Potential, chemical diffusion

Measurements were also made of the potential-composition behavior, as well as the chemical diffusion coefficient, and its composition dependence, in each of the intermediate phases in the Li-Sn system at 415 °C [39]. 

This concept has also been demonstrated at ambient temperature in the case of the Li-Sn-Cd system [47,48]. The composition-de-pendences of the potentials in the two binary systems at ambient temperatures are shown in Fig. 15, and the calculated phase stability diagram for this ternary system is shown in Fig. 16. It was shown that the phase Li4 4Sn, which has fast chemical diffusion for lithium, is stable at the potentials of two of the Li-Cd reconstitution reaction plateaus, and therefore can be used as a matrix phase. 

The same property of entropy generation holds for other processes. In electrical conductance, charged particles move from higher to lower electrical potentials. In diffusion phenomena, all chemical entities are transferred from higher to lower chemical potentials. 

Under equilibrium conditions, the chemical potential of diffusible hydrogen equals the chemical potential of trapped hydrogen, i.e.. 

Membrane potentials are determined by a balance between two physical forces chemical diffusion and electrostatic pressure. Chemical diffusion is the tendency of particles to move toward a uniform distribution throughout a volume. Electrostatic pressure is simply the tendency for like-charged particles to repel and oppositely charged particles to attract each other. 

Diffusion That form of mass transport in which motion occurs in response to a gradient in concentration or composition, itself caused by a gradient of the chemical potential fi. Diffusion is ultimately an entropy-driven process. 

When it comes to the equilibration of water concentration gradients, the relevant transport coefficient is the chemical diffusion coefficient, Dwp. This parameter is related to the self-diffusion coefficient by the thermodynamic factor (see above) if the elementary transport mechanism is assumed to be the same. The hydration isotherm (see Figure 8) directly provides the driving force for chemical water diffusion. Under fuel-cell conditions, i.e., high degrees of hydration, the concentration of water in the membrane may change with only a small variation of the chemical potential of water. In the two-phase region (i.e., water contents of >14 water molecules... 

Can the Chemical and Electrical Work Be Determined Separately In the case of transport processes, the total driving force for the flow of a particular species j, i.e., the gradient of electrochemical potential. 3pj./3bc, was considered split up into a chemical (diffusive) driving force dp/dx and an electrical driving force for conduction, ZjFdty/dx,... 

Figure 13.2 Schematic depiction of chemical diffusion (arrows) induced by chemical potential variations at points of steeply negative gradient (z ) or weakly positive gradient (z2), suggesting the proportionality (13.25a) between chemical diffusion rate and chemical potential gradient that characterizes the near-equilibrium state.

The thermodynamic functions of fc-mers adsorbed in a simple model of quasi-one-dimensional nanotubes s adsorption potential are exactly evaluated. The adsorption sites are assumed to lie in a regular one-dimensional space, and calculations are carried out in the lattice-gas approximation. The coverage and temperature dependance of the free energy, chemical potential and entropy are given. The collective relaxation of density fluctuations is addressed the dependence of chemical diffusion coefficient on coverage and adsorbate size is calculated rigorously and related to features of the configurational entropy. 

These assumptions, however, oversimplify the problem. The parent (A,B)0 phase between the surface and the reaction front coexists with the precipitated (A, B)304 particles. These particles are thus located within the oxygen potential gradient. They vary in composition as a function of ( ) since they coexist with (A,B)0 (AT0<1 see Fig. 9-3). In the Af region, the point defect thermodynamics therefore become very complex [F. Schneider, H. Schmalzried (1990)]. Furthermore, Dv is not constant since it is the chemical diffusion coefficient and as such it contains the thermodynamic factor /v = (0/iV/01ncv). In most cases, one cannot quantify these considerations because the point defect thermodynamics are not available. A parabolic rate law for the internal oxidation processes of oxide solid solutions is expected, however, if the boundary conditions at the surface (reaction front ( F) become time-independent. This expectation is often verified by experimental observations [K. Ostyn, et al. (1984) H. Schmalzried, M. Backhaus-Ricoult (1993)]. 

Uniform chemical potential at equilibrium assumes that the component conveys no other work terms, such as charge in an electric field. If other other energy-storage mechanisms are associated with a component, a generalized potential (the diffusion potential, developed in Section 2.2.3) will be uniform at equilibrium. 

R.A. Robinson and R.H. Stokes, Electrolyte Solutions The Measurement and Interpretation of Conductance, Chemical Potential and Diffusion in Solutions of Simple Electrolytes, 2nd ed., Butterworths, London, 1959,571 pp. 

We will see that in the steady state of the blocking cells, we can extract partial conductivities, and from the transients chemical diffusion coefficients (and/or interfacial rate constants). Cell 7 combines electronic with ionic electrodes here a steady state does not occur but the cell can be used to titrate the sample, i.e., to precisely tune stoichiometry. Cell 1 is an equilibrium cell which allows the determination of total conductivity, dielectric constant or boundary parameters as a function of state parameters. In contrast to cell 1, cell 2 exhibits a chemical gradient, and can be used to e.g., derive partial conductivities. If these oxygen potentials are made of phase mixtures212 (e.g., AO, A or AB03, B203, A) and if MO is a solid electrolyte, thermodynamic formation data can be extracted for the electrode phases. 

Following a phenomenological approach, the driving force for chemical diffusion, in oxides, is the gradient of the electrochemical potential, ri-... 

This adsorbed oxygen can then migrate across the surface or into the interior of the coal particle to a reactive site at which point it becomes chemically bound. The form of this chemical bond is phenolic-OH, carbonyl or peroxide type moieties. As the surface layers become saturated, the oxygen will diffuse deeper into the particles through pores and crevices to react with sites within the coal particle. This is the second, slower part of the adsorption process. At some point the chemical potential against diffusion into the particle becomes great enough that the oxidation from the exterior of the particle ceases. This point will be determined by the porosity of the coal and the temperature at which the oxidation is carried out. As... 

In our hands, EQCM studies of this system have confirmed previous reports of y-FeOOH deposition kinetics and the chemical reaction of ferrous ions with this film after a current interruption step. Figure 12.1 depicts the simultaneous transients of anodic current (Fig. 12.1(b)) and frequency shift (A/) when a potential step (Fig. 12.1(c)) is applied from a potential where there is no reaction on gold to a potential where diffusion controlled oxidation of ferrous ions takes place. The current transient shown in Fig. 12.1(b) can be described by a diffusion process since a linear dependence of the anodic current density with t 1/2 was found as predicted by the Cottrell equation ... 

Technique applied to measure the chemical diffusion coefficient of the intercalating species within insertion-host electrode materials with the help of an electrochemical cell, followed by the current response on the staircase potential signal that is recorded as currenttime curve [i]. The theory of this technique is based on... 

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