Micelles, computer simulations

Computer Simulations of Living Polymers and Giant Micelles... 

M. Kroger, R. Makhloufi. Wormlike micelles under shear flow A microscopic model studied by nonequihbrium molecular dynamics computer simulations. Phys Rev E 55 2531-2536, 1996. 

This chapter is organized as follows. The thermodynamics of the critical micelle concentration are considered in Section 3.2. Section 3.3 is concerned with a summary of experiments characterizing micellization in block copolymers, and tables are used to provide a summary of some of the studies from the vast literature. Theories for dilute block copolymer solutions are described in Section 3.4, including both scaling models and mean field theories. Computer simulations of block copolymer micelles are discussed in Section 3.5. Micellization of ionic block copolymers is described in Section 3.6. Several methods for the study of dynamics in block copolymer solutions are sketched in Section 3.7. Finally, Section 3.8 is concerned with adsorption of block copolymers at the liquid interface. 

Computer simulations of a range of properties of block copolymer micelles have been performed by Mattice and co-workers.These simulations have been based on bead models for copolymer chains on a cubic lattice. Types of allowed moves for bead chains are illustrated in Fig. 3.27. The formation of micelles by diblock copolymers under weak segregation conditions was simulated with pairwise interactions between A and B beads and between the A bead and vacant sites occupied by solvent, S (Wang et al. 19936). This leads to the formation of micelles with a B core. The cmc was found to depend strongly on fVB and % = x.w = %AS. In the range 3 < (xlz)N < 6, where z is the lattice constant, the cmc was found to be exponentially dependent onIt was found than in the micelles the insoluble block is slightly collapsed, and that the soluble block becomes stretched as Na increases, with [Pg.178]

Recent studies showed that amphiphilic properties have to be taken into account for most water-soluble monomer units when their behavior in water solutions is considered. The amphiphilic properties of monomer units lead to an anisotropic shape of the polymer structures formed under appropriate conditions, which is confirmed both by computer simulation and experimental investigations. The concept of amphiphilicity applied to the monomer units leads to a new classification based on the interfacial and partitioning properties of the monomers. The classification in question opens a broad prospective for predicting properties of polymer systems with developed interfaces (i.e., micelles, polymer globules, fine dispersions of polymer aggregates). The relation between the standard free energy of adsorption and partition makes it possible to estimate semiquantitatively the distribution between the bulk and the interface of monomers and monomer units in complex polymer systems. 

I. Benjamin, Chemical reactions and solvation at liquid interfaces a microscopic perspective, Chem. Rev. (Washington, D. C.), 96 (1996) 1449-75 I. Benjamin, Theory and computer simulations of solvation and chemical reactions at liquid interfaces, Acc. Chem. Res., 28 (1995) 233-9 L. R. Martins, M. S. Skaf and B. M. Ladanyi, Solvation dynamics at the water/zirconia interface molecular dynamics simulations, J. Phys. Chem. B, 108 (2004) 19687-97 J. Faeder and B. M. Ladanyi, Solvation dynamics in reverse micelles the role of headgroup-solute interactions, J. Phys. Chem. B, 109 (2005) 6732 10 W. H. Thompson, Simulations of time-dependent fluorescence in nano-confined solvents, J. Chem. Phys., 120 (2004) 8125-33. 

Chem., 59, 6361 (1991). Structure of a Water/Oil Interface in the Presence of Micelles A Computer Simulation Study. 

Many new technologies rely on the unusual properties of interfaces— Langmuir-Blodgett and other films, micelles, vesicles, small liquid drops, and so on. Classical thermodynamics is often inadequate as a basis for treating such systems because of their smallness, and experimental probes of the interface are limited, especially for fluid systems. Computer simulation can play an important role here, both in understanding the role of intermolecular forces in obtaining desired properties and, in combination with experiment, in designing better materials and processes [6, 28]. 

Triphenylenes provided with nonionic di(ethylene oxide) side-chains (25f)132 134 or with ionic alkyl chains (25g)135 form supramolecular polymers in water.136 The arene—arene interactions of the aromatic cores allow for the formation of columnar micelles . At low concentrations the columns are relatively short, and the solutions are isotropic. At higher concentrations the longer columns interact and lyotropic mesophases are formed.133 Computer simulations showed that in the isotropic solution the polymerization of the discotics is driven by solute-solute attraction and follows the theory of isodesmic linear aggregation the association constants for dimerization, trimerization, and etc., are equal and the DP of the column thus can easily be tuned by concentration and temperature.137 138 At higher concentrations the sizes of the columns are influenced by their neighbors, the columns align, and the DP rises rapidly. 

In practice computer simulation has generally been used to predict the variation of with concentration of reactant, surfactant, or added electrolyte in terms of various values of the parameters, k, and This simulation procedure has been used as an indirect method for the determination of the ion exchange constant K, and, for example, for the competition between various counterions for micelles, there is reasonable agreement between the values obtained kinetically and by other methods [25,72-79],... 

Manabe et al. [23] found the formation of the nonionized hydrate, A0T(H20)2, below iVg = 2 by the measurement of its conductivity. Therefore, water below iVg = 2 should correspond to nonionized hydrated water different from bound water below ITo = 10. (Hereafter called immobilized water.) When water in limited amounts is added to the anhydrous AOT solution, immobilized water is formed. A computer simulation showed that neither a spherical micelle nor a water pool is formed below = 2... 

Computer simulation studies have explored translational and rotational dynamics in micellar solutions and shown that both translational and rotational dynamics in the hydration layer of micelles (Stem layer) are significantly slower than that in the bulk. The dipole-dipole time correlation function (which measures the rotational dynamics) shows the appearance of a long-time tail of the time constant in the 100 ps range or above. The dependence of the rotational dynamics on the probe location has also been investigated and it was found that the dynamics becomes faster as the probe moves away from the surface [7]. 

In the case of reverse micelles there is no conclusive signature of such an effect. Computer simulation, however, does indeed show an initial relaxation of water that is faster than in the bulk. 

Recently, Miller and Cacciuto explored the self-assembly of spherical amphiphilic particles using molecular dynamics simulations [46]. They found that, as well as spherical micellar-type structures and wormlike strings, also bilayers and faceted polyhedra were possible as supracolloidal structures. Whitelam and Bon [47] used computer simulations to investigate the self-assembly of Janus-like peanut-shaped nanoparticles and found phases of clusters, bilayers, and non-spherical and spherical micelles, in accordance with a packing parameter that is used conventionally and in analogy to predict the assembled structures for molecular surfactants. They also found faceted polyhedra, a structure not predicted by the packing parameter (see Fig. 8). In both studies, faceted polyhedra and bilayers coexist, a phenomenon that is still unexplained. 

In our recent smdies, we focused on several complicating factors arising in studies of nanoparticles of a non-negligible size (e.g., polymeric micelles, vesicles) that can carry several fluorescent labels. When the dimensions of such particles become comparable to the typical dimensions of the effective volume (coi, (O2), the correlated motion of the fluorophores located on a single particle affects the shape of the autocorrelation function. Recently, an approximate expression for the FCS autocorrelation function of diffusing particles of finite size has been derived by Wu et al. [85]. They have shown that the autocorrelation function of uniformly labeled spherical particles can be expressed in a form similar to (12) where the diffusion time, concentration, and dimensions of the active volume are replaced by corresponding apparent quantities that depend on the particle size. Qualitatively, the same results were obtained in our computer simulations, which are discussed later (see Sect. 4.3). 

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