J. Phys. Chem. 1982, 86, 1449-1456
tively obtain from (13) a corresponding value of -3 X lC5, which is an order of magnitude smaller than the observed one. This discrepancy may arise mainly from the underestimation of of the values of Ai from the back-scattering cross sections, as well as from the crudeness of the assumptions involved in the calculation. Finally, we have estimated the effective valence ,Tieff of the component i from the orifice velocity u: given by (4) and the relations for the terminal solutions: ut
N
Z:fflelE/c?
-
Xi0
-
0
ZrfflelE/{: X: 1 (15) In the dilute solution (X: 0) the friction coefficient of the solute is roughly approximated by that of the solvent." We used the relation = kT Di and the data of DT1 = 1.3 X 10" cm2 s-l for pure T12 and Dh = 3.4 X cm2 s-l for pure In.= The calculated values of &leff are given in the last column of Table 111. Belashchenko et al." have u:
N
c?
L
(24)Reference 14,p 228. See eq 609.4.
1449
reported values of for the molten In-TI alloy system, determined from the steady-state concentration profiles in "long-time" experiments.26 Their "long-time" values of Zhea = +0.24 for Xno = 0.10 and +LO3 for Xmo= 0.86 at 380 "C are in fair agreement with those estimated from the present "short-time" study, ZIneffN +0.2 and 1.5, for the respective compositions.
Conclusion Measurements of electrotransport in molten In-TI alloys show that the T1 atoms migrate to the anode over the whole composition range. These results can be interpreted by the difference in the electron-ion scattering cross section of the respective ions in the alloys. It has been found that the direction of migration and the composition dependence of the values of the electron drag coefficient, Pi, are in good agreement with the prediction based upon the approach of Epstein and Dickey proposed for monovalent liquid alloys such as alkali-alkali metal systems. (25)E.g., ref 2, p 7.
Interaction of Benzene wlth Micelles and Bilayers S. A. Simon;
R. V. McDaniel,t and T. J. McIntosh$
Depertments of Anammy, Anesthesiology. and Fhysblogy, Duke University Medical Center, Durham, North Carolina 27710 (Received: Ju& 28, 1981;I n Final Form: August 17, 198 I)
The organic phaseaqueous phase partition coefficient of benzene was directly measured into nonpolar isotropic liquids, detergent micelles, and phospholipid bilayers above and below their gel-to-liquidcrystalline transition temperature. From these data we conclude that benzene is, on the average, situated in a nonpolar environment. The relatively small difference in the free energy of transfer of benzene from benzene to any of these solvents in their liquid phases is almost entirely accounted for by a positive enthalpy of transfer. Below the transition temperature the entropy of transfer contributes to the more positive free energy of transfer. We also conclude that the Laplace pressure and possible water penetration into the nonpolar phases do not significantly influence the partition coefficient. Attempts to use ultraviolet spectroscopy to determine the location of benzene in micelles were unsuccessful because of the fact that the numbers obtained for the effective dielectric constant are not single valued.
Introduction The interaction of apolar molecules with solvents has been of interest primarily for the information obtained regarding the nature of interactions between relatively simple molecules. Such studies are also of interest to anesthesiologists and toxicologists as virtually all of the smaller apolar molecules are anesthetics' and several are carcinogens.2 Previously many investigators have studied the interaction of small nonpolar molecules with polym e r ~ isotropic , ~ ~ ~ organic liquids,"" and detergent micelle~.'*~' More recently these studies have been extended to planar22and vesicular bilayerswn as well as biological The questions that have usually been asked are the following: (1)What is the partition coefficient and the solubility of the solute between an organic phase (or pseudophase, for micelles and bilayers) and water? (2) Where is the solute located in the solvent? (3) *Departments of Anesthesiology and Physiology. Address correspondence t o this author at the Department of Physiology. + Departments of Anesthesiology and Physiology. t Department of Anatomy. 0022-3654/82/2086-1449$01.25/0
How do the structure and the physical state of the solvent influence the partition coefficient? (4) How does the (1)L. J. Mullins, Chem. Rev., 54, 289 (1954). (2)R. Snyder and J. J. Keusis, Crit. Reu. Toxicol., 3, 265 (1975). (3)A. S. Michaels and M. J. Bixler, J. Polym. Sci., 50, 393 (1961). (4)J. H. Hildebrand and R. L. Scott, 'The Solubility of Nonelectrolytes", 3rd ed., Dover Publications, New York, 1964. (5) K. Shinoda, "Principles of Solution and Solubility", Marcel Dekker, New York, 1978. (6)C. Hansch, J. E. Quinlan, and G. L. Lawrence, J.O g . Chem., 33, 347 (1968). (7)J. Hine and P. K. Mookerjee, J. Org. Chem., 40,292 (1975). (8)A. Leo, C. Hansch, and D. Elkins, Chem. Reu., 71, 521 (1971). (9)C. Tanford, T h e Hydrophobic Effect, Formation of Micelles and Biological Membranes", 2nd ed. Wiley, New York, 1980,Chapters 2,3, 7. (10)S.J. Gill, N. F. Nichols, and I. Wadso, J. Chem. Thermodyn., 8, 445 (1976). (11)R. Battino and H. L. Clever, Chem. Reu., 66, 395 (1966). (12)M. Almmen, F.Grieser, and J. K. Thomas, J. Am. Chem. SOC., 101,279 (1979): (13)A. P. Brady and H. P. Huff, J. Phys. Chem., 62,644 (1958). 114)J. R.Cardinal and P. Mukeriee. J.Phvs. Chem.. 82.1614 (1978). (15)J. C. Eriksson and G. GillGerg, Acta Chem. Scand., 20, 2019 (1966). (16)P.Mukerjee in "Solution Chemistry of Surfactants", Vol. 1, K. L. Mittal, Ed.;Plenum Press, New York, 1978.
0 1982 American Chemical Society
1450
The Journal of Physical Chemlstry, Vol. 86, No. 8, 1982
structure of the solvent change upon the solubilization of the solute? These questions have been asked, and to various extents answered, in the different systems. In this paper we will present data on the interaction of benzene with isotropic liquids, micelles, and bilayers with the purpose of answering the above questions. We have chosen benzene as the solute to study for several reasons: (1)There is a vast literature regarding the interaction of benzene with micelles and organic liquids so that we can compare our results to these. For benzene, in particular, there is disagreement in the literature regarding the regions where benzene partitions in a micelle. The claims range from benzene situated mostly at the micelle-water interface to it residing in the micelle i n t e r i ~ r . ' ~ JAlso ~ J ~a~ ~ ~ two-site model exists where benzene can be located in both regions, with one or the other dominant depending on the benzene-to-detergent mole ratio.l2 (2) Most of the solubility and partition data obtained for nonpolar molecules into micelles have been indirect in that they depended on interpretations of spectroscopic analyses. In this paper we directly measured the partition coefficient of benzene in various solvents at low mole fractions of benzene in the organic phase. (3) We have previously studied the interaction of n-hexane, which is located in the membrane or micelle interior,"^^ and benzyl alcohol, which is confined to the interfacial region of bilayersz8so that the benzene results can be compared to them. (4)By studying the partition coefficient into micelles, multilamellar vesicles, and single-walled vesicles, we may determine the role of the Laplace p r e s s ~ r on e ~the ~ ~partition ~~ coefficient. In this paper we conclude the following: (1)Benzene partitions into a hydrophobic region of micelles and bilayers. (2) The relatively small differences in the free energy of transfer of benzene from itself into bilayers or micellar phases are due to the positive partial molar enthalpy of transfer that arises as a result of uncompensated 'IMinteractions and are not likely due to Laplace pressure or water penetration in micelles. (3) The use of UV spectroscopy to study the microenvironment of benzene in micelles depends on obtaining calibration curves with bulk isotropic liquids. Benzene spectra vary widely among solvents of similar dielectric constant. Consequently, extrapolations regarding benzene's microenvironment using this technique are arbitrary.
Materials and Methods The lipids dilauryl phosphatidylcholine (DLPC), dimyristoyl phosphatidylcholine (DMPC), dipalmitoyl phosphatidylcholine (DPPC), distearoyl phosphatidylcholine (DSPC), dioleoyl phosphatidylcholine (DOPC), and egg phosphatidylcholine (EPC) were obtained from Avanti Biochemicals and used without further purification. These (17)P. Mukerjee and J. R. Cardinal, J. Phys. Chem., 82,1620(1978). (18)H. B. Klevens, Chem. Reu., 47,1 (1951). (19)S.J. Rehfeld, J. Phys. Chem., 74,117 (1970). (20)S.Riegelman, N.A. Allawak, M. K. Hrenoff, and L. A. Strait, J. Colloid Sci., 13, 208 (1958). (21)A. Wishnia and T. W.Pinder, Jr., Biochemistry, 5,1534 (1966). London,Ser. A, 347, (22)J. Requena and D. A. Haydon, R o c . R. SOC. 161 (1975). (23)Y. Katz and J. M. Diamond, J. Membr. Biol., 17, 101 (1974). (24)T.J. McIntosh, S. A. Simon, and R. C. MacDonald, Biochim. Biophys. Acta., 597,445 (1980). (25)K. W. Miller, L. Hammond, and E. G. Porter, Chem. Phys. Lipids, 20,229,(1979). (26)S. A. Simon, W. L. Stone, and P. B. Bennett, Biochim. Biophys. Acta, 550,38 (1979). (27)R. A. Smith, E. G. Porter, and K. W. Miller, Biochim. Biophys. Acta, in press. (28) L. Ebihara, J. E. Hall, R. C. McDonald, T. J. McIntosh, and S. A. Simon, Biophys. J.,28,185 (1979). (29)F. M.Menger, J.Phys. Chem., 83,893 (1979).
Simon et al.
gave single spots with thin layer chromotography. Palmitoyl lysophosphatidylcholine was obtained from Sigma Chemical Co. Sodium dodecyl sulfate (SDS)was obtained from Pierce Chemical Co. (sequanol grade) and used as obtained. The solvents ethanol, hexadecane, l-octanol, methanol, n-hexane, and 2-propanol were either spectral grade or reagent quality. Benzene was Gold-Label grade (Aldrich Chemical Co.). The water was first deionized and then doubly distilled in an all-quartz still. Two batches of [14C]benzenewere used. The first was obtained from ICN Pharmaceuticals Inc. (specific activity, 30 mCi/mM) and the second from Amersham Corp. (specific activity, 100 mCi/mM). These samples were diluted with ultrapure benzene (Aldrich Gold Label) until they had a specific activity of about 7 X lo4cpm/pL. The radioactive samples were dissolved in Aquasol and counted in a Beckman LS-250 liquid scintillation counter. Partition Coefficient. The distribution coefficients of benzene were determined in a Wishnia solubility cell in a manner described in detail elsewhere.z1,z6Briefly, the cell consists of four separate glass chambers that are connected to each other via a gas phase. Each chamber can contain up to 0.25 mL of liquid that never contacts the liquids in the other chambers. The gas phase, which essentially consists of argon (to minimize oxidation), plus the radioactive solute, is circulated throughout the four compartments by a Teflon ball. Each chamber (including the gas phase) is sealed from the atmosphere by stoppers. The total volume of all of the chambers plus the gas phase is e 1 0 0 mL. The chamber is placed in a water bath regulated within 0.2 OC, where it is rotated to facilitate the equilibration of benzene with the solvents. Two of the chambers contained a 0.1 M NaCl solution and the other two contained the same aqueous phase plus dispersed lipid in the form of liposomes, detergent micelles, or single-walled vesicles at a concentration of about 10 mg/mL for the bilayers and about 30 mg/mL for the micelles. The concentration was determined either gravimetrically or by phosphate analysis.3o Once the liquids were in place, small aliquots of [14C]benzene were injected into the gas phase and allowed to equilibrate. Fixed volumes from the gas, aqueous, and dispersed phases were taken at prescribed time intervals to ensure that steadystate values of the partition coefficient were obtained. Usually 2 h or less was necessary for this condition to be fulfilled. To ensure that we were operating in the Henry's law region, we added aliquots of benzene to the gas phase after equilibration was reached. In this way the solubilities of benzene in water and bilayers or micellar phases were determined as a function of gas pressure from 5 to 60 " H g . Henry's law was valid for all experiments reported. Partial pressure of benzene was about 30 mmHg for most experiments presented here. At this pressure the mole fraction of benzene in 0.1 M NaC1, X,,is 1.09 X lo4, which is below the level of saturation in the aqueous phase?^^^.^^ We compared literature values of benzene solubility with our experimental results. To correct for differing salt concentrations in the aqueous phase, we used the data of Morrison and Billet.31 For example, at 25 "C, the solubility, in mole fraction units, of benzene in 0.1 M NaCl was extrapolated to be 3.55 X The numbers of moles of lipid or detergent used in calculating K are those above the cmc of the particular amphiphile. In most cases the correction was negligible. In this paper we have presented (30)G.R. Bartlett, J. Biol. Chem., 234,466 (1959). (31)T.J. Morrison and F. Billet, J. Chem. SOC.,3819 (1952). (32)R. A. Pierotti, J . Phys. Chem., 69,281 (1965). (33)C.McAuliffe, J . Phys. Chem., 70,1267,(1966).
Interaction of Benzene with Micelles and Bilayers
The Journal of Physical Chemlstty, Vol. 86, No. 8, 1982 1451
TABLE I: Thermodynamic Transfer Parameters of Benzene into Various Solvents at 25 "C aqueous phase -aGawo + SD, A G " ~ , ~ , solvent [salt], M 10+~d 10-3K e kcaijmol cal/mol ref benzene water 2.425 4.614 10 benzene 2.493 water 4.630 33 benzene hexane
octanol hexadecane SDS (dilute) SDS SDS (satd) SDS (satd) lysolecithin potassium dodecanate (satd)
0.1
0.1 0.1 0.1 0.1 0.05 0.1
2.812 1.457 1.11 1.50 f 0.96 * 1.10 f 1.32 1.72 1.64t
0.5
1.447
water water
0.14 0.07 0.09
4.700 4.313 4.184 4.33 t 0.047
430 370
4.15 f 0.05 4.254 4.337 4.38~t0.04
553 446 276 317
this work
4.30
395
18
31 8 6
this work 13
0.11
19 12
this work
sodium
oleate (satd) C,,HCl (satd)a HDTAB (satd)b CTAB (satd)c egg lecithin egg lecithin (SUV) DOPC
1.26 0.1 0.1 1.109 0.1 1.19 1.43 0.18 0.1 3.12 .t 0.15 0.1 2.80 f 0.24 0.1 2.80 * 0.21 DLPC 0.1 2.90 t 0.34 DMPC 2.75 t 0.21 0.1 DPPC 0.1 1.12 f 0.14 1.52 f 0.07 DSPC 0.1 1.40.t 0.16 egg lecithin-cholesterol (1:l) 0.1 Dodecyl ammonium chloride. Hexadecyltrimethylammonium mide, Mean t SD. e Per acyl chain.
the partition data in terms of mole fraction units normalized per acyl chain. The reason for this choice is given in the Appendix. Ultrauiolet Spectroscopy. Ultraviolet absorbance spectra were obtained with a Beckman Model 25 spectrophotometer. A slit width of 0.2 mm and a scan speed of 50 A/min were used. All absorbance ratios were measured from strip chart recordings under these conditions. The cuvette path length was 1.0 mm for lysolecithin spectra and 1.0 cm for all other solvents. A fixed volume of benzene was added to powdered lysolecithin or SDS to give a benzene mole fraction of 0.4. To this material was added benzene-saturated water to give a 0.4 M detergent dispersion. This dispersion was bath sonicated for 20 min at 30 "C and allowed to equilibrate at room temperature for 90 min. Benzene was shaken with bulk solvents in a sealed cuvette at 1 and 11 mmol of benzene per liter of solvent. Spectra were then obtained at 20 f 2 "C.
Results Figure 1shows how the benzene partial pressure P (m), its mole fraction in 0.1 M NaC1, X, (x), and its mole fraction in egg lysolecithin, X, (a),change with time after the benzene is introduced into the gas phase at time zero. The first data point was usually taken 2 after the addition of the benzene. After 2 h the ratio of X,to X, (defined as K ) remained constant although both mole fractions decreased. Figure 1 shows that the partial pressure of benzene changed slowly 4 h after its addition to the gas phase. In most cases, 2 h was sufficient to obtain this slope. After 4 h, K H = P I X , became constant within experimental error. At 25 "C the value obtained for Henry's constant, KH, in this and other experiments was 360 f 32 atm (mean f SD). This value is in good agreement with those reported by P i e r ~ t tand i ~ ~Hine and Mookerjee? who gave values of 360 and 325 atm, respectively, in water rather than 0.1 M NaC1. A t 25 "C we found KH to be independent of benzene partial pressure from 5 to 60 mmHg. Also at this temperature we found K to be independent of P over the above
--. -
4.22 473 18 4.15 548 18 4.191 508 50 4.447 333 15 1.70 4.40 f 0.03 this work 296 1.51 this work 366 4.33 f 0.05 1.52 this work 362 4.34 f 0.04 this work 378 1.48 4.32 * 0.07 this work 395 1.44 4.30 f 0.05 this work 3.80 f 0.08 903 0.61 3.70 t 0.04 this work 0.52 886 this work 587 1.04 4.113 c 0.07 bromide, T = 33 "C. Cetyltrimethylammonium bro-
--. --.
T.25-C
D
h hI" x
x 0
= E x% aE
3.2'
IS 4 0 -
2.8-
14 35-
12-
6
I5-
0.8-
4
IO.
0.4-
2
5.
0
0
0
1
4
I
I
I
I
I
I
I
I
I
I
b
I
1
1
pressure ranges for DOPC, SDS, and DPPC (which is below its transition temperature). We assume that such behavior holds for the other reported solvents at 25 "C as well as for other temperatures. Figure 2 shows how the mole fraction partition coefficient, K, changes with temperature for various isotropic liquids and micelles. Points with error bars represent our data. Benzene partition data were calculated from eq 10 in ref 10. The data point below the solid benzene line at 25 "C is taken from M ~ A u l i f f e .The ~ ~ points above the solid benzene line are from the solubility data of Morrison and Billett31 in water and 0.1 M NaC1. The presence of 0.1 M salt produces a significant change in the partition coefficient but a small change in the free energy of transfer (see Table I). Also in Figure 2 are the partition coefficient w. temperature plots of benzene into palmitoyl lysolecithin
1452
Simon et al.
The Journal of Physical Chemistry, Vol. 88, No. 8, 1982 n I
S .I
Y
I n
I I
M-B (O.IM)
2.5-
P
-
x
Y
.
EPC
g 2.0-
'
(I EPC-CHOL(IlI) I
05.1+00
I ,, I
01
0 0
20
30
40
50
20 30 40 Temperature 'C
IO
60
Temporo?urr 'C Flgure 2. Temperature dependence of the organic phase-aqueous phase partttlon coeffkient, K , for benzene in various solvents containing one acyl chain per molecule. The error bars represent the standard deviations from the mean and are the data obtained In this work. The other data are obtained from the literature. The organic phases are labeled.
micelles, n-hexadecane, and SDS micelles. All exhibit similarly shaped curves as benzene but their curvature is not as steep in the high-temperature region. Also shown are the partition coefficients of benzene into other pseudophases or isotropic liquids as found in the literature. These include hexane, 1-octanol, hexadecyltrimethylammonium bromide (HDTAB), cetyltrimethylammonium chloride (CTAMCL), and d u m oleate (NaCls). Data for the micelles were taken at saturation and for hexane and 1-octanol a t infinite dilution. Figure 3 shows K'vs. T plots for benzene into various bilayers. In this f i i e , the partition coefficient, K', is the mole fraction partition coefficient normalized per acyl chain (see eq A-4 in the Appendix). Data for benzene solvent are included for comparative purposes. Bilayers that exhibit phase transitions between 10 and 60 "C are DMF'C, DPPC, and DSPC. Gel-to-liquid crystalline phase transitions are denoted by dotted lines. K' increases by a factor of 3 from below to above the transition. Below T,, the K'vs. T curves are practically flat. Above T, the plots exhibit a slight downward curvature. The mole fractions of benzene in the lipid are quite small ( ~ 0 . 1 ) . At these concentrations the gel-to-liquid crystalline transition temperature is lowered about 1 "Cy and bilayer structure is preserved (McDaniel, McIntosh, and Simon, unpublished data). For those bilayers that do not exhibit phase transitions over this temperature range such as DLPC, egg lecithin, and egg lecithin-cholesterol (l:l),the K'vs. T curves are continuous. The K'values are nearly the same for all lipids above their transition temperature. Addition of cholesterol to egg lecithin at a 1:l mole ratio reduces the partition coefficient by about 38%. Also seen in Figure 3 are the partition coefficients for DOPC and small unilamellar vesicles (SUV's) of egg lecithin at 25 "C. The values of K' for these two systems are the same. Figure 4 shows - a graph of the difference in partial molal free energy, AG"B/o = RT In KWIB/KBIO,of transferring
50
60
Flgwe 3. Partition coefflcbnt normalized per mole of acyl chain, K', vs. temperature for bilayer membranes. The data for benzene are the same as In Flgure 2. The error bars represent the standard deviation from the mean. The dotted lines show the gel-to-liquid crystalline transition temperature reglon. The points for DoPC and EPC-SUV (small unilamellar vesicles) are superimposible.
'
KC#*.DMP C DLPC-
HEXADECANE.DOPC, EPC - 5 U V
/ /
BENZENE
EPC-CHOL(l~l1 C,&tCI HDTAB -NaCI, F D S I-OCTA NOL
-
' C TAB ( T 350 c j
BENZENE
F w e 4. Free energy of transfer difference of benzene from benzene into organic phases. This data corresponds to column six in Table I and is denoted as The units are cal/mol.
sB,o.
benzene from benzene to other organic solvents at 25 "C. These free energy values are calculated by using the energy-balanceequation:AGOwp + A G " B / ~+ A G O o p = 0 In this equation the subscript W is meant to Fepresent salt solutions as indicated (see Table I). The data for moplo a t 25 "C are given in Table I. The zero-energy position represents benzene transferring into itself. The middle positions contain bilayers, above their transition temperature, isotropic liquids, and micelles. The maximal difference in moB,o is -300 cal/mol for all of these different systems. The upper region is for bilayers below their phase transition temperature. In a manner similar to calculating B l ~ the , partial molal enthalpy of transfer B B l o and entropy of transfer ASOBIOcan be calculated. The values of D w I B obtained from calorimetric (25 "C) and solubility measurements (at
Interaction of Benzene with Micelles and Bliayers
The Journal of Physical Chemistty, Vol. 86, No. 8, 1982
TABLE 11: Thermodynamic Transfer Parameters of Benzene from Benzene into Various Solventsa
AG”
solvent SDS
lysolecithin DLPC DPPC DSPC
c$””
T, “C
mol
25 50 25 50 25 50 25 50 25
553 576 317 354 296 363 903 328 900
A=B/O,
call mol
-500 -600 -500 -600 -500 380 500 500
0=
aH”g]n,4- a H ” w p .
A
A
calj (mol deg) -0.2 0.0 0.6 0.1 0.7 0.05 -1.4
x 2-PROPANOL .:lmM
2.5.
I
\\x
xDECANE
SOUMEOH
2.0 -
-
70XYEOH X
81-OCTANOL
:S D S
\
a LPC
I 51
-1.7 cpso”(
x:llmM
I
=BO,
a&$ = 289 K), bPwh= 53.8 cal/(mol deg). a
1453
. HZ0
IO1
TB /
I-OCTANOL HEXANE
x:II m M
4 5
~
o
l
.=lmM
~ X2-PROPANOL ~ N E
DECANE
4.0
-
1-OCTANOL
> n
a
.
t
30-
LPC t
2.0-
-
SDS
Dielectric
Constant
Flgure 8. Ultraviolet spectrophotometric Intensity ratios for benzene absorbance from 2720 to 2550 A. Plot of Rc (A) and R, (6) (defined In text) vs. bulk dielectric constants for selected solvents. The symbols (X or 0 )mean that 11 or 1 mM benzene was dissolved in the given solvent. The lines were drawn by hand. The two horizontal lines Indicated by LPC and SDS are the values for R , or R,, at benzene mole fractions in the micelles of about 0.4 upper and 0.06 lower.
2550
2600 Wavelength
2650
(R1
Figure 5. Ultraviolet absorbance spectra for benzene solubilized in selected solvents. Benzene concentration In water and loctanoi is 11 mM. The mole fraction of benzene in the micellar phases is 0.4. Scale bar indicates 0.1 OD units for SDS and H20 spectra and 0.2 OD for loctanoi spectrum. Path lengths are 1.0 cm in these solvents. Scale bar indicates 0.1 OD for a 1.0-mm path length in lysolecithin. SDS reference cell contained water. Lysolecithin reference cell contalned benzenasaturated water.
50 “C) are -497 and -2180 cal/mol, respectively.l0 The are obtained as described in the Apvalues of pendix. These data are presented in Table I1 for selected solvents. Here it is seen that in all cases m B / o is positive at both 25 and 50 “C and in all cases for solvents above their transition temperature it is greater at 50 OC than at 25 O C . In a l l cases is positive and has a magnitude ~ be either near zero or of -RT. In contrast, A S O B can somewhat positive for solvents above T, and significantly negative for bilayers below their transition temperature. UV Spectroscopy. Figure 5 shows a portion of the long-wave ultraviolet absorbance spectra of benzene in water (11 mM), SDS ( X , = 0.4), lysolecithin ( X , = 0.4), and 1-octanol (11 mM). We note that spectra were obtained from 3600 to 2000 A in all experiments. However,
sw
me
only the portions shown are relevant to this paper. These spectra consist of a small peak at 2690 A followed by the main peak whose maximum occurs at 2600 A for water and about 2615 A for all other solvents used. The first major valley occurs at ca. 2590 A for water and ca. 2600 A in the other solvents. Following the procedure of Cardinal and Mukerjee,14J6we have measured two absorbance ratios, R,, and R,, which are defined as R, = [(OD(2610 A) - OD(2720 A))]/[(OD(2590A) OD(2720 A))]
R,, = [ (OD(peak) - OD(2720 A))]/[ (OD(val1ey)OD(2720 A))] These ratios are plotted in Figure 6, a and b, as a function of bulk solvent dielectric constant for 1(0)and 11 (X) mM benzene solutions. The values of the bulk dielectric constants vary from about 2 (hexane, decane) to 78 (water).34 The ratios R,, and R, are relatively concentration independent for most of the solvents chosen but are concentration dependent in decane and 2-propanol. It is evident that the data points in these figures are not well correlated (r < 0.8) for values of R ,or R, and the bulk dielectric constants of a water-alkanof-alkane series. The R, and R,, values at 0.04 5 X , I0.4 (LPC) and 0.05 IX , I0.5 (SDS) are indicated by lines parallel to the dielectric constant axis. When lines drawn through selected solvent data are used, the effective dielectric constants for SDS (34) R. C. Weast, Ed.,“Handbook of Chemistry and Physics,” 55th ed. CRC Press, Cleveland, OH, 1974.
1454
The Journal of Physical Chemlstty, Vol. 86, No. 8, 7982
are 10 or 67 for R, and 40 or 46.5 if the R,, data are used. For LPC, effective dielectric constants of 78 (R,) and 10, 30, or 50 (for Rpv) may be obtained.
Discussion Partition Coefficient Data. The organic phase-water partition coefficients of benzene into nonpolar isotropic liquids, micelles, and single-walled vesicles have been measured. Within 7%, free energies of transfer of benzene from an aqueous phase into all of these solvents, from infinite dilution to saturation, are the same. We interpret this fact to mean that, on the average, in bilayers above T, as well as in micelles, benzene is partitioning into a hydrophobic environment. However, the main contribution to free energies of transfer is the interaction of benzene with water. Partition coefficients in different micelles are similar when the effects of the salt in the aqueous phase are taken into account. Our value of the partition coefficient of benzene from water to SDS (K = 1100 at 25 "C) is in good agreement with that of Brady and Huff13 ( K = 960), slightly lower than the value obtained by Rehfeldlg ( K = 1320), and significantly lower than the value of 1720 reported by Almgren et a1.12 The results of Rehfeld are probably within experimental error of ours, and the results of Almgren et al. are probably a little high for SDS as they also appear to be for CTAB (compare their results with those of Eriksson and Gillberg15). The value of the partition coefficient and hence the free energy of transfer of benzene from water to hexadecane is similar to that obtained by Leo et a1.* for the free energy of transfer of benzene from water to hexane at infinite dilution. The partition coefficient of benzene into 1-octanol is slightly lower than into alkane, reflecting the larger cohesive energy of l - ~ c t a n o l . ~ As mentioned solubility parameters for pseudophases are not necessarily good indicators for predicting the solubility of nonpolar molecules as they are in isotropic liquids. This is again evident as the solubility parameter for 1-octanol is 10.3 ( c a l / ~ m ~ )and ' / ~ for SDS it is 14.1 ( c a l / ~ m ~ )(ref ' / ~ 4 and 35). The temperature dependence of the partition coefficient and gives the values of the partial molal enthalpies of transfer. As seen in Table I1 and from entropies is experimentally the data in Figures 2 and 3, the equal to zero at 25 "C. These results are consistent with the temperature dependence of the solubility data for benzene in CTAB micelles.36 At 25 "C, m B 0 l -500 cal/mol for both micelles and bilayers. Such a value imis primarily due to a plies that the difference in difference in the enthalpic contribution to the free energy of transfer. This can be most easily understood by the dissociation of the R--?Tcomplexes between benzene molecules that is not compensated in other solvents. Entropically, it makes little difference whether benzene is in itself, in a bilayer, or in a micelle. Two main differences in the thermodynamic transfer parameters for benzene in the bilayer gel phase as compared to the liquid crystalline phase are the increase of AGoB,o to E 1kcal/mol and the now-meaningful contribution of m B / o . The negative value of 0 means that the transfer of benzene into the gel phase bilayer is opposed entropically. That is, below T,, the partial molal entropy of benzene in benzene is greater than it is in the
so
m
mwi0
meB/0
soB
(35)R. C. Little, J . Colloid Interface Sci., 66, 587 (1978). (36)S.J. Rehfeld, J. Phys. Chem., 75,3905 (1971).
Simon et al.
gel phase of a bilayer, most likely because of reduced conformational possibilities in an ordered bilayer gel phase. Above T,, these results are in contrast with partition coefficient results obtained with n-hexane in dilute solutions in micelles and bilayers.26 From a free energy and entropy viewpoint hexane much preferred itself whereas enthalpically hexane preferred the bilayer and micelle phases. At low mole fractions of hexane in the bilayer, it was inferred that hexane is located along the acyl chains. The reason that hexane has a larger entropy loss upon transferring into bilayers than does benzene is that, being chained and much less symmetrical than benzene, it has much - more configurational entropy to lose. The fact that AS"B/o II 0 for benzene suggests that, because of its shape and symmetry, the configurational entropy of benzene is about the same in almost any nonpolar liquid. Following the procedures outlined by Rehfeld'9v36 and Cardinal and M ~ k e r j e e , ' ~ we? ~have ~ attempted to determine the effective dielectric constant of the region in which benzene resides in micelles. The latter authors suggested that benzene is, on the average, in SDS and CTAB micelles in a region that has an effective dielectric constant of 49, whereas Rehfeld claimed that it is situated in a hexane-like environment in both micelles. We have shown that it is possible to obtain both such results from the same data. In addition, it is possible to obtain other values of the effective dielectric constant by choosing appropriate solvents for the empirical calibration curve. Using the same solvents listed by Cardinal and Mukerjee,14 as well as decane and hexane rather than heptane, we conclude that the effective dielectric constant values that may be obtained by using ultraviolet spectroscopy are not single valued. Therefore, this technique is not very useful for determining the location of benzene in micelles. Additional evidence that benzene is not located in a polar environment arises from the work of Rigaud et aL3' These authors measured the diffusion constant of benzene in an egg lecithin bilayer and found it to be about 1order of magnitude faster than it is for fatty acids, which are confined to the interface by virtue of their hydrophilic group. Furthermore, S ~ a l o n t a iusing , ~ ~ Raman spectral analysis, showed that benzene interacts with the nonpolar region of DPPC bilayers. In a later paper we will show that thermograms of saturated lecithins containing benzene are different from those of the same lecithins containing benzyl alcohol,2sa molecule which is located in the interfacial region. Effect of Laplace Pressure on the Partition Coefficient. Previously we and others9~12~23~2"27~39 attributed the difference between the free energy of transfer of solutes (mostly nonpolar gases and chained molecules) between themselves (isotropic liquids) and bilayers or micelles to structural differences between these solvent systems. Firstly, the relative order of the chains in a micelle or bilayer, especially those regions of the acyl chains near the interface, would tend to reduce the partial molal entropy of transfer of a solute (especially for the n-alkanes)26 relative to what they would be in an isotropic liquid. Secondly, not all of the volume in these pseudophases may be available for partition, not only for the above reason but also because of water penetration in the interfacial region.29 However, other explanations have been forwarded to account for such differences. One explanation is attributed to the Laplace pressure16*29 which is presumed (37)J. L. Rigaud, C. M. Gary-Bobo, A. Sanson, and M. Ptak, Chem. Phys. Lipids, 18,23 (1977). (38)B. Szalontai, Biochem. Biophys. Res. Commun., 70,947(1976). (39)C.Tanford, J. Phys. Chem., 78,2469 (1974).
Interaction of Benzene with Micelles and Bilayers to be present in spherical micelles and absent in bulk isotropic liquids. Examination of our partition data will indicate the lack of Laplace pressure effects on bilayers, since isotropic liquids give the same values for benzene partition as do bilayers. For small spherical micelles, it has been estimated that the Laplace pressure can be -300 atmfaJ7 The Laplace pressure for a micelle is given as AP = 2T/r, where T' is the force resultant at the micellewater interface and r is the radius of curvature of the micelle. In the above calculation, it has generally been assumed that T' is equal to the surface tension at an oil-water interface.16J7 This may not be a correct assumption, as will be discussed later. The difference in solubility of a solute in a micelle relative to that of the same material whose radius of curvature is infinite is written as AATp = -RT In X = PAP = 2T"P/r
where X is the mole fraction reduction of solute in the micelle that arises because of the curvature, r is the radius of curvature, T the force resultant, and P is the partial molal volume of the solute in the solvent, which is generally assumed to be the molar volume. Thus, the above equation predicts that the solubility or partition coefficient in micelles should be less than in isotropic liquids because of the curvature of the micelle. This explanation has been questioned by Menger,% who has suggested that water penetration into the micelle, which has the effect of decreasing the volume available for partition, can account for the reduced solubility. However, both of the above explanations assume that micelles in general and SDS in particular are spherical entities. Such an assumption is not based on either t h e o r e t i ~ a lor ~ ?experimental ~~ data for SDS.40 For example, SDS micelles are now believed to be disklike bodies of thickness 38 A having a diameter of 1000 A.@ Therefore, the SDS micelle should, for all practical purposes, look like a bilayer (where it has been shown that the partition coefficient is virtually independent of hydrostatic pressure41). This means that the potential energy barrier should be trapezoidal in shape4g rather than spherical as proposed by Almgren et a1.12 Consequently, the mean radius will now be at the geometric center rather than near the edge of the micelle. As mentioned above, the stress resultant, T', in a micelle or bilayer is not necessarily equal to the interfacial tension at an oil-water interface for either micelles or bilayers. The stress resultant is thought to comprise two opposing terms, an attractive one due principally to the hydrophobic effect and a repulsive one due to the repulsion of the polar head In the natural state, at equilibrium, these two force resultants balance so that it is possible to find bilayers, biological membranes, and under certain conditions micelles in states where T N 0, implying a low value of AP.42 (40)B. J. Forrest and L. W. Reeves, Chem. Reu., 81,1 (1981). (41)K.W.Miller and S . 4 . T. Yu, Br. J.Pharmacol., 61,57 (1977). (42)E. A. E v a and R. Skalak, 'Mechanics and Thermodynamics of Membranes", CRC Press, Cleveland, OH, 1979. (43)R. Kwok and E. Evans, Biophys. J., 35, 637 (1981). (44)D.W.R. Gruen and D. A. Haydon, Biophys. J., 30, 129 (1980). (45)C. Huang and J. T. Mason, Proc. Natl. Acad. Sci. U.S.A.,75,308 (1978). (46) C. R. Cantor and P. R. Schimmel, 'Biophysical Chemistry,"part I, W.H. Freeman, San Francisco, CA, 1980. (47)D.Small, J. Lipid Res., 8,551 (1967). (48)C. Tanford, R o c . Natl. Acad. Sci. U.S.A., 76,3318 (1979). (49)J. E. Hall, C. A. Mead, and G. Szabo, J . Membr. Biol., 11, 75 (1973). (50) G. Hyde and P. Lawrence, Proc. Int. Congr. Surf. Act. 3rd, 1,21 (1960).
The Journal of Physical Chemistry, Vol. 86, No. 8, 1982 1455
For the case of single-walled phospholipid vesicles, Tanforda has pointed out that, since these structures are freely permeable to water, the inside water pressure must be the same as the outside so that no pressure gradient exists from outside the vesicle to inside it. Moreover, Evans arid co-workers have shown experimentally that single-walled vesicles and biological membranes can exist in states where T' = 0.42p43For the case of multilamellar vesicles, Gruen and Haydonu have analyzed this problem and predicted that the solubility of alkanes in single bilayers should be significantly greater than in a multilam e h vesicle preparation because of the pressure gradient. In fact, the solubility of butane is less in small unilamellar vesicles then in multilamellar vesicles.26 Similarly, we found that the partition coefficient of benzene is smaller in the small unilamellar vesicles than in the multilamellar preparations. These differences can be most easily understood by the close packing on the inner monolayer of the small unilamellar vesicle.45 By comparing the free energy of transfer of benzene from an aqueous phase into various solvents, we conclude that benzene is predominately located in a nonpolar environment and not in an interfacial region.
Appendix Choice and Justification of Units. The question of which units to use to express organic phasewater partition coefficients is of concern for essentially two reasons. The first has to do with the choice of a standard state, be it the solute in an ideal gas phase or condensed liquid state, such as water, where it is experiencing numerous interactions with the solvent. Although the interpretation of the partition data may be simpler when the gas phase is taken as the standard state, the advantage of having the aqueous phase as the standard state is that it is the natural state for most biological and commercial processes involving nonpolar molecules. The second factor involves the choice of using molal or mole fraction ( u n i W & )units to express the partition coefficient. The organic solvent-water partition coefficient, KO,,, in mole fraction units is defined as K,,, = [(moles of solute)/(moles of solute + moles of organic solvent)]/[(moles of solute) / (moles of solute + moles of aqueous solvent)] = X o / X , (A-1) whereas in concentration units the partition coefficient,
Pol,, is defined as Pwlo= [(moles of solute)/(liters of organic solvent)]/[(moles of solute) /(liters of water)] = C, / C, (A-2) The relationship between K and P is (A-3)
where M,, d, and Mo,dorepresent the molecular weights and the densities of the aqueous and organic phases and X2is equal to the mole fraction of the organic phase. In the limit of infinite dilution, X 2 1. When the densities of the two phases are about the same, then eq A-3 reduces to its more familiar form.% One problem in deciding which units to use arises because both bilayers and micelles (unlike isotropic liquids) are "pseudophases" in that they are dispersed in water as either micelles, single-walled bilayers, or multilamellar vesicles. In addition, in these pseudophases, unlike for isotropic liquids, not all of the volume may be available for partition. The reasons are a polar head group comprising a significant fraction of the
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The Journal of Physical Chemistry, Vol. 86, No. 8, 1982
solvent molecular weight which excludes nonpolar molecules, the relative order of the acyl chains near the interface, and possibly the presence of water that penetrates into the interfacial region. Thus, if one were to express the partition coefficient in terms of moles of solute per liter of solvent, it becomes apparent that for very nonpolar molecules partitioning into an amphiphilic solvent (such as lysolecithin, where the ratio of the molecular weight of the head group to acyl chain is about 0.4) the partition coefficient expressed in concentration units may be greatly underestimated. This would not, in fact, be such a problem if a homologous series of solutes were compared in one solvent. However, in this paper we are comparing the transfer of a single solute, benzene, in different solvent systems so that the choice of units is of concern. As stated el~ewhere,~7& the major advantage of using mole fraction units is that, if one assumes the simplest expression for the free energy of mixing of solute and solvent, then the difference in standard chemical potentials of the solute in water and in the solvents represents the actual difference in interaction of the solute between the two solvents. One complication that arises in this paper from using mole fraction units if that, if one compares the partition coefficient of a solute between water and a solvent containing either one or two acyl chains per molecule, the results could differ by at least a factor of 2 (for dilute solutions). For this reason, we have presented our data in Figure 3 and Tables I and I1 such that the mole fraction of solute in the bilayer phase is normalized per mole of acyl chain. Thus, for bilayers we may write X , = [(moles of solute)/(moles of solute moles of solvent)] [(number of acyl chains) / (moles of solvent)] A-4)
+
When the data are presented in this format, the partition coefficient is more representative of the partitioning process. The partial molal free energy for transfer of benzene from water (w) to an organic solvent (0)is given by = -RT In K (A-5)
mwfo
In the above equation K = (Xo/Xw)(yo/yw), where y's are the activity coefficients. We wish to state most clearly here that we have assumed in our calculations of the free energy of transfer that yo and yw = 1; i.e., we have an infinitely dilute solution. As we have only measured X,and Xwbut
Simon et al.
not y, this clearly is an assumption. However, the values of y for benzene in various micelles and isotropic liquids have been measured or estimated. Rehfeld19*36 has calculated yoto be 1.43 for benzene in CTAB micelles and 2.10 in SDS micelles both at saturation. Moreover, it has been shown that the activity coefficient of benzene in the normal alkanes from n-hexane to n-dodecane is 1.1 up to a mole fraction of benzene of 0.5.lg3 The magnitude of the excess free energy of transfer term m E = -RT In yo (as yw = l/Xw)is, at 25 "C, -410 and -56 cal/mol for yo of 2.1 and 1.1, respectively. These corrections are in a direction to o more negative and, hence, will bring make ~ " w f even the bilayer and micelle values closer to that of benzene partitioning into benzene (see Table I). If, to a first approximation, the values of y are essentially the same in all organic solvents at the same mole fractions, then AGoB/oshould be representative of the actual differences between solvents. As seen in the Results section, the range of benzene concentration in this paper is 0.047 5 X , < 0.166. Over this range the partition coefficient is independent of concentration of benzene, suggesting a Henry's law behavior. Thus, even though the activity coefficient may not be unity, it is constant over the experimental range. To further emphasize the expected magnitude of y at low Xo's, we will consider the case where benzene only partitions into the hydrophobic region of an egg lecithin bilayer. In this system, the hydrophobic region accounts for 84% of the volume of the molecule. Under these circumstances, the volume fraction of benzene in the membrane, 6,will be 0.0067 and 0.026 for the low and high mole fraction limits stated above. These calculations were done by assuming that the partial molal volumes are equal to the molal volumes. If we take into account the head group, the volume fractions would even be smaller. For regular sol~tions,4*~ y = eB@'2/RT where B is a constant. The partial molal enthalpy of transfer is given by ZQ = R(a In K)/a(i/T) and the partial molal entropy of transfer is given by
aS" = (KP- AT)/T Acknowledgment. We thank Professors M. Harmel and P. B. Bennett for their support. This work was supported in part by grants 5T32GM07046-05 and 6M27278.
