Dynamics of Water and Amphiphile Molecules in Lamellar Liquid Crystalline Phases BY J. B. HAYTER,* A. M. HECHT,~ J. W. WHITE Physical Chemistry Laboratory, South Parks Road, Oxford AND G. J. T. TIDDY Unilever Port Sunlight Research Laboratory, Wirral, Cheshire Received 25th January, 1974 Thin layers of water of controlled thickness may be prepared between the fluorocarbon sheets in the ammonium perfluoro-octanoate/water system at 23°C. Neutron scattering in this system is almost exclusively from the inter lamellar water due to the low scattering cross-section of fluorine and carbon. In a first series of experiments, the modification of water diffusion as a function of layer thickness has been studied and the anisotropy of this effect determined by using oriented samples. The results are compared with nuclear magnetic resonance spin-echo measurements, which measure the same phenomenon but on a timescale approximately lo6 times longer.The difference between these two types of measurements allows some tentative conclusions to be made about the presence of cracks and holes in the lamellae. In the second series of experiments the motion of probe molecules (for example octanol) has been studied in the fluorocarbon layer to determine diffusion kinetics in this region. It is well known that fatty acids and their salts, with or without another component such as a long chain alcohol, form a wide range of pbases in water, depending upon the composition and the temperature. For example, sodium caprylate and water with a little decanol are believed to have phases at room temperature which range from isotropic mixtures through hexagonal close packed cylinders to lamellar liquid crystalline aggregations. Such lamellar mesophases are of particular interest to us here since, by the addition of extra water, they may be swelled to oriented gels.Their structures have been determined, in part, by X-ray diffraction and consist of bilayers of the fatty acid amphiphile molecules separated by layers of water. Amongst the systems showing these properties, the ammonium perfluoro-octanoate- water system shows a particularly simple phase diagram at 23°C consisting of three well-defined regions : an isotropic phase, an intermediate lamellar lyotropic phase and possibly at high concentrations a solid plus lamellar mixed phase.2 At 23°C the range of water layer spacings embraced by the lamellar phase is from about 9 8, to 27 A.The swelling behaviour resembles that in clay+ water systems where only partial crystalline and osmotic swelling occurs. By adding up to 10% by weight of octanol to this system at 23"C, the range of water layer spacings between the lamellae can be increased to several hundred Bngstrom units.2 In this paper we report neutron scattering and nuclear magnetic resonance measurements of the transla- t Now at Cermo, University of Grenoble, Grenoble, France. 1 Now at the Institut Laue-Langevin, Grenoble: France. 130J . B . HAYTER, A. M . HECHT, J . w . WHITE AND G. J . T . TIDDY 131 tional diffusion of water molecules in the inter-lamellar region and at right angles to the lamellae, as well as some preliminary results on the rotational diffusion of the octanol molecules within the bilayers themselves.Neutron spectroscopy has great potential for understanding the relationships between the structure of the phases and the molecular dynamics in such partially crystalline materials. This is because thermal neutrons have wavelengths between 1 and 10A and energies of about one milli-electron volt (8 cm-1 in optical units). The first property means that, for normal scattering angles, diffraction effects from structures of periodicity 1 to 10008, may be readily observed in conjunction with inelastic excitations in the structures. The second feature follows from the low energy of the neutron, which makes detection of changes in its energy quite feasible either by time-of-flight analysis or by measuring the scattered neutron wavelength with a crystal analy~er.~ These features have already allowed the method to be deployed successfully for studies of the inter-atomic forces between molecules 4-6 molecular vibrations 7* * the dynamics of polymers 9 9 lo and liquids." In addition to these features, which define the range of applicability of neutron inelastic scattering spectroscopy, there are also some unique features of the method which establish a contrast between its results and those using electro-magnetic radi- ation.Chief of these, in the present context, is the controllable observation time and range of the neutron experiment. Additionally, the absence of optical selection rule allows all molecular motions, appropriately weighted by the atomic scattering cross sections,12 to be observed by the technique.At the momentum transfers used in the experiments reported here, the observation time scales vary from about lo-'' to s and the range of observation for diffusive motions of the molecular centres of mass, between 10 and 0.5A. As a result it is worthwhile to compare the neutron measurements of translational diffusion with those from nuclear magnetic resonance spin echo experiments.13 Here the time scale of observation is about s and the range of observation for diffusing molecules about lo4 A. One particularly valuable aspect of neutron scattering from molecules is the selec- tive weighting of the scattering cross section by atomic scattering factors within the system.Here this weighting depends upon the very strong scattering cross section of hydrogen compared to the scattering cross sections from fluorine? carbon, oxygen and deuterium nuclei. Thus in the simple two-component system the scattering from the lamellae is always < 1/10 and often < 1/20 of the scattering from the inter- lamellar water. By using D,O, instead of H20, to prepare the phases it is possible to re-emphasize the scattering from the lamellar region and, in particular when octanol is present in the amphiphilic region, its scattering can be selectively observed with good signal-to-noise ratios compared to the scattering from either the perfluoro- alkyl chains or the intervening water. Formally, for a monatomic system we may express the incoherently scattered neutron intensity from nucleus, v, for srngular frequency change 8co and for solid angle change d i 2 , as the differential scattering cross section, d2a/dRi30. This may in turn be connected with the dynamics of the system by the expression a20 k = -b:S(Q, 0 ) 8Rdo k , where S(Q, co) is the scattering law or the intensity frequency-momentum hyper- surface which characterizes the structure and dynamics of the ~arnple.'~ The energy, Aco, and momentum, AQ, transferred to or from the neutron in the scattering event are defined in terms of the neutron mass, rn, and its incident and scattered wave- vectors k,, k by132 LAMELLAR LIQUID CRYSTALLINE PHASES Often the dimensionless momentum and energy transfers a = h2 Q2/2mkT, p = h / k T are convenient to use instead of Q and a.The scattering law for a given nucleus may in turn be related by fourier transforms either to the eigenvalues and eigen- vectors of the time independent Schrodinger equation for the system, where this representation is appropriate, or to the space-time correlation functions, G(r, t), solutions of the full time-dependent Schrodinger equation. l4 For a single nucleus, v, of scattering length b,, the scattering law can be expressed as the space time fourier transform of a propagator, S(Q, o) = 1 exp i[Q r - ot]G(r,!t) dr dr. (3) For nuclei like hydrogen, the scattering is largely incoherent and the appropriate correlation function for eqn (3) is the auto correlation function Gs(rv, t ) for the vth atom. For a number of different atoms in the sample, all with different scattering lengths, b,, the total cross section for the system (considering only the incoherent scattering part) is the sum of the individual scattering laws S,(Q, o) weighted by the squared scattering lengths b$ for the constituents. a20 k m a 0 ko ,, = - b:(inc)S,(Q, w).(4) By choosing the incident momentum and the scattering angles over which inelastic scattering is observed, conditions suitable for observing this part of the whole scatter- ing from the sample can be set up in a neutron experiment. In principle, therefore, complete structural and dynamical information is available from the inelastic neutron scattering experiment. The limitations at present derive largely from the spectrometer resolutions in energy (frequency) transfer, and momen- tum space.These are restricted by the flux of neutrons available to the first mono- chromator and, with present medium flux reactors, the energy resolution of chopper spectrometers in the frequency range 0.5 cm-l to 500 cm-l (75 p eV to 75 meV) is between 0.05 and 15 cm-l. These are the limiting factors on our interpretation of the present experimental results, but the situation is changing rapidly with the intro- duction of novel instruments of greatly improved energy resolution such as the MARX (absolute resolution about 60 peV (0.48 cm-l) F.W.H.M.) which also has excellent momentum resolution, the back scattering spectrometer,l absolute resolution about 3.5 x cm-l) and the spin-echo spectro- meter l7 (absolute energy resolution better than cm-' i.e., about 100 MHz).eV (i.e., 2.5 x eV; EXPERIMENTAL PREPARATION AND PROPERTIES OF THE SAMPLES STUDIED Perfluoro-octanoic acid (Fluorochem Limited, 97 % min.) was neutralized using 0.880 ammonia and dried over potassium hydroxide under a vacuum. The pure product was recrystallized from a petroleum ether/butanol mixture and dried under vacuum for several days. The samples of ammonium perfluoro-octanoate+ water, APO-H20, were prepared from weighed-out quantities of the components using a variety of mixing techniques. This was done because repeated measurements indicated a variability in diffusion coefficient with different preparative methods. The method described previously,2 of mixing componentsJ . B. HAYTER, A. M. HECHT, J .w . WHITE AND G . J . T . TIDDY 133 by centrifugation through a constriction many times was first used. It was found to give results which were reproducible if good equilibration (over a month) was allowed. Alterna- tively, heating the weighed components in a sealed tube to 80°C, where the liquid crystal melted, followed by cooling and equilibration for one day was used. This gave no different results for water diffusion than dispersion of the mixture using sonication for five minutes at 298 K with equilibration for one day subsequently but longer sonication (over 30 min) gave samples with higher D values. The samples of the two component system ranging in water content from 60 % by weight (an isotropic phase) to 20 % by weight ( d ~ ~ o = 9 A) were prepared by 5 min sonica- tion.The mixture after cooling to room temperature was spread and sheared between thin aluminium foils which were then sealed to prevent escape or exchange of water vapour. These planar samples had good orientation of the perfluoro-alkyl chains (typically the co shaft rocking curve was better than 5" and sometimes better than 20") and they were stable for periods of many months at room temperature. The sample of ammonium perffuoro-octanoate-D20 was prepared by low power ultra- sonic mixing at a temperature of about 60°C for 3 hr and subsequent cooling. The samples containing octanol were prepared by the method used for the two component system. Neutron inelastic scattering measurements were made on the two phase samples using the 6H time of flight spectrometer on the DIDO reactor, A.E.R.E.Harwell and the water layer thickness determined for each sample by neutron diffraction on the same specimen before and after the inelastic experiment. To make these measurements, the long wave- length diffractometer installed at 7H2R on the PLUTO reactor, A.E.R.E. Harwell, was used.20 This instrument uses an incident white spectrum filtered by a guide tube and the sample is followed by a graphite monochromator. It thus has an effective, 4.70A neutron beam, which makes measurements on crystals whose c-axis spacing is 10 to 50 A quite convenient. Samples of the three component system were measured in the same way. Preliminary experiments on the anisotropy of water diffusion, were done using the MARX spectrometer AEK Riss, Denmark, both because of its high resolution and because it is readily adapted to make measurements with the vector momentum transfer, Q, along and perpendicular to the water layers.The self diffusion coefficient measurements were carried out using a Bruker-physic variable frequency pulsed n.m.r. spectrometer (B-KR 32%) operating at 16.0 and 35.0 MHz with the Bruker-physic field gradient unit accessory (B-KR-300z 18). The pulsed field gradient technique 18* l9 was used with the following instrumental conditions : n / 2 pulse length = 2-3 p s : field gradient pulse length - 1 ms : time between field gradient pulses - 34 ms. All D values were measured relative to the value for water at 23°C (2.384~ cm2 s-').19 The calibration of the instrument was set up at the beginning of each day and checked several times during the day to avoid errors due to temperature and other drift.Samples for n.m.r., with oriented lamellae were prepared by placing the non-oriented sample contained in a 0.1 x 1 . 0 ~ 3 cm3 silica U.V. cell in the n.m.r. spectrometer with the 0.1 cm side oriented along the magnetic field direction. The sample was melted by raising the temperature to 353 K and then cooled in the magnetic field. The resulting sample had lamellae oriented with the alkyl chains aligned along the magnetic field and perpendicular to the broad face of the cell. Perpendicular and parallel orientations of the sample with respect to the magnetic field were found by adjusting the sample position for minimum or maxi- mum height of the echo after a n12- t - ?I: pulse sequence in the presence of a field gradient.RESULTS NEUTRON DIFFRACTION MEASUREMENTS In the aluminium containers used for the neutron scattering studies, shearing produces alignment of the lamellae with the water layers parallel to the aluminium sheets. For both the H20 and D,O containing samples, lamellar crystallites were well aligned by this technique. Fig. 1 and 2 show the neutron diffraction patterns, for 8,28 scans using the 7H2R diffractometer on PLUTO reactor, A.E.R.E. Harwell. The incident wavelength was 4.70A and the resolution was about 0.24 degrees in 28134 LAMELLAR LIQUID CRYSTALLINE PHASES ammonium fiuoro-octanoate-H20, AP09; d = 37.8 A lyotropic liquid crystal at 296 K B=7.21' r( - j \ / \. \.-.-.- \ ./. . _._.-./.' I l 5 28- ,6 13 . . L+ . . . . . . . . . . - ZERO ANGLE = -0.33' 1000 -500 0 100 50 FIG. 1.-8, 28 neutron diffraction scan of a shear oriented sample of ammonium perfluoro- octanoate + HzO mesophase (7H2R diffractometer). at angles below 20 degrees. To obtain peak widths, this high resolution 7H2R machine was most useful. The curves show a pronounced change in diffraction pattern arising from the substitution of D20 for H20 in the system. The ratio of the first, second and third orders of diffraction for the H20 and D20 samples ammonium perfluoro-octanoate-D20 at 296 K lyotropic liquid crystal d = 37.15 + O x 8, r r J J :t%;P;:* r I 41% D20 59% APFO 1st ordtr 8.5.61' ze=7.22* . . i neutron scattering angle 28, degrees Fro. 2.-0,28 neutron diffraction scan of a shear oriented sample of ammonium perfluoro-octanoate- DzO mesophase (7H2R diffractometer).J .B . HAYTER, A . M. HECHT, J . w . WHITE AND G . J . T . TIDDY 135 were about 50 : 9 : 1 : and 60 : 2 : I : respectively. Present indications are that better sample orientation might be achieved by magnetic orientation so that higher orders of diffraction might be seen and a one dimensional fourier transform used to get the positions of the ammonium ions if they are located at the amphiphile/water interface. In addition to the low angle reflections from the layer structure, it was possible, by tilting the sample into the neutron beam, to observe off-axis reflections associated with the interchain spacing. For example, in the ammonium perfluoro-octanoate- H20 sample illustrated in fig.1, a broad reflection at 28 = 29.5" which we index as the [l , 11 reflection of the layer lattice was found with the Curran diffractometer. When so assigned, this reflection gives an interchain spacing of 5.2 A. This gives an area of about 20 A2 per molecule or 40 A2 per head group which is not an unreason- able value when compared with chain area measurements using surface chemical techniques. A similar reflection was found in the D,O samples although this was broader and indexed on an interchain spacing of about 4.8 Ak0.3. From these diffraction data we can establish the sizes and inter-lamellar geometry of the particles responsible for the liquid crystalline gel. In all cases, the d spacings for the layers were calculated from both the first and second order of diffraction maxima.The water layer spacings derived from them will be listed below, together with the water diffusion constants measured by inelastic scattering. From the breadths of the powder diffraction peaks, it is possible to infer values of the crystallite sizes in the basal plane and in the c direction of the liquid crystals.20 Typically, the breadths of (001) reflections measured with the 7H2R diffractometer (resolution A28 = 0.24" were about 0.7" full width at half maximum. This gives an L, value of about 550A. By contrast, the peaks associated with the hexagonal packing of the perfluoroalkyl chains were about one degree wide (using the Curran diffractometer), which gives a layer lattice extension, La of about 250 to 400A. These figures represent upper limits to the extent of the layers and have not been corrected fully for the resolution functions of the neutron diffractometersPlused. INELASTIC SCATTERING MEASUREMENTS AMMONIUM PERFLUORO-OCTANOATE f WATER TWO COMPONENT SYSTEM At 296 K, water layer thicknesses between 25 A and about 8 8, were conveniently prepared.For the thickest layer studied (about 22A) the percentage by weight of water is 45 % and the ratio of the water scattering to the scattering from the amphi- phile-salt is e 25/1. In the thinnest water layer samples, the ratio was about 10/1. In their general appearance the quasi-elastic and inelastic neutron spectra from the included water closely resemble those from water layers in clay minerals,8* 21 and by the, predominantly H20, scattering shown in fig.5, (upper spectra). In the inelastic region there is a well developed peak at energy transfer near 450cm-l associated with the water torsional motions. This is connected by a fairly featureless region of scattering to the quasi-elastic region. The quasi-elastic peak is noticeably broader than the machine resolution function and this broadening increases both with momen- tum transfer and with the thickness of the water layer at a given momentum transfer. A more detailed analysis of the spectra will be given elsewhere. If one assumes that Fick's law applies to the diffusive motions of the centres of mass of the water molecules in this system, the scattering law in eqn (1) is a Lorentzian in energy (fico) and given by136 LAMELLAR LIQUID CRYSTALLINE PHASES It can be seen that this Lorentzian has a width at half height which is proportional to the square of the momentum transfer, Q2 The diffusion coefficient, D, may therefore be obtained by finding the limiting slope at small Q, of a plot of the energy broadening against the momentum transfer squared.The experimentally measured quasi-elastic peak is a convolution of the Lorent zian with the instrumental Gaussian resolution function. The true Lorentzian widths were obtained from astrophysical 22 tables of the Voigt function and by a method 23 using the peak height and area. The criterion of successful deconvolution was agreement of the two AE values. This was corroboration of the assumed Lorentzian- Gaussian convolution. Table 1 summarizes the diffusion coefficients obtained from neutron scattering by this type of analysis.The plots of AE against Q2 were good straight lines even up to (momentum transfers)2 of about 3.0A-2. AE = 2DQ2. (6) TABLE 1 .-SUMMARY OF DIFFUSION MEASUREMENTS IN AMMONIUM PERFLUORO-OCTANOATES HzO SYSTEM d(water)/A isotropic 22 19.5 17 13 10 9 20 0.046 0.0515 0.059 0.077 0.10 0.1 1 0.05 LAMELLAE :omposition (% H2O) 60 45 40 36 30 22 20 41 D / 10s cm2 s-* 1.61 1.39 1.38 1.32 1.24 1.21 1.03 1.40 U scan, Qli layers V scan, QL layers FIG. 3.-Vector diagram summarizing the quasielastic scattering conditions on the incident and final neutron wavevectors ko, k and the crystal orientation for momentum transfer Q parallel (U scans) and perpendicular (V scans) to the water layers in APO-H20.ANISOTROPY OF THE WATER DIFFUSION I N ORIENTED SAMPLES An exploratory study to detect any anisotropy in the diffusion of the inter-layer water for oriented crystals of the two component APO-H20 system was carried out using the MARX spectrometer at AEK Risar. In such oriented systems the diffusion must be characterized by a tensor D. Since the momentum transfer, Q, is a vector it is possible to determine some of the elements of the tensor by orienting Q with respect to the crystalline directions of the lamellar sample. Q may be placed along or perpendicular to the layers and varied in magnitude by changing both the sampleJ . B . HAYTER, A . M . HECHT, J . w . WHITE AND G. J . T. TIDDY 137 orientation and the counter orientation simultaneously in the neutron scattering experiment. Fig.3 shows the vector diagrams which illustrate the relationship between Q, and the incident and outgoing momenta k,, k, of the neutron involved in the scattering event. got 200 ‘1 Q2/A-” Q2/,&-’ Q2/A-2 FIG. 4.-Quasi-elastic analysis of the neutron scattering from the tensor diffusion of water in thin, 10 A, and thick, 22 A, layers. Fig. 4 show the diffusion plots for Q perpendicular and parallel to the layer directions and two different water layer thicknesses at 296 K. The results are tenta- tive because of poor counting statistics, but are strongly indicative of a rather smaller anisotropy than might have been expected even in the thinnest layer studied (9&. It was these results which led us to make careful measurements, with nuclear magnetic resonance spin echo, of the anisotropy of water diffusion in these systems.In this the effect of the different ranges of observation for neutron and n.m.r. experiments was also tested. SPIN ECHO MEASUREMENTS OF DIFFUSION IN TWO COMPONENT APO-HZO POLYCRYSTALLINE SAMPLES The pulsed field gradient method for measuring self-diffusion coefficients consists in measuring the echo height (h,) following a n/2 - t - 71 radio frequency pulse sequence with the application of equal field gradient (f.g.) pulses between the n/2 and ?I pulses and between the n pulse and the resulting echo. This is followed by a measurement of the echo height (h,) and the self-diffusion coefficient is given by equation138 LAMELLAR LIQUID CRYSTALLINE PHASES where y is the gyromagnetic ratio of the nucleus whose diffusion coefficient is measured, 6 is the duration of the field gradient pulses At is the time interval between field gradient pulses and G, is the amplitude of the field gradient pulses.D is obtained from a graph of In (h,/h,) against L as a2, At or Gt are varied. In practice, the absolute determination of G, is tedious and inaccurate and so a standard such as water is used and the measurements are made relative to it. In the unoriented APO-H20 samples, very considerable difficulty in measuring reliable D values was encountered. The measurements were less reproducible than measure- ments on other samples and so a thorough study of the dependence of the diffusion constant measured on sample preparation and on aging was made.In parallel, studies of the dependence of the observed diffusion constant on the pulse sequence and other experimental parameters were made. TABLE 2.-DEPENDENCE ON WATER CONTENT OF Dr, THE DIFFUSION COEFFICIENT RELATIVE TO WATER AT 296 K, FOR UNORIENTED APO+HzO SAMPLES instrument conditions : S = 1.05 ms, At = 34.5 ms, t = 20 ms) % water 35 32.5 30 27.5 25 22.5 20 temp./K 296.1 296.3 296.6 296.8 297.1 295.4 295.6 D r = DIDH~o 0.46 0.45 0.46, 0.44 0.46 0.31 0.30 0.28 One possible systematic error that would arise in measuring diffusion of water in restricted environments has been discussed by Tanner and S t e j ~ k a l . ~ ~ They report that restricted diffusion leads to non-linear relationships between log (h,/h,) and L. No such dependence was seen in our samples and D values found by varying Gt at different, constant, At values were the same.Another possible source of complica- tion arises because exchange between the ammonium ion and water protons takes place in these samples. The exchange time is probably quite close to the n.m.r. time scale of observation. This results in a more rapid than normal attenuation of the echo amplitude after a n/2-t-n pulse sequence, the effect being larger as t is increased. For low t values (t < 1 ms) the echo observed is derived from both non- exchanged water and ammonium ion protons, while at longer t values ammonium protons undergo the exchange process more frequently than water protons, because of their lower concentration and the echo becomes almost completely due to non- exchanged water protons (t > 10 ms).To check this effect, D measurements were made using pulse field gradient technique in the presence of a sequence of 180" pulses, as described by Packer and co-worker~.~~ The experimental error for these measurements is at least +lo %, and they indicate that D values measured at low values of t (1 to 5 ms) are not reduced by more than 10 % of the value at longer t. To investigate the dependence of D on composition in the polycrystalline samples, it was decided to measure the D values of the samples prepared and stored for one month under the same conditions, (at 301 K) and using the same instrument settings The results are listed in Table 2 and show that the measured self-diffusion coefficients are apparently independent of concentration down to 27.5 % water where a sudden reduction occurs.J .B . HAYTER, A . M . HECHT, J . w. WHITE AND G . J . T . TIDDY 139 SPIN ECHO MEASUREMENTS ON ORIENTED SAMPLES Because of indications from the neutron measurements that the anisotropy of the water diffusion tensor was fairly small and because of the difficulties encountered with polycrystalline samples, some measurements were made on the magnetically oriented samples. The orientation was checked by observing the light transmitted through the short axis of the sample using crossed polarizer and analyzer on a micro- scope. Only those samples in which little or no transmitted light was observed were used. Values of D (parallel) and D (perpendicular) relative to standard water were measured and are shown in table 3.The measurements were difficult to make because of low sensitivity but do appear to indicate that D (parallel) and D (per- TABLE 3.--0, VALUES FOR ORIENTED SAMPLES CONTAINING 35 % WATER (296f2 K) glass slides 0.56 0.40 (orientation by shearing) u.-v. cells (i) 0.8 0.36 (magnetically oriented) (ii) 0.7 0.3 (magnetically oriented) (iii) 0.52 0.26 (magnetically oriented) (iv) - 0.28 (magnetically oriented) Du DI neutron scattering 0.55 ammonium perfluoro-octanoate, octanol, water lamellar mesophases at 296 K 8.0 4.0 2.0 . . neutron time of flightlps m-1 FIG. 5.-Neutron time of flight spectra at scattering angles 8 = 54" and 90" to the incident beam direction for the ammonium perfluoro-octanoate+ water + 10 % octanol system at 296 K. Upper spectra APO + HnO + octanol.Lower spectra APO + D20 + octanol.140 LAMELLAR LIQUID CRYSTALLINE PHASES pendicular) are the same order of magnitude. The variability in the results indicates the very considerable difficulty associated with such n.m.r. measurements but the general trend of D (parallel) and D (perpendicular) to be scattered on either side of the neutron value is apparent. NEUTRON SCATTERING MEASUREMENTS ON THE THREE COMPONENT SYSTEM AMMONIUM PERFLUORO-OCTANOATE-WATER-10 % OCTANOL At room temperature, swelling of the two component APO-H20 system is limited to water layer thicknesses of about 27 A. To obtain larger water layer thicknesses, and so to bridge the gap between these model gels and biologically interesting gel structures, it is necessary to work with the system containing a few per cent of octanol.The phase diagram of this three component system has not been mapped in detail but well defined regions of lamellar, lyotropic order exist and we have worked within these regions. The system also offers for the first time a chance of determining a degree of mobility of chains in the amphiphilic region by observing the neutron scattering from the included octanol molecules. These molecules effectively act as a probe and we can, in principle, observe both their translational and rotational diffusion to obtain the linear and rotational friction constants within the layer. The system also lends itself well to the isotopic or atomic substitution method ammonium perfluoro-octanoate, octanol, water lamellar mesophases at 296 K 2.0 3:*1 9=54O .. QZ= 1.24A.' "O* 1.0 t 8-90' . . . - . - Qz= 3.0 A ' I energy transfer/meV FIG. 6.-Quasielastic neutron scattering laws, S(a, 8) calculated from the data of fig. 5 contrasting the dependence of the spectra on scattering angle and cross section weighting.J . B . HAYTER, A . M. HECHT, J . w. WHITE AND G. J. T. TIDDY 141 whereby we can extract, selectively, information from the neutron scattering spectrum using eqn (4). Fig. 5 contrasts the time of flight neutron scattering spectra taken from the H,O three component system and from the equivalent system made up with D20. In the inelastic region of the spectra, and this is especially noticeable at the higher angle of scattering (0 = 90') the H20 system shows the strong inelastic peak associ- ated with water torsions at a time of flight of about 300 ps m-' (ca.450 cm-I). This is absent in the D20 samples where the scattering from water is rather less than the scattering from octanol. The remainder of the inelastic spectrum is rather featureless. This is in fact quite useful for the subsequent quasi-elastic analysis because it makes corrections for inelastic scattering less difficult. In the quasi-elastic region, near neutron time of flight 1300 p s m-l, the strong peak is broader at higher angles of scattering for both samples. In the case of the sample prepared with light water the scattering is almost entirely from the H20 quasi-elastic scattering analysis ammonium perfluoro-octanoate, octanol, water mesophase, at 296 K 1 1 I - ! --- -4.5 nt u 0 0.84 t t- I t 9 3 .a .-.0 0 0 0 0 0 2 0 . 4 4 b I 1 0 . (momentum transfer)' (Q'/A-") 0, HzO ; a, D20 ; +, vanadium FIG. 7.-Analysis of the quasi-elastic peak intensity and width dependence on squared momentum transfer Q '.142 LAMELLAR LiQUID CRYSTALLINE PHASES (scattering from water compared to the scattering from the rest of the system is about 6 : 1). In the deuterated sample the scattering from octanol compared to the scattering from all other sources is about 2 : 1. When the data are reduced to the form of the scattering law, S(cr, p) it can be seen that the quasi-elastic scattering has an almost symmetrical and almost Lorentzian shape around zero energy transfer. The scattering laws derived from the data of fig. 5 are shown in fig.6. The differential broadening as a function of scattering angle and between the system where water is observed as opposed to octanol, can be readily seen from this figure. TABLE 4.-sUMMARY OF DIFFUSION MEASUREMENTS IN THE THREE COMPONENT APO+ WATER+ 10 % OCTANOL SYSTEMS composition ~/105cm* s-1 d-IlA-1 70 %ItH20 1.64 61 0.01 6 50 %tH20 1.51 27.4 0.036 20 % H20 1.01 8 0.125 70 % D20 1.23 61 0.016 50 %D20 1.02 27.4 0.036 20 % D2O 0.99 8 0.125 A quasi-elastic analysis showing the variation of peak heights and peak widths for the deuterated and undeuterated sample of the same water layer thickness with squared momentum transfer is shown in fig. 7. Also plotted in fig. 7 is the energy width of the scattering from vanadium, a perfectly incoherent scatterer, which defines the resolution function of the spectrometer. It can be seen from the upper part of fig.7 that there is a weak Bragg reflection at a momentum transfers of about 1.2 A-l which does interfere with the quasi-elastic analysis at, and somewhat above, this momentum transfer. Its effects may be seen in the (energy broadening, momentum transfer squared) plots in the lower half of the figure as a dip in the plot for the deuter- ated sample. This occurs because the quasi-elastic scattering is rather narrower in the region of Bragg reflections than it would be if only incoherent scattering were contributing. The figures show data for intermediate water layer thicknesses. Bragg effects are less pronounced in the H20 sample and for samples with greater water content. Even for the thinnest layers, work at low momentum transfers makes it possible to obtain an " effective diffusion coefficient " for scattering from inter-layer water and from octanol depending on whether the H,O or D20 samples are being considered.The results are summarized in table 4. A general conclusion is that in the H 2 0 system the diffusion constants change in line with the expectations from water in the two component APO-H20 systems mentioned above. In the deuterated samples a much smaller variation in the " effective diffusion constant " is found and, indeed, almost no change in diffusion constant between the 50 % D20 and 20 D20 sample can be detected. DISCUSSION CENTRE OF MASS DIFFUSION The inter-lamellar water in gels formed by clay minerals, sodium montmorillonite, lithium montmorillonite and lithium vermiculite has been studied by neutron inelastic scattering 2 1 and it has been shown that the diffusion coefficient is logarithmically related to the inverse of the water Iayer thickness for water layers between about 5 AJ .B. HAYTER, A . M. HECHT, J . w. WHITE AND G. J . T. TIDDY 143 and 60A. The data from tables 1 and 4 now suggest that a similar relationship holds for water diffusion in the ammonium perfluoro-octanoate gel systems. In fig. 8 we plot the logarithm of the diffusion coefficient determined by neutron scattering measurement as a function of the inverse water layer thickness determined by diffraction from the same samples. It is at once obvious that the results here and in table 1 suggest only a weak dependence of diffusion coefficient on water layer thickness in these samples.The measured diffusion coefficients may be, if anything, slightly low for points at high momentum transfers in the (AE, Q2) plots, (previous section) have been given quite high weighting in the analysis because the dependences are best represented by almost straight lines. Good agreement between the Area and Table methods was found throughout and so the results are, at the least, self- consistent. H20 diffusion in ammonium perfluoro-octanoate gels at 296 K 4 Oe2- .4 G v) c 3 z 0.1 2 M CI 0 1 0 \ +?\ - -+y+ I I \ FIG. &-Water diffusion in ammonium perfluoro-octanoate gels as a function of inverse water layer thickness. Two differences between the behaviour shown in fig. 8 and that in the clays, can be noticed.First, if a straight line is drawn through the points its slope is approxi- mately 2 A while that found for the clay+ water systems was about 5 A. Secondly, whereas the line drawn through the points for the clay mineral experiments extra- polated within experimental error to the bulk diffusion coefficient of water at the measuring temperature, this is certainly not so for the ammonium perfluoro-octanoate system. The limiting diffusion coefficient is about 1.75 x cm2 s-l. It should be noticed, though, that the points from the three component system fall on the same line as those from the two component system. Again this supports the argument of self-consistency amongst the data. There it was seen that the logarithmic behaviour of D with inverse layer thickness could be explained if there was a term, in the enthalpy of activation for diffusion between the charged sheets, linear in the reciprocal of the water layer thickness.A simplified thermodynamic model can be constructed using the Kelvin equation and, on this basis, the aqueous layer in APO is much less sensitive to the mean inter-lamellar field (calculated assuming complete dissociation of APFO) than was the water in lithium montmorillonite for example. Fig. 8 can be discussed in an analogous manner to the clay minerals.21144 LAMELLAR LIQUID CRYSTALLINE PHASES The first signs of this difference are already apparent at the microscopic level at high momentum transfers. The quasi-elastic broadening at Q’ = 3 A-’ for approxi- mately 8 A thick layers of water in APFO/H20 and lithium montmorillonite is about 0.4 meV and 0.15 meV respectively and the diffusion plots for the clay are far from linear. At these momentum transfers the scattering from rotational diffusion is more strongly weighted than at lower Q and we may infer that the rotational cor- relation times are rather longer in the clay minerals than in APO-H20 for the same water layer thickness.The details of these phenomena will be explored further as higher energy and momentum resolutions become available. Because the spin relaxation time of the included water is short, due to chemical exchange, it is clear that nuclear magnetic resonance measurements on this system present unusual difficulty. The caesium perfluoro-octanoate-water system avoids this effect and experiments with it have so far been in good qualitative agreement with the general conclusions above, showing accord between the diffusion coefficients measured by neutron scattering and those determined by nuclear magnetic resonance measurements.The rather low anisotropy found by nuclear magnetic resonance measurements supports the exploratory measurements done with neutron scattering on the two component system. Because the observation range of the nuclear magnetic resonance studies is up to six orders of magnitude greater than that for neutron scattering, it appears that microscopic and bulk transport perpendicular to the predominant orientation direction of the layers is relatively fast. This may indicate that the bi- layers are quite porous to the transport of water or that there is a very large amount of inter-crystalline water in the sample.We think that the latter possibility is not very great, particularly in the oriented samples where relatively large crystallite sizes are present as indicated by the diffraction determined values of La and L, and from electron micrographs of frozen s a i n p l e ~ . ~ ~ And so we are left with the conclusion that water diffusion is relatively fast through our compacted crystalline bi-layers. ROTATIONAL DIFFUSION In the APO +water + 10 % octanol system, the most important result is the rather weak dependence of the quasi-elastic broadening on Q2 for the systems where octanol scattering predominates (table 4). At the energy resolution used, this behaviour suggests that rotational diffusion of the probe amphiphile is a much more important contributor to the dynamics on the s time scale than is the diffusion of the molecular centre of mass.Inspection of the scattering law diagrams of fig. 6 supports this view. The curves for APO+H,O+ 10 % octanol are good approxi- mations to a Voigt profile, but the curves for APO + D20 + 10 % octanol suggest a narrow peak superimposed on a broader low intensity feature. This is most notice- able in S(a, /I) for Q2 = 1.24 A-’ and less. Near AE = -0.65 meV there is a break in the smooth rise from - 1.5 meV. The effect requires resolution improved by about a factor of 3-5 times for clarification. Once again, the high crystallinity of the bi-layers in these compounds suggest attractive future experiments such as deter- mination of anisotropy of the centre of mass motion in two dimensions and the diffusion mechanism from the scalar momentum transfer dependence.CONCLUSIONS It is possible to study the microscopic aspects of water diffusion in model bi-layers with good signal to background by neutron inelastic scattering. At momentum transfers around 1 A-l the diffusion can be analyzed by the classical diffusion equationJ . B . HAYTER, A . M. HECHT, J . w. WHITE AND G . J . T. TIDDY 145 and the diffusion constants found from neutron scattering are in good agreement with those from nuclear magnetic resonance spin echo studies. The diffusion of amphiphile molecules can also be studied selectively by using the atomic substitution method,26 although with spectrometer resolutions of about 0.5 cm-' , the quasi-elastic scattering is strongly dominated by rotational diffusion of the amphiphile about its long axis with a rotational correlation time of about lo-' ' s.We thank Dr. P. A. Reynolds and Dr. K. Carneiro of AEK Rim, Denmark for their help with the MARX measurements. K. Fontell, L. Mandell, H. Lehtinen and P. Edwall, Acta Polytechnica Scand., Ch. 74, 1968. G. J. T. Tiddy, J.C.S. Faraday I, 1972, 68, 608. See for example, G. C. Stirling, Ch. 2 in Chemical Applications of Thermal Neutron Scattering, Ed. B. T. M. Willis (Oxford University Press, 1973). W. Hanke and H. Bilz, Neutron Inelastic Scattering, 1972 Proc. Grenoble Symposium I.A.E.A. Vienna 1972, p. 3. G. S. Pawley, ref. (4), p. 175. J. K. Kjems, P. A. Reynolds and J. W. White, J. Chem. Phys., 1974, 60. ' J. W. White in Moleculer Spectroscopy 1971, Ed. P. Hepple (Inst. of Petroleum, 1971), p. 231. * J. W. White, Neutron Inelastic Scattering 1972. Proc. Grenoble Symposium, I.A.E.A. Vienna 1972, p. 315. G. Allen, ref. (S), p. 261. l o J. W. White in Polymer Science, Ed. A. D. Jenkins (North Holland, Amsterdam, 1972), Ch. 27. K. E. Larsson, Neutron Inelastic Scattering, Vol. I Proc. Copenhagen Symposium, I.A.E.A., Vienna 1968, p. 397. "J. W. White in Chemical Application of Thermal Neutron Scattering. Ed. B. T. M. Willis (Oxford Univ. Press, 1973), Ch. 3. l 3 H. G. Hertz, Proc. 24 Reunion de la Societe de chemie physique Orsay, July 1973 (D. Reidel Co., 1974). l 4 W. M. Lomer and G. G. Low in Thermal Neutron Scattering. Ed. P. A. Egclstaff (Academic Press, N.Y., 1965), Ch. 1. * 5 J. K. Kjems, P. A. Reynolds and J. W. White, J. Chem. Phys., 1972, 56, 2928. A. Heidermann and B. Alefeld, Neutron Inelastic Scattering 1972, Proc. Grenobli: Symposium, I.A.E.A. Vienna 1972, p. 851. F. Mezei, 2. Phys., 1972, 255, 146. l 8 G. J. T. Tiddy, Symp. 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