Langmuir 1988,4, 821-826 and useful and gives qualitatively good results. It shows that the quadrupolar interaction is responsible for the herringbone ordering of N2molecules on graphite.
Acknowledgment. We are indebted to Professor J.
821
Stecki for suggesting a related problem and Professor W.
A. Steele from the University of Pennsylvania for a discussion. Registry No. Nz, 7121-31-9; graphite, 1182-42-5.
Adsorption at the Liquid Surface Studied by Means of Specular Reflection of Neutrons J. E. Bradley, E. M. Lee, R. K. Thomas,*'+ and A. J. Willatt Physical Chemistry Laboratory, Oxford University, Oxford, England
J. Penfold and R. C. Ward Rutherford-Appleton Laboratory, Didiot,England
D. P. Gregory Unilever Research, Port Sunlight, Wirral, England
W. Waschkowski FRM Reaktorstation, Garching, Munich, Germany Received August 13, 1987. I n Final Form: November 2, 1987 The technique of specular reflection of neutrons has been used for the first time to study adsorption at the surface of water. Four systems were studied. The reflectivity profile of an insoluble monolayer of fully deuteriated butyl arachidate on water was measured as a function of surface pressure. The changes of reflectivity with surface concentration were found to be easily measurable. The thickness of the layer was found to be 35 f 5 A, about 15% larger than expected for the fully extended molecule. The surface of a solution of partially deuteriated decyltrimethylammonium bromide at about half the critical micelle concentration,where the monolayer is complete, gave a reflectivity profiie correspondingto a layer thickness of 20 f 8 A and an area per molecule of 45 A2. The layer thickness i s again slightly larger than expected for the fully extended molecule. The head group area agrees with independent estimates. Sodium dodecyl sulfate was studied as the protonated form in D20 and the deuteriated form in Hz0/D20 mixtures, demonstrating the potential of contrast variation in the specular reflection technique. The thickness of the layer was found to be 20 A in both cases, and estimates of the distribution of water in the layer were made at different concentrations. The deuteriated surfadant contained about 10% dodecanol as impurity. At low concentrations the layer was found to be 100% dodecanol, but, as the concentration increased above M), dodecanol was increasingly replaced about one-tenth of the critical micelle concentration (8.1 X in the layer by sodium dodecyl sulfate.
Introduction Hayter et al.' have shown how the specular reflection of neutrons may be used to study inhomogeneity at the surface of a liquid. They have demonstrated the sensitivity of neutron reflection to an interface by measuring the reflectivity of deuteriated Langmuir-Blodgett films on glass substrates.2 It has proved difficult to obtain the necessary sensitivity to study the liquid interface because special arrangements have to be made to do specular reflection from horizontal samples. Three general procedures can be identified. The simplest in concept, although not in execution, is to use neutron mirrors or monochromators to deflect the beam from the horizontal down on to the surface of the liquid. The angle of incidence is varied by raising or lowering the liquid sample and simultaneously adjusting the angle of tilt of the mirror. The detector also has to be moved to receive the specularly reflected beam. The second method Current address: Physical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ. Current address: Physical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ.
uses a fixed angle of incidence of a white neutron beam onto the sample, and the reflectivity is measured as a function of the incident wavelength by doing a time of flight analysis of the neutrons. This is the principle of the new CRISP reflectometer at ISISa3 A third method has been employed for some years on the gravity mirror spectrometer at the FRM, GarchingS4p5In this machine the neutron beam passes through a horizontal 100-m evacuated flight tube. Under the influence of gravity neutrons of a given wavelength fall through a distance determined by their time of flight. If the liquid is placed at this height at the end of the flight tube, neutrons of the given wavelength may be reflected off the liquid surface into a detector placed immediately behind the sample. (1) Hayter, J. B.; Highfield, R. R.; Pullman, B. J.; Thomas, R. K.; McMullen, A. 1.; Penfold, J. J. Chem. Soc., Faraday Trans. I 1981, 77, 1437. (2).Highfield, R. R.; Thomas, R. K.; Cumins, P. G.; Gregory, D. P.; Mingins, J.; Hayter, J. B.; Schaerpf, 0. Thin Solid Films 1983,99, 165. (3) Penfold, J.; Ward, R. C.; Williams,W. G. J. Phys. E 1987,20,1411. (4) Koester, L. In Springer Tracts in Modern Physics; Springer-Verlag: Berlin, 1977; Vol. 80, p 24-26. ( 5 ) Koester, L.2. Phys. 1966, 122, 328.
0743-7463/88/2404-0S21$01.50/00 1988 American Chemical Society
822 Langmuir, Vol. 4 , No. 4, 1988
The intensity of the direct beam at this height of fall is obtained by measuring the count rate with the detector in the straight-through beam. By this means the reflectivity is measured as a function of height of fall. Since the height of fall is determined by the wavelength, this is equivalent to measuring reflectivity as a function of wavelength. If there is no wavelength-dependent absorption, which is usually the case for neutrons, the reflectivity is a function only of sin B / X , or of the momentum transfer K = (4r sin @ / A , and therefore all three methods give equivalent results. In this paper we apply two of these techniques to the study of both soluble and insoluble layers at the air-water interface. The purpose is to demonstrate the considerable potential of neutron reflectivity for studying adsorption at liquid surfaces.
Experimental Section The two instruments used for this work were the gravity mirror of the Technical University, Munich, a t Garching, and CRISP a t the neutron spallation source ISIS, a t the Rutherford and Appleton Laboratories in England. Both have been described in full e l ~ e w h e r e . ~ - ~ CRISP was specially built to do experiments on liquid and magnetic samples. Neutrons impinge on the sample at a fixed glancing angle, which may be chosen in the range 1-1.5'. The reflected neutrons are measured by a single detector, at the same angle with respect to the sample, by using time of flight analysis of wavelengths from 1-7 A. The reflectivity is normally determined by ratioing the reflected neutrons at each wavelength to the number incident on the sample, measured by a monitor in the incident beam. The beam was 1mm high and 40 mm wide. At an angle of 1.5' this illuminated an area of sample 40 X 40 mm2. The sample was contained in a Teflon trough 5 mm deep with a liquid surface 200 x 80 mm2. The trough was cleaned between each measurement with the sequence of solvents heptane, 4 % HF in concentrated "Os, and copious amounts of ultrapure water (Elgastat UHQ,Elga, U.K.). The trough was enclosed in an airtight aluminium container with soda glass windows for the neutrons. The effects of vibrations on the liquid surface were eliminated by supporting the enclosed trough on a float immersed in oil. The combination of the viscosity of the oil and the weight of the float (about 20 kg) reduced vibrational contributions to a level lower than required for studying surfactant layers as indicated from the reflectivity from clean DzO.The surface was found to be smoother than the thicknesses of the layers being studied. The typical time to do a complete reflectivity profile on CRISP was about 12 h, but, since these experiments were completed, the full commissioning of the instrument has reduced this by approximately 1 order of magnitude. The principle of the gravity mirror has been described in the Introduction. The illuminated area of sample is now very much larger than for CRISP. The trough was made from a solid block of Teflon, giving a liquid surface area of 85 X 35 cm2. The direction of the neutron beam was along the long axis of the trough, and the moveable barrier was also oriented in this direction so that it could be moved without obstructing the neutron beam. The effective width of the neutron beam could then be adjusted between about 20 and 25 cm. The experimental procedure was to fill the trough with water (in this case a mixture of 80% of doubly distilled H20 and 20% of D20 by weight). The reflectivity profile of the water was then measured after using the barrier to sweep the surface. A known weight of spreading solution (in this case butyl arachidate in 9:l heptane-ethanol) was then deposited on the surface. After evaporation of the spreading solution for about 1 h the trough was enclosed with an aluminium cover with soda glass windows. The surface pressure was measured by means of a roughened Wilhelmy glass plate and a pressure transducer, which had previously been calibrated against a microbalance. Any possible contributions of vibrations to the reflectivity of the liquid surface were eliminated by a special suspension, which has been described elsewhere.6 ( 6 ) Nucker, N. 2.Phys. 1969, 227, 152.
Bradley et al.
Specular Reflection of Neutrons Neutrons are specularly reflected in the same way as light polarized perpendicular to the plane of reflection. The reasons for this are discussed in detail by Lekner.7 Thus any method that has been used for calculating optical reflectivities can be applied to the reflection of neutrons. In this paper we use the optical matrix method: in which the average refractive index profile normal to the surface is divided into a number of elements. The Fresnel reflection and transmission coefficients are calculated for each element and then combined to give the characteristic reflectivity matrix, from which the reflectivity of the surface is obtained. The method lends itself to machine solution, and for the types of system studied here there is no practical restriction on the number of elements into which the interface is divided. However, since the resolution of this first experiment was somewhat limited, the models used to fit the data usually consisted of only one or, at most, two interfacial elements. The advantage of neutrons or X-rays over light is that the refractive index is simply related to composition. For neutrons q = 1- ( X 2 / 2 r ) p s
where
ps is
the scattering length density given by
where ni is the number density and bj the empirically determined scattering length of nucleus i. Thus, with the optical matrix method, the reflectivity profile can be calculated exactly for any model of the interfacial composition. However, the relation between the two is a complicated one, and it is not easy to assess whether it is a unique one, especially where the interfacial profile is itself complicated. This question is discussed in ref 9 but is not important for the present work where the ambiguities depend more on lack of resolution.
Insoluble Monolayer: Butyl Arachidate on Water Our first experiments were done on the gravity mirror. Partly because of the high equivalent angular resolution of this instrument and partly because of the low flux of the reactor, reflectivities can only be measured down to about and then only if samples with a large surface area are used. Neutron reflectivity increases with increasing scattering length density. Because deuterium has a large positive scattering length, deuteriated materials generally have large scattering length densities. On the other hand, protonated materials have low or even negative scattering length densities so, for example, the total reflection of neutrons from the surface of H 2 0 is very much less than from D20. To obtain significant effects from an insoluble monolayer with the gravity mirror it was therefore necessary to have a deuteriated layer with as large a thickness as possible and to include a sufficient proportion of D,O in the water subphase that the critical angle for total reflection fell within the accessible range of the instrument. For this reason we chose deuteriated n-butyl arachidate (n-butyl eicosanoate; C19D39C02C4D9) for the monolayer. The fully deuteriated form was prepared by direct esterification of deuteriated arachidic acid with deuteriated butanol. (7) Lekner, J. Theory of Reflection; Martinus Nijhoff: Dordrecht, 1987. (8)Born, M.; Wolf, E. In Principles of Optics, 5th ed.; Pergamon: Oxford, 1975; pp 51-72. (9) Crowley, T. L.; Thomas, R. K.; Willatt, A. J., to be published.
Liquid Surface Studies
Langmuir, Vol. 4, No. 4, 1988 823
-5
\ I
I
20
I
I
I
+\
30
I
Height of fallfcm
Figure 1. Calculated and observed reflectivity (R) profiles of H20/D20 ( 0 )and a monolayer of deuteriated butyl arachidate at three different surface coverages (area per molecule) of 32 (+), 28 (X), and 26 A2 (0). The calculated profiles are the continuous or dashed lines and assume a model with the molecules at right angles to the surface. For clarity, not all the error bars are included. There are no data on the surface pressure (a)-area (A) isotherms for butyl arachidate, but there have been a number of measurements on other long-chain esters, for which the results are summarized in Gaines.lo Their phase diagrams are not completely understood, but for our purposes, the main features can be deduced from the behavior of the alkyl palmitates. When the alkyl chain has more than two carbon atoms the alkyl palmitates form a liquid phase over much of the a-A range. n-Butyl palmitate forms such a phase and undergoes collapse at an area per molecule of just under 30 A2. Our own measurements on butyl arachidate indicate that it too forms a liquid phase which collapses at an area per molecule of approximately 26 A2. Results from the gravity mirror measurement are shown in Figure 1,together with calculated profiles. Each point on the curves took about 4 h to measure. However, the effects of the monolayer are clearly seen and are very much greater than the experimental error. Also clear is the enhancement of the reflectivity as the density of the monolayer is increased. It is difficult to predict how an ester with two chains of different length will pack in the monolayer. Three factors will be important. At high surface pressures the chains will pack to occupy as small a volume as possible. This may be achieved by the molecules tilting so that neighboring chains may interlock. For straight chains it has been suggeated'l that there are three possible angles of tilt, 90" (vertical on the surface), 63", or 44". The second fador is that the interaction of the solvent with the unsymmetrical head group may cause a tilt of the molecule away from the vertical. Finally, the unsymmetrical chain lengths may also cause a tilt. We have modeled the profiles using the three suggested angles of tilt together with the measured area per molecule to estimate the scattering length density and thickness of the layer. Although the molecule (IO) Gaines, G. L. In Insoluble Monolayers a t Liquid-Gas Interfaces; Interscience: New York, 1966; Chapter 5. (11) Lyons, C. G.;Rideal, E. K. h o c . R. SOC.London Ser. A 1929, A124, 333.
I
, 0 06
0 06
o oe
0 10
0 12 KIA-'
Figure 2. Calculated and observed reflectivity profiles for a layer of butyl arachidate on HzO. The continuous line corresponds to a layer of thickness 35 A and scattering length density 4 X lo4 A-2 and the dashed line to 25 A and 3.8 X lo4 A-2. The background scattering is not shown but is approximately uniform at a reflectivity of about has a rather complex structure, we have used only a simple "slab" profile of the layer to calculate the reflectivity profiles for reasons which will become clearer below. The length of the molecule has been estimated by using the known length of the arachidate ion from measurements on Langmuir-Blodgett films.2 All three angles of tilt give acceptable fits to the observed reflectivity. The fitted parameters for one of the angles of tilt, the 90" orientation, are (a) 32 A2, 30.5 A, 5.1 X lo4 A-2; (b) 28 A2, 30.5 A, 5.8 X lo4 A-2; and (c) 26 A2, 30.5 A, 6.3 X lo4 A-2. The numbers are respectively area per molecule, thickness of the layer, and scattering length density. For a 44" tilt the fit to the observed profiles is just as good but the fitted parameters now become for case b 28 A2, 21 A, and 6.6 X 10-6 A-2. Whilst these measurements show clearly how sensitive neutron reflectivity is to the presence of the monolayer, the analysis of the results also shows that the structural information obtained is somewhat limited at these effectively low glancing angles. A higher range of reflectivities can be measured on the new time of flight instrument CRISP, at ISIS. We were able to make a single measurement on the butyl arachidate layer using this instrument. The film was depostied on an H20 subphase by using the same spreading solution, but this time there was no applied surface pressure so the film was less well defined than in the gravity mirror experiments. At the time of this experiment, CRISP was not yet complete. This meant that it was only possible to measure the reflectivity profile over a limited range of momentum transfer, K. Special procedures had to be taken to eliminate background scatter and in the conversion to absolute reflectivity. We used measurements of the H 2 0 profile to determine the background and of the D20 profile to scale to the absolute reflectivity. After subtraction of the background we first compared the observed D 2 0 profile with the calculated one. The agreement was good but there was some scatter at different values of K . This could have resulted from small variations in transmission of different wavelengths through the windows of the cell. This variation was eliminated by ratioing observed to calculated points and using these ratios to adjust all our other profiles. This is possible because, over this range of K , D 2 0 behaves as if it had a sharp interface: and its reflectivity profile could be calculated exactly. The result of a single measurement of butyl arachidate on H20 is shown in Figure 2. The scattering from H 2 0 is uniform
Bradley et al.
824 Langmuir, Val. 4, No. 4, 1988 throughout this region at about Once again it can be seen that the monolayer has an enormous effect on the reflectivity. Since this was an unconfined monolayer it seemed a valuable test of the sensitivity of the neutron technique to fit the layer parameters independently of any other information. We found that the parameters required to fit the reflectivity fell in a much narrower range than for the gravity mirror calculation. A best fit was obtained for a thickness of 35 f 5 A and a scattering length density of (4 f 0.5) X lo4 A-2. The best fit to the profile is shown in Figure 2. Also shown in Figure 2 is the poor fit of the calculated profile for a 25-A layer, corresponding to a 44O tilt of the molecule on the surface. In this range of momentum transfer the general level of reflectivity is determined by the value of the scattering length density of the layer while the slope of the profile is determined by the thickness of the layer. The separation of these two parameters should become even clearer when measurements are possible at higher values of K . The length of the fully extended butyl arachidate molecule was estimated above to be 30.5 A. The observed thickness of 35 A therefore suggests that the molecule is oriented close to perpendicular to the surface. It is possible for a layer to be thicker than the length of an individual molecule if the molecules are not all at the same level, i.e., the layer may be somewhat diffuse. Combination of the derived scattering length density of the layer with the parameters used to fit the gravity mirror results shows that the area occupied per molecule in this unconfined layer was 41 A2.
Soluble Monolayers When a surfactant is dissolved in water it will generally lower the surface tension because it is adsorbed at the air-water interface. The amount adsorbed can be determined from surface tension measurements via the Gibbs equation. In general the monolayer appears to be complete at about half the critical micelle concentration. The Gibbs equation and other methods such as radiotracer measurements can give no structural information about the adsorbed layer. Neutron reflectivity measurements can, and, as for the insoluble layer, we now attempt to demonstrate the scope of such experiments. We did experiments on three systems. The first was decyltrimethylammonium bromide, C10D21N(CH3)3Br, prepared from decyl bromide and trimethylamine. This has a cmc of 0.065 M. We did a single experiment on CRISP at a concentration of 0.04 M in a 2:l mixture of H 2 0 and D 2 0 by weight in a Teflon trough. The results from the solvent alone and the solution are shown in Figure 3. The statistical accuracy of the measurements on the solvent is poor, but these measurements are only included to demonstrate the large change in reflectivity when a deuteriated surfactant is adsorbed at the surface. The best fit to the data was obtained with a layer thickness of 20 f 8 A and a corresponding scattering length density of (3.05 f 0.5) X lo4 A-2. Once again the precision is not high, but these are the first measurements of their kind. The layer thickness is now appreciably larger than the length of a fully extended Clo chain. This suggests that the layer is definitely somewhat diffuse, possibly because the charged head groups stagger their positions in the vertical plane to reduce electrostatic repulsion. The value of the scattering density allows us to make an approximate estimate of the composition of this 20-A layer. The volume fraction of solute in the surface layer is determined from the average of the bulk value of the scattering length density, 4.3 X lo4 A-2, and the value for the solvent, 1.4
I
,
0 04
1
3 35
3 3e
KIA“
0 10
Figure 3. Calculated and observed reflectivity profiles of a 0.04 M solution of partially deuteriated decyltrimethylammonium bromide in 2:l H20/D,0 and of the solvent alone (lower curve). The scattering length density used for the solvent was 1.4 X lo4 k2and for the layers 3.05 X lo4 A-z. The thickness of the layer was taken to be 20 A. X lo4 A-2, and is found to be 0.56. Combining this with the molecular volume of about 500 A3 and the thickness of the layer gives an area per molecule of 45 f 15 A2. This is in good agreement with other estimates of the head group area, which fall in the range 43-45 A2.I2 The only sure way of determining the composition of the layer is by varying the “contrast”, i.e., the H/Dratio in solvent and solute, and then using such measurements in conjunction with the surface excess. It is not necessary to have a layer of higher scattering density in order to be able to study the surface. A layer of lower scattering density than the substrate will tend to suppress the reflectivity. Alternatively, a layer which has the same scattering length density as air may affect the reflectivity of the solvent by changing the distribution of solvent normal to the surface. We now illustrate this effect with some measurements on solutions of protonated sodium dodecyl sulfate (SDS) in D20. The cmc of SDS is 8X M, and the isotherm has been thoroughly studied by several workers.13 The monolayer is complete at a bulk concentration of about 4 X lo9 M. At this concentration the scattering length density of the adsorbed layer will be small, but its exact value will depend on how much D20 is incorporated into it. The observed profile at this concentration is shown in Figure 4. The poor fit of the profile calculated for a layer of zero scattering length density (this is approximately a match to the scattering density of air) shows that even under these unfavorable contrast conditions the layer may be observed. The best fit to the data is obtained for a layer of thickness of 20 f 10 A and a A-2. scattering length density of (1 f 0.5) X The surface excess of SDS relative to water, rZ1 at 4 X mol cm-2. If we assume that all of M is 3.2 X this is concentrated in the 20-A-thick layer at the surface, then the contribution of the SDS to the scattering length density ps is 0.13 X lo4 A-2. To account for the observed ps of 1 X lo4 A”, five D20 molecules have to be added per SDS molecule. It is interesting to assess where these molecules are in the layer. The observed reflectivity profile is not reproduced if the five molecules are concentrated in a narrow layer around the ionic head group of the SDS since this is more or less equivalent to having a sharp D,O/air interface. On the other hand, it is not necessary (12) Rijnbout, J. B. J. Colloid Interface Sci. 1977,62, 81. (13) Chattoraj, D.K.;Birdi, K. S. In Adsorption and the Gibbs Surface Excess; Plenum: New York, 1984; pp 106-110.
Langmuir, Vol. 4,No. 4, 1988 825
Liquid Surface Studies
1
1
I
0 04
0 06
!
1
0 10
0 06 KIA-’
Figure 4. Calculated and observed reflectivity profiles for a 4 x 10“ M solution of protonated sodium dodecyl sulfate in D20. The dashed line is for D20 with a perfectly sharp surface and
scattering length density of 6.38 X lo4 A-2, the continuous line is for a layer 20 A thick with a scattering length density of 10” A-2.
I I
I
0 06
0 04
to assume such an extreme as the slab model where the five D20 molecules are uniformly distributed throughout the layer. A more realistic model is one where the D20 concentration falls gradually towards the surface according to a half Gaussian. For this type of model it is found that a half-width of about 10 A fits the observed profile very well. The plane at the half-width is approximately where the Gibbs dividing surface is located for a zero surface excess of D20. The overall effect of the SDS in these circumstances may then be that it makes the surface of the solvent more diffuse. To distinguish the two models it will be necessary to make measurements at higher values of K. For more dilute solutions we can again estimate the number of D,O molecules per SDS molecule by using the known surface excess from independent mea~urements.’~ The values found at three separate concentrations are (a) 4X M, 3.2 X mol cm-2, 5; (b) 5.7 X M, 1.4 M, -0.5 X x 10-lomol cm-2, 67; and (c) 1.9 X mol cm-2, ~ 2 0 0 The . values represent the concentration, surface concentration, and number of water molecules per SDS molecule, respectively. It had been our intention to do parallel experiments on deuteriated SDS. However, surface tension measurements showed that our sample was contaminated with about 10% dodecanol. A dodecanol monolayer is complete at a concentration of about lo4 M of pure dodecan01’~or M for our impure SDS. An SDS monolayer normally starts to form at lo4 M and is complete by about 4 X M (see above). These figures assume no interaction between the two species. However, it has been inferred from surface tension mea~urementsl~ that, as the cmc of SDS is approached, dodecanol is incorporated into mixed micelles and removed from the surface. The dodecanol monolayer has a lower surface tension than SDS, so the surface tension rises as the dodecanol is removed. Consistent with this picture we found that there was a strong contribution of the impure surfactant to the reM flectivity even at concentrations as low as 4.8 x (Figure 5a) and, at the highest concentration we used (3.3 X M), the reflectivity was significantly lower (Figure 5b). A t a complete monolayer the area per molecule of SDS is about 50 approximately double that for a do-
w2,
(14) Defay, R.; Prigogine, I. In Surface Tension and Adsorption; Longmans: London, 1966; pp 92-95.
0 08
K A-’
0 10
Figure 5. Calculated and observed reflectivity profiles for solutions of impure sodium dodecyl sulfate in 2:l H20/D20: (a) M. The continuous line is for a layer 4.8x M;(b) 3.3 X 20 A thick with a scattering length densit of 6.2 X 10” A-z and the dashed line for 20 A and 5.0 X 10“
i-2.
Table I. Scattering Length Densities and Adsorption of SDS ~
~
bulk concn. M 4.8 x 10-5 1.6 x 10-4 4.5 x lo4 8.3 X lo4 3.3 x 10-3
scattering
fraction of
length density, A-2
SDS at surface
6.2 X 10” 6.15 X 10” 5.5 x 104 5.0 X lo4 5.0 X 10”
0 0.02 0.19 0.35 0.35
decanol molecule. There are two contributions to the scattering length density of the layer: a large positive contribution from the deuteriated alkyl chain and a much smaller contribution from any water incorporated into the layer. Thus the highest reflectivity is obtained from a complete dodecanol layer and therefore occurs at the lowest concentration of the impure surfactant. As SDS replaces dodecanol at the surface the reflectivity will fall to a limit corresponding to that for a scattering length density of about half the initial value. This limit will be reached when all the dodecanol has been incorporated into micelles, which according to the surface tension measurements should be at about the cmc. The calculated and observed data are shown for the lowest concentration studied in Figure 5a. Once again the enormous effect of the adsorbed layer on the reflectivity can be seen by comparison with the profile of the solvent (the same as in Figure 3). A slab model was used to fit the data, the layer thickness was taken to be 20 A, and the scattering lengths found at different concentrations are given in Table I. The uncertainty in the determination of the scattering length density is small, about 0.1 x lo4 A-2, if the thickness of the layer is assumed constant. If the thickness of the layer is allowed to change from concentration to concentration, then the uncertainty in the scattering length density is larger. However, the overall result is always that the amount of deuteriated material at the surface falls in proportion to the values of the scattering length density given in Table I.
826 Langmuir, Vol. 4, No. 4 , 1988
We can estimate the proportion of SDS in the monolayer as follows. The scattering length density of the complete dodecanol monolayer is 6.2 X lo4 A-1, close to the value for liquid dodecanol, indicating that there is no water incorporated into the monolayer. From the values of the surface excess for SDS given about, the scattering length density of a complete SDS layer should be about 2.5 X lo* AT2. Thus the scattering length density of the mixed layer is 6.2(1 - x) + 2 . 5 ~A-2, where x is the volume fraction of SDS in the layer. Values of x are given in the last column of Table I. Even though the highest concentration used is only about half the cmc of SDS, an appreciable amount of dodecanol must be being solubilized at this concentration to explain the significant adsorption of SDS at the surface.
Conclusion The results presented in this paper demonstrate a number of features about the specular reflection of neutrons from surface layers of solutions. As anticipated in ref 1,the presence of an adsorbed layer is readily detected, especially if suitable isotopic substitution is made. At low values of the momentum transfer, K , such that Kt
