J. Phys. Chem. 1994,98, 6559-6567
6559
Neutron Reflection from a Layer of Monododecyl Octaethylene Glycol Adsorbed at the Air-Liquid Interface: The Structure of the Layer and the Effects of Temperature J. R. Lu, Z. X. Li, and R. K. Thomas' Physical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, U.K.
E. J. Staples, L. Thompson, and I. Tucker Unilever Research, Port Sunlight Laboratory, U.K.
J. Penfold Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, U.K. Received: October 13, 1993; In Final Form: February 15, 1994'
We have determined the structure of a monolayer of monododecyl octaethylene glycol (C12Es) adsorbed at the air/water interface at its critical micelle concentration and at temperatures of 298 and 323 K using neutron specular reflection in combination with isotopic labeling. There is little effect of temperature on the coverage of the pure material, though a significant variation is observed when the material was slightly contaminated with lower members of the series (C12Em with m < 8). However, subtle changes in the structure of the adsorbed layer do occur, the alkyl chain region becoming about 14% thicker at the higher temperature, whereas the thickness of the ethylene glycol chain region does not change. An analysis of these differences and the changes in the separation of the different fragments of the surfactant suggest that the layer is increasingly roughened at the higher temperature and that the ethylene glycol chain region is significantly dehydrated. The structure of ClzEs is compared with other members of the C12Em series at approximately the same area per molecule of 55-65 AZ. The alkyl chain thickness is constant throughout the series, and the values of the structural parameters indicate a large average tilt of the surfactant molecules away from the surface normal and a significant incidence of gauche conformations in the alkyl chain.
Introduction The nonionic surfactants, CnH2,,+l(OC2H,),OH (abbreviated here to C,E,), are a widely used series of surfactants. The role of the area per molecule in determining the progression of C,E,/ water mesophases has been established, and as a result, the dimensions of the alkyl and ethylene oxide chains at interfaces are of considerablerelevance and interest. Nonionic surfactants exhibit an upper temperature of miscibility (cloud point), and for C12E8,the subject of this paper, this upper limit is about 65 OC,l the exact value depending on the concentration of surfactant. It is well-known that the ethylene glycol group dehydrates with increasingtemperature. Furthermore, the surface tension of the oil-water interface in the presence of nonionic surfactants passes through a sharp minimum as a function of temperature? giving rise to a temperature dependence of microemulsion stability. It is therefore expected that the surface properties of nonionic surfactants will be temperature sensitive. Only recently has it become possible to determine directly the structure of surfactant layers at flat interfaces, with much higher resolution than previously available for curved interfaces, and here we apply recent developments in neutron reflection to the examination of the structure of ClzE8 adsorbed at the airfwater interface at different temperatures. Experimental Details
The protonated material, hClzhE8, was obtained from Fluka. The partially deuterated isotope, dClzhE8, was prepared by a standard Williamson synthesis from the deuterated alkyl bromide (Merck, Sharp, and Dohme), an equimolar amount of sodium, and a S-fold molar excess of octaethylene glycol (Fluka). Two
* To whom correspondence should be addressed at Physical Chemistry Laboratory, South Parks Road, Oxford, OX1 342. Abstract published in Advance ACS Absrructs. June 1, 1994. 0022-3654/94/2098-6559$04.5OfO
sets of experiments were performed, one on the material as immediately isolated from the reaction, and one on a sample purified on a silica column.3 The fully deuterated and ethylene glycol deuterated compounds dCl2dEs and hClzdE8 were prepared by reacting ethylene oxide-d4 (Merck, Sharp, and Dohme) with either the deuterated or the protonateddodecanol.4 The partially deuterated compounds hC12hE3dEsand dClzhE3dES were prepared from the appropriate C12E3and ethylene oxide-d4, and the starting C12E3 was prepared using the Williamson synthesis. All these preparations have been described more fully in refs 3 and 4. The chemical purity of the materials was mainly assessed by surface tension measurements. The scattering lengths of the different fragments of the C I ~ depend E ~ on the isotopic composition, and these values are given in Table 1, together with other useful molecular parameters. 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. The Teflon troughs were mounted inside closed aluminum containers whose temperatures were controlled to an accuracy of *O. 1 K by direct heating of the outside of the container. Further temperature stability was obtainedby mounting the thermostated can inside another thermostated enclosure whose temperature was controlled with the same accuracy. This procedure effectively prevented any drop in temperature at the quartz windows of the apparatus and hence any condensationof water on the windows, which would interfere with the accuracy of the measurements. The neutron reflection measurements were made on the reflectometer CRISP at the Rutherford-Appleton Laboratory (Didcot, U.K.). Two types of measuremennt were made, with a single detector, for which the procedure has been described previously,s and with a linear multidetector aligned in the plane of reflection.6 All the measurements were made at a fixed incident 0 1994 American Chemical Society
Lu et al.
6560 The Journal of Physical Chemistry, Vol. 98, No. 26, 1994 TABLE 1: Scettering hngths and Volumes of Constituent Parts of C I A ' extended scattering unit volume/A) length/A length/ 10-5 A CizDzs 350 16.9 245.51 (99.4WD) CizHzs 350 16.9 -13.7 315 17.8 237.0 (9895D) (OCzDWD 190 10.7 14.48 (OCzHAOH 505 28.5 371.84 (9896D) (OC2Dd80D 505 28.5 35.18 (OCzHdsOH 19.14 D20 30 H2O 30 -1.68 0 Volumes and extended lengths are from refs 21 and 22 and scattering lengths from ref 23.
RT
7l --I
70
+
t
x
x 0
0 0
0
I
I
293
303
313
323
Temperature/ K Figure 2. Effect of temperature on the surface coverage of ClzE8 at the air/water interface determined by neutron reflection at a concentration of 1.8 X l e M: (0)dCIZhE8 (impure), (A) dClzhE8 (purified), (+) dCIzhE3dE5, (X) hClzhE3dE5, all in null reflecting water. Also included are the results of Rosen et ai.' ( 0 ) .
1 2
4
6
0
1
I
0
[ C x 1051M1 Figure 1. Adsorption isotherm of C12E8 as determined (a) from neutron reflectivity measurements on dClzhE8 in null reflecting water using a multidetector (0)and (b) from surface tension measurements (+). T = 298 K.
angle of 1.5O and the absolute reflectivities calibrated with respect to D20. For the singledetector measurements, a flat background determined by extrapolation to high values of the momentum transfer, K ( K = (4% sin e ) / k where 0 is the glancing angle of incidence),was subtracted. With the multidetector, thespecular signal was determined by subtracting a background estimated by interpolationfrom either sideof the specular peak. For the systems described in this paper the two methods have been shown to be equivalent.6 Surface tension measurements were performed on a Kruss K10 tensiometer by following the procedure described previ~usly.~
Results Surface tension measurements were used with a view to establishing the purity of the samples. Two problems were encountered. The complete removal of water from the ClzE8 was not always very easy, which would result in an incorrect concentration scale. This was not a problem encountered by Rosen? who purified his samples in aqueous solution. The second problem was that one sample was initially contaminated by small amounts of lower members of the C12Emseries. This was shown very clearly in the temperature dependence of the neutron reflection analysis and is discussed further below. Analysis of the surface tension curves followed the procedure described previously,' and the surface coverage agreed within error with the neutron reflection coverages (see Figure 1). The critical micelle concentration (cmc) was found to be 1.0 (h 0.1) X l ( r M, in good agreement with the value obtained by Rosen et a1.8 The adsorption isotherm was initially measured by neutron reflection using the multidetector to record the reflected signal. For a deuterated surfactant in null reflecting water (nrw) the level of the signal, especially at low K , is approximately proportional to the square of the coverage, and even at K = 0.05 A-l, the lowest K we usually measure for surfactant layers, the typical signal at the cmc is often lk3compared with a background level of 2-5 X 10-6, It has been shown6 that we can make the further
assumptionthat the signal integrated over all K is also proportional to the square of the coverage, and then it is possible to determine the coverage in a very short run indeed (typically a few minutes at thecmc). The absolutecoverage was determined from a single measurement with good counting statistics evaluated in the conventional way with an accuracy better than 596.' The errors in coverage evaluated from integrated reflectivity using the multidetector reflect the lower statistical accuracy associated with the shorter measurement times and were found to be about 10%. This is higher than achievablewith more precise reflectivity measurements but comparable with the normal errors in surface tension determinations of coverage. The resulting isotherm is shown in Figure 1. It is seen that the coverage tends toward a plateau at a coverage of about 2.8 X l0-lo mol cm-l, which corresponds to an area per molecule of 60 h 4 Az.There is some scatter in the data in the region of the plateau of adsorption. There are two possible sources of error, from the approximate methodofdeterminationofthecoverageassociated with the poorer statistical accuracy and from the experiments being performed on the dClzhE8 sample as prepared directly from the Williamson synthesis. It was later found that, owing to impurities in the original octaethyleneglycol,this samplewas slightlycontaminated with C12Em species with m < 8 and this may have caused the coverage to be slightly high, just below the cmc. Above the cmc it would be expected that lower members of the C12Em series would be solubilizedinto the micellar solution and therefore would not affect the surface coverage. At 298 K the limiting coverage is, however, in good agreement with the more accurate measure ments to be described below, and with the coverage determined from the surface tension measurements. The simplest manifestation of the effects of temperature is expected to occur on the coverage. This has been evaluated previously for ClZE8 itself by Rosen et a1.8and for other members of thenonionicseries by several authors, e.g. for C12& by Ottewill et al.,IO using surface tension measurements. Using neutron reflection, weexamined the effect of temperatureon threedifferent samples over the temperature range 298-323 K, on dClzhE8 as originally prepared, on the same material after purification on a column, and on dClzhE3dE5, all in nrw. The latter isotopic species was chosen because it was expected to give greater sensitivity to any change in thickness of the layer because the distribution of high scattering length material in the adsorbed layer is concentrated toward the two extremes of the layer. In the original unpurified dCIzhE8 sample was found a significant temperature effect on the coverageas shown in Figure 2. Ottewill et a1.10 examined the temperature dependence of the surface tension of c12E6, and although they did not explicitly analyze their data in terms of the area per molecule, it is clear
The Journal of Physical Chemistry, Vol. 98, No. ?6,1994 6561
Neutron Reflection from a Layer of ClzEs TABLE 2: Structural Parameters (A)of C& on Null Reflecting Water at the cmc (Single-Layer Model) at T = 298 and 323 K. surfactant A 3/A2 r * I/A a* 1/A Temperature = 298 K
*
dCizdEs
dC12hEs hC12dEs
dClzhE3dEs hClzhE3dEs
69 61 60 63 59
26.5 20.0 22.5 21.5 21.0
23.5 16.5 18.5 23.5 17.5
Temperature = 323 K dCiihEs 62 21.5 18.0 dC12hEidEj 65 21.5 25.0 hC 12hEsdE5 59 21.5 18.0 0 All thicknesses have been rounded to the nearest 0.5 A. that their coverage also increases quite sharply with temperature. Rosen et a1.,8 however, using surface tension measurements, observed a slight decreasein coveragewith increasingtemperature. The subsequent procedure of purifying our dC12hE8on a column indicated that there were trace amounts of lower C12E,,,s, and it is evident that these impurities are responsible for the observed temperature dependence of the coverage because only a slight temperature dependence was observed after purification. Our two sets of measurements are compared with the previous measurementsof Rosen in Figure 2. The temperaturedependence of the coverage obtained from our neutron reflection measurements, when averaged over all the deuterated samples, lies within the experimental error of 5%. The neutron experiments on contaminated and pure materials demonstrate directly the effect of impurities on the temperature dependence of the coverage. Several previous efforts to assess the effects of temperature on the surface properties of the range of alkyl monoethoxylates have produced conflicting results. The impurities present were of a type that is common in the commerciallyavailableC,,E,,, series,and the current measurements now suggest that where large temperature effects have been observed, the results should be treated with caution. In the above measurements we have determined the area per molecule using concentrations in excess of the cmc at all temperatures. Changes in the cmc expected for C12Eg (R0sen)8.~ over this temperature range would correspond to a decrease in adsorption at the interfaceassociated witha decrease in monomer concentration (see Figure 1). However, this assumes that the intrinsic “surface activity- is temperature invariant. Our observations for the pure monolayer are then consistent with an enhanced “surfaceactivity”for C& with increasing temperature, as expected from the dehydration of the ethylene oxide group. The presence of lower C12Emsin the impure surfactant will result in a reduced temperature dependence of the cmc and hence monomer concentration. The changes in “surface activity” that result with increasing temperature will correspondinglymanifest themselves as enhanced adsorption. Despite the negligible change in coverage with temperature, it would be expected that some change in the structure of the adsorbed layer will be associated with the dehydration of the ethylene glycol chain. Furthermore, the area per molecule is similar to that normally associated with spherical micelles in the bulk surfactant phase. This strongly suggests that the area per molecule is determined by the cross section that the E8 group subtends at the surface, the hydrocarbon chain only playing a minor role. In Table 2 we give values of the thickness of the layer based on fitting either a single uniform layer or a Gaussian layer (see below) to the reflectivity profiles. Both structural models show that there is a slight increase in the thickness of the layer as the temperature is increased for all three isotopic species. The increases are close to the experimental error and are different for the different isotopic species investigated. The most sensitive
L
.
25
.
26
.
27
. . . . ZB p 30 31
ThicknessIA
Figure 3. x2 variation for the least-squares fitting of a single uniform monolayer to the thickness of the layer of dClzhEsdE5 in null reflecting water at temperatures of 298 (0) and 323 K (+), at a surfactant concentration of 1.8 X l ( r M.
measurement is for the dCl~hE~dE5, where the change is very small. However, to emphasise that the change in the thickness ofdCl2hE3dEs,althoughsmall,is significant, weshowthevariation of x2 in the least-squares fitting of the uniform single-layer model to the reflectivity for this isotope at the two temperatures in Figure 3. It will be shown below that the changes in the three isotopic species studied combine to demonstrate that there are changes in the structure of the layer with temperature. The structure of the Cl2Es layer is most effectively determined by the semidirect method introduced and discussed in several previous papers,liJ2 rather than through the use of model fitting. Although we do not present the results of model fitting in this paper, we did attempt to fit the structure of C12E8 using the two-layer model successfully developed for other surface monolayers.11J2 The results were found to be unsatisfactory. This is most likely because the previous assumption that the ethylene glycol chain (head group) is uniformly distributed throughout a single layer will be increasingly inappropriate as the E,,, group becomes longer because it will start to develop a distribution more like that expected for a polymer. It is then difficult to devise a more complex model which can be rigorously justified. For the Cl2E8 layer, the aspects of the structure which are of most interest are the relative positions of alkyl and ethylene glycol chains, and water, and the widths of those distributions normal to the interface. The ethylene glycol chain is sufficiently long that the distributions and relative positions of different parts of thechainarealsoofinterest. Theresolutionobtainable by labeling of the different groups of the surfactant is limited on the one hand by the smallest number of deuterated species that will give a satisfactory signal to noise ratio, and on the other hand by the availability of suitably deuterated materials. Here we have labeled the two types of chain, the solvent, and the five ethylene glycol units at the free end of the ethylene glycol chain. The structure of the air/solution interfacecan then be described in terms of the distributions of alkyl chains, c, ethylene glycol chains as a whole, e, or in part, e5, and water (solvent), s. In terms of the three labels, the scattering length density can be written
where ni is the number density profile of species i and bi is its scattering length. For the system with partially labeled ethylene glycol chains, the scattering length density is strictly written as
However, we have used a much simpler, approximate scheme for determining the distribution and relative position of the e5 group, which we discuss further below and which is then represented by eq 1with bca5(z)replacing b&(z). The kinematicapproximation for the reflectivity R ( K )may be written in terms of the partial
6562 The Journal of Physical Chemistry, Vol. 98, No. 26, 1‘994
structure factors hit R(K) = 6?r2(bfh,
Lu et al. terms. The three separations 6,, are not independent because
+ b;h, +
K2
bfhW+ 2b,b,h,
+ 2b,b,h, + 2b,b,h,)
(3)
where hi, are the partial structure factors given by h,i(~= ) Ini(K)12
hji = hij(K) = Re{n,(K)n,*(K)J
(4)
and e representseither the whole ethyleneglycol chain or the five free end units. The n i ( K ) are the one-dimensional Fourier transforms of ni(z).11J2 The reflectivity given by eq 3 is approximateand without further correctionwill lead to incorrect values of the derived partial structure factors, particularly that of the solvent. This has been discussed in detail by Lu et al.,13 who have shown that an equation derived by Crowley14 can be used to convert the experimentaldata into a reflectivity for which eq 3 is essentially exact. There are two types of partial structure factor in eq 3, the self-terms, hrr,and the cross terms, hi,. The self-terms hli are characterized in terms of the width, ui, of the distribution ni, but the value obtained for the width depends on the function chosen to represent ni. We use a Gaussian distribution for parts of the surfactant and a tanh distribution for the solvent.ll These distributions are defined by n = ni exp(-4z2/a:)
(5)
where ni is given in terms of the area per molecule by
ni =
2
ZqG
(6)
and n = no
[i+ f
tanh(z/{)]
(7)
where z is the distance in the direction normal to the interface, ui and t are the width parameters, and is the bulk number density of the solution. For comparison of the widths of the chain distributions, we also use the full width at half-height of the Gaussian, which we designate by u* or fwhh. The self-partial structure factors, hi,,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, h p We have previously shown that both types of chain give predominantly even distributions, whereas the solvent density is predominantly an odd function, and then
and
where 6, and ,6 are the separations of the chain and solvent and alkyl chain and glycol chain distributions. The set of six partial structure factors was obtained from the reflectivity profiles of the combinationsdC12hE8in null reflecting water (nrw) and D20, dClzdE8 in nrw and DzO, hCIzhE8 in D20, and hClzdE8 in nrw, using the appropriatevalues of bifrom Table 1. From the set of six partial structure factors, the six parameters a,, u,, r,, ,6 ,6 and 6, are obtained by fitting Gaussian distributions to the self-termsand using e q s 8 and 9 for the cross-
and therefore within the frameworkof 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 contrastmatched to air. The alkyl chain and solvent can be so matched but not the ethylene glycol chain. Thus, for the most accurate structural determination of the layer, six measurements were necessary. When the ethylene glycol chain is only partially labeled, there is considerable choice for the profiles required to determine a total of four widths and four separations. However, in the present case, we are only considering the width of the distribution of the five end ethyleneglycolunits and their position in the interface, i.e. uesand either 6 , or ~ ~go%. We now make the assumption that the hE3 group has a scattering length of exactly zero. This is not the case, but in comparison with the dE5 (see Table l), it is indeed very small ( ~ 6 %and ) can be neglected. In the case of C12E3, the comparable neglect of the hE3 group led to negligible error when compared with a more thorough analysis.4 In this approximation the reflectivity (eq 3) becomes
We made the full set of isotopic measurements (eqs 3 and 11) at 298 K and a limited set of measurements (eq 11) on the e5 species at the cmc. We also made an even more limited set of measurements,where only the alkyl chain was labeled at 9 X 10-6 M at 298 K, dClzhEs in nrw and D20, and hClzhE8 in D2O. This amounts to neglecting the hEg contribution to the scattering. The effects of this approximation are considered in ref 3. At the cmc, at 298 K, the apparent thicknesses of the different regions of the layer were determined from the set of five reflectivity profiles in nrw and the straight line plots appropriate to the Gaussian distribution, eq 5,12 In(hii) = -2 In A - K ~ u : / ~
(12)
where A is the area per molecule and uI is the full width of the Gaussian distribution at l / e of its height. We have shown in ref 12 that a significant source of error in the cross-terms of the partial structure factor results from variations in the surface coverage between different isotopic samples and that this error is minimized if the reflectivities are normalized to the average area per molecule. This has been done using the values of A from the singlelayer fits in Table 2. The appropriate plots (eq 12) for the five different regions of the layer, after the normalization of the reflectivities to a constant area, are shown in Figure 4, and the thicknesses are given in Table 2. From the measurements at the cmc in nrw (eqs 3 and 11) and from eq 9, the separations,6 and 6,s are easily determined from the cross-termsin the partial structure factors, h, and h , ~ .These are shown in Figure 5, and the three corresponding self-termsha, h,, and hew are shown in Figure 6. The cross-terms are extremely sensitive to the values of 6, which means that the separations are determined to a high degree of accuracy. The values are given in Table 3. The measurements in DzO allow the remaining partial structure factors involvingthe solvent, h,, h,, h,, and hd,. to be determined. The width of the solvent region was fitted by a tanh function, and the fit of eq 8 to the cross-terms is shown in Figure 7. All the fitted parameters are presented in Table 3. The possible effects of temperature on the structure of the layer are (i) a change of surface concentration, (ii) a change in
The Journal of Physical Chemistry, Vol. 98, No. 26, 1994 6563
Neutron Reflection from a Layer of C12E8
-31-
0.01
0.02 0.03
0.04
aos
kZA2 Figure 4. Plot of In(htr) os K~ at 298 K and 1.8 X 10-4 M: dC14EB (0), dClzhE3dEs (A),dClzhE8 (+), hClzhE3dES (X), and hCndE8 ( 0 ) ,all in null reflecting water. The slopes give the Gaussian thickness of the layer (u), and thevalues are (0)24.0, (A)24.3, (+) 16.2, (X) 18.0, and ( 0 )18.0 A.
-1
I
.2.5
OB
om
01s
OM
02s
aa
KIA" Figure 5. Two cross-termsin the partial structure factors, K2h, (0)and K2h,s (A),fitted by eq 9 and values of 6, of 10.5 A ands,6 of 11.5 A. The surfactant concentration is 1.8 X 10-4 M, and the temperature is 298
K.
the thickness of the layer or any of its component parts, and (iii) a change in the position of the layer, or its component parts, in relation to the solvent. We have already shown that the area changes insignificantly and that there are small, but measurable, changes in the overall thickness (see Table 2). The separation of the data into the contributions from the different components, the partial structure factors, makes it clearer where thesechanges are occurring. The largest change is in the overall thickness of the alkyl chain, which is demonstrated clearly by a plot using eq 12 and is shown in Figure Sa. On the other hand, there is essentially no change in the thickness of the end five EO groups in the glycol chain (Figure 8b). The two main contributions to the overall thickness of the layer are the intrinsic length of the isolated molecule projected on the surface normal and the roughness! The interfacial roughness broadens all the selfdistributions and therefore tends to obscure small structural changes, but it may be eliminatedby examiningonly theseparation of parts of the layer from one another, which have been shown to be independent of the interfacial roughness.4 These, in turn, are determined by fitting eqs 8 and 9 to the cross-terms in the partial structure factors. The effects of temperature on the three cross-terms are shown in Figure 9. From the alkyl chain/glycol chain partial structure factor (Figure 9a) it can be seen that there is a decrease in the separation at 323 K compared with the value at 298 K. A change in s,6 with temperature should be linked to changes in the other 6 values. Figure 9b,c shows the effects of temperature on the two partial structure factors h,s and h,. Within the fitting error, 6, and s,6 are the same at the two temperatures, although there are small systematic differences. When the whole set of structural parameters, given in Table 3, is examined in the context of eq 10,which shows that the structure
Figure 6. Partial structure factors for (a) alkyl chains, K2hof,(b) the whole ethylene glycol chain, r2h,, and (c) the end five groups in the ethyleneglycol chain, K2h&s. The fitted widths are u, = 15.0 & 1 A, ud = 19 i 1 A, and u,s = 17.5 & 1 A. The surfactant concentration is 1.8 X 10-4 M, and the temperature is 298 K.
of the layer is overdetermined, it can be seen that the small changes all reinforce one another. This indicates that there is a genuine, systematic change of structure in the layer, which we discuss in the next section. The clearest representation of the experimentally determined structure is to plot the distributions of the individual components. This can be done in terms of either number densities or volume fractions. The former are the most directly determined by experiment and are converted to the latter by inclusion of the estimated volumes of the components. However, the volume fraction representation is clearer and can also reveal inconsistencies in the approximations made in calculating the structure, the most critical assumptions being the use of the model distributions, eqs 8 and 9. Figure 10 shows the volume fractions of the different components at 298 and 323 K using the parameters of Table 3. The total volume fraction rises to a value about 10% above close packing in the region of the head group, but as we have argued elsewhere: this is probably an acceptable error, given that the distributions have been idealized into Gaussian and tanh profiles and that thereare possible errors in the assumed fragment volumes. The increases in the width of the two fragment distributions can be seen by comparison of Figure 10a and lob.
Lu et ai.
6564 The Journal of Physical Chemistry, Vol. 98, No. 26, 1994
TABLE 3 Structural Parameters Obtained from Kinematic Analysis.
value uniform, X Gaussian, u Temperature = 298 K, cmc
parameter
* l /1/A A ~ e s S ( ~ e* s )A I * 1/ 6, OS/A * OS/A 6 d OS/A 6-h i / A * 1/A ued~ed
17.5 20.5
15.0 17.5
uS(71)
23.0 15.0
19.0 9.0(tanh)
ucE(7c)
Gaussian, u* 12.5 14.5 16.0
t
11.0 11.5 10.5
6-5
-9.4 -9’2
2.5 -1 .o Temperature = 323 K, cmc 20.5 17.0 21.0 18.0 14.5 8.5(tanh)
14.0 15.0
11.0
11.0 0.5 uc(Tc)
* OS/A
~s(7J
6, a
2/A 2/A
Temperature = 298 K, 9 X 1V M 17 14 13
11.5
7.5(tanh) 8
All distances have been rounded to the nearest 0.5 A.
.9.751 -10.001
0.01
0.02 0.03
0.04 0.05
I
K2A2 Figure 8. Plot of In(hd us K~ at 298 (0) and 323 K (+): (a) alkyl chains (hm),and (b) the end five groups of the ethylene glycol chain ( h 4 . The slopes give the Gaussian thickness of the layer, and the fitted values are 15 (0) and 17 A (+) for the alkyl chains, and 17.5 (O,+) for Es.
I
I
95
0.05
om
0.5
0.20
025
Klk’
Figure 7. Two cross-terms in the partial structure factors.(a) ~ ~ and h , (b) Kzhm fitted by cq 8 and values of ,6 of 11.0 A and 6, of 2.5 A. The surfactant concentration is 1.8 X l ( r M, and the temperature is 298 K.
Only a limited set of isotopic compositions was studied at a concentration below the cmc, sufficient to determine the alkyl chain width and the separation of the alkyl chain and solvent distributions. The results of analyzing these data in terms of the kinematic approximation are given in Table 3.
Discussion The results for C& add significantly to the body of data we have collected on the series C12Em:J5J6 and it is interesting to compare the structures of the layers as the length of the ethylene glycol chain increases. Table 4 lists some of the relevant data for m = 2, 4,and 6 at an area per molecule of 55 A2, the present results for m = 8 at the slightly larger mean area of 62 A2, and interpolated values for m = 3 corresponding to an area per
molecule of 55 A2. We have already commented that the widths of the distributions are affected by roughness. Some of this roughness must originate in capillary waves, and we first attempt to remove this contribution. The capillary wave amplitude of a pure liquid varies as fi (the surface tension), and the mean square amplitude for water is 2.8 A.17 We can therefore use the measured surface tensions to estimate the contribution for each surfactant. Unit mean square amplitude in terms of capillary waves is equivalent to 2.3 units in terms of the distributions used in the present work, and this is included in the calculated values of capillary wave roughness, w, given in Table 4. Although the capillary wave model for a pure liquid is only a first-order approximationfor a surfactant solution in that thecapillary waves will be affected by a number of damping terms, e.g. the surface viscosity,18it should be adequate to remove most of the thermal roughness at the level of accuracy of the data, although the layer may still be rough from other causes, e.g. structural disorder. The values of u correspond to Gaussian distributions, and it is not obvious how they should be compared with geometrical parameters of the chains, e.g. the fully extended length. One possibility is to note that the amount of a Gaussian distribution lying within the width at l/e of the height is 0.83 and an appropriate correction could then be to multiply the widths by 1/0.83. The width of the distribution would also be increased by about this amount if it were taken to be a uniform layer with Gaussian edges. We have not made any such correction in Table 4, but it should then be remembered in the following discussion that,,a can be expected to be intrinsically slightly shorter than the length of the fragment forming the distribution. The first observation to note is that the corrected alkyl chain lengths all lie within 1.OA (the experimental error) of the average value of 12.0 A, although the uncorrected values do not. Since the alkyl chain width varies significantly with surface coverage: it appears that, within the experimental error, the static width of the alkyl chains depends only on the surface coverage and not on the size of the head groups. The corrected width of the alkyl chain region is nevertheless significantly less than the fully extended chain length of 16.7 A, indicating either that thechains are tilted on average and/or that they contain gauche defects.
The Journal of Physical Chemistry, Vol. 98, No. 26, 1994 6565
Neutron Reflection from a Layer of Cl2E*
Distance normal to surface/A
Figure 10. Distributions of the different componentsof the ClzEs layer at (a) 298 and (b) 323 K: water (dotted line), alkyl chain (solid line),
ethylene glycol chain (E8 and E5) (dashed lines), total volume fraction (dash-not line). In b the Es, but not the Es, distribution is shown (the E8 distribution was not determined).
TABLE 4 Structural Parameters as a Function of Ethylene Glycol Chain Length'
Y(W) uc(umrr) Ue(Umrr) 1. 6, IC8 6, ,6 14(11.7) 6.0 12 50.2(7.6) 8 (2.3) 7.2 C12E2 10.8 6.5 13.8 4 C& 46.1 (8.0) 14.3 (11.9) 11 (8.3) C& 40.9 (8.4) 14.5 (11.8) 14.5 (11.8) 14.4 6.5 15.6 3.5 clzE6 33.5 (9.4) la.O(l2.9) 16.5 (13.6) 21.6 9.0 19.2 ClzE8 36.1 (9.0) lS.O(l1.7) lg.O(l6.7) 28.8 10.5 22.8 a y is the surface tension in mN m-l, w is the calculated capillary wave roughness, u- is the width after the capillary wave roughness has been removed, I, is the length of the fully extended ethylene glycol chain:' ,/ is the calculated distance between the centers of the two chains in the fully extended surfactant molecule,2lSand 6, an 6, are the experimentally determined separationsbetween the two halves of the ethyleneglycol and alkyl chains. All lengths are in angstroms.
I Q
?$ D
r:
N
r
2
I
I
0.05 0.10
0n .
0.20
0.2s
K Id Figure 9. Cross-termsin the partial structure factors at temperatures of 298 (0)and 323 K (A): (a) K2h,s, (b) K%, and (c) K2h,,. The fitted lines use eqs 8 and 9 and values of 6 of (a) 11.5 (0)and 11.0 (A),(b) 11.0 (0,A), and (c) -1.0 (0)and 0.0 (A).
The ethylene glycol chain lengths, neglecting the value for C12E2 which is left with a large error after the capillary wave correction, are comparable with the fully extended chain lengths for the shorter chains but drop well below these values for C12E,5 and C12Es. The most striking observation is that ,6 is never more than about half the value of 1,. Since 6, is given by
,6 = ( t , cos e)
(13)
where 4, is the average separation of the centers of the alkyl and ethyleneglycol chains and 0 is the angle with respect to the surface normal, both chains must either contain gauche defects and/or be strongly tilted away from the surface normal. The values of 6, and 6, in Table 4, although carrying larger errors than, ,a are even smaller than the fully extended center tocenter separation. Another interesting observation is that the ratio 6=/1, is approximately constant for all five compounds, at an average of about 0.5. Some deductions about the nature of the layer may be made from these observations, but it should be emphasized that only a systematic analysis of the segment density distribution of the chains, using either theory or computer simulation, e.g. as in ref 19, can give a true interpretation of the structures as presented, the problem being that the resolution of the experiment is still
somewhat coarse. We have already argued that 6 values are not affected by the roughness of the layer? but the widths u are affected, and we can write
where Ciis the projectionof the fragment ialong thechain direction and w' accounts for any roughness left after removal of the capillary wave roughness. Equation 14 is approximate in that there may be correlation between tilt angles 8, incidence of gauche defects, and the residual roughness, but for simplicity we neglect any such correlation. We have previously also made the approximation that (cos2 8) N ((cos in order to solve eqs 13 and 14 and hence separate contributions from tilting of the chains and total roughness. However, this will be invalid if the distribution of 0 is other than very narrow. If both chains are fully extended and oriented at a fixed angle to the surfacenormal, then from the 6, values, cos 8 is about 0.5 and the tilt from the surface normal is close to 60° for all five surfactants. It then follows that the chain widths are ((0.5)28: + w4)1/2. Taking the maximum value of e,, i.e. li, gives the values of w'(c) and w'(e) in Table 5a. For the three longer surfactants, the two independently obtained values of w' are in good agreement. Thus it would appear to be possible to explain the structure of the layer in terms of uniformly tilted molecules with a large static roughness. However, since it seems inconceivable that such a large static roughness, comparable with the thickness of the layer, could be associated with perfect orientational order, this model is probably inappropriate.
6566 The Journal of Physical Chemistry, Vol. 98, No. 26, 1994
TABLE 5: Structural Parameters for Different Models (a) All Molecules Aligned at a Fixed Angle 0 = cos-I(a,/f,) to the Normal C I zEz CizE3 Cizh C12% CIZEB
Wl4
wle)
8.2 9.5 9.5 10.2 10.0
6.5 10.2 9.1 10.1
(b) Rigid Molecules Aligned with a Distributionj(0) = 1 and Some Roughness CIZEZ C12E3 ClzE4 C& ClzEa
@c
Q
6, (obs)
W'
11.7 11.7(11.9) 12.3 (11.8) ll.g(l2.9) 11.9(11.7)
9.1 (8.3) 11.3 (11.8) 14.3 (13.6) 18.0(16.7)
6 (6.0) 6.9 (6.5) 7.8 (6.5) 9.6 (9.0) 11.4(10.5)
6.6 6.6 7.6 7.0 7
The values shown in parentheses are the experimental values. The next simplest assumption is that the molecules are rigid but have a distribution of orientations. Then expressions for ,6 and u are
,6 = 0.5(1, + le)Jf18) cos 8 sin 8 dO/JflO) sin Odd (15)
and U:
= lzsf(B) COS' 8 sin 8 d8/ J f l 8 ) sin 8 d8
(1 6 )
where f ( 8 ) is the probability distribution for 8, 8 is the angle between the molecule and the surface normal, and 1, are the fully extended lengths. Given the hydrophobic nature of the alkyl chain, it seems reasonable to suppose that the upper integration limit for 0 is r/2; i.e. the molecule cannot rotate beyond the horizontal position. The distributionf(8) may take a number of forms. If it is centered on 8 = 0, then a possible series of distributions are given by
Ae) = COS" e
(17)
which become increasingly peaked around 8 = 0 as n increases. Substitution of eq 17 into eqs 15 and 16 gives
,6 = (n + 1)(1, + 1,)/2(n
+ 2)
(18)
and
+ l)/(n + 3)]'/*
ut = li[(n
(19)
giving ui = 1,/2/3,Ii/2/2
,6 = (1, + 41/49 (1, + 4 ) / 3 for n = 0 and 1, respectively. The values of ,6 for all five surfactants are consistent with a value of n of 0, i.e.f(0) = 1, but the corresponding values for uc are much too low. The u, values are too low at low m but approximately correct at m = 8. On the other hand, a value of n = 1 gives too low a value of 6, approximately the correct uc,and too large values for u,. A value of n = 0 can be reconciled with the observed values of u and 6 if an additional roughness is included and calculated and observed values for this case are compared in Table 5b. The additional roughness is slightly less than for model a but is still quite large. However, since the orientational order is also large, a large roughness does not seem to be so unreasonable.
Lu et al. The calculation above demonstrates that it is difficult to reconcile the relatively large values of u with the small values of 6 without invoking a significant roughness of the layer over and above the roughness calculated for a crude model of capillary wave roughness. Since models a and b represent two extremes for the orientational order within the layer, this suggests that there is definitely significant extra roughness. It is possible that the introductionof gauche defects into the surfactant might reduce the need to include the extra roughness. Thus, if there is a defect between the centers of the two chains, then 4, is less than the fully extended value I, and a larger value of (cos 0) will then account for the observed values of .,6 This in turn means that the angular distribution may be more peaked, i.e. n is larger than 0, and hence ui is increased. However, the introduction of gauche defects may also reduce and then cancel out any increase due to a higher n. We do not pursue this analysis further here because there is no justification for assuming that the incidenceof gauche defects will have comparable effects on all five surfactants, and there is insufficientinformation to treat each surfactant separately. However,the arguments presented do indicate that gauche defects may play an important role, and this question has been considered in more detail by Nikas et al.20 The primary purpose of this paper has been the investigation of the effects of temperature. One of the reasons for doing this is that sharp interfacial tension minima, leading to ultralow tensions, are observed for a number of C I ~ E ,surfactants at the oil/water interface as the temperature is changed.* It has been suggestedthat thiseffect is related to thereductionin the hydration of the ethyleneglycol head groups as the temperature is increased. While a full understanding of the surface tension minimum would require structural investigationof the surfactant at the oil/water interface, changes in the extent of hydration should also be observed at the air/water interface. The one change observed in the present work that is larger than the experimental error is that the thickness of the alkyl chain region increases by 2.5 A. This increase may be caused by either an increase in roughness of the whole layer or a change in chain conformation (either tilt or number and type of chain defects). If it were only roughness, then the glycol chain region would change by the same amount unless the chain conformation of the glycol changed to decrease the thickness by a compensating amount (see eq 14). However, the measured glycol chain thickness is unchanged. There are therefore two extreme possibilities; either the glycol chain region thins by exactly the amount required to compensate the extra roughness of the layer, which is what increases the thickness of the alkyl chain region, or the alkyl chains become more extended and the glycol chains do not change with temperature. If the glycol chain region thins, then by conservation of volume, water must be displaced and therefore the glycol chain/water separation should increase, as observed (note that 6 % ~is negative at 298 K). On the other hand, if the change in alkyl chain thickness is just a change in extension or tilt, i.e. it is not a roughness contribution, then the alkyl chain/water separation would increase by approximately half the increase in the alkyl chain thickness, about 1.25 A. However, this parameter stays the same, at 11.0 A, and the difference of 1.25 A is outside the experimental error. These two observations suggest that the dominant contribution to the increase in alkyl chain thickness is a change in roughness of the layer. This is further supported by the observed decrease of 0.5 A in the alkyl chain/glycol chain separation. We therefore conclude that the intrinsic thickness of the ethylene glycol chain region decreases significantly when the temperature increases. The decrease in thickness of the glycol group is about 142, and since the glycol region is approximately two-thirds water and one-third ethylene glycol chain, the extent of hydration of the ethylene glycol over the temperature range 298-323 K decreases by about 20%.
Neutron Reflection from a Layer of C12Es
Acknowledgment. We thank the Science and Engineering Research Council for support. Z.X.L.also thanks the SineBritish Friendship Society. References and Notes (1) Shinoda, K.J. Colloid Interface Sci. 1970, 31,278. (2) Aveyard, R.; Binks, B. P.; Fletcher, P. D. I. Lungmuir 1989,5,1210. (3) Lu, J. R.; Lee, E. M.;Thomas, R. K.;Penfold, J.; Flitsch, S. L. Lungmuir 1993, 9, 1352. (4) Lu, J. R.; Hromadova, M.;Thomas, R. K.; Penfold, J. Lungmuir 1993, 9, 2417. (5) Lee, E. M.; Thomas, R.K.;Penfold, J.; Ward, R. C. J . Phys. Chem.
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1989. -
(6) Staples, E. J.; Thompson, L.;Tucker, I.; Penfold, J.; Thomas, R. K.; Lu, J. R. fungmuir 1993, 9, 1651. (7) Simister, E. A.; Thomas, R. K.;Penfold, J.; Aveyard, R.; Binks, B. P.: CooDer, P.; Fletcher, P. D. I.; Lu. J. R.;Sokolowski, A. J. Phys. Chem. 1992, 96, 1383. (8) Rosen, M. J.; Cohen, A. W.; Dahanayake, M.;Hua, X . J . Phys. Chem. 1982,86, 541. (9) Rosen, M. J. Surfactants and Interfacial Phenomena, 2nd ed.; Wiley: New York, 1989.
The Journal of Physical Chemistry, Vol. 98, No. 26, 1994 6561 (10) Corkill, J. M.; Goodman, J. F.; Ottewill, R. H. Trans. Faraday Sm. 1961, 57, 1627. (11) Simister. E. A.:. Lee.. E. M.:Thomas. R. K.: Penfold. J. J. Phvs. Chem..1992. 96.’1373. (12) Lu,J. R.; Sinister, E. A.; Thomas, R. K.; Penfold, J. J. Phys. Chem. 1993, 97, 6024. (13) Lu, J. R.; Simister, E. A.; Lee,E. M.;Thomas, R. K.;Rennie, A. R.; Penfold, J. Lunmnuir 1992. 8, 1837. (14).Crowl& T. L. Ph$ca A 1993,195, 354. (15) Lu, J. R.; Li, Z. X.;Su, T. J.; Thomas, R. K.; Penfold, J. Lungmuir 1993. 9., 2408. -. - -(16) Lu, J.R.;Li,Z.X.;Thomas,R. K.;Staples,E. J.;Tucker,I.;Penfold, J. J. Phys. Chem. 1993, 97, 8012. (17) Schwartz, D. K.; Schlossman, M.L.; Kawamoto, E. H.; Kellogg, G. J.; Pershan, P. S.;Ocko, B. M. Phys. Rev. 1990, A41, 5687. (18) . h i & , V. Physicochemical Hydrodynamics; Prentice Hall: Englewood Cliffs. NJ. 1962. (19) B&ker,’J.; Schcnkrich, M.; Bopp, P.; Brickmann, J. J . Phys. Chem. 1992, 96, 9915. (20) Nikas, Y. J.; Puwada, S.;Blankschtein, D. Lungmuir 1992,42680. (21) Takahashi, Y.; Sumita, I.; Tadokoro, H. J . Polym. Sci. 1973, 11, 2113. (22) Tanford, C. J. J. Phys. Chem. 1972, 76,3020. (23) Sears,V. F. Neutron News 1992,3,26.
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