Molar surfaces

The above considerations show that the interfacial energy is of utmost importance in determining the thermodynamics and kinetics of the nucleation process. Unfortunately, however, there are considerable uncertainities on the values of interfacial free energies. Values determined from contact angle measurements are significantly lower than those determined from the dependence of solubility upon molar surface of the crystallites. Furthermore, reliable data on yes are lacking. 

Schindler and his coworkers determined the solubility constants and the influence of molar surface, S, upon solubility (25° C)... 

The change in the free energy AG involved in subdividing a coarse solid suspended in aqueous solution into a finely divided one of molar surface S is given by... 

Modulus, 247 set also Retention modulus Moisture content of eluents, 80, 83 control of, 80-82 determination of, 80 Moisture control, 106 Moisture control system, for eluent, 81-83 Molar surface area, 171, ... 

Adopting this viewpoint, the net interaction parameter for surface mixing in the present model may be seen as a useful way to account for changes in the surface free energy in nonideal mixed surfactant monolayers. Here, the parameter must not only account for the effects due to counterions, but for changes in molar surface... 

The retention caused by different salts in equal concentration is in accordance with the Hofmeister series. The higher the molar surface tension increment of a salt, the greater is its effect on protein retention 55). Higher column temperatures produce prolonged retention in HIC, in contrast to RPC where retention decreases with increasing temperature56). 

To obtain the relationship between the particle size d and the molar surface s, we consider 1 mole of a finely powdered solid consisting of N uniform particles of equal size. The surface of a single particle is S = fed2, where d denotes an arbitrarily chosen characteristic dimension of the particle. The volume is V = id3. Hence, the molar volume is... 

Besides this experimental method, there is a semitheoretical method by which y can be estimated. Assuming Equation 3 to be valid for any value of s and assuming that y is independent of s, we may outline this method as follows. One mole of a coarse crystalline solid consisting of ions A+ and B" is immersed in an aqueous solution. When the large crystal is cut into small pieces, the interface s increases, and the system gains Gibbs energy. This pulverization finally yields the hydrated ions Aaq+ and Ba( ", and the molar surface reaches a value of ... 

Figure 6. Solubility product of ZnO as a function of molar surface s...

For the formulation of a dimensionless adsorption equilibrium constant the definition of a standard state is crucial. The standard state is freely selectable, regardless of the possibility of its physical realization. It is defined according to its expediency. The standard state of adsorption is assumed to be the ratio of a standard molar volume to the standard molar surface [4],... 

Surface Tension.—The values of the surface tension a and density D at two temperatures were determined with the object of calculating the molar surface energy a(M/D) , and its change with temperature.4... 

The surface tension of liquid phosphine indicates a certain degree of association, since the coefficient of decrease of molar surface energy with increase of temperature is about 1-7 instead of 2-0 —... 

SURFACE TENSIONS, DENSITIES AND MOLAR SURFACE ENERGIES OF PBrs. 

The surface tension, as determined by the capillary tube method, was given as 31-91 dynes/cm. at 18° C. and 28-37 at 46-1° C.8 Hence the change of molar surface energy with the temperature is normal. This physical constant, together with some others, was determined in order to obtain the paraehor [P]. The sample of POCl3 had a boiling-point of 108-7° C. at 769 mm. 

Equation (1.15), when applied to monoatomic liquids, predicts that the molar surface energy structural parameter m,. If mi is the same for all metals, scale with the quantity Le / Qm. It was shown in (Eustathopoulos et al. 1998) that equation (1.15), valid in principle only at OK, holds also at TF. As Qm is proportional to vm2/3 (vm denoting the molar volume), one obtains ... 

Qm is the molar surface area of the oxide and the flow of oxygen leaving the drop surface, fl>0, is given by ... 

Following equation (6.28), if E A)/RT is very negative, the slope (d.o will als° be very negative. Conversely, if Eg(A)/R.T is very positive, the slope will be positive but small (Figure 6.28.a). Indeed, the maximum value of (dff/dXB)xB->-o will be equal to RT/Om and substitution of typical values of temperature (1000K) and molar surface area (fim 5 x 104 m2.mol-1), gives the negligible value of 2 mJ/m2 per 1% of solute. This behaviour predicted by the... 

In this equation, Qm is the molar surface area, m i is a structural parameter defined in Section 1.1 (see Figure 1.3) and A is the regular solution parameter of Ni-Si alloy defined by equation (4.3). From the slope of the osL(XNi) curve for XNi— 0, the adsorption energy is found to be E i,(f ) = —8.2 kJ/mole. Thus, in equations (1.2), all the quantities are known (or can be easily estimated), except W and Wf 1 which represent respectively the work of adhesion and the work of immersion of pure liquid Ni in metastable equilibrium with SiC (i.e., for a supposed non-reactive pure Ni/SiC system). The values deduced from equation (1.2) are Wj4 = 3.17 J/m2 and W = —1.35 J/m2 for pure Ni. They are reported in Figure 7.6 along with the corresponding value of contact angle. 

Alternatively, the chemical potential of the adsorbed phase is equal to the transformed Gibbs energy divided by the surface excess amount, i.e. the transformed molar surface excess Gibbs energy ... 

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