Degree of heterogeneity

All gases below their critical temperature tend to adsorb as a result of general van der Waals interactions with the solid surface. In this case of physical adsorption, as it is called, interest centers on the size and nature of adsorbent-adsorbate interactions and on those between adsorbate molecules. There is concern about the degree of heterogeneity of the surface and with the extent to which adsorbed molecules possess translational and internal degrees of freedom. 

From the earliest days, the BET model has been subject to a number of criticisms. The model assumes all the adsorption sites on the surface to be energetically identical, but as was indicated in Section 1.5 (p. 18) homogeneous surfaces of this kind are the exception and energetically heterogeneous surfaces are the rule. Experimental evidence—e.g. in curves of the heat of adsorption as a function of the amount adsorbed (cf. Fig. 2.14)—demonstrates that the degree of heterogeneity can be very considerable. Indeed, Brunauer, Emmett and Teller adduced this nonuniformity as the reason for the failure of their equation to reproduce experimental data in the low-pressure region. 

The value of a to be used in these expressions is given by Eq. (5.45) for the specific mixture under consideration. At the point of gelation - l/(f- 1) according to Eq. (5.46). Equation (5.55) shows that n becomes infinite at this point while n remains finite. This merely means that there are still many molecules present at the gel point in addition to the network molecule of essentially infinite molecular weight. The ratio h /n indicates an immense expansion of the degree of heterogeneity as a ->. Expressions are also avail-... 

AH practical adsorbents have surfaces that are heterogeneous, both energetically and geometrically (not all pores are of uniform and constant dimensions). The degree of heterogeneity differs substantially from one adsorbent type to another. These heterogeneities are responsible for many nonlinearities, both in single component isotherms and in multicomponent adsorption selectivities. 

The exponentials Ki and K2 in the model account for the degree of heterogeneity of the interphase layer. The ratio of these exponentials is representative, as suggested in [121], of the load transmission between the fiber and the matrix (the adhesion factor a). 

Discontinuity between the physical form of the sample and reference material used can lead to error. This is another manifestation of the matrix effect, but one which has to be considered when analyzing biological and environmental samples. There is no easy answer to the relationship between partide size and homogeneity. It is a popular assumption that the smaller the partide size the less the degree of heterogeneity. In some cases this may be true but there are a number of considerations. 

The continually increasing sensitivity of analytical instruments makes it possible to probe smaller samples. For smaller volumes, surface properties become more important. Surface analysis is a rather new and rapidly developing field. Analytical difficulties increase with the degree of heterogeneity, from homogeneous to surface treated, coated, layered, continuously varying composition to totally heterogeneous. 

Heparin is now recognized to be a mixture of polysaccharide chains of variable length and degree of heterogeneity. However, all of the heparin... 

Lifetime heterogeneity itself can be the target of the measurement. In this case, high photon counts and alternative model functions like stretched exponentials and power-distribution-based models can be used [39, 43], These provide information on the degree of heterogeneity of the sample with the addition of only one fit parameter compared with single exponential fits. 

Sharma et al. (2005) developed robust calibrations for some of the key parameters from the spectra or fresh phase I and II composts and found by the laboratory measurement that for phase I samples were greater than those of the phase II samples except for ash, due to a higher degree of heterogeneity in the substrate. 

The size of sample is also restricted in the field of art conservation research. Nevertheless, the degree of heterogeneity of the object imposes an inferior limit to the sample s size, so a compromise between size of sample and size of the confidence interval acceptable should be achieved in each particular case study. 

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