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The use of NMR parameters for the evaluation of the critical micelle concentration of lecithin in reverse micellar systems
Volume 158, number 3,4
CHEMICAL
9 June I989
PHYSICS LETTEKS
THE USE OF NMR PARAMETERS FOR THE EVALUATION OF THE CRITICAL MICELLE CONCENTRATION OF LECITHIN IN REVERSE MICELLAR SYSTEMS M. GIOMINI a, A.M. GIULIANI b, E. TROTTA ’ and CA. BOICELLI d a Dipartimento di Chzmica dell’Universitk “La Saprcnza”, Rome, Italy Ir Dzpartzmento dz Chzmzca dell’linzversitci, Palermo. Italy c ITS5CNR, Area delia Rzcerca dr Roma, Monterotondo Stazione, Italy * Istiruto San Raffaeie, Laboratorio Ricerca NMR, Milan, Italy Received 3 December
1988; in final form 2Y March 1089
Lecithin/water/benzene reverse micellar systems have been studied by ‘H NMR. The dependence of the chemical shift of the water and of the trimethylammonium protons on the phospholipid concentration has been measured at several temperatures and waterjphospholipid molar ratios ( wO) to evaluate the critical micelle concentration of lecithin. Pre-micellar aggregation, with formation of small aggregates comprised of 2-3 monomers, is suggested by the results. The critical micelle concentration has been found to bc practically independent of w,, indicating that the systems can bc considcrcd as binary, provided wg is kept constant while varying the surfactant concentration. Some thermodynamic quantities related to the micellization process have also been evaluated.
1. Introduction The critical micelle concentration (CMC), namely the concentration of a monomeric amphiphile in equilibrium with micellar aggregates, is a fairly well defined concept for aqueous surfactants [ l-31. The situation is less well defined for amphiphiles in nonpolar solvents, where the cooperativity of the aggregation process is much smaller [ 4,5 1. When the aggregation number is small, the change in physical properties with increasing concentration of the surfactant is gradual and it is difficult to extract a meaningful CMC, indeed the CMC concept becomes questionable [ 6,7] Moreover, these systems should be considered ternary, because of the minute amounts of water invariably present in the organic solvent; the CMC would then lose significance, since it changes with the amount of water [ 81. Despite these ambiguities, the CMC has been determined for many surfactants in non-polar solvents [ 3,8]. Obviously, this same problem is encountered when water is added to an amphiphile solution in a nonpolar solvent, to obtain reverse micelles with an aqueous inner pool (microemulsions). However, 334
within the limits of reliability discussed above, an apparent CMC can be obtained for these reverse micellar systems if the waterjsurfactant molar ratio ( wo) is kept constant, while varying the surfactant concentration, so as to deal with a pseudo-binary system. We have studied by ‘H NMR spectroscopy the reverse micelles of egg yolk lecithin in benzene at several w. values, following essentially the procedure suggested by Haque et al. [9] to extract the CMC data.
2. Materials
and methods
Egg yolk L-a-phosphatidylcholine (EPC) from Sigma Chem. Co. (type VII-E, chloroform solution) was used without further treatment after evaporation of the solvent under vacuum. The commercial product contains between three and four water molecules per polar head, as determined by ‘H NMR, which were not removed. The average molecular weight of the hydrated lecithin was 8 19 dalton, as obtained by ‘H and 13C NMR data. Purity was
0 009-2614/89/$ ( North-Holland
03.50 0 Elsevier Science Publishers Physics Publishing Division )
B.V.
Volume 158, number 3,4
CHEMICAL
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checked by TLC. Doubly distilled water and Merck UVASOL [2H,]-benzene (> 99.5% deuteriation) were used. The NMR data were obtained with both a Bruker AC200 spectrometer (NMR Service of the Area della Ricerca of CNR, Rome) and a Bruker WM200 spectrometer (Department of NMR Research, Istituto San Raffaele, Milan), operating at 200 MHz on protons_ The solvent was used for field-frequency lock and as reference (6=7.27 ppm from TMS). The reverse micelies were prepared by low energy sonication in an Ultrasonic water bath kept at z 4”C, using deoxygenated solvent and operating under a current of N2 to avoid degradation of the lecithin. No sign of deterioration was observed by ‘H NMR after the preparation procedure.
3. Experimental
9 June 1989
were performed at 297, 303, 313 and 323 K. The number of water molecules added per polar head of lecithin were: 0 (~~~3-4); 5 (w,=8-9); 10 (wO= 13-14); 15 (w,=18-19); 20 (~~~23-24). The chemical shift of any particular resonance sensitive to aggregation should obey the relationship s=4nic
+
(CnonIc)
(Ismon -dmic)
T
(1)
assuming the “mass-action model” for the aggregation. The equation holds for both single- and multiple-step equilibrium models, provided that equal chemical shifts for all micellar species are assumed [ 71. In eq. ( 1), S, 6,,, and S,,, are the experimental, the micellar and the monomer shift, respectively; C lIl0” and C are the monomer and the weighed-in concentration, respectively. At high concentrations, assuming monodispersity of the micellar aggregates (which has indeed been found [ lo] ), C,,, approaches CMC, while in the very low concentration limit C,,, approaches C and the measured chemical shift approximates &,,. The water resonance is the most responsive to the aggregation process; its chemical shift, S,, is plotted in fig. 1 as a function of 1/C for w,,= 13- 14 at different temperatures.
results
We have recorded the ‘H NMR spectra of pseudobinary EPC/water/benzene systems prepared at a fixed w. and a lecithin concentration varying from 1.22~10~~ to 6.10~10-* M. The measurements -
7
: 5.0
I
I
I
I
2.0
I
6.0 l/C
Fig. 1. Variation of SWwith reciprocal lecithin concentration in[‘H,]-benzene.(0)297K,(W)303K,(n)313K;(A)323K.
I
I
I
4.0
8.0
I
10.0
I
I
12.
I mL/mg)
at w,= 13-14 and different temperatures
for reverse micelles of egg lecithin
335
158,number 3,4
Volume
Table 1 Mrcellar shift, 6;” benzene systems T(K)
CHEMICAL
(ppm from TMS),
PHYSICS LETTERS
The equations of the 6 versus l/C lines at high concentrations and the values of &?Jic(intercept with the ordinate axis, tabIe 1) were obtained from linear regression analysis. The parameter &JJ”‘, obtained from the plot of 8, versus C extrapolated to zero concentration, has been found to be virtually independent of both W, and T and equal to 0.51 kO.01 ppm (from linear regression analysis). This value, which is the chemical shift of free water dissolved in benzene, is in agreement with the value of 0.4 1 ppm reported by Heatly [ 111 for water in benzene (k7.17 ppm). The CMC can be evaluated by extrapolation of the straight lines in the high-concentration region to 6,,,. The values reported in table 2 were calculated from the equations and the extrapolated SE”” values. The water resonance shifts downfield as the lecithin concentration increases, in agreement with the formation of hydrogen bonds [ 8,111, which is maximal in the highly organized structure of the reverse micelles
for egg lecithin/water/
“‘0
291 303 313 323
3-4
8-9
13-14
18-19
23-24
5.26 5.19 5.03 4.96
5.24 5.17 5.01 4.84
5.33 5.28 5.15 5.04
5.41 5.34 5.26 5.16
5.3s 5.33 5.23 5.17
Table 2 Critical micelle concentration bcnzenc systems as determined
297 303 313 323
( lo3 M) for egg lecithin/water/ from SW
3-4
8-9
13-14
1%1Y
23-24
3.07 3.43 4.08 5.58
3.28 3.82 4.81 5.76
3.04 3.54 4.59 6.04
2.83 3.55 4.26 5.24
2.25 3.60 4.34 5.41
9 June 1989
1101. A similar downfield
shift, though much less pro-
r-
e
3.40
0.
On
0.
00
2.0
4.0
6 .O l/C
Fig. 2. Variation
of S, with reciprocal
lecithin concentration
in[2H~]-benzene.(0)297K;(0)303K;(A)313K;(A)323K.
336
at w,=3-4
8.0
10.0
f mL/mgl and
at different temperatures
for reverse micelles ofegg lecithin
Volume 158, number 3,4
CHEMICAL PHYSICS LETTERS
9 June 1989
C
C (mg/mLI
Fig. 3. Variation of 6, with lecithin concentration at w,,=3-4 and at different temperatures for reverse micelles of egg lecithin in L2H6]benzene. (0) 297 K; (a) 303K, (a) 313 K; (A) 323 K
nounced, is shown by the trimethylammonium protons of lecithin, which can be taken as evidence for the aggregation process. Its chemical shift, S,,, is plotted as a function of 1 /C in fig. 2 for w, = 3-4 at different temperatures. Very little information can be obtained from such plots since no linear region is observed at high concentrations and 6,,, cannot be obtained in a reliable way in most cases. Slightly more informative are the plots of 6, as a function of C (fig. 3): the asymptote of the plots in the high-concentration region gives SF’“. An upper limit can be evaluated for the apparent CMC (CMC < 0.6 mM for all w, values) only at 323 K, while at lower temperatures not even such limiting value can be proposed.
4. Discussion
and conclusions
The most interesting result of this study (table 2) is the limited change of the apparent CMC (as calculated from 8, data) with w,, at any given tem-
perature. This quite unexpected result means that the system behaves essentially as binary, thus restoring, at least in part, the concept of the CMC as applied to reverse micelles. The CMC data can then be used to obtain some thermodynamic information on the system under study. The standard free energy values of the micellization process are obtained from the equation AG“=RTln(CMC),
(2)
where R is the gas constant. The enthalpy of the process can be found according to the equation proposed by Stainsby and Alexander [ 12 ] AH’=
-RT’d
ln(CMC)/dT
(3)
from the plot of ln(CMC) against 1/T. Such plots, constructed from the SWdata, are linear for all w. values, except for w. = 3-4 [ 91, indicating that AH0 is independent of temperature (fig. 4). A small negative enthalpy change is involved in the micellization (AP= -0.95 kO.05 kcal/mol); the standard free 337
Fig. 4. Variation of ln( CMC) with 1/I’ for reverse micelles of egg leclthm m [‘H,] -benzene. (0 ) w,= 3-4; (0 ) w,= 8-9; (A)w,=13-14; (a) w,=18-19.
energy involved in the process, calculated from eq. ( 2) I is essentially constant and equal to - 4.8 ? 0.1 kcal/mol. Another point of interest, which requires explanation, is the discrepancy between the CMC values obtained from the chemical shift data of water and trimethylammonium protons, which is well outside the range of experimental uncertainty. The former values are several times larger than the latter. One reasonable hypothesis is that the two sets of data reflect different aggregation phenomena. The trimethylammonium chemical shift might reflect the formation of small non-vesicular aggregates of few phospholipid monomers, where the lecithin polar heads are directly involved; on the other hand, the water chemical shift might respond only to the formation of micellcs, i.c. closed aggregates [ 8 ] with an interior water pool. The existence of aggregates of different size, one of which has a very low value of the mean aggregation number (i.e. 2-4), for lecithin in benzene has already been reported by Elworthy [ 13 ] on the basis of osmotic pressure measurements. In principle [ 91, the mean aggregation number fi might be obtained as the slope of the plot of log C(6-6,,,)/(6,,,-S,,,) 338
9 June 1989
CHEMICAL PHYSICS LETTERS
Volume 158, number 3,4
versus
log C(L,,-6)/
(S,,,.-S,,,). At low concentrations (CG 1-2 mg/ ml) such plots, calculated from S, data, yield a value of fl between 2 and 3. Moreover, in this region, a plot of 6, against C should be linear (as we have indeed found) if the only significant aggregate species is the dimer, when a multiple-equilibrium model and an equal chemical shift for all associated species are assumed [ 71. It must, however, be noted that SWis also a linear function of C in very dilute solutions, indicating that the first aggregate species is the dimer. The log-log plots, on the other hand, show a linear region with slope between 2 and 3 at low concentrations, followed by a very steep rise (fig. 5) suggesting the formation of micellar aggregates with a high value of ti. From previous measurements [ IO], the estimated number of monomers in a lecithin reverse micelle in benzene (~~~25) is in fact of the order of 700-800. These results indicate that an appropriate way of handling the data suggests the forma-
2.0
I_
0
H -2.0 T = 303 K
Fig. 5. A plot of log c(a-s,,,)/(a,,,-s,,,) as a function of log C(a,,,-a)/(~~,,,-d,,,) constructed from the 6, data.
Volume 158,
CHEMICAL
number 3.4
PHYSICS LETTERS
9
June 1989
tion of small, non-vesicular aggregates through the use of accurate SWdata for dilute solutions. It may be added that large values of fi cannot be reliably determined with the log-log plots because of the large errors in the parameters involved (see appendix). It may be concluded that, while the aggregation process in our systems is not highly cooperative, there is a fairly limited range of concentrations of lecithin
tion), although our systems have been found to be, to a good approximation, monodisperse at high lecithin concentrations [lo]. In addition, it should be borne in mind that the experimental definition of the CMC is not unique (see 6, and 6, data) and “the simplest practical procedure is to let the experiment define the CMC” [ 5 1.
within which the micellization takes place and an apparent CMC can be assigned making use of ‘H NMR data. Several points must, however, be stressed. First of all, it appears that small aggregates may form, prior to reverse micelle formation (pre-micellar aggrega-
Acknowledgement The authors wish to thank Mr. A. Ripamonti of the Istituto San Raffaele, Milan, for technical assistance.
Appendix To estimate the reliability of the values of ff obtained from the log-log plot, one can proceed in the following way.
AlogC(6_6,,,)/(6,i,-6,,“)
‘= A log C(&,,
-~)/(&lK-&l0”)
’
that is, 1ogCL(~Z-~mon)/16,,,-6,,,)-1ogC,(6,-6,,”)/(6,i,-6,,“),
A= log C2(Bmlc -s,)!(6,,,-~~;,,“)-logc,(6,,,-s,)/(6,,,-6,,”) rearranging
’
the terms and simplifying
n= log WC, +logt62 -&,,)/(~, logC,IC,+log(6,,,-fi,)/(6,,,-SI) Let the numerator
-&l,,)
be A and the denominator
S, the probable mean-square
d~=~[(~~)1+(~~)^3”~=~[i~~+(~d~~]”2=~~(~2+ri’d82)“2;
error of fi is (A.1)
where ,=,[(~dC,)2+(~dC2j2+i~d6,)2+(~dd,)2+(~ds,,.)l]lil
(A.2)
and d~=i[(~dC,~+(~d~~~+(~d~~i~~+(~d~~~+(~d~~~]”*. Developing
t.4.3)
(A.2) and (A.3)
339
Volume 158,number 3,4
9 June 1989
CHEMICAL PHYSICS LETTERS
Assuming that the precision with which the concentration is known is l%, i.e. dC/C= 0.0 1, and that the error on the chemical shift values, both measured and extrapolated, db, is k 0.01 ppm, we have d/4=-t
(
10-4+10-4+
2x 1o-4 (82_Gmon)2 +
(;rlio_l)J”z=
+ 10--2(2+
(&_;~,“)z
+ (8, _:,,,.J
and 2x 1o-4 (6mic-d1)2
+
At high concentrations, for our system with w,,= 13-14 and T= 303 K, for example, &,,= 5.28, &,,,= 0.51, &=5.00, 6,=4.60 ppm when C,=SO and Cl=20 mg/ml (i.e. C,/C,=2.5), one finds dA=? 1.5x lo-‘and dB= f5.6~ 10-2. In our example the value of B calculated from experimental data is 0.013, while dB= _+5.6 x lo-‘, larger than B itself. Indeed IdAl > (5.6x
IO-‘)/B)A,
(dnj /n> 4.3 a
Therefore, it is impossible to calculate any reliable value of #. At low concentrations, for the same system taken as an example, we have c&=2.01 and 6, = 0.61 ppm for C,=2 and C,=O.l mg/ml (C,/C,=20) giving dA=? 14.2x10-* and dB=? 1.5~ 10e2. With the experimental value of ~~2.3, one obtains dn= kO.13. Similar results have been obtained with different values of wUand at different temperatures.
References [I ] R. Lindman and H. Wennerstriim, in: Topics in current chemistry, Vol 87. Micelles (Springer, Berlin, 1980) p. 1. [2] J.N. Israelachvili, in: Physics of amphiphiles: micelles, vesicles and microemulsions, eds. V. DeGiorgio and M. Corti (North-Holland, Amsterdam, 1985) p. 24. [3] J.H. Fendler, Membrane mimetic chemistry (WileyInterscience, New York, f982) ch. 2. [4] B. Lindman, in: Physics of amphiphiles: micelles, vesicles and microcmulsions. eds. V. DeGiorgio and M. Corti (North-Holland, Amsterdam, 1985) p. 7. [ 5 ] C. Tanford, in: Mlcellization, solubilization and microemulsions, ed. K.L. Mittal (Plenum Press, New York, 1977) p, 119.
340
[ 61 A-S. K&es and H. Gutmann, in: Surface andcolloid science, Vol. X,ed. E. Matijevic (Wiley, New York, 1976) p. 193. [7] N. Muller, J. Phys. Chem. 79 (1975) 287. [ 8] H.-F. Eicke, in: Topics incurrent chemistry, Vol. 87. Micelles (Springer, Berlin, 1980) p. 85. 19] R. Haque, 1.J. Tinsley and D. Schmedding, J. Biol. Chem. 247 (1972) 157. [IO] CA. Boicelli, F. Conti, M. Giomini and A.M. Giuliani, Chem. Phys. Letters X9 ( 1982) 490. [ 1I ] F. Heatley, J. Chem. Sot. Faraday Trans. I 84 (1988) 343. [ 121 G. Stainsby and A.E. Alexander, Trans. Faraday Sot 46 (1950) 587. [13] P.H. Elworthy, J. Chem. Sot. (1959) 813.
CHEMICAL
9 June I989
PHYSICS LETTEKS
THE USE OF NMR PARAMETERS FOR THE EVALUATION OF THE CRITICAL MICELLE CONCENTRATION OF LECITHIN IN REVERSE MICELLAR SYSTEMS M. GIOMINI a, A.M. GIULIANI b, E. TROTTA ’ and CA. BOICELLI d a Dipartimento di Chzmica dell’Universitk “La Saprcnza”, Rome, Italy Ir Dzpartzmento dz Chzmzca dell’linzversitci, Palermo. Italy c ITS5CNR, Area delia Rzcerca dr Roma, Monterotondo Stazione, Italy * Istiruto San Raffaeie, Laboratorio Ricerca NMR, Milan, Italy Received 3 December
1988; in final form 2Y March 1089
Lecithin/water/benzene reverse micellar systems have been studied by ‘H NMR. The dependence of the chemical shift of the water and of the trimethylammonium protons on the phospholipid concentration has been measured at several temperatures and waterjphospholipid molar ratios ( wO) to evaluate the critical micelle concentration of lecithin. Pre-micellar aggregation, with formation of small aggregates comprised of 2-3 monomers, is suggested by the results. The critical micelle concentration has been found to bc practically independent of w,, indicating that the systems can bc considcrcd as binary, provided wg is kept constant while varying the surfactant concentration. Some thermodynamic quantities related to the micellization process have also been evaluated.
1. Introduction The critical micelle concentration (CMC), namely the concentration of a monomeric amphiphile in equilibrium with micellar aggregates, is a fairly well defined concept for aqueous surfactants [ l-31. The situation is less well defined for amphiphiles in nonpolar solvents, where the cooperativity of the aggregation process is much smaller [ 4,5 1. When the aggregation number is small, the change in physical properties with increasing concentration of the surfactant is gradual and it is difficult to extract a meaningful CMC, indeed the CMC concept becomes questionable [ 6,7] Moreover, these systems should be considered ternary, because of the minute amounts of water invariably present in the organic solvent; the CMC would then lose significance, since it changes with the amount of water [ 81. Despite these ambiguities, the CMC has been determined for many surfactants in non-polar solvents [ 3,8]. Obviously, this same problem is encountered when water is added to an amphiphile solution in a nonpolar solvent, to obtain reverse micelles with an aqueous inner pool (microemulsions). However, 334
within the limits of reliability discussed above, an apparent CMC can be obtained for these reverse micellar systems if the waterjsurfactant molar ratio ( wo) is kept constant, while varying the surfactant concentration, so as to deal with a pseudo-binary system. We have studied by ‘H NMR spectroscopy the reverse micelles of egg yolk lecithin in benzene at several w. values, following essentially the procedure suggested by Haque et al. [9] to extract the CMC data.
2. Materials
and methods
Egg yolk L-a-phosphatidylcholine (EPC) from Sigma Chem. Co. (type VII-E, chloroform solution) was used without further treatment after evaporation of the solvent under vacuum. The commercial product contains between three and four water molecules per polar head, as determined by ‘H NMR, which were not removed. The average molecular weight of the hydrated lecithin was 8 19 dalton, as obtained by ‘H and 13C NMR data. Purity was
0 009-2614/89/$ ( North-Holland
03.50 0 Elsevier Science Publishers Physics Publishing Division )
B.V.
Volume 158, number 3,4
CHEMICAL
PHYSICS LETTERS
checked by TLC. Doubly distilled water and Merck UVASOL [2H,]-benzene (> 99.5% deuteriation) were used. The NMR data were obtained with both a Bruker AC200 spectrometer (NMR Service of the Area della Ricerca of CNR, Rome) and a Bruker WM200 spectrometer (Department of NMR Research, Istituto San Raffaele, Milan), operating at 200 MHz on protons_ The solvent was used for field-frequency lock and as reference (6=7.27 ppm from TMS). The reverse micelies were prepared by low energy sonication in an Ultrasonic water bath kept at z 4”C, using deoxygenated solvent and operating under a current of N2 to avoid degradation of the lecithin. No sign of deterioration was observed by ‘H NMR after the preparation procedure.
3. Experimental
9 June 1989
were performed at 297, 303, 313 and 323 K. The number of water molecules added per polar head of lecithin were: 0 (~~~3-4); 5 (w,=8-9); 10 (wO= 13-14); 15 (w,=18-19); 20 (~~~23-24). The chemical shift of any particular resonance sensitive to aggregation should obey the relationship s=4nic
+
(CnonIc)
(Ismon -dmic)
T
(1)
assuming the “mass-action model” for the aggregation. The equation holds for both single- and multiple-step equilibrium models, provided that equal chemical shifts for all micellar species are assumed [ 71. In eq. ( 1), S, 6,,, and S,,, are the experimental, the micellar and the monomer shift, respectively; C lIl0” and C are the monomer and the weighed-in concentration, respectively. At high concentrations, assuming monodispersity of the micellar aggregates (which has indeed been found [ lo] ), C,,, approaches CMC, while in the very low concentration limit C,,, approaches C and the measured chemical shift approximates &,,. The water resonance is the most responsive to the aggregation process; its chemical shift, S,, is plotted in fig. 1 as a function of 1/C for w,,= 13- 14 at different temperatures.
results
We have recorded the ‘H NMR spectra of pseudobinary EPC/water/benzene systems prepared at a fixed w. and a lecithin concentration varying from 1.22~10~~ to 6.10~10-* M. The measurements -
7
: 5.0
I
I
I
I
2.0
I
6.0 l/C
Fig. 1. Variation of SWwith reciprocal lecithin concentration in[‘H,]-benzene.(0)297K,(W)303K,(n)313K;(A)323K.
I
I
I
4.0
8.0
I
10.0
I
I
12.
I mL/mg)
at w,= 13-14 and different temperatures
for reverse micelles of egg lecithin
335
158,number 3,4
Volume
Table 1 Mrcellar shift, 6;” benzene systems T(K)
CHEMICAL
(ppm from TMS),
PHYSICS LETTERS
The equations of the 6 versus l/C lines at high concentrations and the values of &?Jic(intercept with the ordinate axis, tabIe 1) were obtained from linear regression analysis. The parameter &JJ”‘, obtained from the plot of 8, versus C extrapolated to zero concentration, has been found to be virtually independent of both W, and T and equal to 0.51 kO.01 ppm (from linear regression analysis). This value, which is the chemical shift of free water dissolved in benzene, is in agreement with the value of 0.4 1 ppm reported by Heatly [ 111 for water in benzene (k7.17 ppm). The CMC can be evaluated by extrapolation of the straight lines in the high-concentration region to 6,,,. The values reported in table 2 were calculated from the equations and the extrapolated SE”” values. The water resonance shifts downfield as the lecithin concentration increases, in agreement with the formation of hydrogen bonds [ 8,111, which is maximal in the highly organized structure of the reverse micelles
for egg lecithin/water/
“‘0
291 303 313 323
3-4
8-9
13-14
18-19
23-24
5.26 5.19 5.03 4.96
5.24 5.17 5.01 4.84
5.33 5.28 5.15 5.04
5.41 5.34 5.26 5.16
5.3s 5.33 5.23 5.17
Table 2 Critical micelle concentration bcnzenc systems as determined
297 303 313 323
( lo3 M) for egg lecithin/water/ from SW
3-4
8-9
13-14
1%1Y
23-24
3.07 3.43 4.08 5.58
3.28 3.82 4.81 5.76
3.04 3.54 4.59 6.04
2.83 3.55 4.26 5.24
2.25 3.60 4.34 5.41
9 June 1989
1101. A similar downfield
shift, though much less pro-
r-
e
3.40
0.
On
0.
00
2.0
4.0
6 .O l/C
Fig. 2. Variation
of S, with reciprocal
lecithin concentration
in[2H~]-benzene.(0)297K;(0)303K;(A)313K;(A)323K.
336
at w,=3-4
8.0
10.0
f mL/mgl and
at different temperatures
for reverse micelles ofegg lecithin
Volume 158, number 3,4
CHEMICAL PHYSICS LETTERS
9 June 1989
C
C (mg/mLI
Fig. 3. Variation of 6, with lecithin concentration at w,,=3-4 and at different temperatures for reverse micelles of egg lecithin in L2H6]benzene. (0) 297 K; (a) 303K, (a) 313 K; (A) 323 K
nounced, is shown by the trimethylammonium protons of lecithin, which can be taken as evidence for the aggregation process. Its chemical shift, S,,, is plotted as a function of 1 /C in fig. 2 for w, = 3-4 at different temperatures. Very little information can be obtained from such plots since no linear region is observed at high concentrations and 6,,, cannot be obtained in a reliable way in most cases. Slightly more informative are the plots of 6, as a function of C (fig. 3): the asymptote of the plots in the high-concentration region gives SF’“. An upper limit can be evaluated for the apparent CMC (CMC < 0.6 mM for all w, values) only at 323 K, while at lower temperatures not even such limiting value can be proposed.
4. Discussion
and conclusions
The most interesting result of this study (table 2) is the limited change of the apparent CMC (as calculated from 8, data) with w,, at any given tem-
perature. This quite unexpected result means that the system behaves essentially as binary, thus restoring, at least in part, the concept of the CMC as applied to reverse micelles. The CMC data can then be used to obtain some thermodynamic information on the system under study. The standard free energy values of the micellization process are obtained from the equation AG“=RTln(CMC),
(2)
where R is the gas constant. The enthalpy of the process can be found according to the equation proposed by Stainsby and Alexander [ 12 ] AH’=
-RT’d
ln(CMC)/dT
(3)
from the plot of ln(CMC) against 1/T. Such plots, constructed from the SWdata, are linear for all w. values, except for w. = 3-4 [ 91, indicating that AH0 is independent of temperature (fig. 4). A small negative enthalpy change is involved in the micellization (AP= -0.95 kO.05 kcal/mol); the standard free 337
Fig. 4. Variation of ln( CMC) with 1/I’ for reverse micelles of egg leclthm m [‘H,] -benzene. (0 ) w,= 3-4; (0 ) w,= 8-9; (A)w,=13-14; (a) w,=18-19.
energy involved in the process, calculated from eq. ( 2) I is essentially constant and equal to - 4.8 ? 0.1 kcal/mol. Another point of interest, which requires explanation, is the discrepancy between the CMC values obtained from the chemical shift data of water and trimethylammonium protons, which is well outside the range of experimental uncertainty. The former values are several times larger than the latter. One reasonable hypothesis is that the two sets of data reflect different aggregation phenomena. The trimethylammonium chemical shift might reflect the formation of small non-vesicular aggregates of few phospholipid monomers, where the lecithin polar heads are directly involved; on the other hand, the water chemical shift might respond only to the formation of micellcs, i.c. closed aggregates [ 8 ] with an interior water pool. The existence of aggregates of different size, one of which has a very low value of the mean aggregation number (i.e. 2-4), for lecithin in benzene has already been reported by Elworthy [ 13 ] on the basis of osmotic pressure measurements. In principle [ 91, the mean aggregation number fi might be obtained as the slope of the plot of log C(6-6,,,)/(6,,,-S,,,) 338
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Volume 158, number 3,4
versus
log C(L,,-6)/
(S,,,.-S,,,). At low concentrations (CG 1-2 mg/ ml) such plots, calculated from S, data, yield a value of fl between 2 and 3. Moreover, in this region, a plot of 6, against C should be linear (as we have indeed found) if the only significant aggregate species is the dimer, when a multiple-equilibrium model and an equal chemical shift for all associated species are assumed [ 71. It must, however, be noted that SWis also a linear function of C in very dilute solutions, indicating that the first aggregate species is the dimer. The log-log plots, on the other hand, show a linear region with slope between 2 and 3 at low concentrations, followed by a very steep rise (fig. 5) suggesting the formation of micellar aggregates with a high value of ti. From previous measurements [ IO], the estimated number of monomers in a lecithin reverse micelle in benzene (~~~25) is in fact of the order of 700-800. These results indicate that an appropriate way of handling the data suggests the forma-
2.0
I_
0
H -2.0 T = 303 K
Fig. 5. A plot of log c(a-s,,,)/(a,,,-s,,,) as a function of log C(a,,,-a)/(~~,,,-d,,,) constructed from the 6, data.
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tion of small, non-vesicular aggregates through the use of accurate SWdata for dilute solutions. It may be added that large values of fi cannot be reliably determined with the log-log plots because of the large errors in the parameters involved (see appendix). It may be concluded that, while the aggregation process in our systems is not highly cooperative, there is a fairly limited range of concentrations of lecithin
tion), although our systems have been found to be, to a good approximation, monodisperse at high lecithin concentrations [lo]. In addition, it should be borne in mind that the experimental definition of the CMC is not unique (see 6, and 6, data) and “the simplest practical procedure is to let the experiment define the CMC” [ 5 1.
within which the micellization takes place and an apparent CMC can be assigned making use of ‘H NMR data. Several points must, however, be stressed. First of all, it appears that small aggregates may form, prior to reverse micelle formation (pre-micellar aggrega-
Acknowledgement The authors wish to thank Mr. A. Ripamonti of the Istituto San Raffaele, Milan, for technical assistance.
Appendix To estimate the reliability of the values of ff obtained from the log-log plot, one can proceed in the following way.
AlogC(6_6,,,)/(6,i,-6,,“)
‘= A log C(&,,
-~)/(&lK-&l0”)
’
that is, 1ogCL(~Z-~mon)/16,,,-6,,,)-1ogC,(6,-6,,”)/(6,i,-6,,“),
A= log C2(Bmlc -s,)!(6,,,-~~;,,“)-logc,(6,,,-s,)/(6,,,-6,,”) rearranging
’
the terms and simplifying
n= log WC, +logt62 -&,,)/(~, logC,IC,+log(6,,,-fi,)/(6,,,-SI) Let the numerator
-&l,,)
be A and the denominator
S, the probable mean-square
d~=~[(~~)1+(~~)^3”~=~[i~~+(~d~~]”2=~~(~2+ri’d82)“2;
error of fi is (A.1)
where ,=,[(~dC,)2+(~dC2j2+i~d6,)2+(~dd,)2+(~ds,,.)l]lil
(A.2)
and d~=i[(~dC,~+(~d~~~+(~d~~i~~+(~d~~~+(~d~~~]”*. Developing
t.4.3)
(A.2) and (A.3)
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Assuming that the precision with which the concentration is known is l%, i.e. dC/C= 0.0 1, and that the error on the chemical shift values, both measured and extrapolated, db, is k 0.01 ppm, we have d/4=-t
(
10-4+10-4+
2x 1o-4 (82_Gmon)2 +
(;rlio_l)J”z=
+ 10--2(2+
(&_;~,“)z
+ (8, _:,,,.J
and 2x 1o-4 (6mic-d1)2
+
At high concentrations, for our system with w,,= 13-14 and T= 303 K, for example, &,,= 5.28, &,,,= 0.51, &=5.00, 6,=4.60 ppm when C,=SO and Cl=20 mg/ml (i.e. C,/C,=2.5), one finds dA=? 1.5x lo-‘and dB= f5.6~ 10-2. In our example the value of B calculated from experimental data is 0.013, while dB= _+5.6 x lo-‘, larger than B itself. Indeed IdAl > (5.6x
IO-‘)/B)A,
(dnj /n> 4.3 a
Therefore, it is impossible to calculate any reliable value of #. At low concentrations, for the same system taken as an example, we have c&=2.01 and 6, = 0.61 ppm for C,=2 and C,=O.l mg/ml (C,/C,=20) giving dA=? 14.2x10-* and dB=? 1.5~ 10e2. With the experimental value of ~~2.3, one obtains dn= kO.13. Similar results have been obtained with different values of wUand at different temperatures.
References [I ] R. Lindman and H. Wennerstriim, in: Topics in current chemistry, Vol 87. Micelles (Springer, Berlin, 1980) p. 1. [2] J.N. Israelachvili, in: Physics of amphiphiles: micelles, vesicles and microemulsions, eds. V. DeGiorgio and M. Corti (North-Holland, Amsterdam, 1985) p. 24. [3] J.H. Fendler, Membrane mimetic chemistry (WileyInterscience, New York, f982) ch. 2. [4] B. Lindman, in: Physics of amphiphiles: micelles, vesicles and microcmulsions. eds. V. DeGiorgio and M. Corti (North-Holland, Amsterdam, 1985) p. 7. [ 5 ] C. Tanford, in: Mlcellization, solubilization and microemulsions, ed. K.L. Mittal (Plenum Press, New York, 1977) p, 119.
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[ 61 A-S. K&es and H. Gutmann, in: Surface andcolloid science, Vol. X,ed. E. Matijevic (Wiley, New York, 1976) p. 193. [7] N. Muller, J. Phys. Chem. 79 (1975) 287. [ 8] H.-F. Eicke, in: Topics incurrent chemistry, Vol. 87. Micelles (Springer, Berlin, 1980) p. 85. 19] R. Haque, 1.J. Tinsley and D. Schmedding, J. Biol. Chem. 247 (1972) 157. [IO] CA. Boicelli, F. Conti, M. Giomini and A.M. Giuliani, Chem. Phys. Letters X9 ( 1982) 490. [ 1I ] F. Heatley, J. Chem. Sot. Faraday Trans. I 84 (1988) 343. [ 121 G. Stainsby and A.E. Alexander, Trans. Faraday Sot 46 (1950) 587. [13] P.H. Elworthy, J. Chem. Sot. (1959) 813.