Structural investigations of dihexadecyl phosphate small unilamellar

Apr 15, 1991 - Biochemistry, University of British Columbia, Vancouver, British Columbia V6T ..... (21) Hope, M. J.; Bally, M. B.; Webb, G.; Cullis, P...
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Langmuir 1991, 7, 2592-2601

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Structural Investigations of Dihexadecyl Phosphate Small Unilamellar Vesicles Robin Humphry-Baker,? David H.Thompson,$ Yabin Lei,$ Michael J. Hope,l and James K. Hurst'J Institut de Chimie Physique, Ecole Polytechnique Federale de Lausanne, CH-1015 Ecublens, Lausanne, Switzerland, Department of Chemical and Biological Sciences, Oregon Graduate Institute of Science and Technology, Beaverton, Oregon 97006-1999, and Department of Biochemistry, University of British Columbia, Vancouver, British Columbia V6T 1 W5, Canada Received April 15, 1991. In Final Form: June 24, 1991 Freeze-fracture electron microscopy and light scattering methods have been used to determine morphologies of dihexadecyl phosphate (DHP) vesicles formed by ultrasonication. Contrary to an earlier report, the data indicate that the vesicles are highly hydrated spherical,or nearly spherical,particles with mean hydrodynamic radii of 10-13 nm. Vesicle sizes were unchanged when formed in the presence of any of a series of strongly binding N-methyl-N'-alkyl-4,4'-bipyridiniumions or when N-methyl-"-hexyl4,4'-bipyridinium ion was adsorbed to the outer interface of preformed vesicles, but the vesicles underwent progressive swelling with addition of increasing amounts of N-methyl-N'-hexadecyl-4,4'-bipyridinium chloride. This behavior was interpreted to indicate a bimodal binding pattern whereby the short-chain viologen bound at interfacial sites on the membrane surface, and the long-chain analogue intercalated within the bilayer plane, forming part of the membrane structure. The gel-to-liquid crystalline phase transition determined by differential scanning calorimetry was highly dependent upon the composition of the aqueous buffer used. In particular, phase transition temperature shifts and multiple thermogram peaks were observed with cationic amines, indicative of specific interactions with the DHP phosphate headgroups. The complex phase transitionbehavior inferred for DHP in tris(hydroxymethy1)aminomethane was confirmed by examination of the temperature-dependent Raman spectra of the vesicles.

Introduction Synthetic vesicles formed from amphiphilic dialkyl phosphate esters,' dialkyldimethylammonium ions? and similar surfactants have found widespread use in fundamental studies on interfacial structure and dynamics and transmembrane charge separation processes, and as organizing matrices for integrated chemical and photochemical s y s t e m ~ Despite . ~ ~ ~ their attractiveness as simple models for studying functional and structural properties of bilayers, these vesicles are in several respects only poorly characterized. For example, early quasielastic light scattering (QLS) data were interpreted as indicating that both dihexadecyl phosphate (DHP) and dioctadecyldimethylammonium chloride (DODAC) formed vesicles that are highly elliptically distorted prolate spheroids with major to minor axis ratios of about 25:1.616 Nonetheless, several researchers have assumed that the vesicles are spherical, and have cited potential sources of error in the QLS analyses that might have led to an incorrect deduction of shape.BJOAdditional studies are clearly desirable, particularly since quantitative interpretation of physical and

* T o whom correspondence should be addressed a t the Department of Chemical and Biological Sciences, Oregon Graduate Institute of Science and Technology, 19600 N.W. von Neumann Dr., Beaverton, OR 97006-1999. Ecole Polytechnique Federale de Lausanne. t Oregon Graduate Institute of Science and Technology. 8 Univeristv of British Columbia. (1) Mortari R. A.; Quina, F. H.; Chaimovich, H. Eiochem. Biophys.

Res. Commun. 1978,81, 1080. (2) Kunitake, T.; Okahata, Y. J. Am. Chem. SOC.1977, 99, 3860. (3) Fendler, J. H. Membrane Mimetic Chemistry;Wiley-Interscience: New . . York. - -. -, 1982. -(4) Hurst, J. K. In Kinetics and Catalysis in Microheterogeneorur Systems; Grdtzel, M., Kalyanasundaram, K., Eds.; Marcel Dekker: New York, 1991; p 183. (5) Herrmann, U.; Fendler, J. H. Chem. Phys. Lett. 1979, 64, 270. (6) Curiously, these vesicles have often subsequently been depicted as oblate spheroids.7*8

0743-7463191f 2407-2592$02.50/0

dynamical properties of vesicle-organized systems often requires an accurate description of the particle dimensions.7,8,11,12 We report herein results from studies germane to these issues involving measurements of dimensions of DHP small unilamellar vesicles (SUV)using freeze-fracture electron microscopy, integrated light scattering (ILS), and QLS methods, as well as measurement of their membrane phase transitions as detected by calorimetry and Raman spectroscopy. By comparing sizes of vesicles in which the topographic distribution of dopant amphiphilic viologens (N-alkyl-N'-methyl-4,4'-bipyridinium ions, C,MV2+) was varied, we have also obtained evidence that the intrabilayer location of the viologen is critically dependent upon its alkyl chain length.l3-le This capability to control microstructural organization has profound implications toward selection of transmembrane charge separation mechanisms in reactions mediated by membrane-bound redox c o m p ~ n e n t s . ~ J ~ J ~ (7) Nomura, T.; Eecabi-Perez, J. R.; Sunamoto, J.; Fendler, J. H. J. Am. Chem. SOC.1980,102, 1484. (8) Yamazaki, I.; Tamai, N.; Yamazaki, T. J. Phys. Chem. 1990,94, 516.

(9) Tricot, Y.-M.; Furlong, D. N.; Saeee, W. H.F.; Daivis, P.; Snook, I.; Van Megen, W. J. Colloid Interface Sci. 1984,97, 380. (10) Carmona-Ribeiro, A. M.; Yoshida, L. S.; Seeeo, A.; Chaimovich, H. J. Colloid Interface Sci. 1984,100, 433. (11) Hurst, J. K.;Thompson, D. H. P.; Connolly, J. S. J. Am. Chem. SOC.1987, 109, 507. (12) Cuccovia, I. M.; Feitosa, E.; Chaimovich, H.; Sepulveda, L.; Reed, W. J . Phys. Chem. 1990,94,3122. (13) Thompson, D. H. P.; Barrette, W. C., Jr.; H m t , J. K. J. Am. Chem. SOC.1987,109, 2003. (14) H m t , J. K.; Thompson, D. H. P. Inorg. Chem. 1987,26,39. (15) Colaneri, M. J.; Kevan, L.; Thompson, D. H. P.; Hurst, J. K.J. Phys. Chem. 1987, 91,4072. (16) Lei, Y.; Hurst, J. K. J . Phys. Chem. 1991, 95, 7918. (17) Patterson, B. C.; Huret, J. K. J. Chem. SOC.,Chem. Commun.

1990, 1137. (18) Patterson, B. C.; Thompson, D. H.; Hurst, J. K. J. Am. Chem. SOC.1988, 110, 3656.

0 1991 American Chemical Society

Dihexadecyl Phosphate Small Unilamellar Vesicles

Experimental Methods Viologen Syntheses. l-Methyl-4,4‘-bipyridinium Iodide. The procedure reported by GrHtzel and co-workers1swasmodified as follows: 4,4’-Bipyridyl (12.5 g, 80 mmol) was recrystallized successively from HZO and from petroleum ether/benzene and then dissolved in 100 mL of benzene that had been dried by distillation from calcium hydride in a 250-mL flask. Iodomethane (7.5 g, 52.9 mmol) was dissolved in 25 mL of dry benzene and added dropwise to the bipyridyl solution over a 2-h period. A yellow precipitate formed immediately; the reaction was stirred for 24 h and then filtered and the solid washed with 250 mL of warm ether to remove the unreacted bipyridyl starting material. Contamination by dimethyL4,4‘-bipyridiniumdiiodide was less than 2 % as determined by 1H NMR and silica gel TLC (CHCls/ CH30H/HOAc/H20,2515:4:2, by volume, UV visualization);Rf = 0. l-Hexadecyl-l’-methyl-4,4’-bipyridinium Dichloride. l-Methyl-4,4’-bipyridinium iodide (3.32 g, 11.1 mmol) was dissolved in 45 mL of acetonitrile that had been dried by distillation from calcium hydride and l-bromohexadecane (2.6 g, 8.5 mmol) added. This mixture was heated for 44 h, with 1.3-g additions of 1-bromohexadecane occurring at 10 and 34 h. After cooling, the red-orange solid was filtered, washed with 150 mL of acetonitrile and 50 mL of ether, and then air dried. The washed solid was dissolved in 100 mL of H20 and the picrate adduct precipitated by addition of a water-saturated solution of picric acid.20 After stirring for 30 min, the suspension was filtered, the yellow solid washed exhaustively with distilled water until the washes were colorless, and the remaining solid dried in a 50 O C oven. The material was dissolved in acetone that had been dried with calcium sulfate and the white chloride salt precipitated by bubbling with HC1 gas. The product was then purified by filtration and repeated recrystallization from acetone/methanol. Silica gel TLC (CHaOH/H20/50% EtNHsCl, 6:6:2) gave a single UV-active spot with Rf = 0.06 compared with methyl viologen which had Rf = 0.55. All other alkyl methyl viologen dichlorides were prepared in a similar manner. R, values on silica gel TLC were as follows: CsMVC12,0.66; CeMVC12, 0.68 C&lVClz, 0.67; CiZMVCl2,0.63;C1,MVC12,0.50; C&IVClz,0.00;C2oMVClz,0.00. The compounds were both UV active and stained blue with a dithionite spot test. Other Reagents. Dihexadecyl phosphate, all alkyl halides, and 4,4’-bipyridylwere obtained from Aldrich Chemical Co.; these compounds and other reagents obtained from commercial suppliers were best availablegrades and were used without further purification. Water purified by reverse osmosis/ion exchange chromatography was used to prepare reagent solutions and throughout all operations. Vesicle Preparation. For most of the studies reported, DHP SUVs were prepared by ultrasonic dispersal using either Heat Systems Ultrasonics Model W-225 or Branson Model B12 instruments equipped with a standard hom and tip. Appropriate amounts of the surfactant powder in 20 mL of aqueous buffer were sonicated for two 10-minperiods at an output control setting of 4.0 (30 W) with an intervening 5-min period for cooling. In instances where viologen binding at both inner and outer aqueous hydrocarbon interfaces was desired, C,MVz+ dichlorides were added to the aqueous medium before sonication. To prepare vesicles containing C,MV2+bound only at the external interface, portions of the clarified suspension were flow-mixed with viologen stock solutions through a 12-jettangential mixer attached to syringes mounted on a manually driven push plate. This procedure minimized viologen-induced fusion of the preformed vesicles. The vesicle suspensions were then centrifuged for 6090 min at lOOOOOg in a Ty65 rotor of a Beckman L8-M ultracentrifuge or in an Omikron ultracentrifuge. By completion of the centrifugation step, the sample had separated into three fractions consisting of a very small gelatinous pellet covered with a relatively viscous layer representing less than 5% of the total liquid volume and the slightly translucent bulk supernatant, which appeared homogeneous. Portions taken for analysis from (19) Pileni, M. P.; Braun, A. M.; GrHtzel, M. Photochem. Photobiol. 1984, 31, 423. (20) Krieg, M.; Pileni, M. P.; Braun, A. M.; Gr&tzel,M. J. Colloid Interface Sci. 1981,83, 209.

Langmuir, Vol. 7, No. 11, 1991 2593 different levels within the centrifuge tube were isolated by aspiration with a Pasteur pipet to minimize intralayer mixing. Concentration levels of bound viologens were determined after centrifugation by optical spectroscopy using previously determined extinction coefficients;13background interference arising from SUV particle scattering was negligible in the near-WV region. DHP vesicles of varying sizes were also prepared by extrusion to investigate relationships between size and thermal phase transitions. Solid DHP was dispersed by subjecting suspensions in aqueous buffer to 10 freeze-thaw cycles. The suspension was then passed at 90O C under 300-800 psi of pressure through polycarbonate membranes with appropriate pore sizes ranging from 0.03 to 0.2 pm using a device (The Extruder) manufactured by Lipex Biomembranes Inc. For each preparation, the suspensions were cycled through the extruder 3-15 times. Freeze-Fracture Electron Microscopy. Samples were prepared for electron microscopy in a Balzers BAF 400D apparatus using either a quick freeze (liquid propane cryogen maintained at 77 K and copper mesh sandwich grids) or conventional freezing technique (liquid nitrogen coolant and copper cup sample holders; 25% glycerol by volume added to vesicle samples as cryoprotectant).21 Results obtained were independent of the freezing method used. Sample grids were then transferred to a liquid nitrogen cooled stage and fractured with a stainless steel knife. The fractured samples were shadowed with platinum at 45O and coated with carbon at 90° relative to the sample plane. The temperature during fracture and shadowing was approximately 163 K; the chamber pressure was maintained between le7and 2 x 10” Torr during these operations. After warming to room temperature, the replicas were washed with distilled water and bleach and transferred to copper grids. Images were obtained using a Phillips 400 electron microscope;size distribution analysis was carried out as described by Guidot and Baudhuin.22 Light-Scattering Experiments. The light-scattering spectrometer used in these studies is a two-photomultiplierinstrument capable of simultaneously recording QLS and ILS data,m the discriminated output pulses of the photomultipliers were coupled directly to the two inputs of a Brookhaven Instruments BI-2020 correlator which was controlled viaa DMA interface to a HewlettPackard HP-9845computer. For all measurements, the light source was a 5-mW He-Ne laser (632.8nm emission). Proper operation of the spectrometer was checked using various standards prior to making any measurements. The angular independence of the Rayleigh ratios (R(8))of dust-free samples of toluene and a 20 mg/mL aqueous solution of the isotropic scatterer octakis(ethy1eneglycol) mono-n-dodecyl ether (C12E8, Nikko Chemicals, Tokyo) was found to be better than i l %over an angular range of 20-160’. The magnitude of R(8) for ClzEe (6.808 X lod cm-l at 632.8 n m 9 was confirmed by measurement with respect to toluene (R(8)= 1.359 X lod cm-l at 632.8 nms). The autocorrelation functions of polystyrene latex spheres of known size (10.9,25.6,and 48.1 nm) (Polysciences,Inc.) dispersed in 5% sodium dodecyl sulfate solutions were used to evaluate the system performance in QLS. The technique for sample treatment adopted after various trials was to use individual vesicle preparations for a complete series of analyses. Stock solutions were refrigerated following ultracentrifugation, from which a series of samples were prepared by appropriate dilutions with aqueous buffers. Rayleigh ratios of the samples at differing angles and concentrations were calculated with reference to 20 mg/mL of ClzE&. The refractive index increment (dnldc) of the DHP vesicles was determined using a Chromatix, Inc., Model KMX-16 differential refractometer to be dnldc = 0.1345 mL/g at 632.8 nm and 295 K. The intensity autocorrelation function,g2(+),for a typical distribution (21) Hope,M. J.; B a y , M. B.; Webb, G.; Cullis, P. R. Eiochim. Eiophy8. Acta 1986, 812, 55. (22) Guidot, €2.; Baudhuin, P. In Lipouome Technology; Gregoriadir, G., Ed.;CRC Press: Boca Raton, FL, 1984; Vol. I, p 163. (23) B a d e , S.; Schmidt, M.; Burchard, W. hfaCrOmOhbk8 1982,15, 1604. (24) Degeorgio, N.; Corti, M.; Giglio, M. Light Scattering in Liquida and Macromolecular Solutionu; Plenum Prase: New York, 1980. (25) Pike, E. R.; Pomeroy, W. R. M.; Vaughan, J. M. J. Chem. Phys. 1975,62,3188.

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2594 Langmuir, Vol. 7, No. 11, 1991 of DHP SUVs was expressed as a sum of single exponentials:

2(7)= 1 + E a i exp(-rp) Several deconvolution algorithms were used to calculate ai. A coherent reproducible description of the sample was sought in at least three of the methods before the size distribution parameters were accepted. Methods included the cumulant approach,a a nonnegative least-squares method:' the inverse Laplacetransform method of Ostrowskyet ala,%and CONTIN,29 the method distributed by Provencher for inverting the data. Phase Transition Measurements. Thermograms of DHP vesicle suspensions were obtained using a Perkin-Elmer Model DSC7 differential scanning calorimeter and TAC7IPC instrument controller interfaced to an IBM PS/2 Model 50 Z computer. For simple DHP suspensions, the temperature was typically scanned from 10 to 85 O C , whereas for C,MV2+-loadedvesicles a lower limit of 20 O C was used to avoid possible precipitation under medium conditions in which the vesicles were relatively unstable; the applied heating rate was 5 OC/min. Data reduction and analyses were performed using software supplied by the manufacturer,with the exception that transition peak full widths at half-maximum(fwhm)were calculatedmanually from the thermograms. Several DHP vesicle suspensions prepared for DSC analyses were also investigated by Raman spectroscopy using a Dilor Z 16 spectrometer interfaced to an IBM AT personal computer. Samples were sealed in 1.6-1.8-mm4.d. capillary tubes and illuminated with a 150-mW 457.9-nm line from a Coherent Innova 90 argon ion laser; 90O-scattered photons were analyzed using software developed by Professor Thomas M. Loehr (OGI) and associates. Sampletemperatures were adjusted by directing a heated stream of argon gas from a Varian Associates variabletemperature controller directly upon the mounted capillary. A calibration curvecorrelatingthe actual temperatureto instrument settingswaa constructedfrom readings taken with a thermocouple placed in the capillary mounting.

Results Vesicle Sizes by Electron Microscopy. Electron micrographs of freeze-fracture replicas from DHP centrifuge supernatant fractions exhibited small, roughly spherical features (Figure 1). The shapes of these particles were considerably more irregular than those usually found for phospholipid liposomes, although several synthetic diacylphosphoglyceride vesicles have given similarly shaped structures when frozen from their ordered, or gel, phase (M. J. Hope and P. Cullis, unpublished observations). These irregularities might therefore reflect the relative difficulty in cleaving the ordered bilayers. For all samples examined, size distribution analyses indicated that the DHP SUVs formed unimodal populations with relatively narrow ranges of apparent diameters. A representative histogram is given in Figure 2, and quantitative data obtained are listed in Table I. In general, the distributions were quite symmetrical, giving mean diameters that were very nearly equal to the corresponding mode diameters (Table I). Vesicles doped with C18MV2+ion either at the outer or both interfaces were indistinguishable within experimental uncertainty from undoped SUVs. Light Scattering: Particle Size Dependence upon Experimental Protocols. Quasielastic light scattering affords a convenient means for determining vesicle sizes through calculation of z- or intensity-averaged effective hydrodynamic radii ( & ) z from the corresponding z-avobtained from analysis eraged diffusion coefficients (D,) (26) Koppel, D. E. J. Chem. Phys. 1976,57, 4814.

(27) Algorithm supplied by Brookhaven Instrumnt Corp. based upon methods in Measurement of Suspended Particles by QUa8ieh8tiC Light Scattering; Dahneke, B. E., Ed.; Wiley-Interscience: New York, 1983. (28) Ostroweky, N.; Sornette, D.; Parker, P.; Pike, E. R. Opt. Acta 1981,28,1059. (29) Provencher, S. W. Makromol. Chem. 1979, 180, 201.

of the autocorrelation decay curves.90 The exponential sampling method used for treating the correlation dataz8 also provides information on the polydispersity of the vesicles. We have routinely used this technique over the past several years to characterize our DHP SUV preparations, which includes a total number approaching 100 samples. Reproducibilities of individual particle sizes prepared under identical conditions were 1+15%. The precision of the light-scattering instrument is estimated from analyses of latex spheres to be about 594, so the small additional error may represent uncontrolled variations in preparative conditions. Investigation of operational variables including use of a tapered sonicator microtip in place of the standard flat tip, micropore filtration, sonication time (beyond 15 min) and temperature, and centrifugation time (beyond 60 min) revealed no systematic trends in vesicle sizes and polydispersities, although sonication or centrifugation for shorter periods tended to give suspensions with 30 5% larger ( & ) z values and polydispersity indices. All data reported herein were taken on SUV suspensions following the protocols described in the Experimental Methods, which gave high sample-to-sample reproducibility. Furthermore, identical samples were used for comparisons between parameters derived from QLS and ILS measurements to deduce shapes. Despite these precautions, the dataset obtained in early studies deviated significantly from a more recently obtained set. Specifically, in the earlier work, particle sizes and polydispersities were larger than attributable to experimental uncertainty, e.g., with DHP radii ranging from (Rh),= 14-18nm ascompared to ( & ) z = 11-13nm in the recent studies. The only substantive procedural change involved the ultracentrifuge used for final purification; although the gravitational forces applied were nominally the same, the size of the rotor sample tube was larger (25 vs 8 mL) in the earlier studies, which may have contributed to less efficient sizing. Since light scattering is highly biased toward larger particles,3O apparent mean size variations of this magnitude could be the consequence of very small differences in the populations of aggregated or fused vesicles remaining in the supernatant fraction. However, this notion is not well supported by comparisons of population distributions derived from inverse Laplace transforms of the autocorrelation decay f u n c t i o n ~ . ~ * 3 ~ Typical intensity-averaged distributions are displayed in Figure 3, which have very similar shapes. The earlier preparations had larger mode radii and polydispersities, however. Results from both data sets are reported in this section; where cross-comparisons were possible, analysis led to the same qualitative conclusions for both distributions. Experiments were also made to investigate size distribution gradients within the layered zones in the centrifuge tubes. Supernatant.containing either DHP vesicles or CISMV2+-DHP vesicles was separated into three approximately equal layered fractions; the molar ratio for these studies was varied over the range [C16MV2+]/[DHP] = 0-0.06. In all cases, measured mean ( & ) z values were identical to within 2-3 5%. In contrast, radii from the small dense zone at the bottom of the tubes were 100%greater than the supernatant fractions. Radii from vesicle suspensions that had been passed through 0.22-pm pore size filters, but not fractionated by centrifugation, were 3050 5% greater than the centrifuged supernatant fractions.

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(30) See, e.g., Berne, B.; Pecora, R. Dynamic Light Scattering; W. J. Wiley: New York, 1976. (31) Provencher, S. W. Comput. Phys. Commun. 1982,27, 229.

Dihexadecyl Phosphate Small Unilamellar Vesicles

Langmuir, Vol. 7, No. 11, 1991 2595 b

a

C

Figure 1. Freeze-fracture electron micrographs of DHP SUV: panel a, 8 mM DHP dispersed in 20 mM Tris(Cl), pH 8.0; panel b, with 250 pM ClsMV2+added to preformed vesicles; panel c, vesicles formed in buffer containing 250 pM ClsMV2+.

DHP dispersed by bath sonication gave vesicles in the centrifuged supernatant fraction that were about twice as large as the probe-sonicated vesicles. Centrifuged supernatant DHP and C16MV2+-DHP SUVs did not undergo

any change in average size or size distributions when aged at room temperature for up to 5 days, which was the longest period examined. The medium for these studies was 20 mM Tris(Cl),pH 8.0. Supernatant C16MV2+-DHPS u v s

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2596 Langmuir, Val. 7, No. 11, 1991 80 0 0)

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Figure 2. Histogram of DHP SUV from freeze-fractureelectron microscopy (8-16 mM DHP S W in Tris(Cl),pH 8.0).

Table 1. DHP Vesicle Sizes* apparent radius, nm by electron symmetry microscopyd byQLSe 12.6 (13); 9 13.7 (13);8 i/o i/o 11.3 (9.7) 11.6 (9.7) i/o 11.7 (9.6) i/o 12.2 (10.3) i/o i/o 11.8 (9.8) i/o 12.6 (13); 14 o 13.4 (13); 10 12.0 (10.0) i/o i/o 13.0 (10.6)

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Figure 3. z-Averagedistributionof DHP S W (4 mM DHP in 20 mM Tris(Cl),pH 8.0): panel a, Beckman L-8 centrifuged; panel b, Omikron-centrifuged. Mean (mode) radii and polydispersities were a, 11.2 (9.7) nm, 0.16; b, 17.7 (14.6) nm, 0.32.

0 In 20 mM Tris(Cl),pH 8.0. b Mole fraction of C,,MV*+ in the SUV. i/o refers to viologen bound at both interfaces, o to viologen at only the outer interface. d Number-average mean radius (mode radius); Poisson coefficientof variation, % ,definedm 100/t/n, where n is the number of sized particles forming the distribution profile.

e

z-Average mean radius (mode radius).

([C,MV2+]/([DHP] = 0.03) were eluted from a Sephacryl S-10o0Superfine gel sieving column32 as a single peak with a mode radius identical within experimental uncertainty to the mode radius of the applied vesicles. Reproducible results were obtained only after repeated equilibration of the stationary phase with excess DHP vesicles. Integrated Light Scattering. The dimensionsof these vesicles are within the Rayleigh-Gans domain, for which 47rrlAnl/X0