J . Am. Chem. SOC.1987, 109, 2321-2328
2321
Thermodynamic Analyses of the Structure and Growth of Asymmetric Linear Short-Chain Lecithin Micelles Based on Small-Angle Neutron Scattering Data Tsang-Lang Lin,ts5 Sow-Hsin Chen,*t and Mary F. Robertdl Contribution from the Department of Nuclear Engineering and Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 021 39. Received September 17, 1986
Abstract: Small-angle neutron scattering data for a series of five asymmetric short-chain lecithins in aqueous solutions are analyzed in terms of a thermodynamic model for a system of spherocylindrical micelles. This analysis yields five parameters which uniquely characterize the micellar system formed by each lecithin: No, the aggregation number of the minimum size micelle; 6 / k T , the free energy change for a monomer when it is inserted into the cylinder section of the micelle; A / k T , the free energy change when No monomers aggregate to form a minimum size micelle; R,,the transverse radius of gyration; and N I L , the aggregation number per unit micelle length. Growth from the minimum micelle size is determined by the difference in free energy of monomers in the end caps vs. the same number of monomers in the cylindrical section, ( A - No 6 ) / k T . This value is related to the total number of carbons in the fatty acyl chains. It is estimated to be 7 for dihexanoylphosphatidylcholine (12 carbons) and increases to 12, 16, and 23 for lecithins with 13, 14, and 15 carbons, respectively. The conformational nonequivalence of the two fatty acyl chains affects the critical micelle concentrations, the average micelle sizes, and hence the extracted free energy parameters. For compounds with the same total number of fatty acyl carbons, the longer SUI chain species produce smaller, more slowly growing micelles with slightly lower critical micelle concentrations. This can be understood if the short-chain lecithin molecule in micelles assumes a conformation similar to that of the long-chain lecithin in bilayers. IH NMR data assessing the magnetic nonequivalence of the terminal methyl groups are consistent with this view.
Synthetic short-chain lecithins (1,2-diacyl-sn-glycero-3phosphocholines with six to eight carbons in each fatty acyl linkage) are useful model phospholipids. In aqueous solution they form micelles (rather than the multibilayers formed by longer chain phospholipids) whose properties (critical micelle concentration, average size, shape) depend on the total number of carbons in the fatty acyl linkages.'-3 Symmetric short-chain lecithins (where both SN1 and s N 2 fatty acids are identical) have been studied in detail by a number of spectroscopic Dihexanoylphosphatidylcholine (dihexanoyl-PC, where P C = phosphatidylcholine) micelles grow a t most from 18 to 20 monomers as the lecithin concentration is increased from 27 to 360 mM.' When one methylene is added to each chain the resultant lecithin, diheptanoyl-PC, forms micelles which grow rapidly (as monitored by quasi-elastic light scattering6 and small-angle neutron scattering studies*) with increasing lecithin concentration. The next lecithin in this series, dioctanoyl-PC, forms tremendously large m i c e I I e ~ . ~ % ~ We have derived a model for short-chain lecithin micelles which treats them as spherocylinders that grow in the longitudinal direction with increasing lecithin concentration. The growth is due to the free energy of insertion of a monomer in the straight section of the spherocylindrical micelle being lower than that in the end caps of the micelle.* This free energy difference is attributed to the smaller surface area of the hydrocarbon core in contact with water for a monomer in the straight section compared to that in the end caps. Micellar growth measured in terms of the increase in the weight-averaged aggregation number N is roughly proportional to the square root of the micellar concentration ( X where X i s the total lecithin concentration in mole fraction and XI is the concentration (in mole fraction) of lecithins in the free monomer state. The proportionality constant in the high where (A - No6)/kT concentration limit is equal to 2(e(A-Nd)lkr)1/2, is the total difference in free energy (TDF) in units of k T between the monomers in the two end caps and the same number of monomers in the straight section.* It is assumed that micelles grow Department of Nuclear Engineering. f Department of Chemistry. Present address: Department of Nuclear Engineering, National TsingHua University, Hsin-Chu, Taiwan, R.O.C. Present address: F. Bitter National Magnet Laboratory, M.I.T., Cambridge, MA 02139.
0002-7863/87/1509-2321~01 SO10
from a minimum size of No monomers by inserting more monomers into the center portion to form spherocylindrical micelles. Thus, No is also the number of monomers forming the two end caps of a spherocylindrical micelle. 6 / k T is the lowering of free energy in units of k T of a monomer when it is inserted into the cylindrical section of the spherocylindrical micelle, and l / k T is the corresponding free energy change in units of k T when No free monomers form a minimum size micelle. For dihexanoyl-PC, which does not grow much, the T D F is estimated to be 7 with No = 19 rt 1; for diheptanoyl-PC, whose rr,icelles grow significantly, T D F = 16.46 f 0.02 and No = 27 1.8 Further tests of this thermodynamic model can be made by SANS studies of other short-chain lecithins. Asymmetric lecithins have different length S N 1 and SN2 acyl chains and mere variability in the total number of fatty acyl carbons. It has been established that the two fatty acids of lecithins are nonequivalent in mic e l l e ~as~well , ~ as~ in~ ~ ~ ~ This conformational difference may affect the thermodynamic parameters of the micelles. For example, l-hexanoyl-2-octanoy1-PC and 1-0ctanoy1-2-hexanoyl-PC have the same total number of fatty acyl carbons (14) as diheptanoyl-PC but have acyl chains one carbon shorter and one carbon longer than the symmetric species. In forming micelles,
*
( I ) Tausk, R. J. M.; Karmiggelt, J.; Oudshoorn, C.; Overbeek, J. Th. G . Biophys. Chem. 1974, I , 175. (2) Tausk, R. J. M.; Esch, J. van.; Karmiggelt, J.; Voordouw, G.Overbeek, J. Th. G. Biophys. Chem. 1974, I , 184. ( 3 ) Tausk, R. J. M.; Oudshoorn. C.; Overbeek, J. Th. G. B i o.~ h. v s Chem. . 1951,' 2, 53. (4) Burns, R. A., Jr.; Roberts, M . F. Biochemistry 1980, 19, 3100. (5) Burns, R. A., Jr.; Roberts, M. F.; Dluhy, R.; Mendelsohn, R. J . Am. Chem. SOC.1982, 104, 430. (6) Burns, R. A., Jr.; Donovan, J. M.; Roberts, M.F. Biochemistry 1983, -2 -1, -964 - .. ( 7 ) Lin, T.-L.; Chen, S.-H.;Gabriel, N. E.; Roberts, M. F. J . A m . Chem. Soc. 1986, 108, 3499. ( 8 ) Lin, T.-L.; Chen, S.-H.;Gabriel, N. E.; Roberts, M. F. J . Phys. Chem. 1987, 91, 406. (9) Roberts, M. F.; Bothner-By, A. A,; Dennis, E. A. Biochemistry 1978,
17, 935. (IO) DeBose, C. D.; Burns, R. A,, Jr.; Donovan, J. M.; Roberts, M. F. Biochemistry 1985, 24, 1298. ( 1 1 ) Pearson, R. H.; Pascher, J. Nature (London) 1979, 281, 499. (12) Buldt, G.; Gally, H. U.; Seelig, A,; Seelig, J. Narure (London) 1978, 271, 182. (13) Seelig, J.; Browning, J. L. FEBS Lett. 1978, 92, 41
0 1987 American Chemical Societv
2322 J . Am. Chem. SOC.,Vol. 109, No. 8, 1987 t h e minor radius of t h e hydrocarbon core of a globular micelle is expected to be as large as permissible and t o s t a y in a circular or close t o a circular form in order t o minimize t h e ratio of t h e surface area of t h e hydrocarbon core in contact with water t o its volume. For micelles formed by single fatty acyl chain surfactants, t h e minor radius of t h e hydrocarbon core is found t o be equal to t h e fully stretched tail length,I4 a n d t h e cross sectional a r e a of t h e core is expected t o have a circular form due t o symmetric requirements. For surfactants with two fatty acyl chains t h e situation m a y be different from a single-chain case since t h e two chains of a surfactant are not completely independent of each other. Conformational differences in t h e lecithin SNl and s N 2 positions for a pair such as I-hexanoyl-2-octanoyl-PC and l-octanoyl-2-hexanoyl-PC should be reflected in micelle properties such as size, critical micelle concentration ( C M C ) , etc. The present article reports SANS studies of asymmetric short-chain lecithins including l-hexanoyl-2-heptanoyl-PC, 1hexanoyl-2-octanoyl-PC, l-octanoyl-2-hexanoy1-PC, l-heptanoyl-2-octanoyl-PC, and 1-0ctanoy1-2-heptanoyl-PC a n d their analyses in t e r m s of t h e thermodynamic model. Together with ‘H NMR studies of these a s y m m e t r i c species they confirm t h e and s N 2 chains in lecithin micelles a n d nonequivalence of t h e sN1 provide a quantitative understanding of growth characteristics of these short-chain lecithins. The structural parameters derived for this series of compounds are useful in evaluating explanations for t h e higher enzymatic activity of water-soluble phospholipases toward lecithin in micelles as compared to lecithin in bilayers.15J6
Lin et al. NMR Spectroscopy. ‘HN M R spectra of asymmetric short-chain lecithins at 500 MHz were obtained on a home-built instrument at the F. Bitter National Magnet Laboratory of M.I.T. Typical parameters include 4000-Hz sweep width, 60° pulse width, 5-s recycle time, and exponential multiplication of the free induction decay by 2 Hz. Lecithin samples in D 2 0 were the ones used for SANS experiments as well as further diluted monomer samples of 0.05-0.2 mM. The chemical shifts (referenced to external Me&) of the N-methyl, CH2N, and POCH2 groups were monitored as a function of lecithin concentration and were used to determine the C M C value for each lecithin. SANS Analysis. The theory of micellar growth and the methods for analyzing SANS data for a polydisperse system have been presented in detail elsewhere.8 According to a phenomenological theory which is based on the “step and ladder” models of Benedek and co-worker~,’~ the formation and growth of micelles are characterized by three parameters, (A - No6)/kT, 6/kT, and No. These parameters together with the total lecithin concentration in the solution enable one to calculate the concentration (in mole fraction) distribution of the aggregates with N-mer, XN,in equilibrium with monomer as given by8 X, = NpNe-(A-Nd)lkT where
N 2 No
I X,e-dIkT
(1) (2)
The parameter /3 can be determined by using a constraint that the total concentration X in mole fraction is equal to the sum of all XN’s and XI. This material balance equations is given in eq 3. The weight-averaged aggregation number N at a given concentration is predicted to be eq 4.8
Experimental Section Materials. Asymmetric linear lecithins 1-hexanoyl-2-heptanoyl-PC, l-hexanoyl-2-octanoyI-PC,l-octanoyl-2-hexanoyI-PC,l-heptanoyl-2octanoyl-PC, and 1-0ctanoy1-2-heptanoyl-PC were synthesized by reacting the appropriate lysophosphatidylcholine (obtained from Avanti Biochemicals, Birmingham, AL, or prepared by cobra venom phospholipase A2 hydrolysis of the diacyl species) with the desired fatty acid activated by prior reaction with carbonyldiimidazole in CHC1,.4 The acylation reaction was followed by thin-layer chromatography as described previ~usly.~ Upon completion, the reaction mixtures were chromatographed on silicic acid by using methanol in acetone or methanol in chloroform gradients to purify the asymmetric lecithin from an unreacted lyso-PC and free fatty acid. The lyso lecithin was >95% of the 1-acyl-PC isomer. Samples of different concentrations from about 1.5 times the C M C to at least 5 times the C M C were prepared for each lecithin species. This ensures a suitable range of concentrations for testing the thermodynamic theory of micelle growth. Lecithin concentrations were all kept below 35 mM to ensure that the interaction between micelles can be neglected. Sample concentrations, both before and after SANS measurements, were determined by a colorimetric phosphate assay described previously.” Uncertainty in lecithin concentration determined in this way was *2%. Small-Angle Neutron Scattering. Most of the SANS spectra were obtained at the high flux beam reactor (HFBR) of Brookhaven National Laboratory. Samples were kept at 25 ‘C during the measurement. The. sample to the 50 X 50 cm2 position-sensitive detector distance was set at 1.76 m. The neutron beam employed in the scattering measurement 5 8, with a spread AX/X N 10%. This arhad a wavelength X = rangement allowed acqu on of small-Q data in the Q range 0.013-0.22 k’. Q is the magnitude of the scattering vector given by Q 4r/X sin (8/2), where 8 is the scattering angle. The measured neutron scattering intensity distributions were corrected for background, detector efficiency, contribution from the sample cell, and incoherent scattering of the sample and were normalized with scattering from a 1-mm water sample to obtain a scattering cross section per unit sample volume Ice) in a unit of l/cm.’8 For very small Q range, 0.005 5 Q 50.04 (k’), S A N S spectra were acquired with a 30-M SANS instrument at the National Center for Small Angle Scattering Research located at the high flux isotope reactor of Oak Ridge National Laboratory. (14)Bendedouch, D.;Chen, S.-H.;Koehler, W. C. J . Phys. Chem. 1983, 87, 153. (15) Kensil, C. A,; Dennis, E. A. J . Biol. Chem. 1979, 254, 5843. (16) El-Sayed, M.Y.; DeBose, C. D.; Coury, L. A,; Roberts, M. F. Biochim. Biophys. Acta 1985, 837, 325. (17)Eaton, 9. R.; Dennis, E. A. Arch. Biochem. Biophys. 1976, 176,604. (18)Chen, S. H.;Lin, T.-L. In Methods of Experimental Phy3icsNeutronscattering; Skold, K.,Price, D. L.,Eds.; Academic: New York, 1987; Vol. 11.
(4)
The dependence of the weight-averaged aggregation number on the micellar concentration in this theory is given by eq 5.’ The P-dependent
-
I 1 4
part of the right-hand side of eq 5 approaches 2 in the high concentration limit P = 1. But in general it is more accurate to use the complete equation even for the case when p is close to unity. It appears from this equation that N - No is roughly proportional to the square root of (X-X,)’/2. The neutron scattering intensity at Q = 0, Io,for a dilute system, is directly proportional to the weight-averaged aggregation number N,while the neutron scattering intensity profile depends on the polydispersity (size distribution) and the geometrical shape of the micelles in the solution. In general, the neutron scattering intensity distribution I ( Q ) can be written as the product of Io and a normalized form factor P(Q) when the interaction between micelles can be neglected:
Io = ( C - C 1 ) N ( b ,- p,V,)2 (7) C and C1 are the total lecithin concentration and the free monomer
where
concentration in units of molecules per unit volume, respectively. b, is the coherent neutron scattering length of the lecithin molecule, and V , is the dry volume of a lecithin molecule which can be computed for each lecithin species.s ps is the coherent neutron scattering length density of the solvent. It was shown that the diheptanoyl-PC forms spherocylindrical micelles, and a micelle can be modeled as a homogeneous cylinder in computiilg the normalized form factor P ( Q ) . 8 The cylinder can be specified by values of the length L and the radius R. Since the micelles grow only in the longitudinal direction, the cross sectional structure is similar and the parameter aggregation number per unit micelle length, N I L , is a constant for each lecithin micelle. Knowing the micelle concentration distribution, X,, and the value of NIL, one is able to calculate the size (length) distribution of the micelles, which is then used to calculate the normalized structure factor, The spherocylindrical micelles have a transverse radius of gyration R, which is related to the radius R of the cylinder by R, = R/2lI2, Experimental data obtained for samples of five or more concentrations of a given lecithin species were fitted with this model to determine the (19) Missel, P. J.; Mazer, N. A.; Benedek, G.B.; Young, C. Y.;Carey, M. C. J . Phys. Chem. 1980, 84, 1044.
Short- Chain Lecithin Micelles
J. Am. Chem. SOC.,Vol. 109, No. 8, 1987 2323
Table I. Parameters Derived from SANS Data Which Characterize Short-Chain Lecithin Micelles ( A - Noa)/kT R,,A NIL, 118, 7 2 -10.65 f 0.02 12.09 0.02 11.9 0.75 f 0.07 -10.48 f 0.02 16.46 f 0.02 12.7 0.75 f 0.02 1 5 -10.57 f 0.02 16.08 f 0.03 12.6 0.85 f 0.06 5 -10.68 f 0.03 15.17 f 0.02 12.7 0.82 f 0.04 10 -11.20 f 0.01 23.52 f 0.05 15.2 1.06 f 0.10 10 -1 1.34 f 0.01 22.71 f 0.05 13.8 0.94 f 0.06 "(C,),-PC, dihexanoylphosphatidylcholine; parameters derived from SANS data presented in: Lin et al. J . Am. Chem. SOC.1986, 108, 3499. bFor 1-C,-2-Cy-PC, x denotes the number of carbons in the fatty acid esterified to the SN1position and y denotes the number of carbons in the fatty acid esterified to the SN2 position. c(C7)2-PC,diheptanoylphosphatidylcholine; parameters derived from SANS in: Lin et al. J . Phys. Chem. 1987, 91, 406.
NO
lecithin (c6)2-pca 1-C6-2-C7-PCb (c7)2-pcc l-C,-2-C*-PC 1-Cg-2-C,-PC 1-C7-2-C,-PC I-C,-2-C,-PC
6/kT
16 25 f 21 f 32 f 21 f 48 f 45 f
*
n
3 -
I-c~-z-C,Pc
,2
0
I
1
7 O d
2
nom
0 N .
A
0
i
N
u
0
A
a
0 0
"
"
PY)
O
0
0.1
0
0. 2
Q tk'l
0. I
0.2
Q (L-'l
Figure 1. SANS data from 1-hexanoyl-2-heptanoyl-PC ( 1-C6-2-C,-PC) micellar solutions in D20. The solid lines are the fitted curves from the parameters listed in Table I.
Q
Figure 3. SANS data from l-octanoyl-2-hexanoy1-PC(l-c8-2-C6-Pc) micellar solutions in DzO.The solid lines are the fitted curves from the parameters listed in Table I.
I
z
0
,.
0
A
0 .
o
w
"
"
,+
0
0
0.1
0.2
0
0.1
Q tk')
0.2
Figure 2. SANS data from 1-hexanoyl-2-octanoyl-PC ( 1-C6-2-Cg-PC) micellar solutions in DzO. The solid lines are the fitted curves from the parameters listed in Table I.
Figure 4. SANS data from 1-heptanoyl-2-octanoyl-PC ( 1-C7-2-C8-PC) micellar solutions in D 2 0 . The solid lines are the fitted curves from the parameters listed in Table I.
five parameters ( A - NoS)/kT,6 / k T , No, NIL, and R,. The nonlinear least-squares fitting was done by first entering guessed initial values of these five parameters. The fitting routine then refines these parameters, and a converged set is obtained after some iterations. A comprehensive description of this process has been given by Lin et aL8
Results Extrapolation of Micelle Parameters. Figure 1 shows SANS d a t a from 1-hexanoyl-2-heptanoyl-PC micelles a t different concentrations together with t h e fitted curves. T h e fitting results of other series, 1-hexanoyl-2-octanoyl-PC, l-octanoyl-2-hexanoyl-PC,
l-heptanoyl-2-octanoyl-PC, and l-octanoyl-2-heptanoyl-PC, are shown in Figures 2, 3, 4, a n d 5, respectively. In each series all t h e d a t a from low to high concentrations are fitted very well by t h e cylinder model. The scattering intensity a n d profile of 1hexanoyl-2-heptanoyl-PC micelles indicate that they d o not grow m u c h in this concentration range, 7-35.1 m M . In contrast, 1hexanoyl-2-octanoyl-PC and 1-octanoyl-2-hexanoyl-PCmicelles grow appreciably as indicated by t h e rapid increase of t h e scattering intensity in t h e small-Q region (Figures 2 a n d 3). For 1 -heptanoyl-2-octanoyl-PC a n d 1-octanoyl-2-heptanoyl-PCmicelles, the growth is even more pronounced. T h e scattering intensity is higher for 1-hexanoyl-2-octanoyl-PC compared with that a t the same concentration, and this for 1-octanoyl-2-hexanoyl-PC is also t r u e for 1-heptanoyl-2-octanoyl-PC compared with l-oc-
Q ti-')
P
Figure 5. SANS data from 1-0ctanoy1-2-heptanoyl-PC ( 1-C8-2-C7-PC) micellar solutions in D,O. The solid lines are the fitted curves from the parameters listed in Table I. tanoyl-2-heptanoyl-PC. For each lecithin the key parameters ([A - No6]/kT,6/kT, No, R,, NIL) obtained from the fits of the model a r e listed in Table I. For 1-heptanoyl-2-octanoyl-PC and 1-octanoyl-2-heptanoyl-PC systems t h e scattering intensity goes u p to 40 or 50 cm-' in the small-Q region for higher concentration samples. However, t h e experimental d a t a used in the fitting covers a Q region only from 0.013 A-' and up. To be sure that the parameters extracted from
Lin et al.
2324 J . Am. Chem. SOC.,Vol. 109, No. 8, 1987 I
the order of thousands in a concentration range 2-15 mM. The size is more than 10 times larger than the size of micelles formed or 1-0ctanoy1-2-hexanoyl-PC in the by 1-hexanoyl-2-octanoyl-PC same concentration range. The comparative growth rates are best illustrated by plotting the mean aggregation number vs. the square root of X - X I as shown in Figure 8. These curves are close to straight lines with slopes close to 2 exp[(A - N06)/2kT] according to the thermodynamic theory for micellar growth. Thus a slight difference in the value of (A - NoG)/kT would cause a great difference in the mean aggregation number. Another way to examine the dependence of growth rate for different species of lecithins is to look a t the values of (A No6)/KT for each species (Figure 9). Values for (A - No6)/kT can be classified according to the total carbon atoms in the fatty acyl chains of each lecithin species. The 14-carbon species diheptanoyl-PC, l-hexanoyl-2-octanoyl-PC,and 1-0ctanoyl-2-heptanoyl-PC are in one group with similar values of (A - NoG)/kT (TDF), ca. 16, while the 15-carbon species 1-heptanoyl-2-octanoyl-PC and 1-octanoyl-2-heptanoyl-PC are in another group with T D F values around 23. 1-Hexanoyl-2-heptanoyl-PChas 13 carbons in its chains and has a TDF = 12.086. The values of TDF roughly have a linear relationship with the number of fatty acyl carbon atoms as shown in Figure 9 by the broken line. This behavior predicts the T D F to be equal to 7 for dihexanoyl-PC micelles and about 28 for dioctanoyl-PC micelles. The wei&averaged mean aggregation number of dihexanoyl-PC micelles determined by S A N S remained a t 19 f 1 from 27 to 360 mM.' = 20 in this The growth rate is a t most from N = 18 to concentration range. The value of T D F can then be estimated to be about 7 or less. As for dioctanoyl-PC micelles there is no reliable data, since phase separation occurs a t room temperature when salts are not added to suppress it.3*10With a value of TDF around 28 for dioctanoyl-PC species, the micelles are predicted to grow into extremely large rod-like aggregates even at a few millimolar concentration. The interaction between these very large rod-like micelles cannot be neglected even at very low concentrations. In general one has the idea that TDF will increase about 5 when the tails have one more methylene group added. The increase in TDF is in conjunction with the increase of the hydrocarbon core size when the volume of the tails is increased by adding more methylene groups to them. The size (minor radii) of the hydrocarbon core can be and must be increased to accommodate the larger tails. The result is that the surface area of the hydrocarbon core is thus increased, and the difference between the total surface area of the two end caps and the surface area of the same number of monomers in the straight section is thus increased. TDF can be considered as proportional to this
- c y 2-c8 PC
I 0.01
0
0.02
Q
0.03
0.01
th-')
Figure 6. Open circles are the SANS experimental data covering a smaller Q region 0.005-0.04 A-l from a D20solution containing 13.0
m M 1-heptanoyl-2-octanoyl-PClecithin. The solid curve is the calculated behavior using the parameters, listed in Table I, determined from fitting the data shown in Figure 4, which covers the Q range 0.013-0.22 A-l. the fitting are reliable without fitting any data below Q = 0.013 A-', neutron scattering data in the Q range 0.005-0.04 A-' from a 13.0 mM 1-heptanoyl-2-octanoyl-PCsolution taken at the HFIR, Oak Ridge National Laboratory, are compared with the predicted intensity computed by using the extracted parameters. Excellent agreement, as shown in-Figue 6 , is found between the predicted intensity and measured intensity even in this smaller Q region. Figure 7 shows the plot of weight-averaged aggregation number vs. concentration for these asymmetric lecithin micellar systems. For 1-hexanoyl-2-heptanoyI-PC micelles, the mean aggregation number is found to increase from 34 to 44 as the concentration is increased from 7 to 35.1 m M (Figure 7A). The growth is noticeable for this asymmetric species compared to dihexanoyl-PC micelles, but it is still small compared to the growth of diheptanoyl-PC micelles,8 which grow from a mean aggregation number of 48 to 193 as the concentration was increased from 2.2 to 35.0 mM.8 The growth of 1-hexanoyl-2-octanoyl-PC and 1-0ctanoyl-2-hexanoyl-PC micelles with increasing concentration (Figure 7B) is comparable to the diheptanoyl-PC micellar system. The growth rate of 1-0ctanoy1-2-hexanoyl-PC micelles is lower than that of l-hexanoyl-2-0ctanoyl-PC,and the mean aggregation number a t the same concentration is smaller for l-octanoyl-2hexanoyl-PC. The same tendency is found for l-octanoyl-2heptanoyl-PC micelles compared with 1-heptanoyl-2-octanoyl-PC micelles, as shown in Figure 7C. The sizes of the micelles formed by 1-heptanoyl-2-octanoyl-PC or 1-octanoyl-2-heptanoyl-PC are much larger than those formed by the lecithins with 14 carbons in their fatty acyl chains. The mean aggregation number is on
7
I- G-2-h PC
I-
c,- 2-CI
PC
0 0 -
0 0 -
n 0 C Lcl
:
0
0 N
Lcl Lcl
0 0 0 r( -
-
0
10
20
30
s
IO
1s
20
2s
-
0
s
10
IS
PC ( m M ) PC ( m M ) PC ( m M ) Figure 7. The weight-averaged aggregation number (i?) determined by fitting the experimental data is plotted vs. the lecithin concentration for (A) l-hexanoyl-2-heptanoyl-PC, (B) l-hexanoyl-2-octanoy1-PCand l-octanoyl-2-hexanoy1-PC,and (C) 1-heptanoyl-2-octanoyl-PCand l-octanoyl-2heptanoyl-PC.
Short- Chain Lecithin Micelles (A)
J . Am. Chem. Soc., Vol. 109, No. 8, 1987 2325 (B)
0
I - Ce- 2-c, PC
I 0
0..
a 0
" 0
-
0
a N
0 0 r(
-u 0.0 I
OO
m
Oo
0.02
a005
0.010
m
aois
Figure 8. The weight-averaged aggregation number, N,is plotted vs. (X for (A) l-hexanoyl-2-heptanoyl-PC, l-hexanoyl-2-octanoyI-PC, and 1-octanoyl-2-hexanoyl-PC and (B) 1-heptanoyl-2-octanoyl-PCand 1-octanoyl-2-heptanoyl-PC.The slopes of the lines are approximately equal to 2[exp(A - NOB)/kT]1/2. (C)
(A)
F
P
I
t/
t
m D
-
2 12
:t
I3
14
I5
C A R B O N ATOMS
16
: I2
13
14
I5
16
CARBON ATOMS
Figure 9. The following parameters for spherocylindrical short-chain lecithin micelles, determined from fitting the SANS data, are plotted vs. the total number of carbon atoms in the two fatty acyl chains: (A) (A - N,G)/kT; (B) No, the number of monomers in the two end caps (minimum size micelle); (C) R, (A), the transverse radius of gyration; (D) N I L (A-'), the aggregation number per unit micelle length. Asymmetric lecithins with the sN1 chain shorter than its sN2 chain are represented by filled circles while the lecithins with the sN1 chain longer than its sN2 chain are represented by open circles. The diheptanoyl-PC is represented by filled triangles.
surface area difference with a constant hydrophobic interfacial free energy per unit area. sN1/sN2 Chain Nonequivalence. The actual dependence of T D F on the species of lecithins is far more complicated than this general rule. TDF values have been determined in great accuracy from fitting the SANS data since it is a very sensitive parameter in determining the micelle size. In Figure 9 T D F values for asymmetric lecithins with the sN1 chain shorter than its SN2 chain are represented by filled circles while the lecithins with the SN1 chain longer than its sN2 chain are represented by open circles. It can be seen that TDF values are higher for lecithins with shorter SN1chains. The same ordering is also found in other parameters such as No,R,, and N I L as shown in Figure 9 (although R,'s of 14-carbon lecithins are essentially identical). This indicates that
Sn- I
I- c
