Monte Carlo studies of model Langmuir monolayers

Abstract

This paper examines some of the basic properties of a model Langmuir monolayer, consisting of surfactant molecules deposited onto a water subphase. The surfactants are modeled as rigid rods composed of a head and tail segment of diameters sigma(hh) and sigma(tt), respectively. The tails consist of n(t) approximately 4-7 effective monomers representing methylene groups. These rigid rods interact via site-site Lennard-Jones potentials with different interaction parameters for the tail-tail, head-tail, and head-head interactions. In a previous paper, we studied the ground-state properties of this system using a Landau approach. In the present paper, Monte Carlo simulations were performed in the canonical ensemble to elucidate the finite-temperature behavior of this system. Simulation techniques, incorporating a system of dynamic filters, allow us to decrease CPU time with negligible statistical error. This paper focuses on several of the key parameters, such as density, head-tail diameter mismatch, and chain length, responsible for driving transitions from uniformly tilted to untilted phases and between different tilt-ordered phases. Upon varying the density of the system, with sigma(hh)=sigma(tt), we observe a transition from a tilted (NNN)-condensed phase to an untilted-liquid phase and, upon comparison with recent experiments with fatty acid-alcohol and fatty acid-ester mixtures [M. C. Shih, M. K. Durbin, A. Malik, P. Zschack, and P. Dutta, J. Chem. Phys. 101, 9132 (1994); E. Teer, C. M. Knobler, C. Lautz, S. Wurlitzer, J. Kildae, and T. M. Fischer, J. Chem. Phys. 106, 1913 (1997)], we identify this as the L'(2)/Ov-L1 phase boundary. By varying the head-tail diameter ratio, we observe a decrease in T(c) with increasing mismatch. However, as the chain length was increased we observed that the transition temperatures increased and differences in T(c) due to head-tail diameter mismatch were diminished. In most of the present research, the water was treated as a hard surface, whereby the surfactants are only allowed to move within the plane of this surface. However, we have also utilized a more realistic model for the surfactant-water interactions, developed by Karaborni and Toxvaerd, in order to examine the role which the coupled effects of head group size and head group-subphase interactions plays in determining tilt ordering and on the stability of the monolayer. It is found that increasing the head diameter results in a widening of the air-water interface and an associated destruction of orientational order. Furthermore, the onset of capillary waves at lower temperatures for larger head diameters implies that the L2-L1 phase boundary for acids and acetates should move to lower temperatures relative to the L'(2)/Ov-L1 phase boundary for alcohols and esters. This feature has yet to be seen in experimental studies.

Theoretical description of 2D-cluster formation of nonionic surfactants at the air/water interface

“…But, one of the difficulties for such simulations is the adequate definition of effective interactions between the Bgrains.Î nvestigations of the surfactant behavior at different interfaces using the Monte Carlo method are not so numerous. Nevertheless, corresponding studies enable the estimation of the structural features for surfactant films [132,133], chiral effects in monolayers [134], impact of the structural peculiarities of the surfactants on the parameters of the phase transitions in the monolayers [135]. In the framework of the continuum configurational bias Monte Carlo method Howes and Radke [132] got surface tension isotherms of nonionic amphiphiles and calculated the tilt angles of the surfactant molecules with respect to the interface.…”

“…Selinger and Selinger [134] applied the continuum elastic theory together with МС simulations for the prediction of defects in the monolayer resulting in macroscopic chiral symmetry. Investigations of the influence of the diameter of the surfactant hydrophilic and hydrophobic parts done by Opps et al [135] showed that an increasing mismatch of these diameters results in the decrease of the critical temperature for the transition between inclined and upright phases.…”

Systems Involving Surfactants

“…Bead spring models without explicit solvent have also been used to simulate bilayers [40,145,146] and Langmuir monolayers [148,149,150,151,152]. The amphiphiles are then forced into sheets by tethering the head groups to two dimensional surfaces, either via a harmonic potential, or via a rigid constraint.…”

“…Therefore, Haas et al [148,149] represent the amphiphiles as stiff LennardJones chains, with one end (the head bead) confined to move in a plane. In later versions of the model [150,151,152], the head bead interactions differ from those of the tail beads: They are taken to be purely repulsive, and the head size is variable. which is distorted in the direction of tilt.…”

Phase equilibria in model surfactants forming Langmuir monolayers

“…These isotherms show a number of distinct regions that correspond to the two dimensional analogs of the monolayer usual states. [2][3][4] Various studies have reported isotherms where a number of states and the equilibrium between them have been clearly identified as the monolayer is compressed. [4][5][6] When the area per molecule is very large, the monolayer is in a vapor phase ͑V͒.…”