J . Phys. Chem. 1992, 96,6820-6824
6820
isotherm suggests that binding to more than X = 1 may be possible. This is brought about by additional binding of surfactant ions to already bound surfactants on the polymer (piggyback bmding).l6 The present results suggest that the secondary binding can occur even at an early stage of the binding isotherm. Interaction between surfactants appears too strong as well as too complex to be described by a simple Ising model. It will require many additional experiments before a sound bimodal picture can be established.
-
- *O
0.5
References and Notes (1) Hill, T.L. Thermodynamics of Small Systems; Benjamin: New York, 1963;Part 1, Chapter 6.
1
Degree of Binding
Figure 7. True electrophoretic mobility vs degree of binding: dextran sulfate A, carrying only a small amount of surfactant and a large negative charge; and B, nearly saturated with bound surfactant and only a slight charge. These results may be subject to a rather large error due to scattering of data points around theoretical curves and a slightly long extrapolation to the normalized coordinate *0.646 as seen in Figure 6.
time of surfactant in the host polymer may be longer than the micellar lifetime, as it is under the influence of an attractive electrostatic field of the polyelectrolyte. An additional conclusion may be drawn by examining Figure 7. The fast migrating species seems to move a little faster as X increases, while the slower one moves in the reversed direction. As a result of binding a minute amount of surfactant, the host polyelectrolyte may shrink a little, leading to a smaller hydrodynamic resistance. Actually the apparent hydrodynamic radius was observed to decrease from 100 nm for pure sodium dextran sulfate to 54, 41, and 40 nm at X = 0.23, 0.38, and 0.67, respectively. Migration in the reversed direction means reversal of electric charge of the surfactant-polymercomplex. The binding
( 2 ) Reiter, J.; Eptein. I. R. J . Phys. Chem. 1987, 91, 4813. (3)Skerjanc, J.; Kogej, K. J. Phys. Chem. 1989, 93, 7913. (4) Robb, I. D. Anionic Surfactants; Lucassen-Reynolds, E. H., Ed.; Surfactant Science Series 11; Marcel Dekker: New York, 1981;Chapter 3. (5)Gcddard, E. D. Colloids Surf. 1986, 19, 301. (6)Hayakawa, K.; Kwak, J. C. T. Cationic Sulfactants; Rubingh, D. N., Holland, P. M.,Eds.; Surfactant Science Series 37; Marcel-Dekker: New York, 1991;Chapter 5. (7) Shirahama, K.; Oh-ishi, M.;Takisawa, N. Colloids Surf. 1989, 40, 261. (8) Shirahama, K.; Watanabe, T.; Harada, M. In The Structure, Dynamics, and Equilibrium Properties of Colloidal Systems; Bloor, D. M., WynJones, E., Us.; Kluwer: Amsterdam, 1990; p 161. (9)Malovikova, M.; Hayakawa, K.; Kwak, J. C. T. J. Phys. Chem. 1984, 88, 1930. (10)Oka, K.; Otani, W.; Kameyama, K.; Kidai, M.; Takagai, T. J. Appl. Theor. Electrophor. 1990, 1 273. (11) Schwarz, G.Eur. J. Biochem. 1970, 12, 442. (12)Mori, S.;Okamoto, H.; Hara, T.; Aso, K. In Fine Particle Processing Somasundran, P., Ed.; American Institute of Mining Petroleum Engineering; New York; 1980,p 632. (1 3) Jenkins, G.M.; Watts, D. G. Spectral Analysis and Its Applicarions; Holden-Day: San Francisco, 1968;p 53. (14) Kahlweit, M.J. Colloid Interface Sci. 1982, 90,92. (15) Lang, J.; Zana. R. Sulfactant Solutions, New Methods of Inwstigation; Zana, R., Ed.; Surfactant Science Series 22;Marcel-Dekker: New York 1987;Chapter 8. (16)Hill, T. L. Cooperativity Theory in Biochemistry, Steady-Srare and Equilibrium Systems; Springer: New York, 1985;Chapter 4. I
Line Tension between Liquid Domains in Lipid Monolayers Dominic J. Benvegnu and Harden M.McConneU* Department of Chemistry, Stanford University, Stanford, California 94305 (Received: March 20, 1992)
Hydrodynamic shear distorts the shapes of lipid domains at the air-water interface. When the shear stress is removed, the domains relax to their original shapes. The relaxation rate of bolas-shaped domains provides a novel means of measuring the line tension between coexisting immiscible liquid phases. This line tension was measured in a binary mixture of average critical composition 30 mol W cholesterol, 70 mol W dimyristoylphosphatidylcholine(DMPC),as a function of monolayer pressure. The line tension is approximately a linear function of the difference between the applied pressure and the critical pressure. The line tension varied from (1.6 0.4) X lo-' dyn, at 1 dyn/cm pressure, to zero at the critical pressure.
*
Introduction In previous work, we have discussed the shapes and shape transitions of lipid domains in monolayers at the air-water interface in terms of three parameters, 6, p , and X.' Here 6 is an effective distance between neighboring dipoles at the interface, p is the difference in dipole density in neighboring lipid domains, and X is the line tension between these domains. The theory of the domain shapes is particularly simple for coexisting immiscible liquid phases, where the average dipole moments are perpendicular to the monolayer surface. When domaindomain forces are neglected, the theoretical equilibrium radius of a circular domain is 1 2
This and other calculated properties of the domains depend in a sensitive way on the ratio Alp*. In order to test these theoretical calculations, experimental values of X and r2are needed. The value of 6 is expected to be of the order of molecular dimensions, -10 A. The values of p 2 can be obtained by analyzing the amplitudes of Brownian motion of small circular domains electrostatically trapped within larger domains. A representative value for a cholesterol-DMPC mixture is Ipl = 0.7 D/100 A2.3 The present work shows how domain shape recovery following hydrodynamic shear can be used for measurements of the line tension X between liquid phases. Muller and Gallet have used a rate of activated homogeneous nucleation to determine a liquidsolid line tension in amphiphilic monolayers? Their measured lime tension, ( 5 i 0.5) X lO-' dyn, is of the same order as the liquid-liquid line tensions reported here
0022-3654/92/2096-6820$03.00/00 1992 American Chemical Society
Line Tension between Liquid Domains in Lipid Monolayers
The Journal of Physical Chemistry, Vol. 96, No. 16, 1992 6821
I I:
F, = 2L X
a
+ p2 In -
(4)
The two bola at the ends of the stripes are assumed to be circular, with radii R. The combined energy of the two circular bolas is
(
F, = 4xR p 2 In
:: )
-+ A
Let
F = F, + F,
(6)
be the total free energy, and thus neglect the electrostatic energy of repulsion between the two bola and between each bola and the strip. When w does not change, the restoring force tending to bring the two bola toward one another is
C
1force = --aFaLaF, e----
aF,aR
d
Figure 1. Hydrodynamic distortion of domain shapes. (a) In the absence of shear, the lipid domains are circular under the experimental conditions employed. (b) with weak shear, the circular domains distort to ellipelike shapes, inclined at an angle to the direction of shear. (c) With large shear, the lipid domains are distorted to the shapes of bolas. (d) When the shear is removed, the elongated bolas relax to circles.
when the pressure is far from the critical pressure. The method of Muller and Gallet is not applicable to a two-fluid phase system, since the one-liquid to two-liquid transition is continuous (second order) and does not involve an activation energy. Other estimations of line tension between lipid domains have been made by Stine et al.s and by Helm.6 B=kw-d-ry When a binary mixture of cholesterol and DMPC is stained with a low concentration of a fluorescent phospholipid, this lipid partitions preferentially in the cholesterol-poor Thus, in the fluorescence microscope the cholesterol-poorphase appears bright, and the cholesterol-rich phase appears dark. For brevity, these are referred to as the white and black liquid phases, respectively. As discussed below, the circular shapes of liquid domains can be distorted by flow shear, produced by shear in the aqueous subphase, or by shear in the air above the monolayer. Figure 1 sketches domain shapes that can be produced by this flow shear. When shear is removed, shapes such as those in parts b-d relax to the circular shape (a). The restoring force leading to bolas shape changes is discussed be10w.I~ The shapedependent part of the dipolar and line tension energy of a single domain can be written
where p =
(lii - PI2 + 462)'/2
(3)
See refs 1 and 2. The symbol R < R'signifies that doublecounting of pairs of points on the periphery is to be avoided. The perimeter of the domain is p . The energy F, for a rectangular strip of length L and width w has been given previously.2 When L >> w,this energy is
In this case, each bola simply acts as a liquid reservoir. The restoring force is dominated by the first term (provided w
