J. Chem. Soc., Faraday Trans. I, 1985, 81, 553-563 Effects of Surface Heterogeneity on Liquid Adsorption Chromatography with Mixed Mobile Phases Analytical Approximations for Partition Coefficients BY WLADYSLAW RUDZINSKI* AND JOLANTA NARKIEWICZ-MICHALEK Department of Theoretical Chemistry, Institute of Chemistry, U.M.C.S., Nowotki 12, Lublin 20-03 1, Poland AND ZDZISLAW SUPRYNOWICZ AND KAROL PILORZ Department of Chemical Physics and Chromatography, Institute of Chemistry, U.M.C.S., Nowotki 12, Lublin 20-03 1, Poland Received 19th September, 1983 The effects of the energetic heterogeneity of solid/solution interfaces on the behaviour of liquid-solid chromatography systems have been investigated theoretically and the existing theories have been re-examined. This has led to a more rigorous explanation of the theoretical background of some equations which were developed in a semi-intuitive manner.In other cases, e.g. Soczewinski’s logarithmic relationship, a totally new theoretical interpretation has been obtained explaining why the tangent of this linear relationship is < 1 in many cases. The theory of partition coefficients in liquid-solid chromatography (1.s.c.) is only a special case of the theory of adsorption from multicomponent liquid mixtures onto solid surfaces. This is when one component (solute) is at a very low concentration, whereas the others (solvents) are at moderate concentrations. Changing the concen- tration of the solvents in the mobile phase enables a good resolution to be obtained between the various solutes.So it is no surprise that various attempts have been made to provide an equation for the partition coefficient of the solute between the surface and the mobile bulk phase as a function of the composition of the mobile phase. Several authors have proposed equations’ which have played an important role in the development of 1.s.c. The most popular are those of Snyder and Soczewinski relating the partition coefficient k, of the solute to the mole fraction y , of the more active solvent 2 in the mobile phase. Snyder’s equation is2 (1) where k,, and K,, are constants and an, is the ratio of the surface areas occupied by the molecules of the solute and of the more active solvent 2. The constant K,, describes the preferential adsorption of the more active solvent 2 over the less active solvent 1 from their binary mixture onto the solid surface.When solvent 2 is strongly preferentially adsorbed, then, except for small concentrations of that solvent in the - mobile phase, K,, y , $ 1 and eqn (1) reduces to Soczewinski’s relati~nship:~~ In kn = In kn1- a,, In (Y, + K,, v2) Ink, = C, - C, lny (2) where C, = a,,. 553554 SURFACE HETEROGENEITY AND LIQUID ADSORPTION In spite of the long time which has passed since eqn (2) was published, it is probably the most used relationship for the correlation of retention data in 1.s.c. The only explanation for its origin comes from theories of ideal adsorption on homogeneous solid surfaces. This derivation would suggest that eqn (2) is a simplified version of eqn (1). However, the interpretation of experimental data using eqn (2) leaves some intriguing questions to be answered.The good linearity which is usually found in the plot of Ink, against lny, is found at small concentrations of the preferentially adsorbed solvent 2 and fails at higher concentrations y,, contrary to the hypothetical trend predicted by the above derivation of eqn (2). Furthermore, the solute molecules are usually much larger than the solvent molecules. Thus, it is to be expected that the tangent a,, in the experimental plot of In k, against lny, should be > 1. Meanwhile, 1.s.c. systems in which an, < 1 are found experimentally at least as often as systems in which a,, > 1. The third question is why the simplified version of eqn (l), i.e. eqn (2), provides a better correlation of experimental data than eqn (1) itself.These observations suggest that eqn (2) must have a different theoretical background from that which is commonly believed. From the viewpoint of the thermodynamics of adsorption the development of the theories of the partition coefficients in 1.s.c. may be characterized as follows. In the beginning, attention was focused mainly on the interactions between the solid surface and the molecules of the solvents and and on the effects of interactions in the mobile bulk phase.5 Later on, the differences between the surface areas occupied by different admolecules were taken into account. Recently, a third important factor governing the behaviour of 1.s.c. systems has become widely realized. This is the energetic heterogeneity of the actual solid/solution interface.Because of variations in the local chemical composition and the crystallographic structure of the actual solid/solution interface, some areas of these interfaces will exhibit different adsorption features. A recent paper by Rudzinski et aZ.6 has shown that the effects of the dispersion of these adsorption features are at least as important as the effects of interactions between the adsorbed molecules. However, these effects cannot be isolated because of their mutual interference. An adequate, realistic theoretical description of 1.s.c. systems must take into account all the basic physical factors simultaneously. These are: (i) interactions between the molecules on the surface and the mobile bulk phase, (ii) differences between the molecular sizes of various molecules and the different surface areas occupied by them and (iii) the energetic heterogeneity of the actual solid/solution interface.In some systems multilayer adsorption effects may also play an essential role, especially in the case of badly mixing solvents. However, we will postpone discussion of this to future publications. Our attention in this paper is focused on factors (ii) and (iii) above, and especially on the role of the surface heterogeneity and its theoretical description in 1.s.c. We will show that it is the energetic heterogeneity of the actual solid/solution interface which is the source of the linearity of the double logarithmic plot of Ink, against lny,. Our theoretical consideration results in a new derivation of Soczewinski’s relationship which explains all the inconsistencies in its behaviour discussed above.THEORY Let xi (i = 1,2, . . ., n) denote the volume (area) fraction of component i in the adsorbed phase and yi be its volume fraction in the equilibrium mobile bulk phase.w. RUDZI-~KI et al. 555 Let ysr and y,, denote the appropriate activity coefficients in the adsorbed and the mobile bulk phase, respectively. Then, the simultaneous competitive adsorption from an n-component liquid mixture onto a hypothetical homogeneous solid surface is described by8 =Kin, i = 1,2 ,..., n-1 (4) where a,, is the ratio of the surface areas occupied by a single admolecule of ith and nth kinds. To a good approximation the equilibrium constant Kin can be written in the following form:6 Kin = ~ X P [(~i -sin En)/RTl ( 5 ) where E, and en are the adsorption energies of the single molecules i and n.We now introduce the following notation : E,, = E~ -a,, E, (6) and call E,, the ‘adsorption energy’ in the binary system (i+n). The energetic heterogeneity of the actual solid/solution interface will cause some dispersion of E,, values on various adsorption sites (surface areas associated with a local minimum in the solid-adsorbate interaction potential). The usual quantitive measure of the energetic heterogeneity of the actual interface is the so-called differential distribution of adsorption sites among various values of adsorption energy. In our case, it will be an (n - 1 )-dimensional differential distribution of adsorption sites among various sets x({E,,}) normalized to unity: r where C2 is the (n- 1)-dimensional physical domain of the variables tin.Let Xi((Ein}) denote the solution of eqn (4) for component i. In the case of a heterogeneous surface, has to be replaced by its average value xit: The fact that the different adsorption sites are characterized by different sets {E,,) is due to the many physical factors acting during the preparation of an adsorbent. It seems reasonable to assume that x({cin}) should be a Gaussian-like multi-dimensional function, since even when the single adsorption energies E, and E, have a complicated distribution (double maxima for silica gels) their difference usually has a Gaussian-like distribution.6 A more exact a priori assumption about an analytical approximation of this function seems to be difficult at our present state of knowledge.This is because both experimental and theoretical studies of adsorption from multicomponent liquid mixtures onto solid surfaces are still in their infancy. Studies of adsorption from binary mixtures are more advanced. The theoretical studies initiated by Rudzinski and coworkerss99-14 seem to confirm this a priori assumption about the Gaussian-like form of the distribution function : r where the integration is over all variables E ~ , , except the variable For the reasons556 SURFACE HETEROGENEITY AND LIQUID ADSORPTION mentioned above, and for others to be discussed below, we focus our attention on the following energy distribution : defined in the interval (- a, + a).The function xi, from eqn (10) is a Gaussian-like function of g i n , centred about E:,, whose spread is described by the heterogeneity parameter tin. When cin -+ 0, eqn (10) degenerates into a Dirac delta distribution Apart from the fact that an apriori assumption about the form ofX({Ein)) is difficult, the solution of eqn (4) and the subsequent evaluation of the (n- 1)-dimensional eqn (8) represents an extremely complicated problem. To make the problem tractable some simplifying assumptions must be made. The basic approximation accepted here lies in assuming the ratio ( x i / x , ) to be influenced only by the dispersion of the variable So, let us accept this assumption and replace the ratios ( x i / x , ) in eqn (4) by their averaged values ( x i t / x n t ) : B(&in - &&).where f+oo xit = J x ~ ( E ~ , ) x ~ , ( E ~ , ) dEin, i = 1,2, . . ., n - 1 -oo n-i i - 1 x,t = 1 - Xit. The averaging shown in eqn (1 I), together with the accompanying assumption eqn (1 2), reduces our problem to considering adsorption from binary mixtures onto heterogeneous solid surfaces. Therefore it seems necessary to involve some basic results concerning this problem. Let us first consider adsorption from the binary liquid mixture (i+n) onto a hypothetical homogeneous solid surface, characterized by an adsorption energy Let us also assume, for simplicity, that molecules i and n occupy equal surface areas, i.e. ai, = I, and that the adsorbed phase is ideal, i.e. yzi = 1 for i = 1, 2, ..., n. Then, the adsorption isotherm xi can be written as follows: xi = [ 1 +exp (Gn;;in)]-' - where ~f, is a bulk concentration function, which for the adsorption model defined above takes the following explicit form : ct, = -RT ln(ai/a,) (14) where ai and a, are the bulk activities of components i and n, equal to yi yyi and y , yyn.We will evaluate further the integral xit using the following integration by parts: +co xit = xi X i , I? g - (%) Xi, dEin --co aein whereW. RUDZINSKI et a[. 557 In the case of the infinite integration limits (- 00, + GO), the first term on the right-hand side of eqn (1 5) disappears, whereas the function (ax,/a&,,) takes the following explicit form : This is a Gaussian-like function of centred about &fn. We will evaluate the second integral on the right-hand side of eqn (15) by expanding Xi, into its Taylor series around the point = &fn, at which point the ‘sampling’ function (axi/aein) reaches its maximum.Doing so, we obtain where B, is Bernouli’s number. In the hypothetical temperature limit T + 0, when the ‘sampling’ function degenerates into a Dirac delta distribution - &), eqn (18) reduces to cn(ai/an)RTicin 1 + cn(ai/an)RTlcin ’ x . z t =-x. an (&C an ) = i = 1’2, ..., n-I where cn = exp (&/cin). (20) Note that the condition T + 0 is not the only one for eqn (19) to be valid, and it is also valid when the spread of the energy distribution x ~ ~ ( E ~ ~ ) is very large. Then, this function and its higher derivatives are small for any value of In effect, the terms under the sum in eqn (1 8) practically disappear and we have eqn (19).In other words, eqn (19) is also valid at higher temperatures for strongly heterogeneous surfaces. Let us write eqn (19) in the following compact form: RTIc,, , i = 1,2 ,..., n-1. Xnt Assuming in addition that and solving eqn (21) with respect to xit we obtain , i = 1,2 ,..., n-1. Gn<ai Ian) n-1 Xit = 1 + Z qn(aj/an)m j - 1 This equation was proposed by Jaroniec and Patrykiejew15 two years ago, following the numerical results for mixed-gas adsorption on solid surfaces obtained by Cricmore and Wojciechowski.lG Later on, Jaroniec attempted to generalize eqn (23)’ taking into account the important effect of different surface areas occupied by different molecules. He then suggested the following generalization : l7558 SURFACE HETEROGENEITY AND LIQUID ADSORPTION Let us, however, see whether the approach used by us makes a rigorous treatment of this problem possible.In the hypothetical case T - , 0, but also in the physically possible case of strongly heterogeneous surfaces, the sampling function (ax,/ae,,) behaves like a Dirac delta distribution with respect to while performing the integration on the right-hand side of eqn (15). Thus, looking for the maximum effectiveness of our approach, we should expand the function X i , into its Taylor series around the point e:,, at which the sampling function (ax,/aei,), (ain # l), reaches its maximum. This point is found from the condition (-)& = *- This means that in the general case a,, # 1 the function ern has to be replaced by &in which, according to eqn (25), takes the following explicit form: This leads us to the following generalization of eqn (19): where Eqn (27) can be rewritten in the following compact form: which is different from eqn (24).With the additional assumptions accepted when developing eqn (1 1) and (12) we arrive at the following generalization of eqn (23): RTIcjn (30) X i t = , i = 1,2, . . ., n - 1 I - 1 which should describe adsorption from a multicomponent liquid mixture onto a heterogeneous solid surface, characterized by the symmetrical dispersion of adsorption energies ein. In our case it can be used to calculate the adsorption equilibria of the competitive adsorption of solvents onto the solid stationary phase. Since in the usual chromato- graphic situation the solute (analysed substance) appears at extremely small concen- trations, its presence in the mobile phase will not affect the competitive adsorption of the solvents.Neglecting the local correlations in the adsorbed phase, one may consider the chromatographic process as the adsorption of solute molecules onto the solid surface in the molecular environment of solvent molecules, unaffected by the presence of the solute molecules. However, the competitive adsorption of solute will be governed by different rules,W. RUDZINSKI et al. 559 arising from the condition that the solute appears at very small concentrations. Let n denote the solute, whereas the indices 1,2, ,. , ., n - 1 are related to solvents. The experimentally measured partition coefficient k , is defined as follows : k , = lim (z).(31) Y n + O Since the solute n is assumed to appear at infinite dilution, its competitive adsorption with respect to any component i will be like that on a homogeneous surface, characterized by the energy E , ~ equal to &?ln. Thus, for the model of an ideal adsorbed phase considered in this work, the partition coefficient k , should be written where (33) At the same time, however, competitive adsorption of the solvents will still be described by eqn (30). This is because they usually appear at moderate concentrations. It appears that the problem lies in accepting the non-physical integration limits ( - co, + co). Their choice is reminiscent of some mathematical simplifications accepted in the theories of the adsorption of gas on heterogeneous solid surfaces.For the purpose of mathematical convenience it is often assumed there that the adsorption energy of the single molecule i, E ~ , may vary from zero to infinity. A logical consequence of this is to assume that the difference ei, may vary from minus to plus infinity. Meanwhile, for some obvious physical reasons, there must exist a minimum and a maximum energy, cFn and &fax, on an actual solid surface. Consequently, the difference We have shown in our previous publicationla* l9 that choosing the non-physical integration limits (- 00, + co) does not affect the result of integration in eqn (1 5), until the concentration of component i falls below some critical value. Below this critical value the competitive adsorption of i will be like that on a homogeneous surface characterized by the minimum value of ein found on the heterogeneous solid surface.Note that eqn (32) is different from that proposed recently by Jaroniec and will possess certain limits, &en and (Xit)1lrn ani OScik-Mendyk :20 kn = KO,~ (7) (34) where xit was assumed to be given by eqn (24). Now let us consider the explicit form of eqn (32) in which xit is evaluated by eqn (27). We also neglect the non-ideality effects in the mobile bulk phase. (Soczewinski’s linear relationship is also found in 1.s.c. systems in which the bulk solvent mixture is strongly non-ideal.) Then, from eqn (27) we have We now consider the region of small concentrations of the more active solvent, where Soczewinski’s linear relationship is usually found.Suppose that y2 + 0, y1 --+ 1. Then, from eqn (35) it follows that560 SURFACE HETEROGENEITY AND LIQUID ADSORPTION Eqn (36) combined with eqn (32) brings us to a new theoretical interpretation of Soczewinski’s relationship (see Appendix) : - Ink, = In [ e 3 & ) a n 2 ] - (37) Since for a typical heterogeneous solid/solution interface RT/c,, < 1, Ink, should decrease linearly with the logarithm of the more active (preferentially adsorbed) solvent 2. The term (1 - RT/c,,) is positive but still < 1. Furthermore, for typical solid/solution systems 0.7 < RT/c,, < 0.9, so the value of this term lies in the range 0.1-0.3. Thus, it can happen that the product (tangent) (1 - RT/c,,) a,, may be < 1 even when a,, itself is > 1. Thus, our derivation of Soczewinski’s relationship, based on the concept of energetic heterogeneity of the actual solid/solution interface, answers the three questions raised by the experimental observations of retention in 1.s.c.It also shows that energetic heterogeneity is probably the main factor governing the retention mechanism in 1.s.c. at small concentrations of the more active (preferen tially adsorbed) solvent. RESULTS AND DISCUSSION We consider eqn (37) to be the most important result obtained in this work as it provides a new theoretical background for Soczewinski’s linear relationship, eqn (2), applied so successfully by various authors. Note that eqn (37) was obtained with the simplifying assumption that both the bulk and the adsorbed phases are ideal.At the same time, however, the other two important physical factors are taken into account: i.e. the energetic heterogeneity of the actual solid/solution interfaces and the different cross-sectional areas of the different adsorbed molecules. The experimental data which have already been reported in the literature seem to provide an impressive check for the correctness of eqn (37). Let us consider for instance the work by Petrovic et al.,,‘ who chromatographed 15 mono-, di-, tri- and tetra-substituted steroid derivatives on silica-gel thin layers using benzene as the diluent (less preferentially adsorbed solvent), mixed with the following active solvents (solvent 2 in our theoretical consideration) : chloroform, diethylether, ethyl acetate, methyl acetate, methyl ethyl ketone, acetone, dioxane and propan-1-01.In all cases the dependence of the partition coefficient k , on the concentration of the more active solvent could be correlated using eqn (2). The slopes C, obtained from this linear regression have been tabulated by Petrovic et al. and their analysis is very interesting. In many cases C, < 1, although the molecules of steroid derivatives are expected to have larger cross-sectional areas on the silica surface than the above listed solvents. Moreover, for a given solute, the slopes C, for all the active solvents except propan-1 -01 are close to each other. This would suggest that the slopes C, are not very sensitive to the cross-sectional areas of the active solvents. In the case of propan-1 -01 the slopes C, are smaller by ca.20% than those of the others. It is known that propan-1-01 is more preferentially adsorbed from benzene than from the other solvents. In other words, not only geometric effects but also the chemical nature of the competitive adsorption of solvents are responsible for the value of the slope C,. This conclusion cannot be explained on the grounds of the previous interpretation of C, being equal to an2. However, the most impressive support for the validity of eqn (37) can be found in the works of Soczewinski and coworkers. Fig. 1 shows the experimental results ofw. RUDZINSKI et al. 56 1 log Y 2 Fig. 1. Experimental data of Wawrzynowicz22 for chromatography of various solutes (A, V and a) in a propan- 1-01 + n-heptane mixture on two adsorbents : (---) aluminium oxide and (---) silica gel.Wawrzynowicz,22 who chromatographed several solutes in a propan-1 -01 + n-heptane mixture on two adsorbents: silica gel and an aluminium oxide. The results in fig. 1 are presented using the experimental data RF and R,, which are obtained directly by means of thin-layer chromatography : 23 R , = In k’ = Ink, +constant (38 a) where k’ is the capacity factor. According to the previous interpretation of C, = an2, the slope C, for a given solute should be approximately the same for both adsorbents. Meanwhile, the observed slopes for silica gel are approximately twice those for aluminium oxide. This can easily be explained by eqn (37). Namely, it is known that silica surfaces are much more heterogeneous than alumina surfaces.This means that the term (RTIc,,) should, for a given binary solvent mixture, be smaller in the case of silica surfaces. Thus the term (1 - RT/c2,) should be larger and consequently the product C2[ = (1 - RT/c,,) anz] should also be larger, even if an2 is the same for both adsorbents. The trend which is observed in fig. 1 has been confirmed by Soczewinski and J ~ s i a k , ~ ~ Wawrzynowicz and D ~ i d o , ~ and Soczewinski et aLZ5 Table 1 reports some of the experimental values of C,, making a comparison between the two adsorbents possible. This selection is not yet complete, since many experimental data were reported in graphical form only. We may thus summarize our results as follows. The energetic heterogeneity of the actual solid/solution interface is one of the main, if not the main, factors governing562 SURFACE HETEROGENEITY AND LIQUID ADSORPTION Table 1.Comparison of the experimental slopes C, for silica and alumina for two binary solvent mixtures : cyclohexane + di-isopropyl ether and cyclohexane + ethyl acetate. Data selected from ref. (24) and (25). di-isopropyl ether ethyl acetate alumina silica solute alumina silica nitro benzene 2-nitro toluene 4-ni tro toluene 2-nitro-l,3-xylene 1 -nitronaphtalene 1 ,Zdinitrobenzene 1,5-dini tronap h thalene 1,3,5-trinitro benzene 0.43 0.40 0.41 0.39 0.47 0.80 0.84 1.08 1 .o 1 .o 0.7 0.8 1 .o 1 .o 1.7 1.5 0.48 0.39 0.52 0.40 0.57 1.22 0.98 1.33 1 .o 1 .o 1.2 1.1 1.2 1.4 1.9 2.0 the behaviour of the partition coefficient in solid-liquid chromatography. This fact has not been sufficiently realized in previous theoretical studies of 1.s.c.and therefore needs further extensive investigation. LIST OF SYMBOLS heterogeneity parameter in eqn (lo) constants in Soczewinski's relationship, eqn (2) capacity factor partition coefficient of solute n defined in eqn (31) partition coefficient kn in the pure solvent i equilibrium constant defined in eqn ( 5 ) generalized form of Kn, defined in eqn (28) equilibrium constant defined in eqn (20) equilibrium constant defined in eqn (33) heterogeneity parameter defined in eqn (22) and (23) gas constant temperature mole fraction of component i in the adsorbed phase average mole fraction of i in the adsorbed phase on a heterogeneous solid surface mole fraction of the component i in the bulk phase ratio of the surface areas occupied by single molecules of i and n, respectively activity coefficients of component i in the surface (x) and the bulk (y) phases adsorption energy of a single molecule of i difference between E~ and E,, defined in eqn (6) function of bulk phase composition, defined in eqn (14) generalized form of E& defined in eqn (26) most probable value of minimum and maximum values of multi-dimensional differential distribution of adsorption sites among various values of cin on a heterogeneous surfaceW. RUDZINSKI et al.563 x ~ ~ ( E ~ ~ ) Xin(cin) indefinite integral of x ~ ~ ( E ~ ~ ) a differential distribution of adsorption sites among various values of physical domain of the variables tin. APPENDIX Below we outline the derivation of Snyder’s and Soczewinski’s equations, based on the Let us neglect for the moment the non-ideality of both the bulk and the surface phase. concept of a homogeneous solid surface.26$ 27 Then, from eqn (4) it follows that Ink, = In Kn2+ an2 In (A 1) Let us assume in addition that solvent molecules occupy the same surface areas, i.e.that a,, = 1. Then (A 2) x2 Y 2 - = K,lbl+ K,, Y 2 ) - I - Combining eqn (A 1) and (A 2) one arrives at Snyder’s equation: In kn = In k,, - an2 In 01, + K,, y2) kn1 = Kn2(&Jan2- (A 4) When solvent 2 is strongly preferentially adsorbed, then, except for small concentrations of this solvent in the mobile phase, K2,y2 9 y , , and from eqn (A 1) and (A 2) we obtain In k, = In Kn2 - an2 In y 2 (A 5 ) the form of which is the same as eqn (2).M. Jaroniec and J. Okik, Journal of HRC & CC, 1982, 5, 3. L. R. Snyder, in Principles of Adsorption Chromatography (Marcel Dekker, New York, 1968). E. Soczewinski, Anal. Chem., 1969,41, 179. E. Soczewinski, J. Chromatogr., 1977, 130, 23. R. P. Scott and P. Kucera, J. Chromatogr., 1975, 112, 425. W. Rudzinski and S. Partyka, J. Chem. SOC., Faraday Trans. I , 1981,77,2577. W. Rudzinski, J. Narkiewicz-Michalek and S. Partyka, J. Chem. SOC., Faraday Trans. 1,1982,78,2361. D. H. Everett, Trans. Faraday SOC., 1965, 61, 2478. W. Rudzinski, J. Oicik and A. Dabrowski, Chem. Phys. Lett., 1973, 20, 5. lo J. Oicik, A. Dabrowski, M. Jaroniec and W. Rudzinski, J. Colloid Interface Sci., 1976, 56, 403. l1 J. OScik, A. Dabrowski and. W. Rudzinski, J. Colloid Polym. Sci., 1977, 255, 50. l 2 W. Rudzinski, A. Waksmundzki, M. Jaroniec and S. Sokolowski, Ann. SOC. Chim. Pol., 1974, 48, l 3 A. Dabrowski, J. Oicik, W. Rudzinski and M. Jaroniec, J. Colloid Interface Sci., 1978, 79, 287. l 4 A. Darowski and M. Jaroniec, J. Colloid Interface Sci., 1979,73, 475; 1980, 77, 571. M. Jaroniec and A. Patrykiejew, J. Chem. Soc., Faraday Trans. I , 1980, 76, 2486. l6 P. J. Cricmore and B. W. Wojciechowski, J. Chem. SOC., Faraday Trans. 1, 1977,73, 1216. l7 M. Jaroniec, Thin Solid Films, 1981, L97-99, 81. l8 W. Rudzinski, J. Narkiewicz-Michalek, R. Schollner, H. Herden and W. D. Einicke, Acta Chim. lo W. Rudzinski, L. Eajtar, J. Zajac, E. Wolfram and I. Paszli, J. Colloid Interface Sci., 1983, 96, 339. 2o M. Jaroniec and B. Oicik-Mendyk, J. Chem. SOC., Faraday Trans. I , 1981, 77, 1277. 21 S. M. Petrovic, L. A. Kolarov and E. S. Traljic, Anal. Chem., 1982, 54, 934 22 T. Wawrzynowicz, D.Sc. Thesis (Medical Academy, Lublin, 1980). 23 E. Soczewinski and J. Jusiak, Chromatographia, 1981, 14, 23. 24 T. Wawrzynowicz and T. Dido, Talanta, 1977, 24, 669. 25 E. Soczewinski, W. Golkiewicz and W. Markowski, Chromatographia, 1975, 8, 13. 26 D. E. Martire and R. E. Boehm, J. Liquid Chromatogr., 1980, 3, 753. 27 R. E. Boehm and D. E. Martire, J. Phys. Chem., 1980,84, 3620. 1991. Acad. Sci. Hung., 1983, 113, 207. (PAPER 3/ 1646)