Affinity scaling

Szule]ko J E and McMahon T B 1993 Progress toward an absolute gas-phase proton affinity scale J. Am. Chem. Soc. 115 7839-48... 

E. P. Hunter, 1996 NIST Proton Affinity Scale, in preparation. We thank Edward Hunter for sharing his numbers with us. 

In Section IV, from the studies on diffusion towards self-affine fractal interface, the surface fractal dimension as determined by the electrochemical method is characterized as being self-similar, even though the rough surfaces and interfaces show the self-affine scaling property. Finally, in Section V, we exemplified the application of fractal geometry in electrochemical systems in view of the characterization of rough surfaces and interfaces by the surface fractal dimension. 

The word fractal was coined by Mandelbrot in his fundamental book.1 It is from the Latin adjective fractus which means broken and it is used to describe objects that are too irregular to fit into a traditional geometrical setting. The most representative property of fractal is its invariant shape under self-similar or self-affine scaling. In other words, fractal is a shape made of parts similar to the whole in some way.61 If the objects are invariant under isotropic scale transformations, they are self-similar fractals. In contrast, the real objects in nature are generally invariant under anisotropic transformations. In this case, they are self-affine fractals. Self-affine fractals have a broader sense than self-similar fractals. The distinction between the self-similarity and the selfaffinity is important to characterize the real surface in terms of the surface fractal dimension. 

In order to characterize the self-affine scaling properties of the fractal Pt films, the self-affine fractal dimensions of the film surfaces t/Fsa were determined by using the perimeter-area... 

Bearing in mind that diffusing ions move randomly in all directions, it is reasonable to say that the diffusing ions sense selfsimilar scaling property of the electrode surface irrespective of whether the fractal surface has self-similar scaling property or self-affine scaling property. Therefore, it is experimentally justified that the fractal dimension of the self-affine fractal surface determined by using the diffusion-limited electrochemical technique represents the apparent self-similar fractal dimension.43... 

Notwithstanding the large body of PA data, the significant uncertainities of the experimental PA values of water and ammonia (up to 3-4 kcalmol-1) have meant that no absolute affinity scale is yet available. 

The calculation of the affinity scale, in terms of differences in free-energy content between the various ionic forms of these materials, implies that one is dealing with equilibrium systems and that the reaction is both reversible and stoichiometric, i.e., hydrolysis phenomena are absent in the zeolite. Within certain limits, these conditions are generally met however, it is apparent that some discrepancies between experimental data have sometimes been attributed (1) to a failure in the fulfillment of one or more of these basic prerequisites. 

As pointed out by Mayr,28 Ritchie,15 and Hine33,34 KR also measures the relative affinities of R+ and H30+ for the hydroxide ion. It can be regarded as providing a general affinity scale applicable to electrophiles other than carbocations.33,35 It can also be factored into independent affinities of R+ and H30+ as shown in Equations (2) and (3). Such equilibrium constants have been denoted If by Hine.33 AR corresponds to the ratio of constants for reactions (2) and (3) and, in so far as Kc for H30+ is the inverse of Kw the autoprotolysis constant for water, KR = KCKW... 

The hydride affinity scale is also applicable to aqueous solution. In analogy with Kr we can take H30+ as reference as in Equation (8). 

Laurence, C., Gal, J. (2010). Lewis Basicity and Affinity Scales Data and Measurement. New York John Wiley Sons. Includes a discussion of the various acid-base theories and quantitative scales for judging the strengths of Lewis acids and bases. 

The heats of formation of the carbocations are then combined with the heats of formation of the corresponding hydrocarbons [21] and AH ° of H (139 kJ mol-1) [23] to yield the hydride affinity scale of Scheme 2. Although hydride affinities of larger carbocations (molecular formula a... 

Scheme 2 Hydride affinity scale of carbocations. (data from Ref. 23.) With //r°(H ) = 145 kJ mol-1 [20] the calculated hydride affinities are 6 kJ mol-1 greater than listed in this scheme.

Chloride transfer equilibria of triarylmethyl- [34] and diarylmethyl cations [35] have been determined by H NMR spectroscopy they have been combined to give a chloride affinity scale (Scheme 5). 

The relative chloride affinities of the benzhydryl cations from Scheme 5 are now graphically displayed in Scheme 7 (bottom, right). The correlation between the chloride affinities of diarylcarbenium ions and the ethan-olysis rate constants of the corresponding diarylmethyl chlorides [39] allows the chloride affinity scale of the diarylmethyl cations to extend to the less stabilized systems (Scheme 7, bottom left). In the AG° scale shown in Scheme 7, 10 kJ mol-1 corresponds to K = 374. 

If the chloride transfer from diarylmethyl chlorides to metal chlorides MCI followed Eq. (13), one might derive relative chloride affinities of MCI and Aryl2CH + from the same type of NMR experiments, which led to the relative chloride affinities of various Aryl2CH + species. In this way one would also obtain a chloride affinity scale of various metal halides. The situation is more complex, however ... 

Fig. 9 Proton affinity scale [kJ moL1] derived from ab initio calculations [124]...

For a discussion and compilation of MCAs see JE Bartmess. Gas phase equilibrium affinity scales and chemical ionization mass spectrometry. Mass Spectrom Rev 8 297-343, 1989. 

Berard V, Lesniewska E, Andres C, et al. Affinity scale between a carrier and a drag in DPI studied by atomic force microseopy. Int J Pharm 2002 247(1-2) 127-137. 

Krim, J. and Palasantzas, G., Experimental observations of self-affine scaling and kinetic roughening at submicron length scales, Int. J. Mod. Phys. B, 9, 599, 1995. 

Data from C. Laurence and J.-F. Gal, Lewis Basicity and Affinity Scales Data and Measurement, John Wiley and Sons, United Kingdom, 2010, p. 5. The ammonia is 9.25. 

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