Langmuir 1993,9, 1352-1360
1352
Direct Determination by Neutron Reflection of the Structure of Triethylene Glycol Monododecyl Ether Layers at the Air/Water Interface J. R. Lu, E. M. Lee, and R. K. Thomas' Physical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, England
J. Penfold Rutherford-Appleton Laboratory, Chilton, Didcot, Oxon OX11 ORA, England
S . L.Flitsch Dyson-Perrim Laboratory, South Parks Road, Oxford OX1 3QY, England Received August 28,1992. In Final Form: February 9,1993 Neutron reflectivity with isotopic substitution has been used to determine directly the structure of triethylene glycol monododecyl ether adsorbed at the air-water interface. The surface excess has been measured from concentrationsranging from twice the critical micelle concentration (cmc) (-5.5 X 10-5 M)to one fiftieth the cmc. The results are in good agreement with thosefrom surface tensionmeasurements and show that the area per molecule tends to a limiting value of 36 A2. The structure of the adsorbed layer has been determined at four concentrations: cmc, 0.2 cmc,0.0545 cmc, and 0.0182 cmc. Two different methods of analysis of the data have been employed. One is the optical matrix method which fits a single structural model to the reflectivity profides from a set of isotopic species at a given concentration and the other is a more direct approach based on the kinematictheory. The two methods give structures identical within experimentalerror. The variation of the thicknesses of the hydrocarbon chain region of the adsorbed layer and the region where solvent has a density less than ita bulk value (approximatelydescribed as the head group region) and the relative locations of chain and water distributions across the surface with bulk concentrationhave been determined. For the saturated monolayer at the cmc the thickness of the chain region is found to be 20 f 1 A, that of the head group region to be 11f 1A, and that of the mean center to center distribution of chains and water to be 10 f 1 A. The number of water molecules associated with each surfactant molecule is 6. At the lowest concentration(0.0182cmc) where the monolayer is at ita most dilute, it is found that the thickness of the whole layer is 15 f 1 A, that of the head regions is 7 f 1 A, and the separation of the two distributions is 5 f 1 A,with the number of water molecules per surfactant now about 10. Comparison of these values with the width of the chain and solvent distributions shows that the immersion of the hydrocarbon chains in the water varies from about 25% at the cmc to 40% at 0.0182 cmc.
Introduction Studies of the structure of surfactant monolayers adsorbed at liquid surfaces have direct implications for a wide range of surface systems including, for example, emulsions, foams, and membranes. Surface tension measurements have traditionally been the main technique employed to study adsorption a t both air-liquid and liquid-liquid interfaces. From the variation of surface tension with surfactant concentration and the assumption of the Gibbs adsorption equation, the area per molecule ( A )can be obtained as a function of surface pressure (TI. The determination of A from surface tension measurementa may give unreliable results because assumptions have to be made about the activities of surfactant and the binding of the counterions and, for some systems, conventional surface tension techniques may suffer from wetting problems.' Also,such measurements can only be made up to the critical micelle concentration (cmc). The surface tension method gives no information concerning the structure of the adsorbed layer. We have recently shown that neutron reflection is a direct method for determining the structure of soluble (1) Simister, E. A.; Thomas, R. K.; Penfold, J.; Aveyard, R.; Binks, B. P.; Cooper, P.; Fletcher, P. D. I.; Lu,J. R. Sokoloweki,A. J.Phys. Chem. 1992,96,1383.
surfactant layers adsorbed at the liquid ~urface.~JThe experiment determinesthe scatteringlength density profile in the direction normal to the interface and, since the scattering length density is directlyrelated to composition, gives information about the composition profile normal to the interface. An important feature of the technique is that isotopic substitution can be used to vary the scatteringlength density and hence the reflectivitywithout changing the chemical structure. This makes it possible, for example, to highlight the adsorbed layer by matching out contributions from the less interesting parts of the system such as the underlying bulk phase. The application of isotopic substitution also makes it possible to define the structure of any part of the monolayer, for example, the location of the head group, provided that enough signal is available. The advent of the neutron reflection technique therefore now offers the opportunity of addressing important questions about the variation of surfactant layer structureswith coverage,temperature, alkyl chain length, electrolyte concentration, head group type and size, etc. In this paper we present results on the determination of the structure of the nonionic surfactant triethylene glycol (2) Lee, E. M.; Thomas, R. K.; Penfold, J.; Ward, R. C. J.Phys. Chem. 1989, 93, 381. (3) Simister, E. A.; Lee, E. M.; Thomas, R. K.; Penfold, J. J. Phys. Chem. 1992,96, 1373.
0743-7463/93/2409-1352$04.00/0 0 1993 American Chemical Society
Determination of Structure by Neutron Reflection
Langmuir, Vol. 9, No. 5, 1993 1363
monododecyl ether, C12E03, adsorbed at the air-water interface as a function of surfactant concentration.
transform of p(z), the average scattering length density profile in the direction normal to the interface
Theory
P(K) = J-:exP(-iKz)P(z) d2 (4) A full description of the optical matrix method for calculatingneutron reflectivityhas been given e l s e ~ h e r e . ~ , ~ the relationship between the Scatteringlength density and the composition of the layer being given in eq 1. An The method of analyzing experimental profiles is alternative expression, equivalent to (3), but written in straightforward: a structural model is assumed, the terms of dpldz = p(l) is reflectivity calculated exactly using the matrix method, followed by comparison of the calculated and observed profiles and revision of the structure in a leasbsquares interation. The primary parameters usedin the calculation are the thicknesses of the component layers of the model where and their scattering length densities, which depend on the number densities of each atomic species and their known p"' ( K ) = K2p(K) (6) scattering lengths, given by For the adsorption of a nonionic surfactant at the airwater interface, the structure can be described in terms p =znibi of three groups, the surfactant chain c, its head group h, 1 and the solvent s. The scattering length density profile where p denotes the scattering length density of a layer, across the interface in the form of the number densities bi the scattering length of component i, and ni ita number of these three groups can be expressed density. When treating a set of data from different isotopic P(z) = b,n,(z) + bhnh(z) b,n,(z) (7) species, it is necessary to know how the scattering length density of a given layer varies with isotopic substitution Substituting (7) into (4) gives and then to fit the set of reflectivity profiles with an identical model. Since the scattering lengths of H and D are of opposite sign, the water substrate can be prepared with scattering length densities varying over a wide range. The simplest of these contrasts to interpret is water contrast matched where h i i ( ~ )and hij(K) are the partial structure factors to air, null reflecting water (nrw),containing deuterated abbreviated to hii and hij. The partial structure can be surfactant. The surfactant is then the only species in the expressed aslo system contributing to the reflectivity. Under these circumstances, taking the adsorbed layer to be a uniform layer, the area per surfactant molecule is given by
where mi and bi are the number and scattering length of atom i in the molecule. It is possible to vary T over a limited range, varying p accordingly to obtain a good fit, but the variations compensate each other so that A is to a high approximationindependent of the assumptionthat the layer is uniform. The awkward feature of the use of the optical matrix method is that for a complicated interface the fitting procedure may involve considerable effort. There is also no easy way of assessing the uniqueness of the fit. We have recently shown that by using the kinematic approximationit is possible to separate the contributions of different parta of the interfacial layer and to obtain some information about the structure which is model independent to a high level of approximati~n.~~~J In the kinematic approximation the specular reflectivity, R(K), is&Q (3)
where K is the momentum transfer normal to the interface ( = 4 ~sin B/h) and P(K) is the one-dimensional Fourier (4) Born, M.; Wolf,E. Principles of Optics; Pergamon: Oxford, 1970. (5) Lekner, J. Theory of Reflection; Nijhoffi Dordrecht, 1987. (6) Lu, J. R.; Simister, E. A,; Lee, E. M.; Thomas, R. K.; Rennie, A. R.; Penfold, J. Langmuir 1992,8, 1837. (7) Crowley, T.L.; Lee, E. M.; Simister, E. A.; Thomas, R. K. Physica 1991,B173,143. (8) Crowley, T. L. Ph.D. Thesis, University of Oxford, 1984. (9) Als-Nielsen, J. 2.Phys. 1986,64,411.
whereG(n)or&) is the Fourier transform of the number density and can be obtained from an equation similar to (4). Equations 8-10 may equivalently be written in the derivative form using eqs 5 and 6. The relation between the two types of partial structure factor is then h;;)(K) = K'hJK) (11) TheZl can in principle refer to each atom in the layer but in practice a large enough group of atoms must be labeled to give sufficient signal. To determine the structure of a surfactant monolayer requires a carefully chosen set of reflectivity measurements from six differently labeled isotopic species. Because isotopic substitution gives different b,, bh, and b, in each measurement,the six partial structurefactors can be obtained from eq 8. All the partial structure factors can in principle be Fourier transformed to give the Patterson functions P&) and Pij(Z) where"
In reality, this method of analysis is limited by the quality of the data. The main source of error results from the level of background scattering which restricts the range of the reflectivity measurement and, since data can only be obtained over a narrow range of K, the truncation errors in Fourier transformation are too high for the transform to be worthwhile at the present stage. However, the form ) h i j ( ~offer ) the possibility of an interfactors h i i ( ~and (10) Enderby, J. E.;Neilson, G. W. In Water, a Comprehensiue Treatise; Franks, F., Ed.; Plenum: London, 1979; Vol6, p 1. (11) Bracewell, R. N. The Fourier Transform and Its Applications; McGraw-Hill: New York, 1978.
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1354 Langmuir, Vol. 9,No. 5, 1993
mediate stage of analysis, which is valuable for evaluating the uniquenessand resolution limitations of any structural model assumed. Equation 8 also offers a means for reducing a set of isotopic data to the minimum number of functions determining the layer structure. For C12E03 we chose a combination of three isotopic profiles, deuterated surfactant in nrw, protonated surfactant in D20, and deuterated surfactant in D20. Our previous experience with C14TAB6suggests that this set is the best combination for obtaining the structural information we required, which is the chain thickness and the chain penetration into the aqueous subphase. If we assume that the contribution of protonated head is negligible, h c c ( ~ can ) easily be evaluated using eq 8 from just the profile of chain deuterated surfactant in nrw. The ) predominantly solvent partial structure factor h , , ( ~is determined by the fully protonated surfactant in D20, and h,&), which determines the chain/solvent separation, is determined by all three profiles. This is a smaller number of combinations than suggested by eq 8 and we will show below that this makes it necessary to make some adjustments to the analysis. The direct conversion of the reflectivity into partial structure factors via eq 3 or 4 uses the kinematic approximation, which breaks down at K values within the range of our measurements. It has recently been shown by Crowley12that the exact value of R appropriate to eq 8 can be obtained from the observed reflectivity using the following equation
where R, and Rk are the exact and kinematic reflectivities for a perfectly smooth surfacebetween the two bulk phases and K~ is the critical momentum transfer between the two bulk phases. In the above equation R, and Rk can be written respectively
where p1 and pz are the scattering length densities of the two bulk phases. The main correction in eq 13 results from the refractive index change between the two media unless the reflectivityis greater than about 5 X le2, which is not the case for our measurements. We have shown in previous theoretical simulations6 that the use of eq 13 eliminates errors arising from use of the kinematic approximation and we use it in the analysis to follow. The self-partial structure factors, hii(K),contain information about the distribution of the labeled group itself but not about the relative locationsof the different groups. It is the cross partial structure factors, hi,(^), which contain the information about their relative positions. Structural ) information can be obtained directly from h i j ( ~without doing the Fourier transform. Thus it has been shown377 that if the distribution of the chain is perfectly even and that of solvent perfectly odd, the partial structure factor MK) can be expressed as ~ J K ) = f(hcc(~)h~s(~ sin ) ~(KQ 1/2 (16) where 6 is the distance between the centers of the odd and even distributions. We have assessed the validity of this
(12)Crowley, T.L. Physica A , in press.
assumption in a previous publication and found that eq 16 works well up to K 0.15 k1for the thicknesses of typical surfactant layers.6 The accuracy of the determination of the 6 values is extremely high, about f0.5 A.
Experimental Details Chain deuterated triethylene glycol monododecyl ether (Cl2D~5(OCZH4)30H, abbreviated to dClzhEO3) was prepared by the Williamson ether synthesis from dodecanol and triethylene glycol monochlorohydrin (Cl(CzH40)3H). Cl(CzH40)sH was purchased from Fluka and deuterated dodecanol from Merck, Sharp and Dohme (K & K Greeff). The OH group on C1(CzH40)3Hwas first protected as the tetrahydropyranyl (THP) derivative by reaction with 2,3-dihydropyran (DHP) in acidic environment following the procedure in ref 13. A 0.065-mol portion of fresh sodium was introduced into a 250-mL flask containing 100mL of freshlydistilled and dried tert-butyl alcohol and stirred with heating until all the sodium had reacted. A 0.05-mol portion of dodecanolwas added to the mixture followed by 0.05 mol of Cl(CZH40)3THP. Solid NaCl was formed immediately. After refluxing for 6 h the mixture was cooled and transferred into a separation funnel, where it was extracted with 300 mL of ether and washed with 30 mL of water. After separation of the ether phase the ether was removed by rotary evaporation. The THP group was removed following the procedure in ref 13, by refluxing with 50 mL of methanol and 3 mL of concentrated HCl (36%) for 3 h. The residue was neutralized with solid NaHC03 and the excess solid NaHC03 removed by filtration. After evaporation of methanol the remaining material was extracted with ether and water twice to remove residual salt and unreacted (EO)3derivatives. After drying with sodium sulfate the ether was evaporated. The final purification was made by column chromatography, using a silica gel column (40-60 Hm) and ether as flush solvent. dClzhEO3was identified by analytical thin-layer chromatography and its purity assessed from the surface tension measurements to be described below. Fully protonated triethylene glycol monododecyl ether hC12hEO3 was purchased from Nikkei Co, Japan. Althoughthe purity was claimed to be 99 % ,TLC and surface tension measurements revealed traces of impurity (probably hClzhEOz), which was removed by passing through a column using the same conditions as for the deuterated derivativeabove. The surfacetension results (Figure 1) showed that the raw hClzhEO3 had a slightly lower critical micelle concentration (cmc) and the tension values were systematically lower than those of chain deuterated surfactant. These observationswere consistent with the trace of a less soluble impurity indicated by TLC. After chromatography the hC12hEO3 showed no trace of impurity in the TLC test and its surface tension was exactly the same as that of the deuterated derivative. High-purity water was used throughout (Elga Ultrapure system). DzO was from MSD Isotopes, Canada, and used as supplied. The surface tensions of HzO and DzO were in good agreement with the literature value, 72 h 0.3 mN/m.l4 The methods of cleaning the glassware and Teflon troughs for both neutron and surface tension experiments have been described elsewhere.lS2 The neutron reflection measurements were made on the reflectometer CRISP at the Rutherford-Appleton Laboratory (Didcot, U.K.). The procedure for making the measurements has been describedpreviously.2 All the measurements were made at the fixed incident angle of 1.5O and the reflectivity calibrated with respect to Dz0. Flat backgrounds were subtracted for all the measurements. Measurements were made at four surfactant M, 1 X concentrations: 5.5 X M, 3 X le5M, and 1 X 10-6 M, ranging from cmc downward. At each concentration, neutron reflectivity profiles were measured using isotopic combinations of the fully protonated surfactant in DzO and the hydrocarbon chain deuterated surfactant in both D20 and water contrast matched to air. (13)Furniss, B. S.;Hannaford, A. J.; Smith, P. W. G.; Tatchell, A. R. Vogel's Textbook of Practical Organic Chemistry, 5th ed.; John Wiley & Sons: New York, 1989. (14)Weast, R. C. Handbook of Chemistry and Physics, 54th ed.;CRC Press: Cleveland, OH, 1973.
Determination of Structure by Neutron Reflection
Langmuir, Vol. 9, No. 6, 1993 1355 0
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log[C/MI Figure 1. Surface tension as a function of C12E03 concentradC12hE03 in H2O; (A) dC12hEO3in DzO;(+) purified tion: (0) hClzhEO3 in HzO; (X) raw hC12hE03 in H20. The continuous line below the cmc through the first three setsof data is the fitted polynomial from which the slope of dyld log[C] is obtained and hence the area per molecule from the Gibbs equation. Surface tension measurements were made on a Kriias K10 tensiometer using a platinum-iridium ring.15 The surfacetension is determined from the maximum force exerted on the ring without detachment of the meniscus. After calibrationwith pure water, correction factors were used to obtain final values of the surface tension. Both surface tension and neutron reflection measurements were made at 298 K.
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Results and Discussion (a)Surface Excess. The surfacetensions of dC12hE03 with respect to surfactant concentration are presented in Figure 1. The measurementswere made both in D2O (A) and HzO (0) and the results are identical within experimental errors clearly demonstrating that there is no difference in surface activity of the surfactant between DzO and H2O. The cmc of dClzhEO3was found to be 5.50 X M. Also shown in Figure 1 are two sets of results for hC12hE03before (Wand after (+) passing through the silica column. It can be seen that the surface tension values for the raw hClzhEO3 are slightly lower and the cmc is about 5.25 X 106 M. The difference here is small but does appear to be systematic within the experimental errors. After purification both surface tensions and the cmc are consistent with dClzhEO3. The slightly lower cmc of the raw hC12hE03is almost certainly caused by the presence of a trace amount of the adjacent, less soluble, homologue CIZEOZ,as pointed out previously. It can then be concluded from Figure 1 that there is no measurable difference in surface activity caused by isotopic substitution in the chain of the surfadant or by use of DzO. We have shown in an earlier publication that great care must be taken in deriving the areas per molecule from data of the type shown in Figure 1 using the Gibbs equation.’ In order to obtain accurate slopes of surface tension versus log[concentrationl ,we measured more than 30 points below the cmc. The data were then fitted to a second-order polynomial and the local slopes extracted at different surfactant concentrations. The results of this analysis are plotted in Figure 2a in the form of surface excess l? against bulk surfactant concentration and in Figure 2b in the form of surface pressure u versus area per molecule A. We have assiuned that the activity coefficient below the cmc is 1.
The area per molecule tends to a limiting value of 36 A2 at the cmc but varies slowly over the range from half cmc up to the cmc. It changes rapidly when the concentration is less than one-fifth of the cmc. This surfactant system has also been studied by Rosen et al.16who obtained a cmc of 5.2 X lcrS M, which is slightly lower than our value. Their value of the area per molecule at the cmc was 42 A2, significantly larger than our value. However, their value of A was obtained by drawing a simple straight line through the points below the cmc giving only an average slope of surface tension versus log[concentrationl. If we analyzed our data in this way over the same concentration range, the value of our average A would have been identical with theirs. It is interesting at this stage to compare our surface tension excesses with those from the neutron reflection measurements. Other than noting that the determination of surface excesses from neutron reflection is model independent to good accuracy, we defer discussion of the analysis, but it is clear that the findings from the two techniques are in good agreement. At low concentrations ( H 1X 10-6 M)the errors in the surface tension measurements become large because there are not enough measured
(15) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; John Wiley & Sons: New York,1990.
(16) Rosen, M. J.; Cohen, A. W.; Dahanayake, M.; Hua,X. Y.J. Phys. Chem. 1982,86, 541.
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Area per molecule/k Figure 2. (a, top) Plot of surface excesa (r)as a function of &EO3 concentration: (+) obtained from the surface tension obtained from the measurement and the Gibbs equation; (0) neutron reflectivity measurement. (b, bottom) Plot of surface pressure versus area per molecule derived from surface tension measurement.
Lu et 41.
1356 Langmuir, Vol. 9, No.5, 1993
L dA-’ Figure 3. Plots of log[reflectivity] versus momentum transfer at the cmc (5.5 X le5 for dClzhEO3 in null reflecting water: (0) M); (A)1 X 10-5 M (+) 3 X 10-8 M;(X) 1 X 1 P M. The corresponding continuouslines are the fitsusing a two-layer model for the parameters given in Table 111. For clarity the error bars are only marked for the highest and lowest concentrations.
points in the region to guarantee a good polynomial fit. The area per molecule obtained from neutron reflection experimentsat dilute concentration region is still reliable since the signal from the layer is still adequate. The neutron measurements also show that the area per molecule tends to the limiting value of 36 A2 even up to a concentration of twice the cmc. This clearly indicates that in this case the saturated monolayer is formed at the cmc. The value of 36 A2at the cmc is small compared with the values obtained for other soluble saturated monolayer systems1t6but is far from the value of the cross-sectional area of an alkyl chain, which is about 20A2. The saturation here is presumably still limited by repulsion between the hydrated head groups. In our previous measurements on tetradecyltrimethylammonium bromide (C14TAB) adsorbed at the akwatar interface, the adsorption increases gradually through the cmc, decreasing by 15% over the concentration range from the cmc to about 3 times the cmc.1 In such a case a straight line analysis of the yllog c plot up to the cmc is not valid. (b)Structural Analysis. (1) Interpretation Using the Optical Matrix Method. On the basis of the adsorption isotherm shown in Figure 2, we chose four surfactant concentrations to monitor the variation of structure with Concentration. These concentrations were approximately the cmc, Vgcmc, V~ocmc,and l/mcmc. Figure 3 shows the variation of reflectivlty with the concentration of dC12hE03 in null reflecting water (nrw), while Figure 4 shows the profiles from dC12hEO3 in D2O and Figure 5 those from fully protonated C12E03. For comparison,the pureD2O profiles are also shown in Figures 4 and 5. While the general level of reflectivity in Figure 3 increaseswith amount of adsorbedmaterial, the opposite is true in the DzO profiles. Thus in Figure 4 as the surfactant concentration decreases, the depression of reflectivity gradually decreases until the profile is almost identical with that of pure DzO at the lowest concentration measured. The profiles of protonated surfactant in D2O are all quite similar to that of pure DzO. These profiles play an important part in the determination of the partial structurefactor It,(’). The small differences in reflectivity are magnified when the results are plotted as the ratio of reflectivity to that of pure DzO against momentum transfer.3 The profiles on nrw were fitted with a model of a single
I
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0.10
0.15
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KJA-1 Figure 4. Plots of log[reflectivityl versus momentum transfer for the profiles of dClzhEO3 in DzO (0) at the cmc (5.5 X 10-5 M);(A) 1 X 1od M (+) 3 X l(F6 M; (X) 1 X 1P M. The correspondingcontinuouslines are the fitsusing a two layer model for the parametersgiven in Table 111. The dashedline represents the reflectivity of pure D20with a roughness of 2.8 A. For clarity the error bars are only marked for the highest and lowest concentrations.
Figure 5. Plots of log[reflectivity] versus momentum transfer for the profiles of hCl&EO3 in DzO (0) at the cmc (5.5 X M); (A) 1 X 10-5 M, (+) 3 X 1 P M; (X) 1 X 10-8 M. The correspondingcontinuouslinesare the fits using a two-layer model for the parameters given in Table 111. The dashed line represents the reflectivity of pure DzOwith a roughness of 2.8 A. The error bars are only marked for the highest and lowest concentrations. Table I. Scattering Lengths and Volumes of Surfactant Molecules. unit scattering length x 105/A volume/A3 HzO -1.68 30 DzO 19.14 30 Cl2H25 -13.7 350 350 C12D25 245.5 200 (OCzH4hOH 14.5 Scattering lengthe are from ref 19 and volumes from ref 20 or calculated from density. The fully extended length of C12H25 is 16.7 Azo and that of (OCzH&OH is 10.5 A.17
uniform layer and the parameters obtained are presented in Table 11. The signals at this contrast are mainly from the deuterated chains but the protonated ethoxylated groups have a small positive scattering length (see Table I) and will also make a smallcontribution to the reflectivity. We shall discuss the effect on the derived values of the thickness from the protonated heads below. The one-
Determination of Structure by Neutron Reflection Table 11. Fitted Parameters Using One Layer Model concn/M system ?/A A/A2 10-6-/A-2 n 5.5 X 1od dClzEO3/cmw 2 P 36 3.6 dCizE03/DzO 23.sb 36 4.4 6 5.5 X lod 6.5 X 106 hCizE03/DzO 10' 36 3.2 6 dClzEO3/cmw 17.5" 47 3.2 1.0 X 20b 47 4.45 8 1.0 X le5 dClzE03/Dz0 1.0 X hClzE03/Dz0 9 c 47 3.65 8 3.0 X 10-6 dClzEOa/cmw 14a 62 2.65 3.0X 10-6 dCizEOdDz0 16b 62 4.35 9 3.0 X 10-6 hCizEOdDz0 8' 62 3.6 9 1.0 X 10-6 dClzEO3/cmw 13.5" 80 2.15 1.OX 10-6 dCizE03/Dz0 80 4.5 10 1.0 X 10-6 hCizE03/DzO 7' 80 3.5 10 a Thicknesses of chain including small contributions from the protonated EO groups (see text). Thicknesses of the whole mole*des. Mainly the measure of the thicknesses of the head group.
layer model also fits the reflectivity of chain deuterated surfactants in D2O. This is because the association of DzO molecules with the protonated head groups makes the scattering length density of the head group region comparable with that of the deuterated chains. Accordingly, both chain and head group regions contribute to the reflectivity,and the apparent thickness of the layer is now significantlylarger than for the nrw samples. For the same reasons the one layer model also fits the profiles for fully protonated surfactant in D20 but, because the scattering length density of the protonated chain is almost zero and that of the head group region is approximatelyhalf of that of D20, the fitted thickness are measures of the thickness of the head group region only. Because the one layer model results in different thicknesses according to the contrast used, the model must be regarded as an oversimplification but it does give a useful guide for more realistic models. It should be emphasized that it is generally difficult to draw firm conclusionsabout D2O containing systems using just the one layer model. The present system is special because of the large size of the head group and the relatively high surface concentration. A two-layer model fits the whole set of data successfully. In this model: the layer is divided into two parts, the upper part containing no water and no head groups and the lower part containing water, head groups, and fractions of hydrocarbon chain with no spare volume. The chain may be distributed arbitrarily in the two regions but is expected to be mainly in the upper region, which we refer to as the chain region. The adjustable parameters are then the area per molecule, A, the proportion of alkyl chain in the head group region, f , the number of water moleculesassociated with each surfactant molecule, n, and the degree of extension of the chain, c. The relationships between the total thickness of the surfactant layer, T,the scattering length densities, p, and these adjustable parameters are given in ref 3. Relevant constants of the molecule used in the fitting, such as the dodecyl chain length, its volume, and the molecular volume of water, are tabulated in Table I. The physical parameters used in the fittings should be the same at a given surfactant concentration for all three isotopic species. However, we found it easier when using a least-squares routine for a set of reflectivity profiles to fit each profile independently allowing A, f , n, T,and c to float within narrow limits. The results are summarized in Table I11for the four differentsurfactant concentrations. The correspondingfits for the profiles are shown in Figures 3, 4, and 5 as continuous lines. A t the cmc (5.5 X 10-5 M)the area per molecule A = 36 A2 and the total thickness is 23 A of which the chain layer is 12.5 A and the head group 10.5 A, indicating the
Langmuir, Vol. 9, No. 5, 1993 1357 formation of a well-packed monolayer at the interface. Allowing for the fraction of chains in the head group region, the thickness of the (EO)s group is about 7 A, which is approximately 70% of the maximum extension of the (EO)3.17 At the lowest concentration (1.0 X 10-6M), which is the cmc/55, the area is 80 A2 and the thickness drops to 15 A divided into a chain layer thickness of 7.5 A and a head group thickness also of 7.5 A. The errors in A are estimated to be about 2 A2, and those for the length parameters less than 1A. The set of measurementsshows that as A increases, r decreases. The product AT increases as the concentration decreases indicating that the layer is less well packed at lower concentrations, but it is difficult to tell from this information alone what are the structural consequences of this lower packing. Thus it is impossible to deduce whether the chains are systematically tilted in relation to the water surface, as observed in insoluble LB films,le or if the chains are disordered either in relation to each other or within a single chain, i.e. a higher incidence of gauche conformations. If the layer were tilted and close packed, its thickness would be much lower than observed and we therefore believe that the second alternative is more likely. We have already indicated that each isotopic composition is sensitiveto different features of the layer structure. This has also been discussed in detail e l s e ~ h e r e .The ~ errors in the different fitting parameters are based on a least-squares fitting routine and are given in Table 111. First we consider f, the fraction of chains under water. For the set of profiles at 5.5 X 1V M, for example, we found that we could not fit the whole set of profiles with a percentage of chains outsidethe range 18-22 % The upper limit is set by the profile of the fully protonated surfactant in D20. This is sensitiveto the thickness and the scattering length density of the head group region. If more chain is introduced into the head group region, it will either increase the thickness or decrease the scattering length density by displacingwater. When there is a layer of scattering length density about half that of the underlying substrate, the reflectivity is very sensitive to the exact values of scattering length density and thickness.8 This is precisely the situation for the protonated surfactant on D20. The lower limit on f is set by the deuterated surfactant in DzO. The deuterated surfactant in D2O produces larger depressions of the reflectivity from pure D20 than the protonated surfactants and the reflectivity is sensitive to the thickness of both alkyl chain and head group regions. Though f is found to be narrowly defined at the cmc, it becomes less so as the concentration decreases. This is became when the adsorbed layer is more loosely packed, the characteristic features of the reflectivity profiles become less marked. For example, at 1 X 1O-eM it was found that the percentage of alkyl chains in the water could be varied from about 30 to 40% without producing any serious mismatch. However, the other parameters such as area per molecule, the total thickness of the layer, and number of water molecules to each surfactant can still be determined with reasonable accuracy. In the uniform layer models the volume available (74) in the chain region is larger than that occupied by the actual volume of the chain out of the water. The remaining space must be occupied by air. The percent of air in the chain layer in order of decreasing concentration is 40%, 50%, 50%, and 60%, respectively. This is probably a
.
(17) Takahashi, Y.; Sumita, I.; Tadokoro, H. J. Polym. Sci. 1973,11, 2113. (18) Richardson, R. M.; Roser, S. J. Langmuir 1991, 7, 1458. (19) Sears, V. F. Neutron News 1992,3, 26. (20) Tanford, C. J. J. Phys. Chem. 1972, 76 3020.
1358 Langmuir, Vol. 9, No. 5, 1993
Lu et al.
Table 111. Fitted Parameters Using Two Layer Model concn/M
surfactant
substrate
A/A~
T ~ A 10-6pc/A-2
rc/A
36 f 2 12f 1 36 12 36 12' 47 f 2 10.5 f 1 47 10.5 41 10.5" 62 f 3 8.5 & 1 8 62 62 8" 80 3 7 . j i 1 D2O 80 8 dClzhEO3 D20 80 7.5" hC12hE03 0 Denotes insensitive variables in the fitting procedure.
*
10.~ f 10 11 11 9 f 1"
10 10 9&1" 9 8.5
s i 1" 7
7.5
systematic trend, although the errors are large because the actual values are sensitive to the thickness of the layer. The apparent presence of air in the layer may partially result from the inadequacy of the uniform layer model. If Gaussian distributions are used to represent the chain layer, the density will be more liquid-like at the center of the distribution and the air is more localized in the outer part of the layer; i.e. there is a density gradient into the vapor phase. The resolution of the experiment is not yet sufficient to distinguish the uniform layer and Gaussian models. (2) Interpretation by the Kinematic Theory. We have shown in eq 8 that a combination of three isotopic profiles has to be used at each concentration to determine the partial structure factors. The reduction of the structure of a surfactant to three partial structure factors involves some approximations, which we now consider. For the profile of chain deuterated surfactant in nrw, the scattering length of the protonated EO groups is about a tenth of the deuterated alkyl chain but is too small compared with the background for it to be possible to determine hhh(l)with any accuracy. Nevertheless it is clear that the contribution from the EO groups cannot be neglected. Equation 8 can be written as
4.4 4.4 -0.25
3.15 3.15 -0.2
3.4 3.6 -0.2
2.95 2.15 -0.15
10-6pdA-2 1.66 4.5; 3.25 1.8 4.9 3.5 1.45 4.65 3.55 M5
f
n
6fl 6 8fl 8
9*1 9
5.0
1oi2
3.25
10
*
t
0.20 0.02 0.20 0.20 0.25 0.03 0.25 0.25 0.27 & 0.03 0.27 0.27 0.32 f 0.05 0.32 0.32
0.92 0.92 0.92 0.83 0.83 0.83 0.69 0.69 0.69 0.63 0.63 0.63
0.05 * 0.05 0.05 0.05
0.05
* 0.05
9
.Q: 2
z
6
X
-lz -3 c
4
2
0
0.05
0.10
0.15
0.20
0.25 0.:
I
dA-1 Figure 6. Partial structure factors of hail)of C12E03 adsorbed at the air/solution interface at C12EO3 concentrations of 5.5 X 10-5 M (O), 1.0 X le5M (+), 3.0 X 1W M ( 0 ) ,and 1.0 X 10-6 M (x). The corresponding continuous lines are calculated for uniform layers of thicknessesof 20,17.5,16,and 15A,respectively. The fitted thicknesses are dominated by the chains, but there is a small contribution from the protonated EO3 group. The error bars are only marked for the highest concentration.
can be written as 1 6 ~b;h,(l) ' -
(17)
K4
where b,, Ph, and ba denote the scattering length of the deuterated alkyl chain, protonated EO group, and the whole surfactant molecule, respectively. h,(l) represents the partial structure factor of the whole molecule and can be calculated from the profile of chain deuterated surfactant in nrw. For the measurements of the deuterated surfactant in DzO, eq 8 becomes R 2 ( ~=) --[b;h,,(' 16?r2 )
+ 2 b ~ ) ~ h , +~ (p,2hM'" " t
K4
where b, represents the scattering length of D2O. The first three terms in (18) can be replaced by h,(l) from eq 17. The last two terms involve two structure factors, and hb(l) with the form of eq 16. The head/solvent separation distance is expected to be much smaller than that of chain/solvent. Thus sin(&,&will be much smaller than sin(K6,). The last term in eq 18can then be neglected and eq 18 then becomes (19) For the protonated surfactant in D20, a similar equation
where p c and P a represent the scattering length of the protonated chain and protonated surfactant molecule, respectively. The partial structure factors of haa(l), and h,(l) determined using eqs 17-20 are shown for the four surfactant concentrations in Figures 6,7, and 8. It can be seen from the experimentallydetermined partial structure factors that the data rapidly lose accuracy above a K of about 0.3 k1and this is too short a range to use Fourier transformation to obtain the structure directly. We therefore take the alternative approach of using models to fit the structural data. For a uniform layer adsorbed on nrw, the Fourier transform of the number density can be expressed as 2ni ni(K) = -sin(K d 2 ) K
From eq 9, hii(l)(~) can be written as hi/"(K) = 4n: sin2(~7/2) (22) The number density ni here is equal to 1/(7A). For the adsorptionofsurfactant on D2O where a layer of the solvent is associated with the surfactant head group region which
Langmuir, Vol. 9, No. 5, 1993 1359
Determination of Structure by Neutron Reflection 0,
I
1
1
Table IV. Structure Parameter for C~zE03Using Kinematic Fitting conctM 12 AtA2 rdA 6tA n fc 5.5X
20k2
1.0 X 1w 3.0 X 1O-g 1.0 X 10-6 a
-’t -8 I
I
I
I
1
I
1
0.05
0.10
0.15
0.20
0.25
0.30
dA-1 Figure 7. Partial structure factors of of C12E03 adsorbed at the air/solution interface at C12E03 concentrations of 5.5 X 10-5 M (O), 1.0 X 10-5 M (+), 3.0 X 10-6 ( O ) , and 1.0 X 10-6 M (X). The corresponding continuouslines are calculatedusing eq 16 and 6 values of 10,8,7,and 5 A, respectively. The error bars are only marked for the highest concentration.
.l
12
0.05
0.10
0.15 0.20 dA-1
0.25
0.30
Figure 8. Partial structure factors hss(l)of C12E03 adsorbed at M the aidwater interface at C12EO3 concentrationsof 5.5 X ( O ) , 1.0 X M (+), 3.0 X 10-6 M (0), and 1.0 X 10-6 M (X) in water. The corresponding continuous lines are calculated using eq 23 and the fitted thicknesses of the solvent “layer”are given for pure D20 with in Table IV. The partial structurefactor hW(l) asurface roughness of 2.8A is also shown for comparison (dashed line). The error bars are only marked for the highest concentration. is assumed to be uniformly located on the bulk solvent, h@(l)(~) is given h,,(l)(~)= n,,2 + 4n,l(n,l- nso)sin2(~7,/2) (23) where nsoand nd denote the number densitiesof the solvent in bulk and the layer, respectively. The value of nsofor water is 3.33 X 1V2A-3 and that of n,l is equal to n/(72A), where n is the number of water molecules associated with each surfactant molecule. Equation 23 shows that for a perfectly smoothwater surface where there is no surfactant adsorption, hss(l)= nW2= 1.10 X 10-3 A*. The structure factors haa(l)and h,(l) have been fitted using eqs 22 and 23, respectively, and the results are plotted as continuous lines in Figure 6 and 8, and the fitted parameters are tabulated in Table IV. It can be seen from Figure 6 that for all four concentrationsthe fitted curvesare in excellent agreement with the experimental data within error. With eq 22 only two parameters ( T and A) can be varied to
17.5
16 14.5
36k2 llk 1 9.5 47 8 62 80 7
1Ok 1 8 7 5
6 8 9 10
0.27f0.04 0.31 f 0.04 0.31 f 0.04 0.40 f 0.05
1, contains contribution from the protonated (OC2Hd30H.
A(.@) 0.01
80
60
50
40
35
I
I
I
I
I
0.02
0.03
1/A(A*2)
Figure 9. Variation of the thickness of the chain (1,) and separation of the centers of chain and water distributions (6) with the area occupied per moleculeat the surface. The variation is approximatelylinear and the two lines are almost parallel to each other, indicatingthat there is a steady increase in the extent of chain immersion with the area per molecule. adjust the fits. Varying T shifts the peak position, and varying A changesits height. In Figure 8 the highest profile is hss(l)of pure DzO, which has a roughness of 2.8 A. It is clear that from the trend in Figure 8 that the more surfactant in the layer, the greater the effective width of the solvent distribution at the surface. In using eq 23 the area per molecule is taken to be the same as in fitting haa(l) and the number of water molecules per surfactant is adjusted to fill the remaining volume in the head group region. The thickness of the head group region is thus obtained reliably. The numbers of water molecules obtained here are all consistent with those from the optical matrix fitting. The self-partial structure factors h,(l) and hss(l)contain informatidn about the distribution of the surfactant and the solventthemselves,but not about the relative positions of the two. The information about the relative positions is contained in the cross structure terms, hac1). We have fitted the results using eq 16, which allows direct structural information to be obtained without doing the Fouriertransform. Figure 7 comparesexperimentalvalues of h,,C1)and those calculatedfrom eq 16 using experimental values of ha,(l)and hW(l).The errors above K = 0.2 A are such that we have fitted 6 mainly using the data at lower K. The best fits of eq 16 give the values of 6 of 1 0 , 8 , 7 , and 5 f 1 A at the concentrations of 5.5 X 10-5 M, 1 X 10-5 M, 3 X lo4 MI and 1 X 1V M, respectively. Since 6 is the separation between the center of the chain distribution and the midpoint of the water distribution, these values give some indication of the extent of penetration of the chain by the solvent. An estimate of the extent of immersion of the alkyl chains in the water may be made from the values of T , Th, and 6 given in Table IV. If there is no overlap of the two distributions of the chain and the head group, the separation of the two should be the s u m of the two half thicknesses. For example, for the measurements at the cmc this value is 15.5 A,but since the value of 6 is 10 A, the two distributions must overlap by 5.5 A. Because the thickness of the chain layer is about 20 A, a fraction of about 5.5/20 (27%) of the chain must
1360 Langmuir, Vol. 9,No. 5, 1993
therefore be immersed in the water. This value is a little larger than the value calculated from the two layer fitting (see Table 111) but the difference is within the approximations made. For the lowest concentration measured (1 X 10-6 M), the thickness of the chain is 15 A, that of the head group is 7 A, and 6 is 5 A. The overlap is therefore 6 A and the immersion is about 40 7% . The values for the degree of immersion of the alkyl chain in water for the two intermediate concentrations are both 31 7%. These are all somewhat larger than those obtained from the two-layer optical matrix fitting. The degree of immersion of alkyl chain in water is plotted together with the thickness of the chain as a function of area per molecule at the interface in Figure 9. Both vary approximately linearly. If the extent of immersion of the chain were independent of concentration, the change in 6 per unit of A should be half
Lu et al. that of the thickness. That they change at the same rate shows that the chains must be increasingly immersed as the area per molecule increases. We have not been able to distinguish experimentally the detailed conformationof the chains in the layer. More detailed information about the location and stucture of different parta of either the alkyl chain in relation to each other and to the head group and water surface could be obtained by partial labeling of the alkyl chain. Partial deuteration of the ethylene oxide chain could similarly offer the opportunity to determine the segment density profile within this chain. More detailed labeling experiments are now in progress. Acknowledgment. We thank the Science and Engineering Research Council for supporting the project.
