Analysis Of The Excess Adsorption Isotherms For Solid/liquid Systems In Order To Determine The Surface Phase Capacity
ANALYSIS OF THE EXCESS ADSORPTION ISOTHERMS FOR SOLID/LIQUID SYSTEMS IN ORDER TO DETERMINE THE SURFACE PHASE CAPACITY
A. Dąbrowski
Faculty of Chemistry, M.Curie-Skłodowska University,
20031 Lublin, Poland
An essential difficulty concerning the solid/liquid adsorption systems for which the excess adsorption isotherms have been measured over the whole concentration region results from the fact that the amount of the solution undergoing adsorption can not be experimentally determined. Therefore, the most important assumptions deal with the thermodynamic model that consists of the equilibrium system: solid – surface phase – bulk phase. For such a system, the so-called surface phase capacity is defined as a number of molecules constituting the surface phase. If it is assumed that the above mentioned model of adsorption system and the corresponding isotherm equation are reliable, then the following questions come up:
1. will the surface phase capacity for the assumed thermodynamic model true as a consequence?
2. how much obtained results should be accepted?
3. what will the possibility of their thermodynamic verification be?
The first aim of my lecture is to present the theory enabling a numerical, statistical analysis of the errors made applying different methods for determining capacities of the surface phases formed on the real solid surfaces. I will apply the following equations: the Everett equation and Langmuir-Freundlich isotherm. At each case I assume that the molecular areas of both components are identical. Then, the surface phase capacity does not depend on the bulk concentration of the components. This assumption finds justification in many experimental and theoretical studies [1]. E.g., it follows from ref. [2] that the values of the surface phase capacities are only slightly affected by the decrease in rw from 1 to 0.6, where rw is the ratio of the molecular areas of the first of second component. Thus, for the adsorption systems presented in this lecture, the values of rw belong to the interval (0.6, 1.0), and the effects connected with the different molecular areas of both components may be
neglected. On the other hand, in my earlier papers [3,4] the influence of the differences in molecular sizes of components on the surface heterogeneity was studied. This heterogeneity calculated from adsorption date is a global property of a given adsorption systems. It has been shown [4] how large molecules can apparently change the energetic heterogeneity of the solid surface because they may occupy some adsorption sites of different energies.
I intend to present a new insight into the problem both for homogeneous and heterogeneous adsorbents as well as the statistical analysis which provides the answer to the queries one and too [5,6]. It allows to minimize the possibility of random results and to limit the error only to a systematic one which is the function of assumptions underlying the given isotherm equation. To this end, the definite models of adsorption systems and isotherm equations corresponding to them are employed.
In order to obtain the answer to the third query I propose two independent thermodynamic approaches. First of them dwell on the thermodynamic analysis of experimental excess isotherms and is carried out on the basis of thermodynamic equations and some thermodynamic inequalities [7]. These inequalities deal with the stability conditions of systems investigated and can be formulated in terms of the real or excess quantities and apply to the systems far from the critical state. One of the main real quantities is the surface phase capacity. Other possibilities arise in terms of the theory of the surface activity coefficient [8]. These coefficients can be evaluated from the excess adsorption data and characterize non-ideality of the surface phase resulting from differences in molecular interactions which are additionally perturbed by surface heterogeneity of the solid. It is shown that the surface activity coefficients plotted as functions of the bulk or surface phase composition are characteristic for a given adsorption system and are useful both for assessing adsorbent heterogeneity effects as well as for correcting the surface phase capacities determined by means of other independent methods.
References
1. A.Dąbrowski, M.Jaroniec and J.Ościk, Colloid and Surface Science, Plenum Press, New York, 14 (1987) 83.
2. Yu.Eltekov, V.V.Khopina and A.V.Kiselev, Trans.Farady Soc., 68 (1972) 889.
3. A.Dąbrowski, Monats.Chem., 114 (1985) 139.
4. A.Dąbrowski and M.Jaroniec, Adv.Colloid Interface Sci., 27 (1987) 211.
5. A.Dąbrowski and P.Podkościelny, Langmuir, 13 (1997) 3464.
6. A.Dąbrowski and P.Podkościelny, Colloid and Surfaces, 162 (2000) 215.
7. A.Dąbrowski and M.Jaroniec, Adv.Colloids Interface Sci., 31 (1990) 155.
8. A.Dąbrowski and P.Podkościelny, Thermochimica Acta, 259 (1996) 71.
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