Neutron Reflection from Counterions at the Surface of a Soluble

Deuterated sodium dodecyl sulfate (SDS) was obtained from. Cambridge Isotopes and protonated SDS from Polysciences. (99.5% purity) ..... 940 J. Phys. ...
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J. Phys. Chem. B 1997, 101, 937-943

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Neutron Reflection from Counterions at the Surface of a Soluble Surfactant Solution T. J. Su, J. R. Lu, 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 2, 1996; In Final Form: September 19, 1996X

The distribution of counterions at a charged surface has been measured directly using neutron specular reflection with isotopic labeling being used to highlight the scattering from the counterions. The system investigated was the soluble surfactant tetramethylammonium dodecyl sulfate with and without added tetramethylammonium chloride. Depending on the conditions a fraction of ions were found to penetrate the surfactant head-group region. The majority of the counterions observed formed a layer adjacent to the head-group layer which must be part of the diffuse layer. These two layers did not, however, account for all the counterions, and the remainder of the diffuse layer could not be observed with certainty. The reason for this is not understood, although it is probably associated with the roughness of the diffuse layer. Using the measured charge density and surface coverage as parameters, the counterion distribution calculated from the Stern-Gouy-Chapman model of the electrical double layer appears to account quite well for the shape of the distribution, although the effect of the “missing” ions made a detailed quantitative comparison impossible.

Introduction Research into the behavior of counterions at surfaces has mainly been limited to macroscopic observations, using techniques such as foaming,1 calorimetry and specific-ion electrodes,2 NMR,3-5 HPLC,6 and interfacial tension measurements.7-9 With the recent development of several new techniques, it is now possible to obtain information concerning the structure of counterions more directly and on a molecular scale. For example, Duffy et al.10 have observed SCN- binding to a charged surfactant monolayer by using sum-frequency vibrational spectroscopy, Wu et al.11 have used small-angle X-ray scattering to measure the distribution of Cs+ counterions around cylindrical micelles and the same technique has also been used by Chang et al.11 to measure the counterions of Tl+ and Ba2+ around DNA. Berr et al.13,14 used small-angle neutron scattering to study the effect of counterions on the size, structure, and charge of micelles, and Szajdzinska-Pietek et al.15,16 utilized electron spin-echo modulation spectroscopy to obtain information about the structure of counterions in the Stern layer and the same technique combined with electron spin resonance to study structural effects of counterion substitution.15 The technique of neutron reflection has been successfully applied to the direct determination of the structure of surfactants adsorbed at different interfaces. We now use this technique to determine the counterion distribution under a charged planar interface created by the presence of a monolayer at the surface. The system chosen is the air/aqueous solution interface of tetramethylammonium dodecyl sulfate (TMADS). When TMADS is adsorbed at the surface, the orientation of the dodecyl sulfate anion establishes a negative charged surface and the charge is balanced by the TMA+ counterions, giving an electrical double layer. The particular interest of TMA+ is that in a neutron reflection measurement isotopic labeling may be used to eliminate all but the signal from the TMA+ counterions, as has already been shown in a preliminary experiment. Since this first experiment, done by Penfold et al.,18 the technique of X

Abstract published in AdVance ACS Abstracts, January 1, 1997.

S1089-5647(96)01979-7 CCC: $14.00

neutron reflection has improved considerably and it is now worthwhile attempting a more quantitative study using selective labeling to examine the TMA+ counterion distribution. Experimental Details Deuterated sodium dodecyl sulfate (SDS) was obtained from Cambridge Isotopes and protonated SDS from Polysciences (99.5% purity). Deuterated tetramethylammonium chloride (N(CD3)4Cl or d-TMACl) was obtained from MSD Isotopes and protonated tetramethylammonium hydroxide (h-TMAOH) from Fluka (>98% pure). All the solvents used were analytical grade, and ultrapure water (Elgastat UHQ) was used throughout. The preparation of the various isotopic TMADS species was as follows: Silver(I) oxide was prepared from the reaction of silver nitrate (Aldrich, 99%) with sodium hydroxide (Aldrich, semiconductor grade). After the precipitate was washed several times with water, it was added to the acid form of dodecyl sulfate, produced from SDS by ion exchange with Dowex 21K resin (particle size 0.30-0.85 mm),19 the resin having been activated by immersing it in concentrated HCl followed by rinsing with pure water several times. The resulting precipitate of AgDS was washed and dried on a rotary evaporator. d-TMACl was then added to a methanolic solution of AgDS, and after removal of the precipitated silver chloride, crude TMADS was obtained. This TMADS was recrystallized several times from ethanol until no minimum was detected in the surface tension near the critical micelle concentration. This method was used only for the isotopic species C12H25SO4N(CD3)4. The other two species, i.e., C12D25SO4N(CH3)4, and C12H25SO4N(CH3)4, were prepared by neutralizing the acid form of the sulfate with h-TMAOH. These materials were used to make, by mixing isotopic species in the appropriate ratio, “0” C12SO4N(CH3)4 and “0” C12SO4N(CD3)4, which we refer to as hTMA “0” DS and dTMA “0” DS, respectively, where the isotopic composition of the hydrocarbon chains is adjusted to give a scattering length density of exactly zero, instead of approximately zero as in the pure protonated form. Note that, given the starting isotopic species, the scattering length of the © 1997 American Chemical Society

938 J. Phys. Chem. B, Vol. 101, No. 6, 1997

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Figure 1. (a) Surface tension as a function of bulk concentration of dTMA “0” DS (O), hTMA “0” DS (4), and hTMAdDS (+). Only the error bars of hTMAdDS are shown here. The lower concentration curve is for dTMA “0” DS with 0.12 M TMACl (O). (b) Adsorption isotherms calculated from the surface tension and the Gibbs equation of dTMA “0” DS without salt (O) and dTMA “0” DS with 0.12 M TMACl (4).

d-TMA ion in the second of these two compounds is slightly reduced from the value of the fully deuterated species. All measurements were carried out at temperature of 298 K. The surface tension measurements were made on a Kru¨ss K10T digital tensiometer using the du Nou¨y ring method with a platinum/iridium ring. The apparatus was calibrated with respect to high-purity water (72.0 mN/m at 298 K). The neutron reflection measurements were done on the reflectometer CRISP at the Rutherford-Appleton Laboratory (Didcot, U.K.).20 The solutions were contained in Teflon troughs of dimensions about 250 × 70 × 5 mm3 with the neutron beam direction along the long dimension. The meniscus of the solution projected typically about 1 mm above the edges of the troughs. The troughs themselves were enclosed in airtight aluminum containers with quartz windows for the neutron beam. For the system studied here, measurements were made at incident angles of 0.45°, 0.8°, and 1.5°, which gives a range of momentum transfer, κ ()(4π sin θ)/λ, where θ is the glancing angle of incidence) from 0.015 to 0.65 Å-1, and a flat incoherent scattering background was subtracted. The background was calculated using the value of the signal at high momentum transfer. We have shown elsewhere that this is valid provided that there is no small-angle scattering from the bulk of the solution, which occurs only above the critical micelle concentration.21,22 The conversion of the measured signal to absolute reflectivity can be made either by calibration with a reference liquid (D2O is the most convenient) or by direct measurement of the signal below the critical angle for total reflection, where the reflectivity is unity. The main measurements in this paper were done using null reflecting water (NRW) whose isotopic composition is adjusted so that its scattering length density is zero. Since the scattering length density of air is also zero there is no reflected signal from NRW, and hence calibration has to be made by comparison with the known reflectivity of D2O. Results Surface Tension. In the neutron specular reflection measurements, hydrogen/deuterium substitution is used to vary the scattering length densities. The determination of the structure of an adsorbed layer by neutron reflection depends on the assumption that isotopic substitution does not change the actual structure. Surface tension measurements were used to check the reliability of this assumption in the case of TMADS, as an

independent means of determining the surface coverage, and as a check on the purity of the samples. Figure 1a shows plots of surface tension γ versus ln(concentration) for three isotopic species, dTMA “0” DS, hTMA “0” DS, and hTMAdDS. The discontinuity in the plot corresponds to the critical micelle concentration (cmc). The three curves show no trace of a surface tension minimum, and have similar cmc’s at (5.3 ( 0.3) × 10-3 M, in agreement with literature values.23 Although there are slight differences between the samples below the CMC, the surface tension values are within the experimental error of 0.5 mN m-1 and we therefore conclude that isotopic substitution does not affect the surface properties of aqueous TMADS solutions. Also shown in Figure 1a is the surface tension of dTMA “0” DS in the presence of 0.12 M TMACl. The addition of 0.12 M TMACl lowers the cmc to (7.9 ( 0.3) × 10-4 M. The area per molecule A was determined by assuming an activity coefficient of unity and fitting a second degree polynomial to the data (γ -ln(concentration)) below the cmc and then using the Gibbs equation to give the adsorption isotherms shown in Figure 1b. The prefactor in the Gibbs equation is 2 for a solution without salt and 1 with 0.12 M salt. The area per molecule at the cmc was found to be 52 ( 5 Å2 for TMADS solution without salt and 42 ( 5 Å2 for TMADS solution with 0.12 M TMACl. Neutron Reflection. (a) Structure of the Whole Layer. Neutron reflectivity profiles were measured for four different isotopic compositions of TMADS adsorbed at the liquid/air interface at its CMC, hTMAdDS and dTMA “0” DS in null reflecting water (NRW), and hTMA “0” DS and dTMA “0” DS in D2O, all shown in Figure 2. Since NRW has exactly the same scattering length density as air there is no reflected signal from its surface in the absence of any adsorbed and suitable labeled species. Thus, for the second of the profiles listed above (Figure 2b) the signal is strongly dominated by the counterion layer, the only other nonzero scatterer being the sulfate head group, with a scattering length only about 20% of that of the counterion. The structure of a layer can generally be determined by fitting a single model structure to the set of reflectivity profiles from the different isotopic species. Two types of approach have been most widely used for surfactant layers,24 the exact optical matrix method which uses a number of uniform layers to describe the fragment distribution normal to the interface25 and the kinematic

Neutron Reflection from Counterions

J. Phys. Chem. B, Vol. 101, No. 6, 1997 939 TABLE 1: Structural Parameters of the Calculated Curves for the Whole Layer in Figure 2 scattering length density F × 106/Å-2 layer

τ/Å

hTMAdDS

solvent chain head TMA1 TMA2

9(4 10 ( 4 16 ( 4 700 ( 200

NRW 3.9 1.65 -0.07 -5.3 × 10-4

dTMA “0” DS

dTMA “0” DS

hTMA “0” DS

NRW

D2O

D2O

0.82 0.86 6.9 × 10-3

5.4 6.4 6.35

4.7 6.1 6.35

of four layers is needed to represent the whole surface layer. The first layer contains the alkyl chains in air (the chain layer), the second contains a fraction of the alkyl chains immersed in water, the heads and some counterions (the head layer), and the other layers contain the remainder of the counterions. The residual space in each layer except the first is filled with water. The structural parameters of each layer are defined as follows: (i) the chain layer:

Figure 2. Neutron reflectivity profiles of the four isotopic species of TMADS at CMC, (a) hTMAdDS in NRW, (b) dTMA “0” DS in NRW, (c) dTMA “0” DS in D2O, and (d) hTMA “0” DS in D2O. All the continuous lines are calculated using the parameters in Table 1. The dashed lines in (a) and (b) are calculated using a model of a single uniform layer (thickness 19 and 30 Å, respectively) and those in (c) and (d) using a model of two uniform layers.

approximation where more realistic distributions are used for the fragments, although the method is not exact. The difficulty of using the kinematic approximation is that it relies on differences in the profiles and therefore demands high accuracy in the measurements. For the TMADS system we found it impossible to obtain consistent results using the kinematic approximation mainly because the signal from the counterion is weak and the distribution needed to describe the layer somewhat complicated. We have therefore restricted the analysis to the optical matrix method. Assuming the dodecyl sulfate anions form a uniform layer at the surface, a model of a single uniform layer was used first to fit the data of hTMAdDS in NRW, which gives information about the structure of the dodecyl sulfate anion adsorbed at the surface. With this model the measured profile can be fitted well with a scattering length density of 2.8 × 10-6 Å-2 and a layer of overall thickness τ of 19 Å. The calculated curve is shown as the dashed line in Figure 2a. Using the derived scattering length density F of the layer the area per molecule A can be calculated from

F)

∑bi/Aτ

(1)

where the bi are the scattering lengths of the constituent nuclei of the anion. The value of A was found to be 51 ( 3 Å2, in good agreement with the result from the surface tension measurements. Note that we have not included any surface roughness in the modeling of the dodecyl sulfate layer. At the relatively low resolution of the present experiment it is not possible to distinguish roughness contributions from small geometrical differences in the layer. In any case, inclusion of roughness has no effect on the derived value of A. The process of finding an appropriate model for the distribution of the counterions is more complicated and is discussed in detail in the next section. However, since this is needed to fit the whole layer we note that two layers are necessary to fit the counterion distribution, with a third layer needed if electroneutrality is to be maintained. Since three layers are needed to describe the TMA+ counterions, a structural model with a total

τc ) (1 - fc)lc

(2)

Fc ) (1 - fc)bc/τcA

(3)

Fh ) (fcbc + bh + fTMAhbTMA + nwhbw)/τhA

(4)

(ii) the head layer:

(iii) the first counterion layer:

FTMA1 ) (fTMA1bTMA + nwTMA1bw)/τTMA1A

(5)

(iv) the second counterion layer:

FTMA2 ) [(1 - fTMAh - fTMA1)bTMA + nwTMA2bw]/τTMA2A (6) where τi is the thickness of the i th layer, fc the fraction of an alkyl chain in the water, lc the fully extended alkyl chain length,  the degree of extension of the alkyl chain, Fi the scattering length density of the ith layer, bi the scattering length of the molecule, A the area per adsorbed surfactant, fTMAi the counterion fraction (the ratio of the number of counterions in the ith layer to that of adsorbed surfactant ions, i.e., NTMAi/NSO4), and nwi the number of water molecules in the ith layer. The amount of water in the layers must also satisfy space-filling requirements, i.e.

τiA ) Vh + fiVTMA + nwiVw + fcVc

(7)

where Vi is the molecular volume of the molecule i. Although the reflectivities from the different isotopic species have different sensitivities to the adjustable parameters,26 equal weight was given to each profile in deriving the above parameters. In principle all the experimental profiles should be fitted with a single set of values of the parameters above, but in order to prevent distortion of the result by systematic errors in one profile, each profile was fitted independently, allowing A and the number of water molecules to float within a limited range. The resulting fits are shown as continuous lines in Figure 2, and the fitted parameters are given in Table 1. The whole set of data could be fitted with the structural parameters A ) 53 ( 3 Å2, fc ) 0.25 ( 0.1,  ) 0.72 ( 0.1, fTMAh ) 0.15 ( 0.15, fTMA1 ) 0.63 ( 0.12, and fTMA2 ) 0.22. This gives 12 ( 2 water molecules surrounding the head group and 25 ( 4 water molecules per TMA+ ion in the first counterion layer. The basic parameters of the various fragments in the system used in the calculation are given in Table 2. These results are in reasonable agreement with the earlier study of ref 18.

940 J. Phys. Chem. B, Vol. 101, No. 6, 1997

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TABLE 2: Volumes and Scattering Lengths

a

species

vol/Å3

scattering lengtha/10-5 Å

C12H25 C12D25 SO4 N(CH3)4+ N(CD3)4+ H2O D2O

350b 350b 58c 175d 175 29.9e 30.2e

-13.7 246.55 26.05 -8.88 116.04 -1.68 19.14

Reference 27. b Reference 28. c Reference 29. d Reference 30.

Figure 3. Comparison of the neutron reflectivities of dTMA “0” DS in NRW in the three conditions: 5.3 × 10-3 M without salt (O), 3.0 × 10-4 M with 0.12 M TMACl (4) and 7.9 × 10-4 M with 0.12 M TMACl (+).

(b) Structure of the Counterion Layer. For the isotopic composition dTMA “0” DS in NRW the main contribution to the reflectivity is from deuterated TMA+ ions and any effects of added salt are best studied using this contrast. As well as determining the reflectivity at a TMADS concentration of 5.3 × 10-3 M with no added salt we also measured neutron reflectivity profiles with 3.0 × 10-4 M and 7.9 × 10-4 M dTMA “0” DS in NRW in the presence of 0.12 M TMACl, the three profiles being shown in Figure 3. The concentration of 3.0 × 10-4 M was chosen because it has the same surface excess of surfactant ion as that of 5.3 × 10-3 M without salt. It should be noted that although any contribution to the reflection from dodecyl chains and water has been eliminated by mixing deuterated and protonated materials in such a ratio that the mixture has a scattering length density of zero, the contribution of the SO4 heads cannot be completely eliminated. The SO4 group, which has a scattering length of 26.05 × 10-5 Å, does make a small contribution to the reflectivity of dTM “0” DS in NRW. In general, the slope of a reflectivity profile is proportional to the thickness of the adsorbed layer. The slope of the reflectivity profile of the 3.0 × 10-4 M TMADS solution with 0.12 M TMACl is more gradual than that of 5.3 × 10-3 M without salt from which it can immediately be concluded that, at the same surface charge density, the counterion layer is thinner in the presence of salt, as would be expected. The general level of the reflectivity is largely determined by the amount adsorbed at the surface. The greater the adsorption, the higher the reflectivity. The reflectivity of 7.9 × 10-4 M TMADS + 0.12 M TMACl solution in the κ range measured is generally always higher than that with 3.0 × 10-4 M TMADS + 0.12 M TMACl, which indicates that, for the same salt concentration, more

Figure 4. Neutron reflectivity profile of dTMA “0” DS in NRW at 5.3 × 10-3 M without salt. The continuous line in (a) is the best fit using a one-layer model, in (b) the best fit using a two-layer model, and in (c) the best fit using the three-layer model (Table 3).

counterions are present at the surface when the surface charge density is higher, again as expected. We interpret the data using the optical matrix method and the profile of dTM “0” DS at 5.3 × 10-3 M as an example. Assuming the SO4- groups and TMA+ counterions together form a uniform layer, we start by using just one uniform layer to fit the profile. The continuous line in Figure 4a is the best fit using this model with one counterion present for every surfactant ion, the surface coverage of the surfactant being determined from the profile in Figure 2a. This does not fit the data at all (this is also shown as a dashed line in Figure 2b). The profile can be fitted with a single uniform layer with only 78 ( 10% of the counterions (continuous line in Figure 4b) but this would mean that the surface was not electroneutral. Since it has to be neutral we conclude that the remaining 22% of the counterions are distributed so diffusely that they effectively contribute nothing to the reflectivity. The continuous line in Figure 4c is the best fit using this model with the parameters given in Table 3a. There are two points that need to be emphasized. The first is that since the reflectivity depends

Neutron Reflection from Counterions

J. Phys. Chem. B, Vol. 101, No. 6, 1997 941

TABLE 3: Structural Parameters of the TMA Ion Layer in NRW Determined Using the Optical Matrix Method and the Two Uniform Layer and Three-Layer Models (a) Two Uniform Layer Model TMADS (M)

TMACl (M)

A ( 3/Å2

FTMAb × 106/Å-2

τTMAb (Å)

FTMAd × 106/Å-2

τTMAd (Å)

0.12 0.12

53 53 42

0.85 1.12 1.26

26 ( 2 23 ( 3 22 ( 2

6.9 × 10-3 0.01 0.012

g700 g100 g500

5.3 × 10-3 3.0 × 10-4 7.9 × 10-4

(b) Three-Layer Model TMADS (M) 5.3 × 10 3.0 × 10-4 7.9 × 10-4

TMACl (M)

A ( 3/Å2

Fh × 106/Å-2

τh (Å)

FTMA1 × 106/Å-2

τTMA1 (Å)

0.12 0.12

53 53 42

0.82 1.04 1.31

10 ( 4 10 ( 6 10 ( 5

0.86 1.18 1.22

16 ( 4 13 ( 6 12 ( 5

-3

on the square of the scattering length density of the layer, a shortfall of 22% in the number of counterions corresponds to a reflectivity that is approximately 50% too low, a long way outside any experimental error. The second is that the inclusion of the missing 22% of ions in the calculation has only been made to demonstrate what would be the minimum thickness of a layer that both included the missing ions and contributed fully to the reflectivity. We discuss the possibility that this remaining 22% of the counterions are actually not present below. A correct model should fit all the profiles of different contrasts, and it was found that the profile from dTM “0” DS could be fitted reasonably well but that from hTM “0” DS in D2O could not (see dashed lines in Figure 2c,d). It was also found that to fit the data of hTM “0” DS in D2O, the thickness of the counterion layer would have to be less than 20 Å, which is smaller than the minimum value of 24 Å required for a satisfactory fit of dTM “0” DS in NRW. This indicates that the single counterion layer observed directly from the reflectivity, i.e., the 78% of the counterions, is probably not uniform and it is therefore necessary to divide it. Including the residual 22% of the counterions for neutrality, this now gives three layers of counterions. One is the head layer, and we name the others counterion layers one and two. We reiterate that the counterion layer labeled 2 effectively contributes nothing to the reflectivity. Combined with the physical constraint of the size of TMA+, the continuous line in Figure 4c is the best fit using this threelayer model and the fitted parameters are given in Table 3b. The same procedure was applied to the structural determination of dTM “0” DS at 3.0 × 10-4 and 7.9 × 10-4 M with 0.12 M TMACl. The dotted lines in Figure 5 are the best fits using the one layer model and the fits using a two layer model with the parameters given in Table 3a are represented by a continuous line. The labels TMAh and TMA2 in Table 3a denote the layer determining the reflectivity profile and a diffuse counterion layer, which is included only for electroneutrality. The area per molecule used in the fitting of these structures to the 3.0 × 10-4 and 7.9 × 10-4 M dTM “0” DS with 0.12 M TMACl was obtained from the surface tension data (Figure 1b). For consistency with the measurements in the absence of added TMACl, the two profiles were also fitted by using the model of three layers, although the fits are indistinguishable from the two-layer model, shown as continuous lines in Figure 5. The results for the three layer model are given in Table 3b. The counterion fractions fTMAi of TMA+ in the different layers can be obtained by using eqs 4-6 and are given in Table 4. The error in fTMAh is comparable with the actual value of fTMAh, but this merely reflects the inaccuracy of the division between layers h and 1 rather than in the total fraction of ions in these two layers. Discussion We first discuss the overall structure of the layer in terms of the results from fitting uniform layers to the structure (optical

FTMA2 × 106/Å-2 6.9 × 10 0.01 0.012

τTMA2 (Å) g700 g100 g500

-3

Figure 5. Neutron reflectivity profiles of dTMA “0” DS in NRW at (a) 3.0 × 10-4 M, and (b) 7.9 × 10-4 M with 0.12 M TMACl. The dotted line is the best fit using a model of one layer. There is almost no difference between the fits using two and three layers, and they are represented by a single continuous line in each case.

TABLE 4: TMA+ Fractions in Each Layer (a) Two-Layer Model TMADS/M

TMACl/M

ASO4 ( 3/Å2

fTMAb

fTMAd

5.3 × 3.0 × 10-4 7.9 × 10-4

0.12 0.12

53 53 42

0.78 ( 0.10 0.95 ( 0.10 0.78 ( 0.08

0.22 0.05 0.22

10-3

(b) Three-Layer Model TMADS/M 5.3 × 10-3 3.0 × 10-4 7.9 × 10-4

TMACl/M

ASO4 ( 3/Å2

fTMAh

fTMA1

fTMA2

0.12 0.12

53 53 42

0.15 ( 0.15 0.25 ( 0.25 0.25 ( 0.25

0.63 0.70 0.63

0.22 0.05 0.22

matrix method, Table 1) and compare TMADS with sodium dodecyl sulfate (SDS).19 For added clarity the overall structure of the layer is shown in the form of the volume fraction profile normal to the surface in Figure 6. The total chain length of TMADS (including the head) is 19 Å, which is similar to that of SDS (18 Å). The fragment of TMADS protruding out of the water is, however, less extended than SDS while that below

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Figure 6. Volume fraction distribution normal to the surface of the various fragments comprising the interface as calculated from the reflectivity profiles for a concentration of 5.3 × 10-3 M TMADS without salt, dodecyl chain and TMA ion (continuous lines), water (dashed line), sulfate head group (dotted line). The parameters used are from Tables 1 and 2.

water is more extended. Since A is larger for TMADS, there is more lateral space for the flexible hydrocarbon chain and this is probably the reason that the thickness of the chain layer above water is 2 Å thinner than that of SDS (11 Å). The value of 0.25 for fc means that there are approximately three CH2 groups overlapping the water distribution whereas for SDS this number is four. However, the head layer thickness of TMADS is 3 Å thicker than that of SDS, indicating that the chain fragment of TMADS in the head layer is more extended, even though there is one less CH2 group involved. Except for the three CH2 groups, the SO4 groups, and a part of TMA+, the remainder of the space in the head layer is filled by water molecules and there are about 12 water molecules surrounding the head of TMADS, about twice that surrounding the head of SDS. The length of chain immersed in water is about 4 Å, and the diameter of the head is about 5 Å. The sum of these two dimensions is 9 Å, which is the minimum thickness that the head layer can have. If the TMA counterion is situated below the head group, its diameter of 7 Å will give a maximum thickness for the head layer of 16 Å, neglecting any contribution from roughness. The observed thickness of the head layer, including part of the chain, the head, and 15% of the TMA+ ions, is, however, only 10 Å, which is closer to the minimum possible thickness. This implies that the 15% TMA+ ions, equivalent to one TMA+ being shared by seven SO4 groups, actually penetrate the head layer. Not surprisingly, if the TMA+ ions penetrate the head group layer to some extent the area per molecule at the cmc is 53 Å2 for TMADS, significantly larger than the value of 44 Å2 for SDS.19 The conventional description of the electrical double layer splits the counterions into Stern and diffuse layers, the Stern layer being in some sense bound to the charges on the surface, in this case the head groups. For TMADS the layer that most closely corresponds to a true Stern layer is the layer coplanar with the sulfate head groups. The main layer, situated below the head group plane, must then be regarded as the start of the diffuse layer. It is interesting to compare our experimental results with the classical model of the electrical double layer, the Stern-GouyChapman model. The Stern layer in micelles has been defined as the region of the micelle that contains the heads, the associated counterions and possibly a part of the hydrocarbon

Figure 7. Neutron reflectivity profiles of dTMA “0” DS in NRW in the three conditions: (a) 5.3 × 10-3 M without salt, (b) 3.0 × 10-4 M with 0.12 M TMACl and (c) 7.9 × 10-4 M with 0.12 M TMACl. The dashed lines are the curves calculated using the Stern-Gouy-Chapman model and the continuous lines are the best fits using the structural parameters in Tables 3 and 4, included for comparison.

chains.33 The head group layer in our model will be the Stern layer if the same definition is applied. The neutron reflectivity measurements give the value of the negative surface charge from the area per dodecyl sulfate anion, and the positive charge of the TMA+ counterions in the Stern layer from fTMAh in Table 4. The difference between the two is the charge in the diffuse layer and is related to the boundary potential, ψ0, between the Stern layer and the diffuse layer by

( )

zeψ0 2D0kTξ sinh ze 2kT

(8)

ξ ) (2e2n0z2/D0kT)1/2

(9)

σ) where

The results of the calculation are shown in the form of a comparison between calculated and observed reflectivities in Figure 7. The values of Fdiff estimated by the Stern model are,

Neutron Reflection from Counterions on average, about 30% higher than the observed values. This indicates that the number density of TMA+ counterions obtained from the Stern model is still too high. However the curve calculated by using the Stern model fits the profile of TMADS at 3 × 10-4 M with 0.12 M TMACl reasonably well. This is probably because of the effect of salt. The added salt pushes more TMA+ counterions into both the Stern layer and the adjacent diffuse layer and partially suppresses the volume effect of the counterions. For the cases of TMADS at 5.3 × 10-3 and 7.9 × 10-4 M with 0.12 M salt, however, the volume of the TMA+ counterion has to be considered, especially at a distance from the surface of the order of the sum of the ionic radii. The dashed lines in Figure 7 are the reflectivity profiles calculated using the Stern model and have similar shapes to the measured curves but with a generally higher level of the reflectivity. This indicates that, although the Stern model overestimates the number concentration of TMA+ counterions near the charged surface, the shapes of the calculated reflectivity profiles still qualitatively agree with the empirical data. It is interesting to compare the structure of the TMADS planar monolayer adsorbed at the surface with that of TMADS in micelles. Berr et al.13 used the technique of neutron smallangle scattering to investigate the structure of TMADS micelles. Their results showed that the number of “wet” methylene groups is about five and that there are 18 water molecules surrrounding the head. Since both of these numbers are larger than ours, this indicates that there is greater water penetration into the micelles than into the planar monolayer. Berr et al. also found that TMA + counterions act as space fillers between the head groups of the micelle. The same result was obtained by Szajdzinska-Pietek et al.15 using electron spin-echo. The penetration of TMA+ counterions into the head-group layer observed here also indicates that TMA+ counterions behave as space fillers in the case of a planar monolayer. The failure to observe all of the counterions is not understood. There are two possible explanations. The first is that impurity ions may be present. As shown by An et al.31 and by Cross and Jayson,32 it is extremely difficult to eliminate the effects of impurities in the counterion of anionic surfactants. However, this usually manifests itself in discrepancies between the surface excesses determined by neutrons and surface tension, which are not observed in the case of TMADS at its cmc. The second possibility is that the roughness of the diffuse counterion layer is sufficiently large that a proportion of the neutrons are scattered off-specularly. Although the ion distribution is always expressed in terms of a smooth decay in the direction normal to the surface (e.g., eq 8), it must be extremely rough because of the strong, unscreened, repulsion of adjacent, like charges. Unfortunately, since the Gouy-Chapman model of the ion distribution is a mean-field model, there is no model of this roughness. Given also that there are no comparable systems for which models of the roughness have been given we cannot test this hypothesis. It may be possible in the future to measure both the specular and off-specular contributions to the reflectivity. The major difficulty in the present system is that the relatively high incoherent background from null reflecting water makes it difficult to observe any off-specular scattering and, so far, noone has been able to do such an experiment. The neutron reflection experiment on dTMA “0” DS in NRW is almost as direct a measurement of the counterion distribution at a charged surface as might be thought possible. Although there are a number of experimental difficulties, the low resolution, the possibility that not all the counterions are observed, and the ever present difficulty of attaining the necessary high ionic purity, which is difficult to assess (see, for example, ref 31), there are nevertheless a number of features

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