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Adsorption of slightly soluble compounds to lipid monolayers
Adsorption of Slightly Soluble Compounds to Lipid Monolayers MAKOTO TAKEO, BARBARA A. SINHA, AND GERTRUDE F. REMPFER Department of Physics~Environmental Sciences and Resources Program, Portland State University, Portland, Oregon 97207 Received November 23, 1983; accepted March 26, 1984 A surface solution approach is used to derive the thermodynamic equation of state for a monolayer of long-chain surfactant molecules in the liquid expanded state. Bending of the chains of the surfactant is taken into account by a surface pressure-dependent term. This equation of state is extended to the case of two surfactants or, equivalently, a mixed monolayer of one surfactant plus adsorbed molecules of a c o m p o u n d which is only slightly soluble in the aqueous subsolution. The two equations of state are used in a derivation of the adsorption coefficient (fl) and m a x i m u m adsorbed surface density (Fro) for the adsorbed species. Both quantities are shown to be a function of the surface pressure (~r). Experimental r - a r e a per molecule curves illustrating the effect of adsorbed 3-phenylindole (3PI) on a monolayer of lipid in the liquid expanded state are presented. For 3PI, fl increases slightly with ~r, attaining a value of 1.6 X 10-4 m at 7r = 40 d y n / c m while rm decreases slightly with increasing ~r, reaching a value of 1.0 X 10-6 m o l e / m 2 at 7r = 40 dyn/cm. I. I N T R O D U C T I O N
The process by which neutral molecules adsorb to lipid bilayers and thereby change the ion-transport properties of the bilayer is an active area of investigation (1-3). A theoretical treatment of this adsorption process is suggested by the observation of Gershfeld (4) that surface films formed by adsorption from solution are in principle identical with spread monolayers. Thus it is possible to treat a lipid monolayer together with adsorbed molecules of a compound which is only slightly soluble in the aqueous subsolution as a mixed monolayer. A surface solution approach in deriving the equation of state for surface-active materials at the air/water interface is particularly suited to long-chain surfactants. The advantages of the surface solution approach using the concept of a Gibbs dividing surface have been succinctly outlined by Lucassen-Reynders (5). This approach has been shown to lead to good agreement with experimental surface pressure-area curves of"gaseous" monolayers (6, 7) and has broadened our understanding of the role of the water subsolution for mono-
layers in the liquid expanded state (7). In this paper the effect of bending of the surfactant molecules, i.e., allowing different conformations for the long-chain surfactant, is incorporated into surface solution theory, and the surface solution approach is applied to a lipid monolayer and to a mixed monolayer with adsorbed molecules. Expressions for the adsorption coefficient and maximum adsorbed surface density are derived. The surface pressure dependence of these quantities appears in an explicit fashion and also indirectly through the area per lipid molecule and an empirically obtained constant. In addition to the theoretical treatment, we present the results of an experimental investigation of the adsorption of 3-phenylindole (3PI), an antimicrobial compound whose site of action is the lipid portion of the cell membrane (8), to lipid monolayers in the liquid expanded state. II. T H E O R E T I C A L T R E A T M E N T OF SURFACE PRESSURE A N D A D S O R P T I O N
The aim of this section is to relate the surface pressure and surface area of a monolayer
384 0021-9797/84 $3.00 Copyright© 1984by AcademicPress,Inc. All fightsof reproductionin any form reserved.
Journalof Colloidand InterfaceScience,Vol. 101, No. 2, October 1984
ADSORPTION TO LIPID MONOLAYERS in the expanded state, so that the maximum amount of information can be extracted from the type of data typically collected in a monolayer experiment, namely, surface pressure versus area per molecule isotherms (9). Among theories providing a basis for the relationship, the easiest approach is probably to formulate surface thermodynamics assuming equilibrium conditions.
Equation of state for two- and three-component systems. Consider a system of two components, 1 and 2, with component 1 being the solvent, i.e., water. The surface pressure rr is given by ~r =
k T 1 f sl X l n
601
flXl
[1] '
where x] and f ] are, respectively, the mole fraction and activity coefficient of the surface excess of component 1 (5). Similarly, xl and f~ are the mole fraction and activity coefficient of component 1 in the bulk phase (subsolution). The partial molar surface area of component 1 is denoted by 601 while k and T are Boltzmann's constant and the absolute temperature, respectively. If the surfactant (component 2) is insoluble or dissolves in the solvent very slightly, then xl =J] = 1 and we have zr =
k T In x] - 7to,
[2]
601
where 7r0 is related to the activity coefficient by a-0 = (kT/600 In f ] . (If there is only one component (water), then a-o identically vanishes.) Equation [2] can be rewritten in another form. For the two-component system the total area of the monolayer, S, is given by
S = Z60iN~,
( i = 1,2),
[3]
where N~ is the number of molecules of component i in the surface phase and 60i is the partial molar surface area. For the case in which component 2 is insoluble, we define the surface area per molecule by
A~ = S/N~.
[4]
385
Then we can write ~ = -~ITIn(1 + A "76~ 2 - ~-22) - l r ° "
[5]
For water as a solvent, 601 = 9.65 A 2 (6). By utilizing the fact that the activity coefficient or 7r0 remains almost constant in the liquid expanded region of a monolayer, both constant values of 602 and ~ro may be determined by comparing Eq. [5] with experimental 7rA ° curves. The method is described in detail by Gaines (7). However, long-chain molecules like lipids seem to behave differently from Eq. [5], and Gaines' method then does not provide a satisfactory determination of 602and r0. The disagreement seems to be related to the observation that long hydrocarbon chains can bend. Mittleman and Palmer (1 0) proposed a model for the bending of the chains, like cases b, c, and d illustrated in Fig. 1, in which the area changes according to a Boltzmann factor. (Case a, which is upright without bending, is not allowed, as discussed later.) The energy of a given configuration with a portion of length 1' in solution with a single bending is given by = (7r + W)BI' + d, [6] where ~rBl' is the work done against surface pressure, B being the width of the chain. W, if multiplied by the projected area of a CHz group, is the work of adhesion of CH2 groups to water and ~' is the work to rotate a C - C bond for the bending. W and ~' are assumed to be constant, independent of the location of the CH2 group and the bending bond in the chain. Then if there is always one bending
Q
oir
b
d
n
~£q
1
O
£---q
water
FIG. 1. Model of a long-chain surfactant in the liquid expanded state. Case a is not allowed (see text). Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
386
TAKEO,
SINHA, AND REMPFER
bond somewhere along the chain the statistical average of BI' is l
B ~ l' exp(-E/kT) Bl----7,=
t'=0 t
- k- T ~r+W"
exp(-,/kT)
[7]
/'=0
This is the area contributed by the bending of a chain on the average. The last expression in Eq. [7] is obtained by assuming that (lr + W)Bl ~ k T a n d that l' varies continuously. If/-~ 30 • or longer, this last expression gives a value within a few percent of the exact value. We are interested in the case of two chains per molecule so that, on the average, each lipid molecule occupies an area of
2kT WE+ 2Bl ~= w2 + - -
[8]
7r+W"
Equation [3] therefore becomes
2kT
S= ~w~NT+~N
71" "~ W
~
[9]
2.
Then the equation of state for the two-component system obtained from Eq. [2] is ~r=--ln
wl
1+
AO
2kT
-~ro.
7r + W
w2
/
[10]
A third component may be added to the twocomponent system. If the third component, denoted by subscript 3, is only slightly watersoluble or the concentration in the subsolution is very low, Eq. [2] gives "Jr ~
kT
m 6O l
× ln(1 + \
Wl(N~2 + N~3) (A2
2kT~V
I
w2)Nsz - ~o,
[111
where A2 is defined by Eq. [4] but without superscript 0. If the third component is soluble, N~ in Eq. [11 ] is less than the number of molecules of component 3 introduced to the sysJournal o f Colloid and Interface Science,
Vol. 101, No. 2, October 1984
tem. The difference is the amount dissolved in the subsolution and adsorbed on the walls of the container. Therefore, N~ is in general unknown. In principle, N~ depends on the convention used for choosing the location of a dividng surface, but Lucassen-Reynders has pointed out that surfactant adsorption or penetrations are virtually insensitive to choice of convention (5). The convention used here is to choose all wi values. Thus, we may simply choose w3 from the geometry of molecule 3 and determine N~ from experimental data on 7r and A2 by means of Eq. [ 11 ]. However, we need ~rb, which may depend on the extent of penetration of component 3 in the monolayer, i.e., on N~, although ~r~is approximately equal to 7r0 for the two-component system when the penetration is small. Adsorption of component 3. The number of adsorbed molecules of component 3 must be related to the concentration of component 3 in the bulk subsolution, for instance, in the manner of a Langmuir isotherm describing adsorption of molecules to a solid surface (11). However, in determining the relationship for adsorption to lipid monolayers at an air/water interface, we must take into account the fact that when penetration occurs the area changes; consequently, the density of penetration sites may in general change. Thus, the rate equation for penetration must be in terms of the total number of molecules in the monolayer. For a given surface pressure,
dN~3 - - ~ = -kdN~3 + (rR(N~3,~ - N~3), [12] where kd is the rate constant for desorption, is the cross section leading to penetration (per surface collision), and R is the number of surface collisions of component 3 per unit area per unit time. The saturated value of the penetration is N~,¢~, which we assume is independent of the concentration. Since R is proportional to the concentration of component 3 in the subsolution, for a steady state process we have
N~ N~,~ - N~
= Co [component 3],
[13]
ADSORPTION TO LIPID MONOLAYERS where Co is a combination of constants, and [component 3] is the concentration of component 3 in the aqueous subsolution. Equation [13] may be reduced to an expression relating directly observable quantities. Using the two equations of state, Eqs. [10] and [ 11 ], we have
N~3 =
2 - A° + wl E -
:
1
E'
1
A3 ' [14]
where E = exp[(wl/kT)(Tr + 7ro)], E' = exp[(wl/ kT)(lr + a%)], and A3 = 603 + [wd(E' - 1)]. Therefore, we can rewrite Eq. [13] as 1 A2-A2°
+
Wl
(, )?- 1
E'
,)
AO _ 1 -- = I'3
387
L
1 E' 1_ 1)))A3c'
[component 3]
+ (A0 _ ~Ol(E 1 - 1
1 E'-1))
[18] Comparison of Eq. (18) with an adsorption isotherm for adsorption to a fixed number of sites (11) of the form 1
1
1
I'--~ =/3 [component 3] + ~m'
1
1
(A°-wl(E-1
1
1
))A3c,
E'- 1
[20a]
[15]
Here c2 = c o c l = N~/(AaN~3,~). These coefficients depend on surface pressure only. If 7% = 7r~,Eq. [15] reduces to the simple expression
[19]
leads to the identifications
3=
cl + c2. [component 3]
A3c2+A3"
=
[20b] 1
C1
A2 - A °
[component 3]
+ c2,
[16]
where c~ and c2 can be obtained experimentally if the condition is satisfied. We note that Eq. [16] is independent of the convention used for setting a dividing surface. The number density 173 of adsorbed component 3 is often very useful in discussing transport processes in membranes and surface chemical reactions. This information can be found easily if we utilize the relationship I'3 = Ns3/(N~A2). From Eq. [14] it follows that
where/3 is the partition coefficient and Pm is the maximum adsorbed surface density. The coefficient/3 has units of length and can be thought of as the thickness of aqueous solution which would contain the same amount of component 3 as is adsorbed to the monolayer. From Eqs. [20a] and [20b] it should be noted that for adsorption to compressible lipid monolayers, /3 and I'm depend on surface pressure since A °, A3, E, E', Cl, and c2 all vary with surface pressure. For 7to = ~'~, Eqs. [20a] and [20b] reduce to
/3
1))/
E'- 1
A2A3.
[17]
Solving Eq. [17] for A 2 , substituting in Eq. [15] and rearranging gives
=
1
cIA3AO
[21a]
,
, lb,
rm = (c2Ao + 1)A3
In the next section we describe an experimental investigation of the adsorption of 3PI Journal of Colloid and Interface Science. Vol. 101, No. 2. October 1984
388
TAKEO, SINHA, AND REMPFER
cooled to room temperature, enough water (-~ 1500 ml) was added to dissolve the ammonium chloride and the excess hydrazine salts. The solution was filtered several times, III. EXPERIMENTAL INVESTIGATION OF THE the liquid being discarded at each step. The ADSORPTION OF 3-PHENYLINDOLE precipitate was dried in a desiccator in the TO LIPID MONOLAYERS presence of KOH pellets for 90 min and then recrystallized from toluene/hexane. After Materials and Methods sublimation the product was granular, with L-o~-Phosphatidylcholine(PC) from egg yolk an ivory color, and had a distinctive, not un(Sigma Chemical Co., St. Louis, Mo.) showed pleasant odor. The melting point was 86.5a single spot by thin-layer chromatography 87.5°C, in agreement with published values and was used without further purification. The (12, 13). final lipid solution also contained 0.22 mole Surface pressure and surface potential were fraction of recrystallized, lyophilized choles- measured simultaneously as a function of area terol. The cholesterol was included in order per lipid molecule by means of an automated to have the same lipid composition used in Langmuir trough. The trough and barriers lipid bilayer studies of ion transport which were made from virgin Teflon and regularly were being done in conjunction with the cleaned with a mixture of concentrated sulmonolayer investigation. The amount of cho- furic acid:nitric acid (9:1). Surface pressure lesterol was small enough that the monolayer was monitored by a glass Wilhelmy plate couremained in a liquid expanded state. The pled to a linear differential transformer (Auspreading solvents, chloroform and hexane, tomatic Timing and Controls, Inc., King of were of the highest quality (Matheson, Cole- Prussia, Pa.) whose output signal was fed to man and Bell; Omnisolv grade). Both ana- an X- Y recorder. lytical grade acetone (Amachem, Portland, The aqueous solution was prepared fresh Oreg.) and chromatography grade acetone each day. Since 3PI is surface active and nearly (Mallinckrodt, St. Louis, Mo.) affected the insoluble in water, it was necessary to inject surface pressure and surface potential iso- 3PI in acetone beneath the surface of a KC1 therms to the same extent; therefore the an- solution which was being constantly stirred. alytical grade was routinely used. Potassium The amount of acetone in all aqueous soluchloride (Mallinckrodt, A.R.) and distilled, tions, both with and without 3PI, was held deionized water from a Millipore Q2 system constant at 0.5%. Lens-cleaning tissue was (MiUlpore Corp., Bedford, Mass.) were used used to remove the monolayer and also to for all aqueous solutions. clean the surface prior to each run. Lipid from 3-Phenylindole (3PI) was synthesized fol- a dilute solution was dropped onto the lowing the method of Fischer and Schmidt aqueous surface by microliter syringe and the (12) with minor modifications. Phenylhydra- solvent was allowed to evaporate for a period zinc (MC/B) was added in equimolar quantity of typically 15 min, after which time the to 100g (0.83 mole) phenylacetaldehyde monolayer was compressed at a rate of about (Aldrich, technical grade), heated in a steam 6 AZ/molecule/min. All measurements were bath for an hour, and then diluted with about taken at room temperature. 300 ml of absolute alcohol. To the mixture was added 200 ml of absolute alcohol which had been saturated with hydrogen chloride Lipid Monolayer Results and Discussion gas. The solution was then refluxed in nitrogen Compression curves for ~r vs A° were obenvironment for 45 rain, again with the use of the steam bath. When the solution had tained for monolayers of phosphatidylcholine/ to lipid monolayers and analyze the results in terms of this theoretical treatment.
Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
389
ADSORPTION TO LIPID MONOLAYERS
cholesterol. The area per molecule was determined from the ratio of the monolayer area to the number of lipid molecules spread, including both PC and cholesterol, as calculated from the concentrations and volumes of the lipid solutions. By comparing the experimental 7r-A° curve to Eq. [10] it is possible to determine the values of 0;2, a-0, and W for the best fit, but the accuracy of determining W by this procedure is very poor since the bending term in Eq. [ 10] is a rather small correction. Therefore, we used the value of 600 cal/mol deduced by Langmuir (14) for the work of adhesion of CH2 groups to water, implying a value of 28 dyn/cm for W. With this value for W, and setting 0;1 = 9.65 A 2 at 21°C, the ~--A2° curve was compared with Eqs. [5] and [10] by the method of Gaines (7). Table I and curve A in Fig. 2 show a comparison of the observed A° (mean of four runs) with A2° as predicted by the simpler equation of state, Eq. [5], and also with the equation of state incorporating bending of the hydrocarbon chains, Eq. [ 10]. Note that at high surface pressures the bending term becomes significant and Eq. [10] agrees better with the observed values. The best fit of Eq. [10] yields 0;2 = 37 __+ 1.5 A 2 and 7r0 = 11.5 __+ 1.0 dyn/cm. The physical significance of these quantities can best be seen by examining the behavior
of the simpler equation of state, Eq. [5], at large area. When the area per molecule is very large, so that (A° - 0;2) ~> wl, Eq. [5] can be reduced by expansion to a form of van der Waals type: (71" -~- 71"0)(.4 0 - - 092) =
kT.
[22]
From this we see that 7r0represents interactions among surfactant molecules (a'0 is positive if interactions are attractive) and 0;2 is some minimum geometrical area of the molecule. From the form of Eq. [22], ~0 for the longchain lipid under investigation may be considered as due to van der Waals forces of attraction between the hydrocarbon tails of PC. The head groups are known to have less effect on the value of 7to. According to Adam (15), the cohesion of hydrocarbon chains is proportional to the number of CH2 groups in the chain with a value of approximately 1 dyn/ cm/CH2 group. Since the hydrocarbon tails extend mostly toward the air phase for lipid monolayers in the liquid expanded state, there are on the average 17 CH2 groups per chain above the water surface for the PC molecules. Thus, the present result of 11.5 dyn/cm agrees well with Adam's value if bending of the tails is allowed. In addition, according to Wiegel and Kox (16), the cross section of the head
TABLE I Comparison of Observed Area per Lipid Molecule, A°, with Areas Predicted from Equations of State ~r (dyn/cm)
5 10 15 20 25 30 35 40 45
Observed mean A° (A s)
82.1 73.2 67.4 63.2 60.0 57.2 54.6 52.4 49.4
__+ 1.4 __+ 1.7 _+ 1.8 ___ 1.9 + 1.7 + 1.6 + 1.4 _+ 1.1 _+ 1.5
Theoretical A° from Eq. [i0] a (A 2)
Theoretical A° from Eq. [5]b (A s)
81.9 73.0 67.0 62.7 59.4 56.8 54.7 53.0 51.6
83.4 71.8 65.7 62.0 59.5 57.7 56.4 55.4 54.6
Note. Both theoretical fits were obtained from using w~ = 9.65 A 2. a Best fit given by w2 = 37 ~2, 7r0 = 11.5 dyn/cm, and W = 28 dyn/cm. b Best fit given by w2 = 50.5 A 2 and 7r0 = 5.75 dyn/cm. Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
390
TAKEO, SINHA, AND REMPFER 50
'
I
r
I
A2
(~2)
i
I
i
I:: 2o Io o
40
60 At
or
80
I00
FIG. 2. Surface pressure of phosphatidylcholine/cholesterol monolayers as a function of apparent area per lipid molecule. Aqueoussubsolution 0.11 M KC1with or without the indicated concentration of 3-phenylindole: (A) without 3PI, (1) 5# M, (2) 15 #M, (3) 25/LM, (4) 40 #M, (5) 55 gM, (6) 70 gM. Comparison of curve A is made with Eq. [10] using values in text (.. •) and with Eq. [5] using values ~l = 9.65 A2, ~o2= 50.5 A2, and ro = 5.75 dyn/cm (- --). group o f a phospholipid is about 40 ,~2, which is very close to the present value of 37/~2. This agreement indicates that there is always one C - C bond bending except for case d in Fig. l, so that the electric dipole vector of the polar head is almost parallel to the water surface (cases b, c, and d) and case a does not occur. If case a is allowed, Eq. [7] must be multiplied by a factor of exp(-~'/kT), assuming that ~' is constant. This modification leads to a disagreement with the experimental results, since e' is 800 cal/mole (15).
curves toward greater area per lipid molecule, indicating that 3PI strongly favors partition into the lipid phase. In addition, 3PI changed the slope of some portions of the curves. The number of adsorbed 3PI molecules, N~, may be found by comparing these curves with Eq. [11]. The values of 0o2 and W already mentioned can be used for this purpose, but ~3 and 7rb are not known. As stated in Section II, a small error in w3 does not affect N~ very much, so that 0o3 can be taken as 42.8 A 2 based on the projected area of a Corey-Pauling-Koltun model of the 3PI molecule. The best analysis of our 7r-A2 data and surface potential -A2 data (not shown) was obtained when 7r~ = ~ro. Previously, we discussed the interpretation of ~ro as the quantity representing interactions among hydrocarbon tails, which appear above the water surface. Since a-o is constant in the liquid expanded phase, the finding that r b = ~o may mean that 3PI was adsorbed near the water surface instead of in the hydrocarbon chains and did not significantly perturb the interactions among the chains. Probably this is not a case of ideal mixing where the water activity coefficient
@
-
-
0.10-
Adsorption of 3-Phenylindole We found that 3PI did not form a compressible monolayer by itself at the air/water interface. However, when 3PI was present in the subsolution, it did adsorb to a lipid monolayer in such a way as to increase the apparent area per lipid molecule at each 7r. Representative 7r-A2 curves of PC/cholesterol monolayers in the presence of various aqueous concentrations of 3PI are shown in Fig. 2. The most striking feature to be seen in these data is that 3PI caused a large shift of the 7r-A2 Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
0.05-
0
I
I
I
I o~.l ll(3Pl)
I
I
I
I I o.2
p M -l
FIG. 3. Plot of Eq. [16] for 7r = 30 dyn/cm. Error bars are the standard deviation for at least four monolayers.
ADSORPTION TO LIPID MONOLAYERS TABLE 1I Partition Coefficient, 13,and Maximum Adsorbed Surface Density, Fro, of 3-Phenylindole Adsorbed to Lipid Monolayers at Various Surface Pressures, 7r 7r (dyn/cm)
~ ( 10-4 m)
I~= ( 10-6 mole/m s)
20 25 30 35 40
1.4 1.4 1.4 1.5 1.6
1.3 1.2 1.2 1.1 1.0
391
which incorporates the effect o f bending o f the chains into a surface solution treatment. The adsorption o f a c o m p o u n d which is only slightly water-soluble was considered and, utilizing the new equations o f state, it was shown that adsorption parameters 13 and I ' m a r e a function o f the surface pressure o f the m o n o layer. The theoretical treatment presented is then shown to yield reasonable values of/~ and I'm for adsorption o f the lipophilic c o m p o u n d 3-phenylindole to lipid monolayers. ACKNOWLEDGMENTS
f ] is required to be equal for pure monolayers and for a mixed film (7). By plotting 1/(,42 - A °) against 1/[3PI] for each zr, c~ and Ca were obtained by fitting a straight line as suggested by Eq. [ 16] (see Fig. 3). For 20 ~< a- ~< 40 d y n / c m , we found that c~ = 0.44 - 0.00032 × (~- - 36) 2 u M / A 2
[23]
and c2=0.0013+0.0011
× T r A -2,
[24]
where [3PI] in Eq. [16] is in micromole/liter ( = u M ) . Using these values ofc~ and c2, 13and Fm were f o u n d by m e a n s of Eqs. [21 a] and [21b]. Table II shows the values for/3 and pm at values o f ~r between 20 and 40 d y n / c m . Although the variation o f / 3 and I'm with 7r was slight, it is significant that fl increased with increasing 7r while I ' m decreased as 7r increased. At ~r = 40 d y n / c m , which is close to m a x i m u m compression o f the m o n o l a y e r within the liquid expanded state, /3 was 1.6 × 10 -4 m and I'm was 1.0 × l0 -6 m o l e / m 2. These high values o f ~3 and Fm quantitatively support the observation o f other investigators that when 3PI is present in aqueous nutrient solution in which fungi mycelium are growing, 3PI preferentially accumulates in the lipid fraction o f the fungi (17). IV. CONCLUSION W e have presented a new equation o f state, suitable for insoluble long-chain surfactants,
We are indebted to Dr. Lloyd Dolby for the synthesis of the 3-phenylindole and to Dr. David McClure for the purification of the cholesterol. REFERENCES 1. Szabo, G., Nature (London) 252, 47 (1974). 2. Andersen, O. S., Finkelstein, A., Katz, I., and Cass, A., J. Gen. Physiol. 67, 749 (1976). 3. Smejtek, P., and Paulis-lllangasekare, M., Biophys. J. 26, 441 (1979). 4. Gershfeld, N. L., Annu. Rev, Phys. Chem. 27, 349 (1976). 5. Lucassen-Reynders, E. H., Prog. Surf Membr. Sci. 10, 253 (1976). 6. Fowkes, F. M., J. Phys. Chem. 66, 385 (1962). 7. Gaines, G. L., Jr., J. Chem. Phys. 69, 924 (1978). 8. Hoppe, H. H., Kerkenaar, A., and Sijpesteijn, A. K., Pest. Bioehem. Physiol. 6, 422 (1976). 9. Gaines, G. L., Jr., "Insoluble Monolayers at LiquidGas Interfaces." Wiley--lnterscience, New York, 1966. 10. Mitfleman, R., and Palmer, R. C., Trans. Faraday Soc. 38, 506 (1942). 11. Delahay, P., "Double Layer and Electrode Kinetics." lnterscience, New York, 1965. 12. Fischer, E., and Schmidt, T., Bet. Dtsch. Chem. Ges. 21, 1811 (1888). 13. Dekker, W. H., Selling, H. A., and Overeem, J. O., J. Agr. Food Chem. 23, 785 (1975). 14. Langmuir, I., 3".Amer. Chem. Soc. 39, 1848 (1917). 15. Adam, N. K., "The Physics and Chemistry of Surfaces." Oxford Univ., Press, London/New York, 1941. 16. Wiegel,F. W., and Kox, A. J., "Advances in Chemical Physics" (I. Prigogineand S. A. Rice, Eds.), p. 195. Wiley, New York, 1980. 17. Hoppe, H. H., Kerkenaar, A., and Sijpesteijn, A. K., Pest. Biochem. Physiol. 6, 413 (1976).
Journal of Colloid and Interface Science, Vol. I01, No. 2, October 1984
The process by which neutral molecules adsorb to lipid bilayers and thereby change the ion-transport properties of the bilayer is an active area of investigation (1-3). A theoretical treatment of this adsorption process is suggested by the observation of Gershfeld (4) that surface films formed by adsorption from solution are in principle identical with spread monolayers. Thus it is possible to treat a lipid monolayer together with adsorbed molecules of a compound which is only slightly soluble in the aqueous subsolution as a mixed monolayer. A surface solution approach in deriving the equation of state for surface-active materials at the air/water interface is particularly suited to long-chain surfactants. The advantages of the surface solution approach using the concept of a Gibbs dividing surface have been succinctly outlined by Lucassen-Reynders (5). This approach has been shown to lead to good agreement with experimental surface pressure-area curves of"gaseous" monolayers (6, 7) and has broadened our understanding of the role of the water subsolution for mono-
layers in the liquid expanded state (7). In this paper the effect of bending of the surfactant molecules, i.e., allowing different conformations for the long-chain surfactant, is incorporated into surface solution theory, and the surface solution approach is applied to a lipid monolayer and to a mixed monolayer with adsorbed molecules. Expressions for the adsorption coefficient and maximum adsorbed surface density are derived. The surface pressure dependence of these quantities appears in an explicit fashion and also indirectly through the area per lipid molecule and an empirically obtained constant. In addition to the theoretical treatment, we present the results of an experimental investigation of the adsorption of 3-phenylindole (3PI), an antimicrobial compound whose site of action is the lipid portion of the cell membrane (8), to lipid monolayers in the liquid expanded state. II. T H E O R E T I C A L T R E A T M E N T OF SURFACE PRESSURE A N D A D S O R P T I O N
The aim of this section is to relate the surface pressure and surface area of a monolayer
384 0021-9797/84 $3.00 Copyright© 1984by AcademicPress,Inc. All fightsof reproductionin any form reserved.
Journalof Colloidand InterfaceScience,Vol. 101, No. 2, October 1984
ADSORPTION TO LIPID MONOLAYERS in the expanded state, so that the maximum amount of information can be extracted from the type of data typically collected in a monolayer experiment, namely, surface pressure versus area per molecule isotherms (9). Among theories providing a basis for the relationship, the easiest approach is probably to formulate surface thermodynamics assuming equilibrium conditions.
Equation of state for two- and three-component systems. Consider a system of two components, 1 and 2, with component 1 being the solvent, i.e., water. The surface pressure rr is given by ~r =
k T 1 f sl X l n
601
flXl
[1] '
where x] and f ] are, respectively, the mole fraction and activity coefficient of the surface excess of component 1 (5). Similarly, xl and f~ are the mole fraction and activity coefficient of component 1 in the bulk phase (subsolution). The partial molar surface area of component 1 is denoted by 601 while k and T are Boltzmann's constant and the absolute temperature, respectively. If the surfactant (component 2) is insoluble or dissolves in the solvent very slightly, then xl =J] = 1 and we have zr =
k T In x] - 7to,
[2]
601
where 7r0 is related to the activity coefficient by a-0 = (kT/600 In f ] . (If there is only one component (water), then a-o identically vanishes.) Equation [2] can be rewritten in another form. For the two-component system the total area of the monolayer, S, is given by
S = Z60iN~,
( i = 1,2),
[3]
where N~ is the number of molecules of component i in the surface phase and 60i is the partial molar surface area. For the case in which component 2 is insoluble, we define the surface area per molecule by
A~ = S/N~.
[4]
385
Then we can write ~ = -~ITIn(1 + A "76~ 2 - ~-22) - l r ° "
[5]
For water as a solvent, 601 = 9.65 A 2 (6). By utilizing the fact that the activity coefficient or 7r0 remains almost constant in the liquid expanded region of a monolayer, both constant values of 602 and ~ro may be determined by comparing Eq. [5] with experimental 7rA ° curves. The method is described in detail by Gaines (7). However, long-chain molecules like lipids seem to behave differently from Eq. [5], and Gaines' method then does not provide a satisfactory determination of 602and r0. The disagreement seems to be related to the observation that long hydrocarbon chains can bend. Mittleman and Palmer (1 0) proposed a model for the bending of the chains, like cases b, c, and d illustrated in Fig. 1, in which the area changes according to a Boltzmann factor. (Case a, which is upright without bending, is not allowed, as discussed later.) The energy of a given configuration with a portion of length 1' in solution with a single bending is given by = (7r + W)BI' + d, [6] where ~rBl' is the work done against surface pressure, B being the width of the chain. W, if multiplied by the projected area of a CHz group, is the work of adhesion of CH2 groups to water and ~' is the work to rotate a C - C bond for the bending. W and ~' are assumed to be constant, independent of the location of the CH2 group and the bending bond in the chain. Then if there is always one bending
Q
oir
b
d
n
~£q
1
O
£---q
water
FIG. 1. Model of a long-chain surfactant in the liquid expanded state. Case a is not allowed (see text). Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
386
TAKEO,
SINHA, AND REMPFER
bond somewhere along the chain the statistical average of BI' is l
B ~ l' exp(-E/kT) Bl----7,=
t'=0 t
- k- T ~r+W"
exp(-,/kT)
[7]
/'=0
This is the area contributed by the bending of a chain on the average. The last expression in Eq. [7] is obtained by assuming that (lr + W)Bl ~ k T a n d that l' varies continuously. If/-~ 30 • or longer, this last expression gives a value within a few percent of the exact value. We are interested in the case of two chains per molecule so that, on the average, each lipid molecule occupies an area of
2kT WE+ 2Bl ~= w2 + - -
[8]
7r+W"
Equation [3] therefore becomes
2kT
S= ~w~NT+~N
71" "~ W
~
[9]
2.
Then the equation of state for the two-component system obtained from Eq. [2] is ~r=--ln
wl
1+
AO
2kT
-~ro.
7r + W
w2
/
[10]
A third component may be added to the twocomponent system. If the third component, denoted by subscript 3, is only slightly watersoluble or the concentration in the subsolution is very low, Eq. [2] gives "Jr ~
kT
m 6O l
× ln(1 + \
Wl(N~2 + N~3) (A2
2kT~V
I
w2)Nsz - ~o,
[111
where A2 is defined by Eq. [4] but without superscript 0. If the third component is soluble, N~ in Eq. [11 ] is less than the number of molecules of component 3 introduced to the sysJournal o f Colloid and Interface Science,
Vol. 101, No. 2, October 1984
tem. The difference is the amount dissolved in the subsolution and adsorbed on the walls of the container. Therefore, N~ is in general unknown. In principle, N~ depends on the convention used for choosing the location of a dividng surface, but Lucassen-Reynders has pointed out that surfactant adsorption or penetrations are virtually insensitive to choice of convention (5). The convention used here is to choose all wi values. Thus, we may simply choose w3 from the geometry of molecule 3 and determine N~ from experimental data on 7r and A2 by means of Eq. [ 11 ]. However, we need ~rb, which may depend on the extent of penetration of component 3 in the monolayer, i.e., on N~, although ~r~is approximately equal to 7r0 for the two-component system when the penetration is small. Adsorption of component 3. The number of adsorbed molecules of component 3 must be related to the concentration of component 3 in the bulk subsolution, for instance, in the manner of a Langmuir isotherm describing adsorption of molecules to a solid surface (11). However, in determining the relationship for adsorption to lipid monolayers at an air/water interface, we must take into account the fact that when penetration occurs the area changes; consequently, the density of penetration sites may in general change. Thus, the rate equation for penetration must be in terms of the total number of molecules in the monolayer. For a given surface pressure,
dN~3 - - ~ = -kdN~3 + (rR(N~3,~ - N~3), [12] where kd is the rate constant for desorption, is the cross section leading to penetration (per surface collision), and R is the number of surface collisions of component 3 per unit area per unit time. The saturated value of the penetration is N~,¢~, which we assume is independent of the concentration. Since R is proportional to the concentration of component 3 in the subsolution, for a steady state process we have
N~ N~,~ - N~
= Co [component 3],
[13]
ADSORPTION TO LIPID MONOLAYERS where Co is a combination of constants, and [component 3] is the concentration of component 3 in the aqueous subsolution. Equation [13] may be reduced to an expression relating directly observable quantities. Using the two equations of state, Eqs. [10] and [ 11 ], we have
N~3 =
2 - A° + wl E -
:
1
E'
1
A3 ' [14]
where E = exp[(wl/kT)(Tr + 7ro)], E' = exp[(wl/ kT)(lr + a%)], and A3 = 603 + [wd(E' - 1)]. Therefore, we can rewrite Eq. [13] as 1 A2-A2°
+
Wl
(, )?- 1
E'
,)
AO _ 1 -- = I'3
387
L
1 E' 1_ 1)))A3c'
[component 3]
+ (A0 _ ~Ol(E 1 - 1
1 E'-1))
[18] Comparison of Eq. (18) with an adsorption isotherm for adsorption to a fixed number of sites (11) of the form 1
1
1
I'--~ =/3 [component 3] + ~m'
1
1
(A°-wl(E-1
1
1
))A3c,
E'- 1
[20a]
[15]
Here c2 = c o c l = N~/(AaN~3,~). These coefficients depend on surface pressure only. If 7% = 7r~,Eq. [15] reduces to the simple expression
[19]
leads to the identifications
3=
cl + c2. [component 3]
A3c2+A3"
=
[20b] 1
C1
A2 - A °
[component 3]
+ c2,
[16]
where c~ and c2 can be obtained experimentally if the condition is satisfied. We note that Eq. [16] is independent of the convention used for setting a dividing surface. The number density 173 of adsorbed component 3 is often very useful in discussing transport processes in membranes and surface chemical reactions. This information can be found easily if we utilize the relationship I'3 = Ns3/(N~A2). From Eq. [14] it follows that
where/3 is the partition coefficient and Pm is the maximum adsorbed surface density. The coefficient/3 has units of length and can be thought of as the thickness of aqueous solution which would contain the same amount of component 3 as is adsorbed to the monolayer. From Eqs. [20a] and [20b] it should be noted that for adsorption to compressible lipid monolayers, /3 and I'm depend on surface pressure since A °, A3, E, E', Cl, and c2 all vary with surface pressure. For 7to = ~'~, Eqs. [20a] and [20b] reduce to
/3
1))/
E'- 1
A2A3.
[17]
Solving Eq. [17] for A 2 , substituting in Eq. [15] and rearranging gives
=
1
cIA3AO
[21a]
,
, lb,
rm = (c2Ao + 1)A3
In the next section we describe an experimental investigation of the adsorption of 3PI Journal of Colloid and Interface Science. Vol. 101, No. 2. October 1984
388
TAKEO, SINHA, AND REMPFER
cooled to room temperature, enough water (-~ 1500 ml) was added to dissolve the ammonium chloride and the excess hydrazine salts. The solution was filtered several times, III. EXPERIMENTAL INVESTIGATION OF THE the liquid being discarded at each step. The ADSORPTION OF 3-PHENYLINDOLE precipitate was dried in a desiccator in the TO LIPID MONOLAYERS presence of KOH pellets for 90 min and then recrystallized from toluene/hexane. After Materials and Methods sublimation the product was granular, with L-o~-Phosphatidylcholine(PC) from egg yolk an ivory color, and had a distinctive, not un(Sigma Chemical Co., St. Louis, Mo.) showed pleasant odor. The melting point was 86.5a single spot by thin-layer chromatography 87.5°C, in agreement with published values and was used without further purification. The (12, 13). final lipid solution also contained 0.22 mole Surface pressure and surface potential were fraction of recrystallized, lyophilized choles- measured simultaneously as a function of area terol. The cholesterol was included in order per lipid molecule by means of an automated to have the same lipid composition used in Langmuir trough. The trough and barriers lipid bilayer studies of ion transport which were made from virgin Teflon and regularly were being done in conjunction with the cleaned with a mixture of concentrated sulmonolayer investigation. The amount of cho- furic acid:nitric acid (9:1). Surface pressure lesterol was small enough that the monolayer was monitored by a glass Wilhelmy plate couremained in a liquid expanded state. The pled to a linear differential transformer (Auspreading solvents, chloroform and hexane, tomatic Timing and Controls, Inc., King of were of the highest quality (Matheson, Cole- Prussia, Pa.) whose output signal was fed to man and Bell; Omnisolv grade). Both ana- an X- Y recorder. lytical grade acetone (Amachem, Portland, The aqueous solution was prepared fresh Oreg.) and chromatography grade acetone each day. Since 3PI is surface active and nearly (Mallinckrodt, St. Louis, Mo.) affected the insoluble in water, it was necessary to inject surface pressure and surface potential iso- 3PI in acetone beneath the surface of a KC1 therms to the same extent; therefore the an- solution which was being constantly stirred. alytical grade was routinely used. Potassium The amount of acetone in all aqueous soluchloride (Mallinckrodt, A.R.) and distilled, tions, both with and without 3PI, was held deionized water from a Millipore Q2 system constant at 0.5%. Lens-cleaning tissue was (MiUlpore Corp., Bedford, Mass.) were used used to remove the monolayer and also to for all aqueous solutions. clean the surface prior to each run. Lipid from 3-Phenylindole (3PI) was synthesized fol- a dilute solution was dropped onto the lowing the method of Fischer and Schmidt aqueous surface by microliter syringe and the (12) with minor modifications. Phenylhydra- solvent was allowed to evaporate for a period zinc (MC/B) was added in equimolar quantity of typically 15 min, after which time the to 100g (0.83 mole) phenylacetaldehyde monolayer was compressed at a rate of about (Aldrich, technical grade), heated in a steam 6 AZ/molecule/min. All measurements were bath for an hour, and then diluted with about taken at room temperature. 300 ml of absolute alcohol. To the mixture was added 200 ml of absolute alcohol which had been saturated with hydrogen chloride Lipid Monolayer Results and Discussion gas. The solution was then refluxed in nitrogen Compression curves for ~r vs A° were obenvironment for 45 rain, again with the use of the steam bath. When the solution had tained for monolayers of phosphatidylcholine/ to lipid monolayers and analyze the results in terms of this theoretical treatment.
Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
389
ADSORPTION TO LIPID MONOLAYERS
cholesterol. The area per molecule was determined from the ratio of the monolayer area to the number of lipid molecules spread, including both PC and cholesterol, as calculated from the concentrations and volumes of the lipid solutions. By comparing the experimental 7r-A° curve to Eq. [10] it is possible to determine the values of 0;2, a-0, and W for the best fit, but the accuracy of determining W by this procedure is very poor since the bending term in Eq. [ 10] is a rather small correction. Therefore, we used the value of 600 cal/mol deduced by Langmuir (14) for the work of adhesion of CH2 groups to water, implying a value of 28 dyn/cm for W. With this value for W, and setting 0;1 = 9.65 A 2 at 21°C, the ~--A2° curve was compared with Eqs. [5] and [10] by the method of Gaines (7). Table I and curve A in Fig. 2 show a comparison of the observed A° (mean of four runs) with A2° as predicted by the simpler equation of state, Eq. [5], and also with the equation of state incorporating bending of the hydrocarbon chains, Eq. [ 10]. Note that at high surface pressures the bending term becomes significant and Eq. [10] agrees better with the observed values. The best fit of Eq. [10] yields 0;2 = 37 __+ 1.5 A 2 and 7r0 = 11.5 __+ 1.0 dyn/cm. The physical significance of these quantities can best be seen by examining the behavior
of the simpler equation of state, Eq. [5], at large area. When the area per molecule is very large, so that (A° - 0;2) ~> wl, Eq. [5] can be reduced by expansion to a form of van der Waals type: (71" -~- 71"0)(.4 0 - - 092) =
kT.
[22]
From this we see that 7r0represents interactions among surfactant molecules (a'0 is positive if interactions are attractive) and 0;2 is some minimum geometrical area of the molecule. From the form of Eq. [22], ~0 for the longchain lipid under investigation may be considered as due to van der Waals forces of attraction between the hydrocarbon tails of PC. The head groups are known to have less effect on the value of 7to. According to Adam (15), the cohesion of hydrocarbon chains is proportional to the number of CH2 groups in the chain with a value of approximately 1 dyn/ cm/CH2 group. Since the hydrocarbon tails extend mostly toward the air phase for lipid monolayers in the liquid expanded state, there are on the average 17 CH2 groups per chain above the water surface for the PC molecules. Thus, the present result of 11.5 dyn/cm agrees well with Adam's value if bending of the tails is allowed. In addition, according to Wiegel and Kox (16), the cross section of the head
TABLE I Comparison of Observed Area per Lipid Molecule, A°, with Areas Predicted from Equations of State ~r (dyn/cm)
5 10 15 20 25 30 35 40 45
Observed mean A° (A s)
82.1 73.2 67.4 63.2 60.0 57.2 54.6 52.4 49.4
__+ 1.4 __+ 1.7 _+ 1.8 ___ 1.9 + 1.7 + 1.6 + 1.4 _+ 1.1 _+ 1.5
Theoretical A° from Eq. [i0] a (A 2)
Theoretical A° from Eq. [5]b (A s)
81.9 73.0 67.0 62.7 59.4 56.8 54.7 53.0 51.6
83.4 71.8 65.7 62.0 59.5 57.7 56.4 55.4 54.6
Note. Both theoretical fits were obtained from using w~ = 9.65 A 2. a Best fit given by w2 = 37 ~2, 7r0 = 11.5 dyn/cm, and W = 28 dyn/cm. b Best fit given by w2 = 50.5 A 2 and 7r0 = 5.75 dyn/cm. Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
390
TAKEO, SINHA, AND REMPFER 50
'
I
r
I
A2
(~2)
i
I
i
I:: 2o Io o
40
60 At
or
80
I00
FIG. 2. Surface pressure of phosphatidylcholine/cholesterol monolayers as a function of apparent area per lipid molecule. Aqueoussubsolution 0.11 M KC1with or without the indicated concentration of 3-phenylindole: (A) without 3PI, (1) 5# M, (2) 15 #M, (3) 25/LM, (4) 40 #M, (5) 55 gM, (6) 70 gM. Comparison of curve A is made with Eq. [10] using values in text (.. •) and with Eq. [5] using values ~l = 9.65 A2, ~o2= 50.5 A2, and ro = 5.75 dyn/cm (- --). group o f a phospholipid is about 40 ,~2, which is very close to the present value of 37/~2. This agreement indicates that there is always one C - C bond bending except for case d in Fig. l, so that the electric dipole vector of the polar head is almost parallel to the water surface (cases b, c, and d) and case a does not occur. If case a is allowed, Eq. [7] must be multiplied by a factor of exp(-~'/kT), assuming that ~' is constant. This modification leads to a disagreement with the experimental results, since e' is 800 cal/mole (15).
curves toward greater area per lipid molecule, indicating that 3PI strongly favors partition into the lipid phase. In addition, 3PI changed the slope of some portions of the curves. The number of adsorbed 3PI molecules, N~, may be found by comparing these curves with Eq. [11]. The values of 0o2 and W already mentioned can be used for this purpose, but ~3 and 7rb are not known. As stated in Section II, a small error in w3 does not affect N~ very much, so that 0o3 can be taken as 42.8 A 2 based on the projected area of a Corey-Pauling-Koltun model of the 3PI molecule. The best analysis of our 7r-A2 data and surface potential -A2 data (not shown) was obtained when 7r~ = ~ro. Previously, we discussed the interpretation of ~ro as the quantity representing interactions among hydrocarbon tails, which appear above the water surface. Since a-o is constant in the liquid expanded phase, the finding that r b = ~o may mean that 3PI was adsorbed near the water surface instead of in the hydrocarbon chains and did not significantly perturb the interactions among the chains. Probably this is not a case of ideal mixing where the water activity coefficient
@
-
-
0.10-
Adsorption of 3-Phenylindole We found that 3PI did not form a compressible monolayer by itself at the air/water interface. However, when 3PI was present in the subsolution, it did adsorb to a lipid monolayer in such a way as to increase the apparent area per lipid molecule at each 7r. Representative 7r-A2 curves of PC/cholesterol monolayers in the presence of various aqueous concentrations of 3PI are shown in Fig. 2. The most striking feature to be seen in these data is that 3PI caused a large shift of the 7r-A2 Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
0.05-
0
I
I
I
I o~.l ll(3Pl)
I
I
I
I I o.2
p M -l
FIG. 3. Plot of Eq. [16] for 7r = 30 dyn/cm. Error bars are the standard deviation for at least four monolayers.
ADSORPTION TO LIPID MONOLAYERS TABLE 1I Partition Coefficient, 13,and Maximum Adsorbed Surface Density, Fro, of 3-Phenylindole Adsorbed to Lipid Monolayers at Various Surface Pressures, 7r 7r (dyn/cm)
~ ( 10-4 m)
I~= ( 10-6 mole/m s)
20 25 30 35 40
1.4 1.4 1.4 1.5 1.6
1.3 1.2 1.2 1.1 1.0
391
which incorporates the effect o f bending o f the chains into a surface solution treatment. The adsorption o f a c o m p o u n d which is only slightly water-soluble was considered and, utilizing the new equations o f state, it was shown that adsorption parameters 13 and I ' m a r e a function o f the surface pressure o f the m o n o layer. The theoretical treatment presented is then shown to yield reasonable values of/~ and I'm for adsorption o f the lipophilic c o m p o u n d 3-phenylindole to lipid monolayers. ACKNOWLEDGMENTS
f ] is required to be equal for pure monolayers and for a mixed film (7). By plotting 1/(,42 - A °) against 1/[3PI] for each zr, c~ and Ca were obtained by fitting a straight line as suggested by Eq. [ 16] (see Fig. 3). For 20 ~< a- ~< 40 d y n / c m , we found that c~ = 0.44 - 0.00032 × (~- - 36) 2 u M / A 2
[23]
and c2=0.0013+0.0011
× T r A -2,
[24]
where [3PI] in Eq. [16] is in micromole/liter ( = u M ) . Using these values ofc~ and c2, 13and Fm were f o u n d by m e a n s of Eqs. [21 a] and [21b]. Table II shows the values for/3 and pm at values o f ~r between 20 and 40 d y n / c m . Although the variation o f / 3 and I'm with 7r was slight, it is significant that fl increased with increasing 7r while I ' m decreased as 7r increased. At ~r = 40 d y n / c m , which is close to m a x i m u m compression o f the m o n o l a y e r within the liquid expanded state, /3 was 1.6 × 10 -4 m and I'm was 1.0 × l0 -6 m o l e / m 2. These high values o f ~3 and Fm quantitatively support the observation o f other investigators that when 3PI is present in aqueous nutrient solution in which fungi mycelium are growing, 3PI preferentially accumulates in the lipid fraction o f the fungi (17). IV. CONCLUSION W e have presented a new equation o f state, suitable for insoluble long-chain surfactants,
We are indebted to Dr. Lloyd Dolby for the synthesis of the 3-phenylindole and to Dr. David McClure for the purification of the cholesterol. REFERENCES 1. Szabo, G., Nature (London) 252, 47 (1974). 2. Andersen, O. S., Finkelstein, A., Katz, I., and Cass, A., J. Gen. Physiol. 67, 749 (1976). 3. Smejtek, P., and Paulis-lllangasekare, M., Biophys. J. 26, 441 (1979). 4. Gershfeld, N. L., Annu. Rev, Phys. Chem. 27, 349 (1976). 5. Lucassen-Reynders, E. H., Prog. Surf Membr. Sci. 10, 253 (1976). 6. Fowkes, F. M., J. Phys. Chem. 66, 385 (1962). 7. Gaines, G. L., Jr., J. Chem. Phys. 69, 924 (1978). 8. Hoppe, H. H., Kerkenaar, A., and Sijpesteijn, A. K., Pest. Bioehem. Physiol. 6, 422 (1976). 9. Gaines, G. L., Jr., "Insoluble Monolayers at LiquidGas Interfaces." Wiley--lnterscience, New York, 1966. 10. Mitfleman, R., and Palmer, R. C., Trans. Faraday Soc. 38, 506 (1942). 11. Delahay, P., "Double Layer and Electrode Kinetics." lnterscience, New York, 1965. 12. Fischer, E., and Schmidt, T., Bet. Dtsch. Chem. Ges. 21, 1811 (1888). 13. Dekker, W. H., Selling, H. A., and Overeem, J. O., J. Agr. Food Chem. 23, 785 (1975). 14. Langmuir, I., 3".Amer. Chem. Soc. 39, 1848 (1917). 15. Adam, N. K., "The Physics and Chemistry of Surfaces." Oxford Univ., Press, London/New York, 1941. 16. Wiegel,F. W., and Kox, A. J., "Advances in Chemical Physics" (I. Prigogineand S. A. Rice, Eds.), p. 195. Wiley, New York, 1980. 17. Hoppe, H. H., Kerkenaar, A., and Sijpesteijn, A. K., Pest. Biochem. Physiol. 6, 413 (1976).
Journal of Colloid and Interface Science, Vol. I01, No. 2, October 1984