This thesis describes theoretical results of supramolecular polymers in inhomogeneous systems. Supramolecular polymers are linear assemblies of which the monomers are joined by reversible bonds. Many types of supramolecular polymers have been synthesized in recent years. Moreover, there are numerous compounds in nature which exhibit similar behavior. Simulations of coarse-grained models of supramolecular polymers yielded new insights into the properties of supramolecular polymers in inhomogeneous systems.Self-consistent-field calculations on the quasi-chemical level of approximation were used to obtain information about adsorbed supramolecular polymers (chapters 2 and 3). In chapter 2, we describe the effect of adsorption on the mean chain length of supramolecular polymers. It is generally agreed that <N> always increases with concentration in homogeneous systems. Adsorbed supramolecular polymers exhibit qualitatively different if the adsorption energy per segment is strong enough.A very interesting non-monotonical concentration dependence of <N> of adsorbed supramolecular polymers was found. In other words: there exists a regime where <N> decreases with increasing concentration.This has never been shown before. The physical background is a change of the structure of the adsorbed layer: the adsorbed layer changes from flat to fluffy when the monomer concentration is increased.Chapter 3 also deals with adsorbing supramolecular polymers, but focuses on the adsorbed amount. This chapter describes how the model parameters influence the shape and position of the adsorption isotherms. Moreover a comparison is made with the adsorption isotherms of macromolecular polymers. It is found that supramolecular polymers adsorb at relatively high volume fractions and the filling of the surface occurs within a narrow range of concentrations. As a result, supramolecular polymers can be desorbed from the surface by diluting the surrounding solution. Macromolecular polymers usually cannot be desorbed in this manner. This has important implications for the use of supramolecular polymers as surface-active agents since the usefulness increases when they can be removed from the surface. Cleaning the surface requires little effort: diluting the surrounding solution is sufficient.Chapters 4 and 5 describe a different type of inhomogenous systems: phase-separated systems. The results of these chapters were obtained byMonte Carlosimulations. In chapter 4, we introduce the ``Helmholtz ensemble'', a formalism to calculate the compositions of two coexisting liquid phases by aMonte Carlosimulation. The general idea of this method is to use three simulation boxes (or more, if more than two coexisting phases are present). The only perturbations that are needed are molecule swaps and changes in the orientation of the molecules. Molecule displacements are only needed if a continuum model is used. Unlike the well-known Gibbs ensemble method, volume moves are unnecessary. As a consequence, an interface is formed in one of the simulation boxes. The compositions of the simulation boxes that contain homogeneous phases are used to obtain the compositions of the coexisting liquids.For a succesful simulation it is required that a flat interface is formed. Several tests are proposed to check the net curvature of the interface. If a curved interface is formed, then the simulation should be repeated with a different starting composition.The restraint that a flat interface should be formed therefore does not affect the range of applicability of the technique. The Helmholtz ensemble method is especially useful for liquids that are modeled on a lattice, since no volume moves are necessary as is the case in the (related) Gibbs ensemble method. It is shown that the Helmholtz ensemble reproduces the phase behavior of the 3D Ising problem very accurately.Supramolecular polymer systems are often polluted by monofunctional contaminants which are very difficult to remove. A new purification method aimed specifically at removing monofunctional contaminants is put forward in chapter 5. The idea is to decrease the solvent quality (e.g., by cooling) and to let the supramolecular polymer solution separate into two phases. It is to be expected that the phase that is poor in polymer has a relatively high concentration of monofunctional monomers. Therefore the solution can be purified by discarding the dilute phase.In chapter 5, the effectivity of the proposed purification method is investigated by means ofMonte Carlosimulations. The compositions of the concentrated and the dilute coexisting phases are calculated by means of the Helmholtz ensemble method. The entire phase diagram of bifunctional monomers, monofunctional molecules and solvent can be constructed. The efficiency of the several purification steps could be calculated directly from the phase diagram. Moreover, a parameterization of the phase diagram can be found. For purification purposes, the phase diagram can be described by three parameters. Only two simulations are needed to obtain these parameters. It therefore becomes feasible to predict the effectivity of the purification method for a wide range of linking energies. Extrapolations show that the vast majority of monofunctional contaminants can be removed by a single purification step if the conditions are well chosen. Several recommendations for experimental systems are also provided.
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