J. Phys. Chem. 1993,97, 8012-8020
8012
Neutron Reflection from a Layer of Monododecyl Hexaethylene Glycol Adsorbed at the Air-Liquid Interface: The Configuration of the Ethylene Glycol Chain J. R. Lu, Z. X. Li, and R. K. Thomas' Physical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, U.K.
E. J. Staples and I. Tucker Unilever Research, Port Sunlight Laboratory, Quarry Road East, Wirral M 3 3JW. U.K.
J. Penfold Rutherford-Appleton Laboratory, Chilton, Didcot, Oxon OX1 1 OQX, U.K. Received: March 5, 1993; In Final Form: May 14, 1993
We have determined the structure of a layer of monododecyl hexaethylene glycol (C12Ea) adsorbed at the air/water interface at its critical micelle concentration using neutron specular reflection together with isotopic substitution. For both the Clz hydrocarbon chain and the E6 ethylene glycol chain distributions the full width at half height, Q*, was found to be 13.5 f 1 A, to be compared with fully extended chain lengths of 16.7 and 21.6 A, respectively. The separation of the alkyl and ethylene glycol chain regions was found to be 9 f 0.5 A, 1 A less than the alkyl chain water separation of 10 f 0.5 A. Labeling experiments were also used to establish the widths of the two halves of the E6 chain. The E3 at the free end was found to be 14 f 2 A thick ( u * ) and at the "anchored" end 12 f 2 A, and the separation between the distributions of the two fragments was found to be 3.5 f 1 A. The complete set of measurements on the labeled E6 fragment, the first measurements of their kind, indicate that the E6 distribution is characteristic of a significant incidence of gauche conformations in the ethylene glycol chain. The separate labeling experiments also show that the layer is roughened, probably by capillary waves. When the contribution of this roughness is removed from the overall thickness of the alkyl chain the chain is found to be significantly tilted away from the surface normal.
Introduction The monododecyl ether of hexaethylene glycol, Cl2H25(OC2H&oH (designated here by CI2E6), is a widely used nonionic surfactant, and it is therefore of interest to determine its configuration in the adsorbed layers it forms at the air-liquid interface or the solid-liquid interface. Of particular interest, from the point of view of understanding the factors underlying adsorption at these interfaces, is the configuration of the ethylene oxide chain, which is sufficiently long that it may be expected to show signs of disorder. We have already demonstrated that the use of isotopic substitution in conjunction with neutron reflection is an effective way of studying interfacial structure,' and here we present results on C12E6 at the air/water interface at its critical micelle concentration (cmc). We also show here, for the first time, how it is possible to use selective deuterium labelling of parts of a chain to determine some of the details of the shape of the chain distribution. We apply this to the ethylene glycol chain. Experimental Details The protonated material, hClzhE6, was obtained from Fluka and purified by chromatography as described in ref 2. The partially deuterated isotope, dC12hE6, was prepared by standard Williamson synthesis from the deuterated alkyl bromide (Merck, Sharp, and Dohme), an equimolar amount of sodium, and a 5-fold molar excess of hexaethylene glycol (Fluka) and purified on a silica column.2 The fully deuterated and ethylene glycol deuterated compounds, dClzdE6 and hC12dEs, were prepared by reacting ethyleneoxide-d4 (Merck, Sharp, and Dohme) with either the deuterated or the protonated dodecanol.3 The partially deuterated compounds hClzhE3dE3 and dCllhE3dE~were prepared from the appropriate C12E3 and ethylene oxide-d4, and the starting Cl2E3 was prepared using the Williamson synthesis. All these preparations have been described more fully in refs 2 and 0022-3654/93/2097-8012%04.00/0
4. The chemical purity of the materials was mainly assessed by surface tension measurements. High purity water was used for all the measurements (Elga Ultrapure). All the glassware and Teflon troughs for the neutron and surface tension measurements were cleaned using alkaline detergent (Decon 90) followed by copious washing in ultrapure water. Surface tension measurements were made on a Kruss K10 maximum pull tensiometer using a Pt du Nouy ring. The ring was flamed in between each measurement. All the experiments were performed at 298 K. The neutron reflection measurements were made on the reflectometer CRISP at the Rutherford-Appleton Laboratory (Didcot, U.K.), and the procedure for making the measurements has been described previ~usly.~ All the measurements were made at a fiiedincident angleof 1S0,and theintensitieswerecalibrated with respect to DzO. A flat background was determined by extrapolation to high values of the momentum transfer; K ( K = (4.rrsin @ / A where 0 is the glancing angle of incidence) was subtracted. This is a valid procedure provided that there is no small angle scattering from the bulk solution. Since this only starts to become a problem at concentrations of the order of 1% by volume, well above the concentrations used in the present experiments, the procedure is valid for the experiments described here.
Results The surface tension as a function of concentration is shown for dC12hE6 in Figure la. Thecmc was found to be 8.0 0.5 X in reasonable agreement with previous measurements by Corkill et a1.6 We did not make detailed measurements of the surface tension of all the different isotopic combinations, but it is worth noting that the area per molecule at the cmc determined from neutron reflection was remarkably consistent from isotope. to
*
0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 30, 1993 8013
Configuration of the Ethylene Glycol Chain
O
TABLE II: Scattering Lengths and Volumes of Constituent Parts of C&g extended scattering unit volume, A3 length, A length, 10-5 A
0
350
CIZD25 C
0
.9
E 451 dl
I
0
I
0
0
Log KIM1 35 T
I
I
b 1.01 0
2
4
6
8
10
C xlOs IM Figure 1. (a) Surface tension of dC12hE6. (b) Adsorption isotherm of dClzh& calculated from the surface tension and the Gibbs quation (A) and neutron reflection (0). The value at the cmc (8.0 X 1ks) is the average value from the neutron reflection measurements on five isotopic species. Other points are determined with slightly lower precision from neutron reflection.
TABLE I: Structural Parameters (A)of CI~ES on Null Reflecting Water at the cmc (Single Layer Model). surfactant Ah3,A2 T * ~ , A u*l,A 55 24.5 21.7 dCiidE6 56 19.0 16.0 dCizh& 57 20.5 16.5 hCizd% dCl2hE3dE3 53 24.5 22.5 hClzhEidE3 56 21.0 16.0 hC izd&/hC I 2hbdE3 53 20.0 16.5 hCizd&/dCizhE3dE3 54 25.0 21.5 a T applies to a uniform layer and u to a Gaussian (defined by q 17). isotope (see Table I), indicating that if there are any isotope effects, they are small. The surface excess was determined by fitting a second degree polynomial to the data (y - ln(concentration)) below the cmc and then using the Gibbs equation to give the adsorption isotherm shown in Figure 1 b. The most accurate neutron reflection profiles were measured at the cmc where the surface pressure was 38 mN m-1 and the area per molecule approximately 55 A2. Using a single uniform layer model to fit the data with the scattering lengths of the constituent units given in Table I1approximate areas per molecule for the five partially deuterated species and two combinations of deuterated species were obtained and are given in Table I. The average of these values is 55 A2 and their spread indicates an error of about f3 AZ, which is consistent with the total error expected at this coverage. As argued in a previous paper the error in A determined from reflectivity should be significantly less than that from the surface tension measurements. Nevertheless the agreement with A from the surface tension measurements (53 AZ) at the cmc is good. The neutron surface excess was also measured with lower accuracy (f8%) over a range of
16.7
245.51 (99.4BD)
CizH2s 350 16.7 -13.7 190 10.7 147.1 (9896D) (OCzDd3OD 190 10.7 14.48 (OCzHd3OH 380 21.0 281.9 (9896D) (OC2D4hOD (OCzH4)60H 380 21.0 34.4 DzO 30 19.14 Hz0 30 -1.68 a Volumes and extended lengths are from refs 18 and 19 and scattering lengths from ref 20. concentration, and, although it is systematically higher than the surface tension value (see Figure 1b), the two agree within error. We have shown in earlier papers how it is possible to analyze a set of reflectivity profiles from samples of different isotopic composition using a direct method based on the kinematic approximation.’ We use this here in preference to model fitting, although we will later show the results from model fitting. For the layer features of interest are the relative positions of alkyl and ethylene glycol chains and water and the widths of those distributions normal to the interface. However, given that computer simulations of layers are capable of examining these distributions at much higher resolution, e.g., the distribution of individual methylene groups, we decided to examine the Cl2E6 structure at higher resolution by subdividing the ethylene glycol chain into E3 group nearest the alkyl chain, designated el, and the E3group furthest from the alkyl chain, e2. The structure of the air/solution interface can then be described in terms of the distributions of alkyl chains c, ethylene glycol chains either as one unit, e, or as two subunits, el and e2, and water (solvent), s. In terms of the maximum number of labels the scattering length density can be written P(Z) = bcnc(z)
+ belnel(z) + bezncz(z) + b,n,(z)
(1)
where ni is the number density profile of species i and bi is its scattering length. We will also use the simpler labeling scheme and then
bene(4 = be,nel(z) + be2ne2(z) (2) The kinematic approximation for the reflectivity R ( K )may be written in terms of the partial structure factors hii
2bcbe1h,1
+ 2bcbe2h,2 + 2bcb,h, + 2be1b,heb +
2be2b,he, + 2belbe2hek2l (3) or, in the simpler labeling scheme
2bCb$,
+ 2bcb,h, + 2beb,h,)
(4)
where hij are the partial structure factors given by
The n i ( ~ )are the one-dimensional Fourier transforms of ni(z), the average number density profile of atom, or group, i in the direction normal to the interface,
n i ( ~= ) Kexp(-irtz)ni(z)dz
(6)
Analtemativeexpression, equivalentto (3) and (4), can bewritten
8014 The Journal of Physical Chemistry, Vol. 97, No. 30, 1993 in terms of dnldz = n(1) and is
R(K)
1 6?r2 -F,y,bibjht)(~) i
K4
(7)
where P ( z ) represents the correlation of the number density with itself. Because the Fourier transforms are one-dimensional the relation between h ( ~in) eqs 3 and 4 and N ( K in)eq 7 is K'~(K) = h(')(~) (9) R ( K )and h ( ~decay ) rapidly with K and, although it is simpler to
discuss reflectivities in terms of the partial structure factors hii, it is more convenient to plot and fit data in terms of K % ( K ) . The reflectivitygiven by eq 3 is approximateand without further correction leads to errors in the partial structure factors. This has been discussed in detail by Lu et al.' who have shown that an equation derived by Crowley* can be used to convert the experimental data into a reflectivity for which eqs 3 and 4 hold almost exactly. The equation is
where Rf and Rk are the exact and kinematical reflectivities for a perfectly smooth surface between the two bulk phases and K~ is the momentum transfer at which total reflection would occur for the two bulk phases. There are two types of partial structure factor in eqs 3 and 4, the self terms, hii, and the cross terms, hij. If the data do not extend over a sufficient range of K to make it feasible to Fourier transform the hii to obtain the Patterson function, and this is generally the case, then these terms can be characterized simply by the width, ui, of the distribution ni. The value obtained for the width depends on the function chosen to represent ni. We shall generally use a Gaussian distribution for parts of the surfactant and a tanh distribution for the solvent, given respectively by
n = ni exp(-4z2/u2)
for all z
(11)
and tanh (z/f)]
where z is the distance in the direction normal to the interface and f is the width parameter. For comparison of the widths of the chain distributions with other data it is more convenient to use the full width at half height of the Gaussian, which we designate by u* or FWHH. The self partial structure factors, hii, contain information about the distribution of each labeled component but not about the relative positions of the components. The information about the relative positions is contained in the cross partial structure factors, hij, and these may give important structural information without being Fourier transformed. It can be shown that the cross term between two distributions centered at 6i and Sj is hij(K)
Re(ni(K)nj*(K) eXp[-iK(bi - 6j)])
and
h, = (h,h,)
P(z) = J-Ini(u)ni(u-z)du
+
value at large positive z and is therefore predominantly an odd function. When ~ ( z and ) n,(z) are exactly even about their centers and n&) is exactly odd, eq 13 gives the following results
j
In principle it is possible to Fourier transform ( n i ( ~ )to I ~obtain the "Patterson" function for the number density,
n=
Lu et al.
(13)
It may often be the case that the distributions are either perfectly even about their centers or perfectly odd. Thus both types of chain have distributions which are zero at large positive and negative values of z and are 'therefore approximately symmetric about their centers, Le., predominantly even functions, whereas the solvent density is zero at large negative z but has its bulk
"'COS
K6,
(15)
where we have taken the simpler labeling scheme of eq 4. We have shown in several previous publications that, if eq 4 is being used, a good set of reflectivity profiles for obtaining the whole set of six partial structure factors is from dC12hE6 in null reflecting water (nrw) and D20, dCl2dEs in nrw and D20, hCl2hE6 in D20, and hCl2dE6 in nrw. From the set of six partial structure factors, the six parameters, uc, ue,7sr,6 , ,6 and 6, are obtained by fitting the distributions (11) and (12) to the self terms, and using eqs 14 and 15 for the cross terms. However, the three separations 6ij are not independent because
,6 - ,6 = ,6 In principle, therefore, within the framework of the partial structure factor description it would be sufficient to determine only five structure factors and to omit one measurement. However, this would only be possible if each of the three units could be separately contrast matched to air. The alkyl chain and solvent can be so matched but not the ethylene glycol chain. Thus, six measurements were necessary. If eq 3 is to be used, there is considerable choice for the profiles required to determine a total of four widths and four separations, the minimum needed to characterize the structure. If, as had happened in the present case, the set of six parameters listed above has already been determined, then the center of the alkyl chain distribution may be taken as a reference point and the most obvious choice for the additionalmeasurementsbecomes hClzhE3dE3,hClzdE3hE3,dCl2hE3dE3, and dClzdE3hE3, all in nrw. To reduce the burden of preparation of labeled surfactant we used instead thecombination hC12hE3dE3,hC12hE3dE3/hC12dE6,dCl2hE3dE3/hCI2dE6, all in nrw, the mixtures being 5050 ones. We first discuss and interpret the self partial structure factors hii obtained from eq 4. The alkyl chain partial structure factor, h,, is shown in Figure 2a and the ethylene glycol chain partial structure factor, he, in Figure 2b. Both hii are equally well fitted by a Gaussian or by a uniform layer, any difference between the two fits being within the margin of error. The width parameters are given in Table 111. There is evidence from computer simulation that a Gaussian distributions is more appropriate.9 The partial structure factor for the Gaussian distribution given in eq 11 is
where the surface excess for the distribution (1 1) is
which, when substituted into (17) gives
The most direct way of obtaining ui and A is to plot ln(h") against K ~ The . ~ intercept is -2 In A and the slope is - u2/8. This gives an immediate check on the consistency of a set of h" for the isotopic series of a given surfactant because the plots for all the species should have a common intercept. A further check is that, by treating the surfactant molecule as a whole, a similar plot may be made for ha, where a designates the whole surfactant. This
Configuration of the Ethylene Glycol Chain
The Journal of Physical Chemistry, Vol. 97, No. 30, 1993 8015
K21A" Figure 3. The determination of coverage and thickness of the different parts of the C1& layer at its cmc using eq 20, ethylene glycol chains (O), alkylchains (A),and thewholemolecule(+). Thefittedwidthparameters, u, are 16.5, 16, and 22
or by using the Gaussians that have been fitted to hii and hjj. In the latter case the following expression for h, can then be determined from eqs 14, 17, and 19
't / 0.05
1 (20) A2 Since A, a,, and ue are already known 6, can be determined directly from h,. A similar equation may be written for h, and h, using the expression for a "roughn solvent for ha,' a Gaussian distribution for h, and h,, and eq 15
h, = -exp(-K2( u: + u:)/ 16)cos ~6~
0.n
0.15
0.20
025
t
K /A
Figure 2. (a) Alkyl chain partial structurefactor, K%,, and (b) ethylene glycol partial structure factor, rZhohat the critical micelle concentration
for C1&. The continuouslines are calculated for Gaussian distributions
of full width at half height of 13.5 in each case.
his = "0 exp(-K2(u2
TABLE III: Structural Parameters Obtained from Kinematic hlvsis ~~
uniform, T
value Gaussian, u
Gaussian, u*
19 19.5
16 16.5 8 (tanh)
13.5 13.5
13.5
A, respectively.
10.0 9.0
17
1.o 14.5
19.5
17
12 14
7.0 11.5 3.5
also gives a clear way of demonstrating the different thicknesses of the component parts of the layer. We show a set of plots for C&6 at its cmc in Figure 3 where the values of A have already been normalized to each other. The similarity of the thickness of the alkyl and ethylene glycol chains is immediately obvious from this diagram. It is interesting to compare the values of ui obtained from Figure 3, 22.0 A for the whole molecule, 16.0 A for the alkyl chain, and 16.5 A for the ethylene glycol chain in C&6 at its cmc. Since the overall thickness is much less than the sum of the thicknesses of the two constituent parts there must be extensive mixing of the two types of chain, as already observed for C12E, wheremisJessthan6.4 Thewidthsof thealkylchainandethylene glycol chain distributions determined from plots using eq 19 and from more direct fitting of the partial structure factors are given in Table I11 for both Gaussian distributions and the uniform layer model. Values of u* are also given in Table 111. There are two ways of determining the separations 6~from the cross partial structure factors, by substituting the observed, hii, hjj, and hij into the appropriate equation of the pair (14) and (1 5)
+
87%)/16]sin~6, (21) A2 where no is the number density of bulk water. Alternatively, the solvent may be handled in terms of the model of the uniform layer. We have shown in ref 10 that an important sourceof error in the hij results when, for whatever reason, the values of A for each of the isotopes in nrw are not identical. This error is almost totally eliminated if the reflectivities are first normalized to the average A, and this has been done here (see also Figure 3). The result of fitting eqs 20 and 21 to the data is shown for h,, h,, and h, in Figure 4 (parts a, b, and c, respectively) and the values obtained for,6 ,6 and ,6 are given in Table 111. As we have found previously, the values obtained for 6 are independent of the model chosen to fit the self partial structure factors. The self consistency of the three 6 values is also good (eq 16). As found for the lower members of the series C12E, ,6 is smaller than ,6 indicating that the ethyleneglycol chain is not completely immersed in the water. Using the more detailed labeling scheme appropriate to eq 3 we obtained the partial structure factors of the two halves of the ethylene glycol chain shown in Figure 5 from which the fitted widths, assuming Gaussian distributions were uol = 14.5 f 2 and uc2 = 17 f 1 A, respectively. Surprisingly, the difference in the widths of the two groups is small, indicating a large degree of overlap. The overlap is more clearly assessed from the value of the separation between the distributions, determined using eq 19 from the partial structure factors. The values obtained for the different se arations were 61, = 7, 6-2 = 11.5, and 6c102 = 3.5 A, all f l Once again the consistency of the three values, linked by an equation similar to (16), is excellent. The fits of equations 19 to the data are shown in Figure 6. We have also used the more conventionalmethod of fitting the data, using a model for the interfacial profileand theexact optical matrix calculation. The two layer model for the interfacial profile was that used by Lu et al.4 and consists of a region that is mainly
1.
8016 The Journal of Physical Chemistry, Vol. 97, No. 30, 1993
Lu et al.
0 KIh‘
Figure 5. Ethylene glycol partial structure factors (a) ~ ~ h . and l ~ l (b) Zh-. The continuous lines are calculated for Gaussian distributions with full widths at half height of (a) 12 and (b) 14 A.
1
0.05
OD
015 K
020
0.25
/k’
Figure 4. (a) The alkyl chain-solventirtial structure factor, x2ha, and (b) the alkyl chaimthylene glycol chain partial structure factor, ~ * h - , and (c) the ethylene glycol chain-water partial structure factor, K % ~ , at the cmc. The continuous lines are calculated using eqs 14 and 15 and values of 6 of (a) 10, (b) 9, and (c) 1 A. alkyl chain, not only containing a fraction of alkyl chains, (1 -
fc), but also containing a small fractionfh of ethylene glycol head
group, and a region containing the remaining head groups and a proportion of alkyl chains,& with the residual space filled with water. It is assumed that there is no water in the alkyl chain dominated region. The results of fitting this model to the different sets of data are given in Table IV. The errors quoted forfc and T, are relatively large because the two parameters are quite strongly coupled in the fitting procedure. With this proviso the dimensions of the different fragments obtained from the two model fitting procedureand the direct analysisare comparableand both indicate that a small proportion of the ethylene glycol chain is out of the water, Le., fh > 0.
Discussion The most direct way of assessing the structure of a surface layer is in terms of the number distribution of the three
components,alkyl chains, ethylene glycol chains, and water. This is shown for the set of data where the hexaethylene glycol is considered as a single unit in Figure 7c. Also shown in Figure 7 (parts a and b), for comparison, are the number distributions forC12E2andC12E4atthesamearea per molecule. Weemphasize that the distributions of Figure 7 contain all contributions to the structure of the layer, including dynamic1 fluctuations, and the only way of interpreting the significance of these experimental distributions is by comparison with computer simulation. Nevertheless, we now attempt todeduce some of the structural features of the layer from the experimental data. The most common measure of the thickness of a Gaussian distribution is the full width at half height, u*. At a constant area of 55 A2 the value of u* for ~6 in C12E6 is 13.5 1 A to be compared with 12 f 1 A for E4 in and 6.5 i 2 A for E2 in C I ~ E The ~ . possible ~ contributions to u* are the roughness of the surface, the tilt of the chains with respect to the surface normal, and the intrinsic length of the chain. The value to be taken for the intrinsicchain length for comparisonwith a Gaussian distribution is not obvious. In the absence of both tilt and roughness, u* will be smaller than the fully extended chain length 1. The fraction of a Gaussian distribution lying within u* of its center is 0.77, and we will therefore assume that the appropriate comparison is between u* and 0.771, which we designate I! The length of a fully extended ethylene glycol group is 3.6 A so the values of I’are 16.5,11, and 5.5 A for c12E6, C12E4, and C12E2, respectively. Although it is difficult to make a direct comparison, becauseof the contribution of roughness to the layer, tkeethylene glycol chain seems to be proportionately less extended as the number of units in the chain increases. This raises the question as to when a chain becomes sufficiently disordered that it starts to behave like a polymer. Sarmoria et al.11 have done simulations on the free and anchored oligoethyleneglycols using the rotational isomeric state model which suggest that the polymer-like square root dependence of radius of gyration on the number of units
Configuration of the Ethylene Glycol Chain
The Journal of Physical Chemistry, Vol. 97, No. 30, 1993 8017
.........
,
e...
(a)
.(X’lx)
.
3.
‘., ’.
.\
I
I
1 1
.’t
16
12
e
4
0
4
e
n
1t
Distance normal to surkce/P Figure 7. The experimental number distributions of the different components of layers of (a) C12E2, (b) C I Z ~and , (c) C1& at a fiied areaper moleculeof 55A2. Thealkylchainsarerepresentedbycontinuous lines, the ethylene glycol chains by dashed lines, and the solvent by dotted lines. The distributions of both types of chains have been assumed to be Gaussian in shape and the water distribution to be a tanh function. Thea origin has been taken arbitrarily a t the centre of the alkyl chain distribution.
I
u IA4
Figure6. The alkyl chain-ethylene glycol chain partial structure factors (a) ~2h-l and (b) K%&. (c) The ethylene glycol l-ethylene glycol 2 partial structure factor, ~ ~ h , l aThe . continuous lines are calculated using eqs 14 and 15 and (a) 7, (b) 11.5, and (3) 3.5 A.
TABLE Iv: Parameters for Calculated Profdm Using Two Layer Optical Matrix Metbod A & 3 , fc& fa& 7cf2.5, 71)&1, A2 0.15 0.05 A A n*l
species
contrast
dCl2db dcizhb hC12db dC1& dC12hb hC12hb dClzhE3dE3 hCllhEsdE3 hCi2dE6 dClzhEsdE3 hCizdE6 hCl2hEsdE3
nrw nrw nrw D20 DzO D20 nrw nrw nrw
56 55 55 53 55 55 53 56 54
0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35
0.18 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17
13.5 13.5 13.5 13.5 13.5 13.5 13.5 13.5 13.5
13.0 7.0 13.0 13.0 13.0 13.0 13.0 13.0 13.0
nrw
55
0.35 0.17
13.5
13.0
11 10 11
occurs at about m = 10 (in &E,) for chains attached to a hard wall and at m = 4 for free chains. Whilst we have not made measurements at large enough m to establish the square root dependence of thickness that would be expected for a polymer,
it is clear that the first stage toward it, which must be a significant drop of the thickness below l’, is occurring at m = 6. Nikas et al.lz use their ‘polymer” model to predict an ethyleneglycol chain thickness of 10.5 A ( I / = 8 A) for ClZE6. This is much less than our experimental value. However, as we have pointed out in ref 4, the prediction of 10.5 A is based on the chain being anchored at a hard wall. The distributions in Figure 7 show that the alkyl and ethylene glycol chains overlap sufficiently to give this wall a finite thickness (there will be two contributionsto this thickness, from thermal fluctuations and fromstatic disorder). From Figure 7 the full width at half height of the overlap distribution is approximately 9 A, and, if this is taken to be the roughness of the interchain region, it will contribute significantly to the measured thickness of the ethylene glycol chain. The overall distribution of the E,,, will then be the convolution of the E, distribution anchored at the hard wall with the wall distribution. Taking 13.5 A for the observed width of the E6 chain and taking the wall distribution to be a Gaussian with full width at half height of 9 A (estimated from Figure 7) leads to an intrinsic chain width of about 10 A, much closer to Nikas et al’s. value of approximately 8 A. At first sight this suggests that Nikas et al’s. assumption of polymer-lie chain behavior is not unreasonable for ethylene glycol chains in these surfactants. However, such a conclusion cannot be made on the basis of the evidence so far presented. This is because it would be equally valid to argue that the ethylene glycol chain is fully extended but has an average tilt away from the surface normal which reduces its root mean square projection in the normal direction. We now show that this question is partially resolved when the distribution of the separate halves of the ethylene glycol chain is considered. Initially, we suppose that the ethylene glycol chain is fully extended and tilted on average at an angle of 0 to the surface
Lu et al.
8018 The Journal of Physical Chemistry, Vol. 97, No. 30, I993 normal. We then have
*
__
,.".............................
-
a
is Since uc H ucl H uz2 eq 22 can be fitted only if I'(cos2 less than about 4 A, w taking a value of about 13 A. Since l'is 16.5 A this would imply that the ethylene glycol chains are lying almost horizontallyon the surface,which does not seem reasonable. Given the discussion in the previous paragraph, the corollary is that it is likely that the ethylene glycol chains are fully extended. The followingcrude argument also supports a more polymer like model. The characteristic segment length when an ethylene glycol chain is treated as a random flight chain is slightly longer than the length of one E2 group, as determined from the radius of gyration of 73 A for a 20 000molecular weight PEO." Thus the E6 chain should behave on average approximately as though it consists of three freely jointed links, each 7.2 A long. Initially we assume that the first one, at the alkyl chain end, is oriented normal to the surface. It is this link that principally determines the thickness of el. The projection of the second link largely determines thevalue of 6ele2. The mean orientation of this second link must be such that
-
6cls2 N (3lcos 0 ) / 2
(23) where -1 is the full length of a link, Le., 7.2 A. This leads to a value of cos 8 H 0.37. The thickness of the e l layer is 0.6(1
+ 6cle2/3)2 + w2
(24) where the factor of 0.6 allows for the relation between fully extended length and half width. Equation 24 gives a value of 11 A, compared with the 12 A observed, where a value of 9 A has been used for w. The combination of these two results means that, within this crude model, the first link may be approximately normal to the surface. If it were not, then the thickness ull could only be maintained at its observed value if the second link were oriented closer to the surface normal, but then belc2 would be much larger than observed. Note, however, that if the roughness of the layer were greater than 9 A, then deviationsfroma normally oriented first link become possible. It is not possible to make a quantitative estimate of the thickness of e2, but it is obvious that for freely rotating links its thickness must be larger than e l , as observed. Although this model is crude, it nevertheless gives a semiquantitative explanation of the observations and therefore supports the type of approach used by Nikas et al. The separate determination of the el and e2 distributions also allows some tentative conclusions to be drawn about the overall shapeof the ethyleneglycol distribution. We construct the overall distribution from the two subunits in Figure 8, using both the uniform layer model and the Gaussian distribution for each half of the chain. The composite uniform layer model shows both that the distribution is skewed and that it is not well described as a uniform layer, i.e., the calculated composite layer is not at all similar to the original uniform block. On the other hand, the calculated composite Gaussian is almost indistinguishable from theoriginalGaussian, althoughit is slightlyskewed. This indicates that a Gaussian distribution is a better approximation to the distribution of the ethylene glycol chains. That the distribution is only slightly skewed also shows that the use of eqs 14 and 15 is justified as far as the E, chain is concerned. We have already analyzed the effects of introducing nonsymmetric components into the distribution,"f and at the level shown in Figure 8 the resultant errors in the derived values of 6 would be negligible. When the E, chain width is compared at constant surface pressure (38 mN m-1) the values of u: are 9 A for m = 2 ( A = 37 A2), 13 for m = 4 ( A = 48 A2), and 13.5 for m = 6 ( A = 55 N
Distance normal to surface/A-' Figure8. The distributions of the two halves of the ethylene glycol chain in C& at its cmc. The number densitics of el (dotted line), e2 (dashed
line), (el + e2) (solid line), and e (dashed-dotted line) as fitted by (a) the uniform layer model and (b) Gaussian distributions using the values given in Table 111.
A2). It is clear that as the area per molecule decreases the chain width increases, but it is not possible to decide whether the thickening of the E2 and E4 layers results because steric repulsion causes chain extension or because of extra broadening of the wall. Thealkylchainlengthfor thedifferent C12E,shows the opposite behavior to the ethylene glycol chain length in that it is the same at constant pressure but different at constant area. Thus at constant area the values of u,' are 11.5 A for m = 2, 12 A for m = 4, and 13.5 A for m = 6, but at constant pressure the values are 13 A form = 2, 13 A for m = 4, and 13.5 A for m = 6. The absolute error in these values is about 1.5 A, comparable with the differences, but the relative errors, because of the systematic method of fitting, are much smaller than the differences, about 0.5 A. They suggest that the alkyl chain thickness for any member of the series depends on the surface pressure rather than on surface area. The origin of this effect is not known but may be connected with differences in the overlap of the ethylene glycol and alkyl chains. This can be estimated from a plot of the distributions of Figure 7 but in terms of volume fractions rather than number densities. The number density distributions of each component obscure the true packing situation because the E, groups are of very different size. In Figure 9 we plot the distributions asvolume fractions, Le., the volume of an individual unit divided by the total volume, for the three E,,, chain lengths at constant area per molecule. For Cl2E6 (Figure 9c) there is significant overlap of the ethylene glycol chain and alkyl chain distributions but this diminishes with m. The equivalent plots, shown for C12E4 and C12Ez at constant pressure in Figure 10 (C12Ea at this pressure is Figure 9c), indicate that the E4 and E2 chains are slighly squeezed out of the water into the alkyl chain region at the higher surface pressure. What may therefore be happening is that the variation of surface pressure, by causing ethylene glycol groups to switch in and out of the water, imposes additional variable packing restraints on the chains. However, as discussed below, some care must be taken in interpreting the overlap of these distributions because of the contribution of roughness. The absolute value of the thickness u* of the alkyl chain layers is comparable with the length l'of 13A. This may be interpreted in the two ways used to interpret the thickness of the ethylene glycol chain region. Thus, after removing the contribution of the wall thickness (9 A) an alkyl chain layer thickness of 13.5 A becomes an intrinsic anchored chain length of 10 A, which may 8 0.75 (8 = 40), as a be interpreted as a mean tilt with
Configuration of the Ethylene Glycol Chain
The Journal of Physical Chemistry, Vol. 97, No. 30, 1993 8019
tal
b
Figure 10. The experimentalvolume fraction distributionsof the different componentsoflayersof (a) C12Ezand(b) C&at afixedsurfaceprcasure of 38 mN m-l. Figure 8c is the equivalent plot for C12E&. The alkyl chains are represented by continuous lines, the ethylene glycol chains by dashed lines, and the solventby dotted lines. The overallvolume fraction is represented by a dash-dot sequence. The distributions of both types of chain have been assumed to be Gaussian in shape and the water distribution to be a tanh function.
Distance n o m i to surface/b; Figure 9. The experimental volume fraction distributions of the different components of layers of (a) C12E2, (b) C12E4, and (c) C& at a fixed area of 55 A2. The alkyl chains are represented by continuous lines, the ethylene glycol chains by dashed lines, and the solvent by dotted lines. The overall volume fraction is represented by a dash-dot sequence. The distributions of both types of chains have been assumed to be Gaussian in shape and the water distribution to be a tanh function.
chain with one or two gauche links, or as a combination of both. From the arguments already presented concerning the E6 chain the experiment cannot distinguish the three possibilities,although it has been suggested that the average chain probably has at least one or two gauche links (see, for example, ref 15). We have previously assumed that the extent of hydration of a chain may be deduced directly from the overlap of the water and chain distributions.' However, this is not necessarily the case, and the higher effectiveresolution of the present experiment allows us to discuss this question more quantitatively. It is clear from the discussion so far that the layer is appreciably rough (w 9 A). Some, if not all, of this roughness must arise from capillary waves with wavelengthsmuch greater than the separation of the amphiphiles in the surface plane. These capillary waves
will generate an overlap of the measured distributions, which has nothing to do with the true local overlap, or interpenetration of the different species. The local penetration of chains and water must therefore be estimated after elimination of the "capillary wave" overlap. Assuming all of thevalue of w come8 from capillary waves reduces the width parameters of the three distributions to 10 A ( u " ) for both chains and 7 A (tanh) for water. The extent of hydration of the Ea chain is then made by calculating the number of water molecules overlapping the E6 distribution, after applying the correction above. This gives n H 12, to be compared with the value of 10-11 from the model fitting in Table IV. However, the distribution of water throughout the E6 layer is extremely uneven with most of the water in the lower half, as can be seen from Figures 9 and 10. In Figures 9 and 10 we show that the total volume occupied by the two chains and water through the interface. This shows that the structure obtained from the kinematic model cannot be entirely correct. Thus, there is too much material at the solvent end of the layer and this means that the detailed shape of either the water or the E,,, profile is not accurate. As already stated above, the experiment is not directly very sensitive to the shape of the water profile. If a half Gaussian, which has a profile experimentally indistinguishable from the model of a rough surface, is taken to represent the water distribution, the volume packing discrepancy is larger than for a tanh distribution. This is the reason for preferring the tanh distribution in Figures 7,9, and 10. The tanh distribution would imply that the overlap of the tail of the water distribution with the hydrophobic region of the layer is greater. At present there seems to be no obvious way
8020 The Journal of Physical Chemistry, Vol. 97, No. 30, 1993 to obtain a more precise experimental description of the water distribution. On the other hand, the two layer model description of thewater distributionis now shown to beinadequate. It imposes a sharp division between space and nonspace filling regions, which is inconsistent with the more directly obtained distributions of Figure 9. The position of the division between the two layers would have to occur in the nonspace filled region, Le., the model overestimates the size of the space-filled region. Furthermore, there is clearly a significant amount of water in the “forbidden” chain region. It is interesting tocompare the structureof the C1&monolayer at the air/water interface with the structure of the bilayer at the silica/water interface.16J7 The resolution of the experiment at the solid/liquid interface is intrinsically lower, partly because the range of accessiblemomentum transfer is lower, partly because the additional complexity of the surface profile means that the value of any one geometrical parameter is coupled with the values of other parameters, and partly because the reflectivity must be fitted by a model rather than directly using the kinematic approximation. In the bilayer the area per molecule at 44 Azis less than the air/water interface, and the thickness of the alkyl and ethylene glycol chain regions are 16 and 17 A, respectively, to be compared with 19 and 19.5 A (uniform layer values). The hydrocarbon region is not directly comparable because it is a double layer. At first sight the greater thickness of the E6 layer in the more loosely packed monolayer at the air/water interface is surprising. However, this is almost certainly because of the contribution of the more diffuse alkyl/ethylene glycol wall at the air/liquid interface. An approximate estimate of the “wall” thickness in the bilayer can be obtained by scaling the uniform layer thicknesses to Gaussian Q*, taking the “random coil” thickness of 11 A, and combining the two as described above for the air/water interface. This gives a value of 5 A for the wall thickness in the bilayer. However, this is likely to be an overestimate because at an area per molecule of 44 A2 the E6
Lu et al. chains will be sufficiently close that steric repulsions may cause them to be more extended than their ‘random coil”configurations.
Acknowledgment. We thank the Science and Engineering Research Council for support. Z.X.L. also thanks the SineBritish Friendship Society. References and Notes (1) Simister, E. A.; Lee, E. M.; Thomas, R. K.; Penfold, J. J . Phys. Chem. 1992,96, 1373. (2) Lu, J. R.; Lee,E. M.; Thomas, R. K.; Penfold, J.; Flitsch, S. L. Lungmuire, in press. (3) Teo,H.H.;Yeate.s,S.G.;Price,C.;Booth,C.J. Chem.Soc.,Faraday Trans. I1984,80, 1787. (4) Lu, J. R.; Li, X.Z.; Su,T. J.; Thomas, R. K.; Penfold, J. Lmgmuir,
submitted for Dublication. (5) Lee,E. M.; Thomas, R. K.; Penfold, J.; Ward, R. C. J. Phys. Chem. 1989. 93. 381. (6) Corkill, J. M.;Goodman, J. F.;Harrold, S . P. Trans. Faraday SOC. 1964,60,202. (7) Lu, J. R., Simister, E. A,, Lee,E. M., Thomas, R. K., Rennie, A. R., Penfold. J. Lunamuir 1992,8, 1837. (8).Crowl+, T. L. Physica A 1993, 195,354. (9) Bocker, J.; Shlenkrich, M.; Bopp, P.; Brickmann, J. J . Phys. Chem. 1992,96,9915. (10) Lu, J. R.; Simister, E. A.; Thomas, R. K.; Penfold, J. J . Phys. Chem. 1993,97,6024. (111 Sarmoria, C.; Blankschtein, D. J . Phvs. Chem. 1992. 96. 1978. (12) Nikas, Y. J.; Puwada, S.; Blanbchteh, D. Lungmuir 1992,8,2680. (13) Venneman, N.; Lecher, M. D.; Oberthur, R. C. Polymer 1987,28,
1738. (14) Simister, E. A.; Lee, E. M.;Thomas, R. K.; Penfold, J. Macromol. Reports 1992,A29, 155. (15) Gruen, D. W. R. J. Phys. Chem. 1985,89,146. (16) Lee, E. M.; Thomas, R. K.:Cummins. P. G.;StaD1e.s. . . E. J.:. Penfold. J.; Rennie, A. R. Chem. Phys. Lett. 1989,162, 196: (17) McDermott, D. C.; Lu, J. R.; Lee, E. M.; Thomas, R. K.; Rennie, A. R. Lungmuir 1992,8,1204. (18) Takahashi,Y.;Sumita, I.;Tadokoro, H. J . PoLSci. 1973,11,2113. (19) Tanford, C. J. J . Phys. Chem. 1972,76, 3020. (20) Sears, V. F. Neutron News 1992,3 (3), 26.
