Langmuir 1997, 13, 6881-6883
6881
Determination of Surface pKa by the Combination of Neutron Reflection and Surface Tension Measurements S. W. An and R. K. Thomas* Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ, U.K. Received August 11, 1997. In Final Form: November 5, 1997X A new method for the determination of the surface pKa of molecules adsorbed at the air-water interface is reported. This method is based on the combination of neutron reflection and surface tension measurements. The surface excess of the ionizable species is determined directly by neutron reflection, and the Gibbs adsorption isotherm is applied to the surface tension measurements to give the sum of the surface excesses of ionizable species and adsorbed counterions. From these two results, the fractional charge on the ionizable species adsorbed at the interface is obtained, which is directly related to the interfacial pKa. We have applied the method to a diblock copolymer of methyl methacrylate and (dimethylamino)ethyl methacrylate adsorbed at the air-water interface. The surface pKa of the polyelectrolyte part of the polymer was found to be 6.7 ( 0.2 to be compared with a bulk value of 7.3 ( 0.1.
Introduction When molecules are adsorbed at interfaces, their local enviroment is different from that in the bulk solution and it is expected that some of their properties will be significantly changed. Because of the widespread occurrence of interfaces in materials and biological systems, it is of some importance to be able to characterize any change in behavior at the interface. A common example is the question of whether the dissociation constants of acidic and basic groups differ from those of their analogues in solution. Several factors are expected to contribute to these differences, including the presence of a region of low dielectric permittivity around the acidic or basic group, and changes in the degrees of freedom of the species immobilized at the interface.1,2 Methods that have been used to study this relatively inaccessible phenomenon include, for solid interfaces, contact angle titration,3 chemical force microscopy,2 and electrochemically determined interfacial capacitance.4-6 For liquid interfaces, attempts have been made to determine pKa in insoluble monolayers using surface potential measurements,7 and more recently second-harmonic generation has been suggested as a means for assessing interfacial pKa values.8 As a spur to experimental work in this area, recent simulations of the surface titration of amine groups at the air-water interface indicated large negative shifts in pKa as the amine groups lost their solvation at the interface.9 Here we report a new method for the determination of the surface pKa, which can be applied to adsorbed weak polyelectrolytes, species for which experimental determination of pKa presents particular difficulties. The method is based on the comparison of the surface excess determined from application of the Gibbs isotherm to * To whom all correspondence should be addressed. X Abstract published in Advance ACS Abstracts, December 15, 1997. (1) Zhmud, B. V.; Golub, A. A. J. Colloid Interface Sci. 1994, 167, 186. (2) Vezenov, D. V.; Noy, A.; Rozsnyai, L. F.; Leiber, C. M. J. Am. Chem. Soc. 1997, 119, 2006. (3) Holmes-Farley, S. R.; Reamey,R. H.; McCarthy, T. J.; Deutch, J.; Whitesides, G. M. Langmuir 1985, 1, 725. (4) Smith, C. P.; White, H. S. Langmuir 1993, 9, 1. (5) Fawcett, W. R.; Fedurco, M.; Kovacova, Z. Langmuir 1994, 10, 2403. (6) Bryant, M. A.; Crooks, R. M. Langmuir 1993, 9, 385. (7) Betts, J. J.; Pethica, B. A. Trans. Faraday. Soc. 1956, 52, 1581. (8) Zhao, X.; Ong, S.; Wang, H.; Eisenthal, K. B. Chem. Phys. Lett. 1993, 214, 203. (9) Smart, J. L.; McCammon, J. A. J. Am. Chem. Soc. 1996, 118, 2283.
S0743-7463(97)00906-2 CCC: $14.00
surface tension measurements with that measured by neutron reflection.10 The basis of the method is that neutron reflection is related to the square of the total surface concentration of polymer in the surface region, whereas the Gibbs adsorption isotherm gives the total molar excess of both polymer and counterions at the surface. In the simpler case of adsorption of a monovalent ionic surfactant the difference is simply a factor of two because there is adsorption of surfactant ion and its counterion, and this is normally allowed for in the Gibbs isotherm. However, in a case where the charge is unknown and no prefactor is included in the Gibbs isotherm, the ratio between the two measurements is just the total number of species at the interface. The above does, of course, assume that there are no regions of depletion, but these will not introduce significant errors in the analysis below. Theory The Gibbs isotherm of a multicharged species p is
-
dγ ) Γp d ln fpcp + Γion d ln fioncion + RT Γco-ion d ln fco-ioncco-ion (1)
where Γ represents surface excess (measured relative to water), c represents concentration, f is the activity coefficient, and the subscripts refer to the multicharged polymer species (p), the counterion (ion), and te co-ion (co-ion). We choose to measure the variation of γ under the condition of constant charge on the multivalent polymer, which is achieved approximately by keeping the polymer/acid ratio constant (i.e. at constant pH). In the absence of any added electrolyte there is a negligible concentration of co-ion. Equation 1 then reduces to
-
dγ ) Γp d ln cp + nsΓp d ln cion + Γp d ln fp + RT nsΓp d ln fion (2)
where ns is the number of counterions required to maintain surface neutrality (i.e. the charge on the adsorbed polymer species). The concentration of ions in the bulk is nbcp, where nb is the charge on the polymer in the bulk, and hence (10) Su, T. J.; Styrkas, D. A.; Thomas, R. K.; Baines, F. L.; Billingham, N. C.; Armes, S. P. Macromolecules 1996, 29, 6892.
© 1997 American Chemical Society
6882 Langmuir, Vol. 13, No. 26, 1997
-
Letters
dγ ) Γp(1 + ns) d ln cp + nsΓp d ln nb + RT Γp(d ln fp + ns d ln fion) (3)
At the constant level of neutralization deliberately being maintained in the measurements, the second term in eq 3 vanishes; that is,
nsΓp d ln nb )
nsΓp dnb = 0 nb
(4)
Finally, if any variation of the activity coefficients with concentration is neglected, the Gibbs surface excess ΓG will be given by
ΓG ≈ Γp(1 + ns)
(5)
Γp is determined directly from the neutron reflection and, since ΓG can be obtained from the Gibbs equation, ns can be obtained from the combination of the two sets of data. The value of ns gives the charge on the multicharged polymer species adsorbed at the surface and is related to the interfacial pKa for the neutralization by
pKas ) log
ns (n - ns)
+ pH
Figure 1. Determination of the surface coverages from neutron reflection profiles obtained for poly(DMAEMA-b-MMA) in null reflecting water. The bulk polymer concentrations are 0.2 (×), 0.1 (b), 0.07 (4), and 0.04 (0) wt %. The solid lines are the best fits of eq 8.
(6)
where n is the number of sites at maximum ionization. The assumptions in the derivation are discussed below. The basis of the determination of the surface coverage of the multicharged species, Γp, using neutron specular reflection is to adjust the isotopic composition (H/D ratio) of the water so that there is no reflected signal from the water (null reflecting water) and then to measure the reflectivity from a dilute solution of the deuterated, or partially deuterated, charged species.11 Any signal obtained under these circumstances is only from the adsorbed layer. If we represent the density F of adsorbed species along the direction normal to the surface as a Gaussian
( ) 2
Figure 2. Surface tension of poly(DMAEMA-b-MMA) as a function of copolymer concentration at pH ) 7.5. The solid lines are for guidance.
determination is model independent, although this is not the case for the thickness σ.11 Results
Thus the extrapolation of a linear plot gives the surface excess of deuterium-labeled species directly. Although the method is approximate and involves an assumption about the distribution profile of the adsorbed species, all plausible shapes of distribution extrapolate to the same intercept as a Gaussian distribution; that is, the coverage
We illustrate the method by determining the pKa of the water-soluble diblock copolymer poly(2-(dimethylamino)ethyl methacrylate-b-methacrylate) (poly(DMAEMA-bMMA)) (Mn ) 10 000, Mw/Mn ) 1.11, 30 mol % MMA content, MMA block fully deuterated) adsorbed at the airwater interface.12 The hydrophilic block of the copolymer is a weak polyelectrolyte, and the charge density of this block can be varied by varying the pH of the solution. Neutron reflection measurements were carried out on the reflectometers CRISP and SURF at Rutherford Appleton Laboratory, and the surface tension of the aqueous copolymer solutions was determined on a Kru¨ss K10T digital tensiometer using the du Nou¨y ring method with a Pt/Ir ring. Figure 1 shows the plots of ln(κ2R) according to eq 9 determined from the neutron reflection profiles obtained for the copolymer in null reflecting water, and Figure 2 shows the surface tension curve, for copolymer solutions with the pH maintained at 7.5. Taking the set of values of Γp from the neutron reflection measurements and ΓG from the slope of the surface tension curve at the four corresponding concentrations gives the set of values of ns in Table 1. The average value of ns gives a fractional charge on the polymer of 0.23 ( 0.05 and hence, using eq
(11) Lu, J. R.; Lee, E. M.; Thomas, R. K. Acta Crystallogr. 1996, A52, 11.
(12) An, S. W.; Su, T. J.; Thomas, R. K.; Baines, F. L.; Billingham, N. C.; Armes, S. P.; Penfold, J. J. Phys. Chem., in press.
F ) F0 exp -
4z σ2
(7)
then the reflectivity R is given approximately by 2
κ R=
16π2b2pN2aΓ2p 1040
(
)
-κ2σ2 8
exp
(8)
where bp is the known scattering length (Å) of species p, κ is the momentum transfer ()(4π sin θ)/λ) (Å-1), and Γp is in moles per square meter. Hence
(
ln(κ2R) ) 2 ln
)
4πbpNaΓp 20
10
-
κ2σ2 8
(9)
Letters
Langmuir, Vol. 13, No. 26, 1997 6883
Table 1. Surface Excess and Charges on Adsorbed Molecules of Poly(DMAEMA-b-MMA) at Two pH Values from Neutron Reflection (Γp) and Surface Tension Measurement (ΓG) pH ) 7.5 conc/ wt % 0.2 0.1 0.07 0.04
ΓG/ mg m-2
ΓG/ mg m-2
25.9 24.1 21.4
3.33 2.35 1.98 1.87
pH ) 6.5 ns 10 11 10.5
ΓG/ mg m-2
ΓG/ mg m-2
ns
34.6 24.3 17.2
1.48 1.16 0.775 0.527
29.8 31.4 32.6
6, a pKa value of 6.8 ( 0.1 at the air-water interface. A parallel set of measurements made at a pH of 6.5 gave values of ns (Table 1) which lead to 0.61 ( 0.05 for the fractional charge and a similar value for the pKa of 6.7 ( 0.1. Measurements at a pH of 8-8.3 were also in approximate agreement, but the smaller fractional charge and correspondingly much larger relative error (0.12 ( 0.05) make them considerably less accurate. Note that the abrupt change in slope of the plots in Figure 1 is associated with a switch to adsorption of micelles at the higher coverage.12 Direct titration of the copolymer gave a bulk pKa value of 7.3 ( 0.1, which is similar to values obtained for poly(DMAEMA) of 7-7.5.13,14 Thus the pKa of poly(DMAEMAb-MMA) at the interface is lower than that in the bulk by ∼0.6 units, which indicates that DMAEMAH+ is more acidic by a factor of 4 at the interface. The magnitude and direction of this change are similar to the result obtained in SHG measurements on a monolayer of CH3(CH2)21NH3+ by Zhao et al.,8 for which the pKa was found to be 9.9 ( 0.2 compared with 10.6 in bulk aqueous solution, a shift of ∼0.7 pKa units. Smart and McCammon9 have shown that the surface equilibrium will shift in favor of the less ionized species the more the ionizable group is exposed to air because of the large reduction in relative permittivity. In the case of a polymer the situation will be more complex in that adsorption of the polymer at the air-water interface will generate a situation where the hydrophobic parts of the polymer will themselves contribute to a lowering of the permittivity. There is also the possibility that not all the ionizable groups of the polymer (13) Hoogeveen, N. G.; Cohen-Stuart, M. A.; Fleer, G. J. Faraday Discuss. Chem. Soc. 1994, 98, 161. (14) Hoogeveen, N. G.; Cohen-Stuart, M. A.; Fleer, G. J. J. Collid Interface Sci. 1996, 182, 133.
will be in equivalent environments. Thus some may lie outside the water, completely embedded in a partially condensed polymer phase, as has been suggested by Li et al.,15 while some may lie fairly deep in the aqueous phase. What we have measured here is the average. At the low concentrations of polymer and ions being considered here (about 0.1 wt %) the assumption that the bulk activity coefficients are unity in the bulk, which we used in the derivation of eq 3, should be reasonable. Another possible source of error is the isotope effect which occurs both in the measurement of pH and pD and in the dissociation constants themselves.16 This effect is of the order of 0.5 on changing from H2O to D2O. Since the neutron measurements were made in less than 10 mol % of D2O, any apparent shift of pK should be no more than about 0.05 units. The neglect of co-ion concentration will only be justified provided the pH range does not deviate too far from neutrality because H+ and OH- ions are generated in the neutralization. We did not assume that the ionization of the adsorbed polymer was constant, but in practice, our results indicate negligible variation over the concentration range covered by the measurements in Figure 1. Finally, since the microenvironment of the polyelectrolyte at the surface is not necessarily the same at different pH values because the nature of the adsorbed layer changes, the pKa might also vary with pH. However, we observe no such variation within the experimental error. We note that, although this method has been applied to the case of a polyelectrolyte, it can in principle be applied to soluble or insoluble monolayers of singly charged species adsorbed at a surface. It is also important to realize that any independent measurement of Γp, such as by ellispometry or by radiotracers, could be used in combination with ΓG to determine the surface pKa. However, at present, these techniques do not have the accuracy of neutron reflection. Acknowledgment. We thank F. L. Baines, S. P. Armes, and N. C. Billingham, of the University of Sussex, for the polymer samples. We also thank the staff of the neutron spallation source ISIS, where the neutron reflection measurements were made. LA970906R (15) Li, Z.; Zhao, W.; Quinn, J.; Rafailovich, M. H.; Sokolov, J.; Lennox, R. B.; Eisenberg, A.; Wu, X. Z.; Kim, M. H. W.; Sinha, S. K.; Tolan, M. Langmuir 1995, 11, 4785. (16) Glasoe, P. K.; Long, F. A. J. Phys. Chem. 1960, 64, 188.
