Langmuir 1995,11, 3676-3684
3676
Order in the Bilayers of Gel-Phase Sodium Sulfopropyl Octadecyl Maleate. Wide-Angle X-ray Scattering and Molecular Modeling Hans von Berlepsch*t+ Max-Planck-Znstitut f u r Kolloid- und Grenzflachenforschung, Kantstrasse 55, 0-14513 Teltow, Germany
Dieter Hofmann GKSS Research Center Geesthacht, Znstitute of Chemistry, Kantstrasse 55, 0-14513 Teltow, Germany
Johannes Ganster Fraunhofer Znstitute of Applied Polymer Research, Kantstrasse 55, 0-14513 Teltow, Germany Received March 15, 1995. Zn Final Form: June 29, 1995@ The order in the bilayers of a metastable gel state of the long-chain surfactant sodium sulfopropyl octadecyl maleate (SSPOM)is investigated by wide-angleX-ray scattering (WAXS)and molecular modeling. The WAXS patterns indicate an ordered and rather dense in-plane structure, consisting of hexagonally packed, untilted, and interdigitated molecules. Three hexagonal reflections are found for a 60 wt % sample. Fourier analysis of the WAXS data reveals that the spatial correlation between the chains reaches almost 50 A. The estimated area per molecule in the bilayer is 40.0 A2. Based on the experimental results, the in-plane packing is simulated and the hexagonal arrangement of molecules proves t o be energetically possible. Amodel packingwith the majority ofthe sodium counterions in the water phase near the SSPOM packing surface shows the best agreement with the experimental WAXS data.
I. Introduction It is well-known that surfactant molecules composed of a hydrophilic headgroup and a hydrophobic chain can selfassemble to yield various complex supramolecular structures. A variety of aggregates like spherical micelles, rodlike micelles, bilayers, reverse micelles, and vesicles have been observed. The polymorphism forms the basis of many biochemical processes and is used in several technical applications.1,2 A detailed understanding of selfassembly is therefore of great importance for science and technology. In a series of recent papers, we investigated the physicochemical properties of a homologous series of sodium sulfopropyl alkyl maleate^^-^ which were synthesized aiming a t their application as polymerizable emulsifiers.6 During the investigations of these surfactants in aqueous solution, the CIS derivative SSPOM HCCOO(CH2)3S03Na
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attracted our special attention because of its iridescence
* To whom
correspondence should be addressed. Present address: Institut Charles Sadron (CRM-EAHP), 6 r u e Boussingault, F-67083Strasbourg Cedex, France. Abstract published in Advance A C S Abstracts, September 1, 1995. (1)Meunier, J.; Langevin, D.; Boccara, N. Physics of Amphiphilic Layers; Springer: Berlin, 1987. (2) Chen, S.-H.; Huang, J. S.; Tartaglia, P. Structure and Dynamics of Strongly Interacting Colloids and Supramolecular Aggregates i n Solution; Kluwer Academic: Boston, MA, 1992. (3) von Berlepsch, H.; Strey, R. Ber. Bunsenges. Phys. Chem. 1993, 97,1403. ( 4 ) Goebel, K.-H.; Stahler, K.; von Berlepsch, H. Colloids Surfaces A: Physicochem. Eng. Aspects 1994, 87,143. ( 5 ) von Berlepsch, H.; Dautzenberg, H.; Rother, G.; Jager, J. J . Phys. Chem., submitted. (6) Tauer, K.; Goebel, K.-H.; Kosmella, S.; Stahler, K.; Neelsen, J. Makromol. Chem., Macromol. Symp. 1990, 31, 107. +
@
when illuminated with white light. This phenomenon is well-known for a couple of years for many surfactant systems. The iridescence arises from the interference of the light being scattered from periodic colloidal structures having dimensions of the wavelength of visible incident light. The SSPOM surfactant is characterized by a Krafft boundary a t T K = 37 “C as estimated by conductivity measurements and differential scanning calorimetry. In detailed investigations on microstructure and phase behavior using different experimental method^,^^^ we found below the Krafft boundary and for surfactant concentrations higher than 0.6 wt %, a gel-like state of lamellar structure displaying iridescent colors. On passing TKfrom the high-temperature isotropic liquid phase (Ld or the hexagonal phase (Ha), respectively, surfactant crystallites first precipitate, which transform after further lowering of the temperature and without the intervention of mechanical shear into the remarkably long-lived and gel-like lamellar state. A very similar gel-forming phenomenon was also observed for the water-dioctadecyldimethylammonium chloride ~ y s t e m . According ~,~ to Laughlin et al.s and as proved for the present SSPOM ~ y s t e mthe , ~ gel state is not a single phase but a colloidally structured dispersion of crystal hydrates in the dilute liquid phase. We called this metatable state the Gp phase.3 Figure 1 shows a partial phase diagram of the waterSSPOM system. Apart from these nonequilibrium gel states, thermodynamically stable “gel phases” have been observed for different surfactant systems,lOJ1which are located in the phase diagram between a crystalline (sub(7) Kawai, T.;Umemura, J.;Takenaka, T.; Kodama, M.; Ogawa, Y.; Seki, S. Langmuir 1986,2, 739. (8)Laughlin, R. G.; Munyon, R. L.; Fu, Y.-C.; Fehl, A. J. J . Phys. Chem. 1990,94,2546. (9) von Berlepsch, H. Langmuir, submitted. (10)Ekwall, P. In Advances in Liquid Crystals; Brown, G. H., Ed.; Academic: New York, 1975; Vol. 1, p 1. (11)Kodama, M.; Seki, S. Adu. Colloid Interface Sci. 1991, 35, 1.
0743-7463/95/2411-36’76$09.00/0 0 1995 American Chemical Society
Langmuir, Vol. 11, No. 10, 1995 3677
Order in the Bilayers of Gel-Phase SSPOM 70 7'' ' ' ' ' ' ' ' ' ' """
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Figure 1. Partial phase diagram ofthe water-SSPOM system. L1, Ha,Gp, and X denote the isotropic liquid phase, normal hexagonal phase, gel state, and crystal phase, respectively.The Go phase extends from the vertical broken line up to 30 wt % and terminates on its high-temperature side at the broken steplike line. Between these boundaries, the gel state is longlived. In the region on the left side of the vertical broken line, the sample phase separates macroscopicallyduring a few days, whereas the upper phase is an isotropic liquid and the lower phase the gel. The lowest surfactant concentration for which the gel state has been resolved is 0.1 wt %. If the steplike upper boundary is crossed from the low-temperature side, the gel state collapses and crystals appear, which are in coexistence with a nonspecified liquid phase. The data points are derived from visual inspection, electrical conductivity, and different scattering investigation^.^^^ gel) phase at low temperature and a micellar phase at high temperature. Gel phases have been considered as intermediate states between the liquid-crystalline and the crystalline state with completely ordered chains. The formation of a gel state in the case of the present surfactant is obviously connected with the buckled conformation of the molecule forced by the cis double bond and the high length of one of the tails. This conformational structure of SSPOM is reminescent of certain lipids with different lengths of the hydrocarbon chains. The sodium sulfopropylalkylmaleates differ, however, from the lipids in that the hydrophilic SOS- headgroup is located at the end of the shorter chain. We found the same reciprocal chain-length dependence of the Krafft temperature for mixtures of c14 and CIS derivativesg as the observed one for the chain-melting transition temperature of lipids.12 Moreover, the enthalpy and entropy changes associated with the KraM boundary are within the same range of typical values of lipid^.^ For lipids with large differences in the tail lengths, extended interdigitated bilayers have been found mostly in the gel state.13 On this background, the question as to the kind of chain packing which is realized in the metastable GB phase of SSPOM arises. Additionally, the present system is of special interest because, contrary to the lipids, the hydrophilic headgroup is buried in the interior of the bilayer, which might be important for the location of the counterions and thus also for the stability of the membranes. X-ray diffraction in general has been proved to be a powerful tool in investigating the structure of surfactant systems. WAXS is uniquely sensitive to the gel state. A sharp line at a wave vector of about 1.5 k1is generally seen for gel-state lipids, whereas a diffuse 1.3-A-l reflection (12)Cevc, G.;Marsh, D. Phospholipid Bilayers. Physical Principles and Wilev: New York. 1987:D 231. .. ... Models: ...... ~~
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(13)Slat&, JTL:; Huang,C:In TheStructure ofBiologica1 Membranes; Yeagle, P. L., Ed.; CRC: Boca Raton, FL, 1992;p 175.
is usually observed for lipids in the liquid-crystalline state.14 In early work, the gel phase of lipid bilayers has been characterized as having conformationally ordered, nearly all-trans hydrocarbon chains that pack into ordered arrays that give rise to one or at most two refle~ti0ns.l~ The ordered hydrocarbon chains are in most cases tilted with respect to the nearly hexagonal lattice of packed chains.16J7 However, it is now becoming clearls that the considered hydrated systems possess only order in the sense ofhaving a layered structure but are also disordered enough not to form crystals. The characterization ofboth the order and the disorder inherent in such partially ordered, anisotropic systems needs a n approach which goes beyond the conventional model of treating the gel phase as a n ordered two-dimensional crystal. We apply in the present work the radial distribution function (RDF) method,lg a typical technique for the characterization of amorphous low-molecular-weight substances and amorphous polymers,20 to elucidate the packing structure of gel-state SSPOM. The wide-angle data are used to build a packing model which is applied in the following as a n appropriate starting point for a computer simulation of the structure using molecular dynamics methods. From the comparison of measured and calculated scattering functions, one can obtain a more comprehensive picture of the state of order and disorder of the GBphase. 11. Materials and Methods Samples. SSPOM was synthesized following a procedure described in ref 4. For purification, the surfactant has been recrystallized at least 3 times from a water-acetone mixture. The purity was checked by lH NMR spectrometryand thin-layer chromatography, but no impurities were detected,indicating at least 99% purity. Due to the high KrafR temperature of 37 "Cand the appearance of the viscous hexagonal Ha phase for surfactant concentrations higher than 20%,the preparation of X-ray samples required an involved technique. The samples up to a concentration of 25 wt %wereprepared by adding deionizedwater to weighed quantities of surfactantto the desired concentration. The slurriesof crystals and water were homogenized by centrifuging back and forth through the sample tubes. The mixtures of surfactant crystals and water were then warmed up to the complete dissolution of crystals. For the 25%sample, a temperature of about 80 "Cwas necessary. After cooling down to room temperature, the transparent, slightly turbid, gel-like solution is formed and loaded into the heatable sample holder consisting of an aluminumframe of 3-mm thickness, covered by 12-pm-thick polyester foils. In order to remove air bubbles, the samples were then heated once more to the low-viscousmicellar state above TKand cooled down to room temperqture. The reproducibility ofour results obtained on samples prepared in this way is sufficient. The highlyconcentrated samples were obtained by definite drying of lowconcentrated samples in the sample holders under laboratory atmosphere conditions. The drying process required several weeks, during which the samples did not change visually. The small-angleX-ray scattering (SAXS) patterns show two equidistant reflections vs scattering vector and thus indicate the preserved lamellarstructure of the Gp phase. From the measured (14)Luzzati, V.; Husson, F. J . Cell B i d . 1962,12,207. (15)Tardieu, A.;Luzzati, V.; Reman, F. C. J . Mol. Biol. 1973,75, 711. (16)Janiak, M.J.;Small, D. M.; Shipley, G. G. J . Bid. Chem. 1979, 254,6068. (17) Smith, G.S.;Sirota, E. B.; Safinya, C. R.; Clark,N. A. Phys.Reu. Lett. 1988,60, 813. (18)Sun, W.-J.; Suter, R. M.; Knewtson, M. A,; Worthington, C. R.; Tristram-Nagle, S.; Zhang, R.; Nagle, J. F. Phys. Rev. E 1994,49,4665. (19)Klug, H.P.; Alexander, L. E. X-ray Diffraction Procedures for Polvcrvstalline a n d AmorDhous Materials; Wilev: New York, 1974. (20i Mitchell, G. R. I n b r d e r in the Amorphous State of Polymers; Keinath, S. E., Miller, R. L., Rieke, J. K., Eds.; Plenum: New York, 1987;p 1.
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3678 Langmuir, Vol. 11, No. 10, 1995
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Figure 2. WAXS spectra of SSPOM solutions: (a) spectrum of pure water at room temperature (20 "C); (b) 15wt % solution of SSPOM in water at 60 "C; (c) 15 wt % SSPOM at 20 "C; (d) 25 wt % SSPOM at 60 "C; (e) 25 wt % SSPOM at 20 "C. linear relation between the repeating distance of the bilayers we estimated the and the reverse of the volume fra~tion,~ concentration ofthe WAXS samples after drying by extrapolating this relation to higher concentrationswith an error of about &5%. X-rayScattering. The measurementswere carried out using a horizontal diffractometer in symmetrical transmission geometry.zl The incident Mo Ka radiation (wavelengthI = 0.7107 was monochromatized by a flat LiF crystal, and the diffracted beam (includingCompton scattering) was detected by a scintillation counter, discriminating the 1/2 component by a pulseheight analyzer. Within 640 angular positions between Bragg angles (half of the scattering angle) of 0 = 1.3" and 65.3" and with a step width of A0 = 0.1", the scattering was detected. Up to 0 = 13", the counting time per point was 5 min, while for higher angles the average of six runs having the same counting time of 5 min per point has been taken. Parasitic scattering was measured separately with an empty holder arrangement and a statistical accuracy better than 0.05. Molecular Modeling. Models of molecular packing were constructed and simulated by means of the CeriusWOLYGRAF software of Molecular Simulations Inc.22The DREIDING force fieldz3was applied for all static and dynamic simulations. An IBM RS 6000-370with a memory and swap space of 128 Mbyte each was used as hardware.
111. Data Goniometer traces for two samples of 15 and 25 wt % SSPOM measured a t 20 and 60 "C, respectively, as well as for pure water are shown in Figure 2. A sharp peak a t a n angle of about 5" is seen a t room temperature for the gel phase, with the other features being very similar to those ofwater. At 60 "C, the peaks are stronglyreduced and only visible as shoulders slightly shifted to the smallangle side and indicating a melting of the ordered structure. According to the phase diagram of Figure 1, the 15 wt % sample is now in the isotropic liquid phase L1 consisting of spheroidal micelles5 and the 25 wt % sample in the liquid-crystalline hexagonal H, phase. The observed loss of order is expected. A WAXS spectrum of a 60 wt % sample measured a t T = 20 "C is depicted in Figure 3. The 5" peak is very pronounced, a second one evolves a t about 8.5", and a shoulder appears around 10". The wave vector ratios of the three reflections are nearly 1, 4 3 , and 2 and are characteristic of a hexagonal two-dimensional structure. It is to our knowledge for the first time that more than one sharp hexagonal reflection could be detected for a gel-like bilayer system. On comparing Figures 2 and 3, ~
(21) Ganster, J.; Fink, H.-P.; Zenke, I. Polymer 1991,32, 1566. (22) Cerius2, POLYGRAF, Molecular Simulations Inc.; Burlington, MA, 1994. (23)Mayo, S.L.; Olafson, B. D.; Goddard, W. A,, 111. J . Phys. Chem. 1990,94,8897.
40
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Figure 3. WAXS spectrum for a 60 wt % solution of SSPOM in water at 20 "C. it is evident that the increase of surfactant concentration sharpens the WAXS pattern against the water background. The structure generating the peaks is concentrated up there by facilitating the Fourier analysis of the data. In what follows, therefore, only the RDF results for the 60 wt % sample are presented. The raw scattering data (Iraw) were corrected according to the formula
with
@t),= - [ln(z,)l
@tIf= - [ln(z,)l
(2)
The factor A in eq 1 scales the parasitic scattering (I,,) to the primary beam level of the sample measurement. The term in the denominator is the polarization factor for the LiF crystal ((200)plane). In eq2, tsand tfarethe measured transmissions of sample and foils, respectively, the latter being, in fact, unity for our thin foils. The contribution from multiple scattering was neglected. The scattering function (reduced intensity) is defined asz4
i
where s = 4n(sin 9)lA is the magnitude of the scattering vector, Icoh and Iinc are the structure-independent theoretical coherent and incoherent intensities, c is a normalization constant, shifting the corrected experimental intensity (Icorr) to the absolute scale, and xi and fi are the mole fractions and the atomic scattering factors of atom {i} (i = H, C, 0, Na, S),respectively. It is often more instructive to compare the measured and calculated reduced intensities than the i(s) functions. Thus, in the following, we will mostly rely on those reduced scattering density considerations. The experimental scattering functions si(s)were calculated as described in ref 21, where further details of data treatment may be found. The reduced intensity is shown in Figure 4 together with the curve for pure water and the difference curve between both. No smoothing has been applied to the SSPOM sample scattering, showing the comparatively good statistical accuracy of the measurement. The total measuring (24)Pings, C. J.;Waser, J. J . Chem. Phys. 1968, 48, 3016.
Order in the Bilayers of Gel-Phase SSPOM
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Langmuir, Vol. 11, No. 10, 1995 3679
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Figure 4. Experimental scattering functions si(s) for a 60 wt % solution of SSPOM in water (above) and for pure water (middle) at 20 "C. The lowest curve is the difference curve between both.
Figure 6. Radial distribution functions G(r) of scattering functions of Figure 4 in the short distance range: (above) 60 wt % solution of SSPOM in water; (middle)pure water, (below) difference curve.
TV. Model and Simulation Details Basic Crystal Model. The simplest basic twodimensional crystal model which is consistent with the observed hexagonal WAXS reflections is the hexagonal packing of interdigitated molecules. For a hexagonal arrangement of chains, we obtain a lattice constant (nearest-neighbor distance of chains) of a = 4.81 A from the first reflections using the relation Shk = 4n[h2 K 2 hk]1/2/aJ3, where the first three reflections correspond to (h,K)= (LO), (l,l), and (2,O). The normal distance between the lattice planes is b/2 = ad312 = 4.16 A, giving a n area per molecule of A0 = ab = 40.0 Az. Such a low value indicates a dense packing of chains. Because the structural unit of this model consists of two molecules with interdigitated chains, the rotational symmetry of the structural unit is lacking and the structure is not strictly hexagonal. However, for lipids with very similar structures, it has become established to describe the repetitive nature of the chain packing, that is, the three-dimensional packing of methylene groups, in terms of a small subcell of the true unit cell of the ~ r y s t a l . ~ 'Examination ,~~ of a large number of crystal structures of lipids has revealed that the chain packing could be described by a relatively limited number of hydrocarbon sub cell^.^^ Simple alkanes show a solidsolid transition on increasing temperature which is characterized by the onset of chain rotation about the long-chain axis. At this transition, the chains convert from one of the subcell packing modes (e.g., triclinic or orthorhombic) to a rotationally-disordered hexagonal chain packing mode.30 Analogous structural transitions in chain packing have been observed also for hydrated lipid^.^^!^^ and this (sub-gel)crystal-to-gel transition has been thoroughly monitored by WAXS. Thereby, it was revealed that (i) the hydrocarbon chain subcell expands in volume, (ii) the subcell alters its dimension and symmetry, and (iii)chain rotationis induced. For example, typical values for the area per chain in the crystal phase and the (untilted) gel phase are 18.8 and 19.4 Az for dihexadec lphosphatidylcholine (DHPC),r e ~ p e c t i v e l y , ~ ~ and 20.5 for the (untilted) gel phase of dilauroylphos-
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Figure 5. Radial distribution function G(r)of the difference curve of Figure 4. time was half a n hour per point for s > 4 A-1 accumulated from six runs. The smoothed water curve has been scaled to the water content of the SSPOM sample before subtraction. The difference function should show to a certain approximation the pure structure of the bilayers. The radial distribution function, G(r),defined as
(4) has been calculated for the just mentioned difference function after smoothing and dumping according to L o r ~ h giving , ~ ~ the oscillating function represented in Figure 5. The spatial correlations almost reach 50 A, which is also valid for the 15 and 25 wt % samples due to the same sharpness of the 5"peak. A regular structure is encountered with a characteristic distance of about 5 It should be noted that the system considered is isotropic so that some spherically symmetric distance statistics are produced. A closer inspection of the short-distance range of the radial distribution functions depicted in Figure 6 reveals that the subtraction of water merely removes the typical oxygen-oxygen peak of waterz6 and only slightly influences the peak between 4 and 6 A. The next but one carbon-carbo? neighbor peak of aliphatic hydrocarbons a t about 2.5 A deyelops, and the next-neighbor carbon peak a t about 1.5 A is amplified. aIt must be considered, however, that the region below 2 A is strongly influenced by errorneous long wave oscillations in si(s),which are difficult to avoid for the weakly scattering samples investigated.
A.
(25) Wright, A. C . Adu. S t r u t . Res. 1974,5,1. (26) Narten, A. H.;Venkatesh, C. G.;Rice, S. A. J.Chem. Phys. 1976, 64,1106.
K
(27) Vand, V. Acta Crystallogr. 1951,4,104. (28) Maulik, P. R.; Ruocco, M. J.; Shipley, G. G. Chem. Phys. Lipids 1990,56,123. (29)Abrahamsson, S.;Dahlen, B.;Lofgren,H.;Pascher, 1.Prog. Chem. Fats Other Lipids 1978,16,125. (30) Muller, A. Proc. R. SOC.London, Ser. A 1932,138,514. (31) Fiildner, H. H. Biochemistry 1981,20, 5707. (32) Ruocco, M. J.; Shipley, G. G. Biochim. Biophys.Acta 1982,691,
309. (33) Laggner, P.;Lohner, K.; Degovics, G.; Muller, K.; Schuster, A. Chem. Phys. Lipids 1987,44,31.
von Berlepsch et al.
3680 Langmuir, Vol. 11, No. 10, 1995
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Figure 8. Idealized (SSP0M)z unit.
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Figure 7. schematicrepresentation ofthe IXJlecularpacking of SSPOM: orthorhombic(pseudohexagonal)hydrocarbonchain subcell packing. phatidylethaqolamine (DLPE).34 The area per chain of Ad2 = 20.0 A2 for SSPOM ranges between the corresponding values for the gel phase of the lipids. The assumption of free rotation ofthe chains leads to the simple face-centered rectangular subcell with axes of a = 4.81 and b = 8.33 as shown in Figure 7 . Because the ratio of the parameters of the orthorhombic cell is equal to bla = 43, a hexagonal scattering pattern is expected for the simplified structure in agreement with the experiment. Due to the real connection between two chains, further reflections should be possible but have never been detected by WAXS. The important question ofwhether the chains are tilted or not should be answered, in principle, by the experimental scattering spectrum. For lipids with tilted chains, a shoulder appears very near to the sharp first reflection on the high-angle side.35,36A pronounced shoulder is not found in the present case, as evidently shown by Figure 4, suggesting a vanishing or a t least very low tilt angle. The estimated area per molecule is also in accordance with experiments and simulations on the packing of untilted or slightly tilted (below4") amphiphilic molecules at the air-water i n t e r f a ~ e . ~Besides, ~ , ~ ~ the bilayer thicknesses estimated from the partial specific volume and area per molecule of about 38 as well as those from the SAXS studiesg are also in rough agreement with the theoretical bilayer thickness for untilted interdigitated chains using molecular models (cf. section V). The dense bilayer of charged surfactant molecules is only stable if the counterions screen the strong electrostatic interactions between the molecules. The degree of counterion condensation can be estimated from the simple formula etr= 1- o b , derived in ref 39 as a solution of the Poisson-Boltzmann equation for the case of two charged parallel plates with a n intervening aqueous solution containing the counterions, etris the fraction of trapped counterions, a, = 0.66e/L~d,, a critical charge density, and a = e/Ao, the net surface charge density of the plates. Lg is the Bjerrum length (7.2 A in aqueous solution a t room temperature) and d, the separation between the plates. From the repeating distance ofbilayers measured by SAXS3,9and the volume fraction, we obtain a fraction of trapped counterions of 0.85 and 0.97 for the 60 and 25 wt % samples, respectively. The simple phenomenological theory shows, in fact, that a very large portion of the
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(34) McIntosh, T. J.;Simon, S. A.Biochemistry 1986,25,4948. (35)Watts, A.;Harlos, K.; Marsh, D. Biochim. Biophys. Acta 1981, 645, 91. (36) Tristam-Nagle, S.;Zhang, R.; Suter, R. M.; Worthington, C. R.; Sun, W.-J.; Nagle, J. F. Biophys. J. 1993,64, 1097. (37) Kjaer, K.; Als-Nielsen, J.; Helm, C. A,; Tippmann-Krayer, P.; Mohwald, H. J . Phys. Chem. l989,93,3200. (38) Karaborni, S.Tenside Surf. Det. 1993,30,256. (39) Engstrom, S.;Wennerstrom, H. J.Phys. Chem. 1978,82,2711.
charges of headgroups should be compensated by counterions. However, their local distribution remains unknown. SimulationModels. In the first stage, the Structural unit consisting of two molecules with interdigitated chains, hereafter denoted as (SSPOM)z, was constructed in a n all-atom representation using the standard bond-length and bond-angle values of the DREIDING 2.21 force field. All necessary details about this force field can be found in rep3. Allconformation angles inside the long (CH2ln sequences were set to be trans (180"). A bump check was performed in order to avoid unacceptable atomic overlaps between the two constituent molecules of the structural unit. This idealized structure was subjected to a static geometry optimization using an energy minimization algorithm of the Cerius2 software (cf. ref 22). The main result was a considerable increase of the six bond angles closest to the top and the bottom of the structural unit, which was obviously necessary to relax intramolecular atomic overlaps. In the second stage, the following average values were assigned to these bond angles, with the respective standard values being given in parentheses: C-0-C, 123" (109"); 0-C-C, 126" (109");C-C=C and C=C-C, 132" (120"). All other structural parameters remained as chosen in the first stage. The structural unit obtained in this way is shown in Figure 8. (A large-scale picture of the structural unit including the lables of all atoms and a Cerius-bgf file with all atomic coordinates and partial charges may be obtained from the authors.) In the third stage, the idealized (SSPOM)2units of stage two were hexagonally packed as indicated by the X-ray data. A pseudohexagonal orthorhombic unit cell with th? lateral lattice parameters a = 4.808 and b = 8.328 A in the x and y directions, respectively, and y = 90" was chosen to represent the packing. The long-chainaxes were considered to show a perpendicular orientation relative to the hexagonal packing plane; Le., the tilt angle was assumed to be zero. Two types of periodic boxes (volume elements to be periodically repeated during the simulation) were filled with the (SSPOMI2 units: (i) a rectangular array of 8 x 8 SSPOM molecules and (ii)a box with outerhexagonal (rhombohedral) symmetry. These two geometries were chosen to check whether this additional symmetry of the model might have an influence on the results of this study. The evaluation of the molecular simulations did, however, not reveal any considerable differences between both types of starting geometry. Therefore, only the results obtained for the second type of symmetry ofthe packing cell will be disussed in the following. Since there is no sufficient experimental information about the positions of the sodium counterions in the Gp phase, three different idealized situations were realized: (i) all Na+ ions put close to the SO3- groups; (ii) all Na+ ions positioned in the water phase a t a distance of about 4.3 A above the bilayer surfaces as defined by the centers ofthe outermost hydrogen atoms (the radius of a hydrated sodium ion is about 4.3 A); (iii) all Na+ ions placed within the (SSPOM)2 bilayer between the solvent phase and the plane of terminal SO3- groups. Then, all different chain packings were placed in boxes of rectangular or rhombohedral cross section, respectively, with a box height (z
A
Order in the Bilayers of Gel-Phase SSPOM axis) of 62 A. The thickness of the constructed idealized (SSPOM12 double layers without Na+ ions is about 38 A. Finally, the remaining empty volume above and below the bilayer patch was solvated with water molecules utilizing the solvation module of the POLYGRAF software. This left the centers of the water molecules on a periodic lattice. It was, therefore, necessary to relax the water structure in each case via a first molecular dynamics stage. Partial charges were to be assigned to all atoms prior to this stage. The respective values for the (SSPOM)2single molecule were obtained by utilizing the charge equilibration module of the Ceriusz program. Each sodium ion was assigned a (+1)elementary charge, and for the water molecule, the values given by the Cerius2-Gasteiger procedure40were used. (The standard potentials for water, i.e., 0-3 and H--A of the DREIDING force field,23were utilized. The partial charges were qo = -0.4116 and q H = 0.2058.). A typical model e.g., with a type ii Na+ distribution using a rhombohedral packing box, was then composed of 6730 atoms with lateral packing cell dimensions of 38.46 A. The chosen model size fits quite well in the recent relevant literature, e.g., refs 38 and 41-43, although a much larger lipid bilayer simulation including 27 000 atoms was also recently reported.44 Here it should be noticed that the model just described shows a SSPOM concentration of about 60 vol %, i.e., about 80 wt % (64 SSPOM and 558 HzO molecules, respectively, for case ii packing). This is above the experimental value. However, no further increase of the box height beyond 62 A was possible. The reason was that under the given simulation conditions, the additionally necessary water molecules would have brought the total number of atoms over the limit possible on the available hardware. This procedure should not constitute any principal problems, since as stated in section I11 an increase in SSPOM concentration mainly just sharpens the WAXS pattern against the water background. The POLYGRAF softwarezz was applied to the first water equilibration. All SSPOM and Na+ positions were kept fixed (which was not possible with the Ceriusz 1.5 software). The cut-off for nonb9nd intractions (including Coulombic terms) was set to 12A, with a smooth switching function being used for all interatomic distances greater than 9 A. This cut-off choice ensures minimum image periodic boundary conditions in a strict enough manner to avoid the development of artificial periodicities in the spatial distribution ofthe Na+ions during the simulations of the whole system. The relative dielectric constant was set to cr = 2. Using these parameters, the water phase was subjected to a molecular dynamics run with a step width of 1 fs utilizing a temperature program starting with 800 K and ending with 300 K after a few picoseconds. The 300 K r u n was continued for another few picoseconds until the potential energy of the system approximately reached a constant level. The preequilibration was followed by a 200-step static structure optimization of the water phase. The procedure, just described, is certainly a rather rough one, but it was successful to remove most of the artificial order which was brought into the system during the solvation stage. A more detailed relaxation of the water phase had to occur in the course of the subsequent molecular dynamics simulation of the whole system. Furthermore, it should be stressed that we were (40) Gasteiger, J.; Marsili, M. Tetrahedron 1980, 36, 3219. (41) Raghavan, K.; Reddy, M. R.; Berkowitz, M. L. Langmuzr 1992, 8, 233. (42) Stouch, T. R. Mol. Simul. 1993, 10, 335. (43) Egberts, E.; Marrink, S.-J.; Berendsen, H. J. C. Eur. Biophys. J . 1994, 22, 423. (44) Heller, H.; Schaefer, M.; Schulten, K. J . Phys. Chem. 1993,97, 8343.
Langmuir, Vol. 11, No. 10, 1995 3681 0
Figure 9. Top views of idealized packing (a) and the results of static (b) and dynamic (c) structure optimizations for a type ii Na+ ion starting distribution [seetext]. Periodic boxes with rhombohedral cross section. not particularly interested in the detailed water structure in this paper but rather in the general packing of the molecules, conformational disorder inside the double layers, and some rough information about the possible preferred locations of the Na+ ions. In the next phase of the simulation, the whole system was subjected to a static structure optimization followed by a 70- 100-psmolecular dynamics run a t 300 K. Thereby no further qualitative changes in the packing of the SSPOM molecules, the distribution of Na+ions, and the calculated isotropic WAXS pattern ofthe respective models were observed after about 30 ps. Here the Cerius2software solved Newton's equations of motion for all the atoms for a constant volume (V), constant temperature (T), and constant number of atoms ( N )ensemble. Periodic boundary conditions with the same cut-off conditions and step widths as in the case of the water preequilibration were used. The temperature coupling was achieved via exponential dampi@ with a characteristic time constant of 0.1 ps. The reduced isotropic scattering of all idealized, structure-optimized, and dynamically simulated packing models was calculated via the amorphous diffraction module of the Cerius2 software. This was accomplished by first using the standard Debye formula and a sphere smear model size correction according to ref 46 to calculate the scattering intensity, I(s). Then, si(s)was obtained from s(l(s)- Icoh(s))with Icoh(s) already having been defined in section IIIb The calculation was performed in the range 0 < s < 16 A-l with a sampling rate of As = 0.04 k l . That means the accuracy of the calculated eak positions discussed below is usually about h0.02
I-'.
V. Discussion Figure 9 contains the top views of the idealized packing (a) and the results of the static structure optimization (b) and the molecular dynamics stage for a case ii Na+ ion starting distribution (c). The water molecules and sodium ions are omitted for the sake of clarity. The respective pictures for the case i and iii packings are a t least visually similar and therefore not shown here. Static Structure Optimization. Figure 10 shows the calculated reduced scattering intensities for the idealized chain packing (b) and the structure-optimized type i t o iii models (c-e) in comparison with the measured reduced intensity of the real sample (a) roughly corrected for the scattering of the water molecules (cf.lower curve in Figure 4). In the following, we will index scattering peaks up to s % 7 A-1 according to the pseudohexagonal orthorhombic unit cell introduced above. For this purpose, it is sufficient (45) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; Dinola, A.; Haak, J. R. J . Chem. Phys. 1984, 81, 3684. (46) Mitchel, G . R. Acta Crystallogr. 1981, A37, 488.
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3682 Langmuir, Vol. 11, No. 10, 1995
- b i i i i k k i i
I
,
l
\
I
#
I
I
I
0
2
4
6
8
10
12
14
16
SiP)
S(B;')
Figure 10. Reduced scattering intensities si(s): (a)measured on the 60% sample and corrected for the scattering of water (lower curve in Figure 4); (b) calculated for idealized chain packing; (c) calculated for structure-optimized type i Na+ ion starting distribution;(d)calculated for structure-optimizedtype ii Na+ ion starting distribution; (e) calculated for structureoptimized type iii Na+ ion starting distribution.
to consider just equatorial reflections, what is due to the double-layer character of the investigated structure with a considerable thickness of about 40 A. The following standard formula was utilized to calculate the (hkO)peak positions: ShkO = 2~c[(h/a)~(k/b)2]1'2.All calculated and measured patterns shcw the three main equatorial reflections a t s = 1.51 A-l (110)/(020),a t s = 2.61 A-l(200)/(130), and a t s = 3.02 A-1 (220)/(040) that are characteristic of a laterally hexagonal packing symmetry. Additionally, termination ripples due to the limited size of the model packings are clearly to be seen on both sides of the (110) reflection of the model structures. Furthermore, as compared with the measured si(s),the simulated models reveal additional packing peaks of two types: (i) reflections that are usually observed in samples with a ;ea1 hexagonal lateral packing symmetry, e.g., a t s = 4.00 A-l (240)/(310)or a t s = 6.04 A-l (440); (the presence of these peaks simply indicates a more perfect lateral order in the models than found in the real sample);(ii)reflections that are possible in the discussed pseudohexagonal orthorhombic lattice but which would not be observed in strictly hexagonal molecular packings, e.g., a t s = 2.00 A-1 (1201, a t s = 3.29 (140), a t s = 4.71 k1(1601, or a t s = 5.28 k1(410). These peaks probably result from symmetry breaks that are related with the specific character of the (SSPOM)2 unit (e.g., the chosen pseudohexagonal orthorhombic unit cell does not show a real centrosymmetry) and as in the foregoing case from a more perfect lateral order in the simulated than in the real structures. By and large, it can be stated that the general features of the scattering pattern are already closer to reality for the structure-optimized arrays than for the idealized starting structure. The structure-optimized type ii packing model (Figure 10d) where the starting position of the sodium ions is in the water phase, however, shows the
+
Figure 11. Calculated reduced intensities for type ii Na+ ion starting distribution after structure optimization (a) and molecular dynamics simulation (b), respectively. closest resemblance to the measured data if the intensity ratios between the three main hexagonal scattering peaks are mainly considered. These findings indicate that the assumed pseudohexagonal packing structure is energetically possible, as expected. The most significant visual difference between the idealized (cf. Figue 9a) and the structure-optimized molecule packings (cf. Figure 9b) consists in the introduction of a certain degree of conformational disorder into the long (CH& and short (CH& sequences ofthe SSPOM unit. This is the expected feature for the tails' state oforder in the gel phase, showingneither a perfect all-trans conformation nor a complete rotational disorder.47 This result agrees with other simulations on gel-phase lipid bilayer^.^^,^^ For all structure-optimized packing models, an average value of 168 AZ 9" was obtained for the C-C conformation angles along the backbone in the flexible regions of the SSPOM molecules. It should be noticed that in this paper, all conformation angles are considered to be between -180" and +180°. No real gauche angles, Le., conformation angles between -120" and 0" (anti-gauche)or between 0" and 120" (gauche),are detected. In addition the following average bond angles in the top and bottom regions of the structural unit (SSPOMIZwere obtained for the same model structures: C-0-C, 124"; 0-C-C or C-C-0, 126"; C-C=C or C=C-C, 132"; with standard deviations between 2" and 3". This shows that the almost identical values chosen for the idealized model and derived from a very simple (SSPOM)2 model were well justified. Furthermore, now as far as the lateral packing is concerned, the two long sides of each (SSPOM)2structural unit show a tendency to act more as individual entities than just being constituent parts of a unit. Molecular Dynamics Simulation. Figure 11 contains the calculated reduced scattering intensities for a type ii Na+ ion starting distribution after about 70 ps of molecular dynamics simulation of the kind described (47) Nagle, J. F. Biophys. J. 1993,64, 1110
Langmuir, Vol. 11, No. 10, 1995 3683
Order in the Bilayers of Gel-Phase SSPOM above, as well as the full s i b ) function up to s = 16 k1 for the respective packing that was only structure optimized. Again the scattering of the water molecules was omitted. On comparison with the lower curve in Figure 4,we find a n acceptable fit between the model scattering data and the measured and water-scatteringcorrected values only in the s > 6 A-1 range of the scattering vector. In this region, the fit for the dynamically-optimized structure is also even better than for the just energyoptimized structure. The same situation is true for the type i and iii models. Because of the reciprocity between real space and scattering space, this finding in a certain, though not exact, manner indicates that our simulation a t least approximately represents the real intramolecular short-range order of the investigated gel state. Thus, it should make sense that we do derive average values, e.g., for conformation and bond angles. The mean absolute value for the C-C conformation angles along the backbone in the flexible regions of the SSPOM molecules was determined to be 168". This compares well with the average value already obtained for the just structureoptimized modeled double-layer structures. But after the dynamics simulation, the standard deviation is f21",e.g., considerably increased. This higher standard deviation reflects the influence of thermal vibrations on the molecular structure. Now, on average, every molecule shows one gauche or anti-gauche angle in the flexible C-C backbone sequences with about 70%of these angles being concentrated in the headgroup regions. That means, the trans-angle content is about 95% what is probably to be related with the determined, rather restricted area per chain and the fact that in the case of (SSP0M)z units the cross section of the headgroups is about the same as for the long (CH& tails. This might be a major reason why in the given case three hexagonal packing peaks could be found in our measured WAXS pattern, while usually just one real packing peak is observed in the investigations on lipids.15,33,36 Molecules with straight tailsjust tend to form more perfect lateral packing assemblies. A moderate conformational disorder seems to be a quite common feature in slightly distorted hexagonal packings of organic molecules of different types, as was found, i.e., for statistic copolyesters of hydroxybenzoic and hydroxynaphthoic acid48 or qualitatively for the (CH& sequences of a hexagonal Langmuir-Blodgett packing of discotic pentaalkyne~.~~ The following average values were obtained for the bond angles in the headgroup region starting from the (CH2118 side of the molecule: C-0-C, 126" i.4";0-C-C, 125" & 3", C-C=C, 132" f 3"; C=C-C, 131" & 4", C-C-0, 126" & 4", and C-0-C, 129" i. 5". While the first five angles are in reasonable coincidence with the idealized values introduced above, the C-0-C angle toward the SOs- side of the molecule is remarkably increased by the influence of the simulated thermal vibrations. For the s < 6 k1range, however, Figure 11 reveals considerable differences as compared with the measured data, namely, a splitting of the first packing peak that was experimentally detected a t s = 1.52 A-l in two peaks a t s = 1.407 and 1.84 k l and some shifting of the maximum positions of the other peaks. Considerable deviations from a hexagonal packing are also clearly visible in Figure 9c, which shows a top view onto the simulated double-layer patch after the described 70-ps molecular dynamics run. There are still small regions with some remainder of hexagonal packing order, while most notably (48) Hofmann, D.; Schneider, A. I.; Blackwell, J. Polym. 1994, 35, 5603. (49) Janietz, D.; Hofmann, D.; Reiche, J . Thin Solzd Fzlms 1994, 244, 794.
on the right-hand side of the figure other chains tend to form a more general orthorhombic lattice. Here it is interesting to refer to a recent paper on molecular dynamics simulation of phospholipid double layers by Egberts et al.43 There a picture of the positions of the centers of gravity of their chains after a 80-ps molecular dynamics run for the gel phase a t 335 K also showed a mixture of different packing order (hexagonal and more liquidlike regions in their case), although these authors chose a considerably different approach than we did to model the bilayers. We utilized experimental WAXS data, indicating a relatively high degree of lateral hexagonal packing order and a relatively low area per (CHz)18 sequence of 20.0 piz, to set up an idealized starting structure which was then further refined. In contrast to this approach, Egberts et al., partly used a kind of ab initio procedure, insofar as they adopted random configurations of their molecules and then, using these molecules, formed a bilayer allowing restricted rotations and out-of-plane displacements. The outer starting dimensions of their rectangular packing cell were, of course, adopted from experimental data in the literature. In their further course of the simulation, a constanttemperature and constant-pressure dynamics run was performed a t 335 K and 1 bar. It should be noted that the simulated gel phase of Egberts et al. should have shown a tilt angle because of the large headgroups. This was, however,not the case and was related to an overestimation of electrostatic interactions in the headgroups and the partial use of united atoms. Thus, each of the tails of the molecouleshad a quite large cross-sectional area of about 24.2 A2. This fact might have been one reason why the quoted authors obtained regions of liquidlike disorder besides roughly hexagonally packed molecules. The available area per tail is also the most probable cause why Egberts et al. found a slightly lower content of trans conformations (88-89%) in the tails than we obtained for the SSPOM bilayers. The fact that we, despite a very different simulation approach, ended up with a similar problem as the cited paper due to the lateral chain packing after the molecular dynamics simulation leads us to the conclusion that the cause for this behavior is not just the limited simulation time, as supposed by these authors. Gel states in lipid and other surfactant systems are generally long-lived, and the question as to whether these states are real equilibrium phases or metastable states remains sometimes open.50 We have evidence from different experim e n t that ~ ~ the gel state of the water-SSPOM system is a colloidally structured dispersion of crystal hydrates and not an equilibrium phase. Thus, the equilibrium molecular dynamics techniques used here and in the referenced paper just may not be completely adequate for the simulation of all relevant features of such a system. Counterion Distribution. Due to the problem just mentioned with the distortion of the lateral packing order, we will not discuss the lateral charge distribution in detail. There should, however, not be much influence of the specific lateral packing of the SSPOM molecules on the simulated longitudinal charge distribution. In the case of type i molecular assemblies, the ions remain close to the SOs- groups even after the molecular dynamics stage. This is easy to understand, because the starting distance between the ions and this group is much below the Bjerrum length, that is, even much higher in the bilayer than in the surrounding water phase. Thus, the attractive electrostatic interactions could dominate ~
~
_
_
(50) Laughlin, R. G. The Aqueous Phase Behavzor of Surfactants; Academic: London, 1994; Chapter 11.
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3684 Langmuir, Vol. 11, No. 10, 1995
a
b
C
in the outer layers and 12 ions in the inner ones. to interpret the difference between the experimentally estimated bilayer thickness from SAXS and the corresponding one for the simulated packing of SSPOM molecules of about 38 A, it has to be consideredthat besides the Na+ ions, the terminal SO3- groups located in the interior of the bilayer, the ester groups more outside, and the water oxygen also contribute to the electron density, and the SAXS experiment will see this whole composite structure as a unit. Finally, it is worth mentioning that there was no tendency ofwater penetrating into the headgroup regions of the SSPOM assembly observed in our simulation. Obviously the most probable reason for this finding is that the strongly hydrophilic SO3- groups are buried in a considerable depth of about 8 A from the surface of the bilayer and that the surface region contains a considerable amount of hydrophobic groups.
VI. Conclusions
L
.
.
a
.
Figure 12. Two representative side views (above and below) of the simulated membrane after structure optimization (a) and a h r 30 ps (b)and 70 ps (c) ofmolecular dynamicssimulation time. Type ii Na+ ion starting distribution. The water is omitted for clarity. The sodium ions are the black circles. The dashed lines indicate the edges of the periodic boxes. over the influence of thermal vibrations introduced by the dynamic simulation. The case iii packings after the dynamics stage show a distribution of the sodium counterions over the whole region between the plane of SOsgroups and the solvent phase. This results from the combined effect of the relatively small distance between the SO3- groups and the Na+ counterions in the idealized starting structure, the thermal vibrations introduced by the dynamics simulation, and effects of sterical hindrance introduced by the presence of the headgroup atoms. The type ii model constitutes the most interesting case. Figure 12 shows two representative side views of the Na+ ion distribution after structure optimization (a) and after 30 ps (b) and 70 ps (c) of molecular dynamics simulation time. First, this picture confirms that there are no further qualitative changes in both the distribution of Na+ ions and the packing and local order of the SSPOM molecules for simulation times above 30 ps. The same effect can be found in the respective calculated WAXS patterns (not shown). The difference between the average z coordinates of all the counterions above and below the double layer is 42.8 A, while the respective value was 46.5 A for the idealized starting structure. The simulated value corresponds quite well with the result obtained for the thickness of the double layer from a fit of our previous SAXS results. The SAXS rofiles show an intensity minimum around s = 0.073 1 l (for the 16 wt % sample), which has been attributed to the form factor of the cross section of the bilayer^,^ giving an effective thickness of about 43 A. A closer look a t the detailed structure of the dynamically simulated Na+ion distribution a t either side of the SSPOM packing reveals a bimodal aspect. Most of the counterions are located in a layer with an average distance of about 4.3 A (the radius of a hydrated sodium ion) from the SSPOM bilayer. A minority of sodium ions, however, is concentrated in the headgroup region of the SSPOM assembly and behaves like the Na+ ions in the type iii packing. After the simulation, there were 52 ions
The long-chain surfactant sodium sulfopropyloctadecylmaleate forms a metastable gel state of stacked bilayer membranes below its Krafft boundary. The measured WAXS patterns indicate a well-orderedand dense in-plane structure of the membranes, consisting of hexagonally packed, untilted, and interdigitated molecules. The correlation length reaches almost 50 A. The estimated area per molecule in the bilayer is 40.0 A2and agrees with typical values for the gel phases of phospholipids. The in-plane packing of molecules has been simulated using molecular dynamics methods. Static molecular modeling leading to energy-minimized models for the investigated molecular assemblies gives the best fit to the experimentally observed intermolecular long-range lateral packing order. The simulation indicated conformational disorder in the flexible (CH21nregions ofthe bilayer. But the degree oforder of the statically simulated models is still too high, as indicated by the presence of higher order packing peaks that are not observed in experiment. The molecular dynamics modeling,however,gives a better representation of the short-range intramolecular order of the SSPOM molecules and some reasonable idea about the counterion distribution. Summarizing, the experimental and theoretical results characterize the investigated gel state of SSPOM as an extended bilayer structure, with the majority ofthe sodium ions formingdayersperpendicular to thez axis in a distance of about 4.3 A from both surfaces ofthe SSPOM assembly. The lateral order is hexagonal with considerable packing disorder. The long (CH& tails are not freely rotating but show a considerable distribution of backbone conformation angles, with the trans state being dominant.
Acknowledgment. This work was performed in the department of Prof. M. h t o n i e t t i to whom H.v.B. is indebted for support. We also thank Dr. P. Fink and Prof. D. Paul in whose departments the WAXS experiments and molecular simulations, respectively were carried out. H.v.B. is further grateful to Dr. K.-H. Goebel for providing the surfactant and Dr. G. Forster for valuable discussions. Supporting Information Available: Figure of the structural unit with all atom names and Cerius-bgffile including the atom names (third column), atomic coordinates (seventh to ninth columns), and partial charges (last column) (7 pages). Ordering information is given on any current masthead page. LA95 02094
