J. Phys. Chem. 1992,96, 10971-10978
10971
Structure and Composition of Dodecane Layers Spread on Aqueous Solutions of TetradecyitrimethyiammoniumBromide: Neutron Reflection and Surface Tension Measurements J. R. Lu,R. K. Thomas,* Physical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, England
R. Aveyard, B. P. Binks, P. Cooper, P. D. I. Fletcber, A. Sokolowski? School of Chemistry, University of Hull, Hull, HU6 7 R X England
and J. Penfold Rutherford-Appleton Laboratory, Chilton, Didcot, Oxon OX1 1 ORA, England (Received: August 19, 1992)
Neutron reflection and surface tension measurements have been used to study the composition and structure of a mixed (alkane + surfactant) monolayer at the air-water surface, formed either by adsorption from vapor or by spreading dodecane from small lenses placed on the surface of an aqueous solution of tetradecyltrimethylammoniumbromide (C,,TAB). The highest concentration of dodecane in the mixed monolayer occurs when the solution concentration of surfactant is about one-third of the critical micelle concentration (cmc), at which point the area per surfactant molecule is about 60 A*, some 20%higher than its value at the cmc but similar to its value in the absence of dodecane. At lower bulk surfactant concentrations (and hence lower surface concentrations), the amount of dodecane in the mixed layer also decreases. At a surfactant concentration of 2.6 mM (cmc = 3.7 mM) the surfactant chain is found to be slightly more extended (20 A when modeled as a uniform layer) in the presence of dodecane than in its absence, while the dodecane forms a layer significantly thicker (22 A) than its fully extended chain length (17 A). The separation of the centers of the surfactant chain and dodecane distributions at this concentration was found to be 5 f 2 A, which together with the separation of each component from the water subphase, 7.5 and 13 A, respectively, indicates that the oil is completely out of the water and that the surface of the mixture is very similar to that of pure dodecane.
Introduction When small quantities of liquid alkane are placed on the surface of an aqueous solution containing an adsorbed surfactant monolayer, a number of possible situations may arise. Short chain alkanes commonly spread to give a fdm of macroscopic thickness. Long chain alkanes generally spread initially but then retract to form lenses of small but finite contact angle. In this case the equilibrium situation consists of macroscopic oil lenses coexisting with a mixed monolayer of surfactant and penetrating or solubilized alkane molecules. Using surface tensiometry, the mixed monolayer composition has been quantified for a range of surfactant and alkane chain lengths as a function of the surfactant surface The extent of oil penetration into surfactant monolayers at the oil/water interface is believed to be an important factor in determining the spontaneous curvature and bending elasticity of monolayers at the oil/water interface and hence microemulsion behavior in so-called Winsor s y ~ t e m s . ~ - ~ In addition to the two possibilities of macroscopic oil spreading and formation of lenses in equilibrium with a mixed monolayer containing solubilized oil, a third situation has recently been demonstrated experimentally using ellipsometry? Addition of oils to surfactant monolayers in systems where the oil/water interfacial tension is low (KO.1 mN m-l) can lead to the formation of a multilayer oil film (of thickness up to 60 A) in equilibrium with bulk oil. Tension measurements alone cannot distinguish directly between the situations of mixed monolayer formation and multilayer oil films. Changes in tension c a d by addition of alkane essentially reflect the mixing of alkane with the surfactant monolayer. Conceptually, it can be supposed that the tension is made up of contributions from the head group region in the water and the chain region in contact with air. If alkane is progressively added to a mixed monolayer to give an alkane multilayer, the alkane-air contribution to the total tension will be expected to change very little. To whom correspondenceshould be addressed. Permanent address: Institute of Organic and Polymer Technology, Technical University of Wroclaw, 50-370 Wroclaw, Poland.
In the present study we have used surface tensiometry and neutron reflection to investigate the composition and structure of surface films at the air-water interface formed in systems containing n-dodecane and the cationic surfactant tetradecyltrimethylammonium bromide (CL4TAB).Oil/water interfacial tensions for this system are relatively high (approximately 8 mN m-l), and hence the surface film is expected to be a mixed monolayer.
Experimental Details The CI4TABwas made and purified as described in ref 7. Dodecane was obtained from Fluka (protonated) and Merck, Sharp, and Dohme (deuterated). Polar impurities were removed by passing over a column of alumina. Water was purified by ion exchange (Elgastat). Surface tension measurements were made using a Kruss K12 maximum pull tensiometer using a Pt du Nouy ring. Two methods were used to add dodecane to the surface under test. In the fmt method small volumes, usually a few microliters, of dodecane were added directly to the surface using a microsyringe. The glass measuring dish was enclosed with a glass cover to minimize evaporation. The measured tension was found to be independent of the exact volume added. It has been shown previously that the presence of small oil lenses on the surface does not interfere with the tension measurements.2 In the second method dodecane was not added directly to the surface but was added as a drop adhering to the underside of the glass lid of the measuring dish and allowed to reach the surface by evaporation. Values of the surface tension lowering caused by the oil addition using the two methods were in close agreement for high surfactant concentrations around the critical micelle concentration (cmc). At lower concentrations the evaporation method generally gave a slightly larger tension lowering than the lens method of up to about 10% of the value of the tension decrease. The reasons for this difference are not clear. Values of the tension lowering quoted here refer to the mean of the values obtained by the two methods. Neutron reflectivity profiles were measured using isotopic combinations of the fully protonated and chain deuterated sur-
0022-3654/92/2096-10971~03,00/0 @ 1992 American Chemical Society
Lu et al.
10972 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992
no dodecane
J
lool
kkm 100E! m 0
3.5
2.5
0
P-
80 * 80. 60
4.5
.O 0
-
1
-log ([C14 TAB]/M) Figure 1. Surface tension of CllTAB solutions with (0)and without (0) dodecane.
Figure 2. Area per surfactant molecule as a function of Ct4TABcon-
factant, tetradecyltrimethylammonium bromide (abbreviated to hC,,hTAB and dC,,hTAB), fully protonated or deuterated dodecane (abbreviated to hC12and dC12),and either null reflecting for determining the rewater (nrw) or D20.The p “ s flectivity profiles have been fully described elsewhere.* The measurements were made on the reflectometer CRISP at ISIS, England. The instrument was calibrated using the reflectivity profile of pure D20, and a flat background at high momentum transfer was subtracted before fitting model structures to the profiles. For the reflection measurements the solutions were contained in Teflon troughs mounted in a sealed thermostat4 container. At the start of each experiment possible surface active impurities were removed by foaming the solution in situ and moving the foam. Dodecane was added into a recesssurrounding the trough and in contact with the solution and as a small quantity of lenses onto the surface. This ensured that the closed space above the solution was fully saturated with vapor. The neutron reflectivity is affected by the presence of lenses but, provided that the lenses cover less than about 10% of the surface, the effect should be small. Nevertheless, this undoubtedly led to some lack of reproducibility in the measurements which, in turn, led to a larger error than we normally expect for surface coverages determined by reflection. We discuss this further below. All the measurements were made at 25 OC.
TABLE I: Values of the Area per Surfactant rad Oil Derived from Tension Data
RcslrlCs from Surface Tension Measurements Figure 1 shows the variation of the air/water tension with surfactant concentration for CI4TABsolutions with and without M) is reduced by a p added dodecane. The cmc (3.7 X proximately 8% in the presence of dodecane. Tension measure ments were made with both hydrogenated and deuterated dode cane, and no differences were observed. This is important for the neutron reflection studies where there are considerable advantages if the assumption can be made that isotopic substitution does not affect the surface behavior. It has been shown previously that inotopic substitution of the surfactant does not affect its adsorption properties.’ For any particular surfactant concentration the addition of dodecane causes the tension y to decrease by Ay. As has been shown pteviouSly,12the area A, per alkane in the mixed monolayer is given to a good approximation by A, = k T / Ay (1) The area A, per surfactant in the presence or absence of dodecane may be determined from the data of Figure 1 using A, = - k q 2 + 2(d lnf*/d In c,))/(dy/d In c,) (2)
centration with (@) and without (0)dodecane.
‘%/A2 IC,,TABl/mM 0.3 1 .o 2.6 4.5
oure film
~
160 68 58
mixed film 120 I1 63
AdA2 hC,, 41A3 48*5 54*3 61*3
dCi, 47h3 41h5 55f3 58h3
where f* is the mean activity of the surfactant, which can be estimated using the DebytHuckel limiting law, and c, is the surfactant concentration. In order to obtain values of A,, the tension data sets were fitted using seventh-order polynomials (shown as solid lines in Figure 1) from which the appropriate differential equations were obtained and used to calculate 4. The activity coefficient comction modifies A, by only a few percent for the systems of interest. Figure 2 shows the dependence of A, on surfactant concentration for both the pure and mixed monolayers. The values of A, at the cmc were found to be 56 and 61 f 5 A2 for pure and mixed monolayers, respectively. For CI4TABconcentrations in the range from the cmc down to 1 mM, the areas are only weakly dependent on concentration. In this range the adsorption of surfactant in the absence of oil seems to be approximately 5-1096 higher than for the mixed film, but at lower concentrations the situation is reversed with adsorption being higher in the mixed film than for the pure surfactant monolayer. However, the differences arc comparablewith the errors and there are dismpances with the neutron reflection results, which we discuss further below, so it may be premature to draw any conclusions from the observed differences. The variation of the area per dodecane in the mixed film with surfactant concentration is shown in Figure 3. The area passes through a minimum as the surfactant surface concentration is approaching its maximum value. At this concentration, a p proximately onathird of the anc, the surfactant area is about 20% higher than its value at the cmc. It appears that expansion of the film to thii point, effectad by decreasing the surfactant concentration from the cmc, increases a h n e adsorption whereas further expansion leads to decreased adsorption. For the later, comparison of the arms derived from tension with those from neutron reflection selected values of A derived from the tension measurements is given in Table I. Tbeory of Neutron Reflection The neutron reflectivity can be calculated exactly for any model
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10973
Dodecane Layers Spread on Solutions of C,,TAB
going from P(z) to n(z), a knowledge of P(z) is often sufficient to determine n(z) unambiguously. This is especially true if the range of K used for the experiment is large enough to avoid errors in the process of Fourier transformation. In principle, the complete set of partial structure factors for each atomic species in the interface determines the structure normal to that interface. In practice, the sensitivity is not large enough and it is necessary to use a restricted set of partial structure factors, and furthermore, these may not have been obtained over a sufficiently wide enough K to do a Fourier transform. For a mixture of oil and surfactant at the surface of water the main features of interest accessible in a reflectivity experiment are the relative positions of oil and surfactant chains, the positions of both of these relative to the water, and the widths of oil and surfactant distributions normal to the interface. A simple description of the structure of the air/solution interface can then be made in terms of the distributions of surfactant A, oil 0, and water (solvent) S. In terms of these three labels the scattering length density can be written
100
I
80
3-.- 60
ermr bar In
ersa per oil
h
0
ia!i
p! 40
a
20
0
I
I
I
3.8
d
I
3.4
I
I
3.0
I
I
2.6
P(Z) and eq 4 becomes 16r2 R ( K )= -{b2haa
I
2
-log ([C14 TAB]/M) Figure 3. Area per dodecanc molecule in the mixed monolayer as a function of C,lTAB concentration.
of the neutron scattering length density p normal to the interface using the optical matrix methods?Jo The scattering length density is given by P
= Cb,n,(z)
(3)
i
where n, is the number density profile of atom i and 6, is its empirical scattering length. The difficulty with this method of analysis is that more h n one structural model may give the same reflectivity profile. Fitting the same structural model to reflectivities from different isotopic compositions greatly reduces the number of possible alternatives and may be used to determine the structure with more certainty. For analyzing the reflectivity of a mixture of two species adsorbed at an interface a less ambiguous procedure is to use the kinematic approximation, in which the reflectivity R(K)may be written in terms of the partial structure factors hi," (4)
In this expression K is the momentum transfer normal to the interface (=4r sin e/A) and the h, are the partial structure factors given by hji(K)
hj,
= Inj('o12
= hij(K) = Re Int(K)
nj*(K)I
(5)
The n , ( ~are ) the one-dimensional Fourier transform of n,(z), the average number density profde of atom, or group, i in the direction normal to the interface:
n , ( ~ =) lIexp(-iKz)n,(z) dz
(6)
An alternative expression, equivalent to (4), but written in terms
of dn/dz = n(')is
(7) It is possible to Fourier transform lnr(~)I2 to obtain the 'Patterson" function for the number density P(z) = l:n,(u) n,(u-z) du
(8)
where P(z) represents the correlation of the number density with itself. A corresponding expression can be written in terms of dl). Although there may in principle be a phase problem involved in
K2
bana(z) + bono(z) + bsns(2)
(9)
+ b:h, + b?h, + 2b,b,hn0 + 2beb,h, +
2~ob*h,l (10) The equivalent of (9) but in terms of the derivative h t ) ( ~may ) be used and then
hj,I)(~)= K%,,(K) (11) The procedure for determining the structure of the interface at this level of resolution is to measure six reflectivity profiles using isotopic substitution to give different values of be, bo,and b,, from which the six different h,, in (10) can be obtained. A particularly simple example of this method is when the isotopic compositions of water and oil are adjusted so that their scattering length densities match that of air (null reflecting) when all terms in q 10 except the first one vanish. Multiplication of this reflectivity profile by ~ ~ / 1 6 r ~ bgives : h, directly, and this may be transformed to give Paa(z), from which the distribution of surfactant can be determined. P,(z) and P,(z) can similarly be determined directly in separate experiments. The self partial structure factors, h,,, 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,jl and these may give important structural information without being Fourier transformed. A property of Fourier transforms is that when a distribution is moved a distance 6 from the origin its Fourier transform is changed by a phase factor;I2 Le., if d(z) = n(2 - 6) then n t ( ~ )= n ( ~exp(-iKb) ) and the cross term between two shifted distributions is h j ( 4 = Re MK) n , * ( ~ exp[-iK@, ) - 6JlI
(12) (13)
where b (= 6, - 6j) is the separation of the two distributions. It may often be the case that the distributions are either perfectly even about their centers or perfectly odd. For example, both surfactant and oil have distributions which are zero at large positive and negative values of z and are therefore predominantly even functions, whereas the solvent density is zero at large negative z but has its bulk value at large positive z and is therefore predominantly an odd function. When ne(z) and n,(z) are exactly even about their centers and %(z) is exactly odd, eq 13 shows that
h,, = f(hnphas)'/*sin ~b
(14)
and ha,
(heah,)'/'
COS K b
(15)
10974 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992
Lu et al.
TABLE II: Surface Coverages of Surfactant and OU and Various Concentrations Derived from the Fit of a One-Layer Model to the Neutron Reflection Data' AJA~ A,/A~ A,+jAi surfactant(A) oil substrate c, /mM 106p/A-2 r,/A (AI) r,/A (&2) (&IO%) (&IO%) (AS%) 1.o 2.6 4.5 0.3 0.3 1 .o 2.6 4.5 2.6
hCl4hTAB hCl4hTAB hCl4hTAB dCl4hTAB dCl4hTAB dCl4hTAB dCl4hTAB dC14hTAB dC14hTAB
0 2.3 1.8 1.9 1.5 1.4 2.6 2.8 3.0 4.5
18 20 20
17 17 18 19 20 22
22
56 65 60 105 112 60 52 46 52
~
62 50 43 75
75 62
50 43 50
65
'A,* is the area per surfactant molecule in the absence of oil.'
If the positive roots of ha, and h,, are taken, the negative sign applies in eq 13. However, the formula is more correctly written ha, = nan, sin ~6 which leads to a phase uncertainty in deriving (14) from (13) and is the cause of the ambiguity of sign. However, it is usually possible to determine the sign from other knowledge of the physical situation at the interface. There are three difficulties in applying the method described above to real data. The first is that eq 4 is only approximate, the second is the extent to which any values of 6 deduced from eqs 14 and 15 are affected by n, or n, not being exactly even or odd, and the third is the effect of incomplete contrast matching of one of the components. We have addressed all these problems in previous publications,13J4and we only summarize what has to be done here. The first problem is overcome by correcting the observed reflectivity using 1 + (1 - K : / K ~ ) I / ~
1-'
Robs- Rf
-- R - R k
(17)
where Rf and Rk are the exact and kinematical reflectivities for a perfectly smooth surface between the two bulk phases and K, is the critical momentum transfer between the two bulk phases.'* When this formula is applied to the simulated reflectivities described above followed by the application of eq 10, any error introduced by the kinematic approximation becomes negligible over the K range of our experiments. The second problem has been shown not to be serious provided that KT is less than about ?r/2 where T is the thickness of the layer. We will show that this condition is fulfilled for the present system. The third problem can be allowed for in an approximate way provided that the loss of contrast is not too great. In the present work it arises because the surfactant is treated as a whole rather than being subdivided into, for example, chain and head groups. We will discuss the resulting errors below.
Neutron Reflection Measurements Two sets of measurements were made, the first to determine the adsorption isotherm of CI4TABin the presence of a saturated surface of dodecane and the second to determine the structure of the layer at a fixed concentration of 2.6 X M C14TABin the presence of a saturated layer of dodecane. In the first set of measurements we used protonated dodecane, deuterated surfactant, and null reflecting water. To obtain the adsorbed amount of surfactant, we fitted these reflectivity data with a single layer model, a procedure we have already demonstrated to be accurate.' The area per molecule is then determined using the simple formula ba
P =
+ boAa/Ao AaT
(18)
where A, and A, are the areas per molecule of surfactant and oil, respectively. The results of the isotherm experiment are given
TABLE 111 Parameters Used in Two-Layer Fits to Data' 1O6pC/
surfactant hC14hTAB dCI4hTAB dC14dTAB hCl4hTAB dC14hTAB hCl4hTAB
oil substrate A-2 nrw 1.67, dCI2 3.43* hCI2 nrw 4.87* dC12 nrw dCI2 D20 1.84* 4.20' hCl2 D20 hCl2 D20 -0.36
rcfA
(*2) 22.0* 11.5* 169 20.0*
9.0' 15.0
106p,l
A-2
-0.07
1.75 1.81 2.81. 4.42* 2.40*
Q/A (&I) 8.0
9.0 9.0 9.0* 9.5* 10.5*
"The optimum fits to the whole set of data were found with molecular areas of the surfactant and oil of 52 and 64 A2, respectively, and a constant fraction of surfactant chains of 28%. Asterisks denote the parameters that dominate the fitting.
in Table 11. In calculating these areas, we have used the effective scattering length density of each component to allow for the negative contribution of protonated chains. The values of the coverage only just agree within experimental error with the surface tension measurements given in Table I. We have discussed in a previous publication the main sources of error in both types of experiment and concluded that the neutron reflection method gives the more reliable and accurate coverage. Thus, for the pure surfactant film the values of A, in Table I are likely to be underestimates in comparison with the values in the last column of Table 11. However, in the presence of oil,the situation is different because the presence of lenses adversely affects the neutroq measurement of either oil or surfactant coverage and for both protonated and deuterated dodecane. However, the values of A, from the two techniques do agree within error. Measurements of the surface excess of dodecane using protonated CI4TABand deuterated dodecane were analyzed in a similar way and are also given in Table 11. In the case of added dodecane, where the equilibrium is not easy to maintain over the length of time required for the experiment, we found that the reproducibility limited the accuracy to about 10%. Unfortunately, this error obscures any systematic variation with surfactant concentration, although only a slight variation is expected from the surface tension measurements (see Table I). The structure of the layer was determined at just one concentration of surfactant (2.6 mM) with the layer saturated with dodecane. At this surface composition six isotopic combinations were measured for which the reflectivity profiles are shown for nrw in Figure 4 and for D20in Figure 5. Using a twelayer model in conjunction with the matrix method of calculating reflectivity, good fits were obtained to this set of data (continuous lines in Figures 4 and 5 ) with the parameters given in Table 111. The full procedure for fitting such a model has been described in refs 8 and 14. In Figures 6-9 we show the more direct method of analysis outlined in eqs 3-16. In Figure 6, a, b, and c, are shown the partial structure factors h, for the surfactant, h, for oil, and h, for water, respectively. The mean width of these distributions is found by fitting a uniform single layer model to be 20, 22, and 10 A, respectively. The areas per molecule are consistent with the values in Table 11. The distance between oil and surfactant distributions is found by applying eq 15, and the results of this calculation are
Dodecane Layers Spread on Solutions of C,,TAB
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10975
TABLE I V Pvrmetem Obtained from the Direct Fitting Procedure at a C,,TAB Concentration of 2.6 mMa
%/A 20 20 20
+1
%/A 22 22 22
+ 26
%/A lo+ 1 10 10
L/A-.
a,iA 7.5 7.5 7.5
1
5.0 2.5 6.0
*2
s,/A 13.0 13.0 13.0
+ 0.5
AJA2 52 + 2 52 52
4 A 2 64 71 58
5
n 7+1
“Data in the second and third rows are the results of introducing errors artificially. The important parameters in the calculation are in bold. *The width of the oil distribution using a symmetrical Gaussian distribution is 18 A.
0.05
ox)
015
0.20
K /k‘
0.25
Figure 4. Reflectivity profiles of C14TAB(2.6 mM) and spread dodecane mixtures on null reflecting water. The points are the observed profile, and the lines the fits using the parameters given in Table 11. (a) hCI4hTAB/dCl2,(b) dC14hTAB/hClz,and (c) dCI4hTAB/dCl2.
Figum 5. Reflectivity profiles of C14TAB(2.6 mM) and spread dodecane mixtures on DzO.The points are the observed profile, and the lines the fits using the parameters given in Table 11. (a) hC14hTAB/dCIz,(b) dC14hTAB/hC12,and (c) hCl,hTAB/hCIz.
shown in Figure 7. The separation between the two distributions is found to be 5 f 0.5 A. The error here refers to the fitting of the equation only, but should be somewhat larger because of the slight problems with the oil spreading. We examine this more closely below. The calculation cannot distinguish which way round the two species are, but one would expect on simple physical grounds that the dodecane is further away from the aqueous phase. In Figures 8 and 9 we use the direct method to determine the distance between surfactant and water and between oil and water. The separations are found to be respectively 7.5 and 13 A with an accuracy of hO.5 A. The difference between them is close to the surfactant/oil separation and confirms that the center of the dodecane distribution is further from the solvent boundary than the center of the surfactant distribution. The Width over which the solvent falls from its bulk value in solution to that in air is
10 A. The agreement in the relative separation of the three components at the interface determined by the direct method (Table IV) and the model fitting is excellent. The lack of reproducibility in the coverage of dodecane noted earlier may give rise to errors in the use of the direct method of fitting. Apart from accounting for the effect of the error in the present work, it is interesting to consider such errors more generally. When data from different isotopes are combined, the assumption being made is that of no change in the structure of the interface on isotopic substitution. This may not always be the case, although we have observed no isotope effects in the present system. However, it is difficult to maintain an equal standard of purity between different samples, and there may be genuine chemical differences between samples. Our system has the further possibility that the experimental conditions are difXcult
10976 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992
Lu et al.
o,
KIA-? 0.05
0.10
0.!5
0.20
0.r
Figure 8. Comparison of the observed h (0)with that calculated from ha, and h, using eq 14 with I,, = 7.5 A"(A).
KIA-' 0.05
2t
Y
I
ox1
0.15
K /A"
A
X
P
I
L 0.05
0.1
2-5
I
'11 I
0.20
0.25
0.25
0.20
Figure 6. Partial structure factors for (a) surfactant, h,, (b) oil, h, and (c) water, h,, determined from the profiles in Figures 4 and 5.
$
0.15
Figure 9. Comparison of tbe observed h, (0)with that calculated from h, and h, using eq 14 with ,& = 13 A (A).
1
0.05
0.10
A
TI
/I
KIA.' figure 7. Observed ha,, ( 0 )compared with that calculated from h, and h, using q IS with I,, = 5 A (A).
to reproduce with accuracy. We have estimated the possible consequential error in the two values of 6 when one of the set of six measurements is 10% in error. This is done by allowing the surface concentration of oil to vary by &lo%, but with an un-
changed thickness, for the isotopic combination of deuterated dodecane, protonated surfactant, and nrw. To incorporate this into the set of data, we apply the change first to h, by scaling the observed h, by a factor consistent with the 10% change in merage. This is then used to calculate the reflectivity of the single isotopic combination. The calculation of the partial structure factors is then made from the five genuine sets of data and the anomalous one. Because of the weightings of the isotopic combinations used, the anomalous h, is recovered almost exactly, and no significant changes are introduced into h,, h,, and h,. However, h, and h, are significantly altered. We then calculate 6, and 6, using eqs 14 and 15. There is then potentially a double error because the erroneous h, and one of the erroneous ha, and h, are used in the calculation. What is found is that the errors reinforce each other in the determination of 6, and cancel in the determination of .,6 Indeed, when the surface coverage error is -lo%, the fit to eq 14 becomes very poor. The 10% error in one measurement thus leads to no additional error to that already quoted for ,6 but to an additional f2 A for 6,. The two sets of calculations are shown in Figure 10 and the values of the parameters for the best fits as the second row (-10%) and third row (+lo%) in Table IV. While the procedure for testing the consequences of one erroneous measurement is somewhat empirical and it may be that a substantial error in a different profile might have reversed the effect, nevertheless it demonstrates that the conclusions from the direct method of analysis are not too vulnerable to an error at the 10% level. This is especially the case if the oil/surfactant separation is being determined in two different ways, as here.
Dodecane Layers Spread on Solutions of C14TAB
The Journal of Physical Chemistry, Vol. 96,No. 26, I992 10977
30
(a)
Figure 11. Schematic diagram of the structure of the mixed C,,TAB/ dodecane monolayer as derived from neutron reflection measurements at a C,4TAB concentration of 2.6 mM.
05
1
*: a
1
I
t
* A * -
K&' Rgme 10. Analysis of the effects of errors on the direct determination of 6, and 6:, (a) experimental h, together with simulated 10%increase and decrease in the coverage of oil, (b) the correspondingvalues and fits for ha, from the two simulated sets of data with a,, = 2.5 and 6 A, (c) and the corresponding values and fits for ha from the two simulated sets of data with 6, = 13 A in all three cases.
csachrsiolrs The neutron reflection measurements show that mixed monolayers are formed when dodecane lenses are added to the surface of aqueous solutions of C14TABin the concentration range varying from one-third of the cmc to above the cmc. This is an important result bemuse surface tension measurements alone cannot distinguish between mixed monolayer formation and the presence of a multilayer oil film coexisting in equilibrium with lenses of oil. This type of multilayer film has been observed recently for surfactant systems in which the oil-water interfacial tension is ultralow.'j The reflection data give the approximate dimensions of the different parts of the mixed layer so that one can attempt to rationalize the packing of the oil into the layer. The volumes of C2H4 and C2H5units are respectively approximately 50 and 75 A3, making the volumes of the C14 and C12chains respeztively 375 and 350 A3. From the structure of the unperturbed CI4TAB layer,14 we know that about 75% of the C14 chains are out of the water in a layer about 10 A thick. The area per surfactant in the mixed layer is 52 A2 so that of the 520 A3 available for the C14 chains only 260 A3 is actually occupied. Thus, per CI4chain there is 280 A3 available for the oil. This is sufficient for a fraction
280/350 of an oil molecule, which would give an area per oil molecule of 65 A2if the layer were a close-packed smooth liquid layer. This is exactly the area observed. For such a situation the separation of the two distributions would then only differ from zero because of the 25% of the surfactant chain immersed in the water. Taking the C14 chain to be 14/12 times the length of the oil, Sa, would then be one-sixth the total thickness of the surfactant chain, i.e., about 3 A, rather less than the 5 A observed. Thus, although the packing argument seems to account exactly for the amount of oil that can be incorporated into the layer, it does not account for the surfactant chain/oil separation. There are two other features of the structural data that indicate that the factors determining the structure of the surface layer are somewhat more complex. First, the surfactant chain region is slightly more extended in the mixed monolayer than in the pure surfactant layer, which creates more available volume than occupied by the oil at saturation. Second, the simple picture above would give a total thickness of the hydrocarbon region of little more than 10 A, whereas it is 22 A, about 25% larger than the fully extended dodecane chain length of 17 A. The other extreme model of the mixed layer would be to take the observed thickness of the surfactant chain, 20 A, and assume in accord with ref 14 that 75% of this forms a hydrocarbon layer above the water, putting the center of its distribution about 7.5 A from the edge of the water layer. If the oil is now taken to be uniformly distributed between the edge of the water and the outer limit of its range, 22 A, then Sa, would be 3.5 A, again less than observed. Since neither of the extremes accounts for the observed separation, it seems probable that the oil is unevenly distributed in the surfactant layer, with a greater proportion lying effectively outside the surfactant chain region. When capillary wave motion is included, it may be that the actual surface of the system consists of just dodecane or fragments of dodecane molecules, forming a roughened layer. We have attempted to represent this schematically in Figure 11. This picture suggests that the surface of the mixed monolayer should be energetically similar to that of a bulk alkane surface. This has been confirmed using surface tension measurements for a range of alkanes on monolayers of dodecyltrimethylammonium bromide at a concentration above the cmc.2 Table I1 shows that the thickness of the surfactant a1 1chain region of the mixed monolayer increases from 17 to 20 as the bulk concentration increases from 0.3 to 4.5 mM, which is slightly thicker than that for the pure surfactant in the absence of oil. The thickness of the dodecane layer in the mixed film also appears to increase slightly from 18 to 20 A as [C14TAB]changes from 1 to 4.5 mM. However, the discrepancies between the one- and two-layer fits to the data show that these differences are within the errors. .
2
Acknowledgment. We thank the Science and Engineering Council for their support of the project. P.C. and AS. thank Rhone-Poulenc and Unilever, Port Sunlight, respectively, for support of this work.
References and Notes (1) Aveyard, R.; Binks, B. P.; Cooper, P.; Fletcher, P. D. I. Adu. Colloid Interface Sci. 1990, 33, 59. (2) Aveyard, R.;Cooper, P.; Fletcher, P. D. I. J. Chem.Soc., Furuduy Trans. 1990,86,3623. (3) Mukherjee, S.;Miller, C. A.; Fort,T. J . Colloid InterfuceSci. W83, 91, 223.
J . Phys. Chem. 1992,96, 10978-10982
10978
(4) Aveyard, R.; Binh, B. P.; Mead, J. J . Chem. Soc., Faraday Trans. I 1%. 82, 1755. (5) Binh, B. P.; Kellay, H.; Meunier, J. Europhys. Lett. 1991, 16, 53. (6) Kellay, H.; Meunier, J.; Binh, B. P. Phys. Rev. Lett., in press. (7) S i t e r , E. A.; Thomas,R. K.; Penfold, J.; Aveyard, R.; Binh, B. P.; Cooper, P.; Fletcher, P. D. I.; Lu,J. R.; Sokolowski,A. J. Phys. Chem. 1992, 96, 1383. (8) Lee,E. M.;Thomas, R. K.; Penfold, J.; Ward, R. C. J . Phys. Chem. 1989, 93, 381. (9) Born, M.; Wolf, E. Principles of Optics; Pergamon: Oxford, 1970.
(10) Lekner, J. Theory of Reflection; Nijhoff Dordrecht, 1987. (1 1) Crowley, T. L.; Lee, E. M.; Simister, E. A.; Thomas, R. K. Physica 1991,8173, 143. (12) Bracewell, R. N . The Fourier Transform and its Applications; McGraw-Hill: New York, 1978. (13) Simister, E. A.; Lee, E. M.; Thomas, R. K.; Penfold, J. Macromol. Rep. 1992, A29, 155. (14) Simister,E. A.; Lee, E. M.; Thomas,R. K.; Penfold, J. J. Phys. Chem. 1992, 96, 1373. (1 5) Crowley, T. L. Physica A , in press.
Hydrogenation of the (1OiO) Graphite Edge. Structural Considerations from Band Calculations S.P.Mehandru,+ Alfred B. Anderson,**tand John C . Angus* Chemistry Department and Department of Chemical Engineering, Case Western Reserve University, Cleveland, Ohio 441 06 (Received: September 1, 1992)
In this study, we have investigated, using the atom superposition and electron delocalization (ASED)band technique, the structures and energetics for the sequential addition of hydrogen atoms to the extended { lOT0)zigzag edge of a graphite sheet. The calculations show that H can chemisorb strongly on the unsaturated rings located on the edge of the graphite sheet, transforming them to their fully saturated analogues. Cluster model calculationsshow that hydrogen atoms can adsorb to a graphite sheet far from the edge, causing a distortion toward the tetrahedral structure for the carbon atoms to which they are bound, but the CH bond strengths are significantly less than at the edge. In our first edge model, hydrogen addition commences at the outermost zigzag carbon chain and proceeds into the sheet by progressively distorting an increasing number of planar rings to the all-chair saturated ring configuration. In this case, H atoms are added successively and alternately on the top and bottom of various carbon rows along the zigzag edge. In our second model, the H atoms are added to only one face of the sheet, resulting in the formation of saturated rings in the all-boat configuration. This causes the edge of the sheet to curl over on itself, and H addition beyond the third zigzag carbon chain leads to strong steric interactions which will limit this mode of hydrogenation and may cause fragmentation. At high temperatures, H insertion will compete with H addition, which will be responsible for the formation of a variety of products including various saturated ring systems as observed by Rye. In a low-pressure diamond growth environment, diamond nucleation is likely to commence on the hydrogenated graphite edges.
Introduction Despite intensive interest in diamond films during the past decade, the chemistry of low-pressure chemical vapor deposition (CVD) of diamond using hydrocarbon/hydrogen mixtures are relatively moderate temperatures is not well understood at the present time.'-5 A few growth mechanisms have been proposed,but the nucleation step has not been characterized. Graphite is sometimes observed during CVD diamond synthesis, but it disappears because of the atomic hydrogen environment. It is believed that the graphite is etched away, leaving diamond behind. Gill et al. investigated the reaction of atomic hydrogen produced at a hot tungsten filament with graphite, lamp black, and diamond.'O Gaseous hydrocarbon species (Cl-C,) were produced, and an unidentified higher-molecular-weight compound was formed from graphite. Furthermore, graphite was found to be more reactive with atomic hydrogen than was diamond. Rye studied the reaction of atomic hydrogen with a carbon film held at 340 OC and identified a number of ring compounds, including cyclohexane, with methane being the major product." It is now well established that diamond seed crystals are not required to nucleate diamond from the vapor phase. Matsumoto and Matsui12proposed a series of hydrocarbon cage compounds (e&, adamantane, tetracyclododecane, hexacyclopentadecane) as possible precursors to diamond nucleation. Angus et al.13 proposed another class of compounds, Le., the multiply twinned fully saturated polycyclic hydrocarbons (boat-boat bicyclodecane is the smallest example), as possible precursors to diamond nucleation. It was suggested that these and related molecules may 'Chemistry Department. f Department of Chemical Engheering.
constitute a certain fraction of the hydrogenated compounds formed by the reaction of atomic hydrogen with unsaturated graphitic deposits under the CVD environments. They also argued that adamantane and its derivativeswith structural resemblance to diamond are not likely to be efficient nucleation promoters because of the absence of easy sites for further atom additions. On the other hand, the multiply twinned saturated hydrocarbons could easily grow by the addition of C, or Cz fragments. In order to test the hvpothesis that the graphitic structurescould be the precursors to diamond nucleation, a series of seeding experiments were performed re~ent1y.l~ It was found that the addition of powdered graphite and 3,4,9,1O-perylenetetracarboxylic acid dianhydride to silicon substrates enhanced diamond nucleation. Additionally, there was a preferential nucleation of diamond along the edges of the basal planes of highly oriented pyrolytic graphite. The (1 11) diamond planes appeared to be approximately parallel to the (OOO1) graphite basal plane, s u p gesting that graphite might be serving as a nucleation seed and not just as an additional source of carbon. Our recent molecular orbital calculations have shown that atomic hydrogen will bind to the aromatic ring systems, such as benzene, naphthalene, and perylene, to achieve partial to complete hydr~genation.'~The allchair d o r m e r s were found to be more stable than any combination of chairs and boats, consistent with well-accepted ideas in organic chemistry. Using large-cluster results for the localized models, we also presented some interaction of atomic hydrogen with the (lOT0)and (1 120) edges and comers of a graphite sheet. It was shown that a single H atom should chemisorb strongly on the edges and weakly on the basal plane of graphite. Also, the planar carbon rings, located near the comers and edges of a graphite sheet could be distorted
0022-3654/92/2096l0978$03.00/0 0 1992 American Chemical Society
