus can be unambiguously related to a particular morphological domain. The size and time scale of the experiments are such that the fundamental hopping events of diffusing molecules can be sampled. 

Four distinct hopping events were considered in the calculations, which correspond to the movement of the benzene molecules between the cation and window sites of minimum energy in NaY, i.e., cation to window (C-W), C-C, W-C, and W-W. The associated rate constants of these processes were used to calculate the activation barrier to each hopping process and the Arrhenius prefactor. The MEP of benzene molecules was followed by a constrained optimization method that drags benzene from its initial site of minimum energy, through the transition state, to the final state. 

To summarize, we find that for two very different systems coherent nuclear motion can survive surface-hopping events and persist in condensed-phase systems for comparatively long times. We now turn to a discussion of how nuclear motion influences electronic energy gaps. 

In the electron transfer literature it has become common to describe electron transfer reactions that occur through vibrational distributions below the intersection as having occurred by nuclear tunneling and the actual electron hopping event as electron tunneling . 

A characteristic property of surface migration is that ((Ar)2 varies linearly with time. Note that the very definition of a hopping frequency Th tacitly implies statistic averaging over many hopping events. The time difference between the individual jumps of a specific particle varies stochastically. The corresponding tracer diffusion coefficient is defined as ... 

PDAs A Model of CPs Without Disorder In PDAs one would expect to have only two processes to consider transport along a really periodic chain, and all similar interchain hopping events. The case of PDAs illustrates the ambiguities of transport studies on CPs. Early time-of-flight experiments yielded mobilities ==5 cm2/V s along the chains, and 10 3 along the perpendicular directions [217]. A mobility of a few cm2/V s is typical of a molecular crystal, and the polymer character was not apparent. 

The model was constructed by decomposing the electrolyte into layers, which contain a certain number of cations, anions, and vacancies, as shown in Figure 1. During the simulations, the cations remain fixed, while the anions and vacancies can hop from layer to layer (while preserving the overall charge neutrality of the system). An important consideration in this work is the treatment of the electric field, and its influence on the diffusive ionic motion within the electrolyte. For instance, a hopping event (i.e., diffusion of an ion from one layer to a neighboring... 

The exponent value of 0.6 in Jonscher regime is considered to arise by the ion-ion interactions, usually of the coulombic type. During the process of the hopping of the ions, even separate hopping events may have a broad distribution of relaxation times, and this effect can manifest as stretching of the relaxation times. Ngai s coupling model accounts for stretched exponential relaxation and considers it as a consequence of... 

Figure 1 Schematic PESs, with the diabatic curves, corresponding to well-defined spin states (solid lines), and the adiabatic curves (dashed lines). The hopping event of a classical particle as it moves through the crossing region is schematically illustrated.

For a brief introduction, we refer again to Fig. 25.5(a), which immediately reveals that it requires an activation energy of for an atom (or a molecule) to be transferred from a site A to another, geometrically identical site B on the same periodic surface. In the classical view, this two-dimensional diffusion process can be thought of as a sequence of individual and statistical hopping events of frequency v, each activated with an energy as pointed out, for example, by Roberts and McKee [35]. The inverse of this frequency then yields the residence time, t, of the particle in the respective site. For thermally equilibrated particles, the temperature dependence of the classical surface diffusion is described by the well-known Arrhenius relation... 

FIGURE 13.13 (Left) Snapshots of a water hopping event in simulated PVP containing 10% water over a approximately 100 ps time span. The yellow-tagged water molecule underwent a rapid displacement from one free volume pocket to another approximately 20 A to the left. The red arrow tracks a second water molecule that co-migrated with the first water molecule. Right The displacement of the yeUow-tagged water molecule versus time is marked with an arrow. 

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