Similarities and Dissimilarities

The present review is not the first in which gas-phase and electrochemical processes have been compared. The question was briefly treated by Bockris et aO and at a much greater depth by Stonehart, who after an in-depth theoretical treatment, to which the reader is referred, found surprisingly good correlations between the rates, in both cases, for simple reactions such as hydrogen oxidation. The only significant comparative publication that approaches the concept of this chapter is a relatively recent one by Beck where an attempt is made to show the similarities and dissimilarities between liquid-phase hydrogenation and electrochemical reduction. With over one hundred references, this is an extremely important publication and reference is made to its key points below. 

2 Gas-phase and Electrochemical Catalysis Similarities and Dissimilarities. - The most audacious of all hypotheses, advanced by Merenkov and others, is that gas-phase catalysis can in fact be electrochemical. He proposes that, just as in the case of corrosion, a pair of simultaneous half-cell reactions take place, (A) and (B), and certainly such a mechanism cannot be ruled out on a metallic catalyst indeed in recent years a range of reaction studies has been devoted to this question. The 

Hendra and M. Fleischmann, in Topics in Surface Science , (Proceedings of International Symposium, 1977). 

Fleischmann, P. J. Hendra, and I. R. Hill, J. Electroanal. Chem., 1981, 117, 243, and other papers by the first-named author. 

In gas-phase catalytic processes, the important parameters which characterise a reaction are- 

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Similarity is often used as a general term to encompass either similarity or dissimilarity or both (see Section 6.4.3, on similarity measures, below). The terms "proximity" and distance are used in statistical software packages, but have not gained wide acceptance in the chemical literature. Similarity and dissimilarity can in principle lead to different rankings. 

The total number of bits set on A is a + c. and the total number of bits set on B is b + c. These totals form the basis of an alternative notation that uses a instead of a + c, and b instead oib + c [16]. This notation, however, lumps together similarity and dissimilarity components" - a disadvantage when interpreting a similarity measure. 

We should mention here that using just similarity or dissimilarity in a similarity measure might be misleading. Therefore, some composite measures using both similarity and dissimilarity have been developed. These are the Hamann and the Yule measures (Table 6-2). A simple product of (1 - Tanimoto) and squared Eucli-... 

The relative contributions of each type of interaction to the total van der Waals interaction has been determined by Israelachvili [95] for pairs of similar and dissimilar molecules theoretically by comparing the magnitudes of the terms within the square brackets, using reported values for the polarizability and the ionization potential of these molecules. These results are summarized in Table 1. 

In terms of matching mentors with mentees, BAT takes the view that there should be balance between the similar and dissimilar personalities or backgrounds of the two parties. Compatibility depends on the individuals personality type, learning, and communication style. 

Kutateladze, S. S., and A. I. Leont ev, 1966, Some Applications of the Asymptotic Theory of the T urbu-lent Boundary Layer, Proc. 3rd Int. Heat Transfer Conf, vol. 3, pp. 1-6, AIChE, New York. (5) Kutateladze, S. S., and L. G. Malenkov, 1974, Heat Transfer at Boiling and Barbotage Similarity and Dissimilarity, Proc. 5th Int. Heat Transfer Conf., Tokyo, vol. IV, p. 1. (2)... 

Since the discovery of alkylation, the elucidation of its mechanism has attracted great interest. The early findings are associated with Schmerling (17-19), who successfully applied a carbenium ion mechanism with a set of consecutive and simultaneous reaction steps to describe the observed reaction kinetics. Later, most of the mechanistic information about sulfuric acid-catalyzed processes was provided by Albright. Much less information is available about hydrofluoric acid as catalyst. In the following, a consolidated view of the alkylation mechanism is presented. Similarities and dissimilarities between zeolites as representatives of solid acid alkylation catalysts and HF and H2S04 as liquid catalysts are highlighted. Experimental results are compared with quantum-chemical calculations of the individual reaction steps in various media. 

According to the data, the procedure can also be applied to the determination of the similarities and dissimilarities of natural pigment mixtures. 

Fig. 3.5. Similarities and dissimilarities between the selectivity of solvents, simultaneously taking into consideration each tetrazolium salt. Two-dimensional nonlinear selectivity map. Number of iterations, 547 maximal error, 1.42 X 1CT2. Reprinted with permission from E. Forgacs et al. [85].

To further identify the electro-oxidation products of 1 , the C. V. of 1 and I3 were also recorded. There are similarities and dissimilarities in the cyclic voltamogram. While (Ep) = 0.690 V is same in both the C.V. s, there is another anodic peak at 1,054 mV (absent in the r - e 1 case) for the same concentration of 1-and two corresponding cathodic peaks at 787 and 406 mV as compared to that of 1. It was also noted that the anodic peak in the case of [1] = 0.5 mM was quite sharp manifesting a two-electron oxidation. It is not so in the case of I3. Thus recombination I.to form Ij, followed by the reaction of 1 with (excess) 1 in solution to form 1 and oxidation of 1 is not involved in the electro-oxidation of 1. 

Because of their proximity ( 770 km) and similar Class 2 kimberlite designation, some discussion of the similarities and dissimilarities between the Buffalo Head Hills and Fort a la Come fields is warranted. Both fields are dominated by primary pyroclastic, volcaniclastic and resedimented volcaniclastic kimberlite, and have large, multi-aged bodies. Hence, a favourable consequence to diamond explorers is that the inter- and extra-crater morphologies of Class 2 kimberlite in the WCSB could cover vast areas. 

Kubinyi H. (1998) Similarity and Dissimilarity A Medicinal Chemist s View. Perspect. Drug Discov. Des. 9-11 225-252. 

Adamson, G. W. and Bush, J. A. (1975) A comparison of the performance of some similarity and dissimilarity measures in the automatic classification of chemical structures../. Chem. Inf Comput. Sci. 15, 55-58. 

Holliday, J. D., Hu, C.-Y., and Willett, P. (2002) Grouping of coefficients for the calculation of inter-molecular similarity and dissimilarity using 2D fragment bit-strings. Combi. Chem. High Through. Screen. 5, 155-166. 

Indices of molecular similarity and dissimilarity based on the electron momentum density have been found useful by Allan, Cooper and coworkers [388-393] and Ho et al. [394]. 

The above consideration of the similarity and dissimilarity of ILs and conventional extraction solvents ignores one particularly striking feature of ILs. In sharp contrast to common solvents immiscible with water, ILs are capable of ion exchange. We exemplify this very important ability by considering the extraction of amino acids on the basis of our work [24],... 

A new additive dose method is proposed to obtain the age directly without extrapolating the growth curve.1115 The experimental growth curve at the artificial irradiation dose rate gives simply the defect production efficiency (G-value) from the initial growth and the interaction distance, d, between spins from the saturation behaviour. The latter involves the effect of magnetic dipolar and exchange interactions of similar and dissimilar spins and also destabilization of a spin in a distorted area by a local lattice distortion. 

The equations derived above, describing the A + B —> B reaction kinetics in terms of the correlation functions g and g2, have the form of the nonlinear generalised multi-dimensional diffusion equation. Ignoring the multidimensionality of the operator terms in (5.2.11), these equations could be formally considered as similar to the basic non-linear equations for the A + B — 0 reaction (Section 5.1). Equations studied in both Sections 5.1 and 5.2 are derived with the help of the Kirkwood superposition approximation, the use of which leads to several equations for the correlation functions of similar and dissimilar reactants. 

The temporal evolution of spatial correlations of both similar and dissimilar particles for d = 1 is shown in Fig. 6.15 (a) and (b) for both the symmetric, Da = Dft, and asymmetric, Da = 0 cases. What is striking, first of all, is rapid growth of the non-Poisson density fluctuations of similar particles e.g., for Dt/r = 104 the probability density to find a pair of close (r ro) A (or B) particles, XA(ro,t), by a factor of 7 exceeds that for a random distribution. This property could be used as a good aggregation criterion in the study of reactions between actual defects in solids, e.g., in ionic crystals, where concentrations of monomer, dimer and tetramer F centres (1 to 3 electrons trapped by anion vacancies which are 1 to 3nn, respectively) could be easily measured by means of the optical absorption [22], Namely in this manner non-Poissonian clustering of F centres was observed in KC1 crystals X-irradiated for a very long time at 4 K [23],... 

Below we take into account the non-linear terms in the kinetic equations containing functionals J (coupling spatial correlations of similar and dissimilar particles) but neglect the perturbation of the pair potentials assuming that il(r, t) = l3U(r). This is justified in the diluted systems and for the moderate particle interaction which holds for low reactant densities and loose aggregates of similar particles. However, potentials of mean force have to be taken into account for strongly interacting particles (defects) and under particle accumulation when colloid formation often takes place [67],... 

As it was mentioned above, up to now only the dynamic interaction of dissimilar particles was treated regularly in terms of the standard approach of the chemical kinetics. However, our generalized approach discussed above allow us for the first time to compare effects of dynamic interactions between similar and dissimilar particles. Let us assume that particles A and B attract each other according to the law U v(r) = — Ar-3, which is characterized by the elastic reaction radius re = (/3A)1/3. The attraction potential for BB pairs is the same at r > ro but as earlier it is cut-off, as r ro. Finally, pairs AA do not interact dynamically. Let us consider now again the symmetric and asymmetric cases. In the standard approach the relative diffusion coefficient D /D and the potential 1/bb (r) do not affect the reaction kinetics besides at long times the reaction rate tends to the steady-state value of K(oo) oc re. 

Fig. 6.36. The defect concentration vs time. The dotted line shows neglect of the similar particle correlation in the full line it is incorporated for the case Da = 0 and in the broken line - for the Da = DB case. The elastic interaction constant A of similar and dissimilar particles is the same UAb = UBB = -Ar-3, whereas Uaa = 0.

In conclusion of Section 6.3 we wish to stress that the elastic attraction of similar defects (reactants) leads to their dynamic aggregation which, in turn, reduces considerably the reaction rate. This effect is mostly pronounced for the intermediate times (dependent on the initial defect concentration and spatial distribution), when the effective radius of the interaction re = - JTX exceeds greatly the diffusion length = y/Dt. In this case the reaction kinetics is governed by the elastic interaction of both similar and dissimilar particles. A comparative study shows that for equal elastic constants A the elastic attraction of similar particles has greater impact on the kinetics than interaction of dissimilar particles. 

The non-equilibrium particle distribution is clearly observed through the joint correlation functions plotted in Fig. 6.47. Note that under the linear approximation [74] the correlation function for the dissimilar defects Y (r, t) increases monotonically with r from zero to the asymptotic value of unity Y(r —y oo,t) = 1. In contrast, curve 1 in Fig. 6.47 (f = 101) demonstrates a maximum which could be interpreted as an enriched concentration of dissimilar pairs, AB, near the boundary of the recombination sphere, r tq. With increasing time this maximum disappears and Y(r, t) assumes the usual smoothed-step form. The calculations show that such a maximum in Y(r, t) takes place within a wide range of the initial defect concentrations and for a random initial distribution of both similar and dissimilar particles used in our calculations X (r, 0) = Y(r > 1,0) = 1. The mutual Coulomb repulsion of similar particles results in a rapid disappearance of close AA (BB) pairs separated by a distance r < L (seen in Fig. 6.47 as a decay of X (r, t) at short r with time). On the other hand, it stimulates strongly the mutual approach (aggregation) of dissimilar particles leading to the maximum for Y(r, t) at intermediate distances observed in Fig. 6.47. 

The role of the non-equilibrium charge screening is emphasized by calculations neglecting such screening, i.e., when equations (5.1.54) are omitted and Uv r) — L/r is postulated. In this case mutual repulsion of similar particles accompanied by the attraction between dissimilar particles are characterized by the infinite interaction radius between particles which leads immediately to the Coulomb catastrophe - an infinite increase in K(t) in time shown in Fig. 6.47. This effect is independent of the choice of the initial defect distributions for both similar and dissimilar particles. On the other hand, incorporation of the Coulomb screening makes equations (6.4.1), (6.4.2) asymptotically valid for any initial distribution of particles. 

In Fig. 7.4 the joint correlation functions are plotted for distribution of geminate partners created randomly within narrow interval ro r Rg. Two important conclusions suggest themselves from this figure (i) due to similar and dissimilar reactant correlation back-coupling the narrow peak of Y at short distances is accompanied by the decay in X, (ii) for great doses, n joint correlation functions are quite similar to those observed for uncorrelated distribution, i.e., an aggregation manifests itself mainly at high defect concentrations. 

As it was discussed in Chapter 3, neutral point defects in all solids interact with each other by the elastic forces caused by overlap of deformation fields surrounding a pair of defects. These forces are effectively attractive for both similar and dissimilar defects (interstitial-interstitial, vacancy-vacancy and interstitial-vacancy, respectively) and decay with the distance between defects as... 

The distribution functions of similar and dissimilar defects also have a distinctive form. Thus, in the steady-state distribution function of dissimilar defects one observes a maximum at small distances (in the region of relative distances corresponding to the interpair correlation). On the other hand, the distribution function of similar defects in the region of small r values takes respectively on smaller values than in the case of absence of interpair correlations. This also agrees well with the analytical calculations for the continuum model [30, 31, 34] discussed in Section 7.1. 

The behaviour of the correlation functions shown in Fig. 8.5 corresponds to the regime of unstable focus whose phase portrait was earlier plotted in Fig. 8.1. For a given choice of the parameter k = 0.9 the correlation dynamics has a stationary solution. Since a complete set of equations for this model has no stationary solution, the concentration oscillations with increasing amplitude arise in its turn, they create the passive standing waves in the correlation dynamics. These latter are characterized by the monotonous behaviour of the correlations functions of similar and dissimilar particles. Since both the amplitude and oscillation period of concentrations increase in time, the standing waves do not reveal a periodical motion. There are two kinds of particle distributions distinctive for these standing waves. Figure 8.5 at t = 295 demonstrates the structure at the maximal concentration... 

Chemists are trained to recognize the significance of compound similarity and dissimilarity in the context of the problem at hand. This cognitive approach, when... 

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