1001
Langmuir 1996,11,1001-1008
Structure of a DodecyltrimethylammoniumBromide Layer at the Airmater Interface Determined by Neutron Reflection: Comparison of the Monolayer Structure of Cationic Surfactants with Different Chain Lengths D. J. Lyttle, J. R. Lu, T. J. Su, and R. K. Thomas* Physical Chemistry Laboratory, South Parks Road, Oxford OX1 3Q2, U.K.
J. Penfold Rutherford-Appleton Laboratory, Chilton, Didcot, Oxon, U.K. Received August 8, 1994. I n Final Form: January 3,1995@ We have determined the structure of a monolayer of dodecyltrimethylammonium bromide (C12TAB) adsorbed a t the aidwater interface at three surface concentrations corresponding to areas per molecule of 4448,and 60 A2,usingneutron reflection. We have used isotopiclabeling to distinguish the hydrocarbon chain, head group, and solvent distributions. We have also labeled the two halves ofthe hydrocarbon chain to obtain information about the mean conformation of the chain. At the highest surface concentration we find that the inner half of the chain (next to the head group) is oriented closer to the surface normal than the outer half of the chain indicating that chain defects contribute to the chain structure. We also find that the surfactant layer is substantially rougher than that predicted from the simple capillary wave model of a pure liquid. We have compared the structure of the different C,TABs with chain lengths varying from Cl2 to CISat an area per molecule of about 44 k and from Clo to c16 at an area per molecule close to 60 A2. The most remarkable observation about the lower area measurements is that the thickness ofthe layer is the same for the four chain lengths even though the extended length of the chain increases by 50%. When account is taken of surface roughness, the intrinsic thickness of the chain region of the monolayer is also constant and for C18 is less than half the extended length. Comparison of the thickness of the layer and the separation of the chain and head distributions indicates that the mean orientation of the outer half of the chain is further from the surface normal than is the inner half of the chain, and this difference increases with chain length. At the higher area per molecule the CloTAB forms the thickest layer and this is associated with the chains being closer to the surface normal than for the other C,TABs.
Introduction The combination of isotopic labeling with neutron reflection has recently emerged as a technique able to give hitherto inaccessible information about the structure of layers of surfactants adsorbed at the aidwater interface and in equilibrium with bulk solution.'S2 The type of information that can be obtained includes the surface excess, the mean thickness of the different regions of the layer, and the separation of different fragments within the layer. To advance our understanding of the factors which determine the structure of an adsorbed surfactant layer, it is necessary to determine the effects on the structure of the layer of changing different parameters such as, for example, the chain length, the type of head group, and the temperature. To this end we have been using neutron reflection to make a systematic study of the series of cationic surfactants C,TAX, where C, denotes a hydrocarbon chain of 10to 18carbon atoms and X denotes the a n i ~ n . ~In- this ~ paper we complete the series where X is the bromide ion with results for dodecyltrimethylammonium bromide (ClzTAEl),and we make comparisons between the different alkyl-chain-length compounds. @
Abstract published in Advance A C S Abstracts, February 15,
1995. (1)Lu. J. R.: Hromadova, M.: Thomas, R. K.; Penfold, J. Langmuir 1993,9,2417. (2)Lu. J. R.:Simister. E. A,: Thomas. R. K.: Penfold, J. J.Phys. Chem. lb93,97,6024. (3)Lu, J.R.;Hromadova, M.; Simister, E. A.; Thomas, R. K.; Perfold, J. J . Phys. Chem. 1994,98,11 519. (4)Simister, E. A.; Lee, E. M.; Thomas, R. K.; Penfold, J. J. Phys. Chem. 1992.96.1373. (5)Lee, E: M.; Thomas, R. K.; Penfold, J.;Ward, R. C. J.Phys. Chem. 1989,93,381. '
Experimental Details Six isotopic species of dodecyltrimethylammonium bromide were used in the experiments,CI~DZEN(CD~)~B~, C1zDzsN(CH3)3Br, CIZHZ~N(CD~)~B~, CnHzsN(CH3)3Br,C ~ D I ~ C ~ H I ~ N ( C H ~ ) ~ B ~ , and C&I1&6D12N(CH3)3Br,which we refer to as dC12dTAB,dC12hTAB, hC1zdTAB, hClzhTAB, dC6hC6TAB, and hC6dCsTAB respectively. The method of preparation and purification was identical to that used for &TAB and described by Simister et a1.6 The raw materials used for the first four preparations were C12Dz5Br and N(CD3)3from Merck, Sharp & Dohme and C12H25OH from Larodan. The latter was convertedinto C I Z H ~ E using B~ standard procedures.' The half deuterated ClzBr was prepared as describedin ref 1. Two or three recrystallizationsof the crude surfactant were usually necessary to obtain satisfactory purity as assessed from surface tension measurements. High-purity water was used throughout (Elga Ultrapure system) and the methods of cleaning the glassware and Teflon troughs for the neutron experiment are also described elsewhere.5 All the experiments were performed at 25 "C. The neutron reflection measurements were made on the reflectometer CRISP at the Rutherford-Appleton Laboratory (Didcot, U.K.) using a procedure described previou~ly.~,~ The measurements were all made at a fxed incident angle of 1.5" and the intensities calibrated with respect to DzO. A flat background determined by extrapolation to high values of the momentum transfer, K (K = (4nsin e)/I where 0 is the glancing angle of incidence) was subtracted. The background signal is a combination of incoherent and multiple scattering from the solution and unless there are large scale structures,micelles, for example, in the solution, is expected t o be flat. This has been (6)Simister, E. A.; Thomas, R. K.; Penfold, J.;Aveyard, R.; Binks, B. P.: Cooper, P.; Fletcher, P. D. I.; Lu, J. R.; Sokolowski, A. J. Phys. Chem. 1962,96,1383. ( 7 )Furniss, B. S.; Hannford, A. J.; Smith, P. W. G.; Tatchell, A. R. Voael's Textbook of Practical Organic Chemistry, 5th ed.; Longman: EGex, U.K., 1989.'
0743-7463/95/2411-1001$09.00/00 1995 American Chemical Society
Lyttle et al.
1002 Langmuir, Vol. 11,No. 3, 1995
Table 1. Structural Parameters of ClzTAB on Null Reflecting Water Determined from Neutron Reflection Using a Single Uniform Layer Model” c / ~ O - ~ M[NaBrYM surfactant tlA uIA MA2
dCizhTAB 17.5 15.5 48 dCizdTAB 19.0 16.5 48 hCizdTAB 15.0 12.5 i 2 48 dCshC6hTAB 15.0 13.5 46 48 “O”CsdC6hTAB 14.5 13.5 44 dCizhTAB 18.0 16.0 dCizdTAB 19.5 17.0 43 hClzdTAB 15.0 12.5 f 2 44.5 dCshC6hTAB 15.0 13.5 45 “O”CsdC6hTAB 15.0 13.5 42 dCizhTAB 15.0 12.5 67 dCizdTAB 17.0 14.5 68 hClzdTAB 12.0 9.0 f 2 67 a t applies to a uniform layer and u to a Gaussian distribution defined by eq 8. 14 14 14 14 14 4 4 4 4 4 4 4 4
I
0.05
0.x)
0.15
0.20
0.25
0.30
KIA1 Figure 1. Neutron reflectivity profiles of different isotopic species of ClzTAB in null reflecting water at the cmc (14 mM): (0)dCizdTAB;(A) dCizhTAB; (+) hCi2dTAB; ( X ) dCshCshTAB. We have not included hCsdChTAB,but the reflectivityis within error identical to dCshCshTAB. The continuous lines are two layer model fits using the parameters given in Table 3.
Table 2. Scattering Lengths and Volumes of Constituent Parts of C12TABa
unit C6H13 C6D13
verified on the many occasions where the background has been determined either directly by off-specular measurements or indirectly by suitable choice of contrast. Thus the subtraction of a flat background should be 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 concentrationsused in the present experiments, the procedure is valid for the experiments described here. For a more detailed discussion of this question the reader is referred to Lu and Thomas.8 The surface chemical purity of the ClzTAB was assessed by surface tension measurements. There was no minimum in the plot of surface tension ( y ) against the log of the concentration and the critical micelle concentration(cmc)was found to be 14.7 mM, in good agreement with literature value^.^
0 0 0 0 0 0.15 0.15 0.15 0.15 0.15 0 0 0
C6HlZ C6Dl2
ClZH26 C12D25
N(CH3hBr N(CDd3Br HzO DzO
volume/A3 190 190 160 160 350 350 135 135 30 30
extended 1engtW.A
scattering iengtw10-5 A
9.1 9.1 7.6 7.6 16.7 16.7
-8.7 125.9 (99.4% D) -5.0 119.3 (99.4% D) -13.7 245.5 (99.4% D) 2.5 94.5 (98.0% D) -1.68 19.14
a Volumes and extended lengths are from Tanford, C . J. J . Phys. Chem. 1972, 76, 3020. Scatteringlengths are from Sears, V. F. Neutron News. 1992, 3, 26.
Results Figure 1shows the reflectivities offour ofthe five isotopic species in null reflecting water (NRW) at the cmc (the two half chain compounds gave indistinguishable profiles). The incoherent flat background (approximately has been subtracted and in each case the reflectivity is almost entirelyfrom the deuterated part of the surfactant. These profiles were fitted using a model of a single uniform layer to give a surface excess with a n accuracy of about f5%. The value of the surface excess found by this means has been shown to be independent of the model used to fit the reflectivity.6 The fitting procedure also gives a measure of the mean thickness of the layer, which is given together with the area per molecule in Table 1 for three surface concentrations. The corresponding bulk concentrations were the cmc (14.7 mM), 4 mM, and 4 mM with 0.15 M added sodium bromide. The parameters of the different fragments used for the calculation are given in Table 2. The combination of data at different isotopic compositions can be used to determine the structure of the layer in more detail. We have done this at the cmc and in the presence of sodium bromide, where we have measured the reflectivity from ten different isotopic compositions. At the lowest surface concentration we have determined the structure in less detail using only six isotopic combinations. The six compositions measured at all three concentrations were dClzdTAB, dClZhTAB,and hClzdTAB (8) Lu, J. R.; Thomas, R. K. Nucl. Znst. Method, in press.
(9) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfactant Systems, NSRDS-NBS 36, National Bureau of Standards, 1971.
Figure 2. Neutron reflectivity profiles of different isotopic species of ClzTAl3 in DzO at the cmc (14 mM): ( 0 )dC12dTAB; (A) dC12hTAB; (+) hC12hTAB. The continuous lines are the two-layer model fits for the parameters given in Table 3. in null reflecting water (Figure 11,and dClZdTAB, dClzhTAB, and hClzhTAB in DzO, shown in Figure 2. The fully protonated chain has a scattering length close to zero and hence hardly contributes to the reflectivity. Additional compositions used to obtain better resolution of the surface were dC6hC6hTAB and hC6dCshTAB in NRW and in DzO. These give indistinguishable profiles in NRW but quite different profiles in DzO (Figure 3). In previous papers we have fitted the data in two ways, using a model of two uniform layers similar to that used by Simister et a1.2and a direct method using the kinematic approximation. We believe the latter to be the much better
Monolayer Structure of C1zTA.B
Langmuir, Vol. 11, No. 3, 1995 1003
where K is the momentum transfer as defined earlier and g ( K ) and g'(K) are the Fourier transforms of the scattering length density profile normal to the interface or its gradient, respectively. The scattering length density profile is given by
K/k' Figure 3. Neutron reflectivity profiles of (0)dCshCsTAB and
( x ) hCsdCshTAB in DzO at the cmc (14 mM). The continuous lines are two layer model fits using the parameters given in Table 3.
Table 3. Structural Parameters from the Two Layer Model Fits Using Optical Matrix Method species contrast A TI 01 72 02 f, n (a) [ C ~ ~ A = B] dCizdTAB NRW 48 10.2 3.0 10.0 4.1 0.40
dClzhTAB hC1zdTAB"
NRW NRW
48 48 48 48 47 46 48 47 48
10.2 9.0' 10.2 10.2 10.0' 10.2 10.2
3.0 0.3 3.0 3.0 -0.2 2.4 2.3 6.0* 1.9 1.5 7.0'
8.5' 2.5 10.5 1.4 10.5 7.3 DzO dCizdTAB 10.5 5.4 DzO dCizhTAB 10.5 5.2 DzO hCizhTAB dCshCshTAB NRW 9.0' 0.4 10.5 3.5 dCshCshTAB DzO hCsdCshTAB NRW 10.0 1.5 10.5 4.8 hCsdCshTAB DzO (b) [C~ZTAB] = 4 mM, [NaBr] = 0.15 M dClzdTAB NRW 42 11.5 3.3 9.5 4.6 dClzhTAB 3.2 9.0' 2.3 NRW 43 11.5 hC1zdTAB' NRW 44 11.5' 0.2 9.5 1.7 44 11.5 3.2 9.5 7.6 DzO dCizdTAB 3.2 9.5 5.5 DzO 43 11.5 dClzhTAB 43 11.0' -0.2 9.5 3.2 DzO hClzhTAB dCshCshTAB NRW 46 11.5 2.2 9.0b 0.3 2.3 9.5 3.5 44 11.5 dCshCshTAB DzO hCsdCshTAB NRW 41 7.0' 1.9 10.0 1.6 1.5 10.0 4.6 44 7.0 dCshCshTAB DzO (c) [CizTAB] = 4 mM dCizdTAB NRW 68 9.0 2.0 9.0 3.6 2.0 7.5' 2.5 dCizhTAB NRW 66 9.0 0.4 9.0 1.2 hCizdTAB' NRW 65 5.0' 2.0 9.5 5.0 DzO 67 9.0 dClzhTAB 67 9.0' -0.1 9.0 5.0 DzO hCizhTAB
0.40 0.40 0.40 0.40 0.40 0.15 0.10 0.55 0.55
9 9 9 9
+
@ ( z )= bclncl(Z)+ bC2nc2(z) bhnh(z)+ bsns(z) (3)
Equation 1may be written in terms of the partial structure factors hii
2bclbhhclh
+ 2bclbshcls + 2bc2bhhc2h + 2bc2bshc2s + 2bc2bclhc2cl
+ 2bhbshhs}
(4)
where ho are the partial structure factors given by
9
h i i ( K ) = lnik)I2 0.35 0.35 0.35 0.35 0.35 0.35 0.10 0.10 0.55 0.55
hji = h&) = Re{n,(K)n,*(K)} 7 7 7 7 7
0.50 0.50 0.50 0.50 10 0.50 10
In fitting this contrast a fraction of 20% head group has to be assumed to be in the chain region. Insensitive parameters. a
where bi is the empirical scattering length of nuclear species i and ni(z) is its number density profile. For the ClzTAJ3layer the main features of interest are the relative positions of half chains, heads, and water, and the widths of their distributions normal to the interface. The structure of the airlsolution interface can then be made in terms of the distributions of half chains, c l and c2, where c l is taken to be the fragment nearest the head group, the heads h, and water (solvent) s. In terms of these three labels the scattering length density can be written
'
method and to give more significant results. However, because this paper completes the series of measurements on the C,TABs and, because the fitting of block models is still used extensively by others, we include for completeness the parameters obtained by using the model of two uniform layers in Table 3. The fits are shown as continuous lines in Figures 1-3. Since we started this project 5 years ago the quality of the data has improved considerably and it is worth noting that it now probably justifies a more detailed model, which would certainly give a better fit to the whole set of data. However, since we are only including the uniform layer fits for comparison with old-style fits, we do not pursue this problem further. The kinematic method of analyzing the data has been described in full previously2and we only outline it briefly here. The basic equation is
(5)
n i k ) is the one-dimensional Fourier transform of ni(z), the average number density profile of atom, or group, i in the direction normal to the interface. We did not study the complete range of isotopic composition that would give the ten partial structure factors in eq 4 because, as will be shown below, the number of independent structural parameters is less than ten and can be derived without determining all ten partial structure factors. Thus we did two sets of experiments, one corresponding to a reflectivity given by 162
R(K)= ,-{b:hCc K
-k b2hhh
+ bs2hss+ 2bcb,hcs + 2bCbhhch+ 2bhbshhs} (6)
which requires six independent measurements, and one corresponding to the reflectivity being given by
which again requires six independent measurements, but two of them are common to both ( 6 ) and (71, the dC12hTAB/NRW and hC12hTABD20 measurements. The advantage of studying the system accordingto the schemes ( 6 )and (7)rather than (4) was that two less isotopic species were needed, thus saving on the chemical preparation. The division into ( 6 )and (7) is only possible because the
Lyttle et al.
1004 Langmuir, Vol. 11, No. 3, 1995 scattering length density of the protonated headgroup is almost exactly zero (see Table 2). The partial structure factors are in principle calculated directly from the different isotopic reflectivities using the set of simultaneous equations obtained from (6) or (7). However, to avoid systematic errors, it is necessary to make two manipulations of the data, both described in full in a previous paper.2 The first is to correct the observed reflectivity for multiple scattering effects to obtain the reflectivity appropriate for use in eqs 6 and 7. This correction only involves the known theoretical exact and kinematic reflectivities for the uniform bulk solvent.1°The second correction is to normalize the reflectivities to the average coverage observed for the whole set of isotopic data. This can be done using the areas per molecule obtained from the fitting of the uniform layer model (Table 1)and then recalculating the reflectivity to allow for the small differences between the area observed and the average. This assumes that the structure of the layer is not affected by whatever it is that caused the original discrepancy. Given general observations on the way the thickness of a layer varies with surface coverage, this is probably a n acceptable procedure provided the deviations from the average are not more than about 5%. Figure 4a compares h,, and hcia,where h, is the average of hclcland hcZc2,in the presence of NaBr. We have used this average to bring out the difference between the structure factor for the whole chain and that for the two fragments with rather better statistics. Within error hclcl and hc2,2 are the same. We use a Gaussian distribution to describe the chain or chain fragment distribution, defined by
n = n, exp(-4z2/o,2)
-1
(8)
We have shown elsewhere that a Gaussian distribution is a more accurate representation of the chain distribution than a uniform layer model’ (see below for further discussion). The continuous lines in Figure 4a correspond to values of a,of 16 f 1and u,i of 13.5 f 2 Figure 4b shows h a under the same conditions and this corresponds to a width of the head group distribution, Oh, of 12.5 f 2 Figure 4c shows h,,, and the continuous line is fitted for a tanh profile defined by
A.
*t
+ -21 tanh(z/t)]
(9)
A.
The width parameter, Cs, was found to be 5.5 f 1 The self partial structure factors, hii,containinformation 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, hu. Figure 5 shows the main cross terms in the partial structure factors, hch,h,,, and hhs,in the presence of NaBr, Figure 6 shows the cross term between chain and solvent, h,,, a t the three surface concentrations, and Figure 7 shows h,,, hcls,and hcasalso in the presence of NaBr. The cross term between two Gaussian distributions separated by dch is
and between Gaussian and tanh distributions
h,, = h(hc&ss)1/2 sin ~ d , , Since the selfterms are already known, the various values of 6 may be determined by fitting eqs 10 and 11 to the (IO)Crowley, T.L.Physica A 1993, 195, 354.
I 5
A.
1 n =n 42
(cl
12
Figure 4. The self partial structure factors (a)h,, (0) and (hclcl+ hCzcz) (A), (b) h ~and , (c) hBs.The continuous lines are the best fits of Gaussian distributionst o (a)and (b) and a tanh and 13.5 distribution to c), with width parameters (a) 16 (0) ( x ) A, (b) 12.5 , and (c) 5.5 A.
a
cross terms. These fits are shown as continuous lines in Figures 5, 6, and 7,where we have used the best fitted Gaussian or tanh profiles for the hii. It should be noted that the values of 6 are not affected by the choice of distribution to represent the fragment layers, eqs 10 and 11 holding whatever the shape of hii and hj. All the parameters for the three surface concentrations are given in Table 4. The parameters in Table 4 are not all independent of one another but represent independently determined values. In terms of the set of parameters the structure is then overdetermined. The self-consistency of the 6 values, apparent from Table 4, is one of the factors that makes it possible to resolve the phase ambiguity which causes the sign ambiguity in eqs 10 and 11. The reflectivities a t five isotopic compositions of CloTAB were also measured in order to analyze this structure using the kinematic approach. We do not show any of the results here but they were of much higher quality than previously determined5 and enabled us to obtain the parameters given in Table 6. Although we have made no direct comparison of the present structural data with that obtained previously, the agreement on surface coverage
Langmuir, Vol. 11, No. 3, 1995 1005
Monolayer Structure of ClzTAB
t
-z
0.05
0.10
0.15
0.20
0.25
K A’ Figure 6. Cross partial structure factor between chain and solvent at three different concentrations (0) 14 mM, (+) 4 mM, and (A) 4 mM with 0.15 M NaBr. The continuous lines are fittedusingeq 11 with d,, = 6.5 (0),5.0 (+), and 7.0 (A), all f0.5
A.
1
c (c’
+t
I
I 1
0.05
0.10
0.15
0.20
0.25
K A-l Figure 6. Cross terms in the partial structure factors (a)hch, (b) h,,, and (c) hhs in the presence of NaBr (A = 43.5 k). The continuouslines are the best fits of eqs 10 and 11using Gaussian and tanh distributions with values of (a) dch = 6.5 f 0.5 A, (b) 6,, = 7.0 f 0.5 A, and (C) a h a = 1 f 1 A.
Figure 7. Cross partial structure factors between chain or chain fragments and solvent at a bulk concentration of 4 mM with 0.15 M NaBr: h,, (0); hcls(A); hC2,(+I. The continuous lines are fitted using eq 11 with d,, = 7.0 (01,6,lS= 4.5 (A), and dC2, = 9.0 (+), all f 0 . 5 A.
was good. At the cmc (0.065M) the area per molecule was found to be 57 f 3 A2.
Table 4. Structural Parameters of ClzTAB Obtained from Kinematic Analysis 14 10-3 M 4 10-3 M (cmc) ([NaBrl = 0.15 M) 4x M 16.0 12.5 15.5 f 1 12.5 f 1 9.0 12.5 13.5 13.5 f 2 13.5 f 2 13.5 5.5 5.0 6.0 f 0.5 6.5 5.0 5.5 f 0.5 7.0 5.0 6.5 f 0.5 I f 1 1.0 f 1 4.5 3.5 f 1
Discussion We have determined the detailed structure of the Cl2TAB layer a t two surface concentrations, with mean area of 48 and 43.5 A2. There are slight differences between them in that the chain is slightly more extended at the lower surface area. Our measurements of the structure of the other C,TAJ3s have mostly been made a t the smaller area, and for the purposes of comparison we therefore examine the layer a t this smaller area. The structure of the layer is most conveniently displayed in terms of the volume fraction profiles of solvent, heads, and chains, which is shown in Figure 8a. A test of the consistency of the structural analysis is that the overall volume fraction does not become larger than physically possible a t any point in the layer, i.e., above unity. Given that there is some uncertainty in the volumes to take for the different fragments and that analytic expressions have been used to describe the three fragment distributions, which can only be approximate descriptions, this limit
5.0 f 0.5 8.5 f 0.5
4.5 9.0
can be relaxed to about 1.1,and this condition is then satisfied. Also shown in Figure 8 are the corresponding volume fraction profiles for C14TAB,C16TAJ3, and C1sTA.B a t a similar area per molecule. The main changes in the layer structure with chain length are that the maximum density of the chains increases substantially with chain length, from about 0.55 for ClzTA13to 0.75 for ClsTAJ3,
Lyttle et al.
1006 Langmuir, Vol. 11,No.3, 1995 1.2,
[,,TAB
There are two possible contributions to the roughness of the surface, static disorder and thermal fluctuations (capillary waves), which we do not attempt to distinguish. For Gaussian distributions, when two independent factors contribute to the width the observed width u is given by
02 = (ZZ2)
+w2
(12)
where w accounts for all contributions to the roughness and (Zz2) is the mean square projection of the length of the fragment along the surface normal. Various factors contribute to the value of (lZ2); the extended lengths of the components of the fragment, the incidence of different chain conformations, and the average of the orientational distribution about the normal direction. We write
where (13)assumes 1and cos 8 to be uncorrelated and (12) assumes that there is no correlation of 1, and w . The values of the separations between different fragments are determined only by
4P
(C) 1.0:.
0.e-
.. -
- ...,
ClbTAB
' \ .
where 1~ is the separation between fragments i a n d j along the chain direction. The measured 6 values may therefore be used in conjunction with the assumption that the chain or chain fragments are fully extended to estimate (cos 60). The maximum possible value of the distance between the centers of two fragments is the distance taken along the fully extended chain and we take this to be the same as lo, an assumption that becomes increasingly valid as the length of the fragment decreases. For the hydrocarbon chain the length of a C2H4 group is 2.5 and we take the distance from the center of the head group to the a-CH2 to be 1.75 A.1 There are two 6 values that contain information about the orientation of the chains, dch and dclc2. If, for simplicity, we assume a single average chain orientation and that the chain is on average fully extended, eq 14 leads to two values of (cos e) from Table 4. The value from dch is 6.5/(7.6 0.5) = 0.8 and from dclc2 is 4517.6 = 0.6. Since the latter represents a fragment further away from the head group, we can conclude that the part of the chain nearest the head group is oriented closer to the surface normal on average than the middle part of the chain. It is interesting to fit a slightly more detailed model to the whole set of data. This also gives a better estimate of the contribution of roughness to the layer. Since the labeling scheme divides the hydrocarbon chain into two, we use the model we have already used for C12E3,I where each half of the chain can be independently oriented. The 6 values can be written in terms of eq 14 to obtain the following set of equations
A
+
Distance normal to wrface/A Figure 8. Volume fraction profiles of chains (continuousline), heads (dotted line), and water (dash-dot line) for the different chain length C,TABs: (a)C12TAB; (b)C14TAB; (c) CETAB;(d) CISTAB. The total is shown as a dashed line. although the width of the chain region does not change, and the center of the chain distribution moves away from the water (or the head). The head distribution and its relation to the water only change slightly down the series. We have shown elsewherelJl that roughness makes a large contribution to the widths of the distributions for each fragment. The main evidence comes from a comparison of a, for the whole chain with a1 or a 2 for each half chain and from the width of the head group region. If there were no roughness, a,would be double u1 or u2 and it is not. Also, the width of the headgroup distribution is only 1A smaller than the width of either half of the chain and much larger than would be expected from the head group dimensions. The values of the various u depend on both the intrinsic fragment dimensions and roughness whereas the values of 6 depend only on the intrinsic dimensions normal to the interface, and it is possible to use the same simple model to interpret the structural data in Table 4 and to derive quantitative information about the roughness. (11)Lu, J. R.; Simister, E. A,; Thomas, R. K.; Penfold, J. J.Phys.: Condens. Matter 1994, 6, 1.
dClc2= $1,
COS
e,)
+ (zI COS e,)]
where s is the separation of the centers of the water and
Langmuir, Vol. 11, No. 3, 1995 1007
Monolayer Structure of ClzTAB Table 6. Structural Parameters of CISTABat A = 44 dj2, Calculated for a Model of Disordered Chains and a Roughened Surfacea
Table 6. Miscellaneous Experimentally Determined Parameters of the C,TABs property
CIO
parameter observed calculated parameter observed calculated 0, 0 C l
De2
dch
6,s L1
16.0 13.5 13.5 6.5 7.0
16.0 13.5 13.2 6.5 7.3
dhs dele2
del, dC28
1.0 4.5 4.5 9.0
0.7 5.3 4.2 9.5
The calculated values osed are (cos 01) = 0.8, (cos 02) = 0.6, and
w = 12.0 A.
head group distributions, h is the extra distance arising from the difference between the average length of a CH2 fragment and the a-CH2 head distance (=0.5), and 11 is the length of a C6H12 fragment (Table 2). Equations 15 will fit the data for the NaBr solution more or less exactly for (cos el) = 0.8 and (cos OZ) = 0.6 (see Table 5). This gives a more quantitative picture ofthe relative orientation of the two halves of the chain than the simple calculation in the previous paragraph and, even though the calculation is still an approximate one, it provides convincingevidence that the part of the chain nearest the head group is oriented closer to the normal than the outer part of the chain. To obtain the roughness, we assume that (Zz2) is identical with d2 where the 6 values are the appropriate values from eq 15. The approximation results from the different effects of averaging cos f3and cos2 8 and should become less critical as the fragment decreases in size because, as the contribution of (lZ2)in eq 12 decreases, the value of u2 is increasingly dominated by w2. Thus
+ COS e2)i2+ w2
o~~~ = [(I,COS e1)i2 w2
0~22= [(z2
(16)
The mean value of w is found to be 12 A and the values of u calculated from eq 15 and 16 are given in Table 5. The values of (cos 61) and (cos 82) obtained for ClzTAB are different from those obtained for the same length chain in the surfactant C12E3l where (cos 01) were found to be 0.46and 0.60,respectively, a t a n area per molecule of 36 A2. At a very low surface concentration these values both changed to 0.4. The difference suggests that the more anisotropic E3 group has a strong influence on the orientation of the first part of the hydrocarbon chain. In ref 1 we reconstructed the overall chain distribution from the widths and separation ofthe two c6 halves, using two extreme models for the two fragment distributions, a uniform layer or a Gaussian distribution. This gave the result that the Gaussian distribution is the more self consistent description. Inspection of the results for ClzTAB gives the same result, which justifies the use of eq 8 in the analysis. The proofthat the distribution is exactly Gaussian can only be obtained by dividing the chain into smaller labels and measuring the separation of all the fragments. This would remove any dependence of the shape on the assumed shape of each fragment distribution because the shape would be dominated by the values of the different 6, which, to a good approximation, are model independent. We have recently done this for Cl6TAB.l' The data for the whole set of C,TABs are given for the different values of n for two surface coverages in Table 6. The most surprising feature is that the width of the chain region, a,, hardly changes with the length of the chain. Thus, a t a n area per molecule of about 44 A2, the fully (12) Lu, J. R.; Li, Z. X.; Smallwood, J.;Thomas, R. K. J.Phys. Chem., in press.
ak3A IC
f1A 0,flA Uc1 f 1 A d,, f 1 A dClS f 1 A
14.2
dch
Uhk3A k 1.5 A aef2A dch
10.5 6.5 16
CIZ
c14
(a)A=44A2 12.5 13.0 16.7 19.2 6.5 6 f 1.5 16.0 16.0 13.5 7.0 7 f 1.5 4.5 (b)A=60A2 9 5 6" 12.5
c16
ClS
14.0 21.7 8.5 16.5 14.0 9.0 5.5
14.0 24.2 9 17
10 7 14
This value assumes that dch = de,, which is usually found to be the case a t this lower surface concentration.
extended chain length increases from 16.7for ClzTAB to 24.2A for CISTAB but uconly changes from 16.0to 17.0 A, i.e., is constant within error. Therefore the main change in the hydrocarbon fraction of the layer from C12 to CIS must be an increase in density of about 50%. This can be seen clearly in Figure 8. The change in thickness is even more remarkable a t the lower surface coverage (A = -60 A2)where the shortest chain ((310) gives the thickest layer. Indeed, given that the chain thickness decreases by 2025% when A increases from 44 to 60 A2, it is remarkable that the thickness of the C ~chain O a t A = 60 A2is as large as that of the other chains at A = 44 A2. It is also interesting that a, is less than the fully extended chain length for all the C,TABs except CloTAB. The comparison of layer thicknesses for different soluble surfactants, given in Table 6,is the first of its kind and there is little to compare with. For close-packed alkyl chains, of the type that form insoluble monolayers, the observation has generally been that the chains are fully extended and that they may be uniformly tilted with respect to the surface normal (see, for example, ref 13). This would mean that the thickness of the layer should increase with the length of the alkyl chain unless the tilt also increases. There is no systematic study of the effects of chain length on layer thickness to give any guidance on this possibility. For soluble monolayers the crosssectional area a t the surface is almost double that of a typical insoluble monolayer. The packing is therefore very loose indeed. Furthermore, the fact that the surfactant is completely soluble in the subphase means that, unlike the insoluble monolayers, the head group water interactions must play as important a part in determining the possible orientations of the molecule as the chain-chain interactions. The combination of these two factors should lead to considerable disorder in the layer and this has been substantiated by computer ~imu1ation.l~ The results that we have so far obtained for the C,TAB series of molecules suggest that the molecules are tilted away from the surface normal, that there is some disorder in the internal chain conformation, and that the roughness of the layer is not very different from its intrinsic thickness. The lack of variation of the thickness of the layer with chain length would then seem to be associated with a tendency of the chains to cohere more strongly as their length increases. Given the large area per molecule this can only be achieved by the longer chains tilting more strongly away from the surface normal. This increasing tilt apparently compensates,by coincidence for the change in chain length. One study of the relation between chain (13) Bohm, C.; Leveiller, F.; Jacquemain, D.; Mohwald, H.; Kjaer, K.; Als-Nielsen, J.; Weissbuch, I.; Leiserowitz, L. Langmuzr 1994,10, 830. (14) Bocker, J.; Schlenkrich, M.; Bopp, P.; Brickmann, J. J. Phys. Chem. 1992,96,9915.
Lyttle et al.
1008 Langmuir, Vol. 11, No. 3,1995 Table 7. Miscellaneous Derived Parameters of the C,TABs property
CIO 14.2
9 13 13
ClZ c14 (a)A 44Az 11.0 12.0 16.7 19.2 11.5 11 13 12 16 (b)A = 60A2 8 10 9.5
c16
ClS
13.0 21.7 10 17 20
13.0 24.2 11 18
9 14 11
length and layer thickness has been made on a series of spread polymer monolayers, which gives some support to the present observations, although the nature of the layer is such that it falls in between a typical insoluble monolayer and a soluble surfactant mon01ayer.l~ The thicknesses of spread layers of poly(N-alkyl-4-vinylpyridinium bromide) with alkyl chain lengths of 8,10,12,14, 16,18,20, and 22 carbon atoms were measured a t areas per segment of 30-40 A2 by X-ray reflection. The ratio of the observed thickness (modeled by uniform layers) to the fully extended chain length decreased from 1.3 a t c8 t o 0.7 a t c16 and c18 before increasing to 0.8 a t CZOand C22. Although these are insoluble monolayers, an important factor in the layer structure is the polymer backbone and it is this that competes with the alkyl chain interactions. The parallel with the C,TAB layers is that the attractive alkyl chain interactions are not able to overcome the roughness of the polymer backbone until there are more than 18 carbon atoms. Up to about C16 or CIS this roughness, which is related to the effective head group substrate interaction, dominates over the alkyl chain interaction. Thus we might expect that, depending on the strength and nature of the head group solvent interaction, the transition from disordered to ordered chains will occur somewhere between C14 and (220. It may well be that this transition strongly parallels the Krafft point, the temperature above which micelles may form, which is also very dependent on the nature of the head group (see data in ref 9). Whereas a, is less than the fully extended chain length in four of the five compounds, a h is considerably larger than the dimensions of the head group. The maximum dimension of the head group is about 5 A and so most of the width of the head group region must be from the roughness of the layer. There appears to be a slight systematic increase in the roughness of the layer with chain length a t A 44 k , but this may not be significant because it is only about half the experimental error for this parameter. Taking the size of the head group to be 5A, we can estimate the roughness ofthe surfactant layer by using eq 12. These values are given in Table 7. The results are not sensitive to the exact value of the intrinsic size of the head group because ah is dominated by the roughness contribution. The value of the roughness is in reasonable agreement with estimates for the whole C12TAB structure (Table 5) and for Cl6TAEL3 The value of w estimated from the thickness of the head group region of the layer may now be used to calculate the intrinsic width of the chain distribution in the absence of roughness, a,,,, using eq 12. The values of o,,,,,given in (15) Styrkas, D. A,; Thomas, R. K.; Adib, Z. A,; Davis, F.; Hodge, P.; Liu, X. H. Macromolecules 1994,27, 5504. (16) Schwartz, D. K.; Schlossman, M. L.; Kawamoto, E. H.; Kellogg, G. J.; Pershan, P. J.; Ocko, B. M. Phys. Rev. A 1990,41, 5687.
Table 7, are mostly much shorter than the lengths of the fully extended chains. Some care needs to be exercised in making this comparison because a refers to a width of a Gaussian distribution a t lle of its height, which may differ from the mean projection of the chain along the surface normal by a multiplicative factor. However, there are reasons for supposing that it is approximately correct. Thus, once the roughness has been removed,the maximum width of the chain is the fully extended length and, if a,,, is a n appropriate measure of the intrinsic chain dimensions along the surface normal, its maximum value will also be the fully extended chain length, 1,. In the case of Clothe value of a,,, is found to be close to 1, and therefore a,,, is a n appropriate measure of the intrinsic chain dimensions in the case of C ~ OIt. is therefore also likely to be appropriate for the other chain lengths. Also included in Table 7 are the values of 26ch and 4dclh. dch measures the projection of the lower half of the chain along the surface normal and 26ch is therefore the intrinsic thickness of the whole chain if the upper half of the chain has the same projection as the lower half. Correspondingly, 46,lh is the intrinsic thickness of the whole chain if the upper three quarters of the chain has the same projection as the lowest quarter. At the lower value ofA a,,, is the same as 26ch for CloTAB and &TAB, which indicates that the two halves of these chains have identical projections on the surface normal a t this surface concentration. For &TAB 26,h is larger than a,,, and this can only be explained by the upper half of the chain having a much smaller projection along the surface normal than the lower half. At the higher value ofA the effect occurs for all the surfactants and is very pronounced for the two longer chain surfactants. This indicates that a t the highest surface coverage the upper halves of all the C,TABs are more tilted away from the surface normal than their lower halves, a conclusion in agreement with the analysis leading to Table 5. It is important to note that tilt here should not be interpreted as meaning that each molecule is rigid and tilted a t a definite angle. The observations made above regarding the tilt can only refer to averages over a wide range of gauche defects in the alkyl chains and their orientation. There are no direct measurements of the surface roughness for surfactant solutions, although roughness is often incorporated somewhat arbitrarily as a fitting parameter when uniform layer models are used to fit specular reflectivity data. However, off-specular scattering has been used to examine the roughness of pure liquids and, in particular, the roughness of pure water has been determined t o be 3 A, close to that predicted from the capillary wave model.16 Since the capillary wave roughness varies inversely as the square root of the surface tension, we can calculate what it would predict for the surfaces of C,TAB solutions. Allowing for a factor of 2.3 because of difference in our definition of the roughness, we obtain a value of 8.5 A for comparison with our values in the region of 11-12 A. Thus the capillary wave prediction falls a long way short of the observations, especially when eq 12 is taken into account, which shows that there is a n additional 8.5 A roughness not accounted for by the simple theory.
Acknowledgment. We thank the Science and Engineering Research Council and Unilever Research, Port Sunlight for support. LA940624G
