J. Phys. Chem. B 1998, 102, 185-192
185
Neutron Reflection Study of Phenol Adsorbed at the Surface of Its Aqueous Solutions: An Unusual Adsorbed Layer Z. X. Li and R. K. Thomas* Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ, U.K.
A. R. Rennie CaVendish Laboratory, Madingley Road, Cambridge, CB3 0HE, U.K.
J. Penfold ISIS, CCLRC, Chilton, Didcot, Oxon., OX11 0QX, U.K. ReceiVed: July 24, 1997X
Neutron reflection has been used to determine the coverage and distribution along the surface normal direction for the air/solution interface of solutions of phenol in water. The coverages are in reasonable agreement with surface tension determinations of the surface excess over the whole range of concentration up to the solubility limit of 8.6 wt % of phenol. At the highest coverages the layer is found to be substantially thicker than expected for a layer one molecule thick, with a full width at half-height of 17 ( 2 Å, which becomes about 14 Å after allowance for the contribution to the roughening of the surface by capillary waves. The experimental results at high coverage disagree with the only available computer simulation which predicted a full width at half-height much less than that measured in the neutron reflection experiment, for example, about 5 Å at a coverage where the neutron measurements give 14 Å after removal of an estimated capillary wave contribution, which was not included in the simulation. It is suggested that in such a diffuse layer the phenol molecules are unlikely to be inclined at a single angle to the surface normal, as suggested from the interpretation of second harmonic generation measurements. The agreement between the simulation and neutron reflection is good at about half the maximum coverage, where the phenol appears to form a single molecular layer. At the highest coverages, the width of the phenol distribution is comparable with that obtained for many surfactant layers, although surfactant molecules are intrinsically much longer, and the layer seems to have a multilayer character unlike those found for the short chain alkanols.
Introduction The last decade or so has seen the development of several new techniques capable of investigating structural aspects of layers adsorbed at the air/liquid interface. Prominent among these are second harmonic generation (SHG), sum frequency spectroscopy, neutron and X-ray reflection, and grazing incidence X-ray diffraction. For the types of disordered layer expected to be formed by small molecules no one of these techniques on its own is capable of giving all the information needed to understand the structural properties of a given layer. Furthermore, the type of information obtained by experiment is often such that further data from modeling, by computer simulation, for example, are needed to maximize the understanding of the results. The development of all the techniques above is sufficiently new that there is no system to which they have all been applied, although there are several examples where computer simulations of amphiphilic layers have been compared with neutron and X-ray reflection results (see refs 1-3). For smaller adsorbed molecules (less than about 10 carbon atoms) there are even fewer experimental studies or simulations. The surface of ethanol/water mixtures has been studied by neutron * Please address all communications to Dr. R. K. Thomas, Physical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ, U.K. X Abstract published in AdVance ACS Abstracts, December 15, 1997.
reflection4 and by computer simulation,2 but not by any other of the new techniques, and phenol has been studied by SHG5 and by simulation.6 A particular feature of the latter simulation was that it sought to interpret the SHG results at a deeper level than possible from the experiment on its own. However, information about the distribution of the phenol layer in the direction normal to the interface, which can be obtained by neutron reflection, was not available to test the basic correctness of the simulation at the time of its publication. We have now done these measurements, and we find that the surface of aqueous phenol solutions is rather unusual. The determination of the surface excess of phenol using surface tension measurements and the Gibbs equation has a long and interesting history. Langmuir7 deduced that close to the solubility limit (8.6 wt %) the phenol molecule was lying flat on the surface with an area per molecule of 34 Å. Harkins and Grafton8 then found a surface area of 36.6 Å2 at a bulk phenol concentration of 2.8 wt %, arguing that no activity correction should be necessary up to this concentration and, by comparison with other substituted phenols, that the molecules were oriented vertically. A little later Goard and Rideal9 also measured the surface tension and used activity data to make a correct Gibbs plot. The activity data had been obtained from freezing point measurements but were deemed to be unreliable above a phenol concentration of about 3 wt %, and so they used a graphical
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186 J. Phys. Chem. B, Vol. 102, No. 1, 1998 extrapolation for the region 3-8 wt % and found a limiting area of 24 Å2 at the saturation limit. Jones and Bury10 remeasured the activity of phenol/water solutions and obtained values different from both Goard and Rideal and other earlier measurements. Fu and Bartell11 used Jones and Bury’s activity data to calculate the adsorption of phenol, and they found an area of 30.7 Å2 at a phenol concentration of 4.5 wt %, which was the maximum concentration of phenol that they judged the activity coefficient data to be satisfactory. In a detailed comparison of the phenol isotherm with other small molecule isotherms they also found that, although phenol obeyed a Langmuir rather than a BET isotherm, the phenol was somewhat different in that, in their description, the surface solution remains ideal up to the coverage limit of their isotherm. What is clearly unsatisfactory about all these coverage determinations is that the deviation from ideal behavior of phenol solutions is large and, because the activity in systems with a consolute temperature is often temperature dependent, activities determined from freezing point measurement may not be compatible with surface tension measured at room temperature. The phenol/water system is also interesting because it is one of the few systems where the surface excess has been measured by the direct method of McBain, using a microtome.12 Three surface coverages were determined up to a bulk phenol concentration of about 3 wt %, which are in reasonable agreement with the data of Goard and Rideal, although the errors are quite large. We make a comparison of the different measurements of surface coverage later in the paper. Surface potential measurements on phenol at the surface of its aqueous solutions indicate that the net surface dipole is very small.13,14 However, this cannot necessarily be used to deduce anything about the orientation of the phenol molecule itself because several factors may contribute, including any preferential orientation of the water molecules. In principle, a more direct measurement of surface orientation can be made using second-harmonic generation. From measurements by Hicks et al.5 it was deduced that the phenol molecules were oriented at 50° to the surface normal over the whole surface concentration range. Because they found that the tilt of the phenol is invariant with surface coverage, these authors were further able to deduce values of the surface coverage out to bulk phenol concentrations of about 2 wt %, which they regarded as the completed monolayer. However, Hicks et al. also observed that the second-harmonic signal continues to increase linearly above this point right up to the solubility limit of 8.6 wt %. The authors were not able to explain this but noted that, whatever the origin of this effect, the tilt angle would have to remain constant at 50° to be consistent with their polarization data. Sokhan and Tildesley6 made their computer simulation on a sandwich consisting of an approximately 30 Å thick layer of water with phenol layers on either side. The calculations were done for a range of surface concentrations with areas per phenol molecule from 590 to 22 Å2. They found that there was a distribution of orientations of the phenol molecules, but that over much of the range of concentration the mean value of 〈cos θ〉, where θ is the tilt from the surface normal, agreed with the value obtained from the SHG data, although Hicks et al. fitted their data with a single orientation. The simulation also gave a half-width of the phenol distribution normal to the interface of up to about 5 Å, with which we will compare our data below, and gave a large surface potential, very different from the small value obtained by Paluch et al.13,14 Two further papers have some bearing on the nature of the surface of phenol/water solutions. Gracia et al.15 measured the
Li et al. contact angle between the phenol rich and water rich phases and found that it never vanishes, indicating that in the twophase region the phenol rich layer never completely wets the water rich layer. This unusual result was later confirmed by direct observation using ellipsometry by Guzman and Schmidt, who also deduced that the thickness of the film at the surface of the water rich phase was about 20 Å.16 Specular reflection of neutrons has been shown to be an effective technique for investigating the structure and organization of wet interfaces,17 but there are few applications to small molecules adsorbed at surfaces. We have applied the method to the ethanol/water system4 and to the higher alcohols, butanol and hexanol.18 The technique is very sensitive to surface coverage and now appears to be the most accurate and direct technique available for such measurements. Its sensitivity for determining any structural features of layers of small molecules depends strongly on the number of atoms in the molecule, the amount adsorbed, and the thickness of the layer. Provided that the number of atoms (assumed to be mainly carbon and hydrogen or deuterium) in the molecule is greater than about 10 and the molecular area in the layer is less than about 40 Å2, the sensitivity of the experiment is high. Thus the structural data for butanol should be experimentally sound, but those for ethanol may not be. Phenol just fulfills the necessary criterion in terms of number of atoms and satisfies the coverage criterion over much of the interesting range of concentration. Experimental Details Deuterated phenol (98% D) was obtained from Aldrich and purified by sublimation in vacuum. Protonated phenol was purified by sublimation. Pure water from an Elgastat (Elga, U.K.) was used throughout, and heavy water (D2O) was obtained from Fluorochem. The solutions were made up in terms of grams of phenol per 100 milliliter of solution, which we refer to as wt %. For the reflectivity measurements on deuterated phenol the concentrations were adjusted for isotopic weights to give solutions of exactly the same molar compositions as the protonated samples. The concentrations of these are then given as though they were protonated. For the reflection measurements, samples were placed in PTFE troughs of about 50 mL capacity, and these were enclosed in airtight aluminum containers with silica windows. The temperature was controlled to within 1 K of 298 K. Because of the large amount of solution in relation to the volume of the container, problems of evaporation were negligible. Neutron reflectivity profiles were obtained on the instruments SURF19 and CRISP, and the general procedure for obtaining the reflectivity profiles has been described elsewhere.20 A flat background, determined by extrapolation to large values of the momentum transfer (defined below), was subtracted from each measured profile to account for the incoherent scattering. This background depends on the isotopic composition being studied and varies in the range (2-6) × 10-6 measured relative to total reflection. Determination of Surface Coverage Although a single uniform layer is rarely a realistic model for an adsorbed layer of a small molecule such as phenol, it is a convenient one for discussion of the neutron reflection results. Neutron reflection is sensitive to the scattering length density of the system defined by
F(z) )
∑j bjnj(z)
(1)
Phenol Adsorbed at the Surface
J. Phys. Chem. B, Vol. 102, No. 1, 1998 187
TABLE 1: Scattering Lengths and Scattering Length Densities of the Pure Components speciesa
volume/Å3
scattering length × 105/Å
C6H5O(H) C6D5O(H) H2O D2O
150 150 30 30
27.0 79.05 -1.7 19.1
a The parentheses around H indicate that this atom will always adopt the equilibrium solution H/D composition.
where bj is the scattering length and nj the number density of atomic species j. The reflectivity of a uniform monolayer (labeled 1) on a substrate (labeled 2) is given exactly by21
R ) |R|2 )
r201 + r212 + 2r01r12 cos(2β) 1 + r201r212 + 2r01r12 cos(2β)
(2)
where rij are the Fresnel reflection coefficients and β is the phase shift on traversing the layer once and equals q1τ where θ1 is the wavevector of the radiation normal to the interface in the monolayer, τ is the thickness of the layer, and θ1 is the glancing angle of incidence at the interface between layers 1 and 2. It is customary in neutron reflection to express the reflectivity in terms of the momentum transfer κ rather than the angle of incidence, where κ is defined in terms of the grazing angle of incidence by
κ)
4π sin θ0 ) 2q0 λ
(3)
Equation 2 can be generalized to any number of layers. Defining the momentum transfer at which total reflection occurs between layers i and j as κci, which is given by22
κ2ci ) 4q2ci ) 16π(Fi+1 - Fi)
(4)
Figure 1. Division of surface into a null reflecting solution and surface excess such that the Gibbs and neutron surface excesses are the same.
chosen to be null reflecting, can be fulfilled at all phenol concentrations up to the solubility limit of 8.6 wt %. The surface coverage of phenol can be determined by fitting the model of a uniform monolayer to the reflectivity from the solution of perdeuterated phenol in null reflecting solution, using eq 2. The two fitted parameters F and τ combine to give the surface coverage Γn using
Fτ 1 ) NaA Nab
Γn )
where A is the area per molecule, Na is Avogadro’s number, and Γn is the surface coverage. When the contrast situation is as described above, i.e. deuterated phenol in null reflecting solution, the experiment is extremely sensitive to Γn because of the quadratic dependence of the reflectivity on Γn. The thickness τ of the layer is sensitive to the choice of model for the distribution of phenol along the surface normal, but the derived coverage is not at all model dependent. This is because, although a range of τ will usually fit a given profile, especially at lower coverages, the corresponding values of F exactly compensate.22 An alternative method for determining the coverage is to assume that the phenol distribution along the normal direction is described as a Gaussian,
( )
the Fresnel coefficients are
F ) Fnexp -
2
ri,j )
κc
[κ + x(κ2 - κc2)]2
(5)
There is a large difference between the scattering of the isotopes of hydrogen for which bH ) -3.74 × 10-5 Å and bD ) -6.67 × 10-5 Å. It is therefore possible to choose the isotopic composition of either component so that the scattering length density of the bulk phase is the same as that of air, i.e. zero. There is no reflection at all from the surface of such a solution. For the case of a deuterated solute in null reflecting solution, reflection only occurs if there is segregation of the deuterated solute at the surface. For this special situation substitution of eqs 4 and 5 into eq 2 gives22
κ4R = 2F2 - 2F2cos(κτ) ) 4b2n2sin2(κτ/2)
(6)
where we have also used eq 1 and b and n are the scattering length and number density of the monolayer. Equation 6 shows that the level of the reflectivity is determined by F ()bn), but the shape is determined by the thickness of the layer τ. Since b is known, the number density of the solute can be determined from F. The scattering lengths of deuterated and protonated phenol, and heavy and ordinary water, are given in Table 1, and the compositions of their solutions of interest are such that the conditions for eq 6 to hold, i.e. that the solution, as a whole, is
(7)
4z2 σ2
(8)
where σ is the full width at 1/e of the maximum for which the reflectivity, at the same level of approximation as eq 6, is 2
κ R=
16π2bp2Na2Γp2 1040
(
exp -
)
κ2σ2 8
(9)
where bp is the scattering length of phenol (Å) and Γp is the surface excess (mol m-1). Taking logarithms, we obtain
(
ln(κ2R) = 2ln
)
4πbpNaΓp2 10
20
-
κ2σ2 8
(10)
Even though the Gaussian distribution is completely different from the uniform monolayer, the value of Γp obtained is not affected by the choice of model. The final question concerns the comparison between the Gibbs surface excess and the neutron surface excess. In Figure 1 we give a schematic diagram of a possible distribution of the two components. The phenol is divided into two parts, one which exactly parallels the water distribution and the remainder. In the experiments we choose the uniform solvent to be null reflecting by adjusting the H/D ratio, and therefore the scattering length density of the water plus the phenol distribution that mimics it is zero right through the interface. In this case, the
188 J. Phys. Chem. B, Vol. 102, No. 1, 1998
Li et al.
Figure 2. Neutron reflectivity profiles of deuterated phenol in null reflecting solution in water. The concentrations are 0.2 (+), 1.0 (3), 2.0 (O), 4.3 (×), 6.0 (4), and 8.6 wt % (0). The continuous lines are calculated for a uniform layer model with parameters given in Table 2.
TABLE 2: Fitted Parameters for a Single Uniform Layer conc/wt % F × 106/Å-2 τ ( 2/Å σ ( 2/Å σ1/2 ( 1.5/Å area/Å2 0.2 1.0 2.15 4.3 6.0 8.6
1.71 1.77 1.62 1.90
13 16 21 22
11 15 20 20
9 12.5 17 17
83 ( 10 45 ( 3 36 ( 3 28 ( 1 23 ( 1 19 ( 1
Gibbs excess of phenol relative to null water excess is identical with the excess phenol measured by neutron reflection. It is easy to show that this will always be the case, however complex the distribution, for this contrast combination, provided the surface excess is determined by extrapolation to low κ, for example using eq 10. Figure 2 shows a set of reflectivity profiles of deuterated phenol in null reflecting solution at different compositions in the single-phase region on the water rich side of the phase diagram. To achieve the null reflecting condition for the solvent, the isotopic composition of the water was adjusted by including the appropriate amount of D2O. This was just possible to maintain up to the solubility limit of 8.6 wt %. The continuous lines represent the best fits of eq 2 to the data; that is they are exact calculations based on a single uniform monolayer, and the derived coverages are given in Table 2. However, as the coverage is reduced, the signal becomes too low for it to be possible to deduce an accurate value for the thickness, and we only quote the derived areas per molecule at the two lowest coverages. One of the more surprising features of the phenol layer is that the density of the phenol in the adsorbed layer is more or less constant over a range where the surface excess almost doubles. We also note here that, in comparison with other systems that we have studied by neutron reflection, this was one of the most difficult to reproduce, for which we have no explanation. In general the coverage was well reproduced, but there was variation in the thickness of the layer. The values of the thickness given in Table 2 are the mean results of up to four independent measurements in nearly all cases. Three different values of the thickness are given in Table 2, τ for the uniform layer and σ for a Gaussian distribution being obtained from the best fits to eqs 6 and 9, respectively, and σ1/2, which is the full width at half-height of the best fitted Gaussian distribution, from 0.8σ. To emphasize that the choice of the model for the layer does not affect the determination of the coverage, we have also determined the coverage by fitting the Gaussian distribution, i.e. eq 9, and by using the linear plot, eq 10. The results of the
Figure 3. Use of eqs 9 and 10 to analyze the reflectivity data. (a) haa, which is proportional to κ2R, plotted aa a function of κ at various concentrations. The continuous lines are the best fits of the Gaussian distribution, eq 9 with the values of σ given in Table 3. The concentrations are 2.0 (O), 4.3 (×), 6.0 (4), and 8.6 wt % (0). (b) Determination of the surface coverages using eq 10 applied to the data of Figure 1. The bulk concentrations are 2.0 (O), 4.3 (×), 6.0 (4), and 8.6 wt % (0). The straight lines are the best fits using the parameters in Table 3.
Figure 4. Comparison of surface excesses determined by surface tension (O),11 neutrons (4), microtome method (×),12 and the SHG signal (0).5 The single point (3) is from the surface tension and the activity coefficient data of ref 9.
former are shown in Figure 3a and the latter in Figure 3b. The slopes of the lines give the width of the distribution (assumed to be a Gaussian), and the intercepts give the coverage. The results of the linear plots, the direct fitting to a Gaussians, and the fit of the uniform monolayer model agree within experimental error. The width parameters are different for the two basic models, and we discuss this further below. In Figure 4 we compare the surface excesses determined by neutron reflection with those determined from other methods. These include the full Gibbs equation results of Fu and Bartell, the single full Gibbs equation result of Goard and Rideal at saturation coverage, the results of the SHG experiment, and the
Phenol Adsorbed at the Surface
J. Phys. Chem. B, Vol. 102, No. 1, 1998 189
results of McBain’s microtome measurements. The SHG results were originally plotted as signal intensity and scaled to match the results from the surface tension data, but Hicks et al. made their own analysis of the surface tension data using the full Gibbs equation, but using the rather less satisfactory activity coefficient measurements of Goard and Rideal. It would be possible to rescale their data to the more accurate analysis of Fu and Bartell, but we have not done it here. There are a number of interesting features in Figure 4. First, there is a distinct knee in the isotherm at about 2 wt % of phenol, where a coverage of only about 55% of the maximum value was reached. This knee is most marked in both the surface tension and the SHG data. The activity coefficient measurements are only reliable up to about 3 wt % phenol, and some extrapolation was used to determine the coverages at the higher concentrations. Nevertheless, the agreement with the absolute neutron measurements is acceptable. If the SHG signal were rescaled to either the neutron data or to Fu and Bartell’s surface tension results, they too would agree within error up to a bulk concentration of about 4 wt % phenol. Thus, the agreement between four independent measurements, including the current measurements, up to just above the knee is reasonable, although not excellent. However, above this bulk concentration only the neutron measurement is absolute and independent of extra assumptions. In this region the deviations from ideal behavior are large, and since the activities were measured at a temperature different from those of the surface tension, they may not be suitable to use in the Gibbs equation. Thus Goard and Rideal’s saturation area per molecule of 24 Å2 must be regarded as too low. The rescaled values of the SHG signal would also show that it does not vary linearly with coverage at higher concentrations and indeed no such assumption was made by Hicks et al. Determination of the Structure of the Phenol Layer In the determination of the coverage of phenol we have already determined the width of the phenol distribution in terms of either a uniform monolayer or a Gaussian distribution, and the values of the corresponding width parameters are given in Table 2. The value of σ (the 1/e width of the Gaussian) is always smaller than that of τ (the uniform layer) for an adsorbed layer.25 More revealing is to compare either parameter with the corresponding value for butanol, which is a molecule of comparable dimensions. For butanol σ varies from 11 to 14 ( 1 Å at areas per molecule from 39 to 25 Å2. For phenol σ varies from 11 to 20 ( 2 Å for a similar variation of area per molecule from 45 to 23 Å2. The value of the width of the phenol layer at the highest concentration is, in fact, larger even than those determined for large surfactant molecules such as C18H33N(CH3)3Br,24 for which σ for a saturated layer is only 17 Å. In the fits of the data we have only used two models which are both symmetrical about their centers. The resolution of the experiment is such that, just as we cannot distinguish a uniform layer from a Gaussian, we would we be unable to distinguish any asymmetry in the distribution. Thus the layer may have an asymmetrical distribution of phenol, but this would not affect the conclusion that the width of the distribution is surprisingly large. More detail about the structure of the layer can be determined as follows. In general, the reflectivity may be written approximately as22
R)
16π 2
κ
2
where the hjj are self partial structure factors given by
hjj ) |nˆ j|2 and the hij are cross partial structure factors given by
hij) Re{nˆ inˆ j}
(11)
(13)
The nˆ (κ) are the one-dimensional Fourier transforms of ni(z), the average number density profile of the number density of group i in the direction normal to the surface. The shift theorem of Fourier transforms23 states that if a one-dimensional distribution is moved by δ, then its Fourier transform is changed by a phase factor, exp(iκδ), and eq 13 becomes
hij ) Re{nˆ inˆ j exp(iκδij)}
(14)
where δij is the separation of the two distributions. It can be shown that eq 14 then becomes
hij ) ([hihj]1/2sin(κδij)
(15)
where one distribution is even and the other is odd,22 and where the ( arises from the uncertainty in the phase. For a phenol/water mixture eq 11 becomes
R)
16π2 2 [bp hpp + bw2hww + 2bpbwhpw] κ2
(16)
where the subscripts p and w denote phenol and water, respectively. To determine the three partial structure factors in eq 16 requires three measurements of the reflectivity with different values of bi. The most obvious combinations to choose are the two measurements with bp and bw made zero by suitable hydrogen/deuterium substitution. Any measurement with one of the bi zero gives the other self partial structure factor directly. The cross partial structure factor is obtained by combination of these two measurements with one where the two bi are nonzero, the most convenient being with both components deuterated. There is an immediate difficulty in determining the structure of phenol/water surfaces by combining isotopic data, because the system is very isotope sensitive. Even well away from Tc, where the phase diagram would be expected to be isotope sensitive, it is strongly affected by H/D substitution. Thus the solubility limits of phenol in H2O and D2O are respectively 8.66 and 6.2 wt %,26 and only a small fraction of this difference results from the difference in density. These large differences made it risky to determine the partial structure factors directly by solving the three simultaneous equations resulting from three different isotopic compositions since any isotope effects might cause very large errors in the differences between different reflectivity profiles. Instead, we followed the procedure devised by Lee and Milnes27 where the set of three reflectivities is fitted by simultaneous nonlinear least squares using distributions of each component with analytical Fourier transforms. This does not eliminate structural errors resulting from isotope effects, but it does reduce them (see ref 24 for a discussion of this problem). For phenol the most natural distribution to use is a Gaussian, and the distribution that is most suitable for water is the tanh distribution
[21 + 21tanh(ζz)]
F ) F0 2bibjhij ∑j bj2hjj + ∑j ∑ i
