Langmuir 1993,9,2190-2201
2190
Total Surface Segregation. A Fresh Look at the Gibbs Adsorption Isotherm for Binary Liquid Mixtures Ian A. McLure,’ Virgflio A. M. Soarea: and Ann-Marie Williamson Department of Chemistry, University of Sheffield, Sheffield S3 7HF, U.K. Received December 26,1990. In Final Form: November 16, 1992 A quantity termed the total surface segregation is discussed and evaluated as a measure of relative adeorption at the gas-liquid interface of binary liquid mixtures. Ita calculation from the surface tension and nonideality of the liquid mixture is detailed, and results are presented for 17 systems covering the recognized classes of liquid mixtures. The results for argon + krypton, in particular, are compared with theoretical calculationsbased on the density functional treatment of Telo da Gama and Evans which yields the local surface segregation whose integral through the interface is a close approximation to the total surface segregation. The absolute magnitude, composition dependence, relation to surface azeotropy (aneotropy) and bulk azeotropy, and proximity to a consolute point of the total surface segregation are explored. Useful relationships with the known underlying intermolecular forces are presented which c o n f i i broadly the utility of the total surface segregation for the purpose of representing adsorption at the gas-liquid interface of mixtures.
I. Introduction There is asyet no widely-acceptedmeasure of adsorption at the liquid-gas interface in binary liquid mixtures that gives useful information across the entire composition range. With this in mind, our aim here is to reinvestigate the Gibbs adsorption equation with a view to extracting from it and exploringthe propertiea of a little-used measure of adsorption that, for reasons given later, we term the total surface segregation. This quantity has been proposed’ as superior to those employed previously not least because ita behavior for a variety of well-characterized liquid mixtures can be interpreted to some extent in terms of the accepted molecular interpretation of the observed bulk behavior. The principal manifestation of the interface between a binary liquid mixture and ita coexisting vapor phase is the different composition at the interface compared to those in the coexisting bulk phases. For coexisting liquid and vapor phasea, the mole fraction of component i in the vapor (yi) can be obtained from a knowledge of ita mole fraction (xi) in the coexisting liquid, vapor pressure @i*), and activity coefficient (n),and the total vapor pressure of the system @) according to eq 1. yi = XiYSi*/P
(1)
Unfortunately, no equivalent simple relation exists between the composition of the surface layer and those of the bulk liquid or vapor phases; indeed no simple universally-acceptable quantity exists to express the surface composition itself. Traditionally, the adsorption of component i at the interface (ri)has been defined by employingGibbs’device of considering the interfwe to be a planar surface parallel to the surface of tension such that the phases on either side of the interface remain homogeneousup to the position of the interface. For a binary liquid mixture this results in a jump discontinuity in the composition of component i at the interface. Using this specification of the interface, ri is given by the following equation:
* To whom correspondence should be addressed. t Present addrw: Centro da QuImica Eetrutural, Complex0 I, Instituto Superior Tbnico, 1096 Lieboa Codex, Portugal. (1) McLure, 1. A.; Sipowska, J. T.;Pegg, I. L. J. Chem. Thermodyn.
1982, 14,133.
0743-7463/9312409-2190$04.00/0
ri = n(sIi/a
(2)
where a is the area of the interfacial plane and n(s)i is either the number of moles of i adsorbed at the surface or the surface excess of i defined in either case by nWi = nj- n(g)i - n(lIi
(3) with n(g)i and n(l)i the number of moles of component i in the gas and liquid phases, respectively, and ni the total number of moles of component i in the combined system. This model in effect defines the thickness of the interface aa zero although in reality the interface is a region of indeterminate, albeit small, finite thickness. A serious drawback of the model is the sensitivity of the actual value of ri to the choice of the position of the interface. Therefore, a more realistic measure of adsorption invariant to the position of the dividing surface is needed. Such an acceptable measure of adsorption at the gas-liquid interface of a liquid mixture should possess the following attributes: (i) ready calculation from experimental measurements, (ii) “significant” value over the entire composition range from x = 0 to x = 1, (iii) magnitude and composition dependence in some way immediately reflecting the nature of the intermolecular interactions between the components of the mixture, and (iv) ready calculation from molecular theory and computer simulation for purposes of comparison with experiment. Until now, the quantity predominantly employed to represent adsorption has been the relative adsorption, l’2,1, derived directly from the Gibbs adsorption equation:
r2,’= r2- txz/x,)r,
= -(BUI~P~)~
(4)
where ri is the amount of component i of a mixture adsorbed onto a unit area of the interface, xi is ita mole fraction and pi ita chemical potential, and u is the surface tension of the mixture. rz,lis an accessible quantity for study since it can be determined from the experimentallydeterminable quantites u and p2. A drawback of r 2 , l is that ita sign is dependent on the assignment of the labels 2 and 1 to the components. The principal use of r2,l hitherto has been for solutionsdilute enough to be deemed ideal and studied over a limited composition range such that x 2
