J . Phys. Chem. 1993,97, 6686-6691
6686
Surface Dipole Densities in Lipid Monolayers Dominic J. Benvegnu and Harden M. McConnell' Department of Chemistry, Stanford University,Stanford, California 94305 Received: February 2, 1993; In Final Form: April 9, 1993
Surface dipole density differences, p, between coexisting liquid phases in lipid monolayers have been determined from an analysis of the Brownian motion of trapped lipid domains, as well as from surface potential measurements on each liquid phase. The coexisting liquid phases arise in binary mixtures of dimyristoylphosphatidylcholine (DMPC) with cholesterol or with dihydrocholesterol. Values of p determined from Brownian motion, surface potential measurements, and measurementsof domain electrophoreticmobility provide support for the theoretical equivalentdipole model used previously to describethese monolayers. Air oxidationand ozonolysis of cholesterol in monolayers is detected through the effect of an oxidation product-mediated reduction of interdomain line tension. It is shown that a cholesterol oxidation product, cholestenone, is strongly line active, reducing the line tension between liquid domains relatively rich in cholesterol and liquid domains relatively rich in DMPC.
Introduction
Epifluorescence microscopy has made possible the observation and study of a variety of phase equilibria in lipid monolayers at the air-water Phase equilibria in these quasi-twodimensionalchemical systems are unusual in that thesizes, shapes, and ordering of lipid domains are strongly affected by long-range electrostatic forces. A theory for the sizes and shapes of lipid domains has been developed that involves only two parameters, p and A, in the case of co-existing liquid phases that are each isotropic in two dimensions2 Coexisting monolayer liquid phases are exhibited for example by binary mixtures of cholesterol and phosphatidylcholines.46 In such systems the theory treats a competition between the line tension X between the coexisting liquid phases and p, the difference in dipole densities in these phases. The line tension favors large circular domains, whereas the long-range dipolar forces favor small and/or extended domain sizes and shapes. The phenomenological theory involving X and p is quantitative and potentially encompasses a wide variety of monolayer phenomena. This in turn offers the possibility of quantitatively testing the theory, and that is a major motivation for the present study. The theoretical work has implicitly employed an "equivalent dipole model" to discuss the electrostatics of lipid monolayers at the air-water interface. In this model, the lipid molecules as well as all ions and water molecules (the entire trough) are replaced by a hypothetical two-dimensional planar array of dipoles. The number density of these dipoles is assumed to be of the same order of magnitude as the number density of molecules at the air-water interface. In the case considered here, where all coexisting phases are isotropic liquids in two dimensions, the equivalent dipoles are all oriented perpendicular to the monolayer plane. As discussed below, the dipole moment densities in the equivalent dipole model can be used to calculatesurface potentials, the amplitudes of Brownian motion of electrostatically trapped lipid domains, a n d - a s discussed elsewhere-the field gradient electrophoretic mobility of lipid domain^.^ Thus, comparisons of experimental measurements of these quantities with the calculations permit a significant test of this aspect of the theory. Background Theory
In the equivalent dipole model, the dipole densities p1 and p2 in each of the two coexisting phases are related to the measured surface potentials VI and V2 by means of the equations8 Vl = 4rpl + constant
V2= 4 r p 2 + constant (1)
0022-3654/93/2097-6686$04.00/0
Figme 1. Coexisting liquid domains. A small domain of radius a is electrostaticallytrapped within a large domain of radius A. The presence of white domains outside of the large domain has the effect of lowering the potential energy of the small trapped dark domain. The outer white domains do not penetrate closer than the radial distance labeled B. See Appendix A for a further discussion of the electrostatic effect of the outer white domains.
The dipole density difference p = p1 - p2 is then
cc = ( 1 / 4 r W , - V-1 (2) This dipole density difference can be compared with that determined from Brownian motion, described below. In previous work9it has been shown that circular lipid domains can be electrostaticallytrapped within larger domains, as sketched in Figure 1. In this figure the dark region depicts the liquid monolayer phase that is rich in cholesterol; the fluorescent lipid probe present to an average concentration of 1 mol % is preferentially excluded from this phase, and thus this phase appears darker in the epifluorescence microscope. As shown previously,an analysis of the Brownian motion of electrostatically trapped lipid domains can be used for a determination of p2, using the equivalent dipole model.9 The present work extends this earlier work in a number of respects. An extension of the previous calculation of the displacementdependent electrostaticenergy to terms in p4leads to the following expression for the electrostatic energy of a dark domain of radius
0 1993 American Chemical Society
Surface Dipole Densities in Lipid Monolayers
The Journal of Physical Chemistry, Vol. 97, No. 25, 1993 6687
a trapped within a bright domain of radius A:
Experimental Section (3)
where (4) p is defined in Figure 1. In our previous work, we (i) assumed
the outer black domain to extend to infinity in two dimensions and (ii) neglected all terms in eq 3 other than the leading term, which depends on p 2 . It is shown in Appendix A that for our experimentsassumptions i and ii lead to errors that are small and nearly cancel one another. Thus, to simplify our discussion, we shall continueto use assumptionsi and ii. Using these assumptions and the equipartition of energy, it follows that a measurement of the mean square displacement of a domain from the center, ( p 2 ) can be used to determine p2:
A major objective of the present work has been to test the equivalent dipole model by comparing values of p obtained from surface potential measurements with values of N~ obtained from measurements of Brownian motion. The surface potential measurements require the use of two separately prepared, singlephase, homogeneous monolayers, each having a composition identical to one of the coexisting phases used for the measurement of Brownian motion. The preparation of such homogeneous monolayers in turn requires a knowledge of the phase diagram of the binary mixture of lipids employed. In previous work, both epifluorescence microscopy and pressure-area studies have been used as evidencethat binary mixtures of cholesterol and DMPC form immiscible liquid phases at low pressures (u= 0-10 mN/m), and that thereis a mixing-demixing critical point at u = 10-11 mN/m and x&ol = 0.30 (mole fraction).M In the present work we have reexamined this phase diagram since any error in the location of the low-pressure phase boundaries would obviate the central purpose of our work. Two special points are noted here. In the equivalent dipole model, the sizes and shapes of lipid domains having an area uR2 can be discussed in terms of the equation
Cholesterol (Chol), dihydrocholesterol (DChol), 4-cholestenone, and 5-cholestenone were purchased from Sigma. Dimyristoylphosphatidylcholine (DMPC) was purchased from Avanti Polar Lipids. Four fluorescent lipid probes were used during the course of the experiments: N-(Texas red sulfonyl) dipalmitoylL-a-phosphatidylethanolamine(TR-DPPE), and 1,l’-dioctadecyl3,3,3’,3’-tetramethylindocarbocyanine perchlorate (DiI) were purchased from Molecular Probes;1-palmitoyl-2-[6-[7-nitro-21,3-bemxadiazol-4-ylamino]caproyl]phosphatidylcholine (NBD PC) and N-(7-nitro-2-l,3-benzoxadiazol-4-yl)dipalmitoylphosphatidylethanolamine (NBD-PE) were purchased from Avanti Polar Lipids. All compounds were used without further purification. All cholesterol solutions were made fresh on the day of an experiment. 4-Cholestenone was added to spreading solutions from a 2 mM ethanol stock solution. A small Teflon trough (27 X 75 mm2) was used to measure isotherms, record Brownian motion data, and measure shape transition pressures and mixing pressures. The monolayer was viewed with a Cohu low-light-levelvideo camera connected to a Zeiss epifluorescence microscope. Video images were recorded with a JVC BR601MU recorder. Brownian motion data were measured directly from a television screen. All monolayers were spread on distilled, deionized water unless otherwise noted. Surface potentials were measured using a Trek Model 320B electrostatic voltmeter. A large Teflon trough (KSV, Finland) was used for all surface potential measurements. The atmosphere surrounding the monolayer and vibrating electrode was flushed with nitrogen in order to minimize spurious readings due to water vapor condensing onto the vibrating electrode. Surface potential measurements were independent of electrolyte concentration in the subphase over the range 0-150 mM NaCl. Area fractionsof white and black phases, for a given composition and pressure, were measured from digitized video images using the image analysis software, IMAGE (NIH, version 1.41). We definefb as the area fraction of black (steroid-rich) phase. If dW) and db)are the molar areas of the white and black phases, respectively, then
R, = eZt3R,
where dW) and db) are the total number of moles in the white and black phases, respectively. By inversion of eq 8, an equation is obtained that allows us to verify that the lever rule is satisfied for our phase diagram:
R, = (e38/4)eX/’2
l/fb = Q4 + 1
where
(7) representsa nominal “equilibrium radius”of a circular domain.2*10 In eq 7,8 is a nearest-neighbor intermolecular distance between the equivalent dipoles. A circular domain of radius R 1R,(where z is an integer greater than or equal to 1) is unstable with respect to distortion to shapes of lower sy”etry.”-I3 These shape transitions are easily recognized experimentally and can be used to map out the higher pressure regions of the coexistence curve. This is because as one approaches the coexistence region from below (pressure increasing), the line tension X approaches zero rapidly compared to p2, and circular domains change shape and/ or become smaller, and disappear. As discussed in Appendix B, a potential problem in these experiments arises if oxidation products are line active, reducing X. (For example in the presence of 10mol 96cholestenoneimpurity,the two liquid phases disappear in the fluorescencemicroscope,presumably because the domains are too small to see.) For this reason, our experiments have also been carried out with dihydrocholesterol, which resists air oxidation.
(9)
where Q = dw)/db) and q5 = dw)/db). According to the lever rule, q5 is given by
In eq 10, x ( ~is) the mole fraction of steroid in the black phase, and x ( ~is) the mole fraction of steroid in the white phase. x is the total mole fraction of steroid.
Figure 2 shows the pressure-area isotherms and the phase diagram for the DChol-DMPC system. The isotherms and phase diagram of the Chol-DMPC system are the same as those in Figure 2 to within our experimental error. It isdiMicult to measure the mixing pressures of the Chol-DMPC system accurately because an oxidation product of cholesterol is line active and this
Benvegnu and McConnell
6688 The Journal of Physical Chemistry, Vol. 97, No. 25, 1993 40
0.54
a 30 A
E \
f
e
0.46
-+
Q
20-
0
Y
L
10 -
>
0.38 0
I
0
20
60
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Area (A2/moIecuIe)
0.30
Lo-.' 0
9-
I
I 20
60
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'DChol
I
L
b 0.46 Chol-Dh
A
-+
I
0
0.1
0.2
0
p 0.38 0.3
0.4
0.5
t-
0.6
0.30 'DChol
0
Figure 2. Phase behavior of the binary liquid mixture. (a) Pressur+ area isotherms for the DChol-DMPC binary mixture. The bamer was compressed at a rate of approximately 0.5 A2/(moIecuIe min). (b) Pressurevs composition phasediagram of DChol-DMPC binary mixture. Region I is the two liquid-phase coexistence region. Region I1 is the onephase region. The solid line corresponds to pressures and compositions at which the two distinct phases disappear with increasing pressure. The dots indicate shape transition pressures for a given composition. All measurements were made by visual inspection of several monolayers. Above 35 mol % DChol, only NBD-PE could be used as a fluorescent probe. All other probes used preciptated out above 35 mol % DChol and led to phase heterogeneity. The Chol-DMPC phase diagram is very similar, except that shape transition pressures are slightly higher (by about 1 mN/m) than for the DChol-DMPC mixture.
causes mixing pressures to appear smaller than they actually are. See Appendix B for a discussion of cholesterol oxidation. It was found that above 35 mol % dihydrocholesterol (or cholesterol), all of the fluorescentprobes except NBD-PE became partially insoluble. The probe insolubility resulted in phase heterogeneity in the pressure range040 mN/m. The data points in the phase diagram above 35 mol % dihydrocholesterol were obtained with NBD-PE as the lipid probe (Figure 2b). Below 35 mol %, the data points are independent of which lipid probe is used. Surfacepotential versus composition data are shown in Figure 3. The data are plotted as constant-pressure curves. At a given composition, there is a measurable differencein surface potentials between the DChol-DMPC and the Chol-DMPC systems. Only the ?r = 0 curve is shown for the Chol-DMPC system. The Brownian motion data for the DChol-DMPC and the Chol-DMPC systems are summarized in Figure 4. For the DChol-DMPC system, 16 different electrostatic traps were measured. For each trap, a value of p2 was obtained using eq 5. The average of the sixteen measurements of 1p1 is 0.54 D/nm2, with a standard deviation of 0.1 3 D/nm2. For the Chol-DMPC system the average value of &I is 0.85 i 0.20 D/nm2. Area fraction measurements at a pressure of 1 mN/m are shown in Figure 5. Values of 4 were calculated using the phase diagram in Figure 2, where ~ ( =~0.65 1 and x ( ~=) 0.015. The measured slope in Figure 5 is a(w)/a(b) = 1.6. During the course of this work our major concern was the accuracy of the Chol-DMPC phase diagram. Our data do agree reasonably well with earlier To avoid problems associated with cholesterol oxidation, we determined the phase diagram for
20
60
40
80
100
x Figure 3. Surface potentials of binary liquid mixtures. (a) Surface potential vs composition for DChol-DMPC mixtures. Each curve corresponds to a fixed surface pressure. The error associated with each point is 10.01V. (b) Comparison of the surface potential vs composition for the Chol-DMPC and the DChol-DMPC mixtures. Only the r = 0 mN/m curves are shown.
""h
0
6
12
18
24
30
36
42
48
54
60
q (x10-3pm) Figure 4. Brownian motion histograms. Histograms of the number of occurrencesas a function of r) for the 3096dihydrocholestml, 69% DMPC, 1% TR-DPPE mixture and the 30% cholesterol, 69% DMPC, 1% TRDPPE mixture, at a pressure of 0 mN/m. r) is defined by the equation r) = a2p2/A3(see Figure 1). The curves shown are the theoretical curves given by the equation P(r)/i) = Cexp(v/$. The normalization factor, C,is chosen so that the integral of P from 0 to infinity equals the area under the histogTam. For the DChol-DMPC mixture, in a total of 256 measurements, r) = 0.0096 pm, the standard deviation was 0.0105 pm, and C = 80.0. The value of CI given by eq 5 is 0.54 D)nm2. For the Chol-DMPC mixture, in a total of 242 measurements, r) = 0.0038 pm, the standard deviation was 0.0036 pm, and C = 64.0. The value of M given by eq 5 is 0.85 D/nm2.
the DChol-DMPC system and obtained substantially the same phase diagram. The data in Figure 5 support the validity of the phase diagram (lever rule test). The data in Figure 6 also test the phase diagram, in that the average surface potential (and, therefore, the average dipole density) should be a linear function
The Journal of Physical Chemistry, Vol. 97, No. 25, 1993 6689
Surface Dipole Densities in Lipid Monolayers
TABU I: Dipole Density Differences (D/nm2) for tbe Bianry cbol-DMPC ind Dchol-DMPC' is
surface potential Brownian motion electrophoretic mobility'
14
2 10 % c
a
0
DChol-DMPC
0.48 i 0.05 *0.85 0.20 0.64 0.07
+0.54 & 0.13
*
* 0.05 0.48 * 0.07 0.35
The results of three independent techniques are shown. Surface potential measurements and Brownian motion of electrostatically trapped domains aredescribed in this work. Electrophoreticmobility experiments are dtscribed in ref 7. As pointed out in this reference, the maximum possible experimental errors and uncertainties can be larger than the standard deviations given here.
12
-
Chol-DMPC
0
2
4
6
8
1
0
@
Figure 5. Lever rule test of the phase diagram. For the DChol-DMPC system at a pressure of 1 mN/m, the area fraction of the black phase is denotedfb. In the graph, the inverse Offb is plotted as a function of I$ = dW)/db), the ratio of moles of white phase to mol= of black phase. Equation 10 was used to calculate 4, where the values of x ( ~=) 0.65 and x(*) = 0.015 were obtained from the phase diagram in Figure 2. The four data points are for DChol mole fractions of 0.15, 0.20, 0.30, and 0.50. The error bars indicate errors of *lo% in the area fraction measurements. Equation 9 describw the predicted linear relationship between the inverse offb and I$, with a slope bcing the ratio of the area densities of the white and black phasca. The line in the graph has a slope of 1.6.
0.44
0.40
0.36
0.32
fb
Figure 6. Surface potential test of the phase diagram. Surface potential vs area fraction of black phase for the DChol-DMPC system at 1mN/m. fb was measured for six mole fractions of DCho1(0.10,0.15,0.20,0.30, 0.50, and 0.60) using digitized video images. The observed linear relationship between Yandfb corresponds to an area-weighted average of the surface potentials of each coexisting phase, and provides additional evidence for the validity of the phase diagram in Figure 2. See eq 11.
of the area fractions of the coexisting phases. Thus
Y = v'"' +A( v'b' - v'"') The observed data are in accord with this result. DiscPPsion
The results of our measurements for the dipole density differences p are given in Table I. Also included are values of p recently measured by Klingler and McConnel17 using measurements of the electrophoretic mobility of lipid domains. It will be seen that despite the different assumptions and approx-
imations used for each method, the overall concordance of the various values of p is within the experimental uncertainties. The biggest discrepancy involves dipole densitiesmeasured by surface potentials, which appear to be approximately 30%lower than the densities obtained using the other methods. At present we are uncertain whether the various discrepancies are due to experimental error or to some inherent limitation in the equivalent dipole model for the electrostatic properties of these monolayers. It is stressed that the equivalent dipole model is only an approximation, albeit evidently a goad approximation. To see this, imagine that quadrupole forces between molecules at the interface were large; this would affect the Brownian motion experiments but not the surface potentials. Of course, quadrupole forces are not expected to be large at large distances. At the present time we know of no reason to suspect that the differences between the dipole densities in Table I are due to limitations in the equivalent dipole model. However, other theoretical approximations used may contribute to the discrepanciesin Table I, in addition to experimental error. As examples, the surface potential measurementsrequire a knowledge of the phase diagrams of steroid-DMPC mixtures. The measurements of Brownian motion involve approximationsconcerning the outer boundary of the outer domain as discussed in Appendix A. Finally, the determination of the dipole density differences by the measurements of the electrophoretic mobility of lipid domains is based on a theoretical calculation of the electric field gradient. The concordance of all of the results is satisfactory in view of these various approximations, and sources of experimental error. The present study does not test the equivalent dipole model for dipolbdipole forces at short distances. These forces play a role in the electrostatic contribution to line tension and to energies involved in equilibriumdomain sizes and shapes. It is to be hoped that experimental studies of these properties of lipid domains may be usedto test the equivalentdipole model at short distances.
Acknowledgment. It is a pleasure to acknowledge that Toru Murakami in this laboratory (a visiting scholar from the NEC Corp.) observed an effect of cholesterol oxidase on domain shape transitions that led to our studies of the effect of cholestenone on interdomain line tension. We thank H. Gaub for his valuable assistancein the surfacepotential measurements. We areindebted to J. Klingler for helpful discussions. We also thank the KSV Corp. for the use of their trough system. This work was supported by NSF Grant NSF DMB 8619320 and an NIH Training Grant in Biotechnology.
A?-
A
To study the effect of the ( P / A )term ~ in eq 3, define the variable x = (P14z
Then the mean of x is given by the equation
Using eq 3 to calculate the integrals leads to
(AI)
6690
The Journal of Physical Chemistry, Vol. 97, No. 25, 1993
Benvegnu and McConnell DChol, 0, and 0,
where 20
0
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Time (min)
In addition to the p4 term, we also consider the effect of the white outer domains in Figure 1. In our experiments, there is a radial distance, B, inside of which the outer domains never penetrate. If FI is the potential energy if the black phase extends from A to infinity, Fz is the potential if the black phase extends from B to infinity, then the effect of the outer white domains can be expressed as the difference where f is a number between 0 and 1 and expresses the fact that not all of the area outside of the radial distance B is white phase. Under these circumstances, eq A4 is modified as follows:
'.I, b -
+Tempo1
-
112
I
\ -Tempo1
e* 4
2t 01 0
'
' 20
'
' 40
'
' 60
'
'
80
'
' 100
'
I I 120
Time (min)
P=-
a 21/Bl
q2=B
To calculate the magnitude of the second-order correction, parameters from one of the 16 electrostatic traps for the DCholDMPC mixture were used to calculate ( x ) using eq A3. The initial value of p used in the calculation was the first order value from eq 5. The value of p was then changed until the calculated value of ( x ) agreed with the measured value. For example, one experiment had the following parameters: a = 0.73 X 10-4 cm, A = 8.3 X 10-4cm, B = 9.3 X l w c m , f = 0.64,T = 295 K . (The value for f is the measured area fraction of the white phase at 1 mN/m). The first-order value for is 0.56 D/nm2. To obtain the measured value of ( x ) = 0.138 in eq A3, a value of p = 0.58 D/nmz was necessary. Thus, the second order correction to p is very small (1-2%), due to the fact that the p4 term opposes the effect of the outer white domains. If only the p4term is considered by setting B to infinity, then the value of p = 0.45 D/nmz is needed in eq A3 to obtain the observed value of (x). Similar results were obtained with other experiments. On the basis of the above calculations and the fact that the histograms in Figure 4 fit well the first-order theoretical curves, we conclude that the second-order corrections considered are sufficiently small to ignore. Appendix B
It has been observed that for a 30% cholesterol, 70% DMPC monolayer under an air atmosphere, the pressure at the onset of shape transitions, ?Tshape, decreases gradually with time (see Figure 7). Furthermore, when the monolayer is exposed to ozone, the shape transition pressure decreases much more rapidly with time. (A high concentration of ozone is created by placing a mercury finger lamp in the plastic house surrounding the trough.) The decrease in Pshape with time can be partially inhibited by flushing the atmosphere above the monolayer with nitrogen or by adding to the subphase a free radical scavenger, TEMPOL (4-hydroxy2,2,6,64etramethylpiperidine,N-oxyl). The decrease in Pshape can be totally inhibited by substituting dihydrocholesterol for cholesterol in the binary mixture (see Figure 7a). The above observations can be explained by the hypothesis
Figure 7. Oxidation of cholesterol in monolayers. By monitoring the shapetransition pressure as a function of time, the effectsof a line active oxidationproduct of cholesterolcan be observed. (a) Theeffects of oxygen and ozone are shown for a Chol-DMPC mixture and a DChol-DMPC mixture,both at a composition of 30 mol 5% steroid. DChol is unaffected by both oxygen and ozone. The oxygen was ambient in the atmosphere and subphase. The omne was created by a placing a mercury fmger lamp inside the plastichousing surroundingthe trough. (b) Air oxidation of Chol can be decreased by saturating the atmosphere above the monolayer with nitrogen, or by adding TEMPOL (4-hydroxy-2,2,6,6tetramethylpiperidine,N-oxyl), a free radical scavenger, to the subphase at a concentration of 0.1 mM.
that the decrease in rghapc is related to the oxidation of cholesterol, whereby an oxidation product decreases the interdomain line tension. The effect of cholestenone on the line tension between the two liquid phases of a 30% cholesterol, 70% DMPC monolayer was measured using the technique previously describad.14 It was found that at a given pressure, line tension is decreased as the concentration of cholestenone is increased. The lowering of line tension is first measureable when 4 mol % cholesteoone is added to the monolayer. When 10 mol % cholestenone is added, the monolayer appears in the microscope to be one homogeneous phase at all pressures. The line activity of cholestenone is most conveniently shown by plotting 5fShapc as a function of cholestenone concentration. It can be seen in Figure 8 that cholestenone has the same effect on both the Chol-DMPC and the DChol-DMPC mixtures. Several other molecules were tested for their effect on line tension, including the cholesterol oxidation product, 7-ketocholesterol. None of the molecules tested, except cholestenone, is line active. It is not known what products are produced by the air oxidation and ozonolysis of cholesterol. Cholestenone is not necessarily one of the products; however, the cholestenone data shown in Figure 8 can be used to estimate the rate of production of the line active oxidation product, assuming that the line-active product has the same effectiveness as cholestenone. In Figure 7a, it can be seen that Pshapc decreases to 0 mN/m in approximately 2-4 h, under the given experimental conditions for air oxidation.The cholestenone data in Figure 8 indicate that a shape transition pressure of 0 mN/m corresponds to the addition of 10 mol 96 cholestenone. Thus, it can be estimated that for air oxidation of cholesterol,a line-activeproduct is produced at a rate equivalent to the addition of 2.5-5.0 mol % cholestenone/h. The number
The Journal of Physical Chemistry, Vol. 97, No. 25, 1993 6691
Surface Dipole Densities in Lipid Monolayers
0.02
0.04
0.06
0.08
0.1 0
Mole Fraction Cholestenone
F i p e 8. Effect of 4-cholestenone on line tension. The shape transition pressure r a ~ is shown p as a function of mole fraction of 4-cholestenone added to the monolayer. The two curves shown are for a Chol-DMPC mixture and a DChol-DMPC mixture, both having a composition of 30 mol 96 steroid. The repeatability of each measurement is about fl mN/ m.
of cholesterol molecules present in such a monolayer is about 1014/cm2. The rate of 0.5 mol %/(h cm2) corresponds to lo9 molecules/(s cm2) being oxidized to the line-active product. Cholestenone has no significant effect on the surface potential of 30 mol % cholesterol, 70 mol % DMPC monolayer (up to a cholestenone concentration of 5 mol %).15
References and Notes (1) (2) (3) 207-36. (4) 18.
Mdhwald, H. Annu. Rev. Phys. Chem. 1990, 41, 441. McConnell, H. M. Annu. Rev. Phys. Chem. 1991,42, 171-95. Knobler, C. M.; Desai, R. C. Annu. Rev. Phys. Chem. 1992, 43, Subramaniam, S.; McConnell, H. M.J. Phys. Chem. 1987,91,1715-
( 5 ) Hirshfeld, C. L.; Seul, M. J. Phys. 1990, 52, 1537-52. See also: Albrecht, 0.; Gruler, H.; Sackmann, E. J. Colloid ZnterfaceSci.1981,79 (2), 319-38. (6) Rice, P. A.; McConnell, H. M. Proc. Nutl. Acad. Sci. USA.1989, 86,6445-48. (7) Klingler, J. F.; McConnell, H. M. J . Phys. Chem. 1993, 97, 29622966. (8) Adamson, A. W. Physical Chemistry of Surfaces; John Wiley and Sons: New York, 1982. See also: Cadenhead, D. A.; Phillip, M. C. Adv. Chem.Ser. 1968,84,131-148. Muller-Landau, F.; Cadenhead, D. A. Chem. Phys. Lipids 1979, 25,315-28. (9) McConnell, H. M.; Rice, P. A.; Benvegnu, D. J. J . Phys. Chem. 1990, 94,8 965-8. (10) The use of the expression in eq 7 for the equilibrium radius does not imply that the domains in this work have area equilibrium. The combination of eqs 6 and 7 nonetheless yields the correct instability condition. (11) McConnell, H. M. J . Phys. Chem. 1990,94,4728-31. (12) S a l , M.; Sammon, M. J. Phys. Rev. Loft. 1990, 64, 19034. (13) Vanderlick, T. K.;Mllhwald, H. 1.Phys. Chem. 1990,94886490. (14) Benvegnu, D. J.;McConnell, H. M. J. Phys. Chem. 1992,96,682& 24. (15) This result is interesting in connection with the phase behavior of dipolar monolayer systems as the critical point is approached from the t w e phase region. From the classical theory of interfaces, one might anticipate that domain boundaries would become more diffuse as the critical point is approached. Set: Rowlinson, J. S.;Widom, B. Moleculur Theory of Capillarity;Clarendon Press: Oxford, 1982. Andelman and collaborators have treated these systems in terms of ‘weakly modulated phases” using LandauGinzberg theory. See: Andelman, D.; Brochard, R.; de Gennes, P. G.; Joanny, J. F. C.R. Acad Sci. (Pans) 1985, 30, 675. Andelman, D.; Brochard, R.; Joanny, 1. F. J. Chem.Phys. 1987,815,3673. Inour experiments we have never seen domain boundaries become diffuse as the putative critical point is approached; the boundaries remain sharp, so the phases are ‘strongly modulated”. The observed behavior appears to be accounted for by theories of domain sizes and shapes that depend on the factor exp(A/p2) when A 0 faster than pz -P 0 as the critical point is approached. Thus,domains ‘disappear” because one or more of their dimensions become smaller than the resolution of the light microscope. This view is consistent with the rtsults of the present expcrimentpwith thecholestenone‘impurity”, whichclearlyreduces A and has no observable effect on p2. Of course, the experiments provide no information on the domain behavior when their dimensions are less than the wavelength of light.
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