J. Phys. Chem. 1989, 93, 381-388
;
I\
in the clay. These bands are assigned to twisting motion of the five-membered rings and could arise from interactions with the O H groups extending into the clay interlayer.
!I h 2 8 , ,
I
-
(b) 60
JLVLkI
w
&Q-
381
Raman shift (cm-1)
-7i50.o--
1 00.0
Figure 7. (a) Raman spectrum and (b) X-ray diffraction Pattern of nickel(I1) phthalocyaninetetrasulfonate exchanged [A12Li(oH),]+.
-
phthalocyanines are parallel to the aluminate layer and not arranged in a stacked fashion (spacing 17 A). The arrangement of such a large molecule in the interlayer spacing is of interest and indicates the potential for novel ion exchange into these materials. The resonance Raman spectrum is shown in Figure 7a. This resembles the published spectrum of phthalo~yanine,~~ except for shift of bands at 512,608, and 664 cm-' to 520,598, and 653 cm-I (32) Bovill, A. J.; McConnell, A. A.; Nimmo, J. A.; Smith, W. E. J . Phys. Chem. 1986, 90, 569.
Conclusions The vibrational spectra of the A12Li(OH)6+framework exhibit bands characteristic of the A106 and OH groups. A D3 site symmetry for the A106 group has been proposed. The Raman spectra of the anions intercalated into the clay layers also provides information about the siting and interaction with the clay. Incredible selectivities toward ion exchange were discovered for the higher charged species in a series of oxyanions, e.g., Po43-> HP042-> H2PO4-. Organic anions can also be ion exchanged into the clay, and it was found that benzoate ions can stack up in an arrangement perpendicular to the aluminate layer. This study illustrates that the anionic clays provide opportunities for diverse chemistry complementary to that of the extensively studied cation-exchange materials. Acknowledgment. We gratefully acknowledge the support provided by the National Science Foundation (CHE-8510614). We also thank Dr. Umit Ozkan for doing the BET measurements on the clay. Registry No. [A12Li(oH),]+,117872-71-6;NO,-, 14797-55-8;SO,", 14808-79-8;PO:-, 14265-44-2; HPO:-, 14066-19-4;H2P04-. 1406620-7; C~HSCOO-,766-76-7; Fe(CN),&, 13408-63-4; [A12Li(OD),]+, 1 17872-69-2; nickel(I1) phthalocyaninetetrasulfonate, 102497-93-8; [A12Li(OH),]C1,68949-09-7; [A12Li(OH)6]N03,117872-70-5; [A12Li(OH6]2S04, 117872-72-7; [A12Li(OH)6].C6HIC00, 117895-85-9; [A1,Li(oH),].'/4Fe(CN),, 117895-84-8.
Structure of Aqueous Decyltrimethylammonium Bromide Solutions at the Air/Water Interface Studied by the Specular Reflection of Neutrons E. M. Lee, R. K. Thomas,* Physical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford, OX1 3QZ England
J . Penfold, and R. C. Ward Rutherford-Appleton Laboratory, Oxford, OX1 3QZ England (Received: March 18, 1988; In Final Form: June 13, 1988) The technique of specular reflection of neutrons has been used to investigate the adsorption of decyltrimethylammonium bromide (DTAB) at the aqueous solution/air interface over the concentration range 0.002-0.1 M. Hydrogen-deuterium substitution in both surfactant and solvent has been used to highlight different features of the adsorbed layer and to distinguish between solvent and solute in this layer. At the lowest concentration the thickness of the adsorbed layer is 16 & 3 A, indicating that the molecules are aligned with the long axis perpendicular to the interface. At a concentration of 0.05 M, where the monolayer is essentially complete, the thickness is found to be 21 & 1 A. This suggests that in the more closely packed monolayer the head groups, which carry a positive charge, may be "staggered" in order to minimize their mutual repulsion. A detailed analysis of the structure at 0.05 M indicates that the layer may be divided into two regions: a head group region, 6 8,thick, containing the trimethylammonium head group, counterion, water, and about 10% of the alkyl chain tails; and a tail group region, 15 A thick, containing only tail groups. The area per molecule of surfactant at the saturated monolayer is found to be 58 f 5 A2.Above the critical micelle concentration (0.065 M) the structure of the interface is more complex. The monolayer itself is some 15% more dense than the saturated monolayer formed below the cmc. The shape of the reflectivity profile is shown to be consistent with some ordering of the micelles beneath the surface, separated from the monolayer by a thin layer of water, which contains no surfactant and which has a density more akin to that of water in hydrates. Mixtures of DTAB and sodium decanoate have also been investigated. Equimixtures of the two oppositely charged surfactants are much more strongly adsorbed than either of the two individual components. Even at the low total concentration of 0.01 M the area per surfactant molecule of the mixed monolayer is 36 AZ compared with 73 A2 for 0.01 M DTAB alone.
Introduction It has been shown in two earlier papers how the specular reflection of neutrons may be used to determine the structural .. properties of adsorbed layers at the air/water interface.'J In this paper we apply the technique to the determination of the *Towhom correspondence should be addressed. 0022-3654/89/2093-0381$01.50/0
structure of a decyltrimethylammonium bromide (DTAB) layer adsorbed at the air/water interface. DTAB was chosen for two (1) Hayter, J. B.; Highfield, R. R.; Pullman, B. J.; Thomas, R. K.; McMullen, A. I.; Penfold, J. J. Chem. Soc. Faraday Tram, I 1981,77, 1437. (2) Bradley, J. E.; Lee,E. M.; Thomas, R. K.;Willatt, A. J.; Gregory, D. P.; Penfold, J.; Ward, R. C.; Waschkowski, W. Lungmuir 1988, 4, 821.
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reasons. Firstly, it is very soluble in water so that it is easy to follow the structure of the air/solution interface over a wide range of conditions both above and below the critical micelle concentration (cmc). Secondly, we are studying the structure of black films formed from a mixed solution of DTAB and sodium decanaoate and we need information about the structure of the respective monolayers and the mixed monolayer in order to understand the structure of the films.
Experimental Details The reflectivity measurements were done on the reflectometer CRISP at the neutron spallation source ISIS, at the Rutherford-Appleton Laboratory in England. The instrument has been described in full e l ~ e w h e r e . ~ CRISP was built to measure the reflectivity of a wide range of systems. It has a horizontal scattering geometry specifically for the investigation of liquid samples. Neutrons impinge on the sample at a f i e d glancing angle of incidence, which may be chosen in the range 0.25-1.5O. The neutrons reflected from the sample are measured at the specular angle by a single detector. The incident neutron beam contains neutrons of wavelengths from 0.5 to 6.5 A, which are analyzed by time of flight. The reflectivity is determined by ratioing the reflected neutrons at each wavelength to the number incident on the sample, measured by a monitor in the incident beam. For the work described in this paper the incident angle was set at 1.5' and the beam dimensions were 4 mm high and 40 mm wide. At an angle of 1 . 5 O the neutrons illuminated an area of sample 160 X 40 mmz. The sample was contained in a Teflon trough 5 mm deep with a liquid surface area of 200 X 80 mm2. The trough was cleaned initially by prolonged soaking in heptane, followed by overnight soaking in a mixture of 4% HF in concentrated H N 0 3 . It was then rinsed in ultrapure water (Elgastat UHQ, Elga, U.K.). Between each measurement the trough was cleaned with 4% H F in concentrated H N 0 3 , followed by rinsing in ultrapure water. It was enclosed in an airtight aluminum container with soda glass windows, which are reasonably transparent to 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 40 kg) reduced vibrational contributions to a level where no vibrations of the surface could be detected in reflected laser light at a distance of about 2 m from the surface. The liquid surface was aligned in the neutron beam by means of a laser, w u c h could be placed in the beam, and by adjusting the level of the float by varying the amount of oil in the outer container. Four isotopic species of DTAB were used. The fully protonated form was obtained from BDH, and the partially deuteriated forms were made bv direct reaction of decvl bromide and trimethvlamine. The protonated materials were obtained from BDH h d the deuteriated ones from Merck, Sharp, and Dohme. The raw' material was washed with hexane and recrystallized from acetone/methanol following the procedure described by M i n g i n ~ . ~ 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 Leknere5 Thus, any method that has been used for calculating optical reflectivities can be applied to the reflection of neutrons. In this paper we generally use the optical matrix method,6 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 systems studied here there is no (3) Penfold, J.; Ward, R. C.; Williams, W. G. J . Phys. E 1987, 20, 141 1. (4) Mingins, J.; Owens, N. F.; Iles, D. H.J . Phys. Chem. 1969, 73,2118. (5) Lekner, J. Theory of Reflecrion; Martinus Nijhoff: Dordrecht, 1987. (6) Born, M.; Wolf, E. In Pinciples of Uprics, 5th 4.; Pergamon: Oxford, 1975; pp 51-72.
practical restriction on the number of elements into which the interface may be divided. The advantage of neutrons or X-rays over light is that the refractive index is simply related to composition. For neutrons 7
= 1 - (P/27r)ps
where p s is the scattering length density given by pS =
Cnbi
where n, is the number density and bi the empirically determined scattering length of the nucleus i. Thus, by use of the optical matrix method, the reflectivity profile can be calculated exactly for any model of the interfacial cornpition. 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 further in the analysis of the results. An important feature of the specular reflection of neutrons is that the scattering lengths of D and H , and as a consequence the scattering length densities of DzOand HzO, are of opposite sign. It is therefore possible to make an HzO/DzO mixture that has the same scattering length density as air and therefore gives no specular reflection at any angle. The molar ratio of DzO to HzO in this mixture is 0.088. We will refer to it as contrast matched water. At low concentrations of solute in contrast matched water, such as used in these experiments, the contrast of the bulk solution remains sufficiently close to that of air for there to be negligible specular reflection unless the solute is adsorbed at the surface. In practice, the situation is slightly less ideal in that there is an incoherent scattering background because of the large incoherent cross section of protons. However, incoherent scattering is approximately isotropic and is therefore distributed over a large solid angle. In the reflection experiment a narrow acceptance angle is used so that the incoherent background is small, in the region of 5 X lo4. In the present experiments the background consisted mainly of an incoherent component from the sample with a much weaker instrumental component. The total background was measured very accurately by using contrast matched water in the sample position and was subtracted from the raw reflectivity measurement to give the final reflectivity profiles shown in the results section. Separate experiments on an instrument with a multidetector confirmed that there is no specular reflection from contrast matched water. As well as being able to examine the solute profile independently of the solvent, we were able to measure the solvent profile by matching the scattering length density of the solute to that of air. This is approximately achieved simply by using the fully protonated surfactant in D 2 0 .
Results and Discussion The reflectivity profiles of fully deuteriated DTAB in contrast matched water as a function of concentration are shown in ~i~~~~ 1. The critical micelle concentration is 0.065 M.' The formation of a monolayer at the surface of surfactant solutions is usually complete well before the cmc is reached.* Thus, the monolayer should be complete at the highest concentration of 0.05 M studied here. Because solutions of the compositions shown in Figure 1 are close to contrast match, the reflectivities shown arise entirely from adsorption of the DTAB a t the surface. Qualitatively, the slope of a reflectivity profile in this region of momentum transfer is inversely proportional to the thickness of the adsorbed layer. This can be shown by using the kinematic approximation for the reflectivity, which gives R =1 6 ~ ~ m h ( ~ ) / ~ ~ where m is the excess scattering length density integrated over the interfacial region, K is the momentum transfer ( K = 4 1 sin (7) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfactant System; U.S.Department of Commerce: Washington, DC, 1971. (8) Chattoraj, D. K.; Birdi, K. S . In Adsorption and the Gibbs Surface Excess; Plenum: New York, 1984; pp 106-1 10.
The Journal of Physical Chemistry, Vol. 93, No. 1, 1989 383
Adsorption of DTAB at the Air/Water Interface
Figure 2. Specular reflectivity of a 0.05 M solution of fully deuteriated decyltrimethylammonium bromide in contrast matched water. The two calculated profiles are for uniform layers of thickness 19 and 23 A and respective scattering length densities of 2.59 X lod and 2.15 X lod A-2. The lines are distinguished at 0.20 A-1 by the 19-A line being the upper one.
I 0
010
020 0 0IOo Momentum transfer A-'
0 20
I
Figure 1. Observed and calcu!ated specular reflectivity profiles of fully deuteriated decyltrimethylammonium bromide in contrast matched water. The concentrations are (a) 0.05, (b) 0.01, (c) 0.005, and (d) 0.002 M. Continuous lines are the calculated profiles for the model of a uniform layer obtained by using the parameters given in Table I. TABLE I: Parameters of the Fully Deuteriated DTAB Layer concn/M 0.05 0.01 0.005 0.002 17f1 thicknessu/A 21fl 17f2 16f3 2.40 1.85 1.15 p x 106c/A-2 2.38 r x 10IO/M 2.81 2.28 1.77 0.98 area per mole/A2 58 f 5 73 f 7 94 f 10 170 f 20 13f1 13&2 l l f 4 thicknessb/A 1 5 f 1 "For a layer of uniform density. bThe full width at half-height of a Gaussian surface profile. c p is the scattering length density of the uniform layer. O/A), and h(K) is the form factor of the interface? The form factor is the normalized modulus of the Fourier transform of the scattering length density profile of the solute across the interface
h(K) =
lP(K)12/lP(o)12
The thicknesses of surfactant layers will generally be in the range ) be approximately 10-30 A. For layers of this thickness h ( ~will unity in the region of the critical angle, and the critical region therefore contains no direct structural information about the layer. The range of momentum transfer that can be studied in a single experiment on liquids on CRISP is at present restricted. It was selected to attempt to maximize the structural information obtained from the experiment. The range of momentum transfer in Figure 1 is such as to correspond to the initial decay of the form factor. For a constant amount adsorbed this is more rapid the thicker the layer. It can then be deduced approximately from Figure 1 that the layer is thicker at 0.05 M (Figure l a ) than at 0.01 M. The general level of the reflectivity is largely determined by the total scattering length density in the layer. Again, this is clear from the expression above from kinematic theory where m, which is the integrated scattering length density over the interface, determines the overall.leve1 of the reflectivity. Thus, the decreasing reflectivities as the concentration is reduced correspond to decreasing adsorption of the surfactant at the interface. The quantitative analysis of the profiles has been done using the optical matrix method. The fits shown as continuous lines in Figure 1 are for a model of a single uniform layer with the parameters given in Table I. The assessment of the fits has been made by means of the least-squares x2 parameter, although an automatic fitting routine was not used. Figure 2 shows the fits of calculated profiles with thicknesses differing by f 10% from (9)Crowley, T. L.;Thomas, R. K.; Willatt, A. J., to be published.
the best fit shown in Figure 1 for the 0.05 M solution. In each case the fit has been optimized by adjusting the scattering length density of the layer so that the two calculated lines in Figure 2 represent the best possible fit to the data for the two thicknesses given. It is apparent from this comparison that, within the assumption of a uniform layer, we determine both thickness and composition of the layer to an accuracy of about * 5 % at a concentration of 0.05 M. The results are less accurate at the lower concentrations because the errors in the reflectivity are progressively greater as the amount adsorbed at the surface decreases. The final errors are given in Table I. A more realistic model of the surface layer might include both a contribution from capillary waves, which would give a roughness to the air/surfactant interface, and also a gradual change of scattering length density at the surfactant/water interface. The simplest model of this kind is a symmetrical Gaussian distribution: where the peak scattering length density occurs at z = 0 and the full width at half-height is 26(ln 2)1/2. Such a distribution of scattering length density exaggerates the roughness of the two interfaces but is a convenient model to test the sensitivity of the reflectivity profiles to the shape of the adsorbed layer. We have fitted Gaussian distributions and models intermediate between the uniform layer and a Gaussian to the data of Figure 1. The intermediate models consist of a uniform layer with half-Gaussians on either side, characterized by 6, and b2. It always proved possible to fit the data with the Gaussian, and the results of the best fits are included in Table I. The thicknesses quoted are the full widths at half-height of the Gaussian. For intermediate models the thicknesses obtained are also intermediate between the two extreme values given in Table I. Over the range of momentum transfer used here, the experiment cannot therefore distinguish accurately the shape of the distribution. On the other hand, the relative accuracy of the thickness measurement for a given model is extremely good except at the lowest concentration and, in any case, the difference in the thicknesses obtained from the two extreme shapes of the distribution is not large, the Gaussian width being the thinnest value obtained. The scattering length densities given in Table I are proportional to the density of solute in the adsorbed layer. Using the known scattering length of the molecule together with the thickness of the layer, it is possible to calculate the surface excess and the area occupied per molecule. Values of these at each concentration are also given in Table I. In the case of the Gaussian distribution it is necessary to integrate over the whole distribution rather than using just the thickness, but the resulting values of surface excess and area per molecule are sufficiently similar to those obtained from the uniform layer model that they are not included in Table I. The four measurements of surface excess are not sufficient to give a complete isotherm. However, they are plotted in Figure 3 together with the general shape obtained for isotherms for this kind of systems in order to show that it would be possible to obtain
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The Journal of Physical Chemistry, Yo/. 93, No. 1 , 1989
0 01
0 02
0 03
0 04
0 05
I
ClM
Figure 3. Approximate adsorption isotherm obtained for decyltri-
methylammonium bromide at the air/solution interface from neutron reflectivity data. The continuous line has been drawn to have a shape typical of isotherms where a complete monolayer is formed, although it has no definite functional form. the isotherm by this method and to demonstrate that the mono. layer is probably complete by a concentration of 0.05 M. There appear to be no other measurements of the area occupied per DTAB molecule at the airlwater interface. Rijnboutlo has obtained a value of 45 A2 for hexadecyltrimethylammonium bromide. Decyltrimethylammonium bromide is likely to occupy a larger area than this. Haydon and Taylor" have obtained a value of 51 A2 for DTAB at the decane/aqucous solution interface when the solution contained 0.07 M NaCI. This would be expected to be lower than the area occupied at the air/water interface and is therefore qualitatively consistent with our value of 58 A2. The length of the fully extended decyl chain can be estimated to be 14.15 A from relation given by Tanford.lz To this must be added the length of the head group estimated to be 2-3 A. At coverages up to about three quarters of a monolayer the thickness of the adsorbed layer is constant within experimental error at a value very similar to the length of the fully extended molecule. Its value and its constancy down to low wverages show that the molecule is oriented approximately vertically at the liquid surface and that it retains this orientation even when the area occupied per molecule has become large enough for the molecule to adopt a greater range of orientations, although not large enough for the chains to be horizontal on the surface. The layer thickens markedly when the monolayer is completed, although the scattering length densities at 0.01 and 0.05 M a r e the same. The only possible explanation of this is that as the charged head groups are forced into a smaller area their mutual electrostatic repulsion causes them to adopt the staggered configuration shown in Figure 4a. The vertical orientation of the chains at the surface and the staggering of the head groups in the completed monolayer can be established in a different experiment. The protonated alkyl chain has a scattering length density close to that of air. Thus, the reflectivity profile of the isotopic species with protonated chain and deuteriated head group in contrast matched water will he determined only by the surface profile of the trimethylammonium head groups. Correspondingly. that of the species with deuteriated chain and protonated head group will depend only on the surface profile of the alkyl chains. The reflectivity profiles of the three species dDdTAB, dDhTAB, and hDdTAB at a concentration of 0.05 M in contrast matched water are shown in Figure 5. The slope of the reflectivity of the dDhTAB solution is steeper than for the dDdTAB solution, showing that the layer is indeed thinner when the head group no longer contributes to the reflectivity. When the data are fitted by using the model of the uniform layer, the thickness is reduced from 21 A for dDdTAB to 17 A for dDhTAB, while the area occupied per molecule remains the same, (IO) Rijnbaut. I. B. J. Colloid Inrc@eSci. 1977, 62. 81. (11) Haydon, D.A.:Taylor, F. H.,Trom. Forodnysoc. 1962.58. 1233. (12) Tanford. C . 1. J. Phys. Chem. 1972, 76,3020.
I
156
8 5A
Figure 4. Distribution of water and decyltrimethylammonium molecules at the air/solution interface. (a. b) Configuration of decyltrimethylammonium bromide molecules within the adsorbed layer at (a) 0.05 M and (b) 0.01 M or less. (c) Full structure of the layer at 0.05 M deduced from isotopic substitution measurements.
0
0 10 0.20. Momentum transfer A-'
Figure 5. Observed and calculated spsular reflectivity profiles of isotopic species of 0.05 M decyltrimethylammonium bromide in wntrast matched water. In order of decreasing reflectivity the isotopic species are dDdTAB, dDhTAB. and hDdTAB. The continuous lines are profiles calculated for the uniform layer model by using the parameten given in Table I1
TABLE II: Sbuehlnl Pannetem of Adsorbed dDbTAB wncn/M 0.0s 0.01 0.005 17f1 15f2 15*2 2.05 1.65 1.35 area per mole/A2 58 82 100
$?$;
.The thickness is based on the model of a uniform layer.
as it should do. At lower concentrations, for which the reflectivities are not shown here, the change in thickness on isotopic substitution is smaller, as shown in Table 11. The areas per molecule obtained for the more dilute solutions of dDhTAB are larger than for the corresponding solutions of dDdTAB hut are within the experimental error of about 15%. These measurements confirm both that the molecule is oriented approximately vertically at the interface and that the head group is more diffusely distributed in the direction normal to the interface at the higher coverage.
The Journal of Physical Chemistry, Vol. 93, No. 1, 1989 385
Adsorption of DTAB at the Air/Water Interface
TABLE III: Structural Parameters of the Adsorbed Layer at 0.05 M region A/8, region B/8, tail fraction in A p(A) X 106/A-2
p(B) X 106/8,-2
dDdTAB
dDhTAB
6 15 0.1 3.16 2.14
6 15 0.1 0.46 2.14
hDdTAB 6
15 0.1 2.53 -0.13
The reflectivity of the hDdTAB is much lower than for the other two isotopes and results in the reflected signal dropping into the background level a t quite low values of the momentum transfer. The effect is that it is not possible to extract from these data an independent value of the head group thickness. However, even if, as in this case, a particular isotope cannot give an independent measurement of some feature of the layer, the information it gives is still important. This is because any chemical structure proposed for the layer must be the same for all isotopes (to a good approximation). The more isotopic variations that can be measured, the more constraints that are put upon the proposed model, leading to a better definition of the structure of the layer. This is the most important feature of the technique of contrast matchingg and is well-illustrated by the present set of data. We now show that the process of fitting a chemical model of the interface to three independent measurements on different isotopes yields more information than is possible to obtain from any one isotope alone. It is impossible to fit the hDdTAB profile at 0.05 M with the double constraint of a uniform layer model and a surface area per molecule of 58 K2. This simple model of the structure must therefore be wrong. The next simplest model would be to divide the layer into two uniform regions; region A, nearer the bulk solution and containing all the head groups and a fraction Ft of the tails, and region B, containing the remaining fraction (1 - Ft) of the tails. Since all three sets of data were obtained for contrast matched water, we can neglect the solvent because it makes no contribution to the reflectivity. With this two-layer model we can fit all three reflectivity profies at 0.05 M with a layer of overall thickness 21 8,. Good fits are obtained over a range of values for the thickness of the head group region ( A ) of 4-8 A, Ft being suitably adjusted. Taking the value in the middle of the range, we obtain a thickness of 6 f 2 A with a tail fraction of 0.1 f 0.06. This value is also consistent with the overall change of 4 8, in thickness of the dDdTAB layer on going from 0.05 to 0.005 M. Thus, if this is interpreted as a transition from a rough to a smooth layer, the thickness of the head group region must be 4 8, plus the thickness of the actual head group, which is about 2-3 giving a total of 6-7 8,. The parameters for the best fits to all three isotopes at 0.05 M are given in Table 111. The small fraction of tails in the head group region shows that the head and tail groups are quite well segregated in the layer. It could be argued that even this two-layer model oversimplifies the structure of the interface. However, there is no point in introducing a more complex model that goes beyond the resolution of the experiment. Also, any greater complexity is more likely to result from the water distribution throughout the layer. This makes no contribution in the case of solvent contrast matched to air. We consider the water distribution separately when we examine the reflectivity of the fully protonated isotope in D20. It is interesting to compare the geometrical parameters obtained for the monolayer with those of alkyltrimethylammonium bromide micelles, obtained by neutron small-angle scattering. Several measurements have been All are agreed that the head groups form a “smooth” layer of thickness 2-3 8,. At first sight, this might be thought to disagree with our result that the complete monolayer is “rough”. However, the area occupied by a head group in the micelle is close to 65 A2. This is half way between the areas of 58 and 73 A2 where our measurements give “rough” (13) Hayter, J. B.; Penfold, J. Colloid Polym. Sci. 1983, 261, 1022. (14)Tabony, J. Mol. Phys. 1984, 51, 975. (15)Berr, S.S.;Caponetti, E.; Johnson, J. S.; Jones, R. R. M.; Majid, L. J. J . Phys. Chem. 1986, 90,5766. (16)Berr, S.S.J . Phys. Chem. 1987, 91,4760.
0
0.10 0.20 Momentum transfer A-’
Figure 6. Observed and calculated specular reflectivity profiles for (a) 0.005 M dDhTAB, (b) 0.005 M sodium decan~ate-d~~, and (c) 0.005 M in each of dDhTAB and deuteriated sodium decanoate, all in contrast
mathced water. Continuous lines are for the uniform layer model with respective thickness and scattering length density of (a) 15 8, and 1.35 and (c) 17 A and 3.33 X lod X IO4 (b) 17 8,and 1.77 X lo4 A-2.
and “smooth” layers, respectively. Hayter and Penfold13obtained a value of about 21 8,for the radius of ClzTABmicelles. Allowing for the extra two methylene groups, the comparable value for DTAB would be 18.5 8,. This is intermediate between our values for “smooth” and “rough” monolayers. Given that they find that the head group region is “smooth“, the appropriate comparison is with our value of 17 A, in which case the agreement is quite good. It should be noted that the reflection experiment is more sensitive to the structure of the layer both because it does not depend on assumptions about a model of micellar interaction and because it is a higher resolution experiment, the measurements being taken to a higher value of momentum transfer. That electrostatic repulsion causes the staggered structure of the head groups shown in Figure 4a can be indirectly confirmed in another way. For a layer consisting of a mixture of surfactants of opposite charge but the same overall length, it would be expected that the head groups would lie in the same horizontal plane forming a “smooth” layer because the electrostatic repulsion has been replaced by electrostatic attraction. Figure 6 shows the reflectivity profiles of 0.005 M dDhTAB, 0.005 M sodium decanoate-d2,, and a solution 0.005 M in each surfactant, all in contrast matched water. Once again the continuous lines are the fits of the uniform layer model to the data. The parameters for the calculated profiles are those of Table I1 for dDhTAB and, for the others, a thickness of 17 A with scattering length densities corresponding to areas per molecule of 69 and 36 A2,respectively. The mixed solution has a much higher surface excess than the complete DTAB monolayer, but its thickness is unchanged from those of the dilute layers of each of the components. Note that the area per molecule in a 0.01 M solution of dDhTAB is 82 A’. The electrical repulsion has therefore been removed by having a mixture of opposite charges, and the head groups are now at the same height in the surface layer, in a configuration of the type
386 The Journal of Physical Chemistry, Vol. 93, No. I, 1989 L
i
I
Lee et al. in which case the reflectivity at low K is again diminished relative to the sharp interface by the factor exp( -u22) where u is now 0.466, and 6 is the half-width of the distribution describing the decay of the density across the i n t e r f a ~ e .Over ~ the range of momentum transfer of these experiments the two contributions cannot be distinguished by measuring the specular reflection alone. Indeed, it may not be possible to distinguish them either theoretically or experimentally. We have fitted the pure D 2 0 profile in Figure 7 with a value of 6 of 6.8 A. While we do not consider this an accurate value a t this stage of development of the techni ue, it is nevertheless in close agreement with the value of 3.3 determined for u for H20by X-ray reflection.I7 The protonated surfactant decreases the reflectivity of the D 2 0 significantly. Since the scattering length density of the protonated surfactant is close to that of air, this decrease must largely be determined by the distribution of the D 2 0 in the surface region. The measurement is therefore complementary to those using deuteriated surfactant and contrast matched water. The distribution of D 2 0 in the layer must be consistent with the twdayer model used to fit the reflectivities of the three isotopic species of surfactant in contrast matched water. Thus, in the head group region, region A, the available volume is 58 X 6 A3. This will contain the head groups, counterions, and water, whose volumes are expected to be approximately 120-150, 30, and 30 A3, respectively. Thus, in the head group region there are a proximately 6-7 molecules of water in a layer of thickness 6 Taking this layer to be uniform gives it a scattering length density of about 4 X IO” A-2. The fit of such a model to the reflectivity profile of hDhTAB at 0.05 M in D 2 0 is shown in Figure 7b. It can be improved slightly by replacing the uniform layer by a half-Gaussian distribution containing the same total amount of water and with a half-width varying in the range 3-6 A. An alternative is that water may also fill the dead volume in the tail group re ion, region B. The volume available in this region is of which about 300 A3 is the volume of the alkyl tail 58 X 15 itself. There is therefore room for about 30 molecules of D 2 0 per surfactant tail. If this is now included, the calculated reflectivity profile is quite different from that observed, as shown in Figure 7c. Furthermore, this cannot be improved sufficiently to fit the data by replacing the two uniform layers with Gaussian distributions of the scattering length density profile. The problem with including this amount of water in the tail group region is simply that, whatever its distribution, it depresses the reflectivity far too much. We therefore conclude that there is little or no water in the tail group region, although the fit to the data shown in Figure 7b is not totally convincing. The tail group region then consists of the alkyl chains and air as shown in Figure 4c. This does not mean that the layer literally consists of fully extended chains separated by air sticking out into the vapor phase. It probably means that the chains form a liquidlike layer with large-amplitude fluctuations in their distribution normal to the surface. Little is known about the structure of the interfacial region of surfactants above the cmc. Radiotracer measurements indicate that a monolayer of surfactant is still present. The Gibbs equation becomes almost impossible to apply above the cmc making it difficult to deduce anything directly from surface tension measurements. That a monolayer is still present is demonstrated by the reflectivity profile of 0.091 M hDdTAB in contrast matched water. The reflectivity at this concentration is higher than at 0.05 M, and if it is assumed that the thickness of the layer is unchanged, fitting of the data with the uniform slab model gives an area per molecule of 50 A2, lower than for the monolayer below the cmc. Thus, a monolayer about 15% more concentrated than below the cmc is present. The reflectivity of a 0.1 M solution of hDhTAB in D 2 0is shown in Figure 8a. For comparison the calculated profile for perfectly sharp D 2 0 is also shown. The experimental profile of pure D 2 0 lies below the calculated profile for sharp D 2 0 so the reflectivity of the solution is substantially greater than observed for D20. This
w
1;
Momentum t r a n s f d ’
Figure 7. Calculated and observed specular reflectivity profiles of (a) D20 and (b, c) a 0.05 M solution of fully protonated decyltrimethylammonium bromide in D20. The calculated profile for D20is for a roughness ( u ) of 3.1 A. The dashed line is the calculated profile for
perfectly smooth D20.The calculated profiles for hDhTAB are (b) for water in the head group region only and (c) for water in both head and tail group regions. shown in Figure 4b rather than in Figure 4a. The density of the surface layer of the completed monolayer of DTAB is lower than would be estimated for a layer containing only DTAB. This is not surprising because the staggering of the head groups creates some dead volume which must presumably be filled with water. The experiments with the deuteriated surfactants in contrast matched water give no direct information about the amount of water incorporated into the layer because it has zero scattering length density. However, it is possible to determine how much water is in the layer by measuring the reflectivity of protonated DTAB, which has approximately the same scattering length density as air, in D 2 0 . The profiles of pure D 2 0 and of a solution of 0.05 M hDhTAB in D 2 0 are shown in Figure 7. The profile of pure D 2 0 shows the effects of “roughness” of the surface. This causes the reflectivity to fall increasingly below the value for a perfectly sharp interface as the momentum transfer increases. There are two possible contributions to this “roughness”. The first is from capillary waves. This decreases the reflectivity by the factor exp( -2K2) where u is the mean-square amplitude of the capillary wave~.~J’ The second contribution a r k from the finite width of the interface where the density falls from its value in the liquid to its value for the vapor. The density profile over this region could be described by, for example, a half-Gaussian profile P(Z) = Apo z 0 p ( z ) = Apo exp(-z2/62)
z
>0
(1 7) Braslau, A.; Deutsch, M.; Pershan, P. S.; Weiss, A. H.; Als-Nielsen, J.; Bohr, J. Phys. Reu. Lett. 1985, 54, 114.
i3,
jl; y
Adsorption of DTAB at the Air/Water Interface
;10-L E
1o
-~
'\
1
0 10 0 20 Momentum transferk'
0.10 0 29 Momentum transferlA-'
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Figure 8. (a) Observed and calculated specular reflectivity profiles of a 0.1 M solution of fully protonated decyltrimethylammonium bromide in
D20. The calculated profile is for the interfacial structure shown in (c). (b) Ratio of the observed reflectivity in (a) to the calculated reflectivity of perfectly smooth D20. The continuous line is calculated for the structure shown in (c). (c) Scattering length density profile of the interfacial region of a 0.1 M solution of hDhTAB in DzO. is shown more clearly in Figure 8b where we plot the ratio of the reflectivity of the solution to that of DzO with a perfectly sharp surface. Kinematic theory shows that the plot of Figure 8b is the form factor, h(K),of the interfacial regions, for which an expression has already been given above. For a uniform layer on the surface ) the shape it is easy to show that h ( ~has
h(K) = 1 - 4A(1 - A ) Sin2 ( K t / 2 ) where A is the scattering length density of the layer relative to that of the solution and t is the thickness of the layereg This formula gives a periodic variation of h(K) with a phase that is determined by the value of A . If A is positive and less than one, then h(K) initially drops below one to a minimum value of {I 4A( 1 - A ) ) at K = t / ? r . If A is greater than one, h(K) initially rises to a maximum. To account for the reflectivity ratio shown in Figure 8b, there must be either a layer at the surface for which A = 1.2 and the thickness is 15-20 A or one of the same thickness but with A N -0.2. Since A is measured relative to the solution, these two possibilities correspond to scattering length densities of about 7.7 X 10-6 or -1.3 X 10" A-z, respectively. It is impossible to achieve such a large negative scattering length density in any isotopic solution of these materials so the observations shown in Figure 8b can only be explained by the presence of a layer of significantly higher scattering length density than that of DzO. The scattering length density of the protonated monolayer can be estimated from the corresponding measurement on the partially deuteriated monolayer at the same concentration, which has already been discussed above. It is small and therefore makes no significant
The Journal of Physical Chemistry, Vol. 93, No. I, 1989 387 contribution to the reflectivity. The most likely explanation of the layer with the large scattering length density is that it is the layer immediately below the surfactant monolayer from which the weakly scattering surfactant is likely to be excluded. A full calculation of the reflectivity profile using the optical matrix method confirms the broad conclusions from the kinematic theory and gives a best fit to the data with the following parameters: (i) a monolayer of thickness 21 A and area per molecule 50 AZ(this is essentially the structure found below the cmc but with the surface density increased by 1.15); (ii) a layer below the monolayer of thickness 15 A and scattering length density 7.1 X lod A-z; (iii) a third layer of thickness 25 8,and scattering length density 5.9 X 10" A-z. Fits of this structure to the reflectivity profile are shown in Figure 8a,b, and the actual structure is shown in Figure 8c. The fit is not very sensitive to the parameters used for the monolayer so the main conclusion must be that the other two layers bath exist with the parameters shown. Before discussing the uniqueness of this fit to the data, we consider its implications. The scattering length densities of the individual components of the solution are such that, according to this model, the structure of the interfacial region immediately above the cmc consists of a monolayer of surfactant, slightly more concentrated than below the cmc, a layer about 15 8, thick consisting only of water and counterions, and a further layer of about 25-A thickness, containing a significantly higher concentration of surfactant than the bulk solution below the water layer. The aqueous layer, from which surfactant is excluded, contains a high concentration of bromide counterions. Their contribution to the scattering length density of this layer can be estimated from the density of surfactant molecules in the monolayer, since there must be one ion for each surfactant in the monolayer. There will also be an excess of Brions from the presence of excess micelles in the region below the water layer. The maximum number of Br- ions in the water layer (two per surfactant molecule in the monolayer) gives an approximate maximum contribution of the bromide ions to the scattering length density of the water layer of 0.18 X 10" A-'. This can only account for a small part of the anomalously high scattering length density of 7.1, to be compared with 6.38 X 10" A-2 for bulk DzO.This suggests that the density of this water layer near the surface is 9% greater than for bulk water. This is a surprising result. Electrolyte solutions show a decrease in the molar volume of water of typically less than 5%.18 On the other hand, the effective molar volume of water in typical salt hydrates (assuming the ion to be the same size in hydrated and anhydrous salts) is anything up to about 25%. The minimum concentration of water in the layer is estimated to be approximately eight molecules of water per ion (either Br- or N%+). It therefore seems likely that a significant fraction of the water in this layer is specifically hydrating the Br- and NR4+ions. There appear to be no other results of any other kind that give indications one way or the other of such an effect. Surfactant is excluded from the water layer. This can be regarded as negative adsorption of micelles from the surface region. This is not surprising because of the repulsive forces between the similarly charged monolayer and micelles. However, the composition and thickness of this micellar layer deserve some comment. The thickness is just over half the value expected for a micelle. The volume fraction of the layer occupied by surfactant is 7%, about 3.5 times that in the bulk. The area occupied per micelle in this layer can then be estimated to be about 6400 AZ.It seems likely that the distribution of micelles in this layer is best described as resembling the first peak in the radial distribution of micelles in a concentrated micellar s01ution.l~ Starting at the interface between monolayer and solution and proceeding into the solution, there is first a region from which micelles are excluded; their distribution then rises to a maximum before falling to the bulk value. If the concentration of micelles in the layer is not high, as observed, the effective thickness of the micellar region for ~~
(18) Sohnel, 0.;Novotny, P. Densities of Aqueous Solutions of Inorganic Substances; Elsevier: Amsterdam, 1985.
388
J . Phys. Chem. 1989, 93, 388-392
reflection may well be less than the full diameter of a micelle.
Uniqueness of the Interpretation of Reflectivity Data The interpretation of the reflectivity profiles of the protonated surfactant in D 2 0 above the cmc raises the question of the uniqueness of the interpretation. This question is discussed in full in ref 9, and we therefore only discuss it briefly here. It can be seen from the equation for the form factor, h(K), given above that phase information about the Fourier transform of the surface structure is lost in the reflectivity measurement. In addition, there may be ambiguities arising from the truncation of the measurement at a finite value of K . The effect of these two contributions is that it may be possible to fit more than one structural model to the observations. An illustration has already been given above for the profile above the cmc, where one alternative would have required an impossible value of the scattering length density. Other quite sensible physical models can only be eliminated by calculating their reflectivity profiles and comparing them with the data. We have therefore attempted to fit this one reflectivity profile using a number of possible models. For example, we have been unable to fit the data with (i) multilayer structures including a surface monolayer, (ii) a model of hemimicelles actually occupying the surface layer, and (iii) a micellar layer just below a layer of water at the surface. In the general case, there will be a number of constraints on the interpretation. An example was given earlier in the discussion of the reflectivity profiles of the three different deuteriated isotopes in contrast matched water, where the same chemical structure had to account for all three reflectivity profiles. A further example, although not shown explicitly in this work, is that the surface coverage of a surfactant can generally be determined independently of the reflection experiment and any changes in the reflectivity with coverage must then be consistent with the known adsorption isotherm. A final but important constraint is that any proposed structure must not deviate too far from chemical intuition. For example,
enough is presumed known about surfactant solutions that it would have been unreasonable to try to fit structures of the surfactant monolayer where the charged head groups were oriented outward toward the vapor phase. Such a constraint is seldom mentioned explicitly.
Conclusions These experiments show how sensitive the specular reflection of neutrons is to structure at the surface of liquid solutions. Some of the possibilities of using contrast variation have been illustrated. Although some contrast variation is possible in the comparable X-ray reflection technique by variation of the incident wavelength, it is not possible with X-rays to eliminate altogether the reflectivity from either solvent or solute, as has been done here. On the other hand, the X-ray technique would be more sensitive to the ionic structure at the interface. The clearest conclusion from the present work is that the monolayer changes its structure from a smooth layer with the head groups all in the same plane to a roughened layer where the head groups are spread over a range of thicknesses, at a coverage between 0.85 and 1.O monolayer. This changeover presumably results from electrostatic repulsion. Such a roughened layer does not occur in micellar solutions of related alkyltrimethyl bromides because the area occupied by the head groups always remains above the value in the monolayer at a coverage of 0.85. The other interesting result is the enhancement of the reflectivity of D 2 0 when protonated surfactant is added at a concentration above the cmc. This implies that there is a layering of the surface region, which has not previously been observed. Further experiments on other surfactants will be needed to establish the exact nature and cause of this effect. Acknowledgment. This research was supported by the Science and Engineering Research Council and Unilever Research, Port Sunlight. Registry No. DTAB, 2082-84-0;sodium decanoate, 1002-62-6.
Muonium and Free-Radical Ylelds As Determined by the Muon-Levei-CrossingResonance Technique in Aqueous and Micelle Solutions of Acryiamide Krishnan Venkateswaran, Mary V. Barnabas, Robert F. Kiefl, John M. Stadlbauer,’ and David C. Walker* Departments of Chemistry, Physics and TRIUMF, University of British Columbia, Vancouver, B.C., V6T 1 Y6, Canada (Received: May 4, 1988)
Muonated free radicals that form in pure unsaturated organic compounds are also found to occur in dilute aqueous micelle solutions of these compounds, where thermalized muonium atoms are the only possible precursors. For 2 X lo4 M acrylamide solutions in pure water, the fractional yield of the CH2(Mu)CHCONH2radicals is observed by LCR to be 0.2 (consistent with the muonium yield by WSR). The Mu radical yield increases with acrylamide concentration until at -0.2 M it equals 0.38, which, along with the fraction of muons in a diamagnetic environment,account for the entire muon polarization. Hyperfine coupling constants of the protons in the CH2(Mu)CHCONH, radical have also been determined.
Introduction The development of the muon-level-crossing-resonance(LCR) technique’ and its application to free radicals in unsaturated organic compounds2 allows the products of muonium reactions occurring on the microsecond time scale to be ~ b s e r v e d . ~ ”A radio frequency (rf) resonance method has also been demonstrated ‘Department of Chemistry, Hood College, Frederick, MD 21701.
0022-3654/89/2093-0388$01.50/0
to do this,’ although the LCR method has the advantage of not requiring an rf field. Prior to these developments, muonated (1) Kreitzman, S . R.; Brewer, J. H.; Harshman, D. R.; Keitel, R.;Williams, D. Ll.; Crowe, K. M.; Ansaldo, E. J. P ~ Y SRev. . Lett. 1986, 56, 181. (2) (a) Kiefl, R. F. Hyperfine Interact. 1986, 32, 707. (b) Kiefl, R. F.; Kreitzman, S. R.; Celio, M.; Keitel, R.; Brewer, J. H.; Luke, G. M.; Noakes, D. R.;Percival, P. W.; Matsuzaki, T.; Nishiyama, K. Phys. Rev. A 1986, 34, 681.
0 1989 American Chemical Society
