Neutron reflectivity studies of spread monolayers of derivatives of

Feb 1, 1992 - S. W. An, T. J. Su, and R. K. Thomas, F. L. Baines, N. C. Billingham, and S. P. Armes, J. Penfold. The Journal of Physical Chemistry B 1...
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Langmuir 1992,8, 585-593

585

Neutron Reflectivity Studies of Spread Monolayers of Derivatives of Styrene-Maleic Anhydride Copolymers at the Air-Water Interface P. Hodget and C. R. Towns Chemistry Department, University of Lancaster, Bailrigg, Lancaster LA1 4YA, U.K.

R. K. Thomas* Physical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, U.K.

C. Shackleton Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 ORA, U.K. Received June 3, 1991. In Final Form: September 27, 1991

Reaction of alternating styrene-maleic anhydride copolymers with various alcohols gave half ester derivatives. Neutron reflectivity measurements have been used to study monolayers of these derivatives at the aidwater interface. Isotopic substitution has been used to label different parta of the copolymer and to locate different groups within the surface region. For the derivatives prepared using long chain alcohols (dodecyl or undecyl alcohol) the alkyl chains are completely out of the water subphase at high surface pressures (7 = 38 mN m-l) at the expense of the phenyl groups, which are almost completely submerged. At lower surface pressures (7= 30 mN m-l) the phenyl groups are about 50% out of the water and approximately 30% of the alkyl chains are immersed. For the derivatives prepared using ethyl alcohol there is no detectable segregation of ethyl and phenyl groups. The thicknesses of the dodecyl chain layer at 11 A and the undecyl chain layer also at 11 A are substantially less than the fully extended chain lengths (16.7 and 15.5 A, respectively). This is probably associated both with large random tilts of the chains away from the surface normal and with a significant incidence of cis conformations in the alkyl chains. The backbone and phenyl group layer, immersed in the water, is thicker (15-19 A) than expected from the dimensions of the individual groups. This results from the disorder imposed on it by the requirements of the alkyl chains to be out of the water. As the layer is compressed, the disorder increases and the layer is observed to thicken.

Introduction steep isotherms, collapse pressures generally greater than 40 mN m-l) and that LB films can be prepared from them, Monolayers of amphiphilic polymers at the air-water although, as judged by low-angle X-ray studies, the films interface are of interest because such systems are some of are not sufficiently well ordered to show Bragg reflections the simplest involving polymers at interface5.l There are unless the alkyl side chain contains approximately 11or numerous more complex and commercially important more carbon atoms.6J0 Isotherms of polymers based on interfacial systems that might be more fully understood I, where n < 5, show a phase change at surface pressures from a detailed knowledge of these simpler systems. of 25-35 m N m-l, and as n increases, the area per repeat Examples are the stabilization of polymer particles in unit increases up to about c8, after which no further aqueous media2 and the stabilization of emulsions3 by increase in area occurs.6 The aim of the present study was polymeric interfacialagents. Furthermore, the monolayer to understand more fully how polymers of this type film on water is the precursor to Langmuir-Blodgett (LB) organize on the surface of water. films, which, particularly polymeric films:-' have numerous potential applications in micro- and optoelectr~nics.~~~ Experimental Details In this paper we report the results of a neutron reflectivity study of monolayer films of several amphiphilic Styrene-ds(99 atom % D) and dodecanoic-d2a acid (98 atom polymers of type I. Previous studies of this type of polymer 7'% D) were obtained from Merck, Sharp,and Dohme. The dodecanol-d23was obtained by reducing dodecanoic-dB acid with Liindicate that good monolayers are formed on water (fairly AI&. The undecanol-d4was prepared by treating undec-10ynol with deuterium gas in the presence of palladium charcoal. t Now at Chemistry Department, University of Manchester, Oxford The synthesisof the present polymers is describedonly briefly Road, Manchester, M 1 3 9PL. (1)Wallbridge, D. J. In Comprehensive Polymer Science; Allen, G., here. Full details will be given, together with the synthesis of Bevington, J. C., Eds.; Pergamon Press: Oxford, 1989;Vol. 4,p 243. several other closely related polymers, elsewhere.ll Free radical ( 2 ) Dawkins, J. V. In Comprehensiue Polymer Science; Allen, G., Bevpolymerization of equimolar amounts of styrene and maleic ington, J. C.,Eds.; Pergamon Press: Oxford, 1989;Vol. 4,p 231. anhydride gave copolymer (11): Mn = 17 OOO and M, = 33 OOO (3)Ringsdorf, H.; Schlarb, B.; Venzmer, J. Angew. Chem., Int. Ed. by GPC using polystyrene standards. A similar copolymerizaEngl. 1988,27,113. tion using styrene-da gave copolymer I11 M n= 20 OOO and M, (4)Gaines, G. L. Insoluble Monolayers at Liquid-Gas Interfaces; Interscience: New York, 1966. = 38 000. These were reacted with the appropriate alcohol to ( 5 ) Breton, J. J.Macromol. Sci., Reu. Macromol. Chem. 1981,C21,61. give polymers IV-VII. In each case the infrared spectrum of the (6)Hodge, P.; Khoshdel, E.; Tredgold, R. H.; Vickers, A. J.; Winter, C . S. Br. Polym. J. 1985,17, 368. (7) Hodge, P.; Davis, F.;Tredgold, R. H. Philos. Trans.R. SOC.London (10)Tredgold, R.H.; Vickers, A. 3.;Hoorfar, A.; Hodge, P.; Khoshdel, ~

~~

~~

1990,330,153. (8)Vincett, P. S.;Roberta, G. G. Thin Solid Films 1980,68,135. (9)Roberta, G. G. Adu. Phys. 1985,34,475.

0743-7463/92/2408-0585$03.00/0

E.J. Phys. D: Appl. Phys. 1985,18,1139.

(11)Towns, C. R. Ph.D. Thesis, University of Lancaster, and papers in preparation, 1991.

0 1992 American Chemical Society

Hodge et al.

586 Langmuir, Vol. 8,No. 2, 1992 product indicated that the reaction of the anhydride residues with the alcohol was essentially complete. The copolymerization of styreneand maleic anhydrideis known to produce a highly alternating polymer.12 The anhydride ring can be attacked by the alcohol at either carbonylgroup. A NMR study has shown that polymer I1 reacts with methanol to give the two possible products in the ratio 8020, probably with preferential attack on the carbonyl group remote from the phenyl groupi3 It should be noted that, for simplicity, all the formulas in this paper are shown as though alternationwas 100% and that the ring opening proceeded entirely in one direction. The neutron reflection experiments were carried out on the instrument CRISP at ISIS,which uses a fixed angle of incidence and neutrons of wavelengths from 0.5 to 6.5 A. Methods describing the actual measurement and calibration of the reflectivity profiles have been given elsewhere." The polymer monolayers were deposited onto water in a Langmuir trough using ethyl acetate as the spreadingsolvent and after evaporation of the solvent the troughs were enclosed with an air-tight lid.

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Results General Observations. A crucial feature of the neutron reflectivity technique is that the scattering length density profile, and hence the reflectivity, of a given system can be modified by H/D substitution. This makes it possible to locate by isotopic labeling the relative positions of different components of the copolymer with respect to each other and with respect to the subphase. Thus to determine the conformation of the polymer in the monolayer and to determine its position with respect to the subphase, it is necessary to measure the reflectivity for a given system with a variety of isotopic compositions. The most effective combinations are those in which the scattering length density of either the subphase or part of the copolymer is matched to that of air. We refer to null reflecting water (nrw) when the subphase is matched to air because the only contribution to the specular reflection is then from the spread monolayer. The H20/D20 ratio in nrw is approximately 9:l. The scattering length densities of the CH and CH2 fragments of the polymer are closely matched to that of air, and hence, in nrw the re(12) Trivedi, B. C.; Culbertson, B. M. Maleic Anhydride; Plenum: New York, 1982, Chapter 10. (13) Ratzcsh, M.; Zschoche, S.; Steinert, V.; Schlothauer, K. Makromol. Chem. 1986,187, 1669. (14)Penfold, J.; Ward, R. C.; Williams, W. G. J. Phys. E: Sci. Instrum. 1987, 20, 1411.

Table I. Summary of Measurements Made: Compositions, Surface Pressures, and Areas per Segment designation

polymer structurea subalkyl chain phenyl phase */" m-l 34.5 30.5 38.3 35.5 35.0 35.0 15.3, 35.1b 15.3, 35.1b 28.5 collapsed

AIA~ 52 1 2 60*2 42 1 2 5012 51 1 3 51 1 3 65,42 1 2b 65,42 2b 54 2 23 1 5

aSee formula I. Measurements were made at two surface pressures for this sample.

flectivity of the polymer will be dominated by its deuterated parta and its two C02 groups. Thus,measurements of the reflectivity of monolayers of V and VI on nrw should give information about the conformation and surface density of the C12 side chain and the styrene group, respectively,while VI1may be expected to give information about the distribution of the end of the long alkyl side chain. The most sensitive method for determining the distribution of water in the monolayer is to compare resulta obtained for layers on nrw with those on D2O. Hence a total of six measurements should allow the arrangements of V, VI, and VI1 to be studied. The six measurements referred to above were made at the surface pressures given in Table I, entries 1to 6. Ideally, we should have used identical surface pressures but the apparatus was such that we had to dose a fixed area of the surface and under these conditions it was not easy to adjust the pressure to a particular value. The areas per segment at a pressure of about 35 mN m-* are about 50 A2, but this can be determined more accurately by the reflection experiment itself than by direct measurement of the area. This is because it is difficult to remove residual solvent from the polymer after preparation and there is therefore as uncertainty in the concentration of polymer in the spreading solution. This error also made it difficult to be certain about isotope effects on either the isotherm or the original polymer preparation. All areas in Tables I and I11 are therefore those determined from the reflectivity and we do not assume invariance of the structure of the layer to isotopic substitution. The reflectivity profiles of polymers V and VI on null reflecting water are shown as points in Figure 1, and the same two polymers on D2O gave the profiles shown in Figure 2. The profiles were only recorded over a limited range of momentum transfer because, although the reflectivity is much higher a t lower values of the momentum transfer, it contains little structural information in the low momentum transfer region.'5 We also measured the reflectivity of monolayers of VII, where the terminal ethyl group of the undecyl chain was labeled, on both nrw and D20 (Figure 3). Finally, to see whether a decrease in the length of the alkyl side chain affected the structure of the layer, we measured the reflectivity of IV at two surface pressures on both nrw and D20 (Figure 4). Interpretationof Reflectivity Profiles. Long Side Chain Copolymers. Mean Thickness and Area per Repeat Unit. The main information that can be obtained directly from reflectivity profiles on nrw is the area per repeat unit of the polymer and the mean thickness of the E

(15) Crowley, T. L.; Lee, E. M.; Simister, E. A.; Thomas, R. K. Physica 1991, 173, 143.

Langmuir, Vol. 8, No. 2, 1992 581

Neutron Reflectiuity Studies of Spread Monolayers

I

I

'"1 8. 10

I

005

010 015 Momntum transfer&

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Figure 1. Observed and calculated reflectivityprofiles for dodecy1 alcohol derivatives of styrene-maleic anhydride copolymers on null reflecting water: (a) polymer V; (b) polymer VI. Profiles are calculated for uniform single layers of scattering length densities and thicknesses of (a) 2.8 X lo4 and 20 A and (b) 1.8 X lo4 A-z and 18 A. n.i

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K /k' Figure 3. Observed (points) and calculated (continuousline) reflectivity profiles for the undecyl alcohol derivative (VII) of styrene-maleic anhydridecopolymer on (a)null reflecting water and (b) DzO. The calculated profiles are the best fits of a twolayer model with scattering length densities and thicknesses as follows: (a) 1X 10-6A-2, 11A; 0.45 X 10-6A-2, 18A;(b) 1x

A-z, 11A; 5.35 X lo4 A-2, 18 A.

to a first approximation, does saturated hydrocarbon because its scattering length density is also close to that of air. Figure l a shows the fit of a uniform single layer model to the reflectivity of V on nrw. The best fit was obtained with a scattering length density (p,) of the layer of 2.8 X 10-6 A-2 and a thickness of 20 A. For VI a single layer model gave a fit with p, equal to 1.8 X lo4 A-2 and a thickness of about 18 A (Figure lb). Since the alkyl chain is approximately null scattering, the latter result shows that the phenyl and backbone residues have a mean thickness of 18 A, which is surprisingly large. The result for V is less directly interpreted because the protonated phenyl and backbone are not null scattering and make a significant contribution to the reflectivity. The area per repeat unit is derived from p, as follows. The scattering length density of the layer is the scattering length of a repeat unit divided by the volume occupied by the repeat unit, i.e.

a

(bl

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005

10'

nibi

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Figure 2. Observed and calculated reflectivity profiles for dodecy1 alcohol derivatives of styrene-maleic anhydride coplymers on DzO (a) polymer V; (b) polymer VI. Profiles are calculated for single layers of uniformly mixed polymer, containing no water, of scattering length densitiesand thicknesses of (a) 2.5 X 10-6k2 and 20 A and (b) 1.7 X lo4 A-z and 18 A.

deuterated material in the monolayer.16 This is because the water itself does not contribute to the reflectivity nor, (16) Penfold, J.; Lee, E.M.;Thomas, R.

K.Mol. Phys. 1989, 68, 33.

Fz

where bi is the scattering length of nucleus i, ni is the number of atoms i in the repeat unit, A is the area per unit, and T is the thickness of the monolayer. Since bi and ni are known and ps and T are determined from the fit, A can be calculated. The scattering lengths of V and VI are respectively 2913 and 1351 A (see Table 11), which, taken with the values of T and pa derived from the experiment, give areas per repeat unit of 52 and 41 A2, respectively. The error on the former is f 2 A2 but the latter result is model dependent, as will be discussed further below, and the best that can be said at this stage is that the area per repeat unit is 4&46 A2. The difference between the two polymers is outside the experimental error and arises from

588 Langmuir, Vol. 8,No. 2,1992

Figure 4. Observed (points) and calculated (continuous line) reflectivity profiies for the ethyl alcohol derivative (IV)of styrenemaleic anhydride copolymer at two different surface pressures 15 mN m-1; 0 , 3 5 m N m-l) on (a) null reflecting water and (b) D20. The calculated profiies are the best fitsof a two-layer model with scattering length densities and thicknesses of (a) 2.25 X 1o-B A-2,6 A; 1.6 x 104 A-2, 13 A at high pressure and 1.1 X 10' A+, 8 A; 0.95 X 10-6 A-2,14 A at low pressure, and (b) 2.25 X ' 0 1 A-2, 6 A; 5.2 X 10-6 A-2, 13 A at high pressure and 1.1 X lo4 A-z, 8 A; 5.95 x 10-6 A-2, 14 A at low pressure. (e,

Table 11. Scattering Lengths of Copolymer Fragments/A copolymer derivative polymer fragment* IV V VI VI1 -CHz-CH333.1 20.8 339.1 20.8 C a s 732.5 212 732.5 212 -CH(CO2)-CH(C02)- 423.2 423.2 423.2 423.2 -CH&H2191.6 -16.6 -16.6 -CH&H2399.8 X 4 -16.6 X 4 -16.6 X 3.5 -CHrCH3 -54 466.5 -54 362.4 H has been used to denote either H or D. The proton on one of the 4 0 2 groups has been taken to be effectively part of the subphase.

the difference in surface pressure for the two measurements, 34.5 mN m-l for the former and 38.3 mN m-l for the latter. The area per repeat unit for VI1 is found in the same way and is 51 3 A2. Assuming that over this short pressure range the area per repeat unit varies approximately linearly with surface pressure, we obtain the values of A shown in Table I for D2O as subphase. The volumes occupied per repeat unit are respectively 1040 (VI, 740 (VI), and 1300 (VII) A3 all *200 A3. These values are larger than the estimated size of a repeat unit (see below) and show that there is space in the layer to be filled by either air or water. Homogeneity of the Monolayer. The single layer model may also be applied to the DzO results to obtain information about the relative positions of the different component groups and the distribution of water within the layer. Thus, if there were complete mixing of the phenyl, backbone, and alkyl side chains and there were no DzO in the layer, i.e. the copolymer layer lies completely out of the water except possibly for the two hydrophilic car-

*

Hodge et al. boxyl groups, then ps of the layer will be the same as on nrw, after allowing for the differences in surface coverage given in Table I. Figure 2a shows the fit of such a model (ps = 2.5 X lo+ A-2, T = 20 A) to the reflectivity of V on DzO. Figure 2b shows the comparable calculation (pe = 1.7 X lo* A-2 and T = 18 A) for VI. Neither calculated profile fits the data at all, demonstrating that the copolymer layer cannot be both entirely out of the water and a homogeneousmixture of alkyl chains, phenyl groups, and backbone. If there is any penetration of the water into the polymer layer it becomes important to consider the volumes of the polymer fragments in order to estimate the maximum amount of water for which there is space. Estimates were made as follows. The molecular volumes of styrene and succinic acid (the nearest structure to the opened maleic anhydride part of the polymer), calculated from their bulk densities, are 190 and 125 A3, respectively, and we take these values as they stand. Parameters for the alkyl side chain have been given by Tanford17and are 16.7 A for the length of a fully extended C12 chain and 325 A3 for its volume. The volume of a CHz-CH2 unit would then be about 50 A3 and of the terminal CHz-CH3 about 75 A3. The length of a CHz-CHz unit is about 2.6 A. The total volume of a repeat unit of the copolymers V and VI is therefore about 640 A3 and of VI1 is about 615 A3. By taking the difference between the volume per repeat unit and the volume occupied by the repeat unit in the layer (=AT)and assuming that this space is filled with water (molecular volume = 30 A3), it can now be shown that the copolymer layer cannot be both homogeneous and entirely immersed in the water. The fit of this model to the D2O data is shown in Figure 5 and is clearly poor for both copolymers. In this calculation we have taken the areas from Table I and the thicknesses from the fits to Figure 1. We conclude from this simple interpretation of the results on the same copolymers on nrw and on DzO that the copolymers with the long side chains are at least partially ordered in the vertical direction. The extent and nature of the ordering and whether or not water is incorporated into the monolayer require a more quantitative fitting procedure. A Structural Model. The attempts to fit the data in Figures 2 and 5 show that any model of the monolayer should allow both for segregationof alkyl chains from either phenyl groups and/or the rest of the backbone and for incomplete filling of the monolayer by water. Figure 6 shows a drawing of the copolymer from which it is clear that the phenyl groups must always remain close to the backbone while the alkyl chains can to some extent be segregated. In low molecular weight surfactant layers, where the surface chain density is similar to those observed here,ls the alkyl chain region is usually relatively free of water (although not close packed) and the hydrophilic head groups are immersed in water. We assume a similar water distribution here (shown by a dashed line marking the water level in Figure 6); i.e. there are two layers, the upper one consisting mainly of alkyl chains and containing no water. We refer to this layer as the alkyl chain layer. For the moment we place no constraints on the distribution of phenyl groups, alkane residues, or backbone between the two layers. The parameters required to characterize the two-layer model are the thicknesses of the two layers, T~ and Ti,, the (17) Tanford, C. J. J . Phys. Chem. 1972, 76, 3020. (18) Lee,E. M.;Thomas,R.K.; Penfold, J.; Ward,R. C.J.Phys. Chem.

1989, 93, 381.

Neutron Reflectivity Studies of Spread Monolayers

Langmuir, Vol. 8, No. 2, 1992 589

fractions of alkyl chains, phenyl groups, and backbone in the backbone layer, fc, f p , and fb, respectively, the area per segment, A, and the volume fraction of water in the backbone layer, &. Note that 6, cannot exceed (1 - +), where is the volume fraction of polymer in the backbone layer. +,depends on the volume of the different fragments of the polymer for which we use thevalues estimated above. Using the known scattering lengths of the constituent nuclei (Table 11), we can now write expressions for the scattering length densities (in units of lo4 A2) for the different isotopes. (i) V on D20

+,

chain layer: [2257(1- f,) + 212(1- fp)

+ u ( 1 - fb)l/A'r,

backbone layer: [2257fc + 212fp Mfb]/ATb (ii) V on nrw

+ 6.354,

chain layer: as for V on D20 backbone layer: [2257fc + 212fp + ufb]/ATb (iii) VI on D20 chain layer: [-137(1- f,) + 733(1- f,)

+ 756(1- fb)l/A7c

backbone layer: [-137fc (iv) VI on nrw

+ 733f, + 756f,]/A~~+ 6354,

chain layer: as for VI in D20 backbone layer: [-137fC+ 733f, (v) VI1 on D20

+ 756fb]/ATb

005

010 015 020 Momentum tmnSfer/lt-'

025

Figure 5. Observed and calculated reflectivity profiles for d o d e cy1 alcohol derivatives of styrene-maleic anhydride copolymers on D2O: (a) polymer V; (b) polymer VI. Profiles are calculated for single layers completely filled with uniformly mixed polymer and D20 of scattering length densities and thicknesses of (a) 5.6 X lo+ A-2 and 20 A and (b) 4.3 X lo+ A-2 and 18 A.

chain layer: [289(1- f,) + 212(1- f,) backbone layer: (vi) VI1 on nrw

+ U ( 1 - fb)]/A~c [289fc 4- 212fp 4-4 4 4 f , ] / A ~+~6.356,

chain layer: as for VI1 on D20 backbone layer: [289f, + 212fp + "ifb]/ATb For V and VI is limited to

+,

where for VI1 the 325 becomes 300 to allow for one less CH2 group. In preliminary attempts to fit a single structure to the six profiles presented in Figures 1, 2, and 3, it became clear that the structures of the monolayers of V, VI, and VI1 were not the same and that the most likely cause was that the structure changes significantlywith coverage. We have therefore fitted the above model separately to each profile. The sensitivity of a given reflectivity profile to each of the parameters of the model is quite different as is now illustrated by the particular case of polymer VI on D20. Structure of a Monolayer of Derivative VI. The reflectivity profile for polymer VI on D20 is almost unchanged from that of clean D20 and this in itself gives a clue about the alkyl chain-phenyl group segregation at this coverage (A = 50 Hi2). This is because there are only a small number of possible distributions which will give rise to an approximately null effect of the layer on the reflectivity. If the surface were to be covered with a layer consisting only of protonated alkyl chains, the resulting ps would be sufficiently close to that of air that the layer would not contribute significantly to the reflectivity.

Figure 6. Possible conformations of the copolymer in the spread monolayer when the alkyl side chains are projecting out of the water. T w o alcohol side chains are drawn to emphasize the relative position of the phenyl group, although alcohol and phenyl are present in equal amounh. The dashed line indicates a possible limit of the water penetration into the monolayer.

Correspondingly, a close packed layer consisting predominantly of deuterated phenyl groups, which willhave a pe not toofar below that of D20, would also have only a slight effect on the reflectivity. If in the first case any D20 were present in the alkyl chain layer, the scattering length density of the layer would increase to a value intermediate between that of air and D20, causing the reflectivity to be substantially depressed below that of D2O. In the second case, partial replacement of deuterated phenyl groups by D20 would only improve the situation, i.e. the reflectivity would be even closer to that of pure D20, because pa for D20 is slightly greater than for the deuterated hydrocarbon. However, if the layer were less than close packed or included any protonated alkyl chain, then the reflectivity would drop substantially below D20. These effects are all well established for the similar scattering length density

Hodge et al.

590 Langmuir, Vol. 8,No. 2, 1992

[-137(1 -f,) 10

+ 1489(1 -fb)] < 0 . 5 A ~

(1)

and

+

[-137f, + 1489fbI 6 . 3 5 @ ~ > 5.947 (2) The fits to the data in Figure 1 show that the maximum possible value of the thickness of either layer must be 20 A. Thus, from the values of A in Table I the limits for AT probably lie between 500 and 1000 A3, when conditions 1 and 2 become

10‘

1.489fb- 0.137fc > 0.85 or 1.10

glu‘ c

(3)

and

&

2 10’

1.489fb- O.137fc > (5.90 - 6.354,) or (2.95-3.174,) (4) where the second alternative refers to the lower value of AT. To combine with these we have the further conditions that fb and fc must lie between 1 and 0. Thus from 3

mi

0.57 < fb

< 0.67 for AT = IO00

(5)

0.74 < fb < 0.83 for AT = 500 Taking (5) and (6) with (4)

(6)

or 106

Figure 7. Observed and calculated reflectivity profiles for the dodecyl alcohol derivative (VI) of styrene-maleic anhydride copolymer on DzO. Profilesare calculated for a two-layer model with layers of relatively high and low scattering len h densities. (a) Upper layer (on air side)is 0.5 x 10-8A-2 and 12 glower layer is 5.9 X 10-8 A-2 and 12 A. (b) Upper layer is 5.9 X 10” A-z and 12 A; lower layer is 0.5 X 10” A-2 and 12 A.

profiles observed for small molecular weight s~rfactants.’~ Figure 7a compares the observed profile of VI on D20 with the reflectivity calculated for two layers, one with a p s close to that of air (the alkyl chain region) and one close to that of D2O (the phenyl and backbone region). We have taken the thickness of the layer to be 12 A to be comparable with the values used to fit the profiles in Figures 3 and 4. As argued above the profile remains similar to that for D2O alone. The only possible qualitative explanation of the null effect of the copolymer monolayer on the reflectivity of D20 is therefore that the alkyl chains are largely segregated from the phenyl and backbone residues and only the latter are penetrated to any significant extent by D2O. Incidentally, as shown by Figure 7b, for which the layers are reversed, the alkyl chain region must be on the vapor side of the interface if there is to be any agreement between calculated and observed profiles. Figure 7a shows that, for VI on D20, we can fit the data if both p,

< 0.5 and pb > 5.9

where p represents scattering length density in units of lo4 A-2. These two conditions may be used in conjunction with the expressions for the scattering length densities to deduce limits for the alkyl chain backbone segregation. The argument is simplified if f p and fb, and Tb and T,, are taken to be equal. Given the close proximity of phenyl and backbone elements, as shown in Figure 6, it is unlikely that the experiment would resolve any difference between f, and fb, although we will test this assumption further below. Combining the inequalities with (iii) we obtain (19)Penfold, J.; Thomas, R. K.J. Phys.: Condens. Matter 1990, 2, 1369.

6.354, - 0.137fc > 4.90 for AT = 1000

(7)

3.174, - 0.137fc > 1.71 for AT = 500

(8)

and Thus

4, > 0.77 or 0.54 (9) However, there has to be sufficient room for this amount of water in layer b. This is determined by

4, < (315fb + 325f,)/A~l (10) Inequality 9 changes only slowly with fc but (10) changes rapidly. It is then easy to show that fc

< 0.15 for AT = 1O00

(11) and that fc must be even smaller if ATis smaller. Indeed, (9) and (10) cannot be simultaneously satisfied for values of AT less than about 800 A3. Thus we deduce that the alkyl chains are predominantly in the upper layer, c, and, since there is no water in the upper layer, the alkyl chains are also more or less completely out of the water a t this particular coverage. It might be thought that inequalities 5 or 6 show that the styrene and backbone are about 70% immersed in the water. However, the more detailed fitting procedure to be described below showed that the derived value of fb is sensitive to the assumption that Tb = rC.The fraction f,, however, is not sensitive either to this assumption or to any assumption about the relative conformations of phenyl groups and backbone. As expected from the arguments above, a direct fit of this model to the reflectivity profile of VI on D2O is found to be possible only when the alkyl chains are almost completely out of the water. However, the fit is not sensitive to the value of fb and fits of comparable quality are obtained with fb between 1 and 0.6. The reason is that, at the upper end of the range, p s of the backbone layer goes below the crucial value of 5.9 X lo4 A-2 while it remains close to zero for the chain layer. A t the lower end of the range p s for the chain layer starts to increase above the crucial value of 0.5 X 10+ A-2 while the value for the backbone layer compensates by increasing to above 5.9 X 10+ A-2. The best fit to the data is with values of fc = 0 and fb = 0.9 and is shown in Figure 8d. The profile

Langmuir, Vol. 8, No. 2, 1992 591

Neutron Reflectivity Studies of Spread Monolayers

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Figure 8. Fits of the two-layer model to observed reflectivity profiles (points) of copolymers V and VI on nrw and D20: (a) polymer V on nrw, calculatedprofile for 3.5 X lo4 A-2 and 11A, and 1.17 X 106 A-2 and 15 A cfc = 0.3 and fb = 0.35); (b) polymer V on DzO, profiie calculatedfor 3.09 x 104A-2 and 11A, and 5.93 x 10-6 A-2 and 16 A (fc = 0.3, f b = 0.35); (c) polymer VI on nrw, continuous line calculated for -0.1 x 1V A-2 and 11A, and 1.8 X 1o-S A-2 and 19 A (fa = 0.95, fc = 0), dashed line calculatedfor f b = 0.8 and fc = 0; (d) polymer VI on D20, continuous line calculated for 0.02 X lo4 A-2 and 11A, and 5.84 X 1o-S A-2 and 18 A (fc = 0,f b = 0.9)) dashed h e calculated for fc = 0.2 and f b = 0.9. f b = 0.5 and fc = 0 give a profile similar to the dashed line. is not at all sensitive to the thickness of the chain layer but is sensitive to the thickness of the backbone region, for which the optimum thickness is found to be 18 f 3 A. Values of fc of 0.2 and Of f b of 0.5 give profiles which are unacceptable. The former is shown as a dashed line in Figure 8d. Thus we deduce values of fc = 0 (