Critical mixing in monomolecular films :
pressure-composition phase diagram of a
two-dimensional binary mixture
C.L. Hirshfeld, M. Seul
To cite this version:
C.L. Hirshfeld, M. Seul. Critical mixing in monomolecular films : pressure-composition phase
diagram of a two-dimensional binary mixture. Journal de Physique, 1990, 51 (14), pp.15371552. <10.1051/jphys:0199000510140153700>. <jpa-00212466>
HAL Id: jpa-00212466
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Submitted on 1 Jan 1990
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J.
Phys.
France 51
Classification
Physics Abstracts
68.10
64.70M
-
(1990) 1537-1552
-
64.75
-
15 JUILLET
1990,
1537
87.15
,
Critical
mixing in monomolecular films : pressure-composition
phase diagram of a two-dimensional binary mixture
C. L. Hirshfeld
(1)
(2)
(1)
and M. Seul
(2)
Williams College, Williamstown, MA, 01267, U.S.A.
AT&#x26;T Bell Laboratories, Murray Hill, NJ 07974, U.S.A.
(Reçu le
17 novembre 1989, révisé le 7 février 1990,
accepté le
2
avril)
avons mesuré les isothermes pression-surface de monocouches mixtes
dimyristoyl lécithine et de cholestérol à 23,5 °C, et nous les avons analysées afin
d’établir le diagramme de phase pression-composition de ces mélanges bidimensionnels. Ces
mesures sont confirmées par l’observation directe de la séparation de phase. Nous identifions un
intervalle de non-miscibilité des états fluides qui se termine par un point critique, accessible à la
température ambiante. Nous proposons que, dans les phases mixtes coexistantes, la lécithine se
Résumé.
-
composées
Nous
de
trouve dans des états distincts.
pressure-composition phase diagram of mixed monolayers of dimyristoyl
phosphatidylcholine (DMPC) and cholesterol at a temperature of 23.5 °C is derived by numerical
analysis of pressure-area isotherms and corroborated by direct fluorescence microscopic
observations. We identify a fluid-fluid miscibility gap, terminated by an upper critical point which
is accessible near room temperature. We propose that the coexisting mixed phases of cholesterol
and DMPC contain the phospholipid in two distinct states.
Abstract.
-
The
1. Introduction.
The
discovery of domain formation during phase coexistence in monomolecular films of
amphiphiles confined to an air-water interface has provided a major new stimulus to the
investigation of these systems. A rich variety of domain shapes has been documented [1, 2].
Recently proposed phenomenological theories invoke a picture of competing attractive van
der Waals and long-ranged, repulsive dipolar or Coulomb interactions to account for the
appearance of domains of finite size [3, 4]. At the level of the available mean field treatments,
amphiphilic monolayers are viewed to be equivalent to uniaxial ferromagnets [5, 6],
ferromagnetic surface layers [7] and thin ferrofluidic films [8]. Specifically, the mean field
phase diagram contains a coexistence region characterized by intralayer periodic modulations
of the relevant order parameter [3].
Particularly pertinent in ascertaining the range of validity of these theoretical considerations
is the study of monomolecular films in the vicinity of a critical point. The existence of critical
points in several single component monolayer films at the air-water interface has been
demonstrated in film balance studies [9, 10] and computer simulations [11]. In singleArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0199000510140153700
1538
must be varied to reach the critical
and
As
the
of
dynamics of domain walls [12],
point.
quantitative analysis
configurations
recorded by optical video microscopy, requires extended periods of observation of individual
domains in films at the air-water interface, it is imperative to suppress monolayer flow. We
have found this to be a task more readily accomplished when temperature is eliminated as an
experimental variable, because even small thermal gradients generally lead to flow. These
considerations suggest the introduction of composition as a new variable and thus the study of
multicomponent surfactant systems.
The isotherms of monomolecular films containing two constituents have been investigated
by several authors. Mixed films of cholesterol and phospholipids or fatty acids have been of
particular interest, due to the constituents’ biological and physiological significance [13-18].
However, it was the application of fluorescence microscopy which recently enabled
Subramaniam and McConnell [19] to directly observe phase separation phenomena in mixed
films containing the phospholipid dimyristoylphosphatidylcholine (DMPC). They interpreted
their intriguing observations to imply critical mixing, and the existence of an upper consolute
point, accessible at or near room temperature.
Two important experimental considerations render this mixed film system particularly
suitable for detailed experiments. At temperatures exceeding the postulated critical temperature of the liquid-condensed (LC)-liquid-expanded (LE ; for nomenclature, see e.g. [20])
coexistence of DMPC, approximately 20 ° C [10], DMPC simply behaves as a two-dimensional
fluid. This greatly simplifies the behavior of the cholesterol-DMPC mixture. In addition, the
expected absence of internal conformational order in DMPC facilitates dissolution of the
fluorescent phosphatidylcholine analog which is added as an impurity to the host phase and
vénérâtes the contrast enabling fluorescence microscopic observation of phase separation. In
view of the desirability of experiments in the vicinity of a critical point, this system thus offers
itself as a candidate for closer inspection.
We have recently applied techniques of digital image analysis to establish a detailed
characterization of the domain shapes formed in this mixed monolayer system by evaluating
power spectra of domain wall configurations. This analysis permits the identification of
several distinct regimes of domain shape stability as the putative upper consolute point is
approached. As discussed elsewhere [12], the appearance of different stable ground states of
domain wall configurations is in general accordance with stability analyses based on the model
of competing interactions, referred to at the outset.
In the present article, we derive the pressure-composition phase diagram for this binary
mixed film at a temperature of 23.5 ° C, based on the analysis of thermodynamic measurements, i.e. pressure-area isotherms and the bulk modulus curves derived from them by
numerical differentiation. We correlate the thermodynamic measurements with direct optical
observation of phase separation, corroborating the determination of the location of a twophase coexistence region. A rather detailed picture of the global phase behavior may be
deduced. We identify an upper critical point in this mixture which, at 23.5 °C, is located near a
mole fraction of cholesterol of 0.27 and a surface pressure of 11.5 dyne/cm. The coexisting
phases emerge at very low surface pressure (ir 5 0.5 dynes/cm) with respective compositions
of approximately 10 mole% and 55 mole% cholesterol.
We propose a simple rationale for the qualitative features of observed phase behavior by
noting that, to a good approximation, the isobaric increase of cholesterol mole fraction in
mixed films is equivalent to an isothermal compression of the lipid constituent, DMPC.
Specifically, this leads us to suggest that, in contrast to simple fluid-fluid immiscibility, the
miscibility gap in the phase diagram studied here involves a second order parameter, related
to different configurations assumed by DMPC in the two coexisting mixed phases. Based on
component monolayers lateral density and temperature
1539
the
distinctly different compressibilities of the two mixtures and related characteristics, we
argue that these configurations are analogous to those adopted, respectively, in the LE and
LC phases of single component monolayers which have been shown to differ primarily with
respect to the degree of intramolecular chain order [21, 22].
In what follows, we first describe, in section 2, our experimental methods and the digital
filters employed to compute the bulk modulus of the mixed monolayer films. Section 3
contains the results leading to the phase-diagram which we discuss and interpret in section 4.
We summarize our conclusions in section 5.
2. Materials and
expérimental
methods.
2.1 MATERIALS. - For the measurement of 7T-A isotherms it was crucial that the surfactants
and substrate be as pure as possible ; impurities produced substantial distortions in the
isotherms. In particular, it proved difficult to obtain cholesterol free of its oxidation
product(s) [23], and difficult to prevent it from oxidizing at the air-water interface [18].
Cholesterol was purchased from both Sigma (Sigma Grade 99 +%, as well as cell-culturetested grade 99 +% ; Sigma Chem. Co., St. Louis, MO) and Serva (analytical grade, 99.9 %
Serva, Westbury, NY), the latter yielding best results. Recrystallization from ethanol
removed a substantial fraction of oxidized material, as judged from a characteristic inflection
in the isotherm (compare e.g. Fig. 2). However, even careful recrystallization of cholesterol
in an argon atmosphere did not improve the purity of a newly opened supply. DMPC (&#x3E; 99 %
pure) was obtained from Avanti Polar Lipids (Birmingham, AL) and used without further
purification, since its isotherms indicated sufficient purity. The fluorescent probe C6-NBDPC (1-Palmitoyl-2-[6-[7-nitro-2-1,3-benzoxadiazol-4-yl)amino]caproyl]PC), a phosphatidylcholine (PC) analog with the NBD fluorophore attached to one aliphatic chain, was also
obtained from Avanti, and used without further purification.
Stock solutions of DMPC and of cholesterol were made up in spectroscopic grade
chloroform, at approximately 10 mM (8 mg/ml), and diluted to approximately 1 mM with
chloroform to make spreading solutions. 9:1 hexane/ethanol was also tried as a spreading
solvent, but seemed to aggravate cholesterol oxidation (perhaps due to water absorbed by the
ethanol or due to the process of changing solvents). Mixtures of DMPC and cholesterol were
made by diluting appropriately mixed amounts of the two stocks. A new cholesterol stock had
to be made up from a fresh bottle of cholesterol every two or three days because of oxidation,
as judged by the isotherms of cholesterol or cholesterol-rich mixtures.
Those mixtures which were studied by epifluorescence microscopy were prepared with
2 mole% C6-NBD-PC. This dye was also kept in chloroform stock solution. The inclusion of
the dye caused a small ( 5 %) shift of the isotherm of the 30 mole% cholesterol mixture,
leaving its overall shape unaltered.
pure ;
2.2 PRESSURE-AREA ISOTHERMS.
Pressure-area isotherms were recorded under computer
control on a Langmuir-Blodgett trough system (KSV 2200 LB ; KSV Chemicals, Helsinki,
Finland). The entire trough, kept in a laminar flow hood, was placed in a plexiglass enclosure
to reduce monolayer flow. The area of the teflon trough was varied between approximately
15 x 45 CM2 and 15 x 15 CM2 by adjusting the position of a stepping motor driven barrier,
machined from white delrin. To reduce thermal drift, the subphase temperature was held
constant at 23.5 ° C by circulating water through glass tubing submerged in the subphase. The
surface temperature was read with a thermistor (Yellow Springs Instrument Co., Yellow
Springs, OH), while the surface pressure measurement employed a Wilhelmy plate of
roughened platinum, supplied by KSV. Isotherms, usually containing 200-300 points, were
stored on disk for later analysis, as described in section 2.4.
-
1540
Fig.
KSV
1. - Schematic
representation of experimental set-up. Not shown is a dipping well, attached to the
Langmuir Blodgett trough, required in the deposition of monolayer films onto substrates.
At the
beginning of this project, the trough was thoroughly cleaned by allowing purified
overnight, then by rinsing it with water and organic solvents, and finally by
running many isotherms and repeating the cleaning operation, until a standard isotherm of
the phospholipid dipalmitoyl phosphatidylcholine (DPPC) at - 22 ° C was obtained [10]. The
glass tube which carried temperature-controlled water through the substrate was cleaned in a
mixture of sulfuric acid and hydrogen peroxide. The bottom of the moving barrier was given a
new surface finish to remove any irregularities. Thereafter, the only cleaning necessary for the
apparatus consisted of repeated sweeping of the substrate surface after each isotherm. The
entire volume of subphase (of approximately 1.51) was exchanged weekly ; at that time the
trough was cleaned with ethanol.
The aqueous subphase was composed of water of 18 Mfl cm resistivity, obtained from a
water purification unit containing ion-excange, carbon and « Organex » filters (Ultra pure
Cartridge Kit ; Millipore Co., Bedford, MA). The subphase pH drifted to a value of
approximately 5.5 within 2 hrs. Measurements were also made on a subphase containing
100 mM 1-ascorbic acid (Fisher Scientific, reagent grade), added to minimize cholesterol
oxidation at the air-water interface [23]. Here, the typical subphase pH was found to be 3.5.
The addition of ascorbic acid to the subphase helped to stabilize cholesterol, especially in
monolayers of Xchol &#x3E;- 0.5, but had otherwise no effect on the isotherms.
After a monolayer was spread at the air-water interface, the spreading solvent was allowed
to evaporate for twenty minutes under a gentle flow of argon gas. The film was then
water to stand in it
1541
compressed at a rate of approximately 2 Â2/Molecule.min. Compressing more slowly
produced no significant differences in the isotherm ; compressing much faster introduced
substantial noise into the measurement of surface pressure (see Sect. 2.4) and may have
produced kinetic effects on the isotherms as well.
2.3 EPIFLUORESCENCE MICROSCOPY. - A small epifluorescence microscope, adapted from
a beam splitter tube assembly (Rolyn Optics, Covina, CA) in a way previously described [24],
was employed to monitor monolayer films while recording their 1T-A isotherms on the KSV
trough. For these measurements, 2 mole% of a fluorescent lipid (see Sect. 2.1 ) were added to
the monolayer. The 457.9 nm line of a 5 W argon laser (Innova 90-5 ; Coherent, Palo Alto,
CA) was used for illumination. Fluorescence images were collected through a 25X (NA 0.45)
objective, passed through a 495 nm cut-off filter and recorded by a CCD camera (CCD72,
Dage-MTI, Michigan City, IN). The camera head’s small weight and size made it possible to
attach it directly to the microscope barrel. A video processor with a gray scale stretch circuit
(Dage-MTI) was instrumental in obtaining images of acceptable signal-to-noise ratio, given
the low input light levels otherwise found to be insufficient to generate usable output. The
photographs in figures 4 and 5 were taken on a smaller trough with a SIT camera, as described
elsewhere [12], requiring the addition of only 1 mole% of fluorophore.
Pressure-area isotherms were analyzed by application of a seven
point least-squares quadratic or quartic smoothing filter (chapter 3.3 in [25]), followed by a
seven point Lanczos differentiating filter (chapter 6.4 in [25]) to compute the two-dimensional
bulk modulus, i.e. the inverse of the isothermal compressibility :
2.4 ISOTHERM ANALYSIS.
-
where à and TT denote mean molecular area and surface pressure, respectively. Building
vibrations, which coupled into the surface pressure reading via surface excitations of the
subphase represented the primary source of noise in the recordings. While of little concern in
the isotherms themselves, these vibrations necessitated the introduction of a smoothing filter
to minimize noise contamination of the computed 1 / K vs. à curves. Digital filtering was
implemented numerically by executing the equivalent convolution operation as a matrix
multiplication (see e.g. chapter 3 in [26]) on a 32 bit floating point array processor (DT7020,
Data Translation, Marlborough, MA) residing in a personal computer.
3. Results.
A typical set of pressure-area
obvious characteristic features
isotherms, compiled in figure 2, reveals the absence of any
(« breaks ») marking phase transformations in many other
10,
14,
20]. It is this observation which motivated a more careful
monolayer systems [9,
based
on
the
analysis
inspection of the isothermal compressibility ( K ), or its inverse, the twodimensional bulk modulus. Figure 3 contains a representative sample of the results. Several
features are now readily identified. The first is a discontinuous increase in 1 / K indicating a
of the compressibility to a finite value. The corresponding mean molecular area which
we refer to as in.t in what follows (see particularly Fig. 7 below) marks the termination of
liquid-vapor coexistence [13]. The significant decrease of a-onset with increasing cholesterol
mole fraction, X,,h.1, is in accord with the pronounced concomitant shift, revealed in figure 2,
of the entire isotherms to lower molecular areas. We will return to this point in connection
with figure 7.
drop
1542
Fig. 2. - Set of pressure-area isotherms of mixed monolayers of dimyristoylphosphatidylcholine
(DMPC) and cholesterol, recorded at 23.5 ° C on an aqueous subphase, in some cases containing
100 mM 1-ascorbic acid. The mole fractions are as indicated. The features visible near 20 dynes/cm on
the Xh.1 = 0.5 and Xchol
0.6 isotherms signal the presence of oxidized cholesterol.
=
The second characteristic feature in the plots of log ( 1 / K ) vs. li is a distinct break, apparent
from figures 3b, 3c and 3d, corresponding to cholesterol mole fractions of 0.15, 0.30 and 0.45,
respectively. Consistently, this break occurs at the junction of two approximately linear
segments in the semi-logarithmic representation of the 1 / K profiles (see Fig. 3) and thus
signals a discontinuous increase in their slope. At the corresponding point on the isotherm,
the mixed monolayer becomes less compressible. Epifluorescence microscopy reveals that
this « stiffening » of the surface layer coincides with the transition from a phase-separated
regime, characterized by a heterogeneous distribution of fluorescent label in the monolayers,
to a homogeneously fluorescent state which we identify below with a homogeneous mixture
(see Fig. 8). Figure 4 illustrates this conclusion with a series of epifluorescence micrographs,
taken during compression of a mixed monolayer of Xh.1 = 0.3 at increasing pressures.
Figure 5 presents micrographs of monolayers in the two-phase region with compositions fixed
below (Xchol
0.1) and above (Xchol 0.45) the critical value (see below). These images
provide direct evidence for the coexistence of two phases, the bright areas corresponding to
the phase predominantly containing DMPC. We will see below that these optical observations
are entirely consistent with the analysis of the thermodynamic data.
A third feature characterizing the mixed monolayer may be extracted from the
log ( 1 / K ) vs. i curves (of Fig. 3) by plotting the value of 1 / K , assumed at onset and at several
fixed values of the surface pressure, as a function of increasing cholesterol mole fraction. A
selection of such plots is shown in figure 6. They permit the important observation that the
addition of cholesterol to the mixed monolayer does not substantially alter the value of
1 / K from that found for pure DMPC until a threshold value of the cholesterol mole fraction
(Xchol) is attained. This threshold value was estimated by applying a linear regression analysis
to the low X,,h.1 portion of each plot, as indicated by the solid lines in figure 6. As many points,
in order of increasing Xchob as possible were included, until this caused a significant
deterioration of the goodness of fit parameter. The first value of Xchol defined by this
procedure not to lie on the initial linear portion was identified as the threshold value. These
points mark the phase boundary, shown in figure 8 (« V ») which separates region II from the
rest of the diagram. The scarcity of data points available for Xchol :&#x3E; 0.6 currently precludes a
=
=
1543
Fig.
3.
-
Inverse
compressibility 1 / K - -
il
2013
)
a
(bulk modulus)
as a
function of
mean
molecular
increasing values of Xchol 0.05, 0.15, 0.30, 0.45 and 0.55. Also shown, as solid lines, are the
corresponding isotherms from which the bulk modulus curves were computed by application of a seven
point Lanczos differentiating filter (see text, Sect. 2.4). Straight lines serve as a guide to the eye. The left
hand ordinate shows the surface pressure, the right hand ordinate refers to the bulk modulus. The
inversion in the 1 /K curves for Xchol
0.45 and 0.55 centered at J m 47 Â2/Mol , arises from cholesterol
area, for
=
=
oxidation.
the functional form obeyed as 1 / K approaches the limiting value measured
for pure cholesterol.
To identify the partial molecular areas of coexisting phases in the surface monolayer we
follow (in Fig. 7) the classical scheme of plotting the mean molecular area, li, at onset (liquidvapor coexistence), and at several fixed values of the surface pressure, as a function of
cholesterol mole fraction. It is readily apparent that, in contrast to several other phospholipid/cholesterol mixed monolayers [16], simple additivity of the molecular areas of the
meaningful test of
1544
Fig. 4. Fluorescence micrographs of DMPC/cholesterol mixed monolayer containing 30 mole%
cholesterol, and 1 mole% of the fluorescent lipid analog C6-NBD-PC (see Sect. 2.1). a) Fluorescent and
probe excluding phases occupy approximately equal area fractions. In the regime of strong segregation
shown here, domains adopt a circular shape. The photograph is taken at a surface pressure of
approximately 5 dynes/cm. The bar marks 50 fJ.m. b) Upon approaching the upper consolute point the
domain wall energy softens and significant domain shape fluctuations lead to distorted shapes [12]. The
photograph is taken at a surface pressure of approximately 10 dynes/cm. Fluctuations decay on time
scales consistent with rapid, i.e. fluid-like intralayer molecular diffusion in both phases. c) Further
compression yields a homogeneously fluorescent mixture, shown here at a surface pressure of
approximately 14 dynes/cm. The appearance of this homogeneous phase coincides with the « stiffening »
of the monolayer described in connection with figure 3.
-
constituents does not obtain : this would imply â ADMPC( 7r ) XDMPC + achol C Tr ) Xchob and
thus a straight line connecting ii(Xchol
0) aDMPC and a(Xchol 1.0) achol. However, all
15
7r
to
those
dynes/cm) are well approximated by a representation
plots (certainly
up
the
three
distinct
identification
of
regimes, each characterized by a linear decrease
permitting
of â with increasing mole fraction of cholesterol. Construction of the intercepts (see e.g.
chapter 7.4 in [27]) yields the partial molecular areas of DMPC and cholesterol. As implied by
the linear dependence of â on Xchob both of these remain constant throughout each of the
=
=
=
=
=
=
1545
5.
Fluorescence micrographs of DMPC/cholesterol mixed monolayers containing 1 mole% of the
fluorescent lipid analog C6-NBD-PC (see Sect. 2.1 ) and 10 mole% (Fig. 5a) and 45 mole% (Fig. 5b)
cholesterol, respectively. Photographs were taken at surface pressures of approximately 0.5 dyne/cm
and 0.2 dyne/cm, respectively, at molecular areas close to jonset- In combination with figure 4a these
photographs demonstrate that fluorophore excluding regions in the monolayer occupy an increasingly
larger area fraction as Xchol is increased. In section 4 we suggest these regions to be associated with a
DMPC/cholesterol mixture containing DMPC in an ordered conformation. A heterogeneous distribution of labelled domains generally prevails at length scales exceeding 500 jim. The bar in figure 5a
marks 50 fJ-m.
Fig.
-
regimes. To extract the partial molecular areas listed in table 1 below, a linear fit was
applied to the middle portion of each plot. That is, beginning with Xehol = 0.1, the number of
points, in order of increasing Xch.1, included in the linear regression was increased until this
led to a deterioration of the fit. The solid lines shown in the middle portion of the plots in
figure 7 were so obtained. Approximate straight lines, indicated dashed in the figure, were
1.0. The scarcity of
0 and Xchol
than drawn to obtain intercepts with the ordinates Xehol
for
is
the
in
values
0.6
source
of
the
the
for the partial
primary
uncertainty
points
Xchol -molecular areas listed in the table below. It is also reflected in the error bars given for the
points marked by « à » in figure 8.
The existence of three distinct linear regimes in the dependence of â on Xchol indicates the
existence of two phase boundaries, shown in figure 8 (« à »). The first of these separates
region IV from the rest of the phase diagram. As indicated (by « à »), the second phase
boundary coincides, within experimental error, with the phase boundary derived on the basis
of figure 6, which separates region II from the rest of the phase diagram.
The behavior documented in figure 7 and in the table is analogous to that observed and
discussed by de Bernard in his careful early film balance study of mixed monolayers of egg
phosphatidylcholine and cholesterol [13]. It may be understood simply by observing that the
addition of cholesterol, itself quite incompressible as demonstrated by the shape of its
isotherm in figure 2, induces a « condensation » of DMPC which consequently assumes a
molecular area close to its partial molecular area of 51 A2, while the corresponding partial
molecular area of cholesterol coincides with its actual molecular area (= 38 A2), as extracted
from the pertinent isotherm in figure 2. We return to this point in section 4 below.
The findings described so far lead to the phase diagram of DMPC/cholesterol mixed
monolayers at 23.5 °C, shown in figure 8. Its global features exhibit a remarkable similarity to
the phase diagram of DPPC/cholesterol for Xehol &#x3E; 0.1. In addition, a DPPC/cholesterol
three
=
=
1546
Fig. 6. - Examples of plots showing the dependence of 1 / K on cholesterol mole fraction at fixed ’TT
values. The threshold values of Xchol for a finite increase in 1 / K over its baseline value were extracted
from such plots by a procedure described in the text, yielding the solid straight lines on the basis of linear
fits. These threshold values define the appearance of a state of low compressibility of the mixture,
separating the region of high X,,h.1 (region II in Fig. 8) from the rest of the phase diagram shown in
figure 8.
Plots of the mean molecular area as a function of mole fraction, at fixed values of
(« onset »), 5 dynes/cm, 10 dynes/cm, 15 dynes/cm and 25 dynes/cm. Solid straight lines drawn
through the central portions of the top three sets were obtained by linear regression analysis, as
described in the text. Dashed straight lines were drawn by eye, connecting the middle segments to the
ordinates (see text).
Fig.
7r =
7.
0
-
1547
8.
Pressure-composition phase diagram of mixed monolayer of DMPC and cholesterol at
23.5 ° C. The phase boundaries shown here are derived on the basis of figure 3 ( 0 »), figure 6 (« V »),
figure 7 (« à »), as discussed in section 3. Where indicated, they were confirmed by fluorescence
microscopic observation of phase separation (« X », (this work), and « + » [19]). All lines serve as
guides to the eye. Dashed lines were drawn by hand ; the solid line follows a standard functional form
for phase coexistence as discussed in section 3. The three distinct lines separating regions III and II are
argued to coincide within experimental error (Sect. 3) ; an indication of typical error margins is given by
horizontal delimiters ( 1 - &#x3E; 1 ). The various lines delineate a fluid-fluid miscibility gap (region III)
bounded by three distinct regions further described in section 3. The numbering is consistent with
figure 5 in [15]. A highly compressible vapor phase, existing at all values of Xchol for
a &#x3E; aonset and 7T 5 0.5 dyne/cm (see text and Fig. 3), is not shown.
Fig.
-
Table I. - Partial Molecular Areas. Listed are partial molecular areas (in Â2 ) derived from
figure 7 as discussed in the text. The notations « low », « middle » and « high » refer to the 3
linear regimes of the plots in figure 7. Partial molecular areas of DMPC and cholesterol, are
denoted by âdmpc and àchob respectively, and are estimated to be accurate to within
:t 3 Á 2.
mixture containing 30 mole% cholesterol displays behavior qualitatively resembling that of
the analogous DMPC/cholesterol mixture when observed by fluorescence microscopy [28].
This is in spite of the fact that, at the pertinent experimental temperature of 23.5 °C DMPC is
in its disordered state exhibiting a completely featureless isotherm (see Figs. 2, 3). In
contrast, DPPC undergoes a series of transitions which give rise to characteristic features in its
1548
(Fig. 5 in [10]), suggesting that small amounts of added cholesterol (Xchol «
0.1 ) randomly distributed impurity, eliminate the ordered phases of DPPC [29].
On the basis of our analysis we identify region III as a coexistence regime of two immiscible
fluid phases with an upper consolute point near (Xghol
0.27, ir’ 11.5). The data points
obtained
from
the
breaks in the log ( 1 / K ) vs.
were
this
region
( 0 ») delineating
à curves described in connection with figure 3 and confirmed in several cases (« X ») by
epifluorescence microscopy. The data points reported in the fluorescence microscopic study
of Subramaniam and McConnell [19] are also indicated (« + »). The solid line, little more
than a guide to the eye at this stage, follows the standard functional form
isotherm
a
=
=
with the critical values indicated above ; /3 was held fixed at a value of 1/3, generally observed
for fluid-fluid coexistence (see e.g. [30]) and favored by comparison with coexistence curves
computed four 6 1/2, the mean field value, and for f3 = 1/8, the value indicated by a
postulated 2d Ising analogy applied to monolayer films [31]. However, our data set is too
small to make any meaningful detailed test ; the value of 1/3 is certainly not to be taken
literally. We estimate the critical values to be accurate to within dXghol = ± 0.05 and
Air’ = ± 1 dyne/cm.
In region 1 DMPC and cholesterol form a macroscopically homogeneous mixture whose
cholesterol content varies in the range 0.1 _ Xchol S 0.35. This mixture appears
homogeneously fluorescent (see Fig. 4). Characteristic « breaks » in the plots of â as a
function of Xchol in figure 7 suggest that to the left of the line Xchol S 0.1, that is, in region IV,
pure DMPC coexists with a DMPC/cholesterol mixture of Xchol -- 0.1. Monolayers in this
region of the phase diagram also appear optically homogeneous.
In region II, pure cholesterol coexists with a DMPC/cholesterol mixture. When entering
this region, mixed monolayers undergo a transition to a state of low compressibility. Points
marking the phase boundary were extracted from plots of the type shown in figure 3 (« D »),
plots of log ( 1 / K ) vs. Xchol (Fig. 6 ; « V ») and from those showing the dependence of
à on Xchol (Fig. 7 ; « à »). These different determinations of the location of the phase line
differ by approximately 0.1 Xchol. Given the appreciable uncertainty in the data in this region,
we cannot say whether it is this uncertainty which sets the width of the transition region, or
whether the three procedures in fact capture differing signatures associated with the
transition. In any case, it appears likely that the coexistence boundary meets the phase
boundary in a triple point near (Xchol 0.35, ’TT 10 dynes/cm). This is the scenario favored
by Albrecht et al. in their study of mixed monolayers of cholesterol and dipalmitoyl
phosphatidylcholine (DPPC) at 24.9 °C [15]. Epifluorescence microscopy reveals that layers
composed of 40 mole% and 45 mole% cholesterol remain inhomogeneous when compressed
up to surface pressures of 30 dynes/cm, suggesting a direct path between regions III and II at
those values of the cholesterol mole fraction.
=
1
=
=
4. Discussion.
In what follows, we suggest a rationale to account for the qualitative features displayed in the
phase diagram and discuss the notion that DMPC in fact assumes distinct states in the two
immiscible fluid phases which coexist within the miscibility gap (region III in Fig. 8).
To set the stage, we note that the sharp rise in the isotherm of the pure cholesterol
monolayer (shown in Fig. 2) and the implied sudden drop in compressibility closely resemble
the response of a system of hard spheres, or disks. We argue that the global structure of the
1549
(7T, Xcho0 phase diagram of figure 8 may in fact be understood by explicitly making this
identification. That is, one assumes that cholesterol-cholesterol interactions are governed by a
hard-core repulsive potential with a characteristic scale set by the molecules’ van der Waals
radius, and one regards the actual molecular area, ah.1 (as opposed to its partial molecular
area,
àchol),
as
constant.
An immediate consequence of this assumption becomes apparent when considering the
behavior of the binary mixed monolayer along an isobaric trajectory through the (w,
Xchol) diagram. As the set of isotherms in figure 2 demonstrates, the mean molecular area
à at which a given value of ir is attained decreases with increasing Xchol. Figure 7 displays the
dependence of â on Xchol explicitly for a number of fixed values of 7r. Three linear regimes,
readily identified in the plots at 7r x- 15 dyne/cm, indicate that the corresponding partial
molecular areas ( â ) of both constituents remain constant throughout each regime, but
undergo an abrupt change at the transitions between them (see also Tab. I). A linear
dependence of â on Xch.1, in conjunction with the assumption of the incompressibility of
cholesterol, directly indicates an effective compression of DMPC [13]. Consider, for example,
the middle portion of the plot for ’TT = 0 dynes/cm. Here, àdmpc
90 Â2 and àchol
20 Â2 « achob implying that for each molecule of cholesterol (of actual molecular area
achol = 40 A 2) added to the mixture, the total molecular area increases by only 20 Â2. It is the
concomitant compression (or « condensation ») of DMPC which balances the equation. We
may thus regard an increase in Xchol at constant pressure to be effectively equivalent to a
compression of (the remaining) DMPC. Consequently, one expects the conformations
exhibited by DMPC along any isobar in the (ir, Xcho0 diagram to reflect those of the
equivalent pure DMPC monolayer subjected to isothermal compression.
Specifically, this suggests to us that the miscibility gap, corresponding to region III in the
phase diagram depicted in figure 8, involves coexisting mixed phases in which DMPC
preferentially assumes two distinct states. One of the two mixtures, containing predominantly
DMPC, exhibits bright fluorescence (Figs. 4, 5) and a compressibility which is essentially that
of a pure DMPC monolayer (see Fig. 6). In contrast, the second mixture excludes most of the
fluorescent lipid analog, consequently appearing dark (Figs. 4, 5), and develops a markedly
lower compressibility, as discussed in connection with figures 3 and 6. Furthermore, as noted
in section 3 in connection with figure 7, when reaching the phase boundary of region II, the
partial molecular area of DMPC approaches a value of approximately 51 Â2 (see Tab. I). All
these features are strongly reminiscent of the coexistence of the liquid-expanded (LE) and
liquid-condensed (LC) phases featuring prominently in the phase diagram of the pure
phospholipid monolayer (see Figs. 2 and 6 in [10] and inset to Fig. 8). It is therefore tempting
to suggest that DMPC in the two coexisting mixtures assumes configurations similar to those it
exhibits in the LE and LC phases, respectively.
A recent report of experiments probing molecular configurations in monolayers at an airwater interface [21]] states that the transition into the LE phase is characterized by the
excitation of disordered molecular chain conformational states. X-ray measurements have
been interpreted to indicate the existence in the LC-phase of fully extended aliphatic chains
adopting a significant tilt angle [22]. Monte Carlo simulations based on this mechanism [11,
31]] reproduce many of the experimentally observed features. Accepting this scenario, one
would, in the spirit of Doniach’s simple two-state model of chain-melting [31, 32], picture the
predominantly DMPC containing phase as a mixture of cholesterol with DMPC in a
disordered chain configuration, characterized by « gauche » excitations, while in the
coexisting second mixture DMPC approaches an all-trans, ordered conformation. A more
accurate description may require consideration of a series of partially disordered intermediate
conformers [31].
=
=
1550
In support of such a model for lipid/cholesterol mixtures we observe that in the phase
diagram of pure phosphatidylcholine the typical values of the molecular area in the LC phase
are indeed close to 50 Â2 [10]. Figure 7 and the accompanying table 1 of partial molecular
areas reveal that àdmpc, the partial molecular area of DMPC, in the high Xchol region is in fact
of that magnitude, while Jchob the partial molecular area of cholesterol, approaches
achol, its actual molecular area of approximately 40 Â2. To the extent that à ch.1 me
achol, as assumed at the outset of the discussion, àdmpc ADMPO placing DMPC along the
phase boundary separating region II from the rest of the diagram, in the range of densities
characteristic of its LC phase.
Single component lipid monolayers also exhibit a characteristic drop in compressibility
when entering their LC phase [10, 20]. By analogy, one would attribute the sudden increase of
1 / K, described in connection with the log ( 1 / K ) vs. Xchol plots ôf figure 6, to the appearance
of the equivalent state of DMPC in the mixed monolayers. This statement implies that the
phase line delineating the high cholesterol region (region II in Fig. 8) signals the condensation
of the lipid constituent into its all-trans configuration. This transition persists to values of the
surface pressures far exceeding the critical pressure for demixing. Considerations in
accordance with those pertinent to pure lipid monolayers [11]] would suggest a continuous
transition to a mixture of cholesterol and all-trans DMPC above the upper consolute point
(Fig. 8).
Within the context of the proposed model one would attribute the inhomogeneous
distribution of fluorescent label within the miscibility gap to the fact that the type of
fluorescent lipid analog employed here is largely excluded from the phase containing DMPC
in its chain-ordered state. It is this very feature which makes possible the fluorescence
microscopic investigations of the LE - LC phase coexistence in single component monolayers
[1, 2, 33, 34]. For the same reason, one would expect mixed monolayers to exhibit an
inhomogeneous fluorescence distribution in region II, as we have observed.
As the pertinent isotherm in figure 2 demonstrates, the ordered, LC-equivalent state is
inaccessible to pure DMPC monolayers at the temperature of the present experiments,
namely 23.5 ° C. This is the frequently notes « condensing » effect of cholesterol [13, 20, 35] :
according to our phase diagram, the LE-equivalent conformation of the lipid accommodates
cholesterol up to only a modest composition, in the present case approximately 10 mole%.
Further admixture of cholesterol stabilizes the conformation associated with the lipid’s LC
phase. The new phase appears in the present system with a composition of approximately
55 mole% cholesterol at 7T 0 dyne/cm.
Compression of single component monolayers eventually induces a positionally ordered
solid [36]. This appears unlikely in the presence of excess cholesterol. One possible scenario
in the high cholesterol region might be the formation of a glassy DMPC/cholesterol mixture,
coexisting with pure cholesterol. The characteristic response of such a state to mechanical
perturbations (e.g. in torsional oscillator measurements) should be distinctive and interesting
=
=
to pursue.
We believe the preceeding interpretation of fluid-fluid immiscibility in phospholipid/cholesterol mixed monolayers to be plausible. It certainly lends itself to be tested by an
experimental technique which is sensitive to the state of aliphatic chain ordering [21].
However, irrespective of specific microscopic model one may wish to invoke to characterize
the different states of DMPC in the two coexisting fluid phases, a complete theory of mixed
monolayers would in any case have to consider the coupling between an internal degree of
freedom and the macroscopic order parameter, e.g. Ycy)l - X(2)chol, in contrast to simple binary
fluid-fluid coexistence, a problem completely described by a single (scalar) order parameter
1551
[30]. This generic situation is reminiscent of the nematic to smectic A transition
thermotropic liquid crystals and the equivalent phenomenon in superconductors [37].
in
5. Conclusions.
We have investigated the phase behavior of a two-dimensional mixture, a monomôlecular
film confined to an air-water interface containing DMPC and cholesterol. By inspection of the
dependencies of bulk modulus and partial molecular areas on cholesterol mole fraction, we
have established a phase diagram whose global features include a fluid-fluid miscibility gap,
terminated by an upper consolute point near (X’ 01
0.27, ’TTc 11. 5) at 23. 5 ° C. The
location of the phase boundary was confirmed by direct observation of phase separation via
epifluorescence microscopy. We propose that DMPC assumes states oi different chain
ordering in the coexisting fluid phases, corresponding to those characterizing liquidcondensed and liquid-expanded phase, in the pure lipid monolayer. This hypothesis may be
readily tested by experiments sensitive to chain conformational order [21]] and perhaps by
those sensitive to chain tilt [22]. We expect that the possibility of coupling of the mean-field
order parameter to a second degree of freedom must be examined to obtain a correct picture
of the critical mixing.
The probed phase diagram contains three further regions. These are occupied by : firstly,
coexisting pure DMPC and a homogeneous, fluid DMPC/cholesterol mixture of Achoi === 0.1 ;
=
=
secondly, a mixture, also fluid and homogeneous (0.1 Xchol S 0.35, 7r 2: Ir 5 but characterized by a reduced partial molecular area of DMPC ; thirdly, a highly incompressible
mixture, coexisting with pure cholesterol in which DMPC assumes a partial molecular area
coinciding with that marking the appearance of the LC phase in single component layers. The
latter region, with similar properties has also been identified in the phase diagram of DPPC
and cholesterol [10].
The accessibility of a critical point in a two-dimensional monolayer film in a convenient
range of experimental parameters has already been exploited in the study of a series of
domain shape instabilities in the present system [12]. It offers promising possibilities for more
detailed experiments in the critical region.
Acknowledgments.
We would like to thank E. Chin and S. Stuczynski for their advice and the use of their
facilities in the recrystallization of cholesterol under argon. CLH acknowledges support
through the Summer Research Program for Women and Minorities, sponsored by AT&#x26;T Bell
Laboratories.
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