Langmuir 1993,9, 1545-1550
1545
Lateral Diffusion of a Probe Lipid in Biphasic Phospholipid Monolayers: Liquid/Gas Coexistence Films Kaoru Tamada, Sanghoon Kim, and Hyuk Yu' Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706 Received December 7, 1992. I n Final Form: March 8, 1993 The method of fluorescencerecovery after photobleaching has been used to determinethe lateral diffusion coefficient (D)of a fluorescent lipid probe in L-a-dilauroylphosphatidylcholinemonolayers. The surface mass density was varied over a wide range from the liquid expanded/gas coexistence phase (LE/G) to the homogeneous liquid phase. The lateral diffusion coefficient reached a maximum value at the "liftoff" point on the surface pressurearea m e (D= 1.2 X 10-10 m2/s, A = 1.1-1.3 nmVmolecule, T = 22-24 "C), corresponding to the onset of the uniphasic LE state, and decreased from this maximum as the mass density was varied to both higher and lower values of area per molecule (A). The results were analyzed according to the effective-medium theory and the free area model, respectively. The D values in the LE/G biphasic monolayers were evaluated as a function of the area fraction of the LE phase, whereby it was shown that the gas bubbles in the LE/G can be regarded as semipermeable obstacles for the lipid probes, with a relative permeability of the gas bubbles with respect to the LE phase of 0.24.3.
Introduction It was recently reported1 from this laboratory that the lateral diffusion coefficient of a fluorescent lipid probe in L-a-dilauroylphosphatidylcholine(DLPC) monolayers spread on the airlwater interface in conjunction with other monolayer systems was determined by means of the fluorescence recovery after photobleaching (FRAP)technique with confirmation of the earlier results for the same lipid system by Peters and Beck.2 Lateral diffusion in phospholipid monolayer systems has been of interest, as it can be viewed as a measure of the molecular mobility of phospholipids in cell membranes. Hence, the focus in the literature has been placed on the range of surface mass density from the liquid expanded phase (LE) to the liquid condensed phase (LC), where the surface pressures (n) are finite and measurable. The lateral diffusion coefficients D of probe phospholipids in these system have been analyzed in detail on the basis of the free area model?l4 which has ita origin in the free volume model in the bulk state.6 In this paper, we direct our focus on diffusion over a wider range of surface mass density encompassing the liquid expanded/gas (LE/G) biphasic region of the same lipid, DLPC, where the surface pressure is near the detection limit (II = 0). By combining the FRAP measurements with fluorescencemicroscopicobservations of the coexistence phase along the tie line, it was possible to define the phase composition in terms of the area fraction of the LE phase simultaneously with lateral diffusion coefficient determinations. The reason for choosing DLPC as the system for the study is 3-fold. First, there exists the earlier work by Peters and Beck2 in the LE region, with which we made contact in our earlier report.1 Second,we have also examined the subphase viscosity dependence with the same system.' Third, DLPC has been shown to form no solidlikedomains in the biphasic region.8 Unlike some monolayers that are known to form highly viscoelastic films in the gas region (II = 0): other monolayers of the liquid expanded type
are known to exhibit surface viscosities small enowh to be neglected under the condition of II = 0, which haskeen confirmed by capillary wave studies.8 As indicated,DLPC belongs to the latter category,forming a monolayer without solidlike domains, which would further complicate the analysis. In short, it is a relatively simpler phospholipid system with respect to its monolayer behavior. Turning to the point of why we should be interested in lipid lateral diffusion in biphasic systems, we note first that cell membranes are indeed multicomponent multiphasic systems?Jo which can scarcely be modeled as a hydrodynamic continuum. In a three-dimensional isotropic medium, the translational diffusion coefficient Df) of a large solute particle in the limit of infinite dilution (in the absence of interparticle interactions) is given by the Stokes-Einstein relation,ll
(1) Kim,9.; Yu, H.J. Phys. Chem. 1992,96,4034. (2)Petam, R.;Beck, K.R o c . Natl. Acad. Sci. U.S.A. 1983,80,7187. (3)'Muble, H.;Sack", E.J. Am. Chem. Soc. 1972,S4,4499. (4)Galla, H.J.; Hartmann, W.;Theilen, U.;S a c k " , E.J. Membr. Biol. 1979,48,215. (5)Cohen, M.;Tumbull, D. J..Chem. Phys. 1969,31,1184. (6) Mphwald, H.Thrn Splrd hlma lSS8,Ib9,1. (7)Miyano, K.Lungmurr 1990,6,1264.
(8) Miyano, K.;Tamada, K.Lungmuir 1992,8,160. (9) S i e r , S.J.; Nicohn, G.L. Science 1972,175,720. (10)Ehn, E.L. Soc. Den. Physiol. Ser. 1986,40,367. (11)Landau, L.D.;Lifahitz, E.M. Fluid Mechanics;Pergamon Press: Elmsford and New York, 1959. (12)Safhnan,P.G.;Delbrtick, M. R o c . Natl. Acad. Sci. U.S.A. 1971, 72,3111. (13)Saffman,P.G.J. Fluid Mech. 1976,73 (4), 593.
0;') k T / 6 q R H (1) where 7 is the steady shear viscosity of the medium, k T has the usual meaning, and RHis the hydrodynamicradius of the solute particle. An analogous formulation has been proposed by Saffman and Delbriick12Js for the protein lateral diffusion on a membrane surface. They have modeled it as a quasi-two-dimensional problem; the translational diffusion coefficient Di2)of a cylinder with a height h and radius R confined to a viscous continuum layer with a shear viscosity 7 and thickness h sandwiched by a less viscous medium with a viscosity 7' and infinite thickness has where 7 is Euler's constant (0.5772). Analogy between eqs 1and 2 with the logarithmic correction term is to be expected since the latter is based on a set of hydrodynamic stipulations similar to that the former is based on. While there have been numerous applications of the formula, seeminglyall indicative of the plausibility of the model,'c18
0743-7463/93/2409-1545$04.00/0 Q 1993 American Chemical Society
Tamada et al.
1546 Langmuir, Vol. 9, No. 6,1993
(b) Surface Pressure Measurements. Experiments were we find a clear flaw in accepting the model to be relevant carried out in a Teflon trough 10.8 cm X 26.3 cm, which was because it is based on a homogenems hydrodynamic housed in a Plexiglas box for humidity control, with the relative continuum whereas cell membranes ought to be viewed as humidity within the box kept at 65 % or above during the 11-A multicomponent and multiphasic quasi-two-dimensional measurements. The surface tensions of the bare and monolayersystems,wherein the "viscosity" of the phospholipid matrix covered surfaces were determined by the Wilhelmy technique as given by q of the model is not an appropriate physical using a sandblasted platinum plate (10.0 mm X 15.7 mm X 0.1 parameter. Instead, one should provide the lateral selfmm). The surface tension (7) was observed as a function of time diffusion of phospholipid molecules in a multiphasic by a Cahn electrobalance until the time dependence (dyldt) monolayer as a more appropriate measure of the membrane at which point we took reached approximately 1W "/(ma), the measured y to be the equilibrium one. The precision of the "fluidity" after correcting for the phase composition. In surface tension measurement is estimated to be about hO.1 mN/ terms of direct relevance to membrane protein lateral m, and the surface pressure at each mass density is computed diffusion, our point here is to focus on a biphasic system, by the difference between the y value of the bare surface and not to establish the relevance of the LE/G biphasicsystem that of the covered surface. The 11-A determinations were to the membrane problem. In this context, one must performed twice, once before the FRAF' measurements, and understand how the diffusion coefficient is affected by another afterward. All measurements were performed within 4 the phase composition of the matrix and the viscosity of days of preparing the spreading solution, which was kept in a the subphase, corresponding to 'q of the Saffman-Delbnlck freezer during storage. model. (c) FRAP Method. Theinstrument anddataanalysisscheme are the same as those reported earlier.' The signal difference Furthermore, the apparent lateral diffusion coefficient between the fluorescence recovery of the bleached region and of DLPC in the LE/G region (II = 0) is expected to be the fluorescence decay of the unbleached region is fit to a single affected by its phase composition even if its intrinsic exponential model function?l diffusion coefficientremains that of the uniphasic LE state. Miihwald? Liische and Miihwald,17 and Liische et aL18have VU) = V(0)exp(-tlr) (3) reported that the LE/G phase can be observed by with fluorescence microscopy in a region of II I0.5 mN/m with some phospholipid monolayers on water. To the best of l / r = Dk2 (4) our knowledge,no attempt has been reported for examining where k is the spatial wave vector of the imaged pattem; which the diffusion in LE/G coexistencefiis in contrast to liquid is calculated from the Ronchi ruling size and the magnification condensed/liquid expanded (LC/LE) coexistence f i l m ~ . ~ J ~ of the objective; k = 2r/p where p ie the spacing of the ruling
Experimental Section (a) Materials and Monolayer Method. L-a-Dilauroylphosphatidylcholine (DLPC) (1) was purchased from Sigma (99%) and used without further purification. l-Acyl-2-[12-[(7-nitro2-1,3-benzoxadiazol-4-yl)amino] dodecanoyl] phosphatidylethanolamine(NED-PE) (2) (AvantiPolar Lipids, Birmingham, AL) was employed asthe fluorescentprobe and used as purchased. DLPC and NBD-PE were mixed in a 501 weight ratio and dissolved in HPLC grade chloroformto make spreading solutions with total concentrations of 0.1-0.15 mM. The monolayer mass density for all measurements ( E A , FRAP, and fluorescence microscopy) was varied by means of the continuous addition methodat room temperature (T = 22-24 "C) described elsewherem instead of the compression method. The water for the subphase was similarlytreated by the Milli-Q system as has been reported.m
1 DLPC
(14) Peters, R.; Cherry, R. J. h o c . Natl. Acad. Sci. U.S.A. 1982, 79, 4317. (15) Cherry, R. J. Biochim. Biophys. Acta 1979,559,289. (16) Vaz, W. L. C.; Criado, M.; Madeira, V. M. C.; Schoellmann, G.; Jovin, T. M. Biochemistry 1982,21,5608. (17) LBeche, H.; MBhwald, H. Colloids Surf. 1984,10, 217. (18) LBeche, H.; Sackmann, E.; MBhwdd, H. Ber. Bunsen-Ges. Phys. Chem. 1983,87,848. (19) Teissie, J.; Tocanne, J.; Baudras, A. Eur. J. Biochem. 1978,83,77.
imaged on the monolayer surfaces. In this study, we used only a single k value of 3393 cm-*. In order to minimize the surface flow, we used the same barrier described previous1y.l The stainless steel cylinder was put under the subphase surface during monolayer preparation; upon spreading the solution, we routinely waited for approximately 15-20 min for film stabilization. Then, the metal cylinder was raised until it just touched the monolayer surface. F W measurements were performed after observing the monolayer morphology with the fluorescence microscope, to ascertain the absence of surface flow. (d) FluorescenceMicroscopy. The CCD video camera was mounted on the FRAP system in place of the photomultiplier, and the image with the Ronchi ruling pattern was recorded on a videocassette tape immediately after the FRAP measurementa were performed. The recorded image was subaequentlyanalyzed with an image processor to obtain the area fractions of the gas phase in LWG coexistencef i i . Apart from thisstep of recording the phase composition of the coexistence films, another set of microscopic images (without the Ronchi patterns) were taken by the use of the same system, and it was printed out by a thermoprinting system.
Results and Discussion A surface pressure-area (n-A) diagram is shown in Figure 1. Comparison of the II-A curve after a FRAP measurement to that before FRAP revealed a slight discrepancy, the former showing a more expanded II-A profile. We attribute this observed time dependent of II-A to the storage time of the spreading solution as noted in the earlier results.' The 11-A curves show a plateau a t high surface mass densities when A I 0.5 nm2/molecule, corresponding to n = 45 mN/m, which is the equilibrium spreading pressure; it is clearly the end point of a uniformly spread monolayer, as observed by the spread droplets remaining on the surface for a long time and finally fine crystals forming on the water surface. This was also confirmed by fluorescence microscopy. (20) Sauer, B. B.; Yu,H.; Tien, C.; Hager, D. F. Macromolecules 1987, 20, 393.
(21) Lanni, F.; Ware, B. R. Rev. Sci. Instrum. 1982,53,906.
Probe Diffusion in Biphasic LEIG Monolayers
-
50
I
40
-
Langmuir, Vol. 9, No. 6, 1993 1547
.
E
20
.
A
1
50
0
JI
4, 0
1
2
3
5
4
-'
1.2 1.0
0.0
6
A / nm *molecule Figure 2. Lateral diffusion coefficient D vs A for a fluorescent lipid probe (NBD-PE) in phospholipid (DLPC) monolayers at a weight ratio of 1:50 = [NBD-PE]:[DLPC]. Open circles, squares, and triangles are the D values from three separate experimentsunder the same conditions. Filled squares indicate the fluctuation range of the D value at the specified A after first spreading on the bare air/water interface. The solid curve stands for the II-A profile acquired subsequent to the FRAP measurements. Arrows at the bottom indicate the locations along the tie line of the LE/G phase where differentphase morphologies were photographed as shown in Figure 3.
prior film requiring over 30 min for equilibration. The corresponding fluctuations of the apparent D value after the first spreading were also obtained as a measure of the local phase inhomogeneities. These are indicated by the filled squares in Figure 2. The monolayer appeared homogeneous from high II (30 mN/m) down to about 0.2 mN/m (frame A, Figure 3). At this surface pressure (II < 0.2 mN/m) small bubbles began to appear, their size changing according to the surface mass densities as shown by frames B-E of Figure 3. These bubbles were stable and remained intact without disappearing or coalescing at least during our FRAP measurement periods; the stability of the gas bubbles in the matrix lipids is attributed to long-range repulsive interactions caused by electrostatic force^.^*^^ The diffusion coefficient reaches a maximum value at the liftoff point of the II-A curve (A = 1.1-1.3 nm2/ molecule), Le., at the boundary between the uniphasic LE and the biphasic LE/G. As seen in the profile of D vs A in Figure 2, its dependence on A revealed two distinct trends relative to the liftoff point. These were classified according to the II range as follows: (1) Il I0.2 mN/m (LE/G coexistent films). Starting from the maximum value, D starts to retard as the surface mass density is decreased. In this regime, the behavior of D is accounted for by the effective medium model (see below). (2) II > 0.2 mN/m (LC and LE films). D decreases as the surface mass density is increased. In this region, the behavior of D is accounted for by the free area model (see below), provided we restrict this to successful spreadingconditions (II I30 mN/m). Addressing first the observed retardation of D with respect to the mass density decrease in the biphasic region, we may analyze the results in terms of diffusion models in solid domaidfluid two-phase systems, i.e., the effective medium and percolation mode1.2*26The two are shown to be related by Saxton,26and they can be unified with a single parameter called the relative permeability (r),defined as the product of the partition coefficient ( K ) and the ratio of the diffusion coefficients, r = K(Dd/Df)
(5)
where
where Dd is the diffusion coefficient in the domain phase and [Alfluidy e and Dt is that in the fluid phase. [AIdoIn Figure 2, the lateral diffusion coefficient (D), calthe concentrations of the diffusing species in the domam culated via eqs 3 and 4,is plotted against A along with the and fluid phases, respectively, and their ratio is the II-A diagram. The surface morphologies are shown in partition coefficientK. If r > 103,the domains are treated Figure 3with the microscope imagestaken at the respective as semipermeableobstructions,and the observed D is given mass densities indicated by arrows in the bottom of Figure by the Bruggeman-Landauer equation%which is a directly 2. We show in Figure 4 an enlarged portion of Figure 2 useful form of the effective medium model: where A I1.4 nm2/molecule. The error in each D value for both figures is estimated to be k5%. In the microscope images, the bright regions indicate that LE, while the dark regions correspond to the gas phase, as provided by the identification in the l i t e r a t ~ r e . ~ J ~ J ~where x is the phase fraction of the fluid phase. On the Immediately after spreading,the monolayer has a different other hand, if r < 103,the effective medium model is no phase composition from the "equilibrium" conditions, longer applicable. In this region, the domains are treated approximately 10 min after spreading. Large-scale inas impermeable obstructions, and the percolation model homogeneities appearing at the beginning start to give (22) Andelman, D.;Brqhard, F.; Joanny, J.-F. J. Chem. Phys. 1987, way to a more regular morphology as shown by the pictures 86,3673. in Figure 3. Within a reasonable time window, the regular (23) McConnell, H.M.; Moy, V. T. J. Phys. Chem. 1988,92,4620. phase patterns remained constant; hence, we regard them (24) Landauer, R. J. Appl. Phys. 1952, 23, 779. Landauer, R. In Electrical Transport and Optical Properties of Inhomogeneous Medio, as those of the equilibrium conditions. FRAP measureGarland,J. C., Tanner, D. B., Me.;American Institute of Physica: New ments were carried out at such equilibrium conditions. York, 1978. We noted an exception to this routine when we first spread (25) Stauffer, D. Phys. Rep. 1979,54, 1. (26) Saxton, M.J. Biophys. J. 1982,39, 166. a solution on the pristine air/water interface without a
Tamada et al.
1548 Langmuir, Vol. 9, No. 6, 1993
,A=-
50pm Figure 3. Five different frames of fluorescence microscope pictures along the tie line of LE/G with the location identifications given
by the arrows in the bottom of Figure 2: (A) A = 0.96 nm2/molecule, (B) A = 1.28 nm2/molecule, (C) A = 2.56 m2/molecule, (D) A = 3.84 nm2/molecule, (E) A = 5.12 nm2/molecule.
"I
A
a
50
AB
00
- 1.2 - 1.0
- 0.8
Table I. Lateral Diffueion Coefficient at Different Areae mr Molecule and Phase Commeitione
7 v)
-E \
- 0.6 n s - 0.4
- 0.2
s
0 u.40
5.57 5.12 4.64 3.98 3.84 3.48 2.56 1.92 1.92 1.28
0.70 0.53 0.59 0.54 0.40 0.45 0.24 0.10 0.04 0.02
1.10
0.00
0.0
0.60
0.80
1.00
1.20
1.40
-'
A / nm * molecule Figure 4. An enlarged version of Figure 2 for the range A I1.4 nm2/molecule. Open circles, squares, and triangles and the D values from three separate experiments under the same conditions. The solid curve stands for the II-A profile acquired subsequent to the FRAP measurements.
is applied with a percolation threshold at the critical fraction of the fluid phase, xC= 0.668.% In such a case, one can describe the D dependenceon phase composition in terms of the scaling laws above and below the threshold: Above xc, while below xC,D is essentially zero, D * D ~ ( x x , ) ~* 0 (X < xC) (9) where t and u are the appropriate critical exponents. In order to apply these models to our system with the gas bubbles as obstacle domains and the liquid expanded phase as the fluid phase, we need to estimate the relative permeability (r)first. Referring to theD retardation shown in Figure 2, the observed value decreased by no more than a factor of 3 from the uniphasic LE state to point E (about 70% gas phase); hence, r is estimated to be on the order
0.30 0.47 0.41 0.46 0.60 0.55 0.76 0.90 0.96 0.98 1.00
0.45 0.55 0.54 0.55 0.68 0.68 0.85
0.38 0.46 0.45 0.46 0.57 0.57
1.05
0.88 0.94
1.13 1.15 1.20
0.71 0.96 1.00
Uncertainty in each D determination is estimated to be about 15%, and the error bar on each datum in Figure 5 repreaenta such an error range. * Dm is taken to be the maximum value of D, 1.2 X 10-10 m2/s as shown in Figure 2. 0
of 0.1; a brief rationale is provided by the fact that the partition coefficient between the gas phase and the LE phase should be on the order of 1W2 while the diffusion coefficient ratio &/Dm should be around 10 if we draw on the analogy to the bulk liquid- and gas-phase behaviors. Having thus estimated the order of magnitude of r, we apply the Bruggeman-Landauer equation (eq 7) toanalyze the retardation of D in terms of the phase composition ( x ) , which is the area fraction of the LE phase. The results are collected in Table I and shown in Figure 5, where the maximum value of D = 1.2 X 10-lO m2/s in Figure 2 is used for Dm,and the observed diffusion coefficient normalized by DLE,DIDLE, is plotted against x . On the basis of comparison with the calculated retardation profiles (solid curves), we obtained a value of r = 0.2-0.3 for the relative permeability of bubble domains with respect to the LE phase. The results are, as a whole, consistent with the single parameter retardation profile of Bruggeman-Landauer. The strength of this conclusion is weakened by the error limits on the normalized diffusion coefficients (DIDm) which are too large to determine a unique solution for r
Robe Diffusion in B i p h i c LEIG Monolayers
w.w
u.0
0.2
0.6
0.4
0.8
hngmuir, Vol. 9, No. 6, 1993 1549
1.0
(l/af) / nm-'
x Figure 5. Normalized lateral diffusion coefficientD/& va the fraction of LE phase x. Solid curves are the predictions of the effective medium model of Bruggeman-Landauer, eq 7, for different relative permeabilitiea r. Our results are well covered by the profiles with r = 0.2-0.3. in the region of x greater than 0.7. Nevertheless, the data in the region 0.2 < x < 0.7 are of sufficient quality to estimate a value of r = 0.24.3. Clearly this r value is within the applicability range for the effective medium model and is rather comparable to the permeability of solid domains against a liquid phase.n* Following the line of the earlier estimate of r, D G / Dis~set a t about 0.1 from& = 1O-g m2/sand Dm 10-1°m2/s,and the partition coefficient K = [Al~/[A]misestimated as 0.024.03,from which we infer that the number of fluorescent dye probes in the gas phase is less than that in the liquid phase by a factor of 30-50. This corresponds qualitatively to the result of microscopic observation. The reduction profile of D for the range of high II (>0.2 mN/m) in DLPC monolayers has already been studied by Peters and Beck? and our earlier results were in agreement with theirs.' We present here the similar analysis for the uniphasic LE region for the sake of completeness and more importantly to demonstrate the reproducibility of the FRAP measurements in this phase region. Following the free area model of S a c k " , Triiuble, and collaborators,a4 the lateral self-diffusion coefficient (D) of an ensemble of rigid disks (or cylinders with unspecified height) with a cross sectional area a0 is given by D = a exp[-,3a*/atl
(10)
where a is a factor representing the diffusant geometry and ita local velocity, at is the free area defined as af = A - ao, a* is the critical free area for a displacement, and ,3 is a factor accounting for the overlap of free area (0.5< ,3 < 1.0). Figure 6 shows a semilogarithmic plot of D v8 l/af. The best fit line is obtained with 00 = 0.41 f 0.02 nm2/molecule. Furthermore, @a* = 0.26 f 0.04 n m 2 and the limit D l l e = (1.4f 0.1)X 1 0 - l O m2/s were obtained from the slope and intercept, respectively, which are also in agreement with those of Peters and Beck and our earlier ones. We close this section with an open question: How can we be sure that we actually attained the equilibrium phase composition for a given mass density (A-l) at different pointa on the tie line? As stated earlier, we merely employed a criterion of no further time dependence. In (27) Lentz, B.R.;Barenholz,Y.;Thompson,T.E.Biochemistry 1976, 15, 44521. (28) Kapitza, H.G.;S a c k " , E.Biochim. Biophye. Acta 1980,5S5,
66.
Figure 6. A semilogarithmic plot of D va l/or according to the free area model, eq 10. Squares are the measured diffusion coefficients at calculated l/& ( = [ A- @I-9 with = 0.41 nm*. The solid line is the beat fit by a linear regression routine.
E \
0
2
0.4
-
Ax
X
1t' /
0.6
x A x
'A
-
o.2 0.0 0
1
2
3
'
5
4
A / nm molecule
6
-'
Figure 7. D va A, which show a clear departure from that in Figure 2. Both were determined under similar experimental
conditions. Open triangles represent the new set of data while the earlier set shown in Figure 2 is given by crosses; see text for explanation.
trying to answer this question, we repeated the D determinations by FRAP over the entire biphasic region. The resulta are shown in Figure 7 where open triangles stand for the new set and c r w e s for the same ones shown in Figure 2. Though the trend of D vs A resembles the one in Figure 2,the details are obviously different, particularly the retardation profile at the low II region (II I0.2 mN/ m) and the D , value. It is clear from the lack of agreement between the two seta of the data that the phase composition and/or morphology such as the distribution of the gas bubble sizes are not readily reproduced. In short, the true equilibrium atate may rarely be reached and only with difficulty. We are tentatively inclined to attribute this lack of agreement to the initial spreading conditions and the kinetics of coarsening of bubble sizes. It is entirely possible that a given set of D values may depend rather sensitively on the initial spreading conditions. Conclusions The method of fluorescence recovery after photobleaching has been used to determine the lateral diffusion coefficient (D)of a fluorescent lipid probe in ~ - a dilauroylphoaphatidylcholinemonolayers. Over the LWG and LE phase regions, D was shown to peak at the onset of uniphasic LE phase, from which D decreases in either
1650 Lahgmuir, Vol. 9, No.6, 1993 direction with respect to the mass density. For the decreasing profile of D relative to increasing gas-phase composition, the effective medium model with a relative permeability parameter seems to suffice in accounting for the behavior. As shown previously, the free area model accurately describesthe decrease inD with increasingmass density in the uniphasic LE region. A crucial issue however is how one can be assured of equilibrium phase composition and morphology in the LE/G region. We conclude that the complexity of the system is such that one is rarely sure
Tamada et al. of the true equilibrium biphasic monolayers since so much seems to depend on the initial conditions of spreading.
Acknowledgment. Thisresearch is in part supported by an NSF grant (DMR-9203289), Miami Valley Laboratories of the Procter and Gamble Co., and the Photographic Research Laboratories of Eastman Kodak Co. We are most grateful to our colleagues Alan R. Esker, Frank E. Runge, and Professor George Zogrdi for valuable discussions.
