J. Phys. Chem. 1989, 93, 1522-1526
1522
Raman Spectrum of Interstftlal Water in Biological Systems Michel Lafleur, Marie Pigeon, Michel Pczolet, * Centre de recherche en sciences et inginierie des macromoldcules, Departement de chimie, Faculti des sciences et ginie, Universite Laual, Cite Uniuersitaire, QC, G1K 7P4 Canada
and Jean-Pierre CaillC Dipartement de physiologie et biophysique, Faculti de midecine. Uniuersiti de Sherbrooke, Sherbrooke, QC, J1 H 5N4 Canada (Received: May 25, 1988; In Final Form: July 14, 1988)
The Raman spectra of water at different temperatures in suspensions of multilamellar aggregates, unilamellar vesicles and micelles of anionic and zwitterionic phospholipids, as well as the spectrum of water in suspensions of lipid/melittin complexes and in muscle fibers, have been investigated. The results obtained establish a relationship between the size of the water domains in these assemblies and the profile of the 0-H stretching mode region. A decrease of the intensity of the 3240-cm-l component relative to that of the 3440-cm-' component is observed when water is trapped in small interstices (around 1-2 nm), such as those found between phospholipid bilayers or between myosin molecules in muscle fibers, and this effect is independent of the nature of the surface. The presence of small interstices also prevents some of the water molecules from crystallizing at -20 OC. Results on uncoupled 0 - H oscillators show that this spectral change is associated with the decrease of the long-range intermolecular coupling in small water domains displaying greater orientational disorder.
band due to the 0-H stretching vibrations of water in different biological systems. In particular, the influence of the various organized structures formed by phospholipids in aqueous solution and that of the highly ordered protein lattice of muscle fibers will be discussed. The main advantage of these systems is that their supramolecular structure has been well characterized by different physical techniques and can be changed rather easily. The results obtained establish a relationship between the size of the water domains and the profile of the Raman bands due to the 0-H stretching vibrations and are interpreted in terms of long-range intermolecular vibrational coupling.
Introduction The structure of liquid water is very complex because of the dominant role played by hydrogen bonds in the condensed phase. Because of the paramount importance of water, especially for biological systems, it has been the object of several experimental and theoretical Raman spectroscopy has proved to be a powerful technique to study the structure of water and has been widely ~ s e d . ~Many , ~ studies on the effect of partial or total deuteriation of waters7 or hydrogen peroxide8 and on the effect of temperature,6q7s9ions,I0J1 and organic solventsi2 provide information about the 0-H stretching region of the Raman spectrum of water. Nevertheless, the interpretation of the broad band around 3300 cm-l associated with the 0-H stretching vibrations of water is still a matter of controversy. This confusion arises primarily from two sources. First, various conflicting models have been proposed describing the water structure as a continuum of molecular geometry or as an equilibrium between a definite number of types of water m ~ l e c ~ l e s . ~ Seco - ~ Jnd, ~ J the ~ possibility of intra- and intermolecular vibrational coupling and Fermi resonance between the first overtone of the angular bending mode at 1650 cm-' and the 0-H symmetric stretching mode5,i5-i8increases the difficulty of assigning unambiguously the 0-H stretching band. In the following we present some results on the shape of Raman
Experimental Section Dipalmitoylphosphatidylcholine (DPPC), dipalmitoylphosphatidylglycerol (DPPG), myristoyllysophosphatidylcholine (lyso-MPC), and bee venom were purchased from Sigma Chemical Co. (St. Louis). Heavy water was obtained from MSD Isotopes (Montreal, Canada). Melittin (Mel) was purified from bee venom according to the procedure described e l s e ~ h e r e . ' ~Multilamellar *~ dispersions were obtained by hydrating the lipids with 100 mM phosphate buffer, pH 7.6, containing 10 mM EDTA. These suspensions containing 10% lipid by weight were incubated above the liquid-crystalline phase transition and shaken mechanically. Unilamellar vesicles of DPPC were formed by sonication of the lipid dispersion. After this treatment, the sample was centrifuged to remove small particles of the ultrasonic probe, leading to a transparent lipid suspension. DPPC/Mel complexes in the opaque and transparent phases were obtained as described by Lafleur et a1.20 Single muscle fibers were isolated from the depressor muscle of the giant barnacle (Balanus nubilus) and pulled in the lumen of glass capillaries which fitted the diameter of the fibers. The water content of these fibers was adjusted by soaking them in isotonic or hypertonic sucrose solutions, before their insertion in the capillaries. The capillaries were cut in 0.5-0.7 cm segments and incubated in a heavy water relaxing solution (1 50 mM glycine, 40 mM taurine, 50 mM K2S04, 5.0 mM K2HP04, 1.3 mM KH2P04,2.0 mM MgATP, and 0.5 mM EGTA) that mimics the intracellular fluid. Raman spectra were recorded with a spectrometer described elsewhere.21 Spectra excited with the 514.5-nm line of an argon
(1) Eisenberg, D.; Kauzmann, W. The Structure and Properties of Water; Oxford University Press: Oxford, U.K., 1969. (2) Franks, F. In Wafer-A Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1972; Vol. 1, Chapter 1. (3) Walrafen, G. E. In Water-A Comprehensive Treatise;Franks, F., Ed.; Plenum: New York, 1972; Vol. 1, Chapter 5. (4) Scherer, J. R. In Advances in Infrared and Raman Spectroscopy; Clark, R. J. H., Hester, R. E., Eds.; Heyden: London, 1978; Vol. 5 , Chapter 3. ( 5 ) Sokolowska, A.; Kecki, Z . J. Raman Spectrosc. 1986, 17, 29. (6) B a d , R.; Wiafe-Akenten, J.; Taaffe, J. L. J . Chem. Phys. 1982, 76, 2221. (7) Scherer, J. R.; Go, M. K.; Kint, S. J. Phys. Chem. 1974, 78, 1304. (8) Gigusre, P. A.; Pigeon-Gosselin, M. J . Raman Spectrosc. 1986, 17, 341. (9) DArrigo. G.;Maisano, G.; Mallamace, F.: Migliardo, P.; Wanderlingh, F. J. Chem. Phys. 1981, 75,4264. (IO) Walrafen, G. E. J. Chem. Phys. 1970, 52, 4176. ( 1 1) Rull, F.; de Saja, J. A. J . Raman Spectrosc. 1986, 17, 167. (12) Scherer, J. R.; Go, M. K.; Kint, S. J. Phys. Chem. 1973, 77, 2108. (13) Stanley, H . E. J. Phys. 1979, A12, L329. (14) Stanley, H. E.; Teixeira, J. J. Chem. Phys. 1980, 73, 3404. (15) Whalley, E. Can. J. Chem. 1977, 55, 3429. (16) Sceats, M. G.;Stavola, M.; Rice, S.A. J. Chem. Phys. 1979, 71, 983. (17) Ratcliffe, C. I.; Irish, D. E. J. Phys. Chem. 1982, 86, 4897. (18) Green, J. L.; Lacey, A . R.; Sceats, M. G.J. Phys. Chem. 1986, 90, 3958.
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(19) Dasseux, J. L.; Faucon, J. F.; Lafleur, M.; PCzolet, M.; Dufourq, J. Biochim. Biophys. Acta 1984, 775, 37. (20) Lafleur, M.; Dasseux, J. L.; Pigeon, M.; Dufourcq, J.; PCzolet, M. Biochemistry 1987, 26, 1173. (21) Savoie, R.; Boulb, B.; Genest, G.; PCzolet, M. Can. J . Specrrosc. 1979, 24. 112.
0 1989 American Chemical Societv -
Interstitial Water in Biological Systems
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 1523
A ...’
u 3000 3500 Frequency S h i f t ( c m - l )
Figure 1. Raman band due to the 0-H stretching vibrations of water at -20, IO, and 50 OC (a) for 100 mM phosphate buffer, IO mM EDTA, pH 7.6, (b) for a multilamellar DPPC dispersion (10% by weight), and (c) for a 10% by weight suspension of DPPC unilamellar vesicles. The buffer spectra are reproduced with dotted lines in b and c.
laser were recorded with a resolution of 5 cm-I. The power at the sample was between 50 and 400 mW, depending on the optical quality of the sample and the luminescence background. No correction for wavelength dependence of the Raman signal was made and a polarization scrambler was introduced between the sample and the entrance slit of the monochromator to eliminate polarization artifacts from the gratings.
Results Phosphate Buffer. Raman spectra of the 0-H stretching mode region of water in a 100 mM phosphate buffer at -20, 10, and 50 OC are reproduced in Figure la. Within experimental error, the spectra are identical with those of pure water at the same temperatures. At -20 OC, this spectral region is dominated by a sharp band at 3140 cm-’ characteristic of the crystalline ice lattice,22while for liquid water the 0-H band is very broad and displays two maxima at 3240 and 3440 cm-’. When liquid water is heated, there is an increase of the intensity of the band at 3440 cm-l relative to that of the low-frequency component. The assignment of these bands is not yet clearly established. Rull and de Saja” and Sokolowska and KeckiS have associated the band at 3440 cm-l to the 0-H antisymmetric stretching vibration and the 3240-cm-’ feature to Fermi resonance interaction between the symmetric 0-H vibration and the overtone of the 1650-cm-l bending mode. Other groups have assigned these two bands to two different species of water molecules, symmetrically and asymmetrically bound,’ with linear and bifurcated hydrogen bonds,23 and strong and weak hydrogen bonds,24 or with open (tetrahedrally hydrogen bonded) and closed9 structures. Whichever model is the right one, the variation of the profile of the 0 - H stretching band of water is always associated with the existence of the association of the water molecules in the liquid phase. When the structure of water is perturbed by heating7z9 or by addition of salts,I0J1a certain number of hydrogen bonds is affected and there is an increase of the intensity of the highfrequency component of the 0-H band. Besides these two maxima at 3240 and 3440 cm-I, a weak band is always observed as a (22) Sivakumar, T. C.; Schuh, D.; Sceats, M . G.; Rice, S. A. Chem. Phys. Lefr. 1977, 48, 212.
( 2 3 ) GiguEre, P.A. J . Raman Specfrosc. 1984, 15, 354. (24) Dufourcq, .I.; Faucon, J. F.; Fourche, G.; Dasseux, J. L.; le Maire, M.; Gulik-Krzywicki, T. Eiochim. Eiophys. Acta 1986, 859, 33.
Frequency S h i f t (cm-1)
Figure 2. Raman band due to the 0-H stretching vibrations of water at 10 OC for DPPC/Mel complexes (incubation molar ratio of 15 lipid molecules per melittin) in (a) the transparent and (b) the opaque phases. The buffer spectrum is reproduced with a dotted line.
shoulder around 3600 cm-’ and it has been assigned to free or weakly bound 0-H Phospholipids. The spectrum of water in a multilamellar DPPC dispersion (10% by weight of lipid) at different temperatures is shown in Figure 1b. The spectra in this figure are plotted in such a way that the band with the maximum intensity has always the same height. As seen in Figure lb, at -20 OC the intensity of the sharp band at 3140 cm-’ relative to that of the broad feature at higher frequency is smaller in the presence of the lipid. Since the 0-H band of supercooled water is centered around 3200 ~m-’,’,~it appears that a smaller fraction of the water molecules adopts the ordered crystalline structure in the multilamellar dispersion of DPPC. At 10 OC, the intensity of the 3440-cm-’ component of the water band relative to the 3240-cm-I feature is higher in the spectrum of the DPPC multilamellar dispersion than in the buffer spectrum. This phenomenon, already observed on heating pure water or in the presence of structure breaker ions,7*”’ has never been detected in the case of a lipid dispersion. The same effect is also observed at 50 OC, but it is smaller since at this temperature the structure of water is already perturbed. An identical behavior is also observed with a dispersion of the charged lipid DPPG. The spectra of a 10% by weight DPPC suspension of unilamellar vesicles at -20, 10, and 50 OC are shown in Figure IC. As opposed to the case of the multilamellar dispersions, the spectral profile of the 0-H band of water for the suspension of vesicles of approximately 20-100 nm in diameter is very similar to that observed for the buffer. Since the Raman spectrum of water seems to depend on the supramolecular structure of the lipid rather than on the lipid itself, we have also studied a third type of assembly, that is, micelles of lyso-MPC. Like for vesicles of DPPC, micelles of lyso-MPC do not affect the shape of the water 0-H Raman band (data not shown). LipidlMelittin Complexes. Melittin is a small toxin extracted from bee venom that causes the lysis of membranes. After incubation at a temperature higher than that of the gel-to-liquid crystalline phase transition of DPPC, it disrupts the multilamellar structure of the lipid dispersions, inducing the formation of small discoidal particles of approximately 25 nm in diameter as measured by electron microscopy and quasi-elastic light s ~ a t t e r i n g The .~~ structure of these particles is very similar to that of complexes of phospholipids and apolipoproteins and consists of a phospholipid bilayer disk whose hydrophobic edges are shielded by a melittin layer. Samples of DPPC/Mel particles so obtained are transparent and metastable. With time, the samples become opaque due to the aggregation of the discoidal particles, which results in the expulsion of melittin from the bilayer.20 Figure 2 shows the spectrum (2700-3900 cm-I) of DPPC/Mel complexes for a phospholipid to protein mixing molar ratio of 15 in the transparent and opaque phases. When the complex is constituted of small lipid/Mel particles, Le., in the transparent phase, the profile of the 0-H stretching band is very similar to that of the buffer. However, when the sample is incubated at 20 O C and becomes opaque, the intensity of the 3440-cm-’ band relative to that of the 3240-cm-I band increases progressively with the aggregation
1524 The Journal of Physical Chemistry. Vol. 93, No. 4, 1989
2000
2500 Frequency S h i l l
Lafleur et al.
3000
lcm-ll
Figure 3. Raman band due to the 0-D stretching vibrations of D,O at IO ‘C for the relaxing solution (...) and for muscle fibers with water contents of 80% (--) and 61% (-) by weight. Spectra are normalized so that the intensity of their high-frequency component has the same
intensity. of the complexes to reach a value comparable to the ratio observed for a pure DPPC multilamellar dispersion. Muscle Fibers. To generalize the above findings, we have also studied the spectrum of water in barnacle muscle fibers, a real biological system totally different from the first two. The cytoplasm of these fibers is composed mainly of myofibrils stacked parallel to the long axis of the cell. Each myofibril contains several myofilaments that are mainly composed of myosin and paramyosin (thick filament) and of actin and tropomyosin (thin filament). The water molecules are distributed inside and outside the filaments and myofibrils. A fraction of the muscle fiber water does not freeze, even at low temperature,’s and it is generally referred to as bound water. The normal water cantent of these fibers, which is approximately 80% can be reduced by soaking the fibers in an hypertonic solution. Previous results have shown that only the bulk water is removed from the fibers during this treatment.” Raman measurements on the muscle fiber were done in DzO to avoid the weak protein spectral contribution at approximately 3300 cm-’ which is superimposed with the 0-H band of water.’l The bands due to the 0 - D stretching modes of heavy water in the relaxing solution and in muscle fibers with normal and reduced water contents (80% and 61% by weight, respectively) are compared in Figure 3. Spectra are plotted to have the same height for the high-frequency component. As seen, there is a decrease of the intensity of the low-frequency component of the 0 - D band as the water content is reduced, Le., when some of the bulk water is removed.
Discussion Because of their amphiphilic character, phospholipids can adopt several supramolecular structures in aqueous solutions. These structures, represented in Figure 4, all display a locally charged surface because of the stacking of the polar headgroup of the lipid. The bonding of water molecules on this interface by electrostatic or dipolar interactions or by hydrogen bonding can in principle affect the bond energies and the geometry of these water molecules and, therefore, the shape of the broad Raman band associated with the 0-H stretching vibrational modes. However, the above results show that the profile of 0-H Raman band of water in suspensions containing 10%lipid by weight is not sensitive to the surface charges of phospholipids since both anionic and zwitterionic (25) PCmlet. M.; Pigeon-Gasselin, Biophys. Aerr? 1978. 544, 394.
M.; Savoie, R.; CaillC, J. P. Bioehim.
Figure 4. Schematic representation for the organized structures adopted by phospholipids in water: (A) the multilamellar liposome, (B) the unilamellar vesicle, and (C) the micelle.
lipids give similar results and also because the 0-H band is modified only when phospholipids are arranged in multilamellar assemblies. Therefore, the shape of the 0-H band of water depends on the supramolecular structure adopted by phospholipids rather than on surface interactions. This conclusion is further reinforced by the results o f a theoretical study by Scottz6showing that the perturbation induced by the phosphatidylcholine polar headgroup on the ordering of the water molecules is strong only below 0.6 nm and decreases rapidly with the distance. In addition, it has recently been shown by neutron diffraction that the modification of the structural arrangement of water by silica surfaces does not extend beyond 1.0 n ~ n . ~ ’ What is, then, at the origin of the intensity variation of the C-H Raman band of water in a multilamellar lipid dispersion or in muscle fibers? A common characteristic for these two systems is the presence of small interstices in which water molecules are located. Multilamellar lipid aggregates or liposomes are compoxd of several alternating layers of lipid and water in an onionlike structure of diameter between 100 and 800 nm. The maximum value of the long spacing for the fully hydrated gel phase determined by small-angle X-ray diffraction is 6.4 nm for D P P P and 6.2 nm for DPPGZ9a t pH 8. Since the bilayer thickness is approximately 5 nm,the thickness of the interlamellar water layers in DPPC or DPPG liposomes is around 2.0 n~n,’*”~.’’which is enough space to stack approximately seven water molecules. On the other hand, for vesicles and micelles of phospholipids, which do not affect the shape of the 0-H band, small interstices are not present, the inside diameter of the vesicles of DPPC used to obtain the spectra measuring from 10 to 90 nm, which is at least 5 times bigger than the interlamellar distance in DPPC dispersions. Therefore, the present results suggest that the relative intensity (26) Scott, H.L. Chem. Phys. Lett. 1984. 109, 570. (27) Steytler. D.C.; Dore. J. C.;Wright. C. J. Mol. Phys. 1985.48, 1031. (281 Ruocco. M. J.:Shiolcv. G. G. Biochim. Bioohvs. Aero 1982.691.309. . ti95 Watts, A,;Harlos, K.; Marsh, D.Bioehim: iophys. Acto i 9 8 l ; 645, 91. (30) Janiak, M. J.; Small, D.M.;Shipley, G. 0 .Biochemistry 1976, i s . 4575. (31) Alban, N.J . Chem. Phys. 1983. 78, 4676. 1
I.
Interstitial Water in Biological Systems of the two components of the Raman band due to the 0-H stretching modes strongly depends on the extent of the water domains. This spatial restriction that seems to be at the origin of the perturbation of the 0-H Raman band profile of water could also be the source of problems encountered during the subtraction of the infrared water absorption from the spectra of lipid dispersion~.~* The results obtained on DPPC/Mel complexes and muscle fibers support the above interpretation+ For suspensions of discoidal particles of DPPC/Mel complexes, which contain no restricted domains in which some water is trapped, the Raman spectrum of water is almost identical with that of pure water (Figure 2). On the other hand, as the proportion of water located in the interstices between the myosin molecules forming the thick filaments of muscle fibers increases relative to the bulk water around the filaments and the myofibrils, the intensity of the low-frequency component of the 0-D stretching band decreases. It must be emphasized that this effect is observed even though the nature of the surface of the myosin molecules is quite different from that of phospholipid bilayers. The 0 - H stretching Raman spectrum of a DPPC dispersion at -20 OC (Figure lb) reveals the presence of supercooled water a t this temperature. Several techniques, such as calorimetry, nuclear magnetic resonance spectroscopy, and X-ray diffraction, have shown that the hydration layer of DPPC is composed of 10-15 water molecules per lipid that are tightly bound to the lipid surface and that remain unfrozen at low t e m ~ e r a t u r e . ~For ~,~~ a dispersion with a water content of 90%, this corresponds only to 3-4% of the water molecules, which is too small to explain the spectral difference at -20 OC in Figure lb. Therefore, it seems that the presence of small interstices also prevents water from crystallizing. This hypothesis is further reinforced by the fact that a significant amount of the supercooled water is also present is muscle fibers at low temperatureZSand also by the similarity between the spectrum of a suspension of unilamellar vesicles of DPPC at -20 O C and that of ice (Figure IC). Dielectric relaxation experiment^^^ have shown that the reorientation time of water molecules in the interlamellar space of lipid dispersions is decreased. This effect is too large to be explained only by solute/solvent interactions and suggests that particular spatial conditions between the bilayers hinder the formation of the usual three-dimensional structure of water. Several studies have shown that properties such as density, viscosity, thermal conductivity, and dielectric constant of water in pores or in thin film are different from those observed with pure water.36 These differences depend not only on the chemical interactions between the surface and the water molecules but also on the extent of the water domains. This concept suggests that the structure that is responsible for some water properties is possible only if a minimum numbers of molecules are involved. Besides water molecules strongly bound to the surface and free water, several studies have led to the conclusion that a third type of water that is less mobile and forming less hydrogen bonds than free water may exist.36 Our results totally agree with these concepts. This study clearly establishes that the Raman spectrum of water inside small interstices depends on the size of the water domains and not on the nature of the surface. The origin of the perturbation can be explained by several hypotheses. The decrease of the intensity of the 3240-cm-' component relative to the 3440-cm-' feature could be associated to a structure in which more water molecules form weaker hydrogen bonds in restricted spaces. This ~
~~
~
(32) Therrien, M.; Lafleur, M.; Ptzolet, M. In Proceedings of 1985 Znternational Conference on Fourier and Computerized Infrared Spectroscopy; Spie, 1985, 553, 173. (33) Chapman, D.; Williams, R. M.; Ladbrooke, B. D. Chem. Phys. Lipids 1967, I, 445. (34) Hauser, H. L'eau et les systPmes biologiques, Colloques internationaux du C.N.R.S. 1976, 246, 131. (35) Kaatze, U.; Henze, R.; Seegers, A.; Pottel, R. Ber. Bunsen-Ges. Phys. Chem. 1975, 79, 42. (36) Clifford, J. In Ware?-A Comprehensiue Treatise; Franks, F., Ed.; Plenum: New York, 1975; Vol. 5, Chapter 2.
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 1525
u 3200
3500
3800
Frequency Shift (cm-1)
Figure 5. Raman band due to the 0-H stretching vibration of H O D (50%) in D 2 0 a t 10 OC for the 100 mM phosphate buffer and for (e..)
a 10% by weight DPPC multilamellar dispersion (-).
would correspond to an increase of the proportion of less organized water described as asymmetrically bound, closed, with bifurcated 0-H bonds or weakly hydrogen bonded. However, since the relative intensity of the 3600-cm-l component assigned to free 0-H groups is independent of hydration, it seems unlikely that the observed spectral changes are due to free or weakly hydrogenbonded 0-H groups. Long-range vibrational coupling could also be at the origin of the observed results. It is known that intermolecular coupling is strong in liquid water and can affect considerably the Fermi resonance between the first overtone of the bending mode and the 0-H stretching mode and, consequently, the shape of the 0-H Raman band.5J'J2 Recently, Green et aL1*have proposed that the low-frequency component of the 0 - H Raman band of water is due to the in-phase intermolecular collective coupling of the 0-H oscillators. This band requires the presence of patches of water molecules having similar hydrogen bond energies and decreases linearly in intensity with temperature. The decrease of the 3240-cm-' component of the water band in small interstices presented in this paper supports this interpretation. To demonstrate that the spectral change observed for lipid dispersions is due to intermolecular vibrational coupling, we recorded the 0-H band of H O D in a multilamellar dispersion of DPPC hydrated with a solution containing 50% H O D in D20, i.e., containing 25% 0 - H oscillators (Figure 5). In this solution, the intermolecular vibrational coupling is drastically limited by the presence of a large proportion of 0-D bonds. As seen in Figure 5, the profile of the band due to the uncoupled 0-H oscillators in the DPPC dispersion is identical with that of the hydrating solution, as opposed to the result obtained with coupled 0-H oscillators in H 2 0 (Figure lb). Clearly, the decrease of the intermolecular coupling in small size domains showing a greater orientational disorder is at the origin of change of the Raman spectrum of water in small interstices. A similar interpretation has also been proposed to explain other experimental results. For example, it has been shown that the ratio of the intensity of the bands due to the antisymmetric and symmetric C-H stretching modes at 2880 cm-' to that at 2850 cm-' respectively in the Raman spectra of alkanes and phospholipids is quite sensitive to intraand intermolecular vibrational coupling because of the presence of Fermi resonance interactions between the first overtone of the methylene bending mode and the symmetric C-H stretching mode.37 Intermolecular Fermi resonance was demonstrated by (37) Snyder, R. G.; Hsu, S.L.; Krimm, S.Spectrochim. Acta 1978, 3 4 4
395.
J . Phys. Chem. 1989, 93, 1526-1532
1526
the decrease of the h2880/h2850 ratio when normal alkanes were mixed with their deuteriated analogues, thus reducing the possibility of intermolecular vibrational coupling.38 Similarly, it has been suggested that the small discoidal bilayers formed by DPPC/Mel complexes restrict the long-range intermolecular coupling and the C-H stretching mode region of their Raman spectrum displays a very low h2880/h2850 ratio.20 In conclusion, the present results on the Raman spectrum of water in interstices in phospholipid dispersions and muscle fibers show that the shape of the band due to the 0-H vibrations depends markedly on the extent of the water domains rather than on the nature of the surface of these interstices. It is believed that reduced (38) Gaber, B. P.; Peticolas, W. L. Biochim. Biophys. Acta 1977,465,260.
long-range intermolecular vibrational coupling is at the origin of the spectral change since the shape of the Raman bands due to uncoupled 0-H oscillators is insensitive to the size of the water domains.
Acknowledgment. This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by the Fonds pour la Formation de Chercheurs et I'Aide fi la Recherche of the Province of QuEbec. M.L. acknowledges the award of a Centennial Scholarship by NSERC. We also thank Dr. H. H. Mantsch from the National Research Council of Canada for helpful discussion. Registry No. DPPC, 2644-64-6; DPPG, 4537-77-3; lyso-MPC, 13699-45-1; Mel, 20449-79-0; water, 7732-18-5.
Mean Field Analysis of an Ion-Dipole Mixture Next to a Plane Charged Wallt L. B. Bhuiyan Department of Physics, University of Puerto Rico, Rio Piedras, Puerto Rico 00931
and C. W. Outhwaite* Department of Applied & Computational Mathematics, The University, Sheffield SI 0 2TN, England (Received: June 2, 1988)
A mean field analysis is made of a single electrolyte against a plane charged wall with the electrolyte modeled by a mixture of unequal radii hard-charged spheres and dipolar hard spheres. The full set of nonlinear equations are solved numerically for ions of equal size while for ions of different size only the linear and linearized dipole theories are treated. For the linearized dipole theory the capacitances are found to have a nonlinear dependence on the surface charge density. The different ion sizes lead to asymmetry in the capacitance curves and nonzero potentials of zero charge.
Introduction The electric double layer of a primitive model electrolyte against a uniformly charged plane wall is now fairly well ~nderstood.l-~ Increasing attention is now being paid to treating the solvent at the same theoretical level as the solute rather than introducing the discrete nature of the solvent in an ad hoc manner in the compact layer. The theoretical approaches that have received the most attention are the mean spherical model (MSA) equatione7 and the related generalized MSA equation,8 which treat the electrolyte as a mixture of charged hard spheres and dipolar hard spheres. Attempts are also being made to adopt the successful bulk reference hypernetted-chain integral theory to this doublelayer p r ~ b l e m . ~ Another promising approach is that based on a potential approach which uses higher order closures in a generalized Poisson equation.I0 This is the modified PoissonBoltzmann (MPB) theory which has proved to be very successful in the primitive model analysis of the double layer.'," We hope to eventually treat the MPB equation for an ion-dipole mixture, but for the present we look at the predictions of a mean field analysis of the ion-dipole model. Preliminary work has been done in this direction,I2 where it was found for equal ion sizes that the structural form of the capacitance agrees with that predicted by the MSA theoryS4 We extend this work for a single salt to the situation where the two ion species and the dipole species each have different radii. The linear and linear dipole cases are considered in detail and the full nonlinear system solved numerically for equal ion sizes. The theory is flawed through the poor value of the permittivity of the pure solvent and the lack of structure in the singlet distribution functions. However the theory predicts interesting features such as asymmetric capacitance curves, 'Part of this paper was originally presented at the 1987 Spring Meeting of the Electrochemical Society, Inc., held in Philadelphia, PA.
0022-3654/89/2093-1526$01.50/0
nonzero potentials of zero charge, and the qualitative behavior of the Parson-Zobel plots and should be useful in the investigation of nonaqueous solutions. Theory The model chosen to represent the electric double layer is the civilized model electrolyte against a uniformly charged plane wall. The civilized model is the simplest electrolyte model giving structure to the solvent and is a mixture of charged hard spheres and dipolar hard spheres. We shall restrict ourselves to a single electrolyte with the two ion species i and j having charges eiand ej, respectively, and one solvent species a of moment p. The Poisson equation satisfied by the mean electrostatic potential $(x) a distance x into the solution from the wall is d2$
dx2 = -4aCe,n,(x) S
+ 4 a 1 p . V n m ( x , w )dw
(1)
where e, and n, (x) are the charge and mean number density, (1) Carnie, S . L.; Torrie, G. M. Adu. Chem. Phys. 1984, 56, 141. (2) Schmickler, W.; Henderson, D. Prog. Sur/. Sci. 1986, 22, 323. (3) Blum, L. Fluid Interfacial Phenomena, Croxton, C. A,, Ed.; Wiley: New York, 1986; p 391. (4) Carnie, S. L.; Chan, D. Y. C. J. Chem. Phys. 1980, 73, 2949. ( 5 ) Blum, L.; Henderson, D. J. Chem. Phys. 1981, 74, 1902. (6) Carnie, S . L.; Chan, D. Y. C. Adu. ColloidInterfaceSci. 1982, 16, 81. (7) Badiali, J. P.; Rosinberg, M. L.; Russier, V. Mol. Phys. 1985.56, 105. (8) Vericat, F.; Blum, L.; Henderson, D. J. Chem. Phys. 1982, 77, 5808; J . Electroanal. Chem. 1983, ISO, 315. (9) Torrie, G. M.; Kusalik, P. G.; Patey, G. N. J. Chem. Phys. 1988, 88, 7826. ( I O ) Outhwaite, C. W. Mol. Phys. 1983, 48, 599; Mol. Phys. 1988, 63, I1
( 1 1) Outhwaite, C. W.; Bhuiyan, L. B. J. Chem. Soc., Faraday Trans. 2 1983, 79, 707; J. Chem. Phys. 1986, 85, 4206. (12) Outhwaite, C. W. Chem. Phys. Lett. 1980, 76, 619; Can. J . Chem. 1981, 59, 1854.
0 1989 American Chemical Society
