Langmuir 2001, 17, 6037-6040
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Phase Transitions of Soluble Surfactants at a Liquid-Vapor Interface M. S. Tomassone,*,† A. Couzis,§ C. Maldarelli,‡,§ J. R. Banavar,⊥ and J. Koplik‡,| Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, New Jersey 08854, Levich Institute and Departments of Chemical Engineering and Physics, City College of the City University of New York, New York, New York 10031, and Department of Physics and Center for Materials Physics, The Pennsylvania State University, University Park, Pennsylvania 16802 Received February 28, 2001. In Final Form: June 12, 2001 Although medium chain length insoluble amphiphiles are well-known to form gaseous and liquid expanded phases on an air/water interface, the situation for the soluble case is controversial. We perform molecular dynamics simulations of model surfactant molecules dissolved in a bulk liquid solvent in coexistence with its vapor. Our results indicate a transition in both soluble and insoluble surfactants: a plateau in surface tension versus surface coverage, whose instantaneous configurations display two-phase coexistence, along with correlation functions indicating a transition from gaseous to liquidlike behavior.
I. Introduction Surfactants are amphiphilic molecules which contain a polar headgroup and a nonpolar tail, which usually consists of a chain of hydrocarbon groups. At an air/water interface, surfactants arrange themselves with their polar group immersed in water, interacting by dipolar forces, while the hydrocarbon tails are displaced outward into the air. The presence of surfactants at the air/water interface lowers the surface tension,1 and the degree of aggregation and molecular ordering is reflected in the appearance of distinct surface phases as a function of surfactant concentration. For insoluble surfactants, extensive experimental studies have shown the existence of two-dimensional gas (G) and disordered liquid phases (more precisely, the liquid expanded (LE) phase) as well as condensed mesophases and semisolid crystalline-like phases in monolayers.2-4 A soluble surfactant necessarily has a stronger affinity to the solvent, which reduces its ability to aggregate on the surface. For this reason, condensed phases are not expected, and there is even controversy over the existence of a G/LE transition. Soluble surfactant measurements which show depressed critical points relative to insoluble analogues2,5 led to the common perception that under usual conditions soluble surfactants would have only a fluid state. Recently, indirect experimental evidence to the † Department of Chemical and Biochemical Engineering, Rutgers University. ‡ Levich Institute, City College of the City University of New York. § Department of Chemical Engineering, City College of the City University of New York. | Department of Physics, City College of the City University of New York. ⊥ Department of Physics and Center for Materials Physics, The Pennsylvania State University.
(1) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces, 6th ed.; Wiley: New York, 1997. (2) Gaines, G. L. Insoluble Monolayers at Liquid-Gas Interfaces; Wiley: New York, 1966; p 181. (3) Knobler, C. M.; Desai, R. C. Annu. Rev. Phys. Chem. 1992, 43, 207. (4) Kaganer, V. M.; Mo¨hwald, H.; Dutta, P. Rev. Mod. Phys. 1999, 71, 779. (5) Pallas, N.; Pethica, B. J. Chem. Soc., Faraday Trans. 1 1987, 83, 585.
contrary has emerged, based on induction plateaus6 and cusps in surface tension isotherms.7 In no case was the surface structure or concentration directly measured to test for phase separation. This paper focuses on the determination of soluble surfactant adsorption isotherms simultaneously with their phase behavior and surface tension variation, and in particular the G/LE transition, using molecular dynamics (MD) simulations. In the context of insoluble surfactants, this approach has been used extensively to study the structure of monolayers restricted to the surface of a substrate,8-10 obtaining information both complementary to and in semiquantitative agreement with experiment on Langmuir films. There are MD simulations of soluble surfactant monolayers,11 but these do not study the surface-bulk equilibrium which gives rise to the surface phases or the transitions between them. In contrast, MD simulations in liquid-liquid systems12 have studied the equilibrium between the liquid phase and monomeric and surfactant aggregates in the bulk but not surface phase transitions. Our simulations model surfactant molecules placed in a solvent in equilibrium with its vapor, which then migrate to the surface to a degree controlled by the choice of interaction potential. For both insoluble and soluble surfactants, we observe that as their surface concentration increases, the surfactant structure on the liquid/vapor interface ranges from a gas phase containing isolated molecules or small clusters to a coexisting mixture of clusters of various sizes to a single disordered spanning liquid cluster. Further details of this work and other (6) Lin, S.; Tsay, R.; Hwong, W. Colloids Surf., A 1996, 114, 131. (7) Aratono, M.; Uryu, S.; Hayami, Y.; Motomura, K.; Matuura, R. J. Colloid Interface Sci. 1984, 98, 33. (8) Bareman, J. P.; Klein, M. L. J. Phys. Chem. 1990, 94, 5202 and references therein. (9) Karaborni, S.; Toxvaerd, S. J. Chem Phys. 1992, 96, 5505. (10) Schmidt, M. E.; Shin, S.; Rice, S. A. J. Chem Phys. 1996, 104, 2114 and references therein. (11) Bo¨cker, J.; Schlenkrich, M.; Bopp, P.; Brickmann, J. J. Phys. Chem. 1992, 96, 9915. Tarek, M.; Tobias, D. J.; Klein, M. L. J. Phys. Chem. 1995, 99, 1393. Sokhan, V. P.; Tildesley, D. J. Faraday Discuss. 1996, 104, 193. Kuhn, H.; Rehage, H. J. Phys. Chem. B 1999, 103, 8493. (12) Smit, B. Phys. Rev. A 1988, 37, 3431. Esselink, K.; Hilbers, P. A. J.; van Os, N. M.; Smit, B.; Karaborni, S. Colloids Surf. 1994, 91, 155.
10.1021/la0103113 CCC: $20.00 © 2001 American Chemical Society Published on Web 09/08/2001
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Langmuir, Vol. 17, No. 20, 2001
Letters
Figure 2. γ-Γ isotherms for the insoluble and soluble cases.
Figure 1. Snapshots of the simulated system: (a) all atoms in a soluble case, (b) surfactant molecules only in an insoluble case, (c) surfactant molecules only in a soluble case.
results, particularly on the insoluble case, will be presented elsewhere.13 II. Results and Discussion Our calculations are based on standard MD techniques using Lennard-Jones (LJ) interactions, in an NVT ensemble.14 The potential between any two atoms of types 12 i and j separated by distance r is VLJ ij (r) ) 4[(σ/r) Cij(σ/r)6]. Here, Cij is an adjustable coefficient, is an energy scale, σ is approximately an atomic diameter, and the characteristic microscopic time unit is τ ) xmσ2/, with atomic mass m. The surfactant atoms are bound in chain molecules using the finitely extensible nonlinear elastic (FENE) potential15 VFENE ) -(1/2)Kr02 ln[1 - (r/r0)2] which acts only between adjoining atoms on a chain; r0 is the maximum bond length, and K is a spring constant. The system is maintained at a temperature T ) 0.9/kB by a constant kinetic energy thermostat. We have worked with a system of 11 520 atoms in total, with surfactant chains of length 6. The atoms move in a three-dimensional box of size 20.5σ × 20.5σ × 68.4σ, with periodic boundary conditions in all directions, and form a horizontal liquid slab with vapor above and below, with two (statistically) planar liquid/vapor interfaces. A snapshot of a typical configuration is shown in Figure 1a, after an equilibration period of 300τ. The data presented below represent averages over 5000τ runs. The surfactant molecules are initially distributed at random in the liquid and then migrate to the liquidvapor interface to a degree determined by the choice of the coefficients Cij. An insoluble surfactant is achieved by choosing a strong attraction between headgroup and solvent, an antipathy between surfactant tail and solvent, and a strong cohesion among the molecules in the solvent. The full set of interaction coefficients is shown in Table 1, where the subscript convention is as follows: 1, hydrophilic head; 2, hydrophobic tail; and 3, solvent. A (13) Tomassone, M. S.; Couzis, A.; Maldarelli, C.; Banavar, J. R.; Koplik, J. J. Chem. Phys., in press. (14) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, 1987. (15) Bird, R. B.; Curtiss, C. F.; Armstrong, R. C.; Hassager, O. Dynamics of Polymeric Liquids, Vol. 2: Kinetic Theory, 2nd ed.; Wiley: New York, 1987.
Figure 3. Surface excess concentration vs bulk concentration. Table 1. Interaction Coefficients Cij for Insoluble Sixmer Surfactant i)1 i)2 i)3
j)1
j)2
j)3
1.0 1.0 3.0
1.0 0.2 0.6
3.0 0.6 1.15
Table 2. Interaction Coefficients Cij for Soluble Case: Sixmer i)1 i)2 i)3
j)1
j)2
j)3
1.0 1.0 3.0
1.0 0.2 0.8
3.0 0.8 1.1
typical snapshot of the insoluble surfactant phase alone is shown in Figure 1b. To obtain a soluble surfactant system, we first reduce the antipathy between the surfactant tails and the solvent, by increasing C23, and then reduce the cohesion of the solvent, by reducing C33; the full set is shown in Table 2. The surface tension is computed from the standard microscopic expression for a planar interface,16 γ ) (1/ A)〈∑i
