Langmuir 1990,6, 293-294
293
yielded an interlayer distance of 32.1 A. When a probable conformation of DPEM is considered by constructing the space-filling molecular model, according to Hauser et al.’ and Seeling et a1.,8 the length of the long axis of DPEM is in the range 28-37 A. These findings suggest that the long alkyl groups are almost perpendicularly oriented to the layer surface? Thus, this preliminary report provides some information on the morphology of LB mul-
tilayers of phospholipid. Furthermore, the polymerized phospholipid LB multilayer film could possibly be utilized as ultrathin membranes of biomedical sensors or devices.
(7) Hauser, H.; Pascher, I.; Sundell, S. J. Mol. Biol. 1980, 137, 264. (8) Seeling, J.; Seeling, A. Q.Reo. Biophys. 1980, 13, 4919.
(9) Fendler, J. H. Membrane Mimetic Chemistry;Wiley: New York, 1982; pp 121-132.
Formation of Crystalline Monolayers at the Gas-Water Interface at Low Surface Pressures Jerome B. Lando and J. Adin Mann, Jr.’ Departments of Macromolecular Science and Chemical Engineering, Case Western Reserve University, Cleveland, Ohio 44106 Received M a y 19, 1989. I n Final Form: August 1, 1989
In recent years, a body of evidence has developed which indicates that some monolayer-forming amphiphiles that can pack well do form crystalline monolayer islands at low surface pressure. For example, monolayers of the type CH3(CHz)nCdX=C(CH2),COOLi have been found to polymerize a t low surface pressures,’ it being generally accepted that diacetylenes polymerize only in ordered phases. The polymerized monolayer that is formed yields, after transfer to a microscope grid, an electron diffraction pattern that is also one layer of the normal crystal structure.2 The monomer monolayer also yields an electron diffraction pattern after transfer identical with one layer of the normal monomer structure.2 In addition, Brownian dynamics simulations3 of monolayers of CH,(CHJ,,COOH (hexadecanoic acid) a t low surface pressures indicated stable clusters of approximately 25-50 molecules, a surprisingly small number, considering the requirements of three-dimensional stability. Interaction parameters used in computing forces were calculated from simulations of three-dimensional fatty acid crystals, assuming the normal bulk melting point of the amphiphiles and the heat of fusion. Figure 1 shows the clustering obtained; the analogous three-dimensional simulations do not show such an effect. Although this evidence is indirect, it strongly suggests that monolayer crystals can form at low surface pressure. Recently, we have obtained direct evidence for the existence of these island crystals in the case of the two amphiphiles, the diacetylene Li salt and pentadecanoic acid. Synchrotron X-ray scattering in plane a t the gaswater interface has resulted in diffraction maxima identical with or similar (identical spacing along the direction of polymerization, slightly expanded spacing in the perpendicular direction) to those previously observed by electron diffraction.’ Given these data and the fact that crystals must nucleate to form, we have applied nucleation theory to this problem as explained below. The (1) Day, D. R.; Ringsdorf, H. J. Polym. Sci., Polym. Lett. Ed. 1978, 16, 205. (2) Day, D. R.; Lando, J. B. Macromolecules 1980, 13, 1483. (3) Mann, J. A,; Tjatjopoulos, G. A,; Azzam, M. J.; Boggs, K. E.; Robinson, K. M.; Sanders, J. N. Thin Solid Films 1987, 152, 29-48. Tjatjopoulos, G. J. “The Molecular Dynamic Simulation of Monomo-
Registry No. DPEM, 123438-36-8; dipalmitoyl-DL-a-phosphatidylethanolamine, 5681-36-7; methacroyl chloride, 920-46-
7.
results are consistent with the formation of small clusters. We next estimate the free energy of the growing nucleus, AG,, where i refers to the number of molecules in the growing nucleus; AG, reaches a maximum, AG*, at some i which defines the critical nucleus. We do this using a standard argument which invokes formally various interfacial tension and surface free energy density quantities on a very small slab of monolayer taken to be three dimensional. We recognize the difficulties in defining these quantities precisely. Our general assumption in the following calculation is that the water surface is a heterogeneous nucleation surface for the growth of monolayer crystals. We assume that nucleation occurs with aggregates forming a perimeter in the plane of the surface and the molecules standing at some tilt angle clustered together. See Figure I. The clusters are considered three dimensional so that a surface free energy density can be defined on each interface perpendicular to the plane of the water surface that separates the cluster and molecules that are not members of the cluster. The cluster is surrounded by a disordered phase. The equation for AG, in the case of heterogeneous nucleation of a monolayer is AGi = -abC&f + 2aCoy + 2bCoy’ + Ubhyh (1) where a, b (in the plane a = 161, b = 181), and C, are the dimensions of the nucleus at any time, C, is the length of the C axis (not necessarily a crystallographic repeat) of the crystal monolayer projected on the normal to the surface of the water (C, = n-E)and is always constant, Ag, is the bulk free energy per unit volume for crystallization a t a given supercooling, and y and y’ are the interfacial tensions of the side surfaces (see Figure IC). Thus, AG, is an extensive free energy term. The term Ayh will be discussed after the calculation that is done next. Taking the partial derivatives of AG, as a function of a and b, we get aAGilaa = -bCoAgf
aAGilab = -aCo&f So for the critical nucleus
+ 2C0y + b a y h + 2Coy’ + UAyh
where a* and b* are the critical nucleus dimensions. Substituting these values of a* and b* in eq 2, we get
lecular Films”; Ph.D. Thesis, CWRU, 1988.
0743-7463190 f 2406-0293$02.50/0
(2) (3)
0 1990 American Chemical Society
294
Langmuir, Vol. 6, No. I , 1990
Notes
will be intimate contact between the ordered and disordered phases, a term ycmis added. Thus
A.
C.
Figure 1. Molecular simulation of monolayer structure. Projections are shown of an equilibrium configuration of 64 molecules. Cyclic boundary condition? were used for motion parallel to the Gibbs surface (the 8 , b plane). A special potential function3 kept the molecules in the interfacial region; the polar group was not constrained to the Gibbs surface. (A) A 3-D projection showing two clusters each tilting in different directions. This configuration was abstracted from the time series of configurations after equilibrium had been reached corresponding to more than 1 ns from the initial confi uration, At = 10 fs. The control area corresponds to 0.55 nm /molecu_le. (B)Projection of the end-to-end vectors of A onto the d, b plane. The bead corresponds to the carboxyl group; the shank is normalized and points in the direction of the projection. The two clusters show more ordering than the liquid or vapor state a_lo_ne. (C) An ordered cluster showing the planes normal to d X b, b X i., and ii X i. is used in the estimate of the free energy function from which a cluster size can be estimated. The cluster size of ca. 25-50 molecules found in the simulation is consistent with the estimation from simple nucleation theory.
f
To make a sample calculation, we will assume Ag, = lo’ J / m , y = 10 mN/m, y’ = 5 mN/m (all reasonable values for hydrocarbon^),^,^ C, = 3 nm, and Ayh = 0. One gets AG* equal to 6 X lo-,’ J, which is a suitably small value. The corresponding values for a* and b* are 1.0 and 2.0 nm, respectively. Taking the area per molecule as approximately 0.20 nm2, there would be approximately 10 molecules in the critical nucleus. This small size would explain why simulations gave stable clusters about 25-50 molecules in size. The small size is, of course, related to the special conditions at the gas-water interface that we have analyzed. It should be noted that the assumption that Ayh = 0 is the identical assumption made in the simulations, namely, that the bulk melting can be assumed, since with Ayh = 0 there will be no appreciable ab-surface contribution to the crystal free energy. The surface tensions y and y’we have used cannot be considered as or replaced by line tensions, since the C, dimension of the critical nucleus is actually greater than a* or b* and in any applicable case would be of at least similar magnitude. The usual formula for computing the ab-surface free energy contribution, abAy,, can be though of as a free energy change from the state when only the disordered phase is present to the state that involves both the nucleus and the disordered phase in contact. Thus, there will be a contribution from the disordered phase against the substrate, -yms, and the ordered nucleus (crystal) against the substrate, yes. In addition, since in the new state there Turnbull, D.; Cormia, R. L. J . Chem. Phys. 1961, 34, 820. (5) Koutsky, J. A.; Walton, A.; Baer, E. J . Appl. Phys. 1967, 38, (4)
1832.
where ycs,ycm,and -yms are, formally, the interfacial tensions between the crystal nucleus and the substrate, the crystal nucleus and the surrounding disordered phase, and the disordered phase and the substrate, respectively. It is clear from the form of surface pressure-area isotherms that T solid-ordered > T disordered, and so ycs < yms. Furthermore ycm may well be small in specific cases. The interactions across the interface defined by 6 X ? or b X t are that of packed methyl groups for which ycamshould be small; the anisotropy of the pressure tensor-is small when integrated along the directions ti X i. or b X i.. Thus, the possibility exists that Ayh, the free energy density contribution of the two faces in question, may be negative. This unusual situation arises because the two crystal faces parallel to the amphiphile/water interfaces (one crystal monolayer phase and one disordered, lower density monolayer phase) are so different. A t this time, we do not know all of the experimental conditions under which crystal clusters nucleate from the disordered phase. So far we have experimental evidence that pentadecanoic acid spread from solvent to the equilibrium spreading pressure nucleates a more ordered phase. The diacetylene amphiphile nucleates when compressed to a relatively low spreading pressure, the equilibrium spreading pressure. The simulations suggest that nucleation will occur for amphiphiles of sufficient chain length that (CH,), condense to form ordered regions; the terminal methyl groups or the carboxyl group may remain disordered. Chain stiffness aids the process as in the diacetylene system. Apparently K = -Aa?r/aA, the dilational elastic modulus, should be large in the condensed phase. We anticipate that monolayer diffraction techniques can be used to extend greatly our understanding of the conditions under which nucleation occurs to form an ordered phase at relatively low or very low spreading pressures. Finally, one is led to the realization that, if Ayh is actually negative, the “melting point” of the monolayer crystal should be higher than the bulk melting point of the amphiphile. We are attempting to determine if such a phenomenon can be observed. Summary Calculations of the critical nucleus size and free energy of the nucleation of monolayer crystals at the gas-water interface at low surface pressure have been undertaken. The water surface is assumed to act as a heterogeneous nucleation surface. These calculations have demonstrated that the critical nucleus should contain on the order of 10 molecules, a very small number. Molecular dynamics simulations indicate that stable clusters containing as few as 25 molecules can exist, which would be reasonable if the critical nucleus contains only 10 molecules. Acknowledgment. Support by an Office of Naval Research (ONR) contract for the study of the ocean microlayer, a selected research opportunities grant from ONR in graph theory, and a Defense Advanced Research Projects Agency Grant to the Polymer Microdevices Laboratory of Case Western Reserve University are acknowledged with gratitude.
