Average molar area

In a mixture the average molar area A is defined as A/(n°j + n ). This quantity depends on n , of course. As a function of 0, A varies from A to A A possible trend is given by the solid curve in fig. 3.16. This case may be expected for monolayers where molecules si and s2 attract each other. The linear crossing (dashed line) refers to ideal mixing, i.e. to additivity of the individual areas... 

The corresponding values of equilibrium adsorption in these two states are Ti and P2, respectively, with the total adsorption expressed as F = F + F2. The ratio of the adsorption values and the average molar area are given by the expressions... 

Here Fj and Fc are the partial and critical adsorption of monomers, respectively, and the average molar area co should be expressed via the equation... 

The equation contains the average molar area coq = and the surface... 

The average To of the partial molar area for all components or all possible states at the interface is often used in conjunction with the Lucassen-Reynders dividing surface, which can be equivalently described as... 

The average partial molar area is determined by Eq. 12 as l + niFi/Fcr- ... 

Figure 16 shows G(D) of a simulated polymer mixture at two scattering angles ("Q", 14° and 17°). The mixture consists of two polystyrene standards having distinctly different weight average molar masses (3.Ox 105 and 5.9x 106 g/mol) and a high mass polystyrene which is used to simulate the polymer cluster [66]. The area ratio Ar of the two peaks is expressed by... 

Vi are the molar volumes of pure components, and the average surface area per molecule, A, is given by the equation... 

The total mass transferred between phases may be determined by summing the contributions from the bubble formation zone and each bubble population. The total number of moles transferred in the /cth bubble population is the product of the average molar flux given by Eq. 12.1.69 and the total interfacial area in that population ( //, The... 

We have shown (Ref. 2, Figure 6) that at surface pressures from 18 to 26 dynes/cm the partial areas of the constituents are independent of the composition of the mixed films if the molar fraction of component 2 is 0.27-0.70. In this case the error for the partial molecular areas results from the error on experimental average molecular areas equal to 10%. However, an additional error must be considered above 26 dynes/cm resulting from the tangent slope to the curve (Ref. 2, Figure 2) which can be estimated as 10%. 

Subsequent addition of the solid phase to the saturated solution does not result in dissolution of the oxide and leads to a reduction in the saturated solution s concentration owing to decrease in the average molar surface area of the oxide. This change can easily be calculated if we know the quantities of both powders and their molar surface areas. 

An example of the SAM data treatment for zinc oxide is presented in Table 3.7.6. The quantities of ZnO corresponding to points 1-6 do not result in the formation of a saturated solution the e.m.f. (pO) data make it possible to estimate the dissociation constant of ZnO in the KCl-NaCl melt as pKZnQ = 6.37 0.08. Point 7 corresponds to the weight of ZnO which provides saturation of the melt by zinc oxide, thereat the added powder of oxide is dissolved in the melt only partially. Subsequent additions of ZnO to the saturated melt result in an appreciable reduction in the saturated solution s concentration (decrease in the solubility product of ZnO) owing to the reduction in the averaged molar surface area of the deposit and, in turn, the oxide solubility. This reduction ends after the true plateau is achieved, when the changes of molar surface-area are negligible. 

The mean partial molar area (averaged over the two states) can be expressed by... 

It is seen that the additional (nonnalised) activity coefficients introduced in Eq. (2.10) to establish the consistency between the standard potentials of the pure components and those at infinite dilution, can be incorporated into the constant Kj in Eq. (2.15). Therefore, if a diluted solution with activity coefficients of unity is taken as the standard state, the form of Eqs. (2.13) and (2.14) remains unchanged. The equations (2.14) and (2.15) are the most general relationships from which meiny well-known isotherms for non-ionic surfactants can be obtained. For further derivation it is necessary to express the surface molar fractions, x-, in terms of their Gibbs adsorption values Tj. For this we introduce the degree of surface coverage, i.e. 9j = TjCOj or 0j = TjCO. Here to is the partial molar area averaged over all components or all... 

When the molar areas of the components are different, the average area for the mixture can be estimated by... 

When the molar mass distribution is not too wide, the mass average and area average for random coils and flexible rods are, within the experimental error, practially identical. A whole series of other averages, besides these two averages, may also be defined (see also Section 8),... 

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