Macroscopic coefficients

Macroscopic Coefficients and Surface-Site Heterogeneity. Beniamin and heckles model (5) of heterogeneous metal oxide surface sites includes two observations of metal ion/surface site Interactions. 

Membranes classified under (a) and (b) above may be fully characterized by overall (macroscopic) coefficients S and DT or P for all experimental purposes exactly as above. The only difference from strictly homogeneous membranes is that the said macroscopic coefficients are of limited physical significance until they are analyzed into their component microscopic coefficients. 

According to Ferry12 the macroscopic coefficient of thermal expansion, al5 above Tg reflects the appearance of the free-volume. In this case the value a( must be equal to af = cq — ag s Aa. Indeed, the experimental values for Aa are in good agreement with the theoretically calculated values for ctf. 

Now we make contact between the macroscopic coefficients ky T,p), defined by Equation 8.39, and the microstructural details of the reference system, that is, the solvation behavior of the species in the infinitely dilute system, by invoking the solvation formalism discussed in Section 8.2 (and references therein) from which we have that... 

Before employing eq. 6.40 to evaluate the contributions to the macroscopic coefficients k/ (T) from the single-ion anisotropy terms of the Stevens operators of eq. 6.3 must first be transformed to a co-ordinate system with the z-axis along the magnetization direction. Equation 6.40 then yields, for example. 

We now have to verify that the expansion of j [T) converges. Some values of the macroscopic coefficients of (9.5.4)- 9.5.8) are given in Table 9.5.1 for argon and carbon tetrachloride near their melting points. The convergence is rather slow but sufficient for our present purpose. 

EXPERIMENTAL VALUES OF THE MACROSCOPIC COEFFICIENTS APPEARING IN THE EXCESS FUNCTIONSFOR ARGON AT 87.3 K (= BOILING POINT) AND CCI4 AT 273 2°K. PER MOLE )... 

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