Langmuir 1991, 7, 1458-1467
1458
Neutron Reflection Studies of Spread Monolayers of Docosanoic Acid and Pentadecanoic Acid on Water R. M. Richardson* and S. J. Rosert University of Bristol, School of Chemistry, Cantock’s Close, Bristol BS8 ITS,U.K. Received July 25, 1990.I n Final Form: January 14, 1991 Neutron reflection measurements have been used to study the structure of spread monolayers of pentadecanoic acid and docosanoic acid on aqueous subphases. A detailed theory of reflection from a patchy film has been set out and used to interpret the results. Subphase contrast variation has been used to demonstrate the heterogeneous nature of the film below the plateau of the pentadecanoic acid isotherm. The results also suggest that the prominent first-order transition involves an increase in film thickness, possibly due to loss of cis bonds as the area per molecule decreases. For docosanoic acid monolayer to trilayer collapse has been directly observed in the spread film. The film thickness and area per molecule have been accurately determined in the LZregion of the isotherm. The temporal evolution of the island size at high areas per molecules has been studied. 1. Introduction 1.1. Studies of Spread Monolayers. The potential of the Langmuir-Blodgett deposition technique as a means of building a complex structure as well as interest in twodimensional systems have stimulated study of the polymorphic nature of spread monolayers of fatty acids. Much has been learned by measurements of surface pressure (7r) vs surface area ( A )isotherms on Langmuir troughs. Some of these measurements have been done many years ago.lY2 However some questions of phase behavior, such as the first-order transition shown by pentadecanoic acid, have only been resolved in recent years by extremely careful experimental t e ~ h n i q u e . ~The phase behavior of the homologous series of fatty acids has been elegantly summarized by Bib0 and Peterson4 and we will use their nomenclature in this paper. In the last 5 years X-ray and neutron scattering techniques have been applied to spread monolayers in order to elucidate their structure at a molecular level. Glancing angle X-ray reflection616has been used to study the adsorption of subphase cations onto the fatty acid head groups. The high brightness of synchrotron X-radiation has allowed “in-plane” diffraction as well as reflection experiments to be performed on spread monolayers.7~8 We have applied the technique of neutron reflection to spread monolayers because of the high (and variable) contrast between deuterated molecules of docosanoic acid and a (partly) hydrogenous subphase. This has allowed the variation with pressure of the film thickness to be determined unambiguously and demonstrated the existence of islands of close packed molecules at high surface areas.gJO
* Author to whom correspondence should be addressed.
t Present address: Chemistry Department, University of Bath, Claverton Down, Bath, Avon BA2 7AY, U.K. (1) Stenhagen, E.In Determination of Organic Structure by Physical Methoda; Braude,E. A., Nachod,F. C., Eds.;Academic Press: New York, 1955; Chapter 8. (2) Gainee, G.L. Insoluble Monolayers at Liquid Gas Interfaces; Interscience: New York, 1966. (3) Pallas, N. R.; Pethica, B. A. Langmuir 1985, 1, 509. (4) Bibo, A. M.; Peterson, I. R. Adu. Mater. 1990, 2, 309. (5) Richardson, R. M.; Roser, S. J. Liq. Cryst. 1987, 2, 797. (6) Bosio, L.; Benattar, J. J.; Rieutord, F. Reu. Phys. Appl. 1987,22, 775. (7) Barton, S. W.;Thomas, B. N.; Flom, E. B.; Rice, S. A.; Lin, B.; Peng, J. B. Ketterson, J. B.; Dutta, P. J. Chem. Phys. 1988,89, 2257. (8)Kjaer, K.;Ab-Nielsen, J.; Helm, C. A.;Tippman-Krayer,P.; Mbwald, H. J . Phys. Chem. 1988,93, 3200.
Fluorescence microscopy” has also proved a useful technique for visualizing the heterogeneous nature of monolayers doped with a suitable dye. Such experiments have demonstrated the shapes and sizes of the larger islands in pentadecanoic acid film12J3and form a useful complement to X-ray and neutron scattering results. In this paper, neutron reflection results from spread films of docosanoic acid (C22)and pentadecanoic acid (CIS) at room temperature are presented. The schematic isotherms in Figure 1 show the different regions of the isotherms in which measurements have been made. Our attempts at “in-plane” neutron diffraction have not been successful (due to lack of beam intensity), so details of molecular packing in the more ordered phases have not been determined. However neutron reflection has been used to determine the molecular tilt and the area per molecule and to characterize the heterogeneous nature of the monolayers. 1.2. Reflection Technique. The techniques of X-ray and neutron reflection have been thoroughly covered in other work (e.g. refs 5 and 9). The basic principle is to bring a well collimated beam of X-rays or neutrons (of wavelength A) onto a macroscopic surface at a glancing angle, 8, and measure the reflectivity, R, as a function of scattering vector Q (Q = 47r sin 8/A). The specular reflectivity R(Q) can then be interpreted in terms of the scattering length density profile perpendicular to the surface. On the neutron spectrometer CRISP a t the Rutherford Laboratory,14R(Q)is measured at constant 8 with a range of wavelengths that is usually 0.5 < A/A < 6.5, giving an effective scattering vector range 0.05 < Q/A-l < 0.66. It is possible to deduce information on the structure of the surface by comparison of the measured reflectivity with that calculated for theoretical models. 1.3. Summary of Previous Reflectivity Results. Previous neutron reflection data have measured the total thickness of a perdeuterated docosanoic acid film on HzO over an area per molecule range of 20-40 A2. The thickness (9) Grundy, M. J.; Richardson, R. M.; h e r , S. J.; Penfold, J.; Ward, R. C. Thin Solid F i l m 1988,59, 43. (10) Dent, N.; Grundy, M.J.; Richardson, R. M.; Roser, S. J.; McKeown, N.; Cook, M.J. J. Chim. Phys. 1988,85,1003. (11) Lbsche, M.; Rabe, J.; Fischer, A.; Rucha, B. V.; Knoll, W.; MBwald, H. Thin Solid F i l m 1984, 117, 269. (12) Rondelez, F. Physics of Amphiphile Layers; Meunier, J., Langevin, D.,Boccara, N., Ede.; Springer-Verlag: Berlin, 1987; p 20. (13) Moore. B.: Knobler. C. M.:Brosela.. D.:. Rondelez. F. J. Chem. Soc., Faraday TMns. 2 1986,82, 1753. (14) Penfold, J.; Ward, R. C.; Williams, W. G. J. Phys. E 1987, 20, 1411.
0 1991 American Chemical Society
Monolayers of
Langmuir, Vol. 7, No. 7, 1991 1459
and CIS Acids on Water
C22
50r
d
su bphnse \21
I '15
Figure 2. Geometryof reflection from a film (of scatteringlength density pp) at the subphaselair interface.
"\ 20
25
30
A/A~
35
40
(b)
-
'15
20
30
25
A/
35
40
A*
Figure 1. Typical room temperature isotherms measured on a Langmuir trough for (a) docosanoic acid (Cn) and (b) pentadecanoic acid ((216). The areas per molecule for C22 determined by neutron reflectivity are superimposed as points in part a. of the monolayer increases from 24 to 29 A as the area per moleculesis decreased below 24 A2and the surface pressure increases as shown in ref 10. The scattering length density was consistent with that expected from close-packed alltrans hydrocarbon chains at high surface pressures (* > 12 mN cm-l), but the results were less clear at lower surface pressures. These data were analyzed by least-squares fitting of the single layer model to the reflectivity data. It was found that there was considerable correlation between the parameters (i.e. scattering length density, film thickness, and interfacial diffuseness), which prevented their determination with a high accuracy. However, the data were sufficiently good to show the gradual change in tilt angle (from -0' to -35O) over the sloping part of the T-A isotherm (i.e. the LZand L2' regions). This has been confirmed by X-ray specular reflection and "in-plane" diffraction.* At higher areas per molecule, neutron scattering from a monolayer on a H20/D20 subphase at surface area per molecule of -40 A2 (i.e. twice that of the solid phase) shows different effects for a film bound to subphase Cd2+ ions at high pH (> pH 6.0), and a film at low pH, where the acid is substantially un-i~nized.~ Both cases show that the film has broken up into 'large" islands, but in the former case with the molecules retaining their perpendicular configuration, but at low pH with a tilt close to the value at 24 A2 per molecule, and a density near to closepacked. This fragmentation of the monolayer into islands corroborates microscopy data and is implied by the behavior of microcrystals nucleating at the air/film interface at very high areas per m01ecule.l~ (15) Landau, E. M.; Levanon, M.; Leiserowitz, L.; Lahav, M.; Sagiv,
J. Nature 1985,318, 353.
2. Theory 2.1. Resume of Neutron Reflectivity Theory. A neutron wave that is incident on a smooth surface of a nonabsorbing material behaves in the same way as a light wave with polarization perpendicular to the surface. The refractive index, of the material for neutrons, M, is given by the formula
where p is the neutron scattering length density and X is the neutron wavelength. The scattering length density is determined by the types of nuclei in the material p
=CNjbj j
where Nj is the number density of component j and bj is its neutron scattering length. In this work we exploit the large difference in scattering length density of H20 ( p = A-2), and the fully -0.05 X A-2), DzO ( p = 0.64 X deuterated alkyl chains in the fatty acid monolayers ( p 0.66 X 10" A-2). The major effects in the reflectivity profile arise from the contrast between the deuterated chains and the subphase and as we have found a single layer model sufficient for the analysis of the data presented here. The reflectivity R of a uniform nonabsorbing film of thickness d on a nonabsorbing subphase (as shown in Figure 2) is given by the single layer Fresnel formula, which has been discussed in previous work16
-
R=
+ rFSe"l2
lr, lei6
(3)
+ r,rFse-i612
where 6 = 2TpF sin &d/X and where the r values are the Fresnel coefficients for the air/film and film/subphase interfaces. A Fresnel coefficient depends on the scattering length densities either side of an interface and on any interfacial diffuseness. In this paper we have used the single layer Fresnel formula to model the reflectivity data because it remains valid even a t low values of the scattering vector, Q, where the reflectivity approaches unity. However, at higher scattering vector the reflectivity of a single uniform layer is given to a good approximation by the kinematic formula below which shows more clearly how parameters such as scattering length density influence the reflectivity 16~' R(Q)monolayer = -(AP, Q4
2
+A
P F + ~ ZAP,
A P F ~COS
Qd) (4)
where A p m = PA - p~ and A p ~ s= p~ - ps. A plot of R P vs Q is a good way to emphasize the interference effects, since it removes the very strong Q+ dependence of the data and just shows a "film factor". Any diffuseness of (16)Grundy,M. J.; Richardson, R. M.; Roser, S. J.; Beameon, G.; Brennan, W. J.; Howard, J.; O'Neil, M.; Penfold, J.; Shackleton, C.; Ward, R. C. Thin Solid F i l m 1989,172, 269.
1460 Langmuir, Vol. 7, No. 7, 1991
Richardson and Roser
the interfaces may be accounted for by multiplying theappropriate A p by a Debye-Waller type term exp(-Q2V/2). This assumes an error function scattering density profile for the interface and so U M and Um are the root mean square thicknesses of the air/film and film/ subphase interfaces. 2.2. Reflectivity from Islands. If the film is divided into islands on the subphase surface, it has been shown in the Appendix (A17) that the reflectivity observed experimentally is given by = Rp, + F(4) (RL- Rs) (5) where RL and Rs are the reflectivities that would be observed in the limit of very big or very small islands, respectively, and F(() depends on island size 4 and instrumental resolution and is zero for very small islands and unity for very big islands. RL is a linear combination of the reflectivities of the two types of surface
where f is the fraction of the surface covered by the layer and Rclem is the reflectivity of a clean subphase surface which is given by Relean
=
16r2
2
Q4
16n2
Q
+ Apm2 + 2ApMApm cos Qd)
where APM P A - f P F and Apm = fpF - p s . In the special case of a substrate with approximately zero scattering length density (i.e. p s = P A = 01, Rclean = 0 and the reflectivity from the system of islands is given by
where Y depends only on the fractional coveragef and the island size/resolution factor F(4) (0 IF(4) I1; see eq A14)
Y = f(1- F(4))+ fF(5)
(10) There are two important consequences of this result. Firstly, Y and PF only appear as the product ( ~ F ~ Y which ) acts as a scaling factor. This means that it is possible to obtain unambiguously the thickness d of the islands by analyzing the reflectivity profile of a monolayer on a subphase of approximately zero scattering length density such as HzO, but it is not possible to determine PF and Y separately. Secondly, the value of Y can be determined experimentally by comparison with the reflectivity from a uniform monolayer for which Y = 1. The value of Y will lie between f (big islands) and f 2 (small islands). If the value o f f is known, the island size 4 can in principle be estimated by using the equation
4
2 f ( -~P F~) ( P F
- PS)(COSQd - 111 (12)
where f p F 2 cannot be factorized out. In order to demonstrate that some spread monolayers are divided into islands, we have made reflectivity measurements from deuterated fatty acid on HzO and on a H20/D20 mixture. The reflectivity profile from monolayers on H2O subphases has been analyzed first (essentially using eq 9 above) to determine the thickness "d" of the islands. A search has then been made to find the pairs of values off and PF that provide a simultaneous fit to the reflectivity data from a monolayer unde the same conditions on both HzO and H20/D20. 2.3. Reflectivity from Collapsing Monolayer. The reflectivity RpC of a monolayer that has partially collapsed into a thicker film can also be modeled as a linear combination of the reflectivity expected from a monolayer and a collapsed film
= (l-f)Rmonolayer + fRthick T i (13) where f is now the fraction of the surface covered by the thicker film. Again this assumes that the lateral sizes of the different regions are greater than -2000 A on CRISP. 2.4. The Problem of Correlation between Model Parameters. With a good model for the reflectivity, the task of fitting the data reduces to evaluating the possible model structures that best fit the data, using a least-squares fitting technique. In the case of the fatty acid monolayers, because of the limited Q space accessible, it turns out that there is often a large correlation between the different parameters of the model which define the reflectivity. Different models can give very similar simulated data. However we have found it particularly useful to change the contrast of the subphase and find models that will simultaneously fit reflectivity from monolayers spread on both. RPC
(7)
Rs depends on the mean scattering length densities Rs = y ( A p A :
instance, if the islands are large, the reflectivity is given by the equation
[;I; XI
( A Q ~ )tan - ~ --
The resolution AQx is about 5 X 10"' A-1 on CRISP, which implies that the crossover from small to big islands is a t a lateral size of about 2000 A. In the more general case (i.e. ps > P A ) the explicit expression for a system of islands may be derived from eq 5. The reflectivity profile is now sensitive to the separate values of f and P F and not just the product fpF2. For
3. Experimental Method Monolayers of fatty acids were spread from a 10-8 M solution in AnalaFt grade chloroform CHC&onto water from a Milli-Q system with hydrochloric acid added to obtain pH 2.8 f 0.2. For these experimentsdeuterated fatty acids were used as supplied by Larodan, M h o , Sweden. The Langmuir trough used for these experiments was a purpose built for neutron reflection experiments. It was machined out of a slabof PTFE and pressure of the monolayer was controlled by two PTFE booms, regulated by a feedback mechanism on a Gould-Statham force transducer attached to the Wilhelmy plate. The whole of the trough was enclosed in a hermetically sealed and temperature-controlled box to prevent height changes in the liquid due to evaporation. The surface pressure could be controlled with an accuracy of *0.5 mN m-l. The temperature and the pH of the subphase were monitored continuously throughout the experiment. All the neutron reflectivitymeasurements were made by using the CRISP reflectometer1' at the Rutherford Appleton Laboratory, Oxon. The beam definition slits were set at 4 mm width in order to maximize the beam intensity since high Q resolution was not required. The scaling of the reflected intensity was determined by comparison with that from a standard,clean Dg0 surface.
4. Experimental Results One of the original aims of this work was to improve on the statistical accuracy of the previous neutron reflectivity results from C22 fatty acid, and so long counting times
Monolayers of C ~ and Z C16 Acids on Water
Langmuir, Vol. 7, No. 7, 1991 1461
5' O O r
I \
m
-3.00
1
2 f t
t
-1.00
0. 00
0. 10
0.20 0. 30 Q / A**-I
-6. 00' 0. 00
0. 40
Figure 3. Neutron reflectivity profile from perdeuterated docosanoic acid (Cn)at surface pressure of 2 mN m-l on normal water subphase. A background measurement on a clean water surfacehas been subtracted and a pfactor appliedtoemphasize the interference effects. The lines show the best fits that could be obtained with the interfacial diffusenessparameter, u, fixed at 2.5 A (solid line), 4 A (dots),and 6 A (dashed). This confirms that u < 3 A. were employed. Fortunately the data were recorded in short runs which could have been added together to obtain good statistics. However these data often showed an evolution with time which suggested that the film structure was changing. They were not added together but were used to study the evolution of the monolayer structure. (i) Results from C22 Acid. The time-resolved data from the C22 acid falls into three distinct types above T = 0 mN m-l. At low surface pressures ( K less than the equilibrium spreading pressure of the pure acid component), the patterns do not change with time, and the area of the monolayer on the water surface does not changethere is no collapse. Figure 3 shows the data and fit for a monolayer at K = 2 mN m-l. When the surface pressure is increased to 10 mN m-l, the stability of the monolayer decreases, and the film area in these experiments collapsed to '/a of the original area, with the pressure constant. The data in Figure 4a show a remarkable transformation, showing the film going from a monolayer with a thickness of -25 A, to a much thicker layer around 75 A, over a period of ca. 3 h. Figure 5 shows the time dependence of the fraction of 75-A film obtained by fitting eq 13 to the profiles. A t ?r = 15 mN m-l, the same effect is observed, slightly modified in that the data undergoes what appears to be an overall decrease in intensity, superimposed upon the 25-75-A change. At pressures close to and above the kink in the isotherm which signifies complete transformation to the perpendicular close-packed monolayer (T > 25 mN m-l), the reflectivity appears to drop uniformly with time as shown in Figure 4b, and there is apparently no creation of a thicker layer. This collapse behavior was found to be reproducible for one spread monolayer but varied in that it was very much slower for some films than for others. We therefore believe that nucleation (e.g. by impurities or dust particles) is an important step in the process. Two mechanisms for loss of film have been observed directly. At low surface pressures (but above the equilibrium spreading pressure) the film undergoes a monolayer to trilayer transition probably by the mechanism suggested by Ries." It is possible that this collapse behavior is characteristic of the L2 region of the isotherm. A t higher surface pressure there appears to be a decrease in the density of the film. A probable mechanism for this is that small holes (((2000 (17)Ries, M.E.,Jr. Nature 1979,281, 287.
-2.00
0.05
0. 10
0. 05
0. 10
0. 15 Q / A**-1
0. 20
0. 25
0. 15 / A**-1
0.20
0. 25
Ib
-3.00-
a;;
-
-4.00-
0
A
-5.00-
-6. 00' 0. 00
Q
Figure 4. Time evolution of the neutron reflectivityof C22.The data from successive runs have been superimposed to emphasize the changes. At r = 10mN m-l (a)the data are initially monotonic over this Q range indicatinga layer thickness of -25 A. At later 0.085 A-1 suggesting a film times a minimum develops at Qthickness of -75 A ( = 2 r / Q - ) . At 25 mN m-l (b) the minimum does not develop indicating that the film thickness is constant. There is a small downward shift in the data, but no change in slope,which suggests that there is a loss of scattering density of the film.
-
"
o.8
O
t
m
O
0
0
f
I
O ' T 0.4
o.2
0
t
0.0
0 0 0
1
I
I
0
50
100
I
150 t / mins.
I
I
200
250
300
Figure 5. Showing the fraction of the surface covered by trilayer as a function of time for (222 at T = 10 mN m-1.
A) are formed by loss into the subphase but that the high surface viscosity prevents the monolayer flowing to fill the holes. A monolayer of C2z acid expanded from a close packed film with a surface pressure of 30 mN m-l to an area of 120 A-' for molecules (where K < 0.5 mN m-l, below the resolution of the Wilhelmy balance) gave time-dependent neutron reflectivity shown in Figure 6. After a long time the reflectivity is -1/5 that of a close packed film, but initially it is very much less. Since the degree of expansion is -5, inspection of eqs 9 and 10 with f = l / 5 suggests an
1462 Langmuir, Vol. 7, No. 7, 1991
Richardson and Roser Table I. Correlation between U and Other Parameters for Ca on HIO at if = 2 mN m-'
-2. OOr
-3.001
\
1 2 3 4
24.0 23.4 22.8 21.2
23.7 23.7 23.5 23.3
422 427 482 536
Table 11. Results for Cn Monolayers before Collapse (=indicates a fixed parameter) TlmNm-l UlA dlA A /A2 A(isotherm)/A2 0 (area X 5) -6.00' 0.00
0.05
0. 10
0. 15
0.20
0.25
0 / A**-l
Figure 6. Upper points are the neutron reflectivity of C22 at a surface pressure ?r = 2 mN m-1. The three lower sets of data are after expansion of the trough area to a nominal 120 Az per molecule. Initially the lowest reflectivity was obtained, indicating small islands. However after 3 h the reflectivity increased to about 1/5 of the A = 2 mN/m-l data indicating much larger islands. The lines are the model fits described in the text.
--
initial formation of small islands (so Y '/25) which coalesce into much larger ones (so Y l / & . This is in qualitative agreement with the data in Figure 6. These will be considered in more detail in the next section. (ii) Results from C15 Acid. Reflectivity data from pentadecanoic acid monolayers has been taken at surface pressures above and below the plateau in the isotherm shown in Figure lb. In the plateau region, commonly referred to as the liquid-expanded to liquid-condensed transition, it is impossible to control the surface pressure by adjusting the area, and so a monolayer cannot be maintained in the middle of the plateau. The data taken from CIS at u I20 mN m-l show no sign of collapse, presumably because of the equilibrium spreading pressure, which is 20 mN m-l a t room temperature.18 None of the reflectivity data for CISextends to high enough Q in order that the trough of the first fringe in the film factor (which is expected at about Q 0.3 A-' for a 20-A film) becomes visible.
2 10 15 25 40
=3 > AQ, (i.e. the characteristic size of the phases, [is very muchsmaller than the coherence length (AQJ-l), then F(4) = 0 and the apparent specular reflectivity depends only on the scattering length density profile averaged over the x and y directions ( ( p ( Q , ) ) )
c1
c1
The opposite extreme occurs when > 1, the mean reflectivity is observed, whereas if [AQx
