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Additional resources for Adsorption: Theory, Modeling, and Analysis (Surfactant Science Series, Volume 107)

Example text

The calculation of the total monolayer capacity, nsm , is discussed in detail in Section VI. C. The Modiﬁed Volmer Equation Applied to Heterogeneous Surfaces (VT Equation) The thermodynamically consistent (modiﬁed) mV equation and its function cmV ðYÞ have been deﬁned by Eqs. (160) and (157), respectively. Introducing the parameter t proposed by To´th, we obtain  2 wV ; t>0 ð238Þ cVT ðYÞ ¼ wV À Y t Substitution of Eq. (238) into Eq. Àt ð242Þ ' ð243Þ Interpretation of Adsorption Isotherms 49 Taking Eq.

Taking these limiting values into account the different types of isotherm can be uniformly interpreted, as it has been done in Figs. 10–12. In Fig. 20, the functions YðPÞ, zcðPÞ, YðPr;m Þ, CðYÞ, Asr ðYÞ, and Asr ðPr;m Þ corresponding to isotherms of Type I are shown only because these functions occur more frequently in practice than other types. The calculations relating to Fig. 20 are summarized as follows: Top (left):  1 P¼ KFT 1=t   Y BF Yt exp À t ðwF À Yt Þ1=t ð234Þ Interpretation of Adsorption Isotherms 47 FIG.

For the calculation of the total monolayer capacity, a four-parameter iteration may also be possible because Eq. (201) may also be written in this form: P¼ 1 ns t 1=t s ðKT Þ ½wT ðnm Þ À ðns Þt 1=t ð211Þ However, for calculating nsm ; a general method is discussed in Section VI. The mathematically uniform and thermodynamically consistent interpretation of Eq. (199) is shown in Fig. 19, where the functions YðPÞ, cðPÞ, YðPr;m Þ, cðYÞ, Asr ðYÞ, and Asr ðPr;m Þ are plotted. The calculations of these functions have been made as follows: Top (left):  P¼ 1 KT 1=t Y ðwT À Yt Þ1=t ð212Þ or Y¼ ðwT Þ1=t P ½ð1=KT Þ þ Pt 1=t ð213Þ Top (right): cT ðPÞ ¼ KT Pt þ 1 or the values of the function wT cT ðYÞ ¼ wT À Yt ð214Þ ð215Þ are conjugated with values of P caculated from Eq.