Realistic Liquid Phase Model

Taylor et al. conducted DFT simulations using a periodic model of the interface between water and various metal surfaces with an index of (1 1 l).102 The chemistry of water at these charged interfaces was investigated and the parameters relevant to the macroscopic behavior of the interface, such as the capacitance and the potential of zero charge (PZC), were evaluated. They also examined the influence of co-adsorbed CO upon the equilibrium potential for the activation of water on Pt(l 1 1). They found that for copper and platinum there was a potential window over which water is inert. However, on Ni(l 1 1) surface water was always found in some dissociated form (i.e., adsorbed OH or H ). The relaxation of water 

Harting et al. reported the results of DFT and AIMD studies for the oxidation of methanol on the Pt(l 1 1) face in aqueous solution.122 Their work reveals that the oxidation of methanol is initiated at the moment when a hydrogen bond forms between the OH group of the methanol and a water molecule. The initial step of the reaction is the cleavage of a CH bond with the bond direction points towards the platinum surface. This is followed by a rapid dissociation of the methanol OH bond, which leads to formation of a formaldehyde as a stable intermediate within the timescale of the simulation. Charge delocalization is achieved by the formation of a Zundel ion H502+ in the aqueous phase. 

Harting and Spohr investigated oxidation of methanol on the (2 11) face of a platinum single crystal.123 Similar to the reaction pathway on the (1 1 1) crystal face water plays an important role. That is the adsorption of methanol on charged and uncharged surfaces is strongly enhanced by the formation of a hydrogen bond to a 

MODELING OF TRANSPORT PROCESSES IN NAFION POLYMER ELECTROLYTES 

Theoretical Views of Proton Transport in Aqueous Systems and in Hydrated Nafion Membranes 

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For multiple liquid phases (e.g. suspension processes) or increasing concentrations of polymers, some more realistic models are desirable (van Laar, Flory-Huggins, Wilson). ... 

B. LIQUID-PHASE DYNAMICS MODEL. A somewhat more realistic model is obtained if we assume that the volume of the vapor phase is small enough to make its dynamics negligible. If only a few moles of Uquid have to be vaporized to change the pressure in the vapor phase, we can assume that this pressure is always equal to the vapor pressure of the liquid at any temperature (P = P and = p F ). An energy equation for the liquid phase gives the temperature (as a function of time), and the vapor-pressure relationship gives the pressure in the vaporizer at that temperature. 

Reactions carried in aqueous multiphase catalysis are accompanied by mass transport steps at the L/L- as well as at the G/L-interface followed by chemical reaction, presumably within the bulk of the catalyst phase. Therefore an evaluation of mass transport rates in relation to the reaction rate is an essential task in order to gain a realistic mathematic expression for the overall reaction rate. Since the volume hold-ups of the liquid phases are the same and water exhibits a higher surface tension, it is obvious that the organic and gas phases are dispersed in the aqueous phase. In terms of the film model there are laminar boundary layers on both sides of an interphase where transport of the substrates takes place due to concentration gradients by diffusion. The overall transport coefficient /cl can then be calculated based on the resistances on both sides of the interphase (Eq. 1) ... 

A realistic boundary condition must account for the solubility of the gas in the mucus layer. Because ambient and most experimental concentrations of pollutant gases are very low, Henry s law (y Hx) can be used to relate the gas- and liquid-phase concentrations of the pollutant gas at equilibrium. Here y is the partial pressure of the pollutant in the gas phase expressed as a mole fraction at a total pressure of 1 atm x is the mole fraction of absorbed gas in the liquid and H is the Henry s law constant. Gases with high solubilities have low H value. When experimental data for solubility in lung fluid are unavailable, the Henry s law constant for the gas in water at 37 C can be used (see Table 7-1). Gas-absorption experiments in airway models lined with water-saturated filter paper gave results for the general sites of uptake of sulfur dioxide... 

Although the most realistic model for a bubble column reactor is that of dispersed plug-flow in both phases, this is also the most complicated model in view of the uncertainty of some of the quantities involved, such a degree of complication may not be warranted. Because the residence time of the liquid phase in the column... 

The isotherms for the liquid phase on the left side of Fig. 3.2 are very steep and closely spaced. Thus both (dV/dP)T and dV/dT)P, and hence both /3 and k, are small. This characteristic behavior of liquids (outside the region of the critical point) suggests an idealization, commonly employed in fluid mechanics and known as the incompressible fluid, for which /3 and k are both zero. No real fluid is in fact incompressible, but the idealization is nevertheless useful, because it often provides a sufficiently realistic model of liquid behavior for practical purposes. The incompressible fluid cannot be described by an equation of state relating V to T and P, because V is constant. 

The application of Eq. (10.3) to specific phase-equilibrium problems requires use of models of solution behavior, which provide expressions for G or for the Hi as functions of temperature, pressure, and composition. The simplest of such expressions are for mixtures of ideal gases and for mixtures that form ideal solutions. These expressions, developed in this chapter, lead directly to Raoult s law, the simplest realistic relation between the compositions of phases coexisting in vapor/liquid equilibrium. Models of more general validity are treated in Chaps. 11 and 12. 

The temperature gradients inside the catalyst pellet turned out to be negligible, clearly less than 1 K for realistic approximations for AH and heat conductivity. Thus, the final calculations were made by the isothermal model by simply assuming the same temperature inside the catalyst particle as in the liquid phase. 

The recently proposed Exp-6 water model uses a more realistic exponential functional form for the repulsive interaction in Equation (12), and was specifically parameterized to reproduce the vapor-liquid phase coexistence properties (Errington and Panagiotopoulos 1998). However, it does not do as well as the TIP4P, SPC, and SPC/E models for the structure of liquid water, especially in terms of the oxygen-oxygen pair correlation function (Panagiotopoulos 2000). 

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