Born coefficient

Effective Electrostatic Radius, Born Coefficient, and Solvation Energy... 

The conventional Born coefficient ), is related to the absolute coefficient top by... 

The Born coefficients of the HKF model for the various organic species are simply related to their standard partial molal entropies at 25 °C and 1 bar through the effective charge (Shock et al., 1989). 

The Born coefficient n can be derived from the experiment bulk modulus B — — V(iiP/dV), where Vis the volume and P is the pressure (Kittel 1966). With the value BNaF = 0.5143 1012 dyn cm-2 (Sangster and Atwood 1978), nNaF is obtained as... 

The results for the three models are summarized in Table 9.2, which lists the effective Madelung constant n (t, defined by eiectrosuiic = — peff/a the effective Born coefficient, defined by U = — NAncff/a(l — l/neff) and the lattice energy U. 

It is evident that the electrostatic interactions constitute a major component of the lattice energy of ionic crystals. According the treatment for NaF described above, the ratio of absolute values of the electrostatic and repulsive forces to the lattice energy is l l/n, where n is the Born coefficient. With n ff = 7.445 (Table... 

Besides accounting for the effect of repulsion, the geometrical estimation of can be improved further, using the real radii of atoms in polar bonds, and also their hardness. According to the Born-Land6 theory, the hardness of an ion is determined by the factor f =n/(n-l), where n is the Born coefficient of repulsion. These factors are equal to 1.25 for ions with the He electronic sheU, 1.167 for ions of the Ne type, 1.125 for the Ar type and Cu+, 1.111 for the Kr type and Ag+, and 1.091 for the Xe type and Au+. Knowing the bond ionicity, one can calculate the real ionic radii, multiply them by the factor of hardness and so find the real The coordination numbers thus calculated, agree with the observed ones for some 80 % of structures [5]. 

This expression is applicable only to the region of fully developed flow. The heat transfer coefficient for the inlet length can be calculated approximately, using the expressions given in Chapter 11 for the development of the boundary layers for the flow over a plane surface. It should be borne in mind that it has been assumed throughout that the physical properties of the fluid are not appreciably dependent on temperature and therefore the expressions will not be expected to hold accurately if the temperature differences are large and if the properties vary widely with temperature. 

It should be borne in mind that the bond eigenfunctions actually are obtained from the expressions given in this paper by substituting for s the complete eigenfunction i nM(r,0,ip), etc. It is not necessary that the r. part of the eigenfunctions be identical the assumption made in the above treatment is that they do not affect the evaluation of the coefficients in the bond eigenfunctions. 

Items 1 and 2 are experimentally measurable, but it should be borne in mind that highly heat-resistant seals may come at, or near, their glass transition temperature (Tg) during a cooling event, and the coefficient of thermal expansion changes in this region. 

Using liposomes made from phospholipids as models of membrane barriers, Chakrabarti and Deamer [417] characterized the permeabilities of several amino acids and simple ions. Phosphate, sodium and potassium ions displayed effective permeabilities 0.1-1.0 x 10 12 cm/s. Hydrophilic amino acids permeated membranes with coefficients 5.1-5.7 x 10 12 cm/s. More lipophilic amino acids indicated values of 250 -10 x 10-12 cm/s. The investigators proposed that the extremely low permeability rates observed for the polar molecules must be controlled by bilayer fluctuations and transient defects, rather than normal partitioning behavior and Born energy barriers. More recently, similar magnitude values of permeabilities were measured for a series of enkephalin peptides [418]. 

The Butler-Volmer rate law has been used to characterize the kinetics of a considerable number of electrode electron transfers in the framework of various electrochemical techniques. Three figures are usually reported the standard (formal) potential, the standard rate constant, and the transfer coefficient. As discussed earlier, neglecting the transfer coefficient variation with electrode potential at a given scan rate is not too serious a problem, provided that it is borne in mind that the value thus obtained might vary when going to a different scan rate in cyclic voltammetry or, more generally, when the time-window parameter of the method is varied. 

These correlations are applicable to all the systems employed, provided that the initial maximum values of the transfer coefficients are used. This suggests that the extrapolation gives the true gas-film coefficient. This is borne out by the fact that the coefficient remained unchanged for a considerable period when the pores were large, though it fell off extremely rapidly with solids with a fine pore structure. It was not possible, to relate the behaviour of the system quantitatively to the pore size distribution however. 

A third (and usually more profound) cause of error lies in the way that the Nemst equation is formulated in terms of activities rather than concentration. Even if the emf and E are correct, the proportionality constant between concentration and activity (the mean ionic activity coefficient y ) is usually wholly unknown. Errors borne of ignoring activity coefficients (i.e. caused by ionic interactions) are discussed in Sections 3.4 and 3.6.3. 

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