Bangham equation

Langmuir equation for a uniform surface, but by the Zel dovich and Rogin-skii equation or by the Bangham equation. Adsorption equilibrium is described not by the hyperbolic Langmuir isotherm, but by the Freundlich isotherm or the logarithmic isotherm (40). 

If the Freundlich adsorption isotherm is valid than the adsorption rate is proportional to pressure and inversely proportional to a fractional power of surface coverage, giving the Bangham equation... 

Distribution functions (93) and (94) are substantiated by the fact that they lead to the most frequently observed adsorption isotherms for the region of medium surface coverages, viz., the Freundlich isotherm corresponds to distribution (93) with > 0 and T < as it has been demonstrated by Zel dovich (43) and the logarithmic isotherm corresponds to distribution (94) (40). Besides that, if we accept Assumption 1, then distribution (94) will give the equation of adsorption kinetics by Zel dovich and Roginskil and distribution (93) will result in the equation of adsorption kinetics by Bangham. Finally, if Assumption 1 is correct, then distribution (93), including distribution (94) as its particular case, follows from the kinetics of fractional order reactions (44). 

Equation (150) is the well-known equation for adsorption rate found by Zel dovich and Roginskil (45) (sometimes it is erroneously called the Elo-vich equation )- This equation was experimentally confirmed for many cases of chemisorption. It follows from (135) and (146) that on a surface where the Freundlich isotherm is valid, the adsorption rate is proportional to P/6m. Inverse proportionality between r+ and a fractional power of 6 was found by Bangham (46). 

For one specimen of charcoal, Bangham and Razouk measured the heat of wetting directly as 16-0 calories per gramme. The validity of equation (11) was tested in the following ingenious manner as described in Chapter VII, p. 254, charcoal expands on adsorbing vapour, and somewhat further when immersed in the liquid. F is assumed to be proportional to the expansion, X, thus ... 

Equation 2 has been used with some success by Bangham (I), McIntosh (5), Yates (20), and others to correlate adsorption extension data. Equation 3 has also been used with considerable success by McIntosh (15) and Dacey (6), and in some of my own work (8, 15). 

Later, in 1937, Bangham and Razouk showed that the ysv and yLV terms in Young s equation are related to the y and 7l of the pure solid and liquid phases (the components in contact with vacuum) at equilibrium, by the expression... 

The term yg in Equation 1 needs clarification. As Bangham and Razouk [6] pointed out, the vapor of the liquid will be adsorbed on the solid surface, often considerably decreasing its surface free energy. In Equation 1, and also in Dupre s Equation 3,... 

In accord with the critique of Yoimg s equation introduced by Bangham and Razouk [7], Equations 1 explicitly recognize the adsorption of components 1 and 2 at the appropriate interfaces. The notation just discussed permits this to be done with economy and precision. 

Kinetic data can further be used to know about the step offering larger resistance in the overall sorption phenomena using Bangham s equation. 

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