1180
Langmuir 1989, 5 , 1180-1186
available; so the linear fit in Figure 3 may be considered as only a first approximation. (In a narrow region, any sufficiently smooth relationship can be approximated by a linear function.) The response of the asolectin membranes was investigated over a concentration interval involving many orders of magnitude (that can be represented more appropriately with a log concentration scale), which provided better resolution and also a better fit to a different function. It should be noted that the observed change in slope below lo4 M in Figure 6 is probably due to an adsorption effect (most of the very small valinomycin amount present in that range is rather adsorbed to the walls of the cell, instead of influencing the impedance properties of the membrane). Conclusions Up to a point, the fluctuation measurement is a useful altemative to the conventionalac bridge measurement. Its most attractive feature is the fact that the experiment is
done without externally applied voltage, under the conditions of a true thermodynamic equilibrium. However, for the same reason the signal is of low power, requiring high-gain amplification and spectrum averaging. These problems render the information acquisition time unacceptably long for practical applications such as chemical sensing. This situation could be improved, in principle, by employing the cross-correlation technique; however, that would require the measurement to be done on a pair of matched membranes. At present, such an approach is not practical. For studies of impedance and chemical modulation of bilayers, however, the approach of fluctuation analysis can be a useful one, as it is shown by the experimental results presented in this work. Acknowledgment. We gratefully acknowledge the support of this work obtained from the Office of Naval Research. Registry No. Valinomycin, 2001-95-8; concanavalin A, 11028-71-0; D-mannon, 9036-88-8;phloretin, 60-82-2;cholesterol, 57-88-5.
A Chromatographic Method for the Determination of Segmental Adsorption Energies of Polymers. Polystyrene on Silica G. P. van der Beek,* M. A. Cohen Stuart, G. J. Fleer, and J. E. Hofman Laboratory for Physical and Colloid Chemistry, Agricultural University, Dreyenplein 6, 6703 HB Wageningen, The Netherlands Received January 19, 1989. In Final Form: April 28, 1989 Polystyrene adsorption on a silica surface was studied by means of adsorption TLC. This is a very sensitive technique for detecting polymer adsorption/desorption transitions in binary solvent mixtures. Such transitions, which occur at a well-defined solvent composition (the so-called critical point), were earlier shown to be related to the segmental adsorption energy. In this paper we derive a relation between the concept of chromatographicsolvent strength, as defined by Snyder, and segmental adsorption energies. It turns out that solvent strength data, which are available in the chromatographic literature, can now also serve as a useful source of information for polymer adsorption and adhesion studies. Finally, we give some experimental results for the displacement of polystyrene from silica in two different solvents (carbon tetrachloride and cyclohexane)by various weakly adsorbing low molecular weight displacers. Using tabulated solvent strengths, we determined segmental adsorption energies for polystyrene on silica of l.OkT and 1.9kT, from carbon tetrachloride and cyclohexane, respectively. Introduction Thin-layer chromatography, TLC, is frequently used to analyze polymer samples.'-8 This technique has many advantages: simple instrumentation, high sensitivity, rapidity, and ease of detection of separated bands. TLC can be based on either adsorption (ATLC), size exclusion as in GPC (TLGPC), or dissolution-precipitation (extraction and precipitation TLC). These techniques permit the investigation of all kinds of polydispersity: polydispersity according to molecular weight,14 stereoregularity:* microstructure,'-* and chemical composition in copolymer~.'~~~' It is even possible to separate isotopically different polymers by these techniques.8 We are interested in TLC as a technique to study the adsorption of polymers. Hence, we will exclusively consider ATLC. Polymer adsorption has many technological
* Author to whom correspondence should be addressed.
applications. The mechanical strength of polymer composites depends on the strength of adhesion between the matrix polymer and the reinforcing filler. Polymer adsorption can stabilize dispersions, which is important in products like paints, foods, pharmaceuticals, etc. It can also destabilize colloidal systems, which is useful in water purification and improvement of soil structure. The aim of this paper is to establish a relation between ATLC with polymers and polymer adsorption studies as done by Co(1) Gloeckner, G. Polymer Characterization by Liquid Chromatograp h y ; Elsevier: Amsterdam, 1987. (2) (a) Belenkii, B. G.; Gankina, E. S. J. Chromatogr. 1977, 141, 13. (b) Belenkii, B. G. Chromatography of Polymers; English Ed.; Elsevier: Amsterdam, 1983. (3) Otocka, E. P. Macromolecules 1970, 3, 691. (4) Inagaki, H.Adu. Polym. Sci. 1977, 24, 189. (5) Buter, R.Ph.D. Thesis, University Groningen, 1973, p 133. (6)Miyamoto, T.; Inagaki, H. Macromolecules 1969,2, 554. (7) Gloeckner, G.; Kahle, D. Plaste Kautsch. 1976,23, 338. Donkai, N.; Inagaki, H. Macromolecules 1980,13,1021. (8) Tanaka, T.;
0743-7463/ 8912405-1180$01.50/0 0 1989 American Chemical Society
Langmuir, Vol. 5, No. 5, 1989 1181
TLC Detection of Polymer AdsorptionlDesorption hen Stuart et al.1° More specifically, we will show how adsorption (thin-layer) chromatography experiments can be used in the determination of the segmental adsorption energy of polymers on a substrate. Some years ago, Cohen Stuart et al.9J0 proposed a method to estimate segmental adsorption energies, based on polymer adsorption/desorption transitions in binary solvents. Desorption of polymer from an adsorbent can be achieved by increasing the concentration of the more strongly adsorbing solvent component (which was termed “displacer”). At a certain critical composition, the polymer is fully desorbed by the displacer. The central result of the analysis of Cohen Stuart et al. is an equation which relates the critical displacer concentration to the difference in adsorption energy between a polymer segment and a solvent molecule. So far, this method is the only one that yields information on the adsorption energy of polymer segments on a surface. A somewhat parallel development can be found in the chromatographic literature, where the solvent strength concept was introduced by Snyder11J2in order to characterize the interaction strength between solute and stationary phase in chromatographicseparations. Snyder has given an equation from which one can calculate the solvent strength of an arbitrary binary solvent mixture from tabulated solvent strengths of pure solvents. By measuring polymer retention in ATLC, the critical composition or, in Snyder’s terminology, the critical solvent strength can be found. In this paper, we present a quantitative relation between the critical solvent strength and the segmental adsorption energy. The advantage of this relation is that chromatographic data available in the literature can serve as a useful source of information in the determination of segmental adsorption energies. We note in passing that some ideas relative to polymers at interfaces had already been introduced into the chromatographic approach.2 Finally, the relation between Snyder’s solvent strength concept and the treatment of Cohen Stuart et al. is checked by experiments on the polystyrene/silica system, both with ATLC and with batch adsorption studies.
Theory Cohen Stuart et al.9J0used the following simple model in their analysis of the polymer adsorption/desorption transition. The solution is described by means of a lattice adjacent to the solid surface. Each lattice site can accommodate either a solvent molecule (o), a displacer molecule (d), or a polymer segment (p). The coordination number of the lattice is z. Each site has A,,z neighbors in the same layer and Xlz in each of the two adjacent layers. The sites in the surface layer have Xlz contacts with the surface and (A, + Ao)z with the solution. The adsorption energy parameter xsPO was defined by Silberberg13as xSP0 = -(UP - u o ) / k T (1) where up and uoare the interaction (free) energies of the solid surface with a polymer segment and a solvent molecule, respectively, with respect to a suitable reference state (e.g., bare solid surface + isolated monomer unit). Note that by this definition xSP is counted positive if the polymer adsorbs preferentially from the solvent. The (9) Cohen Stuart, M. A.; Fleer, G.J.; Scheutjens,J. M. H. M. J . Colloid Interface Sci. 1984, 97, 515. (IO) Cohen Stuart, M. A.; Fleer, G. J.; Scheutjens, J. M. H. M. J. Colloid Interface Sci. 1984, 97, 526. (11) Snyder, L. R. Principles of Adsorption Chromatography; Marcel
Dekker: New York, 1968. (12) Snyder, L. R.; Glajch, J. L. J. Chromatogr. 1981, 214, 1 . (13) Silberberg, A. J . Chem. Phys. 1968,48, 2835.
parameters (displacer from solvent) and ~d (polymer from displacer) are defined in an analogous way. These xsparameters are related in a cyclic way because of their exchange character: XSP = xsd+ Xsdo
(2)
This relation follows immediately from the definition in eq 1. In a polymer solution in contact with gn adsorbent, not only contact energies with the surface (adsorption energy) but also nearest-neighbor interactions in the solution (solvent quality) play a role. These can be taken into account by using Flory-Huggins x parameters. In our particular case, the relevant parameters are X P (polymer-solvent), xd (polymer-displacer), and xdo(displacer-solvent). We note that adsorption energies may also be expressed with a type of Flory-Huggins parameters, if the adsorbent is considered as a separate component s.14 However, in this paper we still use xs according to Silberberg’s definition because it simplifies the equations. The model of Cohen Stuart et al. leads to relatively simple expressions for the free energy associated with changes in the surface layer composition, provided the simplifying assumption is made that in the neighborhood of the critical point only the segment concentration in the surface layer is different from the bulk solution value (one-layer approximation). The final result of this treatment is a relation between the adsorption energy and the critical displacer volume fraction @cr in dilute polymer solutions. It can be written as exp(xsW - xsc- A h P / k T ) - 1 4cr =
exp(Xsdo - Ahdo/kT) - 1
(3)
Here, AhP and Ahdoare the nearest-neighbor interaction enthalpies corresponding to a polymer/solvent and a displacer/solvent contact. Expressions for these enthalpies in terms of solution concentrations and the various x parameters are given in ref 9. The parameter xsc is the (dimensionless) critical adsorption energy: the minimum value of xsfor which long chains adsorb from the solvent. It has an entropic origin because a bond connected to an adsorbed segment has less orientational freedom than a bond in a polymer molecule in the bulk soIution. A simplified version of eq 3 is obtained by neglecting the terms -1 and substituting Ahm and Ahdo:g xSP
= ~ s d o+ In 4cr + xsc - X I X -~ (1 - @cr)(1 - Al)(xP - xpd - Xdo) (4)
If we ignore all interactions other than those with the substrate (i.e., all x parameters are zero), the result becomes very simple: XSP
- xsc = Xsdo + In 4cr
(5)
The picture presented by Snyder” closely resembles the one sketched above, so that a similar result may be anticipated. In chromatography, it is customary to characterize a solvent by means of its solvent strength E , which is a measure of its (free) energy of interaction with an adsorbent. Values o f t are tabulated by Snyder with respect to the solvent pentane; i.e., the reference state is a surface fully covered by pentane. In order to characterize solvent mixtures of a given composition in the same way, Snyder derives an expression for the solvent strength of binary solvent mixtures, E,. The solvent strength is de(14) Evers, 0. A. Ph.D. Thesis, Agricultural University, Wageningen (in preparation).
1182 Langmuir, Vol. 5, No. 5, 1989
van der Beek et al.
fined in such a way that -2.303aAt (ref 27) is the adsorption energy of a solvent molecule, which occupies a surface area A on the adsorbent. The coefficient a,called activity, is a property of the substrate. It is determined by the type and density of active sites on the adsorbent surface. Apparently, the adsorption energy per unit area can be split into a factor representing the adsorbate (4 and one which stands for the adsorbent (a).Snyder claims that this is reasonable, provided that a single type of interaction is largely responsible for the adsorption. The forces responsible for the adsorption of a polymer on a silica surface (as in our experiments) are almost exclusively of the acid-base type.15 Acid-base interactions have been described quantitatively by Drago et a1.16 These authors analyze the energies of such interactions in terms of a covalent and an electrostatic contribution and show that each of them can be split into two factors, one for each molecule participating in the bond. Snyderll demonstrates that the adsorption energies of functional groups on polar substrates such as silica correlate fairly well with only the electrostatic contribution (the s o - d e d ”hard” interaction). This justifies the separation of the adsorption energy into a contribution of the substrate and one of the adsorbate. We should note here that A is originally expressed in units of 8.5 A2,which corresponds to A = 6 for benzene. Since we prefer the more usual SI units, we write A in Units of nm2. If we define an activity a’as 27.la, we can write the dimensionless molecular energy between a solvent molecule and the adsorbent as -a’At. The numerical fador is 2.303/0.085 = 27.1 nmW2. For the derivation of e, Snyder assumed that the components of the solvent mixture have no interactions with each other (which is equivalent to neglecting the x parameters) and that they occupy the same surface area. The solvent strength c, is expressed in the solvent strengths of the pure components by considering the average probability to create one vacant site on a surface covered with a mixed adsorbate (with fractions od and 8, = 1- od for the components d and 0,respectively). This average probability is simply written as a linear combination of Boltzmann factors. The effective solvent strength t, is now defined by expressing this average probability in one Boltzmann factor with an average potential -a’At, in the surface layer: exp(-a’At,) = (1- 0,) exp(-a’At,) 6, eXp(-a’Atd) (6) The final assumption of Snyder is Langmuirian adsorption of component d from the solvent 0: (7) Here, 4d is the mole fraction of component d in the bulk solution. Combination of eq 6 and 7 leads to the main result of Snyder’s treatment: (& exP[a’A(td - to)] + 1 - dJd) tm = to + (8) CY’A This equation can be rewritten in a form which resembles closely eq 3: exp[a’A(t, - to)] - 1 (9) ” = eXp[dA(td - to)] - 1 This similarity suggests strongly that a simple relation between the xs parameters used by Cohen Stuart et al?Jo (15)Fowkes. F. M.J . Adhesion Sci. Technol. 1987. 1 . 7. (16)Drago, R. S.;Vogel, G . C.; Needham, T.E.J.’Am. Chen. SOC. 1971,93,6014.
and the solvent strengths defined by Snyder should exist, particularly if solute interactions are absent. Let us consider a polymer segment trying to adsorb from a mixture of solvent and displacer onto a substrate. A t the critical point & = &,, the net free energy change just vanishes. In other words, the surface contact energy per polymer segment up plus the entropic contribution x,kT is then equal to the average contact energy of the critical solvent mixture. If we denote the solvent strength of the critical solvent mixture by cw, the segment surface contact energy can be written as up/kT = -a’AeCr - xSc (10) For the monomeric components o and d, for which the bond entropy term is absent, the surface contact (free) energy (with respect to pentane) can directly be written in terms of their solvent strengths: uO/kT = -a’At0
(11)
ud/kT = -cY’Atd
(114
Using the definition of the xs parameters as given in eq 1, we can express them in the solvent strengths eo, td, and tcr:
+ xsc - Ed) + Xsc
x s p O = a’A(tcr -
Xspd = a’A(ccr X?
=
€0)
(r’A(td - to)
(12)
(13) (14)
Equations 12-14 constitute our central result. They show that effective adsorption energies of polymer segments can be related to tabulated solvent strengths of pure solvents (to,td) and the solvent strength (ecr) of the critical mixture of displacer and solvent. The latter quantity is obtained from the measured value of & through eq 8, after substitution of &r for &. In order to check the result for consistency, we substitute tcr, as given in eq 8, into eq 12
which is indeed the athermal version of eq 3. In other words, both theories lead to the same expression, at least in the absence of solvent/solute interactions. If the latter interactions do play a role, a variant of eq 4 can be used, combining eq 4 with eq 5 and 12: xspO= a’A(ccr -
€0)
+ xsc - X1xpd + (1 - 4cr)(1 - X1)Axdo (16)
For shortness of notation, Axdo replaces xpd+ xdo- xpO. The advantage of the latter equation is that the experimental determination of x,do from adsorption experiments, which is very time consuming and often rather inaccurate, can be avoided. Instead, tabulated solvent strengths (the well-known eluotropic series)”J6 can be used. Expressing the dimensionless surface contact energy for a polymer segment ( u p / k T )as d A t p and using eq 10, we get the relation between t,, and the “solvent strength” tp of a polymer segment: ccr = t p - ~ s c / a ’ A (17) The critical solvent strength depends only on a’ by the term xsc/a‘A. If there were no conformational entropic effects (Le., xsc = 0), tcr would be independent of a‘ and thus of the surface group density (which may vary with the kind of silica), provided the segment/surface bond is always the same. Because Xsc/a‘A is often small compared to tp, the critical solvent strength hardly depends on the kind of silica. Since the solvent strength of mixtures is
Langmuir, Vol. 5, No. 5, 1989 1183
TLC Detection of Polymer AdsorptionlDesorption not independent of the activity a' of the adsorbent (see eq 8), the critical composition at a given ea may vary with a'. However, if the solvent strengths of the components in the mixture do not differ very much (as in our experiments), the dependence of the critical composition on the activity is very small, especially when 4, is relatively high. Obviously, the simple model presented above has its limitations. We discuss two important cases. (1) An adsorbent surface may be heterogeneous with respect to some adsorbates. Polar and hydrogen-bonding solvent molecules may preferentially attach to specific groups on an acidic surface. This selective process is caused by the difference in bonding energy between different surface groups, which increases strongly for stronger interacting adsorbates. For such polar adsorbates, a' can be considered as an effective activity, which varies with coverage. At low coverage, a' could be higher than a' at high coverage due to preferential adsorption onto the stronger groups. Snyder refers to this phenomenon as the localization effect and describes it as a decrease in c with increasing surface ~ o v e r a g e . ' ~ J ~This J ~ is not quite consistent, since t is considered to be a property of the adsorbate only, whereas the localization relates to the surface and should show up in a'. According to Snyder, localization is only observed for solvents with t > 0.3.12 In order to avoid this complication, we chose polystyrene (PS)for our experimental test. This polymer has no strong polar or strongly hydrogen-bonding groups and can therefore be displaced from an acidic silica surface by means of weakly polar or apolar solvents (e I0.3). One might speculate that localization effects will be less important for multifunctional (large) molecules if their area of contact with the surface is larger than the typical scale of heterogeneity, so that a kind of "averagingn occurs.12 It is, however, not clear whether this would apply for a polymer near its adsorption/desorption transition. (2) The theory describes displacement on the basis that displacer molecules are more strongly adsorbed on the substrate than polymer molecules. However, displacement is also possible by molecules which have a stronger specific interaction with the polymer rather than with the adsorption sites on the surface. For example, for a basic polymer adsorbed on an acidic surface, displacement can occur by either a basic or an acidic displacer (i.e., by inactivation of either the adsorbent surface or the polymer).15 In the latter case, the concentration of displacer molecules which occupy sites on the polymer will be higher than the concentration in the bulk, 4d. The displacement theory above cannot handle displacement by solvents which bind specifically to polymer segments, since at best average interactions in solution are taken into account through the x parameters in eq 16. Hence, before using the theoretical description of displacement and the concomitant determination of the adsorption strength of a polymer in a particular system, we have to make sure that we are dealing with displacement by inactivation of the adsorbent surface instead of the polymer.
Table I. Polymer Samples
sample PS (Ega-chemie) PS (Polymer Laboratories) PS (Polymer Laboratories)
MW
MwIMn
3.21 X l@ 1.05 X lo6 5.30 X lo6
3.8 1.05 1.06
I
log
+d
Figure 1. Adsorbed amount A and retention, expressed as 1-
Rj, for PS in the solvent mixture carbon tetrachloride-toluene as a function of the logarithmof the volume fraction $Jd of toluene: 0 , batch adsorption experimentwith aerosil; 0 ,batch adsorption experiment with silica scraped off TLC plates; X, 1 - Rj (TLC experiment).
Experimental Section TLC. For the chromatographicexperiments,we have used TLC plastic sheets with a silica layer (Silicagel60 Fm, Merck) of 0.2" thickness. The plates contained a fluorescent indicator for visualizing the polystyrene spots after elution. Before use, the plates were dried in air at 120 "C for at least 10h. Spots of polystyrene (PS) were deposited along a line, 2 cm from the lower edge of the
adsorbent layer, by evaporating droplets of PS in carbon tetrachloride (4ooo ppm). The plates were then placed above the eluent of the appropriatecompition in a closed thermostatedcylindrical tank for 45 min, in order to establish equilibrium between the vapor phase, the liquid phase, and the adsorbedphase on the silica. This vapor pretreatment of the silica layer suppresses the undesirablesolvent demixing during the development. The upward elution was started by lowering the plates just into the eluent, at a temperature of 25 OC. After elution, the plates were dried and the polystyrene spots were visualized by short-wave UV illumination. The Rj values in most of the runs were either 1 or 0. The transition between these two extremes was scanned by changing the eluent composition stepwise, using very small variations in composition. Polystyrene is soluble in all solvent mixtures used, so that retention of PS by precipitation did not play any role. All solvents were analytical grade and used as such with the exception of chloroform,which was washed with purified water in order to remove the stabilizing agent ethanol. After the chloroform fraction was dried with magnesium sulfate,it was kept in the dark as much as possible to prevent photochemical reactions. Since ethanol is a very strong displacer, concentrations as low as 0.1% cause completePS desorption from a silica surface. Indeed, significant differences between the critical points of systemswith pure and ethanol-containingchloroform were found. Batch Adsorption. Batch adsorption experiments were carried out at room temperature with'dispersions of silica. Both silica scraped off the TLC sheets and aerosil (ox 50 ex Degussa) were used. The surface area of silica in the dispersions was 0.19 m2/mL, and the equilibrium polymer concentration (without displacer)was about 100 ppm. The adsorbed amount as a function of the solvent composition was determined by the depletion method. After the dispersions (silicawith polymer) were rotated end-over-end for about 15 h, the samples were centrifuged for 1 h at 20000 rpm. A given amount of the supernatant was evaporated under reduced pressure at 60 "C. The residue was then redissolved in a known amount of carbon tetrachloride. The absorbanceof this solution was measured at a wavelength of 262.5 nm with a Beckman 3600 spectrophotometer. The polystyrene samples used in this study are listed in Table I. We have chosen high molecular weight samples because the retention behavior of high molecular weight polymers ( M > 10') is known to depend little on molecular weight or molecular weight distribution.8 We did indeed fiid no significant differencesin the Rj values for the samples tabulated.
Snyder, L. R. In High-performance liquid chromatography, 3rd ed.; Horvath, C., Ed.; Academic Press: New York, 1983; p 186. (18) Snyder,L. R.; Glajch, J. L. J . Chromatogr. 1982, 248,165.
Results and Discussion In Figure 1, we compare the result of a TLC experiment (crosses) with adsorption experiments on the same silica
(17)
1184 Langmuir, Vol. 5, No. 5, 1989
van der Beek et al. Table 11. Solvent StrenPths and Molecular Areas" solvent €0, A/nm2 cyclohexane ( 0 ) 0.04 0.51 carbon tetrachloride (0)0.11 0.43 toluene (d) 0.22 0.58 benzene (d) 0.25 0.51 chloroform (d) 0.26 0.43 methylene chloride (d) 0.30 0.35 ~~
log
Table 111. Critical Volume Fractions and Solvent Strengths for PS on Silica for Two Solvents and Five
'%
Displacers
Figure 2. Displacement of PS from silica into carbon tetrachloride/displacer mixtures, determined by ATLC, as a function of the logarithm of the volume fraction $d of various displacers: 0,chloroform; 0, methylene chloride; 0, benzene; X, toluene; A, ethylbenzene. I
I
I
I
I
t
I
displacer
methylene chloride benzene toluene chloroform ethylbenzene
cyclohexane methylene chloride benzene toluene chloroform ethylbenzene
c ,
solvent carbon tetrachloride
methylene chloride
&r
,6
0.35
0.23
0.55
0.21
0.68
0.23
0.68 (TLC),0.63 (batch) 0.20 (TLC)
0.92 0.58
0.26
0.71
0.21 0.21 0.24
0.80 0.80 0.93
r
L
-0.5
-0.6
-0.3
- 0.1
-0.2
0
log qd
Figure 3. Displacement of PS from silica into cyclohexane/ displacer mixtures, determined by ATLC, as a function of the logarithm of the volume fraction $d of various displacers: 0, chloroform; 0 , methylene chloride; 0,benzene; x, toluene; A, ethylbenzene. and on a different silica (aerosil) for PS in carbon tetrachloride with toluene as a displacer. It can be seen that the transition in the chromatographicexperiments is much steeper. Hence, TLC is a much more sensitive technique for detecting the critical point (cp) than batch adsorption experiments. The basic reason for this is that polymer mobility (as measured in TLC experiments) is negligible as long as the total adsorption energy per polymer chain exceeds a few kT. Since the number of adsorbable monomers ( N ) in a chain is so high (- l@), it follows that this is always the case as long as x,w exceeds by even a small amount. An additional factor is that the fraction of bound monomers, p, increases also with xsP. Thus, Rf,which follows exp(-NpX,w), switches very rapidly between 1and 0 when x,P" passes through xc The adsorbed mass, on the other hand, increases gradually with xsw. The critical points for both kinds of silica, determined with either TLC or batch adsorption experiments, do not differ very much, as expected. Figures 2 and 3 show the retention of PS on the silica thin layer as a function of the displacer volume fraction for several displacers in the solvents carbon tetrachloride and cyclohexane, respectively. The order of the various displacers is the same in both cases, but the critical points are higher in the solvent cyclohexane. Apparently, polystyrene adsorbs more strongly from cyclohexane than from carbon tetrachloride. The critical solvent strength e, for each of these solvent mixtures can be calculated from eq 8. The required solvent strengths e, and f d and the molecular areas A as taken from Snyder" are given in Table 11. The molecular area of an adsorbate is defined as the specific area of the adsorbent, divided by the number of adsorbed molecules per unit weight of the adsorbent
in a fully occupied monolayer. For the determination of the activity a, we have used the procedure described by Snyder.18 This method is essentially a calibration of the silica with a series of compounds with known Ac values (tabulated by Snyder). For these compounds, the Rf values on this particular silica have to be measured, with pentane as the eluent. For the chromatographic silicas used here, a turned out to be equal to 0.65 (a' = 17.6). In the theory, we have assumed that the components of the solvent mixture occupy equal molecular areas. Table I1 shows that this assumption is not completely true. However, the variation in the A values does not affect significantly the calculated critical solvent strengths. The critical values determined for the various systems are given in Table 111. As explained in the previous section, ecr should be independent of the solvent and displacer used, expressing the interaction between the segments and the surface (see eq 10). This is not strictly true, as can be seen from Table 111. The differences are probably caused by solvency effects,lg which were not considered in the derivation of eq 10. The critical solvent strengths for cyclohexane mixtures are slightly higher than those for carbon tetrachloride mixtures. Carbon tetrachloride (xp" = 0.396) is a better solvent for PS than cyclohexane (xp" = 0.505).20>23 The polymer is expelled from the solution when the solvent is worse. In that case, more displacer is needed to displace the polymer from the substrate, leading to higher e, values. Chloroform is a relatively acidic solvent. A notable specific interaction with the relatively basic phenyl groups of the polymer can then be expected. Fowkes also reports this effect for chloroform and basic p01ymers.l~ Hence, displacement by polymer inactivation could play a role in this case. However, the critical solvent strengths for the mixtures with chloroform are not significantly lower than for the other systems. This indicates that preferential solvation of the polymer by chloroform does not play a significant role. (19) Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Fleer, G. J. In Polymer Adsorption and Dispersion Stability; Vincent, B., Goddard, E. D , Eds.; ACS Symposium Series 240; American Chemical Society: Washington, D.C., 1984; p 53. (20)Bristow, G. M.; Watson, W. F. Trans. Faraday SOC.1958, 54, 1742.
Langmuir, Vol. 5, No. 5, 1989 1185
TLC Detection of Polymer AdsorptionlDesorption Table IV. Flory-Huggins Interaction Parameters component b xnb ref component a -0.05 21 carbon tetrachloride toluene benzene 0.19 22 PS 0.396 20 cyclohexane toluene 1.01 21 benzene 1.29 22 PS 0.505 20 polystyrene toluene 0.432 20 benzene 0.438 20
From the t, and 4- data given in Table 111, xs parameters can be calculated by using eq 16, provided the relevant x parameters are known. Literature data for x are given in Table IV. The theoretical value of xsc in a lattice model is -In (1 - Al). For a hexagonal lattice (Al = 0.25), xsc = 0.288. The experimental xsc might be lower than this value because rotational entropy loss is not taken into account in the lattice model. In special cases, the rotational entropy loss for an attached monomer with respect to the bulk solution might be so much greater than for an adsorbed polymer segment that xsc may even become negative.1° When the monomer unit of the polymer is used as the displacer, it seems a logical first approximation to assume = xp = xdo,and xfi = 0. Equation 4 leads then to xsc= -In &. If this reasoning holds, the xsc value for PS could be determined by displacement with ethylbenzene, which can be considered as the monomer unit of PS. From the displacement isotherms with ethylbenzene (Figures 2 and 3), we find xSc values of 0.08 and 0.07, respectively. However, ref 23 gives a Flory-Huggins parameter for the interaction of ethylbenzene with PS of 0.450. This means that the assumption x p d = 0 is not justified, and a value AlxPd = 0.11 should be added to xsc values given above. The term (1- &J(l- XJAxdoin eq 4 is probably still small if the monomer unit of the polymer is used as the displacer. Hence, a reasonable value for xsc could be 0.2 for PS from carbon tetrachloride and cyclohexane. Clearly, this value is only approximate. Moreover, a small experimental error in #cr affects the value In #cr considerably due to the fact that +cr lies always in the vicinity of 1if a polymer is displaced by its own monomer. It is perhaps interesting to note that xsc is still positive in this weakly polar system. The molecular area A is also needed for the calculation of xs. We used the average surface contact area of the solvent molecule, the displacer molecule, and the PS segment. According to ref 24, the contact area of a PS segment (A,) is equal to 0.57 nm2. The calculation of xs is more sensitive to differences in A than the calculation of eCr. This indicates that we should be careful to determine xs values from systems with components of different molecular size. Since methylene chloride has a low molecular area ( A = 0.35 nm2) compared to the A values of the solvents used and the PS segment, the xs values from the systems with methylene chloride are less reliable than from systems with components of (nearly) the same molecular area. Table V gives the calculated xs values and the mean contact areas for the various systems studied. We have done the calculations for the athermal case (xd= xPo = xdo= 0) and, for those systems where all x parameters are known, also for the nonathermal case. The xaPOvalues for either carbon tetrachloride or cyclohexane as the solvent, (21)Fuchs, R.;Peacock, L. A.; Stephenson, W. K. Can. J. Chem. 1982,
Table V. Calculated x.m Values for PS and Mean Molecular Areas XI”
solvent carbon tetrachloride
dieplacer methylene chloride benzene toluene chloroform cyclohexane methylene chloride benzene toluene chloroform
nonathermal athermal A/nm2 1.1 1.0 0.9
1.9 1.9
1.1
1.0 1.2 2.0 1.8 1.8 1.9
0.45 0.50 0.53 0.47 0.48 0.53 0.55 0.50
Figure 4. Theoretical displacement isotherms (calculated by the Scheutjens-Fleer theory) for P S in the solvent mixture cyclohexane-benzene. Parameters: X,= 0.5, r (number of polymer segments) = 100, &, (volume fraction of polymer in the bulk = (1)xsPO = 2.0 (nonathermal), X? = 1.88 solution) = 0.505, x = 0.438, xdo = 1.29. (2) x,W = 1.9 (athermal),’ido= 1.88, x 8 = 0.505,xfi = 0.438, do 1.29. (3) xaPO = 2.0 (non= = 0. (4) xsPO = 1.9 (athathermal), X? = 1.88, x p = ermal), X? = 1.88, xp = xJ= xdo= 0.
-
3 ido
determined with the displacers methylene chloride, benzene, toluene, and chloroform, are in excellent agreement. In spite of the differences in molecular size for the systems with methylene chloride, the xs values are apparently not affected. The average values for the “nonathermal” x s p parameters for the solvents carbon tetrachloride and cyclohexane are 1.0 and 1.9, respectively. According to the exchange character of xB (eq 21, the difference between these values, which is 0.9, should be equal to x;vh for carbon tetrachloride adsorbing on silica from cyclohexane. We can check the internal consistency of the procedure by calculating x ~ C ’ from ~ the solvent strengths of the pure components (eq 14), using A = 0.53 nm2, the average value of the relevant contact areas given in Table V. We find x;J’ = 0.7. The agreement between these two values for x ~ C ’is~ within experimental error. As can be seen in Table V, the solvent interaction parameter terms Alx$ and Ax”’in eq 18 contribute only hO.1 to the value of xsP. The effect of taking these interaction parameters into account can also be seen in Figure 4. This figure shows calculated displacement isotherms of PS in cyclohexane-benzene mixtures as a function of the volume fraction of benzene. These calculations were done with the self-consistent-field theory of Scheutjens and Fleer, which is based on a multilayer Hence, this model is more general than the one-layer approximation, used by Cohen Stuart et al. for the calculation of the critical point and gives complete isotherms. The adsorbed amount of PS in Figure 4 is expressed in equivalent
60. .., 19.53. - - - -.
(22)Sharma, S. C.; Lakhanpal, M. L.; Rumpaul, M. L. Indian J. Chem. 1981,20A, 770. (23)Orwoll, R. A. Rubber Chem. Technol. 1977,50, 451. (24)Gloeckner, G.J. Polym. Sci. Polym. Symp. 1980, 68, 179.
(25) Scheutjens, J. M. H. M.; Fleer, G. J. J. Phys. Chem. 1980,84,178. (26)Scheutjens, J. M.H. M.; Fleer, G. J. J. Phys. Chern. 1979, 83,
1619.
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Langmuir 1989,5, 1186-1190
monolayers. Because the computer program used had a standard value for xsc of 0.288, we have done the calculations with xsPO parameters based on this value instead of 0.2. Therefore, the xsvalues in the last line of table V were incremented by 0.1. Figure 4 shows four isotherms. For the curves labeled 1and 3, we have taken xsPO values from Table V determined for nonathermal solvent mixtures. The isotherms 2 and 4 are calculated with xsPO values, based on athermal behavior of the solvent mixtures. Displacement isotherms 1and 2 are the results of computer calculations done with literature values for x, given in Table IV. For the curves 3 and 4, we have taken all x parameters equal to zero (athermal). The experimental critical point is also indicated in the figure. Only the critical points of the calculated curves 1 (completely nonathermal) and 4 (completely athermal) correspond with each other and with the experimental value. Curves 2 and 3, where solvent effects were either omitted from the theory or from the experimentally obtained value of xBW, show deviating critical points. This implies that the simplified model of Cohen Stuart et al. and the solvent concept of Snyder are consistent with the extended model of Scheutjens and Fleer, as long as a consistent procedure for the determination of xsW is used. The influence of the solvent-polymer, displacer-polymer, and displacer-solvent interactions on the critical point is shown by the shifted isotherms 2 and 3. Clearly, solvency effects have to be (27) The factor 2.303 arises because Snyder uses decimal rather than natural logarithms.
taken into account for the determination of the segmental energy. Conclusions Adsorption thin-layer chromatographyis a very sensitive technique for determining the critical point in polymer adsorption experiments. The chromatographic solvent strength concept of Snyder is very useful in polymer adsorption studies. The segmental adsorption energy can be easily determined with the help of the well-known eluotropic series. The determination of this energy is more complicated when strongly adsorbing componentsare used, because the substrate may be heterogeneous with respect to these components. A consequence of this is that the adsorption energy of strongly adsorbing components is not a well-defined parameter on heterogeneous surfaces. Specific interactions between polymer and displacer do not play a significant role in the displacement of polystyrene from silica by chloroform. The effective adsorption energy for PS on silica is l.OkT in carbon tetrachloride and 1.9kT in cyclohexane. These values correspond, within experimental error, to the difference in adsorption energy between cyclohexane and carbon tetrachloride. Acknowledgment. This work was supported by a grant from the ministry of Economic Affairs of The Netherlands under program 1OP.PCBP nr. 3. Registry No. PS, 9003-53-6;silica, 7631-86-9; carbon tetrachloride, 56-23-5; cyclohexane, 110-82-7; methylene chloride, 75-09-2; benzene, 71-43-2; toluene, 108-88-3;chloroform,67-66-3.
Small-Angle X-ray Scattering Investigation of the Silica/Water Interface: Evolution of the Structure with P H M. A. V. Axelos,+ D.Tchoubar,' and J. Y. Bottero*vg I.N.R.A. Laboratoire d'gtude des macromolgcules, Nantes 44000, France, Laboratoire de Cristallographie, UA810 CNRS Universitg d'orleans, 45067 Orlgans Cedex, France, and Equipe de recherche sur la coagulation-floculation, UA235 CNRS, CRVM BP40, Vandoeuvre 54501, France Received April 7, 1988. In Final Form: April 27, 1989 Precipitated silica colloids in suspension in water (Ludox HS) were studied by using small-angle X-ray scattering (SAXS) in order to evaluate the modifications of the interface (roughness, gel-like structure, ...) with pH variations. The electrokinetic data show that for pH 28 the surface charge increases sharply. SAXS yields two pieces of information about silica particles: (1)when pH increases from 7 to 10 the volume and the radius decrease from 2.5 X 103to 1.9 X 103nm3and from 7.4 to 7.15 nm, respectively; (2) the structure of the colloid/solvent interface is predicted by the Porod law. At pH 7, the two phases are separated by a sharp density transition. A t pH 10, a transition region appears, modeled by convoluting the ideal sharp density distribution with a smoothing distribution which is assumed to be Gaussian. The thickness of the perturbated region is about 1.1nm, and the radius of the resulting dense core particle is 5.6 nm instead of the 6.7 nm calculated from a log normal size distribution. The stability of colloidal sols depends on the surface properties. In the case of oxides, it is well-known that the surface sites undergo amphoteric dissociation. In some cases, metallic oxides show very different behavior compared to silver iodide or mercury electrode.'p2 For oxides like precipitated silica from an acidic or basic method, the I.N.R.A. Laboratoire d'etude des macromol6cules. Laboratoire de Cristallographie, Universit6 $Orleans.
* * Equipe de recherche sur la coagulation-floculation.
0743-7463/89/2405-ll86$01.50/0
number of silanol groups determined from potentiometric titration can be 25.5 OH/nm2.3 This value is much higher than can be assumed considering a surface area of 0.1-0.12 nm2/0H group. Correlatively, the surface charge can be very high and also exceeds what would be obtained from (1) Lyklema, J. Croat. Chem. Acta 1971,43, 249. (2) Lyklema, J. Interactions in colloidal systems. Ecole des Houches
du CNRS,1985. (3) Yates, D. E.; Healy, T. W. J . Colloid Interface Sci. 1976, 55, 9.
0 1989 American Chemical Society
