Introduction of new functions to speed up sorption measurements
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Introduction of new functions to speed up sorption measurements J. A. Poulis · C. H. Massen · A. D´abrowski · E. Robens
Received: 22 February 2006 / Revised: 6 September 2006 / Accepted: 8 September 2006 C Springer Science + Business Media, LLC 2006
Abstract The procedure suggested by J¨antti enables estimation or calculation of the values of adsorption parameters in an early stage of adsorption measurements. The procedure may also give information about the validity of models used for the explanation of the measurements. In the present paper new functions are introduced to get results easier. Keywords Adsorption . Dynamic . Fast measurement . Sorption . Surface
tion measurements (J¨antti et al., 1970, 1972; J¨antti and Robens, 1981). His method was specially constructed for measurements satisfying: m (t) = A + B {1 − exp(−Ct)}
where m stands for the sorbed mass and where A, B and C are constants (Table 1). J¨antti introduced the function J (t): J (t) =
Introduction In 1970 J¨antti introduced a calculation procedure with the intention to reduce the time necessary for sorpJ. A. Poulis . C. H. Massen Faculty of Applied Physics, Technische Universiteit Eindhoven, P.O. Box 513, NL - 5600 MB Eindhoven, The Netherlands e-mail: [email protected] C. H. Massen e-mail: [email protected] A. D´abrowski Maria Curie-Sklodowska University, Chemistry Faculty, M. Curie-Sklodowska Sq. 2, PL-20-031 Lublin, Poland e-mail: [email protected] E. Robens () Institut f¨ur Anorganische Chemie und Analytische Chemie der Johannes Gutenberg-Universit¨at, Duesbergweg 10-14, D - 55099 Mainz, Germany e-mail: [email protected]
(1)
m 22 − m 1 m 3 2 m2 − m1 − m3
(2)
where t2 = t, t2 − t1 = t3 − t2 and where m 1 , m 2 and m 3 are the masses measured at the times t1 , t2 and t3 respectively. J¨antti used the fact that when Eq. (1) is satisfied, J (t) is independent of t: J (t) = J = A + B
(3)
Equation (3) implies that the value of A + B can be calculated already soon after the starting of an adsorption measurement which can be helpful as such measurements can well take hours. An other feature of J¨antti’s method is that, in the case that J (t) (Eq. (2)), calculated using measured values, proves not to be independent of t, this can be interpreted as a warning of the non-validity of Eq. (1) and that a more complicated molecular model is necessary for the explanation of the measurements. One step further is the possibility that a more complicated molecular model is available and that it allows the possibility to predict the Springer
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Adsorption (2006) 12:213–217
Table 1 List of symbols A, B, C m t
Constants Adsorbed mass Time of adsorption
Aeff (t), Beff (t), Ceff (t) J (t) Indexa , Indexb
function J (t). Such a predicted function will generally contain parameters (Poulis et al., 2002, 2004). Comparison with the measured results can lead to estimation of the values of those parameters. In case the comparison between the predicted and the measured J (t) curves leads to too large a discrepancy, an adaptation o
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