Langmuir 1988,4, 93-96 At higher electrolyte concentrations, when the number of changes of the swamping electrolytes per ionic surfactant molecule is higher than 1(above 0.0002 M), the mono-, di-, and trivalent electrolytes depress the cloud point as expected. The cation of a higher charge is more effective in the reduction of the cloud point of mixed surfactants than one of the lower charge. The most striking feature in Figures 4 and 5 is the enormous variation of the cloud point with electrolyte concentration when the number of charges of the swamping electrolyte per SDS molecule is lower than 1 (below 0.O001 M). In this case the cloud point of a mixed ionic-nonionic surfactant mixture is depressed most effectively by divalent electrolytes (Mg2+,Ca2+). It is interesting to note that such a behavior was noted both for chlorides (Figure 4) and for nitrates (Figure 5). Our in-
93
terpretation of this finding is that polyvalent cations readily hydrolyze, frequently incorporating anions other than hydroxyl in the complex solute. Consequently, the aqueous solution’contains species of various composition and changes, which are not always well-defined. Their effect becomes more evident upon lowering electrolyte concentration.
Acknowledgment. I thank Prof. Dr. R. Piekos for many helpful discussions and for linguistic correction of this manuscript. Registry No. SDS,151-21-3;NaCl, 7647-14-5;NaEir, 7647-15-6; NaI, 7681-82-5; NaSCN, 540-72-7; Na2S04, 7757-82-6; CaC12, 10043-52-4; Ca(N03)2,10124-37-5;MgC12,7786-30-3;Mg(N03)2, 10377-60-3;AlC13,7446-70-0;Al(NOd3,13473-90-0;LiC1,7447-41-8; KC1, 7447-40-7; Triton X-100, 9002-93-1.
The Close Analogy between the Preferential Solvation of Polymers in Mixed Solvents and Adsorption from Liquid Mixtures at Solid/Liquid Interfaces M.Nagy Department of Colloid Science, Lordnd E6tv6s University, 1088 Budapest, Hungary Received November 3, 1986. In Final Form: June 26, 1987 In this work a comparison of some phenomenological aspects of sorption and solvation, the role of the sorbent as a component, and a critique of the traditional plot of isotherms are discussed. It was pointed out that a sorbent-sorbate system can be characterized in a correct way only by a set of isotherms involving a limiting case when the mass of sorbent tends to zero. The treatment was extended to cases when more than one sorbent or more than two mixture components are present in the system.
Introduction In classical and modern colloid and surface science, phenomena occurring at different types of interfaces have always played a central role. There are at least two reasons for this. First, interactions between surfaces or between colloid particles are decisively affected by the extent, structure, and other properties of adsorbed layers, and what is also essential, the stability of colloid systems besides other factors is controlled mainly by interparticular interactions. Second, the adsorption-desorption equilibria and processes are of great practical importance; therefore they have widespread scientific and industrial applications. In one of the commonly used considerations, adsorption interaction occurs at a geometrical surface which divides the phases in contact a t the molecular level into two or more parts, and crossing this borderline is accompanied by a jumplike change in many properties, e.g. in density, polarity, etc. In terms of classical colloid chemistry this is called disc0ntinuity.l From a geometrical point of view the discontinuities can be of a point, a line, or surface type, and for most real solid sorbents, due to their geometrical and energetic irregularities, one can usually count with “mixed” discontinuities. More precisely, if a solid surface is in contact with a liquid or a solution, the molecules of the mobile phase surround the surface elements with different coordination numbers. Furthermore, sorbents with high specific surface area contain channels, holes, i.e. (1) B w h , A. Colloid Systems, 1st ed.; The Technical Press: London: 1937; Chapter 11.
inner surface elements resulting in an energetic spectrum of the interaction of sorbate molecules with the solid. That is why it is somewhat more appropriate to speak of sorption phenomena instead of adsorption in case of solid/ liquid and solid/gas, or vapor, interfaces. However, there is another essential point. It is long known that in mixed solvents macromolecules behave like sorbents, so that an enrichment of one of the mixture components may occur in their solvation Even the more, the same phenomenon can be observed when small ions are present in a mixed solvent instead of macromolecules.s It follows from these experimental facts that the preferential binding of one of the mixture components is not merely a question of being a discontinuity in a classical sense present in the system, but it may frequently emerge when “discontinuities”brought about by intermolecular interactions perturb locally the random spatial distribution of molecules in these multicomponent (2) Flory, P. J. Principles of Polymer Chemistry, 1st ed.; Cornell University Press: Ithaca, N.Y., 1953; Chapter XIII. (3) Ewart, R. H.; Roe, C. P.; Debye, P.; McCartney, J. M. J. Chem. Phys. 1946, 14,687. (4) Strazielle, C.; Benoit, H. J. Chim. Phys. Phys.-Chim. Biol. 1961, 58, 675. (6) Read, B. E. Trans. Fargday Soc. 1960,56, 382. (6) %my, A.; Pouchly, J.; Solc, K. Collect. Czech. Chem. Commun. 1967,32,2753. (7) Nagy, M.; Wolfram, E.; GyBrfy-Szemerei,A. J. Polym. Sci., Part C 1972,39, 169. (8)Grunwald, E. In Eletrolytes; Pesce, B., Ed.; Pergamon: Oxford, London, New York, Paris, 1962; p 62.
1988 American Chemical Society
94 Langmuir, Vol. 4, No. 1, 1988
systems. In other words, there should be a close relationship between the sorption and solvation phenomena. Below we shall discuss briefly this common aspect together with some inadmissible views appearing in the calculation of sorption isotherms from experimental data. A correct solution of the problem also will be proposed. Sorbent as a Component of t h e System In a usual sorption experiment the solid sorbent is immersed at a constant temperature and outer hydrostatic pressure in a given amount of liquid mixture (or solution) with accurately known initial (or average) concentration. Then at equilibrium (i.e. when chemical potentials of the mobile components are the same throughout the system), from the concentration of the supernatant liquid and from the mass balance, the redistribution of mobile components can be calculated
Here mlais the excess mass of component 1sorbed by unit mass of sorbent, clj and are the initial and equilibrium volumetric concentrations of the same component, respectively, say, in kg/dm3, V is the total volume of the mixture, and m, is the mass of sorbent. It has to be noted that quantities in eq 1 can be expressed in other ways, too. So, instead of the volumetric concentration of components, the mass or mole fraction can be applied, and instead of total volume, the total mass of, or the total number of moles in the mixture, can be equally well applied. In a chemical sense, the sorbent added to the mixture is undoubtedly one of the components of the system and in the course of a sorption experiment, in addition to other factors, it would be desirable to keep its chemical potential constant, too. While this can be easily realized for a macroscopic sorbent (it forms a separate phase without Brownian motion), there will be some difficulties with the application of the Gibbs-Duhem equation if macromolecules or small molecules as third components are present in the system.8 Namely, depending on their relative amounts these "sorbents" may alter chemical potentials of mixture components to a considerable extent even when they form an ideal solution. For polymers dissolved in mixed solvents, a general solution of this task has been given by Debye3 and Stockmayerg in their light scattering theory of multicomponent systems. They introduced an "adsorption" constant, a,which is closely related to chapge in chemical potential of one of the components of low molar mass (ap3/am2)T,P,m3
/
(ap3
T,P,m2
=
-(
am3) =CY amz TQPI
(2)
and the right-hand side of eq 2, as we shall see later, has practically the same meaning as that given in eq 1 for sorbed excesses. In eq 2, T and P are the temperature and pressure, respectively, m2is the concentration of polymer, m3is the concentration of one of the solvent components, both given in molality, and p 3 is the chemical potential of component 3. The partial derivative with negative sign means that if a small amount of polymer (component 2) is added to the solvent mixture, a given amount of component 3 is transferred into the solvation layer of polymer (in fact its relative activity is lowered); that is, the sign of partial derivative in this case is negative and hence a will be positive (positive sorption of component 3). Because (9) Stockmayer, W. H. J . Chem. Phys. 1950, 18, 58.
c1 kgdrn-3
f
V = const
Cl,, C1,e C'1.e G,e
m,
1
1
m;
m';
--j
m,/kg
Figure 1. Simple linear form of c1 = f(md function when different amounts of sorbent are added to the mixture at a given initial concentration.
of the competitive and displacement nature of the sorption-solvation equilibrium, the relative amount of component 1in the solvation layer will be less than that in the bulk phase. The constancy of p 3 required can be achieved only if an infinitesimally small amount of polymer is present in the system or performing experiments at finite polymer concentrations one should extrapolate to zero polymer concentration. In this case, however, it is not necessary to apply mathematical approximations when evaluating experimental data in terms of the Gibbs-Duhem equation as has been done in ref 8. Though eq 2 is based on a rigorous thermodynamic treatment, its validity has been checked by application of different experimental methods such as light scattering, equilibrium dialysis, and equilibrium ultracentrifugation.'+l2 T h e Sorption-Solvation Isotherm In the present practice, mlaas a function of equilibrium concentration of the component in question (here it is component 1) is accepted conventionally as a sorption isotherm and with the aid of this relation hundreds of isotherms are taken up for several types of systems ever since the phenomenon has been discovered. A fundamental paper on adsorption from solutions and mixtures on solid/liquid interfaces has been published by D. H. Everett. In addition to the several interesting phenomena listed in this work, the theoretical problems involved are also discu~sed.'~ In the course of a sorption experiment, one of the important tasks is to measure accurately the concentration , 1. Starting from a given difference, Ac, = c,,~- c ~ ,in~ eq initial concentration this difference depends on the binding capacity of sorbent as well as on the ratio Vlm,. To make isotherms comparable only the initial concentration of one of the components is considered and V/msis kept constant. It is, however, only very rare that the independency of right-hand side of eq 1from the mass of sorbent would be c~ntrolled~"'~; therefore it is worthwhile to analyze again what happens in a simple sorption experiment. In Figure 1,the concentration of component 1 is plotted against the mass of sorbent. If this component is assumed to sorb positively, a decrease in c1 in the supernatant will be observed and, at least in principle, several kinds of shapes (10)Okita, K.; Teramoto, A.; Kawakara, K.; Fujita, M. J. Chem. Phys. 1968, 72, 278. (11) Cowie, J. M. G.; Dey, R.; McCrindle, J. T. Polym. J. (Tokyo) 1971, 2, 88. (12)Hearst, J. E.;Vinograd, J. Proc. Natl. Acad. Sci. U.S.A. 1961,47,
999. (13)Everett, D. H.Prog. Colloid Polym. Sci. 1978, 65, 103. (14)Wohler, L.;Wenzel, W. Kolloid-2. 1930, 53, 274. (15)Lottermoser, A.;Ott, A. Kolloid-2. 1930, 52, 138. (16) Mehl, P.Kolloid-2. 1931, 56, 299.
Langmuir, Vol. 4, No. 1, 1988 95
Solvation and Adsorption from Mixtures
(4)
It can also be pointed out that if V / m , >> 1, i.e. if the volume of sorbent is negligible compared to the mixture volume, the ratio V l m , can be replaced to a good approximation with the reciprocal volumetric concentration of the sorbent. So, eq 4 can be rewritten
mlu = -(Acl/Ac,)
(5)
where Acs is a change in sorbent concentration, Ac, = c, ~ (where , ~ c ? , means ~ no sorbent being present in the system), and urlthin brackets we have the slope of the linear c1 = f(m,)function. As can be seen in Figure 1, in the case of positive sorption of the component 1,the equilibrium concentrations are always smaller than the initial one, that is the slope of the c1 = f(m,) function is negative; hence one has to apply a negative sign for the whole expression to get a positive sign for ml". Then, taking the limiting value of the ratio, Acl/AcB, when c, is approaching zero
-c
Figure 2. Schematic representation of isotherms taken up at different values of Vf m,.
for the function c1 = f(m,)can be obtained. However, only the linear c1 = f(m,) function means that ratio Acl/m, is independent of the mass of sorbent at constant mixture volume; i.e. mlu can really characterize the sorption interaction prevailing in the system. Recently, the c1 = f(m,) function was experimentally studied in our laboratory and a linear initial portion of it was f 0 ~ d . lIt~ follows that checking linearity of the c1 = f(mJ or Acl = f(mJ functions at different cl,i ought to be the first step of a sorption experiment. If a linearity is established, one can begin to construct a sorption isotherm. This is shown in Figure 2 where mlbis plotted against equilibrium concentration of component 1. It is clear from the figure that shapes of sorption isotherms being taken up at different values of V / m ,should differ, or in other words, due to this dependence, the isotherms measured at various values of V / m , are not comparable. I t can be easily seen that distortion in the form of isotherms will be particularly significant far sorption from dilute solutions on a sorbent showing high affinity toward one of the components. The multiplicity of the traditional isotherms means that if we took the surface layer as an autonomous phase, the Gibbs phase rule would be violated. However, if we knew the absolute concentration of one of the components in the surface layer, a partitioning diagram could be constructed similar to a vapor-liquid mixture composition curve at constant temperature a t the equilibrium of such a closed system. However, the absolute concentration of a component in the surface layer, according to our present knowledge, cannot be experimentally determined. In order to have a correct isotherm being independent of the ratio V/m,, one has to add less and less sorbent to the mixture (the experimental points, the open circles in Figure 2 will move toward the value of initial concentration) approaching the initial value of the slope of Ac = f(m,) function when m, tends to zero or, in the language of mathematics
where mlUp0is the sorbed excess when infinitesimally small amount of sorbent is present in the system. According to the above treatment, if we plot ml"vOagainst col,i (which is in fact an equilibrium concentration , C O ~ , ~when , m, 0), we always get correct and comparable isotherms. On the other hand, the sorbent-mixture systems can be characterized at different V / m , values only by a set of isotherms all giving sorbed excesses as a function of the actually measured equilibrium concentrations. In order to compare eq 1and 2, the former can be given in the equivalent form
-
(17) Nagy, M. Magy. KGm. Foly. 1987, 93, 42.
mlUfJ = lim Ac.4
[-(2)Tp] -(2) =
(6)
TQPI
we obtain the right-hand side of eq 2 with the application of a completely different reasoning based on only the mass balance of the system and supporting convincinglythe view originating from the theory of mixtures. I t is also an advantage of the idea outlined above that in calculation of the mass balance, the contribution of volume of sorbed layers to the total volume of mixture becomes negligible. Naturally, in the case of fluid interfaces, i.e. for emulsions and gas dispersions, instead of the mass of sorbent the amount of surface available for sorption may be used. This consideration may also provide an explanation when changes in stability of emulsions as a function of stirring intensity are studied. Namely, if the amount of emulsifying agent and volume of the system are fixed, with increasing stirring intensity a decrease in stability may be observed due to the insufficient coverage conditions. This phenomenon is of great practical importance in the case of polymerization carried out in heterogeneous systems (see, e.g. the suspension polymerization of vinyl chloride).
Systems with More Than One Sorbent or with More Than Two Components i n the Sorbate Nowadays it is already well known that the commonly used solid sorbents, with few exceptions, have heterogeneous surfaces. Furthermore, it is also interesting from the point of view of colloid science and practice to calculate sorption isotherms for mixed sorbents or to characterize systems containing one sorbent and more than two components in the sorbate (see, for instance, the increasing number of publications on sorption of polymer mixtures from single s01vents'~J~).Obviously, our task is to find out about the rule of how to calculate a "composite" isotherm from individual isotherms of sorbents denoted A, B, C, and so on. First let us analyze the simplest case with the help of the c1 = f(m,) function when only two sorbents, A and B, are present in a mixture. In Figure 3, the linear portion of the c1 = f(msA)function is plotted at two values of initial concentration when sorbent A is added to the mixture. Difference in the slopes indicates that it is the ascending region of an isotherm. It follows also from this figure, that (18) Thies, C. J . Phys. Chem. 1966, 70, 3783. (19) Csempesz, F.; Rohrsetzer, S. Colloids Surf. 1984, 11, 173.
96 Langmuir, Vol. 4, No. 1, 1988 c1
V=const
msA
ms8
-
m, totollkg
Figure 3. Linear c1 = {(ma) functions in a two-sorbentsystem. Points 0 and P indicate hypothetical equilibrium concentrations if the sorption-demrptionequilibrium for sorbent A is frozen in. ms,Aand ms,B are the masses of sorbents A and B, respectively.
value of slope is varying with the initial concentration unless we are at a maximum or minimum or just in the saturation (horizontal) region of the isotherm. Then, if the sorption equilibrium is attained for sorbent A, we may add sorbent B to the mixture. In the first moment of experiment, the equilibrium concentration for sorbent A will be the initial concentration for sorbent B (point 0 in Figure 3) and, if the sorption-desorption process for sorbent A were frozen in, we would have point B on the c1 = f(ms,bd) curve, i.e. an equilibrium concentration for sorbent B. However, for sorbent A, a decrease in concentration, cl, means that we are moving to another point on its unknown isotherm and desorption of component 1 from it, induced by the second sorbent, also makes it impossible to calculate the exact positions of points 0 and P. Thus we must conclude that sorbed excesses, except cases as indicated above, cannot be determined independently of each other when finite amounts of different sorbents are present in a mixture. Nevertheless, a solution of this problem exists if an infinitesimally small amount of sorbent A and sorbent B is added to the system. In this case, namely, only a very small change in concentration c1 takes place and so the second sorbent will "meet" practically the same initial concentration as given for the first one. Accordingly, for multisorbent systems containing independent sorption or solvation sites m'yol,totalcan be given
where the weighting factors wA and wB are the mass fractions of sorbent A and B, in the mixed sorbent, m'f'l,q(c~l,e)and m'*ol,B(col,e) are the individual characterzstzc isotherms of sorbent components. In our recent works, eq 7 has been applied successfully to evaluate composite isotherms obtained for structurally inhomogeneous poly(viny1 alcohol) (PVA) networks and for gels prepared from poly(viny1 alcohol-vinyl acetate) copolymers with varying composition. In this way, for
Figure 4. mlUs0= ~ ( C O I , ~ c, D Z Jand mza,o= ~ ' ( C O ~ , ~coZJ , surfaces for system containing more than two components in the sorbate.
PVA gels we were able to estimate the individual characteristic isotherms of inhomogeneities fixed chemically in the geh20t21 It would be, however, very illusory if one tried to describe the isotherm of a real sorbent with a distribution of the strength of the sorption sites based on measurements provided only with averaged properties of the different kinds of surface elements. I t has to be also noted that consideration presented in this work can be used fairly well to characterize the sorption interaction at solidlgas, vapor interfaces because it is based only on the mass balance of such systems. Another important problem to be stressed finally is the graphical representation of isotherms referring to systemg which contain one sorbent and more than two components in the sorbate. It is clear the idea discussed previously basically must hold. Here the problem is that the sorbed excess of one of the components is not independent of the others (similar to a two-component system) therefore, in the case of mixtures with three components, the excess of component 1should depend on the equilibrium concentration of component 2 as well. To be correct, it is therefore necessary to determine the equilibrium concentration of both components, and to plot, say, mlUl0as a function of and c ~in ~an ,xyz~ rectangular coordinate , ~ , has two system. Because the function r n l " p O = ~ ( C O ~ co2,,) variables, the points of the experimental iostherms form in general a surface (see Figure 4). Of course, the same holds for the mzglo= f(col,e,co2,J function. The intersection of the two surfaces results in a line in the xyz space along which mlut0 = r n z U p 0 . Obviously, for systems containing more than three components in the mixture, it is impossible to plot the whole set of isotherms, only some of their several projections.
Acknowledgment. My thanks are due to Professor E. Wolfram for reading the manuscript and to Professor P. Benedek and Dr. I. PLzli for the valuable and helpful discussion on the subject. I am also grateful to Veronika KovPcs for her invaluable help in the preparation of the manuscript. (20) Nagy, M.Magy. K6m.Foly. 1981,10, 462. (21) Nagy, M.;Gyargyi-Edelhyi, J. Z+oc.-Conf. Colloid Chern.,4th 1983, 142.
