Additivity principle contributions

Equations 8.107 and 8.108, referring to absolute properties, are equally valid for conventional properties based on equations 8.105 and 8.106. Moreover, the additivity principle is applied to all partial contributions thus, for a generic electrolyte K, we have ... 

The pairwise additivity principle when applied to bichromophoric exciton-coupled systems, such as those composed of 4-bromobenzoate (BB) and 4-methoxycinnamate (MC) derivatives of cyclic polyols, yields more information from the CD spectra of complex molecules173. In such systems both degenerate ( homo") interactions, i.e., BB/BB and MC/MC, and nondegenerate ("hetero") interactions, i.e., BB/MC, contribute to the exciton CD spectra. As the homo exciton Cotton effects arc well separated (BB 236/253 nm, MC 287/322 nm) a unique pattern of CD curves is obtained for each derivative of cyclic tri- or tetraol. This method is particularly useful in identification of glycopyranosides174, a procedure essential for microscale structure determination of oligosaccharides by the exciton chirality method175. 

The extension of the Hammett equation to poly-substituted benzene derivatives has been made for side-chain reactions (Jafife, 1953). The essential features of these treatments are the assumptions that the contribution of each substituent is constant and that the influences of the substituents are simply additive. This postulate is usually cited as the additivity principle. In the case of electrophilic substitution, assuming additivity, the equation may be written... 

The superposition principle for heat flow as measured by power-compensated DSC should apply—just as it would be expected that the water flow into one tank from two pipes would be additive. Assuming Fourier s law holds (steady state heat flow proportional to temperature gradient), the temperature differences measured in DTA (and heat-flux DSC) are additive via contributions from multiple transformation sources within the sample material. 

A powerful tool in the semi-empirical approach in the study of physical properties in general, and of polymer properties in particular, is the use of the additivity principle. This principle means that a large number of properties, when expressed per mole of a substance, may be calculated by summation of either atomic, group or bond contributions,... 

For the evaluation of the main contributions of various factors affecting IS values on the basis of the partial IS (PIS) additivity principle in pseudo- and octahedral low-spin iron(II) complexes, the expected ISs of nioximates and phenanthrolinates were calculated. 

In passing, we note that parametric four-wave mixing processes could in principle contribute to the effects described above. Thus, in the single-beam case, the CARS process co + co cOi + CO2 single center could also result in the synergistic excitation of two chemically different centers. Equally in the double-beam case, the four-wave interaction coi +o 2-> (o + (o followed by absorption of the frequency co, could contribute to the excitation of a pair of neighboring molecules of the same species. However, both of these four-wave interactions will be relatively ineffectual unless (one of) the emission frequencies is stimulated by an additional source moreover, the processes described here are not associated with the wave-vector matching characteristics of CARS and related phenomena. 

In an attempt to overccH e this difficulty, Zahn [102] put forward the suggestion that only part of the energy of a molecule be ascribed to the bonds and that the rest be associated with adjacent pairs of bonds. This proposal was improved upon by Allen [103], who advocated taking into account the contributions from adjacent trios of bonds. For farther details on the early development of these ideas, the reader is referred to the review by Somayajulu ti al [104]. The first graph theoretical formulation of the additivity principle was made by Smolensk) [105] in 1964. The latter worker employed the basic equation ... 

Figure 5.33. Representation of lowering the onset temperature, Tt(b), of the inverse temperature (phase) transition for hydrophobic association from the dissociated state at 37°C to 25°C, that is, to a temperature just sufficient to achieve essentially complete hydrophobic association. Hydrophobic association results from the summation of all of the variables (-(- and -) that contribute to AGha, i.e.. 2iAG HA. This summation represents the AG a additivity principle.

A powerful tool to study the effect of chemical structure on the properties of polymers is the additivity principle. The additivity principle, pioneered by Van Rrev-elen (22), assumes that polymer properties when expressed per mole of substance can be calculated by summation of atomic, chemical group, or bond contributions ... 

Group contributions or additivity principle Extrathermodynamic relationships between rate and equilibrium parameters Poianyi and Brpnsted relations Hammett relationship for dissociation constants... 

Movement of ions can be observed either at the boundary of the sample solution and the empty electrolyte or in the form of bands or spots. In the former moving boundary) method, the solution to be analysed is introduced into a U-tube and the electrolyte is layered upon its surface. The system is stabilized by density. In the case of zoiml (band) electrophoresis, density would disturb the separation or wholly prevent it from taking place rather than contribute to stabilization. Thus, an additional principle must be used to allow and maintain zone separation. The following principles have been used rotation of a horizontal tube around its axis, multiple cells, use of anticonvection media (porous material or gel), and density gradient. 

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