B.E.T. theory

A study of the effects of the adsorbent perturbation on the B.E.T. theory has been reported by Peticolas lOJf). The frequency of an adsorbent molecule, in an adsorbent site, is expected to increase by 10% when it interacts with an adsorbed molecule. Other consequences of the perturbation of the adsorbent have been discussed by Tykodi 106, 106) and Copeland (107). 

DEPENDENCE OF HEAT CAPACITY OF ADSORBATE ON SURFACE COVERAGE ON THE BASIS OF B.E.T. THEORY ASSUMPTIONS. BEREZIN G I KISELEV A V... 

Within the group of isotherms which have been studied, by far the largest number are known to be Type 2 isotherms. In this discussion we will restrict ourselves to the interpretation of Type 2 isotherms using a theory known as the B.E.T. theory based on the work of S. Brunauer, B. Emmett, and E. Teller [5]. For a discussion ofType 1 isotherms, see reference 1. Type 1 is usually found in solids which have a porous structure. 

Figure 10.3. Adsorption studies carried out at low temperature with inert gases yield the adsorbent surface area using B.E.T. theory, a) Low temperature nitrogen adsorption isotherm, b) B.E.T. isotherm.

In the B.E.T. theory, the sigmoid isotherm is explained on the basis of multilayer adsorption. It is assumed that the first monomolecular layer of adsorbate is adsorbed with a constant... 

This explains the success of the well-known B.E.T. method for this analysis. After the excellent discussion by Hill (244) of the B.E.T. and the Hiittig theories, in which he points out the weaknesses of the first and the fallacy of the latter, and after the analysis by Halsey (245), who indicates when a B.E.T. isotherm of satisfactory character is obtained on a heterogeneous surface, little need be said here. 

B.E.T. Brunauer, Emmett and Teller (who developed the theory for calculating B.E.T... 

Physisorption arises from the van der Waals forces, and these forces also condense gas molecules into their liquid state. Thus, in principle, there is no reason to stop upon completion of a monolayer during physisorption. Indeed, the formation of multi-layers, which are basically liquid in nature, is very common in physisorption experiments. Brunauer, Emmett and Teller developed a theory in 1938 to describe physisorption, where the adsorbate thickness exceeds a monolayer, and this isotherm equation is known by the initials of the authors (B.E.T.). The original derivation of the B.E.T. equation is an extension of Langmuir s treatment of monolayer adsorption from kinetic arguments. Later, in 1946, Hill derived this equation from statistical mechanics. In the B.E.T. isotherm, it is assumed that ... 

Thus, it is most suitable for describing chemisorption (except possibly for assumption 1) and low-coverage physisorption where a single layer is probable. For higher-coverage physisorption, a theory that accounts for multiple layers is the Brunauer-Emmett-Teller (B-E-T) isotherm (see [20-24], [63]). 

Surface areas of clay minerals may be derived from vapor-phase adsorption isotherms by applying either the B.E.T. (Brunauer, Emmett, Teller) theory (Brunauer et al. [1937, 1938, 1945]) or the method by Harkins and Jura [1944]. 

Blochl, P. E., Margl, P, Schwarz, K., 1996, Ab Initio Molecular Dynamics With the Projector Augmented Wave Method in Chemical Applications of Density Functional Theory, Laird, B. B., Ross, R. B., Ziegler, T. (eds.), American Chemical Society, Washington DC. 

Fig. 17 B/E-p dependence of the critical temperatures of liquid-liquid demixing (dashed line) and the equilibrium melting temperatures of polymer crystals (solid line) for 512-mers at the critical concentrations, predicted by the mean-field lattice theory of polymer solutions. The triangles denote Tcol and the circles denote T cry both are obtained from the onset of phase transitions in the simulations of the dynamic cooling processes of a single 512-mer. The segments are drawn as a guide for the eye (Hu and Frenkel, unpublished results)...

Schultz, H. P., Schultz, E. B., Schultz, T. P. Topological organic chemistry. 9. Graph theory and molecular topological indices of stereoisomeric organic compounds. J. Chem. Inf. Comput. Sci. 1995, 35, 864-870. 

In the o.s. reaction, the ion pair A+ - B is formed in a first step. The corresponding equilibrium constant can usually be obtained from simple electrostatic models. In this "ideal" case specific chemical interactions can be neglected and the rate constant of the E.T. step follows the theory of R.A. Marcus (see for example Marcus, 1975, or Cannon, 1980). In the i.s. reaction each of the three steps in reaction (9.2) may determine the reaction rates. The lability of the coordinated ligands at the... 

The beliefs are derived from the residuals with the relation (15) with the same threshold than for boolean evolution, i.e., t = 0.4 for a = 0.5. Clearly, the boolean combination leads to an unstable isolation of the faults because the value of ri is often oscillating around 0.4. On the contrary, the approach based on the Evidence theory isolates perfectly the faults and does not induce any oscillation. In another situation where the value of residual rs is not affected as it should be when the fault /s occurs, the boolean combination does not succeed again to isolate the faults (see in particular /s in Figure 7.b) whereas the Evidence theory combination methods correctly the faults most of the time Cf. Figure 7.c). 

E.T. Jaynes Papers on Probability, Statistics and Statistical Physics (R.D. Rosenkrantz ed., Kluwer, Dordrecht 1989) Probability Theory (Cambridge Univ. Press 2003) B. Buck and V.A. Macaulay eds., Maximum Entropy in Action (Clarendon, Oxford 1991). A desperate attempt was made by J.M. Keynes, A Treatise on Probability (Macmillan, London 1921, 1973). 

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