Work term contributions

The diffusion limit will obscure very fast rates of electron transfer (/cobs = for et d) [16]. Even if electron transfer is slow with respect to diffusion ( obs = et), work accompanies the formation of the precursor complex and/or separation of the successor complex (this is especially prevalent when the reactants and/or products are charged). Work term contributions to the observed rate of reaction can overwhelm the intrinsic factors that govern the electron transfer event [19]. For this reason, excluding special circumstances [20-26], intermolecular reactions are not ideal systems for examining the mechanistic details of electron transfer. 

An important issue in the thermodynamics of confined fluids concerns their symmetry which is lower than that of a corresponding homogeneous bulk phase because of the presence of the substrate and its inherent atomic structure [52]. The substrate may also be nonplanar (see Sec. IV C) or may consist of more than one chemical species so that it is heterogeneous on a nanoscopic length scale (see Sec. VB 3). The reduced symmetry of the confined phase led us to replace the usual compressional-work term —Pbuik F in the bulk analogue of Eq. (2) by individual stresses and strains. The appearance of shear contributions also reflects the reduced symmetry of confined phases. 

By employing the variation of the work term Awp in eq 31, we are actually focussing in large part on the electrostatic interaction in the ion pair, since the other structural factors drop out by cancellation in the comparative procedure used in eq 28. Thus the contribution to Awp consists largely of a coulombic potential (i.e., -e2/rpA) the m an separation r in the... 

Table 1.1 Conjugate pairs of variables in work terms for the fundamental equation for the internal energy U. Here/is force of elongation, Z is length in the direction of the force, <7 is surface tension, As is surface area, , is the electric potential of the phase containing species i, qi is the contribution of species i to the electric charge of a phase, E is electric field strength, p is the electric dipole moment of the system, B is magnetic field strength (magnetic flux density), and m is the magnetic moment of the system. The dots indicate scalar products of vectors.

The work required to bring the reactants (assumed to be rigid spheres of radius a and a ) to their mean separation distance in the activated complex (r = a, + aj) then remove the products to infinity. These work terms are w and — respectively, and incorporate electrostatic and nonpolar contributions. 

The total area above the first intrusion curve, A in Fig. 12.1, to the maximum intruded volume indicated by the horizontal dotted line, corresponds to the P-V work of intrusion, IFj. This work term consists of three parts, the first of which is the work of entrapment, W, corresponding to the area between curves A and B. The second contribution to IF. is the work, fV g, associated with the contact angle change from 0, to 0 ... 

Finally, we must consider the contribution of the electrostatic work required to transfer one electron into free space. After overcoming the short range chemical forces, the electron must be moved a certain distance against the electric field in the surface. Under the assumption that the lines of force of the electric field are located between the ion defects in the boundary layer and the surface charges represented by the chemisorbed gas atom, we obtain the expression afi for this electrostatic work term. is the boundary field strength represented in Equation (11), and a is the distance between the surface of the oxide and the centers of charge of the chemisorbed atoms in the a-phase. 

The next task is to develop expressions for the heat-transfer and work terms in Eq. 3.148. We consider two contributions to the heat that crosses the surfaces of a control volume. The first is thermal conduction via Fourier s law, which behaves in the same way for a fluid as it does for a solid. The second contribution is associated with energy that crosses the control surfaces as chemical species diffuse into and out of the control volume. In... 

The work term w makes a relatively minor contribution to AF. In numerical calculations it is usually assumed to be electrostatic in origin and to be given roughly by the shielded coulombic formula, uf = (e e2/ DR) exp (— kR), where and e2 are the charges of the reactants, D is the dielectric constant and k the Debye kappa. (In very dilute solutions exp (—kR) == 1.)... 

In fact, transient assembly of H-bonded water files is probably common in enzyme function. In carbonic anhydrase, for example, the rate-limiting step is proton transfer from the active-site Zn2+-OH2 complex to the surface, via a transient, H-bonded water network that conducts H+. Analysis of the relationship between rates and free energies (p K differences) by standard Marcus theory shows that the major contribution to the observed activation barrier is in the work term for assembling the water chain (Ren et al., 1995). 

Other possible contributions to the work terms for outer-sphere reactions include the likelihood that the ion-solvent interactions will differ in the interfacial region from that in bulk solution resulting from the influence of the metal surface upon the local solvent structure. As noted in Sect. 2.4, this effect may be significant even for ions in the diffuse layer since the perturbation upon the solvent structure is liable to extend several layers out from the metal surfaces [19] (see also Sect. 4.6). 

Since anions and cations adsorb at oxide electrodes positive and negative to the pzc, respectively, electrostatic work terms (double layer corrections) should contribute to the activation free energy barrier for adsorbed electroactive ions depending on the position of the reaction site. Not much attention has been paid to this phenomenon yet. Trasatti and co-workers... 

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