Langmuir 1997, 13, 2133-2142
2133
Neutron Reflection from Counterions at the Surface Formed by a Charged Insoluble Monolayer T. J. Su and R. K. Thomas* Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, U.K.
J. Penfold ISIS, CCLRC, Chilton, Didcot, Oxon OX11 0QX, U.K. Received July 8, 1996. In Final Form: January 24, 1997X Isotopic substitution has been used in conjunction with neutron reflection to make a selective study of the counterion layer beneath a charged insoluble monolayer spread on water. The insoluble monolayer consisted of a mixture of sodium docosyl (C22) sulfonate and docosanol, and its charge was adjusted by varying the relative amounts of anionic and neutral species in the layer. The counterion was the tetramethylammonium ion, TMA+. The counterion distribution was determined at three surface charge densities, corresponding to areas per negative charge of about 30, 60, and 85 Å2, and at three bulk electrolyte (TMACl) concentrations, 0.1, 0.01, and 0.001 M. There was found to be significant penetration of the counterions into the headgroup region of the amphiphile to form a well defined “Stern” layer, and there was also a thicker layer corresponding to part of the diffuse layer. The changes in the behavior of the counterions with changes in surface charge density and bulk electrolyte concentration were qualitatively consistent with double-layer theory. However, a complication in applying theory to the diffuse part of the double layer was that not all the counterions could be observed by the neutrons. This may have been because of preferential adsorption of Na+ present in the original spreading solution or because of roughness of the counterion distribution. The obervation by neutron reflection of penetration of the amphiphilic layer by the counterions was consistent with the unusual behavior of the π-A isotherms on addition of TMACl.
Introduction Several techniques have been used to attempt to obtain direct information about the adsorption of counterions onto a Langmuir monolayer. Grundy et al.1 have used X-ray and neutron reflection techniques to study the binding of Cd2+ counterions at a docosanoate monolayer. Leveiller et al.2 have used grazing incidence X-ray diffraction and X-ray reflection to obtain structural information on Cd2+ counterions bound to a monolayer of arachidic acid at high pH. Bloch et al.3 have used near total external X-ray fluorescence and surface-extended X-ray absorption fine structure spectroscopy measurements to examine Mn2+ counterions distributed under an arachidate monolayer. Only the last of these three studies has been able to observe ions other than the layer of counterions bound to the charged surface. In most systems there will be both a bound layer, often called the Stern layer, and a more diffuse layer. Direct measurements of the latter are very difficult, although in many ways it is this layer that is the most important, since it is related to macroscopic properties such as colloid stability. We showed in an early paper using the neutron reflection technique that in certain circumstances it is possible to observe neutron reflection from just the ion layer adsorbed at a charged surface by using suitable isotopic labeling.4 More recently, we have been able to show that such a signal has contributions from both a bound Stern layer and a more diffuse layer.5 The experiments were done on a soluble surfactant monolayer where the surface charge * Author to whom correspondence should be addressed. X Abstract published in Advance ACS Abstracts, March 15, 1997. (1) Grundy, M. J.; Richardson, R. M.; Roser, S. J.; Penfold, J.; Ward, R. C. Thin Solid Films 1988, 159, 43. (2) Leveiller, F.; Bo¨hm, C.; Jacquemain, D.; Mo¨hwald, H.; Leiserowitz, L.; Kjaer, K.; Als-Nielsen, J. Langmuir 1994, 10, 819. (3) Bloch, J. M.; Yun, W. B.; Yang, X.; Ramanathan, M.; Montano, P. A.; Capasso, C. Phys. Rev. Lett. 1988, 61, 2941. (4) Penfold, J.; Lee, E. M.; Thomas, R. K. Mol. Phys. 1989, 68, 33. (5) Su, T. J.; Lu, J. R.; Thomas, R. K.; Penfold, J. J. Phys. Chem. 1997, 101, 937.
S0743-7463(96)00663-4 CCC: $14.00
is determined by the system itself and cannot be controlled in such a way as to make it possible to follow systematically the effects of, for example, changes in ionic strength at a fixed surface charge or changes in surface charge at a fixed ionic strength. In the present paper we have used a similar labeling scheme with deuterated tetramethylammonium (TMA) as ion and alkyl sulfonate forming the charged layer, but we have used a long alkyl chain to create an insoluble monolayer as the charged surface, labeled in such a way that it makes almost no contribution to the reflection. To some extent the surface charge can then be controlled by varying the applied surface pressure. However, since the monolayer may undergo surface phase changes when the coverage changes, especially over a wide range, we have diluted the surface charge by using a mixture of the charged species and an uncharged species (the equivalent long chain alkanol). Experimental Details Deuterated docosanol (dC22OH) was prepared from deuterated docosanoic acid using lithium aluminum deuteride (CDN isotopes) and recrystallized from acetone before use. Deuterated and protonated sodium docosyl sulfonate, dC22SO3Na and hC22SO3Na, were made by reacting docosyl bromide with sodium sulfonate in an autoclave at 180 °C.6 After removal of organic impurities with petroleum ether and excess salts with water, the sulfonate was recrystallized several times from absolute ethanol. Deuterated tetramethylammonium chloride (N(CD3)4Cl or dTMACl) (MSD Isotopes) was used without further purification. Protonated tetramethylammonium chloride (N(CH3)4Cl or hTMACl) (Aldrich) was recrystallized from absolute ethanol. All solvents used here were analytical grade. Ultrapure water (Elgastat, UHQ, Elga, U.K.) was used throughout. Null-reflecting docosyl sulfonate and docosanol (“0”C22SO4Na and “0”C22OH) were made by mixing the deuterated and protonated species in such a ratio that the scattering length density of the hydrocarbon chain was zero. The spreading solutions were about 0.6 mg/mL in the mixed solvent of 40% (6) Reed, R. M.; Tartar, H. V. J. Am. Chem. Soc. 1935, 57, 570.
© 1997 American Chemical Society
2134 Langmuir, Vol. 13, No. 7, 1997
Su et al.
Figure 1. π-A isotherms of docosanol (left-hand side) and sodium docosyl sulfonate spread at the air/water interface. The lines are dashed for the protonated species, continuous for the deuterated species, and dotted for the null-reflecting species (approximately 10% deuterated, 90% protonated). methanol and 60% benzene. All measurements were carried out approximately at room temperature. The π-A isotherms were measured on a Nima trough with two movable Teflon barriers and two neutron transparent mica windows for the neutron measurements. The surface pressure was measured with a Nima surface tensiometer using the Wilhelmy plate method, and a piece of filter paper was used as a plate. Five minutes after deposition of the spreading solution, compression of the monolayer was started and the isotherm was measured at a compression speed of 17 cm2/min. The time for a complete compression was about 15 min. The isotherm measurements were repeated until a satisfactory level of consistency was achieved, which was (3 Å2 in the area per molecule. Neutron reflectivity profiles were measured using the reflectometer CRISP at Rutherford Appleton Laboratory (Didcot, U.K.).7 The measurements were made at incident angles of 0.8° and 1.5°, which gave a momentum transfer (κ) range of 0.0270.65 Å-1. The momentum transfer is related to the angle of incidence and the wavelength of the incident neutrons by κ ) (4π sin θ)/λ. All the profiles shown here had a flat incoherent scattering background subtracted.
Results π-A Isotherms. Isotopic substitution makes the technique of neutron reflection a powerful tool for the investigation of surface structure, but since it often relies on the assumption that the structure will not be changed by isotopic substitution, it is advisable to check whether or not the surface properties of the two isotopic species are the same. The surface pressure-area, π-A, isotherms of different isotopic species of C22OH and C22SO3Na are shown in Figure 1. The isotherms of the deuterated, protonated, and null-reflecting C22OH are essentially the same with a limiting area of 23.5 Å2. The isotherm of dC22SO3Na is however slightly different from that of hC22SO3Na. The two molecules have similar limiting areas of 26.5 Å2 for hC22SO3Na and 25 Å2 for dC22SO3Na, but at low areas, π for dC22SO3Na increases more gradually than that for hC22SO3Na. This difference may be caused by three factors, a genuine isotope effect, a difference in the (7) Lee, E. M.; Thomas, R. K.; Penfold, J.; Ward, R. C. J. Phys. Chem. 1989, 93, 381.
kinetic stability, or impurities. Lee et al.8 found no isotope effects in the π-A isotherms for spread monolayers of the same chain length material docosylpyridinium bromide, but large differences have been observed in the π-A isotherms of phospholipids.9 Any differences resulting from isotopic effects on the kinetic stability would almost certainly lead to a lack of reproducibility, but the isotherm of dC22SO3Na was found to be completely reproducible. The difference may be caused by impurities, but if so, these impurities have remarkably similar properties to dC22SO3Na because no change in the isotherm was observed after several recrystallizations. For the main purpose of the present work any impurity is likely to be of only minor importance in the determination of the structure of the counterions. This is because we rely mainly on “0”C22SO3Na, which only contains about 10% dC22SO3Na, and because the isotherm of “0”C22SO3Na, shown in Figure 1, is identical with that of hC22SO3Na. An important feature of using a spread monolayer is that the surface charge density may be varied by just compressing or expanding the charged monolayer film. However, when the layer becomes more dilute, the molecules in the monolayer may not be distributed uniformly on the surface. In order to create a uniform monolayer with a variable charge, we maintained moderately close packing of the layer but diluted the charge by using C22OH. To check whether or not “0”C22SO3Na and “0”C22OH are throughly mixed on the surface, we tried spreading the layer in three different ways, and the results are shown in Figure 2b. The dotted line is the isotherm made by spreading “0”C22SO3Na first and then “0”C22OH, the dashed line is that made by spreading “0”C22OH first and then “0”C22SO3Na, and the solid line is that made by spreading premixed “0”C22SO3Na and “0”C22OH. If the molecules mix completely and rapidly, these isotherms should be identical, as observed within error, except for (8) Lee, E. M.; Kanelleas, D.; Milnes, J. E.; Smith, K.; Warren, N.; Rennie, A. R.; Webberley, M. Langmuir 1996, 12, 1270. (9) Naumann, C.; Dietrich, C.; Lu, J. R.; Thomas, R. K.; Rennie, A. R.; Penfold, J.; Bayerl, T. M. Langmuir 1994, 10, 1919.
Neutron Reflection from Counterions
Langmuir, Vol. 13, No. 7, 1997 2135
Figure 2. π-A isotherms of mixed monolayers of (a) “0”C22SO3Na and “0”C22OH in different ratios on subphases of different concentrations of TMACl and (b) “0”C22SO3- and “0”C22OH in the ratio 1:1 using different spreading methods. In part a the lines are continuous for no added electrolyte, dashed for 10-3 M TMACl, dash-dot for 0.01 M TMACl, and dotted for 0.1 M TMACl.
the collapse. All the π-A isotherms of mixed monolayers were therefore made by spreading premixed solutions. Mixed monolayers of “0”C22SO3Na and “0”C22OH at three different ratios, 1:0, 1:1, and 1:2, were spread on four different subphases, water and 0.1, 0.01, and 10-3 M TMACl, and the resulting π-A isotherms are given in Figure 2a. Since we are only interested in the behavior of the charged species in the layer, we use the value of the area per negative charge, A-, in these diagrams. For an adsorbed monolayer, the addition of electrolyte reduces the Coulombic repulsion between the charged headgroups (or ions in the layer) and this should increase the compressibility of the monolayer and result in a smaller area per molecule at a given surface pressure, an effect that has been observed for insoluble monolayers.10,11 The monolayer in the present system has the opposite behavior, which suggests that the adsorption of TMA cations gives rise to an expansion of the negative charged monolayer and that the higher the TMACl concentration, the more expanded the monolayer. This unexpected behavior could only be caused by penetration of TMA+ ions into the monolayer. Taking the π-A isotherm of the “0”C22SO3Na monolayer on the subphase of 0.10 M TMACl as an example, the high ionic strength in the subphase collapses TMA cations onto the monolayer. Although the penetration of TMA+ into the negative charged monolayer is electrostatically favorable and hence reduces the electrostatic interaction between the heads, it also introduces packing problems because of its large size. When the area per C22SO3Na is compressed to 50 Å2, which is about the sum of the cross-sectional areas of the two ions C22SO3(20 Å2) and TMA+ (32 Å2), the surface pressure starts to increase because the interactions between the ions increase. When the monolayer is further compressed to A ) 35 Å2, the space is too small for both ions, and the TMA+ cations in the monolayer are ejected into the subphase. As A decreases the rate of increase of π becomes slower and there is a plateau. When the area is less than 27 Å2, the pressure increases much more rapidly and the (10) Dreher, K. D.; Wilson, J. E. J. Colloid Interface Sci. 1970, 32, 248. (11) Davies, J. T. Proc. R. Soc. London 1951, A208, 224.
monolayer collapses at π ) 65 mN m. The collapse area is usually a good estimate of the cross-sectional area of the monolayer.12 The collapse area of this monolayer occurs at 23 Å2, which is approximately the same as that of the monolayer on the water subphase, i.e. 22 Å2. This indicates that almost all the TMA+ ions are ejected out of the monolayer when the surface pressure is very high. The plateau in the surface pressure is observed only when the concentration of TMACl in the subphase is more than 0.1 M. Almost the same behavior has been observed in isotherms of the corresponding sulfate and was also attributed to penetration of the TMA+ counterions into the monolayer. This was further supported by surface potential measurements.11,13 The conclusions about ion penetration are also supported by the reflection results presented below. Neutron Reflection. (a) Structure of the Layer as a Whole. Although the main purpose of the present work is to examine the counterion layer, it was thought useful to determine the structure of the whole layer at one particular composition. The one chosen was the mixed monolayer of C22SO3Na and C22OH in the ratio 1:1 on the subphase of 0.01 M TMACl. The six neutron profiles required to determine the structure of the mixed monolayer are the deuterated monolayer with “0”TMA+ in nullreflecting water (NRW), the null-reflecting monolayer with dTMA+ in NRW, and the deuterated monolayer with dTMA+ in NRW, whose reflectivities are shown in Figure 3, and the null-reflecting monolayer with “0”TMA+ in D2O, the deuterated monolayer with “0”TMA+ in D2O, and the deuterated monolayer with dTMA+ in D2O, whose reflectivities are shown in Figure 4. The dashed lines in Figure 3 are best fits of a model of a single uniform layer to the data, and it is obvious that the C22SO3-/C22OH monolayer is satisfactorily described with this simple model but that the model is not at all appropriate when only the counterions are labeled, which implies that the counterions do not form a uniform layer (12) McGregor, M. A.; Barnes, G. T. J. Colloid Interface Sci. 1976, 54, 439. (13) Goddard, E. D.; Kao, O.; Kung, H. C. J. Colloid Interface Sci. 1968, 27, 616.
2136 Langmuir, Vol. 13, No. 7, 1997
Su et al.
Figure 3. Neutron reflectivity profiles of 1:1 mixtures of C22SO3Na and C22OH in 0.01 M solutions of TMACl in nullreflecting water: (a) dC22SO3Na, dC22OH, and dTMACl; (b) “0”C22SO3Na, “0”C22OH, and dTMACl; (c) dC22SO3Na, dC22OH, and “0”TMACl. The continuous lines are the best fits of a fourlayer model with the parameters given in Table 1. The dashed lines in parts b and c are the fits of a single uniform layer to the data. The bold type indicates the species dominating the reflected signal.
Figure 4. Neutron reflectivity profiles of 1:1 mixtures of C22SO3Na and C22OH in 0.01 M solutions of TMACl in D2O: (a) dC22SO3Na, dC22OH, and “0”TMACl; (b) dC22SO3Na, dC22OH, and dTMACl; (c) “0”C22SO3Na, “0”C22OH, and “0”TMACl. The continuous lines are the best fits of a four-layer model with the parameters given in Table 1. The bold type indicates the species dominating the reflected signal.
under the charged monolayer. It was found that a model with a minimum of three layers was required to fit the profile with just labeled counterions (Figure 3b) with the constraint of neutrality. Thus, when the C22SO3-/C22OH monolayer is also included, a structural model with a total of four layers was required, the first layer containing the alkyl chains in air, the second layer containing a fraction fc of alkyl chains immersed in water, the headgroups (SO3 and OH), and a fraction fTMAh of the TMA+ counterions, and the other two layers containing the remainder of the TMA+. The residual space in each layer except the first is assumed to be filled with water. If the structure is identical for the different isotopic species, and there are doubts in the present case, the model should fit the whole set of reflectivity profiles. The parameters for each layer are as follows:
Fh ) (fcbc + bh + fTMAhbTMA + Nwhbw)/τhA
(i) the alkyl chain layer τc ) (1 - fc)lc
(1)
Fc ) (1 - fc)bc/τcA
(2)
(ii) the head layer (3)
(iii) the first counterion layer FTMA1 ) (fTMA1bTMA + NwTMA1bw)/τTMA1A
(4)
(iv) the second counterion layer FTMA2 ) [(1 - fTMAh - fTMA1)bTMA + NwTMA2bw]/τTMA2A (5) where τi is the thickness of the ith layer, lc is the fully extended alkyl chain length, is the degree of extension of the alkyl chain, Fi is the scattering length density of the ith layer, and bi is the scattering length of the molecule, A is the area per pair of amphiphilic molecules (they are present in equal amounts), fTMAi is the counterion fraction in the ith layer, and Nwi is the number of water molecules in the ith layer. The constraint of space-filling in the second, third, and fourth layers also leads to
τiA ) Vh + fiVTMA + nwiVw
(6)
where Vi is the molecular volume of the molecule i. Using
Neutron Reflection from Counterions
Langmuir, Vol. 13, No. 7, 1997 2137
Table 1. Best Fitting Structural Parameters for the Whole Layer Calculated from the Optical Matrix Method with a Four-Layer Model scattering length density, F/106 Å-2 system dC22(SO3 + OH) + + NRW “0”C22(SO3- + OH) + dTMA+ + NRW “0”C22(SO3- + OH) + “0”TMA+ + D2O dC22(SO3- + OH) + dTMA+ + NRW dC22(SO3- + OH) + “0”TMA+ + D2O dC22(SO3- + OH) + dTMA+ + D2O -
a
“0”TMA+
τ ) 16 ( 2 Å. b τ ) 15 ( 5 Å. c τ ) 25 ( 5 Å.
d
chaina
headb
5.7
2.7e
5.7 5.7 5.7
0.6 5.2 3.0 5.9 6.6
TMA1c
TMA2d
0.3 6.2 0.36 6.2 6.3
5.4 × 10-3 6.35 5.4 × 10-3 6.35 6.35
τ g 1700 Å. e The thickness of the head layer for this profile is 13 Å not 15 Å.
the optical matrix method to calculate the reflectivity,14 the best fits for this four-layer model are the continuous lines in Figures 3 and 4 with the fitting parameters given in Table 1. All but one of the set of profiles could be fitted with A ) 54 ( 2 Å2, ) 0.73 ( 0.1, fc ) 0.25 ( 0.05, fTMAh ) 0.22 ( 0.22, fTMA1 ) 0.35 ( 0.07, and fTMA2 ) 0.43 ( 0.05. It will be seen in Table 1 that a proportion of the counterions are effectively “invisible” in that the thickness of the last counterion layer is so large that its contribution to the reflectivity could be ignored. No physical significance should be attached to the parameters obtained for this layer, but we have included it just to maintain neutrality. The results lead to 17 ( 3 water molecules surrounding the heads of SO3- and OH and 43 ( 5 water molecules per TMA+ ion in the first counterion layer. The basic parameters of the various fragments in the system are given in Table 2. For the reflectivity profile from dC22SO3-/dC22OH with “0”TMA+ in NRW, the thickness of the head layer required to fit the data was 2 Å thinner than those for the other profiles. As we have shown in other papers concerning amphiphilic monolayers, it is often more effective to interpret reflectivity data using the kinematic approximation and partial structure factors of the different components of the system.15 In the present case the complexity of the structural model needed to fit the reflectivity is such that it is advisable to use a second, independent, method of interpreting the structure in order to assess just how model independent are the final conclusions. In terms of an appropriate set of partial structure factors the kinematic approximation for the reflectivity is
Table 2. Volumes, Radii, and Scattering Lengths of Molecular Groups in the Layer unit
volume/Å3
length/Å
C22H45 C22D45 C22D45 SO3 OH OD N(CH3)4+ N(CD3)4+ H2O D2O
619.2b
29.3b
619.2 619.2 58 16 16 175c 175c 29.9 30.2
29.3 29.3 5.0 3.2 3.2 6.9 6.9 3.8 3.8
a
16π 2 [bc hcc + b2hhhh + b2TMAhTMATMA + b2whww + κ2 2bcbhhch + 2bcbTMAhcTMA + 2bcbwhcw + 2bhbTMAhhTMA + 2bhbwhhw + 2bTMAbwhTMAw] (7)
where the subscripts c, h, TMA, and w denote the chain, the head, the TMA+ counterion, and the water. The results of the optical matrix analysis above suggested that the distribution of the TMA+ counterions is not uniform and that a model of three layers is needed to give an adequate description of the counterions. We therefore divide the distribution of TMA+ into three regions, i.e. the head region (TMAh), the first counterion region (TMA1), and the second counterion region (TMA2), and allow the TMA+ ions in each region to contribute separately to the reflectivity. Equation 7 then becomes more complex with twenty-one terms, instead of ten. We then fit the six neutron reflectivity profiles representing the different contrasts (14) Born, M.; Wolf, E. Principles of Optics, 5th ed.; Pergamon Press: Oxford, 1975. (15) Lu, J. R.; Lee, E. M.; Thomas, R. K. Acta Crystallogr. 1996, A52, 11. (16) Simister, E. A.; Lee, E. M.; Thomas, R. K.; Penfold, J. J. Phys. Chem. 1992, 96, 1373.
-22 408.974 (92%) 385.55 (87%) 20.247 2.06 12.47 -8.88 116.04 -1.68 19.14
Reference 21. b Reference 22. c Reference 23.
shown in Table 1 to this equation. Each reflectivity profile is denoted sequentially by the symbol Rn, where n ) 1-6 and the numbering corresponds to that in Table 1. Each reflectivity profile is related to the partial structure factors as follows:
R′c )
R1κ2 16π2
) b2c hcc + b2hhhh + 2bcbhhch
(8)
R2κ2
) b2hhhh + b2TMAhTMAhTMAh + 16π2 b2TMAhTMA1TMA1 + b2TMAhTMA2TMA2 + 2bhbTMAhTMAh +
R′TMA )
2bhbTMAhhTMA1 + 2bhbTMAhhTMA2 + 2bTMAbTMAhTMAhTMA1 + 2bhbTMAhTMAhTMA2 + 2bhbTMAhTMA1TMA2 (9)
2
R)
scattering lengtha/10-5 Å
R′w )
R′cw )
R′cTMA )
R3κ2 2
16π
) b2hhhh + b2whww + 2bhbwhhw
(R5 - R1 - R3)κ2 16π2
(R4 - R1 - R2)κ2 16π2
) 2bcbwhcw - b2hhhh
(10)
(11)
) 2bcbTMA(hcTMAh +
2 hcTMA1 + hcTMA2) - b hhh (12) h R′wTMA )
[(R6 - R4) - (R5 - R1)]κ2 ) 16π2 2bwbTMA(hwTMAh + hwTMA1 + hwTMA2) (13)
where R′c, R′TMA, R′w, R′cw, R′cTMA, and R′TMAw are “reduced” kinematic reflectivities. They are obtained from the measured profiles using the equations above and are shown in Figures 5 and 6. It was found that a uniform layer description is more suitable than a Gaussian
2138 Langmuir, Vol. 13, No. 7, 1997
Su et al.
Figure 5. Reduced kinematic reflectivities for (a) the amphiphilic monolayer as a whole, (h(1) aa ), (b) water, R′w, and (c) the counterion, R′i. The continuous lines are calculated curves using the parameters given in the text. The dashed line in part a is calculated using a model of a Gaussian distribution.
description for the number density distributions of the chain and the head (see Figure 6a) and this was therefore used to represent the distributions of the chain and the head groups. The self partial structure factor for a uniform layer is given by
κ2hii ) (2/Aτi)2 sin2(κτi/2)
(14)
where τi is the thickness of the region i. A Gaussian distribution was used to represent the number density distribution of the TMA+ counterion in each of its three regions, and a tanh function, to represent that of the water, for which the partial structure factors are respectively
κ2hii )
κ2 exp(-κ2σ2i /8) A2i
(15)
where σi is the width of the i layer and 2 κ2hww ) nw (ζπκ/2)2 cosech2(ζπκ/2) 0
(16)
where nw0 is the number density of bulk water and ζ is the width parameter for a tanh profile. The cross partial structure factors can be obtained using eq 16
hij ) ((hiihjj)1/2 cos κδij
(17)
Figure 6. Reduced kinematic reflectivities for (a) amphiphilic layer/water, R′aw, (b) amphiphile/counterion, R′ai and (c) counterion/water, h(1) iw . The continuous lines are calculated using the parameters in the text.
hiw ) ((hiihww)1/2 sin κδiw
(18)
where δij is the separation distance of the centers of the two layers and the subscript w represents water. There are also the further constraints that
∑fTMA ) 1 i
δci ) δch + δhi
(19)
δTMAiTMAj ) δhTMAj - δhTMAi δwTMAi ) δhTMAi - δhw
(20)
The continuous lines in Figures 5 and 6 are the best fits of this partial structure factor model and give values of τc ) 26 ( 1 Å, τh ) 10 ( 5 Å, ζ ) 4.5 ( 2 Å, σTMAh ) 12 ( 7 Å, σTMA1 ) 23 ( 7 Å, and σTMA2 ) 170 Å. The distances between the centers of each component are δch ) 8 ( 5 Å, δhw ) 5 ( 3 Å, δhTMAh ) 0 ( 2 Å, δhTMA1 ) 19 ( 3 Å, and δhTMA2 ) 760 Å. The one partial structure factor that is very poorly fitted is the cross-term between the counterions and water. There may be two reasons for this. The first is that this partial structure factor is obtained as a small difference between large reflectivities and is therefore very vulnerable to small systematic errors, which are difficult to eliminate. The second is that the calculated partial
Neutron Reflection from Counterions
Figure 7. Number density distributions of the chain, the head, the TMA+ counterion, and the water in the system of C22(SO3+ OH) with 10-2 M TMACl solution as derived (a) from the calculation using partial structure factors (kinematic approximation) and (b) using the optical matrix method. The various distributions are water (continuous line), amphiphile (dashed line), and the two component TMA+ ion layers.
structure factor is much more sensitive to inaccuracies in the assumed shapes of the water and ion distributions than any of the other partial structure factors. Figure 7 shows the number density distribution of each component in the system plotted using both the kinematic approximation and the optical matrix calculation. Given that the basic descriptions of the structure in the two methods are different, there is reasonable agreement in the two structures of the layer. Both indicate that there is some penetration of the TMA+ ions into the headgroup region of the layer. We discuss the structure below after analyzing the counterion distribution at different surface charge densities and bulk ionic strengths. (b) Counterion Layer. When the isotopic combination “0”C22SO3Na, “0”C22OH, and NRW is used with dTMA+ ions, the measured neutron reflectivity is almost entirely from the dTMA+ counterion distribution. The headgroups (SO3 and OH/D) do have a small positive scattering length (see Table 2) which will make a small contribution to the reflectivity. Monolayers of three different surface charge densities on subphases of three different TMACl concentrations, 0.1, 0.01, and 10-3 M, were studied. Variation of the surface charge density was achieved by mixing “0”C22SO3- and “0”C22OH in three different ratios, i.e. 1:0, 1:1, and 1:2, and compressing the monolayers to an area per negatively charged headgroup A-, at which the surface pressure just starts to increase. The values of A- and the corresponding surface charge densities (σ ) e/A-, where e is the charge on the electron) used are given in Table 3, and the neutron reflectivity profiles are shown in two different groupings in Figures 8 and 9. Since the reflectivity is mainly from the dTMA+, the intensity is approximately proportional to the square of the amount of TMA+ under the monolayer. Figure 8 clearly shows that, at approximately the same surface charge density, the adsorption of the TMA+ counterions increases with the concentration of TMACl and decreases with σ. Figure
Langmuir, Vol. 13, No. 7, 1997 2139
Figure 8. Variation of the neutron reflectivity with different electrolyte concentrations under the mixed monolayers of “0”C22SO3Na and “0”C22OH in the ratios of (a) 1:0, (b) 1:1, and (c) 1:2. The TMACl concentrations are 0.01 M (O), 0.01 M (4), and 10-3 M (+). Table 3. Values of the Area per Unit Charge, A-, and the Corresponding Surface Charge Densities, σ, of the Monolayers Used in the Neutron Reflection Measurements SO3:OH ) 1:0
SO3:OH ) 1:1
SO3:OH ) 1:2
[TMACl]/ M
A-/(1 Å2
σ/(0.1 C m-2
A-/(1 Å2
σ/(0.1 C m-2
A-/(1 Å2
σ/(0.1 C m-2
0.1 0.01 0.001
35 30 25
0.46 0.54 0.65
61 59 54
0.26 0.27 0.30
85 84 80
0.19 0.19 0.20
9 shows the effect of the surface charge density on the adsorption of dTMA+ at the three concentrations of TMACl. At a fixed concentration of the TMACl bulk solution, the variation of the reflectivity with σ is relatively small compared with the salt effect. The reflectivity is determined by the contributions from just two species, the mixed heads (SO3- and OH/D) and the dTMA+ counterions. The scattering length density, F, may therefore be expressed as
F ) nSO3bSO3 + nOHbOH + nTMAbTMA
(21)
Taking the adsorbed layer to be a single uniform layer, the ni are given by
ni ) [Ni/τ(ASO3NSO3 + AOHNOH)]
(22)
where ASO3 and AOH are the areas per “0”C22SO3- and per “0”C22OH, respectively, Ni is the number of molecules of species i in this layer, and τ is the thickness of the layer.
2140 Langmuir, Vol. 13, No. 7, 1997
Su et al.
second layer of just TMA+ ions. The best fitted parameters using this three-layer model and the resulting values of fTMA are given in Table 4. The calculated curves are shown as the continuous lines in Figure 9. The measured neutron profiles may also usefully be interpreted using the kinematic approximation. Following a similar procedure to that described above, a model of two Gaussian distributions was used to determine the distribution of the TMA+ counterions. As with the uniform layer it is necessary to introduce a third “layer” to account for electrical neutrality, and therefore a model of three Gaussian distributions was also used to fit the profiles. The best fits for this three-layer description are given in Table 5 and are shown in the form of fits to the ion partial structure factor, h′ii, in Figure 10. Discussion
Figure 9. Variation of the neutron reflectivity with surface charge density for different TMACl concentrations of (a) 0.1 M, (b) 0.01 M, and (c) 0.001 M. The “0”C22SO3Na:“0”C22OH ratios are 1:0 (O), 1:1 (4), and 1:2 (+). The continuous lines are profiles calculated using the three-uniform-layer model described in the text with the parameters given in Table 4.
Substitution of eq 23 into eq 21 gives
F ) [NSO3bSO3/τ(ASO3NSO3 + AOHNOH)] + [NOHbOH/τ(ASO3NSO3 + AOHNOH)] + [NTMAbTMA/τ(ASO3NSO3 + AOHNOH)] (23) In the case of “0”C22(SO3:OH ) 1:m), the numbers of SO3and OH are related by
mNSO3 ) NOH
(24)
and ASO3 and AOH to A- by
A- ) (ASO3 + mAOH)
(25)
By means of these relations and eq 23, the total scattering length density may be expressed as
F ) (bSO3 + mbOH + fTMAbTMA)/τA-
(26)
where fTMA ()NTMA/NSO3) is the counterion fraction. Analyzing the neutron reflection profiles using the optical matrix method and calculating fTMA using eq 26, the distribution of the TMA+ counterions may therefore be obtained. Disregarding charge neutrality, two uniform layers is the minimum level at which the reflectivity of the counterions can be fitted. If charge neutrality is a constraint, which it should be, it is necessary to introduce a third very diffuse layer, which balances the charge but which makes a negligible contribution to the reflectivity. We include this layer in all the calculations. The two layers that determine the reflectivity consist of a head layer containing the heads and some TMA+ ions and a
The first comment to make is that either neutron reflection does not “see” all the counterions or there are fewer TMA+ ions than necessary to neutralize the surface, and this is a conclusion independent of the various models used to fit the data. Although all the models we have used have maintained electroneutrality, this has been by the device of taking the average of the distribution of the residual ions over such a wide region that they effectively contribute nothing to the reflectivity. The penetration depth of the reflection experiment is about 10 µm in H2O, which is sufficient that all the ions should be observed, and therefore, discounting for the moment the possibility that other “invisible” ions are partially replacing the TMA+ ions, the problem must either be that the residual ions are indeed distributed over a wide region or be caused by roughness in the diffuse part of the ionic layer. The diffuse ion distribution is not expected to be sensitive to any fluctuations of the surface; i.e., it will not participate in the capillary wave motion, but it will be very “grainy”. Thus, in the case of the highest charge density (SO3:OH ) 1:0) and lowest salt concentration, where the effect is largest, the area per diffuse layer counterion is about 30 Å2 but the Debye length is 100 Å; i.e., there is on average one counterion distributed somewhere in the 30 × 100 Å3 volume. Although the description of ionic layers is always made in terms of their average distribution, it is clear that, because of the wide range of possible vertical position and because of the strong repulsion between ions of like charge, the real layer will be very rough and it may then be inappropriate to model the reflection in terms of reflection from the average distribution. Unfortunately, because the mean distribution of the ions is very unsymmetrical, there are no models of scattering from rough surfaces which would be appropriate. Thus, for example, the capillary wave model of liquid surfaces17 or Gaussian roughness18,19 would not be at all appropriate. In most models, e.g. the Kirchoff model of scattering from a rough surface,19 the effect of roughness should decrease as κ decreases and the surface should appear smooth at κ ) 0. If roughness is damping down the signal at the values of κ of our measurements, it is probable that our measured specular reflectivities are increasing more rapidly with decreasing κ than is appropriate for specular reflection for a layer of given thickness. This would, in turn, lead to the result that our estimates of the thickness of the layers would be larger than they really are. However, leaving apart the “invisible” layer, which we do not really (17) Schwartz, D. K.; Schlossman, M. L.; Kawamoto, E. H.; Kellogg, G. J.; Pershan, P. S.; Ocko, B. M. Phys. Rev. A 1990, 41, 5687. (18) Sinha, S. K.; Sirota, E. B.; Garoff, S.; Stanley, H. B. J. Chem. Phys. 1988, 78, 1611. (19) Ogilvy, J. A. Theory of Wave Scattering from Random Rough Surfaces; Adam Hilger: London, 1991.
Neutron Reflection from Counterions
Langmuir, Vol. 13, No. 7, 1997 2141 Table 4. Parameters of the Three-Layer Model
(a) Scattering Length Density, F, and Thickness, τ, the Optical Matrix Method with the Three-Uniform-Layer Model SO3:OH ) 1:0 h [TMACl]/ F/106 Å-2 M 0.1 0.01 0.001
SO3:OH ) 1:1
1
2
F/106 F/106 Å-2 τ/Å Å-2
τ/Å
h τ/Å
F/106 Å-2
SO3:OH ) 1:2
1
2
F/106 Å-2 τ/Å
τ/Å
F/106 Å-2
h τ/Å
F/106 Å-2
1 τ/Å
2
F/106 Å-2 τ/Å F/106 Å-2
0.61 15 ( 15 0.6 16 0.01 g1900 0.57 15 ( 10 0.44 22 0.0046 g1000 0.49 20 ( 5 0.42 19 0.44 20 ( 5 0.39 20 0.015 g1900 0.6 15 ( 15 0.3 25 0.0054 g1700 0.58 15 ( 15 0.37 20 0.33 29 ( 5 0.23 16 0.021 g2000 0.3 25 ( 5 0.26 20 0.007 g1800 0.38 20 ( 5 0.29 25
0.014 0.0036
τ/Å g60 g800
(b) TMA+ Fraction and Area per TMA+ in the First Two Layers for the Three-Layer Model Derived from Part a SO3:OH ) 1:0 [TMACl]/M
A-/Å2
fTMAh
0.1 0.01 0.001
35 30 25
0.1 ( 0.1 0.05 ( 0.04 0.03 ( 0.03
SO3:OH ) 1:1 fTMA1
A-/Å2
fTMAh
0.29 0.20 0.08
61 59 54
0.25 ( 0.25 0.26 ( 0.26 0.15 ( 0.15
SO3:OH ) 1:2 fTMA1
A-/Å2
fTMAh
fTMA1
0.51 0.38 0.27
85 84 80
0.5 ( 0.3 0.4 ( 0.3 0.3 ( 0.3
0.59 0.54 0.50
Table 5. Structural Parameters of the TMA+ Counterion Distribution Determined Using Three Gaussian Distributions SO3:OH ) 1:0 [TMACl]/ σh/ Å M 0.1 0.01 0.001
σTMAh/ Å
δhTMAh/ Å
SO3:OH ) 1:1 σ1
δh1
σ2
δh2
σTMAh
δhTMAh
σ1
δh1
SO3:OH ) 1:2 σ2
δh2
σTMAh
δhTMAh
σ1
δh1
σ2
δh2
10 10 ( 10 0 ( 2 16 ( 7 15 ( 2 200 71 12 ( 10 0 ( 5 19 ( 7 18 ( 3 170 72 12 ( 5 0 ( 4 18 ( 7 19 ( 3 10 10 ( 10 6 ( 2 23 ( 10 22 ( 2 250 77 12 ( 7 0 ( 2 23 ( 7 19 ( 3 170 76 12 ( 12 0 ( 7 18 ( 18 17 ( 3 100 70 10 14 ( 14 10 ( 5 23 ( 23 32 ( 5 250 76 14 ( 14 0 ( 5 17 ( 17 23 ( 3 170 98 14 ( 14 0 ( 5 16 ( 16 22 ( 3 100 80
Figure 10. Variation of the reduced kinematic reflectivity at different “0”C22SO3Na:“0”C22OH ratios: (a) 1:0; (b) 1:1; (c) 1:2. The concentrations of TMACl are 0.10 M (O), 0.01 M (4), and 10-3 M (+). The continuous lines are calculated using the Gaussian distributions and the parameters in Table 5.
see at all, the thicknesses that we observe are not unreasonable. There is another quite different possible explanation of the missing ions and that is that the Na+ ions in the original spread material are so much more strongly bound than the TMA ions that they are preferentially adsorbed at the surface. This is consistent with the trend of increasing TMA ions with bulk TMACl concentration. The increase in the number of TMA ions observed as the charge density in the layer drops would then indicate that the packing of ions in the layer adjacent to the surface also
affects the Na+/TMA+ ratio. The TMA+ ion is probably too large to form a complete Stern layer at areas (A-) less than about 50 Å2, as judged by the limiting surface area for the soluble surfactant TMADS.5 Apart from any difference in the energy of binding single Na+ and TMA+ to the surface, the packing restriction may start to favor Na+ very strongly when A- drops below this value. However, [Na+] is typically about 2.5 × 10-7 M, and even at the lowest TMACl concentration this is about four orders of magnitude smaller than [TMA+] and there would therefore have to be an enormous difference in the binding constants of the two ions for a significant proportion of the TMA+ ions to be displaced. It is at present impossible to decide whether neutron specular reflection is failing to see all the counterions or whether they are simply not all there. In other studies we have also found that not all the counterions are observed, but these have been soluble surfactant systems where ion contamination is very hard to eliminate.20 From the point of view of using specular reflection to study the diffuse double layer, a failure to see all the ions is disappointing, although it suggests that a complete model of specular and off-specular scattering might lead to interesting results about the diffuse double layer. The difficulty is that the background incoherent scattering is so high that it will mask all but the very largest off-specular reflection signal. The equivalent experiment with X-rays, where the signal to noise is much more favorable, is not possible because the signal of neither the amphiphilic layer nor the solvent can be eliminated by contrast variation. Although the neutrons do not apparently see all of the ions present at the surface, more than just the bound layer is observed. This is shown most clearly from the values of the thickness of the first two layers given in Tables 4 and 5. The largest value of the thickness for all three surface charge densities at the lowest salt concentration of 0.001 M is 45 Å, which is much larger than would be (20) An, S. W.; Lu, J. R.; Thomas, R. K.; Penfold, J. Langmuir 1996, 12, 2446. (21) Windsor, C. G. Pulsed Neutron Scattering; Taylor & Francis Ltd.: London, 1981. (22) Tanford, C. J. Phys. Chem. 1972, 76, 3020. (23) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: London, 1985.
2142 Langmuir, Vol. 13, No. 7, 1997
Su et al.
Table 6. Parameters Calculated Using the Stern Model SO3:OH ) 1:0
SO3:OH ) 1:1
[TMACl]/M FStern/Å-2 τStern/Å Fdiff/Å-2 τdiff/Å ψb/mV κ-1/Å FStern τStern Fdiff τdiff 0.1 0.01 0.001
0.61 0.44 0.33
15 20 29
1.8 1.8 2.8
16 20 16
-159 -229 -298
9.8 31 98
0.57 0.6 0.3
expected for a Stern layer. As the ionic strength increases, the thickness of this layer decreases sharply for the highest charge density surface but hardly at all for the lowest charge density surface. However, in no case does the thickness approach what would be expected for a Stern layer. Further support for the fact that both the Stern layer and part of a diffuse layer are being observed is the need to divide the layer up into two to obtain a satisfactory fit to the data. This division indicates that the layer that is closest to the usual definition of a Stern layer is the one that coincides approximately with the headgroup plane. The anomalous behavior of the π-A isotherms discussed earlier was interpreted in terms of penetration of the headgroup region by TMA+ ions. It is clear from both types of modeling procedure that there is significant penetration of the headgroup region and that the extent of penetration increases with bulk TMACl concentration and increases as the surface charge density is reduced. The reflection measurements therefore support the conclusions drawn from the anomalous isotherm behavior. Finally, it is interesting to compare the experimental results with the classical model of the electrical double layer. The value of the negative surface charge may be obtained from A-, and that of the positive charge of the TMA+ counterions in the Stern layer, from fTMAh in Table 4b. The difference between the two is the charge in the diffuse layer σ and is related to the boundary potential, ψb, between the Stern layer and the diffuse layer through
σ)
2D0kTχ ze sinh(zeψb/2kT)
(27)
where D is the dielectric constant of the medium and
χ)
(
)
2e2z2n0 D0kT
1/2
(28)
where n0 is the bulk concentration. The results calculated using the Stern model are given in Table 6 and Figure 11. FStern and Fdiff, which are related to the number density of the TMA+ counterions by
F ) bTMAnTMA
(29)
where bTMA is the scattering length, are the scattering length densities of the Stern layer and the adjacent diffuse layer, corresponding to the head layer and the first counterion layer, respectively. Comparison of the scattering length densities from the optical matrix method (Table 4) and from the three-layer model shows that the
15 15 25
SO3:OH ) 1:2 ψb
κ-1
FStern τStern Fdiff τdiff
0.65 22 -121 9.8 0.49 0.55 25 -181 31 0.58 0.86 20 -252 98 0.38
20 15 20
ψb
κ-1
0.35 19 -84 9.8 0.36 20 -152 31 0.37 25 -221 98
Figure 11. Neutron reflectivity profiles of (a) “0”C22(SO3-:OH ) 1:0) with 0.01 M dTMA+ in NRW, (b) “0”C22(SO3-:OH ) 1:0) with 10-3 M dTMA+ in NRW, (c) “0”C22(SO3-:OH ) 1:2) with 0.01 M dTMA+ in NRW, and (d) “0”C22(SO3-:OH ) 1:2) with 10-3 M dTMA+ in NRW. The continuous lines are calculated using the Stern-Gouy-Chapman model of the double layer.
number density of TMA+ counterions estimated using the Stern model is too high. Figure 11 shows that there is a significant deviation in the value of Fdiff between the measured reflectivity profile and the calculation in the case of (SO3:OH ) 1:0) at 10-3 M TMACl, i.e. in the case of high surface charge density and low concentration of salt. The deviation will, however, be smaller when the surface charge density decreases. It is not surprising that the calculation fits the experimental data better in the case of lower surface charge density because fewer counterions are near the surface and thus the assumption of point charges in the diffuse layer of the Stern model is more applicable. The deviation should also be smaller when the concentration of salt increases. This is probably because the increase of the salt concentration pushes more TMA+ counterions into both the Stern and adjacent diffuse layers and thus makes the volume effect of the TMA+ less important. It would, therefore, be reasonable to expect that the calculation for the case of (SO3:OH ) 1:0) at 10-3 M TMACl, i.e. for the case of low surface charge density and high concentration of salt, would agree relatively well with the measured reflectivity profile, and this is exactly as observed in Figure 11c. Acknowledgment. We thank the EPSRC for supporting this work. LA960663N
