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

**Example text**

150) and (151), KmV ¼ ðIV ÞÀ1 ð165Þ and equal to Eq. À1 ð166Þ It is very important to remark that the original and the modiﬁed Volmer equation can only describe isotherms of Type I. It is obvious, because, from Eq. (157), it follows that wV > wV À Y ð167Þ that is, in the whole domain of coverage, it is valid that cmV ðYÞ > 1 ð168Þ This means that the mobility of adsorbed molecules cannot cause a change in the type of isotherm. This change may only happen if the interactions between the adsorbed molecules are taken into account, as it is done by the mFG equation.

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. (212). Middle (left): From Eq. (200), it follows that Pm ¼ ½KT ðwT À 1ÞÀ1=t ð216Þ P ¼ Pr;m Pm ð217Þ so can be calculated.

The values of parameters are as follows: KmB ¼ 0:6 kPaÀ1 , wB ¼ 1:2, BB ¼ 0:7, t ¼ 1:0, Pm ¼ 614:2 kPa (solid line, mBH equation); KBT ¼ 9:0 kPaÀt , wB ¼ 1:2, BB ¼ 0:7, t ¼ 0:6, Pm ¼ 486:4 kPa ð Þ; KBT ¼ 0:01 kPaÀt , wB ¼ 1:2, BB ¼ 0:6, t ¼ 1:6, Pm ¼ 760:6 kPa ð Á Á Þ. This equation has the form Y aYt Bx Yt P¼I exp À t tðwx À Yt Þ ðwx À Yt Þ1=t where I ¼ Pm ðwx À 1Þ1=t exp Àa B þ x tðwx À 1Þ t ð261Þ ð262Þ Interpretation of Adsorption Isotherms 53 In Eqs. (261) and (262), a new parameter, a, is introduced which may have only two values; namely, if the adsorbed layer is mobile, then a ¼ 1; in other cases, a ¼ 0.