Fixed activity path

Fixed-activity and sliding-activity paths (Sections 14.2-14.3) are analogous to their counterparts in fugacity, except that they apply to aqueous species instead of gases. Fixed-activity paths are useful for simulating, for example, a laboratory experiment controlled by a pH-stat, a device that holds pH constant. Sliding-... 

In a fixed activity path, the activity of an aqueous species (or those of several species) maintains a constant value over the course of the reaction path. A fixed fugacity path is similar, except that the model holds constant a gas fugacity instead of a species activity. Fixed activity paths are useful in modeling laboratory experiments in which an aspect of a fluid s chemistry is maintained mechanically. In studying reaction kinetics, for example, it is common practice to hold constant the pH of... 

To calculate a fixed activity path, the model maintains within the basis each species At whose activity at is to be held constant. For each such species, the corresponding mass balance equation (Eqn. 4.4) is reserved from the reduced basis, as described in Chapter 4, and the known value of a, is used in evaluating the mass action equation (Eqn. 4.7). Similarly, the model retains within the basis each gas Am whose fugacity is to be fixed. We reserve the corresponding mass balance equation (Eqn. 4.6) from the reduced basis and use the corresponding fugacity fm in evaluating the mass action equation. 

A complication to the calculation procedure for holding an aqueous species at fixed activity is the necessity of maintaining ionic charge balance over the reaction path. If the species is charged, the model must enforce charge balance at each step in the calculation by adjusting the concentration of a specified component, as discussed in Section 4.3. For example, if the pH is fixed over a path and the charge balance component is Cl-, then the model will behave as if HC1 were added to or removed from the system in the quantities needed to maintain a constant H+ activity. 

Sliding activity and sliding fugacity paths are similar to fixed activity and fixed fugacity paths, except that the model varies the buffered activity or fugacity over the reaction path rather than holding it constant. Once the equilibrium state of the initial system is known, the model stores the initial activity a° or initial fugacity / / of the buffered species or gas. (The modeler could set this value as a constraint on the initial system, but this is not necessary.)... 

The low susceptibility of low carbon steels can be explained by the change in the distribution of carbon which occurs after a deformation processes. Carbon is not generally present at the ferrite grain boundaries [71]. The carbon distribution is intimately related to the active path, and it appears to fix the site of the active path. 

The latter path differs from the closed system calculation because of the effect of C02(g) dissolving into the fluid. In the initial part of the calculation, the C02(aq) in solution reacts to form HCOJ in response to the changing pH. Since the fluid is in equilibrium with C02(g) at a constant fugacity, however, the activity of C02(aq) is fixed. To maintain this activity, the model transfers C02... 

Molecular recognition with rhodium complexes of functionalized porphyrins - The coordination abilities of rhodium(III) porphyrins outlined in Scheme 3 (paths b and g) were used to design porphyrins with special receptor properties, i.e. cis-or trans-5,15-bis(2-hydroxy-l-naphthyl)octaethylporphyrin [H2(npOEP)], trans-5,15-bis(8-quinolyl) porphyrin, or tetrakis(2-hydroxyphenyl) porphyrin. After Rh insertion, these porphyrins provide lateral OH or N donor groups at a fixed distance from the coordination site at the Rh atom. Unlike RhCl(TPP), RhCl(npOEP) activates acetone in a manner that an a-metallation of acetone takes place, yielding Rh(CH2COMeXnpOEP) [283]. 

The dashed line in Fig. 10.1.1 shows, in the gas phase, a calculation at the Hartree-Fock (HF) level with a 6-31G basis set. The electronic energies correspond to a minimum-energy path with a reaction coordinate defined as rc = rccv — reel, where rc = 0 corresponds to the activated complex (Cl CH3 Cl ). The minimum-energy path is optimized in Csv symmetry for fixed values of rc. 

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