BIMOLECULAR (BLACK)LIPID MEMBRANES AT
THE
2723
WATER-OIL-WATERBIFACE
from expected log K values for the interaction of Mg2+ and Mn2+ with SO4+ in aqueous and nonaqueous solvents can be attributed to the changes in the thermodynamic quantities involved in the formation of the contact ion pair Mz+S042-from the approach ion pair Mz+S,S04z-as the solvent (S) is varied. Such solvent effects may also be present in the Hg(CN)2-Tu system. Previous thermodynamic investigations in HzOEtOH solvent mixtures indicate that there may be a change in the solvent structure as the weight per cent of EtOH increases. Martin and Robertsonz7have studied the solvolysis of t-butyl chloride in EtOH-HzO mixtures and attribute an abnormal maximum in theAC, value and minimum in the AH” value at 0.89 and 0.85 mole fraction of H20, respectively, to increased structural stability of the solvent in the water-rich region. Similar variations have been observed in the values of the heat of ionization of H203and the heat of dilution of thiourea14 in H20-EtOH solvent mixtures and in the heat capacities of H20-EtOH mixtures.’* Glover2*J9
*
has shown that observed deviations from the log K values predicted by electrostatics for proton ionization from several organic acids in mixed solvents can be attributed to the formation of solvent-solvent complexes. These complexes affect which specific solvent molecules are available to the interacting species. I n this connection it is interesting to note that the sharp inflections in Figures 2 and 3 occur at approximately a 1:4 mole ratio of EtOH to HzO (39 wt yo EtOH), indicating that the observed changes may be due to the formation of a [(H20)4-EtOH] solvent complex. The thermodynamic quantities for Hg(CN)2-Tu interaction in the HzO-rich region then would be essentially due to H 2 0 solvation, and in the EtOH-rich region, to EtOH solvation. (26) G. Atkinson and H. Tsubota, J . Am. Chem. Soe., 88, 3901 (1966). (27) J. G.Martin and R. E. Robertson, ibid., 88, 5353 (1966). (28) D.J. Glover, ibid., 87,5275 (1965). (29) D.J. Glover, ibid., 87, 5279 (1965).
The Thermodynamics of Bimolecular (Black) Lipid Membranes at the Water-Oil-Water Biface
by H. Ti Tien Department of Biophysics, Michigan State University, East Lansing, Michigan .@823 (Received September 29, 1967)
The formation of bimolecular lipid membranes (BLM) from a number of chemically well-defined substances has been accomplished recently. This has provided a greater opportunity for experimentation and for the gathering of relevant data needed for a comprehensive analysis of the system. Using BLM produced from dodecyl acid phosphate-cholesterol-dodecane in 0.1 N NaCl as a specific example, the temperature variations of the bifacial free energies were measured. A simple thermodynamic theory is suggested for the formation of the BLM at the water-liquid hydrocarbon-water (W-0-W) biface. The entropy, enthalpy, and free energy of formation have been obtained from a numerical treatment of data. These values are, respectively, 0.008 erg om2 deg-l, 53 ergs cm-2, and 50.6 ergs cm-2 a t 25’. An interpretation of these thermodynamic quantities is given. It is concluded that, for the case studied, the formation of the BLM at the W-0-W biface is an exothermic process and is accompanied by a decrease in the entropy and enthalpy.
Introduction When a minute quantity of a lipid solution, made from surface-active phospholipids in an aliphatic hydrocarbon solvent (hexane to tetradecane), is introduced to an opening in the wall of a small polyethylene or Teflon container immersed in an electrolyte solution, a spontaneous thinning takes place. Interference colors followed by the appearance of “black” spots can usually be seen, leading eventually to the formation of a “black”
film under favorable circumstances.1 The black films less than 90 A in thickness produced in this manner have been termed bimolecular lipid membranes (also called bilayer or black lipid membranes or, for short, BLM). They have been studied by several groups of workers and are the subject of a recent reviews2 The (1) P. Mueller, D. 0. Rudin, H. T. Tien, and W. C. Wescott, J . Phys. Chem., 67, 534 (1963). (2) H.T.Tien and A. L. Diana, Chem. Phys. Lipids, 2 , 56 (1968).
Volume 7& Number 8 August 1968
H. T. TIEN
2724 physical properties of BLM thus far investigated correspond to some extent to those of biological membranes. These BLM, assumed to be lamellar in arrangement, have the basic structural organization which is believed to exist in all types of natural membranes including nerve cells, chloroplasts, photoreceptor organelles, and mitochondria. The most commonly investigated properties of the BLM are the electrical conductivity, capacitance, dielectric breakdown strength, ionic selectivity, thickness, and water permeability.’PZ I n a recent article from this laboratory, the interfacial tensions of a number of BLM have been measured using a novel te~linique.~Besides these interfacial free energy data, however, the other thermodynamic properties of the BLM are unknown. This study is, therefore, an extension of previous work, in that it is mainly concerned with a description of experimental details. The present experiments are designed to collect the interfacial free energy values as a function of the temperature so that relevant thermodynamic quantities of the BLM may be evaluated. The principal aim of this article is to apply classical thermodynamics to BLM systems based upon the newly acquired data, which have not’ been considered previously. In addition, factors influencing the stability and formation of these BLM will be discussed. Particular attention will be given to the adsorption and behavior of the constituent molecules at the water-oilwater (W-0-W) biface (the word “biface” is introduced to describe the two coexisting oil-water or membranesolution interfaces). The interpretation of the thermodynamic data in terms of the molecular organization and composition of the membrane will be indicated. Application of Thermodynamic Equations to BLM System. In the treatment which follows, it is assumed that the equations derived for the monolayers are applicable to the BLM system. The thermodynamic argument employed by Cary and Ridea14and by Harkins and his associates6 to the monolayer films is utilized as a starting point. For example, when a barrier separates the water surface (as in a Langmuir trough), of which one side is covered by the monolayer and the other side is left clean, the movement of the barrier can be manipulated in such a way as either to increase the area of the monolayer with a corresponding decrease of the clean water surface or vice versa. Alternatively, Harkins suggested that the area of the monolayer together with its subphase may be increased by a unit amount at constant air-water surface. Clearly the energies involved for the two processes are different. Similarly, we can also visualize two different kinds of process for the BLM. The energetics involved for these two different types of processes shall be designated as (i) the energetics of formation of BLM and (ii) the energetics of generating BLM, and they will be considered separately below. (i) The Energetics of Formation of BLM. AS has The Journal of Physical Chmistry
(A)
(C)
Figure 1. Idealized diagram showing the formation and extension of a bimolecular lipid membrane a t the water-hydrocarbon oil-water (W-0-W) biface: (A) a drop of liquid hydrocarbon introduced on a hydrophobic support immersed in water, thus creating a W-0-W biface; (B) the presence of a surface-active lipid (in either oil or water phase or both) causes the oil phase to thin to a bimolecular lipid membrane (BLM) under favorable conditions; (C) BLM bulges out under applied hydrostatic pressure during the course of the bifacial free energy measurement. yo is the interfacial tension of the clean oil-water interface and yi is the interfacial tension with the lipid monolayer present.
been mentioned above, the equations used in monolayer studies are assumed to be applicable to the BLM. Thus we can write
AFi YBLM - YO-w (1) where YBLM is the bifacial tension of the BLM, is the interfacial tension between two immiscible liquids (e.g.,liquid hydrocarbon such as n-dodecane and water), and A F i is the free energy difference for the process (A-C, as illustrated in Figure 1). The basic assumption here is that the interior of the BLM is considered to be similar to that of a liquid hydrocarbon in bulk. The hydrocarbon chain of the molecule still possesses all the natural degree of freedom, except that the chains are restricted to keep in contact with one another both laterally and perpendicularly. At equilibrium, the change of free energy of the system vanishes. In terms of energetics, A F i is seen to be the free energy of formation of BLM at an initially clean W-0-W biface (the units are expressed in ergs per square centimeter). The latent heat of formation for the process is given by the Clapeyron equation
at constant pressure. Accordingly, the entropy of formation of BLM (Si) can also be obtained from eq 2. The enthalpy of formation ( H i ) may be calculated from the Gibbs-Helmholtz equation (3) (3) H.T. Tien, J . Phys. Chem., 71, 3395 (1967); see also J . ffen. Physwl., 52 (2),125 (1968). (4) A. Cary and E. K. Rideal, Proc. Roy. Soc., A109, 301, 331 (1925). (5) W. D. Harkins, “The Physical Chemistry of Surface Films,” Reinhold Publishing Corp., New York, N. Y.,1952, pp 94-196.
BIMOLECULAR (BLACK)LIPIDMEMBRANES AT
THE
WATER-OIL-WATER BIFACE
(ii) The Energetics of Generating BLM. This process is illustrated in Figure 1B and C. It is visualized that, upon application of a pressure difference across the membrane, a new BLM area is formed from the Plateau-Gibbs (P-G) border at the W-0-W biface, which is in thermodynamic equilibrium with the BLM. As has been discussed previo~sly,~ this Plateau-Gibbs border is essential in the maintenance of the BLM integrity, which also plays the role of an oil “lens,” as in the case of the monolayer. A more detailed analysis of the relationship between the Plateau-Gibbs border (lens) and BLM will be considered in a subsequent paper. I n extending the BLM according to the scheme illustrated in Figure l, steps B and C, the BLM is formed from the monolayers situated at the W-0-W biface. From the well-known thermodynamic equations
+ pdV f PdV + vdp
dw = -YdA dFBLM = -dW
(4)
(5) and at constant temperature and pressure and if the number of moles is kept constant
where F B L M is the free energy of generating BLM and YBLM has the same meaning as given earlier (eq 1). For a saturated W-0-W biface and per unit area change
FBLM = YBLM
(7) Therefore, two similar equations analogous to eq 2 and 3 may be written. The equations for generating BLM are
2725
from which BLM of sufficient stability can be formed so that significant measurements can be carried out. Therefore, with considerable effort, a number of lipid solutions have been established, which can be stored at room temperature for ready use (in contrast to lipid solutions made from egg lecithin in hydrocarbon solvents which are unstable and hence BLM cannot be easily formed). The exact composition of these solutions has been givens3 In the present experiments, the following solutions were used: (a) 1% freshly recrystallized cholesterol from absolute ethanol in n-dodecane and (b) 7 parts of 5% DAP (dodecyl acid phosphate supplied by Hooker Chemical Co.) plus 93 parts of solution a. Reagent grade NaCl was used to prepare 0.1 N NaC1. Doubly distilled water from an all-glass still was used in the preparation of the aqueous solution. Apparatus and Procedure. A detailed description of both has been given previo~sly.~Briefly, the membrane was made on a hole in the side of a Teflon chamber (made from a Teflon sleeve for ground-glass joints) immersed in 0.1 N NaC1. The inner chamber was connected to an infusion-withdrawal pump (Harvard Apparatus Co.) which provided hydrostatic pressure causing the BLM to bulge out at the W-0-W biface. The inner chamber was also connected to one of the ports of the pressure transducer (Sanborn Model 270) via a ballast chamber. The outer chamber of the cell was similarly connected. The signal picked up by the pressure transducer was amplified and was recorded on a strip-chart recorder. The temperature of the membrane chamber was maintained by circulating water through a glass coil (placed around the Teflon sleeve) from a thermostatic bath (Haake, Fe). The temperature of the chamber was measured with an Hg thermometer immersed in the inner chamber, which was constant within f0.1O .
Results and Discussion and
(9)
It is evident that the quantity S B L M can also be checked independently by the use of
SBLN =
HBLM T
YBLM
This straightforward thermodynamic analysis indicates that the experimental data necessary for the calculation of these quantities are those which provide YBLM os. temperature relations (or AFi vs. T data) at the W-0-W biface.
Experimental Section Preparation of Lipid Solutions. One of the major difficulties in studying the BLM is to find a lipid solution
Experimental YBLM Data. The bifacial free energy (YBLM) of the membrane was calculated by the use of formula YBLM =
Pd 8
where P is the maximum pressure across the BLM and d is the diameter of the hole in the Teflon sleeve.
Variation of y of BLM produced from dodecyl acid phosphate-cholesterol-n-dodecane in 0.1 N NaCl (previously saturated with n-dodecane) with temperature is shown in Figure 2 . Clearly, the points are somewhat scattered (each point represents the average of three to five measurements). The results are not very reproducible when taken on different days, although the precision of the readings taken at one setting was more consistent (reproducible from 2 to 10%). The experimental difficulties associated with BLM Volume 78, Number 8 August 1968
H. T. TIEN
2726
a’o
I
pi
I
1
1.0 2s
ao
a2
a4
a13
3s
40
42
44
Temperature, OC.
Figure 2. Variation of the bifacial free energy as a function of the temperature of the BLM produced from dodecyl acid phosphate-cholesterol-dodecane in 0.1 N NaC1. Data taken on different days are represented by different symbols.
studies have not yet been completely overcome. These can be seen from the crude manner by which these BLM were formed (see the Experimental Section and ref 3). Undoubtedly the amount of lipid solution introduced, the wettability of membrane support, and, most of all, the interfacial contamination owing to the presence of trace impurities are the major factors responsible for the scattering of the data. Nevertheless, the data obtained (Figure 2) do indicate an unmistakable trendathat Y B L M increases with increasing temperature. A smoothed curve is drawn through these points, which is used in the following thermodynamic analysis. Manipulation of YBLM-Temperature Data. In the calculation of the slopes ( a A F i / b T ) , the method of graphical differentiation was used.6 From these slopes, the entropies and enthalpies of formation of BLM as a function of the temperature were evaluated with the aid of eq 1-3. The results obtained from a numerical treatment of data together with the interfacial free energies of the BLM as a function of the temperature are shown in Table I. The Meaning of AFi. The free energy of formation of BLM as defined by eq 1 is the difference between two interfacial free energies, which is always a large negative quantity approaching to that of the yo-w of the clean hydrocarbon oil-water (0-W) interface. This large reduction of the interfacial free energy at the W-0-W biface by the presence of surface-active lipids is to be expected as a consequence of positive adsorption in accordance with the Gibbs equation dY = -2I’idpi
(12)
where r and p are, respectively, the interfacial excess of the adsorbed species and the chemical potential of the species. The application of eq 12 to BLM systems will be discussed in a later paragraph. The meaning of AFi may be seen from the following The Journal of Physical Chemistry
Table I : Thermodynamic Quantities of BLM Formation as Calculated from Bifacial Free Energy Data”
25 28 32 34 36 38 40 42
0,008 0.018 0.036 0.051 0.077 0.125 0.190 0.264
50.6 50.5 50.4 50.3 50.2 50.0 49.7 49.2
1.1
1.2 1.3 1.4 1.5 1.7 2.0 2.5
53.0 55.9 61.4 65.9 74.0 88.8 109.2 132.4
Bimolecular (black) lipid membranes produced from dodecyl acid phosphate and cholesterol in n-dodecane solution in 0.1 M NaCl.
thermodynamic argument (for simplicity the change of energy to be considered refers to that of a unit area). The formation of the BLM may be imagined to take place in a series of steps, as shown in Figure 1. The steps are
+ HzO (W) -+
liquid hydrocarbon (0)
W-0-W W-0-W
+ lipid
(13)
--f
monolayer
monolayer
+ AFi
+ P-G
+ P-G
border -iAFz (14) (154
border
BLM
/’no
h L M
+ AFg
(i5b)
where W-0-W represents the water-oil-water biface and AF is the interfacial free energy change involved in each step. The process represented by eq 13 is seen to be similar to that of spreading an oil on a water surface. The free energy change for the reaction, therefore, may be given by
AFi =
YO
+ YO-w -
YW
(16)
where yo, YO-W, and yw are, respectively, the surface tension of the oil, the interfacial tension at the oil-water interface, and the surface tension of the water. In the next section it is shown that AFI 2 0. It is immaterial, therefore, to the energetics of the BLM formation. The energy changes accompanying the reactions given by eq 14 and 15 are determined by
- YO-w
AFa =
YML
AFa =
YBLM
(17)
and
- YML
(18) where Y M L denotes the interfacial tension of the mono(6) T. R. Running, “Graphical Mathematics,” John Wiley and Sons, Inc., New York, N. Y . , 1927,pp 66-66.
BIMOLECULAR (BLACK)LIPIDRIEMBRANES AT THE WATER-OIL-WATER BIFACE layer at the biface. The net result of these two steps is the summation of eq 14 and 15b; hence the free energy change for the over-all process is the sum of the two AF’s; thus
AFz
+ AFB = AFi =
YBLM
- YO-w
(19)
The over-all reaction is W-0-W biface
+ lipid +BLM + A F i
(20)
Therefore, the A F i represents the work done in bringing the surface-active lipids from the bulk phases(s) and in the formation of a BLM. Obviously, the major part of the work done is the migration of surface-active lipid molecules to the W-0-W biface. On the other hand, the work required in the formation of a BLM from the existing monolayers a t the W-0-W biface is a relatively small quantity by comparison. This large driving force (AFJ toward the formation of monolayers at the W-0-W biface with the attendant reduction of yo-W is obviously a prerequisite for the formation of BLM. However, the low y alone is not a sufficient condition for the formation of a stable BLM, as has been shown experimentally in an earlier p~blication.~ Thinning, BLM Formation, and AFi. With the availability of experimental A F i data, we are now in a better position to give a description of the sequence of events leading to the BLM formation. As is illustrated in Figure lA, yo-w represents the interfacial free energy at a clean 0-W interface. It is generally known from surface film work’ that the tendency for a hydrocarbon oil (such as n-dodecane) to spread is nil, owing to the negative spreading coefficient ( A F i > 0). Therefore, when a drop of hydrocarbon oil is introduced onto the support, it will remain as a globule, as shown in Figure 1A. If now a surface-active lipid is present (in either oil or water phase or both), the surface-active molecules will then migrate toward the W-0-W biface according to eq 12. I n Figure lB, the W-0-W biface is now covered by the lipid monolayers in equilibrium with the Plateau-Gibbs border and the aqueous phase. What we have in essence is a situation discussed a t length by Harkins,6that is, a duplex film a t the W-0-W biface. Such a system is unstable because of unfavorable energetics (for a detailed discussion, see ref 5). As has been already discussed in some detail (eq 15a and b), two events may take place. I n the case of eq 15a, our results indicate that when the value of A F i is less the thin layer of the introduced than 40 ergs lipid solution would not readily thin a t the W-0-W biface. If it were made to thin by mechanical means, it would usually rupture either just before or after the appearance of the black spots. In the case of eq 15b, thinning would take place spontaneously ( y < 8 ergs cm-3. The process may be represented by a disproportionation reaction thin lipid layer
--t
BLM
+ P-G bordor
(21)
2727
However, stable BLM’s were obtained only when an appropriate lipid or a mixture of lipids was used. Although the exact reasons for the instability of BLM are not known, it has been suggested that, in addition to the wettability of the membrane support, such factors as charge density, molecular packing, and temperature effects may be crucial in the determination of the final stability of the structure of BLM. Furthermore, effects due to electrostatic interaction at the W-0-W biface and interactions across, as well as in, the membrane itself may also be of major importance. A number of these factors have been discussed by several authors.8-10 A F i and the Structure of BLM. It is pertinent to point out that eq 1is identical with the surface pressure equation H = yo - y (with an opposite sign). The magnitude of H (or A F i ) is an indication of the lateral pressure experienced by the molecules a t the W-0-W biface. The results obtained in the previous studya show that A F i ‘v yo-w, which implies that the molecules in the BLM are highly compressed and that they are probably packed as densely as in crystals. Experimental evidence suggests that the interior of the membrane must be in a liquid state similar to that of a hydrocarbon, as was mentioned earlier. This type of arrangement, with the polar (or ionic) groups packed closely at the W-0-W biface in an orderly array and with the interior liquidlike nature, resembles strongly the so-called liqujd crystals. One would then predict, on the basis of A F i values, that the molecules should occupy their limiting area, since the interfacial pressure is in the region well above the collapse pressure for a monolayer film at an air-water interface. As a consequence of this high A F i value, it seems probable also that the hydrocarbon solvent used initially in the BLM formation will be “squeezed” out, leaving only the “lipids” in the final structure. Further consideration of BLM structure will be given in the paragraph on YBLM. A F i and the Temperature. Inspection of data given in Table I reveals that the free energy of formation of BLM decreases slightly with increasing temperature for the temperature range studied. This slight decrease is consistent with the suggestion that the major portion of the work involved is the formation of a duplex film a t the W-0-W biface. At higher temperatures, the concentration of adsorbed lipid molecules will be less. Therefore, a lower interfacial free energy should result. YBLM and the E$ect of the Temperature. The meaning (7) See, for example, A. W. Adamson, ”Physical Chemistry of Surfaces,” 2nd ed, John Wiley and Sons, Inc., New York, N. Y . , 1967, Chapter 3. (8) R. J. Good, submitted for publication. (9) V. 8. Vaidhyanathan, presented at the 41st National Colloid Symposium, Buffalo, N. Y., June 1967. (10) 8. Ohki, J. Theor. Biol., 15, 362 (1967).
Volume 72, Number 8 August 1968
H. T. TIEN
2728
of YBLM is defined as the work needed to generate a unit area of the BLM at the W-0-W biface which has been covered by a lipid monolayer in equilibrium with the Plateau-Gibbs border (oil lens). As can be seen from the values presented in Table I, the YBLM for the temperature range measured increases with increasing temperature in contrast to AFi. This is interpreted to mean that more work is required to generate the BLM when the concentration of lipid molecules has decreased as a result of rising temperature (i.e., a decrease in positive adsorption) at the W-0-W biface. The surprisingly low values of YBLM obtained deserve an elaboration. The experimental measurements on a number of BLM formed from a'variety of lipid materials indicate that the values lie in the range from slightly As a specific example, above 0 to about 6 ergs an n-dodecane solution saturated with lecithin (chromatographically pure) can produce a BLM with YBLM value of about 0.9 ergs cm-2. Yet when the same solution was measured at the 0-W bulk phase, a value of about 6.5 ergs cm-2 was obtained. This further reduction of the interfacial free energy when a BLM is formed may be explained as follows in the next paragraph. When a thick layer of lipid solution is interposed between two aqueous phases, thinning takes place spontaneously under suitable circumstances, as indicated in eq 15b. As has been discussed earlierj3 the mechanisms of thinning of such a system involve the gravitational flow, the diffusion, and the Plateau-Gibbsborder suction. It has been suggested that, as the lipid layer is thinned, nothing much happens until the oriented monolayers situated a t the opposite 0-W interfaces come into contact, initiating the so-called zipperlike action. Thereafter the rate of thinning is markedly increased, as evidenced by monitoring the reflectance of the membrane vs. time curve." The thickness of the membrane in the black state was shown to be independent of time, as observed from the intensity of the reflection from the membrane. The thickness as calculated from the optical data and by other methods corresponds closely to the length of the two lipid molecules used.3 These experimental observations together with the interfacial free energy data presented here permit the following conclusions to be drawn. (i) The formation of BLM from a thick lipid layer involves two stepwise reductions in the interfacial free energy at the W-0-W biface. The first reduction occurs when the lipid monolayers are formed in equilibrium with the Plateau-Gibbs border. (ii) The low YBLM obtained suggests that a second reduction of interfacial free energy takes place when the BLM is formed. This implies that two monolayers possess a higher interfacial free energy a t the W-0-W biface than the BLM; Le. 2 lipid monolayers -+ BLM The Journal of Physical Chemistry
+ AF
(14)
where A F (expressed in terms of unit area) may be approximated to be the difference between the two interfacial free energy terms. The formation of BLM from lecithin monolayers involves a reduction of A F of some 11 ergs cm-2. Earlier, this conclusion that the formation of BLM is due to a spontaneous, isothermal phase transition was reached intuitively. As long as the integrity of the membrane is maintained, the BLM represents the lowest stable free energy state.l The Entropy and Enthalpy of BLM Formation. The results given in Table I show a negative entropy quantity which is associated with the formation of BLM. From the modified Clapeyron equation (eq 2), this means that the latent heat of formation is also negative. Therefore, in the process of formation of BLM an evolution of heat takes place, which is also accompanied by a decrease in entropy. This is especially marked at higher temperatures (e.g., a more than 20-fold decrease in entropy is seen from 25 to 40'). One explanation of these values lies in the changes of the orderliness of constituent molecules at the W-0-W biface. As would be expected, the lipid molecules possess a higher degree of disorder in the lipid solution than in the BLM state. As has been pointed out earlier, the structure of BLM is considered to be similar to that of liquid crystals. Thus a decrease in entropy is consistent with this picture. The larger decrease a t higher temperature seems to suggest that a change has taken place in the monolayer structure, whereas the organization of the BLM is not much affected by a moderate rise in temperature. I n fact the raw experimental data given in Figure 2 suggest that a transition is occurring in the 36-40' temperature region. It would, therefore, appear reasonable to speculate that a phase transition in the monolayer might have taken place in the aforementioned temperature region. The monolayers could have changed from a liquid condensed state to a liquid expanded state (using Harkins terminology). Similarly, much the same argument may be used to explain the enthalpy of formation data shown in Table I. The Gibbs Adsorption Equation and BLM. As a logical sequence of the considerations presented in the previous paragraphs, the application of Gibbs adsorption equation to the BLN! systems should also be of interest. Unlike the monolayers at the air-water interface, the concentration of the surface-active lipid molecules in the BLM cannot be easily determined. However, since the Gibbs adsorption isotherm (eq 12) relates y and the concentration of the dissolved material, the use of eq 12 may be adopted if the quantity of y is identified with the YBLM. In order to calculate the excess concentration of lipid molecules in the BLM, the usual extra-thermodynamic assumption would have (11) A number of observations were made in connection with the BLM-thinning studies: E. A , Dawidowicz and H. T. Tien, unpublished results, 1966.
BIMOLECULAR (BLACK)LIPID MEMBRANES AT
THE
WATER-OIL-WATERBIFACE
to be used in that the only adsorbed species in the BLM would be the surface-active lipid molecules. If this is assumed to be the case, the Gibbs adsorption equation would allow a calculation of the interfacial concentration excess from which an assessment of the area occupied per molecule might be possible. The implication of this suggestion is that certain structural deductions may be made concerning the BLM. Further work is in progress to test the applicability of the Gibbs adsorption equation to the bimolecular lipid membranes. It is hoped that this approach would be of some value in providing further understanding of the BLM at the W-0-W biface.
Summary A simple thermodynamic explanation is given for the formation of the BLM a t the water-oil-water biface. Two types of processes are considered: (i) the for-
2729
mation of BLM and (ii) the generating of BLM from the monolayers situated at the W-0-W biface in equilibrium with the Plateau-Gibbs border. An analysis of the bifacial free energy data as a function of the temperature is made for a BLM system, from which the various thermodynamic quantities are obtained for the formation of the BLM. It is shown that the free energy, entropy, and enthalpy of formation are all negative, suggesting a more ordered structure and a lower free energy content for the BLM a t the W-0-W biface than for the two separate lipid monolayers. The application of the Gibbs adsorption equation to the BLM system is proposed.
Acknowledgments. Thanks are due to Mise Lynn Sorensen for carrying out most of the interfacial free energy measurements. The financial support provided by National Institutes of Health Grant GM-14971 is gratefully acknowledged.
Volume 78, Number 8 August 1068
