Langmuir 1993,9, 797-801
797
Double Layer Interactions between Silylated Silica Surfaces Alexis Grabbe' Ceramics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 Received September 17, 1992. In Final Form: November 16,1992 Data are presented for the free energy of interaction mediated by water between silica surfaces which have been silylated with (y-aminopropy1)dimethylethoxysilane.The measured interactionsare of classical DLVO type, with no hydration force evident. Measurementsof silylated silica interacting with untreated silica in water indicate an opposite sign of charge between these surfaces and do not exhibit hydration forces. Comparisonof the data with theoreticalcalculations using fully retarded van der Waals interactions and the nonlinear Poisson-Boltzmann equationindicatesthat the amino-functionalsurfaces exhibitcharge regulation behavior, a model for which is presented.
Introduction The surface force apparatus' has been used with great success over the past 15 years for measuring forces of importance to colloidal interactions. The device's use is restricted to optically transparent, molecularly flat surfaces;the material of choice is and has been mica. However, somework has been reported using sapphire singlecrystals, and also silica ~ h e e t s . ~The a use of silica as a substrate bears the advantages of the ability (in principle) to covalently bond a wide range of functional groups to the surface by silane chemistry. Mica, on the other hand, can only be readily functionhlized by the use of self-assembled monolayers or by Langmuir-Blodgett techniques. The long chain nature of such coatings makes it difficult to study short range interactions due to the solvent, because chain packing forces and solvation forces can operate on the same length scale. On silica, the use of covalently bound short-chain silanes ameliorates such difficulties. In this effort, silica treated with (y-aminopropy1)dimethylethoxysilane4J (7APDMS) was used to extend the range of usable surfaces for the measurement technique. It was deemed desirable to investigate the nature of hydration on this surface compared to unreacted silica and to establish the nature of the surface chemistry of the silylated surface. It was expected that there would be a hydration force between treated surfaces, because the amine group is expected to be strongly involved in hydrogen bonding in aqueous solutions; i.e. the surface was expected to be lyophilic. The sign of charge on the surfacewas expected to be positiveand to have a qualitative effect on the resulting hydration force as compared to that seen with bare (negatively charged) silica. Symmetric measurements with silylated silica sheets in NaCl and HC1solutions displayed almost classical DLVO behavior? There was typically a long-range repulsive interaction due to the overlap of opposing double layers Current address: Sandia National Laboratories, Dept 1114, Albuquerque, NM 87185. (1)Israelachvili, J. N.;Adams, G. J. Chem. SOC., Faraday Trans. 1 1978, 74,975-1001. (21 Horn, R. G.: Smith. D. T.: Haller, W. Chem. Phvs. Lett. 1989,162, 404-401. (3)Horn, R. G.; Clarke, D. R.; Clarkson, M. T. J. Mater. Res. 1988,3, 413-416. (4)Obtained from H~ America, Bristol, PA. ( 5 ) Certain trade names and produds of companies are identified in this paper to adequately specifythe materiale and equipment used in this research. In no case does such identification imply that the products are necessarily the best availablefor the purposeor that they are recommended by NIST. (6)Venvey, E. J.; Overbeek, J. Th. G. Theory of the Stability of Lyophobic Colloids; Elsevier: New York, 1948.
that, at a certain distance, turned attractive due to the van der Waals interaction across the solution. In all cases, the range of the attractive force could be accounted for by the van der Waals interaction. A short-range structured repulsion was not observed. Such a solvation, or "hydration= force has been observed between untreated silica ~ h e e t s . ~Furthermore, *~-~ the variations of surfacepotential at infinite separation, and of the free energy of interaction at finite separation, were indicative of charge regulating behavior; that is to say the chemical charge generation mechanism a t the surfaces was dependent on the composition of the electrolyte. A good curve fit to the data was possible only if the charge regulation behavior was accounted for in the solution of the Poisson-Boltzmann equation. The asymmetricsystemof treated silica interacting with bare silica displayed a long-rangeattraction corresponding to the overlap of oppositely signed double layers. A very short-range structured repulsion was displayed, unlike what has been seen in silica-silica interactions.
Experimental Section Silica sheets were prepared in an oxy-hydrogen flame by the method of Horn, Smith, and HallerS2A silica tube of inner diameter 14mm and 1 mm thickness was taken in a laminar flow hood, and the end sealed in the flame. After the closed end was heated for a minute to evaporatesurface impurities,the end was removed from the flame and a bubble blown. The bubble was then reintroduced near a flame of reducedintensity,and portions flattened by exposure to radiant heat. Prepared mica patches of thickness -4 fim were cleaved from a larger sheet of mica, and then attached to the flattened areas of the bubble. Placement of a mica patch onto the silica was necessary to maintain the cleanlinessof the surface prior to experiment;adhesion between the clean surfaces was spontaneous. Patched areas were broken from the bubble and attached to a backing sheet of mica. The samples were than taken to a vacuum chamber where -49 nm of silver was evaporated onto the sample sides which were in the interior of the bubble; the resultant structure is silver-silicamica. The sampleswere then removed and stored in a desiccator. Prior to the start of an experiment, a sample was glued, mica side up, onto a cylindrical silica lens using a low melting point epoxy resin.1° The protective mica patch was then removed, and (7) Rabinovitch, Ya. I.; Derjaguin, B. V.; Churaev, N. V. Ado. Colloid Interface Sci. 1982, 16, 63. (8)Peschel, G.; Belouschek, P.; Muller, M. M.; Muller, M. R.; Konig, R. Colloid Polym. Sci. 1982,260, 444. (9)Grabbe, A.; Horn, R. G. Double Layer and Hydration Forces Between Silica Sheets Subjected to Various SurfaceTreatments. J.Colloid Interface Sci., in press. (10)EPON 1004,a diglycidal ester of bisphenol-A, a product of Shell Oil.
This article not subject to U.S.Copyright. Published 1993 by the American Chemical Society
Grabbe
798 Langmuir, Vol. 9, No. 3, 1993 I
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I Constant charge
5 Lod[NoCIl)
00
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Figure 1. Measured equivalent free energy between flat surfaces that have both been silylated with yAPDMS. The RMS error is f 3 pJ/m2;the scatter in the distance is f0.5 nm in the double layer regime and f0.3 nm in the short range regime. The electrolyte is sodium chloride. The conditions are as follows: X, 1.05 X 10-4 M, pH 5.15, \k = 24.6 mV at infinite separation; 0, 5.25XlWM,pH5.40,\k,=22.3mV;A,1.05X10-3M,pH5.35, \k, = 24.9 mV; +, 5.25 X M, pH 5.25, q, = 26.5 mV. the sample placed in a sealed glass container. The container was partitioned into two parta by a poly(tetrafluoroethy1ene)(PTFE) connector;in the separate compartment rAPDMS was introduced in one end and allowed to react with the sample a t the other end via the gas phase for 24 h. The PTFE connector was used to prevent the silane liquid from creeping and wetting the sample compartment directly. At the end of the aa-hperiod, the samples were removed and mounted in the surface forceapparatus. There was normally an adsorbed layer of =3 nm of silane dimer on the surfaces, but the dimer dissolved in water when the apparatus was filled. The silane dimer has a positive charge in solution and is expected to be repelled from the positively charged surfaces; the total quantity of dimer contributes a negligible amount to the totalelectrolyteconcentration,the apparatus is filled, drained, and refilled before the first set of liquid phase measurements is taken. In the asymmetric case, the silylated sample was rinsed in filtered ethanol and blown dry with filtered nitrogen prior to mounting in the apparatus, in order to prevent any possible silane contamination of the opposing, untreated, surface. When placed in the apparatus, the surfaces were inundated with filtered aqueous solutions and the forces measured by the usual methods.' Whenever a fluid was filtered, the filter used was of the alumina membrane type, 0.02 pm pore diameter. The contact angle of water with the silylated surfacewaa not measured, but estimated values were noted: 45' advancing, 35O receding, f5O. The measured force F is related to the equivalent free energy of interaction between flats by the Derjaguin approximation,ll where the free energy AG,is related to the force by the geometric mean of the radii of the surfaces: AG = F/(2?r\/(R&)). Thermal drifts (which are partially corrected for) and vibrational noise limit the attainable force resolution to approximately f15 p N / m, unless the gradient of the repulsive force is high. The optical computations to extract the distance data were somewhat different than for the mica-mica case due to the asymmetry of the optical cavity. A description may be found in Horn and Smith.12
Results Figure 1 shows data taken at 1 X lo4 to 5 X 10-3 M with symmetric surfaces in aqueous NaC1, and ambient pH. The overlaid curves are charge regulation fits from the Poisson-Boltzmann equation, with the van der Waals interaction (see Appendix A) included. It is clear from the concentration-potential relationship at infinite sep(11)Derjaguin, B. V. Kolloid 2. 1934,69,155-164. (12)Horn,R. G.;Smith, D. T. Appl. Opt. 1991,30 (l),59-65.
Constant5 potential
10
15
20
25
D (nm)
Figure 2. Equivalent free energy between flats for 5.25 X le3 M NaCl as measured, and as fitted, using constant potential, charge regulation, and constant charge boundary conditions.The experimental data clearly display charge regulation behavior, the model for which is described in the text and in Appendix B. The inset is a plot of surfacepotential at infiite surfaceseparation as a function of salt concentration, computed for pH 5.25 by the charge regulation model.
arations that a charge regulation process is necessary to describe the chemical charging process at the surface,that is to say, binding of Na+ and H+ at the surface is evident. The data lie almost evenly between the two possible extreme types of boundary conditions, constant charge and constant potential, that are applicable to the solution of the Poisson-Boltzmann eq~ati0n.l~ This is graphically illustrated in Figure 2 for the highest concentration. The apparatus is capable of measuring forces only in the regime where the negative gradient of the force does not exceed the stiffness of the measuring spring,effectively restricting measurementsto repulsive interactions or very weak attractive forces. This is manifested in the data of Figures 1 and 2 when the point of approach reaches the attractive regime; the surfaces spontaneously jump together due to the mechanical instability of the system. When the surfaces are driven apart from contact, the mechanical instability again comes into play and the surfacesjump apart a distance that is independent of salt concentration. This outward jump permits a measure of the potential energy well, which is -400 &m2. Interactions measured in aqueous salt with HC1 are qualitativelysimilartadataalreadyshown.The 7APDMS layer near pH 7 is stable against hydrolysis for the time period of the experiment14(12 h), but the stability drops rapidly with changes of more than f 3 pH units from neutrality, making interpretation of those data somewhat problematic. The surface potentials at a given concentration of HC1 are higher than those for the same concentration of NaC1, but the regulation parameters may be taken without adjustment from the NaCl experiments to generate a reasonable fit to the HC1 data. Figure 3 shows the interaction of one treated silica surface with one untreated surface in 1.35 X 10-4 M electrolyte. In this case the jump-in point is at a distance where the van der Waals interaction is negligible and the double layers only weakly overlap, and it corresponds exactly to the position expectedfrom the spring constant. Overlaid is a simple weak double layer overlap approximation curve fit. The signs of the two surfaces must be opposite for this behavior to occur, confirmingthe positive (13)Chan, D.Y.C.; Mitchell, D. J. J. Colloid Interface Sci. 1983,s (l), 193-197. (14)Locascio-Brown, L.;et al. Anal. Chim. Acta 1990,228,107-116.
Double Layer Interactions between Silica Surfaces I
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I CH3 =SiO-Si-(CH,),-NH,
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-"-0.1
-50
010
011
* 012
Oil
I D (nm)
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0
*
200
100
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015
014
-
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I
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Figure 3. Measured equivalentfree energy between a bare silica surface and a surface that has been silylated with 7APDMS. A simple overlapapproximationsuffices to draw the smooth curve. A box symbol is at the tocation where the inward jump would be expected to occur, along with an arrow whose slope conforms to the constant of the measuring spring. The distance resolution is f0.5 nm in the double layer regime, f O . l nm in the short range regime (inset). The triangles correspond to measurement in compression and the plus symbols to measurement in decompression. The vertical units of the inset graph are dum2.
sign of the amino-functional surface. The well depth, as measured by outward jumps, is between -1500 and -2000 pJ/m2. The interaction was measured several times in succession, and its repeatibility indicates, as is expected of a covalently modified surface, that no rAPDMS was transferred to the untreated surface or lost to the solution. Of some interest is We very short range repulsive interaction. In the case of the symmetric systems there was no measurable structure within the resolution (h0.3 nm, 90% confidence by the scatter in repeat measurements) of the experiments. The magnitude of the energy minimum, assuming only van der Waals interactions, was consistent with a system whose structure is silicahydrocarbon-silica at the point of closest approach. In the asymmetric case (at a resolution of f0.1 nm, 90% confidence), there was some short range interaction measured, extending out approximately 0.8 nm. In this particular case, there is evidently some hysteresis (shown in the inset of Figure 3). The depth of the energy minimum is consistent with a hydrocarbonlayer half as thick as that of the symmetric case. That is to say, if we consider a systemsilica-hydrocarbon-silica,and we assume that there is a nonretarded van der Waals interaction, AG(L) = -A/ 127rL2(see Appendix A), then we expect the well depth of the asymmetric experiment to be 4 times deeper than in the symmetriccase because the separation distances L at "contactwdiffer by a factor of nearly 2, regardless of the value of the Hamaker constant. Discussion The charge regulation behavior of the system is amenable to the construction of an ionizable surface group model along the lines of Healy and White.15 The number of available data points prohibits unequivocal evaluation of equilibrium constants. Nevertheless, it is important at least to extract qualitative behavior in order to interpret the results. The construction of the model may be found in Appendix B, and we merely write the functional form u
= eN,a
(1)
where (15) Healy, T.;White, L. Adv. Colloid Interface Sci. 1978,9,303-345.
{(kb[Hbl+ k,[MbI) exP(-e+/kT))/(:((k,[H,l + k,[Mbl) eXP(-e+/kT) + k&,[MA12 + k,[HI[AI)
+ 1))
(2) This is a charge-potential relationship derived under the assumption of counterion binding and no amphoterism. The ion binding constants are k b and km, [Hbl and [Mbl are the bulk concentration of H and M, 9 is surface potential, and k E is the counterion binding constant which is assumed to be approximatelythe same for all types of neutral surface complexes. N , is the site density on the surface, a being the fraction of sites that are ionized. It is immediately evident that when the counterion binding contained in k E is turned on, the effect is to depress the surface charge at a given potential. If the measured interaction curve displays sufficient charge regulation behavior, we may fit alone; the curves rather than wing the potentials at infinite separation alone. Three fitting parameters kb, k,, and kE are used, noting that the counterion binding is only taken approximately. The best values for these numbers, using the entire data set and a fixed site area of 0.5 nm2 (see Appendix B), are pkb = -2.72,pkm = -1.14,and k~ = 2000. AS expected,the amine group has a greater affinity to protons than to sodium cations, kb > km. These parameters generate curves that fit the entire data set with a root mean square scatter of f 3 pJ/m2. When combined with the Lifshitz calculation (see Appendix A), the computedinteraction curves overlay the measured data and correctIy predict the jump distances. There is no measurable structural repulsion at short range in any of the symmetricexperiments; but the existence of such forces cannot be ruled out because the resolution was f0.3 nm, due to the thickness of the silica substrate. This is in contrast to the hydration repulsion that is always present and measurablein the silica-water-silica system, regardless of the degree of h y d r o ~ y l a t i o n ~ Jand - ~ Jwhich ~ extends as far as 3.0 nm in separation. Molecular models of the silane chain suggest that the silane monolayer can at most compress -0.3 nm, or -0.6 nm between two surfaces. This suggests that the hydration force on silica is not due to the compressibility of the surface of silica itself but to the repulsion of the adjacent water structures. That is to say, the hydration force seen on silica is almost certainly due to the adjacent water structure. If the hydration force observed on s i l i ~ a ~ *were ~ , ~due J ~to J ~a gel or poly(si1icicacid) layer formed on the silica by exposure to water, then the silane layer would be atop that layer, and the compressibility of such a structure would still be evident. The collapse of a putative gel by the silylation process is an alternative possibility, but that argument implies that the silane molecule can diffuse into the said gel. The simpler view is maintained here, that there is no gel. In the system studied, all of the surface hydroxyls that are not reacted to the silane either are irreversibly bound to a neighboring amine head gr0uplgor are sterically inaccessible. By inference,it is the silanol group that is responsible for structuring the solution to cause the hydration forces observed on bare silica. In the asymmetric case, there is a hysteretic short-range force. Chain packing may account for -0.3 nm and the (16) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991,353, 239-241. (17) Horn, R. G.; Smith, D. T. J. Non-Cryst. Solids 1990,120,72-81. (18)Horn, R.G.; Grabbe, A. Direct Measurements of Double-Layer and Hydration Forces Between Oxide Surfaces. Proceedings of the 1991 NATO Advanced Research Workshop on Clay Swelling and Expansive Soils. Bayeve, P., McBride, M. B., Eds.; Kluwer Scientific, in press. (19) Kelly, D. J.; Leyden, D. E. J. Colloid Interface Sci. 1979,147 (l), 213-224.
800 Langmuir, Vol. 9, No. 3, 1993
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remaining 0.2-0.4 nm may be due to a primary hydration layer of water, but no more. There is certainly no repulsion extending out to 3 nm, as is seen in silica-silica experiments2y9 and silica-sapphire experiments. la Why the amino-functional surfaces display little or no hydration is a question that can only be speculated upon. The reader is reminded that the amino group in 7APDMSis positively charged and is on the end of a flexible chain, whereas the silanols on bare silica dissociate to a negatively charged site with no flexibility at all. It is conceivable that the mobile amino head groups, which are expected to be highly hydrated, are nevertheless capable of burrowing into the structured water next to the surface of bare silica. Note again that the short range force displays hysteresis, being -700 d / m 2 lower in withdrawal than in compression. Because of the attractive force at close range, the surfaces deform to a flattened shape by compressing the underlying glue. For that reason, the measured, very short-range energies are only approximate; as the radius of curvature R increases, the short-range data as presented are increasingly overestimated. However, the well depth, as measured by outward jumps is still correct. The true magnitude of the short-range interaction is monotonically amplified by the distortion, which is equivalent to an ever increasing radius of curvature when under increasing compression. The smoothness of the as-prepared silica has been measured2 to be less than -0.5 nm. The longest range non-DLVO force in this work extends from 0 to 0.7 nm, which is consistent with an RMS roughness on the order of 0.3 nm per surface. An argument that the roughness of the as-prepared silica causes the long-range, 3 nm, hydration force between plain silica sheets, is therefore not tenable. Summary It has been demonstratedthat molecularly smooth silica surfaces may be cleanly functionalized with a monolayer of 7APDMS and that these surfacesexhibitclassicalDLVO behavior. The electrostatic interactions indicate that charge regulation behavior is occurring due to the effects of electrostatic potential on ionizable surface groups. A simple ionizable surface group model incorporating counterion binding has been constructed that, in combination with Lifshitz theory, fits the observed data. In symmetric experiments, no structure in the short-range force was observed. The results strongly imply that hydration forces between silica sheets are just that; an excess interaction due to the perturbation of the water structure by the neighboring surface silanol groups. In an asymmetric experiment, the positive sign of charge was confirmed, and a very short-range, hysteretic force was observed. The application of DLVO theory to lyophobic surfaces is well established and is adequate to describe the results presented in this paper, a single monolayer of rAPDMS being sufficient to convert the lyophilic surface of silica to a lyophobic state. The potential for studies of double layer interactions with different surface functionalities is established. Appendix A Lifshitz calculations were performed in the full nonretarded regime according to the formulation described by Mahanty and Ninham.20 Screening of the zero frequency interaction by ionic conduction was approximated ~~
(20) Mahanty, J.; Ninham, B. W. Dispersion Forces; Academic Press: New York, 1976.
via an analytical form21for a given separationL and Debye constant K
A,(L) = (2.883 X 10-21)J(1+ 2 4 exp(-2KL) (Al) where Ao(L) is the zero frequency component of the Hamaker function. This function gives the correct asymptomatic behavior at very small and very large separations L and the correct monotonic behavior for all L. A correct computation of A0 requires an exact knowledge of the ion distribution profile in the gap between the surfaces. As A0 is coupled to the Poisson-Boltzmann equation for the electric double layer, the problem is too complex to warrant the use of anything more than the approximate equation, A l . The principle difficulty in these calculations is to obtain good dielectric data for the materials at hand. For water, the function of Parsegian22was used. For silica, the refractive index data of M a l i t s ~ was n ~ ~used to construct the complex dielectric susceptibility €(it),with two UV absorptions and one IR absorption. The data of Phillip24 and Sige125 show four W absorptions, but the two absorption peak function yields an adequate €(it)).The infrared term matches the infrared reflectance spectrum of silica.26 The Lifshitz calculations for these systems should incorporate explicitly the effect of the silane coating. An accurate construction of a dielectric function for the very thin, 0.4 nm to 0.7 nm, silane layer is impossible. A gross approximation to €(it)was developed in the ClausiusMosotti form using hydrocarbon data, accounting for the different densities in the surfacs assuming frozen chains. Calculations for flat (0.36 nm) and extended (0.7 nm) chains gave some error bounds to the computation and indicate that a computation using a bare silica surface is adequate in the regime where the surface separation exceeds 2.0 nm. The effect of the coating was therefore neglected in the computations for this work. The functional form of the dielectric susceptibility used for silica is c(i[) = 1
+ 0.89748/(1+ ([/(1.9034 X 10’4))2)+ 0.40794/(1 + (U(1.6204 X + 0.69617/(1 + (U(2.7537 X 1016))2) (A2)
where the units o f t are rad/s, and an additional term of 0.798 is added at zero frequency in order to correctly account for low frequency contributions. Since the Lifshitz computations are feasible but time consuming on a personal computer, the results were computed in the form of a Hamaker function A(L) = &(L)+ A&). The nonzero frequency term was fitted to a convenient functional form similar to one suggested by which is accurate to &0.6% from 0 to 20 nm separation
~~
(21) Prieve, D.C.;Ruasel, W. B. J. Colloid Interface Sci. 1988,125 (l), 1-13. (22) Parsedan, V.A.; Weiss, G . J. Colloid Interface Sci. 1981,81 (I), 285-289. (23) Malitson, I. H.J. Opt. SOC.Am. 1965,55, 1205-1209. (24) Phillip, H.R. J. Phys. Chem. Solids 1971,32, 1935-1945. (25) Sigel, G.H.J. Non-Cryst. Solids 1973/74,13, 372-398. (26) Cleek, G.W. Appl. Opt. 1966,5, 771-775. (27) Russel, W. B.;Saville, S. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, UK, 1989.
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The van der Waals free energy is then computed by combining eqs A1 and A3 AG(L) -A(L)/(12?rL2) (A41 Appendix B An ionizablesurfacegroup model without amphoterism, but with counterion binding, suffices to describe the available data. The model is used to develop a chargepotential relationship to set the boundary conditions for the Poisson-Boltzmann equation d2V?/dL2= (ep/cc,)(exp(eV?/kT)- exp(-e\k/kT))
(B1) whose self-consistent solution provides a calculation of the electrostatic free energy of the system, allowing the model's parameters to be adjusted to fit the data. \k is the electrostaticpotential, k is Boltzmann's constant, p is the bulk ion density,c is the dielectric constant of the solution, and €0 is the permittivity of free space. The potential is implicitly dependent on position L. Equation B14 was used to set the boundary conditions for the self-coneistent solutionof the Poisson-Boltzmann equation, the solutions were computed directly using a numerical relaxation method on a finite mesh.28 For an alkaline surface site B, we may follow along the lines of Healy and Whitel5 and specify the important equilibria
kb
k,
B + H+ = BH+ [H+l,/([Bl[H+l,)
(B2)
B + M+ = BM+
033)
f
[M+l$([Bl[M+l,)
(B1)
(B4)
BM+ + A- = BMA k E % [BMAl/([BM+l[A-l,)
(B6)
BH+ + A- = BHA
037)
-+
(335)
BH+ + OH- = BHOH (B11) k E % [BHOHI/([BH+l[OH-],) (BW Under acidic conditions we may neglect equations (B9B12); the data do not permit distinguishing between different counterion binding constants, so all of those are set to the same k ~ .After some algebraic manipulation, the fraction of ionized groups, a,may be written a e {(kb[Hbl k,[MbI) exP(-eV?/kT)Y(((kb[Hbl+ k,[Md) eXp(-e\k/kl? + k&,[MAI2 4- k+,[HI[Al) + 1)) (B13) Where exp(-e\k/kT) is used to compute the surface concentrations of ions from the bulk as a function of potential 3. The charge density as a function of potential is then u = eN,a (B14) where N, is the site density. Determination of the true site density is worthwhile but not feasible with the available data. The maximum possible site density of a structurally similar silane29130 on silica is ( 2.1 X 1018)/m2.IndependentinformationSabout the density of silanolson silicaprepared in the same fashion as for this work indicates that the density of sites is about (-1.9 X 10ls)/m2. Thus the samples should be able to obtain the maximum possible coverage of silane. Since the treated surfaces are positively charged in water, more than 50% of the silanolsmust react with rAPDMS. The silanol site density must then be between (1X 1018)/m2 and (2 X 10lS)/m2.A 24-h reaction period should be long enough to react all but a tiny fraction of the available ~ilan0ls.l~ Any unreacted silanols are expected to irreS they , ~ ~ versibly interact with neighboringamino ~ ~ O U P or may be irreversibly hydrogen bonded to their nearest neighbor, sotheir chemistrymay be ignored. Amittarionic surface model incorporating unreacted silanols is unnecessary.
-
(B9) (BIOI
Acknowledgment. The author has been the recipient of a NIST/NRC postdoctoralresearch associateship. The help and advice from Roger G. Horn, in whose laboratory the work was performed, is greatly appreciated. Douglas T. Smith and Wolfgang Haller have also been extremely helpful.
(28) Press, W. H.;Flannery, B. P.; Teukolsky, S. A.; Vetterlii, W. T. NumencalRecrpces; Cambridge UniversityPres: Cambridge, UK, 1988. An adaptationof a relaxation algorithm and software described in Chapter 16 thereof.
(29)Szabo, K.; Ha, N. L;Schneider, P.; Zeltner, P.; Kovata, E. 82. Helu. Chim. Acta 1984,67,2128-2142. (30) Foti, G.; Belvito, M. L.; Kovata, E. sz. J. Chromatogr. 1988,440, 315-322.
kE
[BHAI/([BH+l[A-l,)
BM+ OH- = BMOH kE
[BMOHl/([BM+l[OH-l,)
(Bs)
