Micelle Monte-Carlo simulations

Figure C2.3.6. Illustration of micelle stmcture obtained by Monte Carlo simulations of model octanoate amphiphiles. There are 30 molecules simulated in this cluster. The shaded spheres represent headgroups. Reproduced by pennission from figure 2 of [35].

Mesoscale simulations model a material as a collection of units, called beads. Each bead might represent a substructure, molecule, monomer, micelle, micro-crystalline domain, solid particle, or an arbitrary region of a fluid. Multiple beads might be connected, typically by a harmonic potential, in order to model a polymer. A simulation is then conducted in which there is an interaction potential between beads and sometimes dynamical equations of motion. This is very hard to do with extremely large molecular dynamics calculations because they would have to be very accurate to correctly reflect the small free energy differences between microstates. There are algorithms for determining an appropriate bead size from molecular dynamics and Monte Carlo simulations. 

Monte Carlo simulations are additional methods for the study of block copolymer micelles as reviewed by Binder and Muller [202] and by Shelley and Shelley [210]. 

Xing and Mattice (1998) applied Monte Carlo simulation techniques to study the models of BAB triblock copolymeric micelles with solubilizates in a selected solvent. They focused on a microscopic picture regarding the locus of solubilizates in BAB triblock copolymer micelles when the... 

We have studied the phase and micellization behavior of a series of model surfactant systems using Monte Carlo simulations on cubic lattices of coordination number z = 26. The phase behavior and thermodynamic properties were studied through the use of histogram reweighting methods, and the nanostructure formation was studied through examination ofthe behavior ofthe osmotic pressure as a function of composition and through analysis of configurations. 

Wallin T, Linse P. Monte Carlo simulations of polyelectrolytes at charged micelles. 1. Effects of chain flexibility. Langmuir 1996 12 305-314. 

Diffusion is intricately linked with all aspects of the radical-pair mechanism. The CIDNP kinetics for the reaction of a sensitizer with a large spherical molecule that has only a small reactive spot on its surface were studied theoretically. This situation is t)qjical for protein CIDNP, where only three amino acids are readily polarizable, and where such a polarizable amino acid must be exposed to the bulk solution to be able to react with a photoexcited dye. Goez and Heun carried out Monte Carlo simulations of diffusion for radical ion pairs both in homogeneous phase and in micelles. The advantage of this approach compared to numerical solutions of the diffusion equation is that it can easily accommodate arbitrary boundary conditions, such as non-spherical symmetry, as opposed to the commonly used "model of the microreactor" ° where a diffusive excursion starts at the micelle centre and one radical is kept fixed there. 

The electrostatic charges of surfactants seriously affect the localization of host molecules in the water pool. Monte Carlo simulation in which ionic reversed micelles are treated as spherical entities showed the presence of the electrical double layer in the interface of the water pool, and the distribution of counterions followed the Poisson-Boltzmann approximation [51]. Mancini and Schiavo [52] assumed recently, by the yield of halogenation, that the specific interactions between bromide or chloride ions and an ammonium head-group in cationic reversed micelles keep the ions in a defined position on the interface. 

Localization of Radical Pairs in Micelles. CIDNP can often be enhanced by the use of micelles to enhance the recombination probability of photochemi-cally produced radical pairs. Bagranskaya et al have reviewed this techique. Goez and Heun have used Monte Carlo simulations of diffusional trajectories to calculate reencounter probabilitiies of micellized radical pairs. By varying the initial locations, they found that unless at least one of the radicals starts its diffusional trajectory extremely near the micelle boundary, the reencounter probability is essentially the same as in the case of free diffusion. It was concluded... 

These results show that simplified molecular dynamics simulations can qualitatively account for micellization quite well. However, the computation time necessary for even such simple models is too great to allow the model to be useful for the calculation of other micellar properties or phase behavior or for an in-depth study of solubilization. Stochastic dynamics simulations, in which the solvent effects are accounted for through a mean-field stochastic term in the equations of motion, can also be used to study surfactant self-assembly [22], but the most efficient approach to date is still the one based on lattice Monte Carlo simulations, which are discussed next. 

Within the last decade a number of studies have appeared in print on lattice Monte Carlo simulations of surfactant-water-oil mixtures, many focusing on an examination of the simulation method using micellization of short-chain amphiphiles (or block copolymers) in solution. An almost equal number of studies focus on micellar and microemulsion phase behavior. In what follows, we include a brief discussion of a few papers on block copolymers as well, as these are conceptually similar to the systems of interest in this chapter and shed light on what could be expected in short-chain surfactant systems to some extent. 

Finally, Mattice and coworkers have used lattice Monte Carlo simulations for various studies of micellization of block copolymers in a solvent, including micellization of triblock copolymers [43], steric stabilization of polymer colloids by diblock copolymers [44], and the dynamics of chain interchange between micelles [45]. Their studies of the self-assembly of diblock copolymers [46-48] are roughly equivalent to those of surfactant micellization, as a surfactant can in essence be considered a short-chain diblock copolymer and vice versa. In fact, Wijmans and Linse [49,50] have also studied nonionic surfactant micelles using the same model that Mattice and coworkers used for a diblock copolymer. Thus, it is interesting to compare whether the micellization properties and theories of long-chain diblock copolymers also hold true for surfactants. 

Keywords Block copolymer micelles Fluorescence anisotropy Fluorescence correlation spectroscopy Molecular dynamics simulations Monte Carlo simulations Solvent relaxation method Time-resolved fluorescence... 

Pedersen and coworkers [74, 80, 81, 86] have modified Eq. 78 based on Monte Carlo simulation results from chains exhibiting excluded volume effects. Written in terms of a micelle constituted of a A-B block copolymer, this can be written independently of morphology (spherical, ellipsoidal, or cylindrical) ... 

Lagueerr, A., Stoll, S., Kirton, G. and Dubin, P.L. (2003). Interactions of a polyanion with a cationic micelle comparison of Monte Carlo simulations with experiment. J. Phys. Chem. B, 107, 8056-8065. 

Abstract Results are presented from Monte Carlo simulations of a three-dimensional lattice model of a binary mixture of amphiphile and solvent. The amphiphiles are represented by connected chains on a simple cubic lattice and free self-assembly is allowed within the simulations. Earlier work on this model, for chains of length four, has shown that it exhibits a critical micelle concentration and a cluster size distribution which is consistent with those observed experimentally. The results presented in this paper use chains of length six, two of which are head segments and also include the effect of chain rigidity. It is found that the mean aggregation number is greater than that achieved with shorter chains and the cluster size distribution has a significantly enhanced minimum, with the micelles more spherical in... 

Key words Micelle - lattice model -Monte Carlo simulation - entropy... 

Monte Carlo simulations have previously been reported for this model in two [6] and three [7, 8] dimensions and the model exhibits lamellar and micellar-like phases as well as other features consistent with those of amphiphiles including a critical micelle concentration... 

Fig. 4 Monomer concentration [MJ and surfactant concentration in the proper micelle size region (i > 40), against [C]. The results were obtained as final values of Monte Carlo simulations for different values of [C] starting from flat size distributions in the range 1-100 and setting...

Figure 9 Dimensionless apparent molecular weight Mapp times the concentration c of giant surfactant micelles of hexadecyl trimethyl ammonium bromide in brine, obtained by means of light scattering measurements at a temperature of 306 K. Circles experimental data of Buhler and coworkers [50]. Line renormalization group theory for self-assembled flexible chains fitted to the data [51,52], Also indicated by the dashed lines are the predictions of scaling theory in the dilute and semidilute regimes [1,53], which agree well with results of Monte Carlo simulation [52],...

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