Ternary ion exchange. Part 4.—Activity corrections for the solution phase

Abstract

A previously developed model for the evaluation of activity coefficient ratios in mixed dilute solution is employed with particular respect to ternary cation exchange in zeolites in the presence of up to three different coanions in solution. Potential errors arising from ignoring either completely or partially the non-ideality correction for the solution phase are evaluated and discussed. Exchanges involving counterions of the same valency, or involving ions of different valencies, are both considered. It is shown that when all the counter-ions have the same valency, the magnitude of the non-ideality correction is independent of the selectivity of the exchanger. When the valencies of the counter-ions are different it is essential to apply the mixed-salt activity correction for any accurate studies of ternary ion-exchange equilibria.T Throughout this paper, the term 'equivalent' denotes the number of moles of unit charge arising from a species in solution. Thus, for example, the number of equivalents of ion AZA+ in solution equals ZAmA. zA and mA are defined in the text.

AFM Studies of Metal Deposition: Instantaneous Nucleation and the Growth of Cobalt Nanoparticles on Boron‐Doped Diamond Electrodes

“…stant throughout the experiment. However a closer inspection shows that at very short times (less than % 10 seconds) the non steady state behaviour, inferred indirectly by Fletcher in a limited number of other systems, [9][10][11][12] is apparent: It is observed that nucleation rates control the cobalt deposition as endorsed both by AFM and current transient data. Nevertheless the value of the concept of 'instantaneous nucleation' is seen to be an important limiting form of behaviour; beyond the initial few seconds the number of nuclei remains absolutely fixed so that the nucleation is indeed, when viewed from later times, effectively instantaneous.…”

Brownian dynamics simulation of nucleation and growth processes at electrode surfaces: instantaneous nucleation

“…In Fig. 2, where the curves for the temporal evolution of the nuclear radius are shown, it can be seen that the simulation curve obtained with the correction parameter fits properly the theoretical curve that describes the growing of an isolated nucleus with an initial radius R 0 [5][6][7][8][9].…”

“…Each one has its own advantages and limitations. Analytical models exist only for very simple cases and under limiting conditions [1][2][3][4], and they become approximate when the electrode has no simple geometry (flat or hemispherical) or when the process involves single or multinuclear growth [5][6][7][8][9][10][11][12]. The use of numerical methods [13,14] allows the description of processes with a rigid or time-dependent moving boundary.…”

Current–time and current–potential profiles in electrochemical film production. (I) Current–time curves

“…In this regard, they identify two main approaches to classify the models that describe the current transients. On the one hand there are the models that use the Avrami theorem [2,3] and/or adopt the concept of diffusion zones [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. On the other are those models that avoid the Avrami theorem and the extended area concept [18][19][20][21][22][23] to describe the currents.…”

“…They all aim to describe the general behavior of the current transients and they all exhibit current transient expressions that show no connection with potential, temperature or concentration, with the exception of time. In fact these models [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] are applied to situations where these parameters are set to constants; however a realistic description of the transients requires an explicit relation, involving the real parameters and the theoretical ones employed by the models.…”