Amphiphilic systems

Another important class of materials which can be successfiilly described by mesoscopic and contimiiim models are amphiphilic systems. Amphiphilic molecules consist of two distinct entities that like different enviromnents. Lipid molecules, for instance, comprise a polar head that likes an aqueous enviromnent and one or two hydrocarbon tails that are strongly hydrophobic. Since the two entities are chemically joined together they cannot separate into macroscopically large phases. If these amphiphiles are added to a binary mixture (say, water and oil) they greatly promote the dispersion of one component into the other. At low amphiphile... 

Most characteristics of amphiphilic systems are associated with the alteration of the interfacial stnicture by the amphiphile. Addition of amphiphiles might reduce the free-energy costs by a dramatic factor (up to 10 dyn cm in the oil/water/amphiphile mixture). Adding amphiphiles to a solution or a mixture often leads to the fomiation of a microenuilsion or spatially ordered phases. In many aspects these systems can be conceived as an assembly of internal interfaces. The interfaces might separate oil and water in a ternary mixture or they might be amphiphilic bilayers in... 

This method has been devised as an effective numerical teclmique of computational fluid dynamics. The basic variables are the time-dependent probability distributions f x, f) of a velocity class a on a lattice site x. This probability distribution is then updated in discrete time steps using a detenninistic local rule. A carefiil choice of the lattice and the set of velocity vectors minimizes the effects of lattice anisotropy. This scheme has recently been applied to study the fomiation of lamellar phases in amphiphilic systems [92, 93]. 

Theissen O, Gompper G and Kroll D M 1998 Lattice-Boltzmann model of amphiphilic systems Euro. Phys. Lett. 42 419... 

Gompper G and Schick M 1994 Self-assembling amphiphilic systems Transitions and Critical Phenomena vol 16, ed C Domb and J L Lebowitz (New York Academic)... 

FIG. 1 Self-assembled structures in amphiphilic systems micellar structures (a) and (b) exist in aqueous solution as well as in ternary oil/water/amphiphile mixtures. In the latter case, they are swollen by the oil on the hydrophobic (tail) side. Monolayers (c) separate water from oil domains in ternary systems. Lipids in water tend to form bilayers (d) rather than micelles, since their hydrophobic block (two chains) is so compact and bulky, compared to the head group, that they cannot easily pack into a sphere [4]. At small concentrations, bilayers often close up to form vesicles (e). Some surfactants also form cyhndrical (wormlike) micelles (not shown). 

This rich scenario, together with the wide range of applications of amphi-philes, is reflected by an equally wide range of problems which have been addressed in studies of amphiphilic systems. In particular, the interest has focused on the following rather different classes of topics ... 

Mesoscopic structures and phases vesicles and vesicle shapes, structured phases and phase behavior of amphiphilic systems. 

The other class of phenomenological approaches subsumes the random surface theories (Sec. B). These reduce the system to a set of internal surfaces, supposedly filled with amphiphiles, which can be described by an effective interface Hamiltonian. The internal surfaces represent either bilayers or monolayers—bilayers in binary amphiphile—water mixtures, and monolayers in ternary mixtures, where the monolayers are assumed to separate oil domains from water domains. Random surface theories have been formulated on lattices and in the continuum. In the latter case, they are an interesting application of the membrane theories which are studied in many areas of physics, from general statistical field theory to elementary particle physics [26]. Random surface theories for amphiphilic systems have been used to calculate shapes and distributions of vesicles, and phase transitions [27-31]. 

After these introductory caveats, we review some of the work that has been done in realistic simulations of amphiphilic systems. 

Whereas chain models still allow for a relatively unified treatment of various aspects of amphiphilic systems, such as their bulk phase behavior and the properties of monolayers and bilayers, this is no longer true for the even more idealized models at the next level of coarse graining. These usually have to be adapted very specifically to the problem one wishes to study. 

One particularly favored class of models has been the models of Ising type, which represent the particles by states on sites or bonds of a lattice. Those intended to describe bulk amphiphilic systems have been reviewed... 

Lattice models for bulk mixtures have mostly been designed to describe features which are characteristic of systems with low amphiphile content. In particular, models for ternary oil/water/amphiphile systems are challenged to reproduce the reduction of the interfacial tension between water and oil in the presence of amphiphiles, and the existence of a structured disordered phase (a microemulsion) which coexists with an oil-rich and a water-rich phase. We recall that a structured phase is one in which correlation functions show oscillating behavior. Ordered lamellar phases have also been studied, but they are much more influenced by lattice artefacts here than in the case of the chain models. 

The example illustrates how Monte Carlo studies of lattice models can deal with questions which reach far beyond the sheer calculation of phase diagrams. The reason why our particular problem could be studied with such success Hes of course in the fact that it touches a rather fundamental aspect of the physics of amphiphilic systems—the interplay between structure and wetting behavior. In fact, the results should be universal and apply to all systems where structured, disordered phases coexist with non-struc-tured phases. It is this universal character of many issues in surfactant physics which makes these systems so attractive for theoretical physicists. 

FIG. 13 Phase diagram of a vector lattice model for a balanced ternary amphiphilic system in the temperature vs surfactant concentration plane. W -I- O denotes a region of coexistence between oil- and water-rich phases, D a disordered phase, Lj an ordered phase which consists of alternating oil, amphiphile, water, and again amphi-phile sheets, and L/r an incommensurate lamellar phase (not present in mean field calculations). The data points are based on simulations at various system sizes on an fee lattice. (From Matsen and Sullivan [182]. Copyright 1994 APS.)... 

Note that Fig. 13 still has little similarity with the experimental phase iiagram of ternary amphiphilic systems, Fig. 3b. In particular, the region of... 

The model has not been studied very intensely so far in particular, none of the features which are characteristic for amphiphilic systems have been recovered yet. However, it is close enough to the successful vector models and simple enough that it might be a promising candidate for off-lattice simulations of idealized amphiphilic systems in the future. 

The last class of models, which are widely used to describe amphiphilic systems, comprises the phenomenological models. As opposed to all the previous models, they totally ignore the fact that amphiphilic fluids are composed of particles, and describe them by a few mesoscopic quantities. In doing so, they offer the possibility of clarifying the interrelations between different behaviors on a very general level, and of studying universal characteristics which are independent of the molecular details. 

As already mentioned in the Introduction, phenomenological models for amphiphilic systems can be divided into two big classes Ginzburg-Landau models and random interface models. 

Langevin simulations of time-dependent Ginzburg-Landau models have also been performed to study other dynamical aspects of amphiphilic systems [223,224]. An attractive alternative approach is that of the Lattice-Boltzmann models, which take proper account of the hydrodynamics of the system. They have been used recently to study quenches from a disordered phase in a lamellar phase [225,226]. 

G. Gompper, M. Schick. In C. Domb, J. L. Lebowitz, eds. Phase Transitions and Critical Phenomena, Vol. 16, Self-assembling Amphiphilic Systems. London Academic Press, 1994. 

For recent reviews on experimental phase diagrams of amphiphilic systems see K. V. Schubert. Ber Bunsenges Phys Chemie 700 190-205, 1996 R. S. Strey. Curr Opin Coll Interf Sci 7 402-410, 1996. 

For recent reviews on molecular dynamics simulations of amphiphilic systems, see D. J. Tobias, K. Tu, M. L. Klein. In K. Binder, G. Ciccotti, eds. Monte Carlo and Molecular Dynamics of Condensed Matter Systems. Bologna SIF, 1996, pp. 327-344. S. Bandyapadhyay, M. Tarek, M. L. Klein. Curr Opin Coll Interf Sci 3-.242-146, 1998. 

G. Gompper, R. Holyst, M. Schick. Interfacial properties of amphiphilic systems the approach to Lifshitz points. Phys Rev A 45 3157-3160, 1991. 

U. Schwarz. Mesoskopische Modellirung amphiphiler Systeme. PhD thesis, Potsdam University, 1998. 

G. Gompper, M. Kraus. Ginzburg-Landau theory of ternary amphiphilic systems. II. Monte Carlo simulations. Phys Rev E 47 4301- 312, 1993. 

A. Ciach, A. Poniewierski. Description of the geometrical properties and topological structure in amphiphilic systems. Phys Rev E 52 596-601, 1995. 

The sizes of the phase separated HC islands in the mixed monolayers of HC and FC anionic amphiphiles polyion complexed with cationic polymers were increased by addition of a HC cationic amphiphile. The HC islands sat on the FC sea in a structure of on-top in a two story monolayer in the same way as two-component amphiphile systems. By SSPM and conventional and SNOAM fluorescence microscopies, the cationic HC amphiphile was found to dissolve preferentially into the HC islands, although it also dissolved partially in the FC sea phase. 

PIPAAm-PBMA block copolymers form a micellar structures by selfassociation of the hydrophobic PBMA segments in water, a good solvent for PlPAAm chains below the LCST but a nonsolvent for the PBMA chains. This amphiphilic system produces stable and monodispersed micelles from polymer/A-ethylacetamide (good solvent for the both polymer blocks) solutions dialyzed against water. Hydrophobic dmgs can be physically incorporated into the iimer micelle cores with PBMA chains by hydrophobic interactions between the hydrophobic segments and dmgs. 

Amphiphilic systems containing an extended rigid-rod block, rather than a more flexible linear chain, have also been shown to self-assemble into well-defined structures. Stupp s group explored a series of rod-dendron and dendron-rod-dendron hybrids containing two to three biphenyl ester moieties as a rigid rod that was capped by one or two 3,4,5-tra-alkoxy benzoate dendrons (Lecommandoux et al. 2003). The... 

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