By Jozsef Toth
Bargains an outline of the new theoretical and useful effects accomplished in gas-solid (G/S), liquid-solid (L/S), and gas-liquid (G/L) adsorption study.
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Extra info for Adsorption: Theory, Modeling, and Analysis (Surfactant Science Series, Volume 107)
If 1 > tx ð266Þ then it is valid that cT ðPÞ ¼ cFT ðPÞ ¼ cVT ðPÞ ¼ Kx Ptx þ 1 ð267Þ cT ðPÞ ¼ cBT ðPÞ ¼ Kx Ptx þ 1 ð268Þ and Equations (263), (267), and (268) mean that the To´th equation with appropriate parameters Kx and tx can express all properties of an adsorbent–adsorptive system such as the heterogeneity mobility, immobility, and lateral and vertical interactions experimentally reﬂected by isotherms of Type I. This statement is proven and shown in Figs. 23–25. The functions shown in these three ﬁgures are calculated as follows: At the top (left), the functions cðPÞ are plotted; the symbol !
If t > 0, Bx ¼ 0, and a ¼ 1 (heterogeneous surface, no interactions, mobile layer), then we have the VT equation: & ' & ' 1 Y Yt P ¼ Pm ðwV À 1Þ1=t exp À exp tðwV À 1Þ ðwV À Yt Þ1=t tðwV À Yt Þ See Eq. (239). To´th 54 8. If t > 1, Bx ¼ BB , and a ¼ 1 (heterogeneous surface, interactions, mobile layer), then we have the BT equation: & ' & ' 1 B Y Yt BB Yt þ B P ¼ Pm ðwB À 1Þ1=t exp À exp À tðwB À 1Þ t ðwB À Yt Þ1=t t tðwB À Yt Þ See Eq. (251). F. Applicability of the To´th Equation to all Isotherms of Type I Measured on Heterogeneous Surfaces Let us compare the functions cðPÞ corresponding to To´th, FT, VT, and BT equations shown in the top right of Figs.
The above analysis is also represented in Fig. 8. The ﬁrst ﬁgure ðwF ¼ 1Þ relates to the original FG equation, which can describe Types I and V and condensation isotherms. However, for Type V isotherms, the value of BF tends to inﬁnity when Y tends to 1. In this fact is also reﬂected the thermodynamical inconsistency of the original FG equation. In the top (right) of Fig. 8, wF ¼ 1:17, the place of minimum, Ymin , according to Eq. (134) has been increased. So, from the analysis and ﬁgures above, it follows that the Type I isotherm is described when 0 < BF < 1=wF , Type V isotherms can occur when 1=wF < BF < 4=wF , and two-dimensional condensation takes place when BF > 4=wF .