Water random network model

A different test, one less satisfactory because the standard of comparison is simulated water not real water, is obtained by examining the functions hon(R) and dd(-R) predicted. The functions derived from the Narten model are shown in Fig. 54 they should be compared with those for simulated water, displayed in Figs. 27 and 28. Just as for the function hoo R), the curves for simulated water are narrower and higher than those in Fig. 54. In all other respects the agreement between the two sets of functions is excellent. It now remains to be shown that a full calculation, based on precisely the random network model proposed will reproduce the data as well as this (sensibly equivalent ) model. 

This oversimplified random network model proved to be rather useful for understanding water fluxes and proton transport properties of PEMs in fuel cells. - - - It helped rationalize the percolation transition in proton conductivity upon water uptake as a continuous reorganization of the cluster network due to swelling and merging of individual clusters and the emergence of new necks linking them. ... 

The effective conductivity of the membrane depends on its random heterogeneous morphology—namely, the size distribution and connectivity of fhe proton-bearing aqueous pafhways. On fhe basis of the cluster network model, a random network model of microporous PEMs was developed in Eikerling ef al. If included effecfs of varying connectivity of the pore network and of swelling of pores upon water uptake. The model was applied to exploring the dependence of membrane conductivity on water content and... 

This notion is supported by a large number of independent experimental data, related to structure and mobility in these membranes. It implies furthermore a distinction of proton mobility in various water environments, strongly bound surface water and liquidlike bulk water, and the existence of water-filled pores as network forming elements. Appropriate theoretical treatment of such systems involves random network models of proton conductivity and concepts from percolation theory, and includes hydraulic permeation as a prevailing mechanism of water transport under operation conditions. On the basis of these concepts a consistent approach to membrane performance can be presented. 

Stuart s studies of the structure of the liquid-vapor interfaces of metals and alloys can also be related to his previous research. He developed the first theory of transport in dense simple fluids that explicitly recognizes, and accounts for, the different dynamics associated with short-range repulsion and longer-ranged attraction. He has contributed to the theory of the three-molecule distribution function in a liquid and the theory of melting, and he developed the Random Network Model of water and the first consistent... 

In fact, a random network model (RNM) of water was proposed a long time ago by Rice and coworkers [14] who demonstrated via computer simulations and theoretical analyses of spectroscopic data from different experiments that the low density amorphous (LDA) phase of ice can contain a significant number of defects in the form of (5,7) ring pair. They suggested that the inter-conversion between (5,7) and (6,6) ring pairs can constitute an elementary excitation of LDA. 

M. G. Sceats, M. Stavola, and S. A. Rice, A zeroth order random network model of liquid water, J. Chem. Phys. 70 (1979), 3927-3938 M. G. Sceats and S. A. Rice, A random network model calculation oF the free energy of liquid water. J. Chem. Phys. 72 (1980), 6183-6192. 

There are different ways to depict membrane operation based on proton transport in it. The oversimplified scenario is to consider the polymer as an inert porous container for the water domains, which form the active phase for proton transport. In this scenario, proton transport is primarily treated as a phenomenon in bulk water [1,8,90], perturbed to some degree by the presence of the charged pore walls, whose influence becomes increasingly important the narrower are the aqueous channels. At the moleciflar scale, transport of excess protons in liquid water is extensively studied. Expanding on this view of molecular mechanisms, straightforward geometric approaches, familiar from the theory of rigid porous media or composites [ 104,105], coifld be applied to relate the water distribution in membranes to its macroscopic transport properties. Relevant correlations between pore size distributions, pore space connectivity, pore space evolution upon water uptake and proton conductivities in PEMs were studied in [22,107]. Random network models and simpler models of the porous structure were employed. 

Recently, this behavioral difference of nonpolar and polar solutes could be reproduced by heat capacity calculations using a combination of Monte Carlo simulations and the random network model (RNM) of water." "" It was found that the hydrogen bonds between the water molecules in the first hydration shell of a nonpolar solute are shorter and less bent (i.e., are more ice-like) compared to those in pure water. The opposite effect occurs around... 

Efforts of polymer scientists and fuel cell developers alike are driven by one question What specific properties of the polymeric host material determine the transport properties of a PEM, especially proton conductivity The answer depends on the evaluated regime of the water content. At water content above kc, relevant structural properties are related to the porous PEM morphology, described by volumetric composition, pore size distribution and pore network connectivity. As seen in previous sections, effective parameters of interest are lEC, pKa, and the tensile modulus of polymer walls. In this regime, approaches familiar from the theory of porous media or composites (Kirkpatrick, 1973 Stauffer and Aharony, 1994), can be applied to relate the water distribution in membranes to its transport properties. Random network models and simpler models of the porous structure were employed in Eikerling et al. (1997, 2001) to study correlations between pore size distributions, pore space connectivity, pore space evolution upon water uptake, and proton conductivity, as will be discussed in the section Random Network Model of Membrane Conductivity. ... 

Based on the cluster network model, further studies propose an interpretation of the percolation properties of proton conductivity as a function of water content by using a random network model [102], which is a modification of the cluster network model. This model includes an intermediate region wherein the side chains ending with pendant sulfonic acid groups, which are bonded to the perfluorinated backbones, tend to form cluster within the overall structure of the material resulting in the formation of hydrated regions. Unlike the cluster network model, the... 

In general, pores swell nonuniformly. As a simplification, fhe random network was assumed to consist of fwo types of pores. In fhis fwo-stafe model, nonswollen or "dry" pores (referred to later as "red" pores) permit only a small residual conductance due to tightly bound surface water, which solvates the charged surface groups. Swollen or "wet" pores (referred to later as "blue" pores) contain extra water in the bulk, allowing them to promote the high bulk-like conductance. Water uptake by the membrane corresponds to the swelling of wef pores and to the increase of their relative fraction. 

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