Monte Carlo simulation of a lattice model for micelle formation

Abstract

We have investigated the aggregation into micelles of nonionic amphiphiles in water through Monte Carlo simulations of a very simple model system. Amphiphiles and water are modeled, respectively, as three-site and one-site molecules on a square lattice. The model presents characteristic properties of experimental micellization, namely, monomer vs amphiphile concentration with a plateau above a ‘‘critical’’ concentration (cmc) and a distribution of micelle sizes (polydispersity). Results of the numerical experiment were compared with predictions from statistical thermodynamic theory. Sample size and relaxation properties of the simulation have also been analyzed.

Formation of Block Copolymer Micelles in Solution: A Monte Carlo Study of Chain Length Dependence

“…[46][47][48] In fact, a large number of computer simulations of micelle formation can already be found in the literature. [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67] However, only recently has it been clearly realized that for a study of a well-equilibrated micellar size distribution in solution one needs huge systems with a large number of micelles in them simulated over a sufficient time range so that the molecules get exchanged between the micelles often enough. 63,65 These studies 63,65 hence applied coarsegrained models of block copolymers as short as N ) 4 only!…”

A Spin Model for Clustering of Amphiphiles in Two Dimensions

“…Extensive theoretical studies were employed to investigate these special aggregates, including computer simulations [4][5][6][7][8][9][10]. However, simulations of micellar systems require complex algorithms and a huge amount of computation time.…”

Systems Involving Surfactants

“…Most lattice models however abstract from the details of the hydrocarbon chain The Larson model and Larson-type models have been widely used to study micelles [111,114,115,116,117,118,37,119,120], amphiphiles at oil/water interfaces [121,122,118], bilayers [117,123] and various other problems [124,125,126,127,128]. The models differ from each other in the range of the interactions and in the treatment of the amphiphile monomers.…”

“…Some models stay with Larson's simplifying assumption that the amphiphile monomers are identical to oil or water particles [37,119,120], but most of them equip the amphiphiles with new types of particles, often even allowing for more than two different monomer species. A popular description going back to Stauffer and coworkers [114] and to Bernardes and coworkers [115,123] adopts the language of the Ising model and assigns a spin S = −1 to oil particles, a spin S = +1 to water particles, and an integer spin ranging between -1 and +2 to surfactant monomers. The interaction energy is described by a Hamil- Schick [133] have employed it to study the formation and the structure of pores in amphiphilic bilayers.…”

“…Therefore, it is not defined unambiguously. In the simulations, some authors identify it with the concentration where more than half of the surfactants are assembled into aggregates [114]; others determine the intersection point of linear fits to the low concentration and the high concentration regime, either plotting the free surfactant concentration vs. the total surfactant concentration Φ [115], or plotting the surfactant chemical potential vs. ln(Φ) [119].…”