J. Phys. Chem. 1988,92, 508-5 11
508
Solvatlon of Benzophenone Anion Radical in Ethanol and Ethanol/2-Methyltetrahydrofuran Mixture Tsuneki Icbikawa,* Yasubiro Isbikawa, and Hirosbi Yosbida Faculty of Engineering, Hokkaido University, Sapporo 060, Japan (Received: May 6, 1987)
The electron spin-echo modulations and the absorption spectra of benzophenone anion radicals generated by y-irradiation in the glassy matrices of ethanol and ethanol/2-methyltetrahydrofuran mixtures have been measured for elucidating the mechanism of spectral shift observed during the solvation of the anion radicals in alcohols. The anion radical generated at 4.2 K in the ethanol matrix maintains the same solvation structure as that of neutral benzophenone. At 77 K ethanol molecules solvate the anion radical by orienting the 0-H dipoles toward the anion radical. The anion radical is hydrogen-bonded by two ethanol molecules through the pz orbital on the benzophenone oxygen which composes the 7 orbitals of anion radical. Three kinds of anion radicals are observed in the mixed matrix at 77 K. Two of them are essentially the same as those observed in the ethanol matrix at 4.2 and 77 K. The third has the absorption maximum at 700 nm and is attributed to the anion radical hydrogen-bonded by one ethanol molecule through the pz orbital. It is concluded that the spectral shift observed in alcohols is caused by the stabilization of a SOMO r* orbital induced by the hydrogen bonding with the (R0)H--0--H(OR) angle perpendicular to the molecular plane of the anion radical.
Introduction Solvation is one of the major factors affecting chemical reactions of ionic species in condensed media. Since the solvation is a quite fast process, it cannot be studied by regular experimental methods. One of the powerful methods for studying the solvation dynamics is a pulse radiolysis technique. In this method molecules in condensed media are ionized by the irradiation of pulsed ionizing radiation with the width shorter than the solvation time. The change of the absorption spectrum caused by the solvation of the ionized molecules is then observed by using a fast detection system. The solvation process of excess electrons has been extensively studied by using the pulse radiolysis technique. * The solvation dynamics of the anion radicals of aromatic ketones including benzophenone have also been studied by several workemz6 Solvated benzophenone anion radical shows an exceptionally large spectral shift in alcohols,'so that it has been used for studying the solvation dynamics of molecular ions. On the other hand, anion radicals of aromatic hydrocarbons scarcely show the spectral shift, though the total energy of the anion radicals is considerably lowered by the solvation.* Although benzophenone anion radical has been widely used for studying solvation dynamics, the mechanism of the spectral shift has not been fully understood. Shida et al. measured the absorption spectrum of the anion radical in several glassy matrices at 77 K7s9and found that the absorption maximum is 630 nm in ethanol matrix but is 800 nm in the other matrices. They attributed the spectral shift to hydrogen bonding. Hoshino et al. measured the transient absorption spectrum in ethanol at 100 K and found the gradual shift of the absorption maximum from 780 to 630 nm.* They attributed the 780-nm band to the presolvated anion radical. This was further confirmed by measuring the absorption spectrum at 4.2 K.l0 Since the neutral benzophenone or the presolvated anion radical is already hydrogen-bonded with ethanol," they claimed that the spectral shift is not due to the hydrogen bonding but to solvent reorientation. Although the ~~
(1) Lewis, M. A.; Jonah, C. D. J . Phys. Chem. 1986, 90, 5378 and the references therein. (2) Hoshino, M.; Arai, S.; Imamura, M. J . Phys. Chem. 1974, 78, 1473. (3) Ogasawara, M.; Yoshida, H.; Karolczak, S.; Stadovski, Cz.;Kroh, J. Radiat. Phys. Chem. 1984, 23, 711. (4) Huddleston, R. K.; Miller, J. Radiat. Phys. Chem. 1981, 17, 383. (5) Marignier, J. L.; Hickel, €3. Chem. Phys. Lett. 1982, 86, 95 (6) Marignier, J. L.; Hickel, B. J . Phys. Chem. 1984, 88, 5375. (7) Shida, T.; Hamill, W. J . Am. Chem. SOC.1966, 88, 3683. (8) Ichikawa, T.; Moriya, T.; Yoshida, H.J . Phys. Chem. 1976,80, 1278. (9) Shida, T.; Iwata, S. J. Am. Chem. Sor. 1973, 95, 3473. (10) Hoshino, M.; Arai, S.; Imamura, M.; Namiki, A. Chem. Phys. Lett. 1974, 26, 82 (1 1) Becker, R. S. J. Mol. Spectrosc. 1959, 3, 1,
0022-3654/88/2092-0508$01.50/0
quantum-chemical mechanism of the spectral shift was not given, they probably assumed that the solvent reorientation changes the orbital energies through electric dipolar interactions. In the present study the electron spin-echo modulations and the absorption spectra of the benzophenone anion radical generated by y-irradiation in the glassy matrices of ethanol and the mixture of ethanol and 2-methyltetrahydrofuran (MTHF) were measured for elucidating the mechanism of the spectral shift induced by the solvation. The electron spin-echo modulations (ESEM) were measured for obtaining the geometrical information about the solvation structure. The absorption spectra of the anion radical in the ethanol/MTHF mixture were then analyzed as a function of the ethanol concentration in the solvation shell. It was shown that the spectral shift is caused by the hydrogen bonding through the pz orbital on the anion oxygen. Experimental Section Reagent grade deuteriated ethanol (CH3CHzOD)and benzophenone were used as received. Deuteriated ethanol was used instead of protiated ethanol because it gives a stronger ESEM signal. MTHF was used after purification with usual procedure^.^ The concentration of benzophenone in sample solutions was 0.1 mol/dm3. The solutions were sealed in quartz tubes for ESEM measurements or quartz cells with an optical path of 0.2 cm for optical measurements. The samples were irradiated with 6oCo y-rays to a dose of 2.3 X lo3 Cy. The concentration of the benzophenone anion radicals generated by the irradiation was about 0.6 mmol/dm3 in pure ethanol and 0.7 mmol/dm3 in pure MTHF. The ESEM signals were recorded on a homemade X-band electron spin-echo ~pectrometer,'~J~ by using a two-pulse method. The absorption spectra were recorded on Shimazu MPS-500 spectrophotometer. Unless otherwise stated, irradiations and measurements were carried out at 77 K. Results and Discussion Figure 1 shows the ESEM signals of the anion radical in the pure ethanol matrix and the ethanol/MTHF matrix with the ethanol concentration of 60 ~ 0 1 % .The modulation on the ESEM signals arises from magnetic dipolar interactions between the unpaired electron and nearby hydroxyl deuterons. Since the unpaired electron is delocalized over the benzophenone molecule, the precise analysis of the ESEM signal was impossible. However, by using a comparison method,I4 it was possible to estimate the ~~
(12) Ichikawa, T.; Yoshida, H. Bull. Fuc. Eng., Hokkuido, Uniu. 1984, 121, 41. (13) Ichikawa, T. J . Mugn. Reson. 1986, 70, 280.
0 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 2, 1988 509
Benzophenone Anion Radical in Ethanol and M T H F 21
I
I
-.--_---_
‘
L
1
.
1
2
1
0
t
rips
WAVELENGTHInm
Figure 1. Electron spin-echo modulation signals of benzophenone anion radical in (- - -) ethanol matrix and (-) ethanol/MTHF matrix containing 60 vol % ethanol. The signals were measured at 77 K. The dotted line shows the best fit for the solid line obtained from eq 1 by assuming that the volume fraction of ethanol in the first solvation shell is 58%.
Figure 3. Absorption spectra of benzophenone anion radical in ethanol/MTHF matrices at 77 K. The volume fractions of ethanol are (A) 0%, (B) 20%, (C)40%, (D)60%, (E) 80%, and (F) 100%.
p 100 J
m 2
E! e o +
f.
5f
Figure 4. Spectral components composing the absorption spectra of benzophenone anion radical in ethanol/MTHF matrices.
20
W
I
3 9
I
0
I
20
40 60 80 100 VOLUME% C2HsOD I N SOLUTION
1.5
AA
Figure 2. Concentration of ethanol in the first solvation shell for ben-
zophenone anion radical in ethanol/MTHF matrices. concentration of ethanol in the first solvation shell for the anion radical. In this method only the deuterons in the first solvation shell are assumed to give the nuclear modulation effect. Defining the observed ESEM signal for the pure ethanol matrix as E ( ~ , T ) , where T is the time interval between the first and the second microwave pulses, the ESEM signal for the mixed matrix with the volume fraction C of ethanol is given by
+
+
E(C,T) = exp(do d17 d2~2)[E(1,~)]C ( 1 ) where c is the volume fraction of ethanol in the first solvation shell, and is derived from eq 1 as
c = [In E(C,T) + do + d17
+ d2r2]/1n E ( ~ , T )
WAVELENGTH I nm
Figure 5. Absorption spectra calculated from eq 3 by using the spectral components shown in Figure 4. Calculations were made by assuming that the probabilities of finding an ethanol molecule at a hydrogenbonding site are (A) 0%, (B) 20%,(C) 40%, (D) 65%, (E) 85%, and (F) 100%.
(1’)
The parameters di are determined by a least-squares method in such a way that eq 1’ gives a 7-independent constant. Figure 2 shows the concentration of ethanol in the first solvation shell determined from eq 1’. The concentration was approximately the same as the bulk concentration of the mixed solvent. Since the migration of the ethanol molecule is prohibited at 77 K,3 it is concluded that the selective solvation of neutral benzophenone scarcely takes place in the mixed solvent. Although the deuterons out of the first solvation shell contribute to some extent to the modulation, it does not affect the conclusion because the ethanol concentration in and out of the first solvation shell is the same as the bulk concentration. Figure 3 shows the effect of the ethanol concentration on the absorption spectrum of the anion radical in the mixed matrix. Increase of the ethanol concentration caused a blue shift from 800 to 630 nm. The spectra were composed of more than two components, because no isosbestic point was observed on the spectra. The spectrum for 40 vol % ethanol showed double peaks near 800 and 700 nm, which suggests that the spectrum is composed of a few absorption bands. The double peaks cannot be expected if the spectrum continuously changes with the total number of ethanol molecules in the first solvation shell. (14) Ichikawa, T.; Miki, H.; Yoshida, H. J . Phys. Chem. 1985,89, 1211.
The dependency of the absorption spectrum on the ethanol concentration was explained by assuming that the absorption spectrum depends on the number of ethanol molecules hydrogen-bonded to the anion radical. Since the number of hydrogen-bonded ethanol molecules may vary from zero to two, the observed spectrum at wavelength X can be expressed by the equation S ( h ) = [$Z2(X)
+ 2r(l - r)Zl(X)+ (1 - r)2Zo(X)]G(C)D ( 2 )
where r is the probability of finding an ethanol molecule at the are the site for the hydrogen bonding, Z2(X), Z,(X), and lo@) extinction coefficients for the anion radicals with two, one, and zero hydrogen-bonded ethanol molecules, G(C) is the G value for the formation of the anion radical in the mixed solvent, and D is the absorbed dose. The values of [,(A) and lo@) were taken to be the same as those for pure ethanol and MTHF. The value of Z,(X) was calculated from the spectrum for 40 vol 7% ethanol by assuming that the probability of finding an ethanol molecu!e at a hydrogen-bonding site is the same as the volume fraction of ethanol, that is, r = 0.40. The spectral shapes of Z2(X), Zl(X), and Zo(X) are shown in Figure 4. The G value for the mixed matrix was estimated under the assumption that the G value is proportional to the volume fraction of ethanol and MTHF, as G(C) = 2.35C 2.55(1 - C) (3)
+
Ichikawa et al.
I
\.---
1 I
0
1
2
r/ps
Figure 6. Electron spin-echo modulation signal of benzophenone anion radicals in ethanol matrix at 4.2 K (-) and 77 K (- - -).
where the constants 2.35 and 2.55 are the G values for anion formation in pure ethanol and MTHF,Io respectively. Figure 5 shows the best fits for the observed spectra. The best fits were obtained by choosing r = 0.20 for C = 0.20, r = 0.40 for C = 0.40, r = 0.65 for C = 0.60, and r = 0.85 for C = 0.80. The close proximity between r and C indicates that the spectral shift is caused by the hydrogen bonding with the ethanol molecule(s) adjacent to the benzophenone oxygen. Figure 6 shows the ESEM signals for the anion radical in the pure ethanol matrix generated at 4.2 K and measured at 4.2 and 77 K. Although the deuteron modulation was shallow at 4.2 K, it became deeper by heating the sample to 77 K. Heating of the sample also caused the shift of the absorption maximum from 800 to 630 nm. The shape of the absorption spectrum at 4.2 K was the same as that for the pure M T H F matrix at 77 K. These changes were irreversible. Since the modulation depth increases with the decrease of unpaired electron-deuteron distances,I5 it is clear that the ethanol molecules in the first solvation shell were reorientated at 77 K to point the 0-D dipoles toward the anion radical. The solvation structure at 4.2 K is the same as that for the neutral benzophenoneI0 so that most of the 0-D dipoles are not pointed toward the anion radical. Although neutral benzophenone is known to be hydrogen-bonded by ethanol molecules through the nonbonding orbital of the benzophenone oxygen," this hydrogen bonding did not cause the spectral shift. Shida et al. made the molecular orbital calculation of benzophenone anion radicaL9 They assigned the near-IR band appearing at 600-800 nm to the intramolecular charge-transfer band induced by the charge migration from the carbonyl to the two benzene rings. The transition responsible to the near-IR band is therefore the SOMO (singly occupied molecular orbital) a* to LUMO (lowest unoccupied molecular orbital) a** transition. Since the px orbital composing the nonbonding orbital is orthogonalized to the a* and a** orbitals, the hydrogen bonding through the nonbonding orbital does not induce the spectral shift. Since the hydrogen bonding causing the spectral shift must interact with the a* orbital, we propose that the hydrogen bonding is formed through the pz orbital of the benzophenone oxygen composing the a and the a* orbitals. In ethanol the energy of the nonbonding orbital for neutral benzophenone is lowered by hydrogen bonding. When the neutral benzophenone accepts an excess electron in the a* orbital, the orbital energies of a and a* tremendously increase because of the repulsive interaction with the excess electron. Since the energy of the a orbital is higher than the nonbonding orbital and the orbital is highly localized on the benzophenone oxygen? the orbital for the hydrogen bonding changes from px to pz. At 4.2 K the anion radical is not hydrogen-bonded through the pz orbital because the rotation of the ethanol molecules is prohibited.I6 The absorption spectrum is therefore the same as that of the anion radical in the pure MTHF matrix. The rotation of the ethanol molecules in the first solvation shell is permitted at 77 K. The anion radical is then hydrogenbonded by one ethanol molecule when there is only one ethanol (15) Kevan, L. In Time Domain Electron Spin Resonance; Kevan, L., Schwartz, R. N., Eds.; Wiley-Interscience: New York, 1979; Chapter 8. (16) Higashimura, T.; Noda, M.; Warashina, T.; Yoshida, H. J . G e m .
Phys. 1971, 55, 541 1.
molecule near the pz oribtal of the benzophenone oxygen. When there is more than one ethanol molecule, the anion radical is hydrogen-bonded by two ethanol molecules located above and below the molecular plane of the anion radical. These hydrogen bondings lower the energy of the a and a* orbitals. Since the a**orbital has no electron density on the benzophenone oxygen, the a** orbital is not stabilized by the hydrogen bonding. The hydrogen bonding therefore causes a blue shift of the absorption spectrum. The probability of forming the hydrogen bonding is close to the volume fraction of ethanol, which implies that only two specific positions are effective for the formation of the hydrogen bonding. The probability is slightly higher than the average concentration of ethanol in the first solvation shell. The concentration around the neutral benzophenone oxygen might be slightly higher than the bulk concentration because the negatively charged benzophenone oxygen tends to attract polar molecules. Hoshino et al. measured the time-dependent spectrum of the anion radical in ethanol generated by the irradiation of an electron pulse and found that the decay of the absorbance at 750 nm was expressed by the superposition of two exponential functions.2 Marignier and Hickel made the same kind of experiment by using propanol as a solvent.5s6 They also found that the decay at 826 or 900 nm was expressed by the superposition of two exponential functions. From our point of view, the two exponential functions correspond to the formation of the anion radicals hydrogen-bonded by one and two alcohol molecules, respectively. The formation of the hydrogen bonding is expressed by
(C6H5)2C=O---HOR
+ ROH
ki
(C6H5)2C=O---(HOR)2 (4) Since the formation of the hydrogen bonding is a pseudo-first-order process, we obtain the following equations dRo(t)/dt = -k&(t) dR,(t)/dt = -k,R,(t) + koRo(t)
(5)
where &(t) and R l ( t )are the concentrations of the anion radicals hydrogen-bonded by zero and one alcohol molecule, respectively. The solution of eq 5 is given by Ro(t)= Ro(0)e-kof
where &(O) is the initial concentration of the anion radical without hydrogen bonding. The absorbance at the wavelength longer than the absorption spectrum of the anion radical hydrogen-bonded by two alcohol molecules is calculated from eq 6 and the molar extinction coefficients of the anion radicals as
The above equation shows that the decay is expressed by the superposition of two exponential functions. Marignier and Hickel attributed the fast and slow exponential decays to the solvation of the anion radical by alcohol molecules in and out of the first solvation shell, respectively. However, the present study indicates that the fast and slow decays are attributed to the formation of the anion radicals hydrogen-bonded by one and two alcohol molecules. They also claimed that the rate-determining process for the spectral shift is the breaking of solvent hydrogen bonds assisted by the electrostatic interaction between the anion radical and the molecular dipole of the solvent. However, since the electrostatic interactions are the same for alcohol molecules located above and below the molecular plane of the anion radical, it is concluded that the rate-determining process is the formation of hydrogen bonding between alcohol and the anion radical. The rate constant for the formation of the first hydrogen bonding is faster than that of the second one, because, even if the activation energies are the same, the number of hydrogen-bonding sites for
J . Phys. Chem. 1988,92, 511-517 the pre-hydrogen-bonded anion radical is twice as much as that for the anion radical hydrogen-bonded by one molecule. Conclusion The electron spin-echo and the optical spectroscopic studies of benzophenone anion radical in the glassy matrix of ethanol and ethanol/MTHF showed that the spectral shift is caused by the formation of hydrogen bonding with one or two alcohol molecules located above and below the molecular plane of the anion radicals.
511
The alcohol molecules hydrogen-bonded to the neutral benzophenone do not induce the spectral shift because the nonbonding orbital used for the formation of the hydrogen bonding is orthogonalized to the ?r* and A** orbitals responsible to the optical transition. Aromatic ketones show large spectral shifts in protic solvents because they form hydrogen bonding with the solvents through the pz orbital on the ketone oxygen. Registry No. Benzophenone radical anion, 16592-08-8; ethanol, 6417-5;
2-methyltetrahydrofuran, 96-47-9.
Dielectric Relaxation Studies on Analogues of the Polypentapeptide of Elastin Ren6 Buchet, Chi-Hao Luan, Kari U. Prasad, R. Dean Harris, and Dan W. Urry* Laboratory of Molecular Biophysics, The University of Alabama at Birmingham, University StationlP.0. Box 31 1. Birmingham, Alabama 35294 (Received: May 5, 1987; In Final Form: July 22, 1987)
Dielectric measurements of the complex permittivity of coacervate concentrations of two analogues of the polypentapeptide of elastin, (Xxxl-Pr~*-Gly~-Val~-Gly~)~ where Xxx is Val for the elastin polypentapeptideand Ile and Leu for the two analogues, were taken over the frequency range 1-1000 MHz and over the temperature range 0-60 OC. Two relaxation processes were observed in each polypentapeptide. One relaxation has a frequency centered in the low megahertz frequency range, which has been attributed to a low-frequency librational mode within the polypeptide. The other relaxation is located near the gigahertz frequency range. The magnitude of the dielectric increment, A€, of the librational mode of each polypentapeptide analogue increases with increasing temperature from near zero at 0 OC to approximately 40 at 60 OC,showing an inverse temperature transition to a more ordered structure. Conversely, the magnitudes of the dielectric increment of the high-frequency relaxation decrease with increasing temperature and differ in approximate proportion to the hydrophobicity of the pentamer for the polypentapeptide of elastin and the two analogues at temperatures below the inverse temperature transition. It is suggested that clathrate-like water surrounding hydrophobic side chains contributes to the high-frequency relaxation.
Introduction Fibrous elastin from aorta occurs at 5-6-llm diameter fibers.' These fibers are comprised of a single protein, which as the soluble precursor is called tropoela~tin.~.~ A key development in deriving the molecular mechanism of biological elasticity was the finding by Sandberg and colleagues of repeating peptide sequences. The most striking repeating sequence is the polypentapeptide (Va11-Pro2-Gly3-Va14-GlyS),, where n is 11 or greater! It has been demonstrated that this polypentapeptide of elastin, also referred to as (VPGVG), or PPP, on increasing the temperature in water undergoes an inverse temperature transition with the proposed development of a dynamic 0-spiral conformation within which occurs a Va14-Gly5-Va11suspended segment capable of largeamplitude, low-frequency rocking motions (for a review see ref 5 ) . The repeating pentamer in an unrolled perspective of the @-spiral is given in Figure 1. Previous relaxation studies on the polypentapeptide of elastin6 and on a-elastin,' a 70000-D chemical fragmentation product from elastin,s have demonstrated a single Debye-type relaxation with a relaxation time of about 7 ns at 40 O C for the polypentapeptide and about 8 ns at 40 OC for a-elastin. This relaxation has been attributed to the internal dynamics of the polypentapeptide, primarily arising from the rocking motion of peptide moieties in the suspended segment Val4-Gly5-Va11 .699
(1) Gotte, L.; Manni, M.; Pezzin, G. Connect. TissueRes. 1972, I , 61-67. (2) Smith, D. W.; Weissman, N.; Carnes, W. H. Biochem. Biophys. Res. Commun. 1968, 31, 309-315. (3) Sandberg, L. B.; Weissman, N.; Smith, D. W. Biochemistry 1%9,88 294Q-2945. (4) Sandberg, L. B.; Soskel, N. T.; Leslie, J. B. N . Engl. J . Med. 1981, 304, 566. ( 5 ) Urry, D. W. J . Protein Chem. 1984, 3, 403. (6) Henze, R.; Urry, D. W. J . Am. Chem. Sac. 1985, 107, 2991-2993. (7) Urry, D. W.; Henze, R.; Redington, P.; Long, M. M.; Prasad, K. U. Biochem. Biophys. Res. Commun. 1985, 128, 1000-1006. (8) Partridge, S.M.; Davis, H. F.; Adair, G. S.Biochem. J . 1955,61, 11.
Below the temperature of the transition for the polypentapeptide, which is centered a t 31 OC and begins at 24 OC, the polypentapeptide of elastin is soluble in water in all proportions. Above the temperature of the transition at concentrations less than 37% peptide by weight, two phases are observed. One is due to the more dense, viscoelastic coacervate state of the polypentapeptide, and the other is due to the transparent equilibrium solution. The polypentapeptide coacervate is a two-component system which contains by weight 63% water and 37% polypentapeptide at 30 O C . I o Dielectric measurements have been proven to be useful for studying water in protein. A sound discussion of this method is found in several books."J* Recently, the hydration of lipoprotein,I3 protein,I4 ocular tissue,I5 brain ti~sue,'~J'hemoglobin,ls polyadenine,I9and Na-DNA gelsM)has been studied by dielectric relaxation measurements. (For earlier work, see ref 11 and 12.) One of the challenges of dielectric measurements is to determine (9) Venkatachalam, C. M.; Urry, D. W. Int. J . Quantum Chem., Quantum Biol. Symp. 1986, 12, 15-24. (10) Urry, D. W.; Trapnae, T. L.; Prasad, K. U. Biopolymers 1985, 24, 2345. (1 1) Hasted, J. B. Aqueous Dielectrics; Chapman and Hall: London, 1973. (12) Pethig, R.Dielectric and Electronic Properties of Bilogical Materials; Wiley: New York, 1978. (13) Essex, G. C.; Grant, E. H.; Sheppard, R. J.; South, G. P.; Symonds, M. S.;Mills, G. L.; Slack, J. Ann. N . Y.Acad. Sei. 1977, 303, 142-153. (14) Rejou-Michel, A.; Hencry, F.; de Villardi, M.; Delmolte, M. Phys. Med. Biol. 1985, 30(8), 831-837. (15) Gabriel, C.; Sheppard, R. J.; Grant, E. H. Phys. Med. Biol. 1983, 28(1), 43-49. (16) Nitingale, N. R.; Goodridge, V. 0.; Sheppard, R. J.; Christie, J. L. Phys. Med. B i d . 1983, 28(8), 897-903. (17) Steel, M. C.;Sheppard, R. J. Phys. Med. B i d . 1985,30(7), 621-630. (18) Schwan, H. P. Blur 1983, 46, 185-197. (19) Takashima, S.;Casleggio, A.; Giuliano, F.; Morando, M.; Arrigo, P.; Ridella, S.Biophys. J . 1986, 498 1003-1008. (20) Bonincontro, A.; DiBiaso, A,; Pedone, F. Biopolymers 1986, 25, 241-247. (21) Grigera, J. R.; Mascarenhas, S.Studia Biophysicu 1978, 73, 19-24.
0022-3654/88/2092-0511%01.50/00 1988 American Chemical Society
