This chapter presents several theories for polymer-surfactant complexation, covering the range from simple equilibrium models to detailed mean-field lattice approaches and computer-demanding simulations of molecular models. It describes and compares one polymer-centered and one surfactant-centered approach to the category 1 complexation of oppositely charged polymer and surfactant. A striking feature of many polymer/surfactant pairs is their complexation in dilute aqueous solution, The standard evidence for such complexation is in terms of surfactant binding isotherms, obtained by methods such as potentiometry or surfactant self diffusion. The very notion of a binding isotherm seems to suggest what one may call a ''polymer-centered'' viewpoint, where the polymer molecule is thought to contain certain sites that may bind surfactant molecules. The polymer-surfactant interaction constitutes the strong perturbation to the bulk surfactant solution, which is regarded merely as a reservoir of binding ligands.

Systems whose magnetic response can be finely tuned using control parameters, such as temperature and external magnetic field strength, are extremely desirable, functional materials. Magnetic nanoparticles, in particular suspensions thereof, offer opportunities for this controllability to be realised. Cube-like particles are particularly mono-disperse examples that, together with their favourable packing behaviour, make them of significant interest for study. Using a combination of analytical calculations and molecular dynamics we have studied the self-assembly of permanently magnetised dipolar superballs. The superball shape parameter was varied in order to interpolate the region between the already well-studied sphere system and that of the recently investigated cube. Our findings show that as a superball particle becomes more cubic the chain to ring transition, observed in the ground state of spherical particles, occurs at an increasingly larger cluster size. This effect is mitigated, however, by the appearance of a competing configuration; asymmetric rings, a conformation that we show superballs can readily adopt.

Complexation between multiple weak polyacid chains and a positively charged spherical nanoparticle has been studied by means of Monte Carlo simulations. By considering titration curves, it is found that variations in the polyacid chain length and concentration and the polyacid-to-nanoparticle mixing ratio influence the ionization of the system. For larger mixing ratios and longer chain lengths, the titration curves start to exhibit complex shapes with multiple inflection points. We also find that in some cases it is possible to differentiate between free and adsorbed chains, based on the charge probability distribution and the probability distribution of the gyration radius. Furthermore, the adsorption of weak polyacids has been compared with that of strong polyacids, and the fraction of adsorbed monomers is found to be slightly larger for the strong polyacids. In addition, the fraction of adsorbed chains can be much lower for the weak polyacids due to their ability to concentrate charge in few chains.

The interplay between shape anisotropy and directed long-range interactions enables the self-assembly of complex colloidal structures. As a recent highlight, ellipsoidal particles polarized in an external electric field were observed to associate into well-defined tubular structures. In this study, we systematically investigate such directed self-assembly using Monte Carlo simulations of a two point-charge model of polarizable prolate ellipsoids. In spite of its simplicity and computational efficiency, we demonstrate that the model is capable of capturing the complex structures observed in experiments on ellipsoidal colloids at low volume fractions. We show that, at sufficiently high electric field strength, the anisotropy in shape and electrostatic interactions causes a transition from three-dimensional crystal structures observed at low aspect ratios to two-dimensional sheets and tubes at higher aspect ratios. Our work thus illustrates the rich self-assembly behavior accessible when exploiting' the interplay between competing long- and short-range anisotropic interactions in colloidal systems.

The competition between surface adsorption and bulk aggregation was investigated for silica colloids dispersed in cyclohexane in contact with hydrophobized silica substrates. Central to this study is that the colloids and surfaces have the same material and surface properties. Colloid-colloid and colloid-surface interactions were controlled by addition of polymers providing depletion interaction. Bulk instability was determined by turbidity and viscosity measurements and surface adsorption by ellipsometry measurements. At increasing polymer concentration, strong surface adsorption occurred at polymer concentrations below that required for bulk phase separation. Complementary Monte Carlo simulations with the use of a new weak depletion theory support quantitatively the experimental observation of the existence of an interval of interaction strength at which aggregation in bulk is negligible while surface adsorption is substantial.

Dispersions of magnetic ellipsoidal colloids were investigated to study the effect of a magnetic field on their phase behaviour.

An adaptive algorithm optimizing single-particle translational displacement parameters in Metropolis Monte Carlo simulations is presented. The optimization is based on maximizing the mean square displacement of a trial move. It is shown that a large mean square displacement is strongly correlated with a high precision of average potential energy. The method is here demonstrated on model systems representing a Lennard-Jones fluid and a dilute polymer solution at poor solvent conditions. Our adaptive algorithm removes the need to provide values of displacement parameters in simulations, and it is easily extendable to optimize parameters of other types of trial moves.

Thermoresponsive polymer layers on silica surfaces have been obtained by utilizing electrostatically driven adsorption of a cationic-nonionic diblock copolymer. The cationic block provides strong anchoring to the surface for the nonionic block of poly(2-isopropyl-2-oxazoline), referred to as PIPOZ. The PIPOZ chain interacts favorably with water at low temperatures, but above 46 °C aqueous solutions of PIPOZ phase separate as water becomes a poor solvent for the polymer. We explore how a change in solvent condition affects interactions between such adsorbed layers and report temperature effects on both normal forces and friction forces. To gain further insight, we utilize self-consistent lattice mean-field theory to follow how changes in temperature affect the polymer segment density distributions and to calculate surface force curves. We find that with worsening of the solvent condition an attraction develops between the adsorbed PIPOZ layers, and this observation is in good agreement with predictions of the mean-field theory. The modeling also demonstrates that the segment density profile and the degree of chain interpenetration under a given load between two PIPOZ-coated surfaces rise significantly with increasing temperature.

Structural behavior of complexes formed by a charged and branched copolymer and an oppositely charged and linear polyion was examined by Monte Carlo simulations employing a coarse-grained bead-spring model. The fractional bead charge and the branching density were systematically varied; the former between 0e and 1e and the latter such that both the comb-polymer and the bottle-brush limits were included. The number of beads of the main chain of the branched copolymer and of the linear polyion was always kept constant and equal, and a single side-chain length was used. Our analysis involved characterization of the complex as well as investigation of size, shape, and flexibility of the charged moieties. An interplay between Coulomb interaction and side-chain repulsion governed the structure of the polyion complex. At strong Coulomb interaction, the complexes underwent a gradual transition from a globular structure at low branching density to an extended one at high branching density. As the electrostatic coupling was decreased, the transition was smoothened and shifted to lower branching density, and, eventually, a behavior similar to that found for neutral branched polymer was observed. Structural analogies and dissimilarities with uncharged branched polymers in poor solutions are discussed.

The properties of ions confined within spherical dielectric cavities are examined by a splitting field-theory and Monte Carlo simulations. Three types of cavities are considered: one possessing a uniform surface charge density, one with a uniform volume charge density, and one containing mobile ions. In all cases, mobile counterions are present within the dielectric sphere. The splitting theory is based on dividing the electrostatic interaction into long- and short-wavelength contributions and applying different approximations on the two contributions. The splitting theory works well for the case where the dielectric constant of the confining sphere is equal to or less than that of the medium external to the sphere. Nevertheless, by extending the theory with a virial expansion, the predictions are improved. However, when the dielectric constant of the confining sphere is greater than that of the medium outside the sphere, the splitting theory performs poorly, only qualitatively agreeing with the simulation data. In this case, the strong-coupling expansion does not seem to work well, and a modified mean-field theory where the counterions interact directly with only their own image charge gives improved predictions. The splitting theory works best for the system with a uniform surface charge density and worst for the system with a uniform volume charge density. Increasing the number of ions within the sphere, at a fixed radius, tends to increase the ion density near the surface of the sphere and leads to a depletion region in the sphere interior; however, varying the ion number does not lead to any qualitative changes in the performance of the splitting theory.

The modular software MOLSIM for all‐atom molecular and coarse‐grained simulations is presented with focus on the underlying concepts used. The software possesses four unique features: (1) it is an integrated software for molecular dynamic, Monte Carlo, and Brownian dynamics simulations; (2) simulated objects are constructed in a hierarchical fashion representing atoms, rigid molecules and colloids, flexible chains, hierarchical polymers, and cross‐linked networks; (3) long‐range interactions involving charges, dipoles and/or anisotropic dipole polarizabilities are handled either with the standard Ewald sum, the smooth particle mesh Ewald sum, or the reaction‐field technique; (4) statistical uncertainties are provided for all calculated observables. In addition, MOLSIM supports various statistical ensembles, and several types of simulation cells and boundary conditions are available. Intermolecular interactions comprise tabulated pairwise potentials for speed and uniformity and many‐body interactions involve anisotropic polarizabilities. Intramolecular interactions include bond, angle, and crosslink potentials. A very large set of analyses of static and dynamic properties is provided. The capability of MOLSIM can be extended by user‐providing routines controlling, for example, start conditions, intermolecular potentials, and analyses. An extensive set of case studies in the field of soft matter is presented covering colloids, polymers, and crosslinked networks. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

The structure of quasi-2d solutions of dipolar superballs in the fluid state has been determined by Metropolis Monte Carlos simulations in the absence and the presence of an external field. Superballs are 3d objects characterized by a one shape parameter. Here, superballs resembling cubes, but possessing rounded edges, have been used. Examination has been made for several magnitudes of the dipole moment in three different dipole directions. In the limit of a cube, the directions become (i) the center of mass - the center of a face (001) direction, (ii) the center of mass -the center of an edge (011) direction, and (iii) the center of mass -the corner (111) direction. At a small dipole moment, the superballs are translationally and orientationally disordered, and the dipoles become partially orientationally ordered in the presence of the field parallel to the plane of the superballs. At a large dipole moment, chains of superballs are formed, and the chains become parallel in the presence of the field. The chains remain separated for the dipole in the 001-direction and form bundles for the 011- and 111-directions. The different structures obtained for the different dipole directions are interpreted in terms of how compatible the dipole-dipole interaction is with the cube-cube interaction at short separation for the different directions of the dipole moment. Hence, the structural richness arises from an interplay of the different symmetries of a cube and of the field of a dipole.

On the basis of a T = 1 icosahedral capsid model, the capsomer-polyion co-assembly process has been investigated by molecular dynamics simulations using capsomers with different net charge and charge distribution as well as linear, branched, and hyper-branched polyions. The assembly process was characterized in terms of the time-dependent cluster size probabilities, averaged cluster size, encapsulation efficiency, and polyion extension. The kinetics of the capsid formation displayed a two-step process. The first one comprised adsorption of capsomers on the polyion, driven by their electrostatic attraction, whereas the second one involved a relocation and/or reorientation of adsorbed capsomers, which rate is reduced upon increasing electrostatic interaction. We found that increased polyion branching facilitated a more rapid encapsulation process towards a higher yield. Moreover, the hyper-branched polyions were entirely encapsulated at all polyion-capsid charge ratios considered.

We used isotension-ensemble Monte Carlo simulations to study the properties of brush layers of bottle-brush polymers under lateral compression. The polymers were represented by a freely jointed hard-bead model with one side chain grafted to each bead of the main chain, and we considered variations in side-chain length and bead size. Brush properties, including brush height and surface pressure, were analyzed in the context of a generalized box model. The surface pressure was found to have a steeper dependence on the grafting density than predicted by classical theories of polymer brushes. This discrepancy could be traced to the equation of state of the polymer fluid composing the brush, which was found to be more reminiscent of the concentrated regime than of the semidilute conditions normally expected in polymer brushes. The conformational properties of individual polymer molecules were found to be insensitive to lateral compression; in particular, the side-chain end-to-end distance remained essentially constant.

Multigraft polymers comprise a subclass of branched polymers where more than one side chain is attached to each node (branching point) of the main chain. We have investigated structural properties of single multigraft polymers under good solvent conditions by Monte Carlo simulations, employing a flexible bead-spring model. Beside the grafting density, denoting the linear density of grafted side chains, we have introduced the concept of branching density, denoting the linear density of nodes. At high branching density, both the branching density and the branching multiplicity controlled the structure of the side chains, whereas at lower branching density only the branching multiplicity influenced the side-chain structure. The spatial extension of the main chain and side chains as a function of side-chain length and grafting density was analyzed using scaling formalism. The dependence of the main-chain extension on side-chain length, branching density, and branching multiplicity could be collapsed on a universal curve upon relevant rescaling. Multigraft polymers with equal number of side-chain beads but unequal numbers and lengths of side chains displayed unconventional bending properties. Few and long side chains gave rise to a still relative low locally stiffness but considerable long-range rigidity, whereas more numerous and shorter side chains lead to a higher local stiffness but to a smaller long-range rigidity.

Numerical properties of the smooth particle mesh Ewald (SPME) sum [U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen, J. Chem. Phys. 103, 8577 (1995)] have been investigated by molecular dynamics simulation of ionic solutions and dipolar fluids. Scaling dependence of execution time on the number of particles at optimal performance have been determined and compared with the corresponding data of the standard Ewald (SE) sum. For both types of systems and over the range from N = 10(3) to 10(5) particles, the SPME sum displays a sub O(N ln N) complexity, whereas the SE sum possesses an O(N(3/2)) complexity. The breakeven of the simulation times appears at O(10(3)) particles, and the SPME sum is ≈20 times faster than the SE sum at 10(5) particles. Furthermore, energy truncation error and the energy and force execution time of the reciprocal space evaluation as function of the number of particles and the convergence parameters of the SPME sum have been determined for both types of systems containing up to 10(6) particles.

Current theoretical attempts to understand the reversible formation of stable microtubules and virus shells are generally based on shape-specific building blocks or monomers, where the local curvature of the resulting structure is explicitly built-in via the monomer geometry. Here we demonstrate that even simple ellipsoidal colloids can reversibly self-assemble into regular tubular structures when subjected to an alternating electric field. Supported by model calculations, we discuss the combined effects of anisotropic shape and field-induced dipolar interactions on the reversible formation of self-assembled structures. Our observations show that the formation of tubular structures through self-assembly requires much less geometrical and interaction specificity than previously thought, and advance our current understanding of the minimal requirements for self-assembly into regular virus-like structures.

Complexes formed by one charged and branched copolymer with an oppositely charged and linear polyion have been investigated by Monte Carlo simulations. A coarse-grained description has been used, in which the main chain of the branched polyion and the linear polyion possess the same absolute charge and charge density. The spatial extension and other structural properties, such as bond-angle orientational correlation function, asphericity, and scaling analysis of formed complexes, at varying branching density and side-chain length of the branched polyion, have been explored. In particular, the balance between cohesive Coulomb attraction and side-chain repulsions resulted in two main structures of a polyion complex. These structures are (i) a globular polyion core surrounded by side chains appearing at low branching density and (ii) an extended polyion core with side chains still being expelled at high branching density. The globule-to-extended transition occurred at a crossover branching density being practically independent of the side chain length.

We present rapidly convergent expressions for the Green's function of the Poisson equation for spherically symmetric systems where the dielectric constant varies discontinuously in the radial direction. These expressions are used in Monte Carlo simulations of various electrolyte systems, and their efficiency is assessed. With only the leading term of the expansion included, a precision of the polarization energy of 0.01 kJ mol(-1) or better was achieved, which is smaller than the statistical uncertainty of a typical simulation. The inclusion of the dielectric inhomogeneity leads to a 2.5-fold increase of the computational effort, which is modest for this type of model. The simulations are performed on six types of systems having either (i) a uniform surface charge distribution, (ii) a uniform volume charge distribution, or (iii) mobile ions, which were neutralized by mobile counterions. The ion density distributions are investigated for different dielectric conditions. These spatial distributions are discussed in terms of the importance of (i) the direct mean-field Coulomb interaction, (ii) the surface charge polarization at the dielectric discontinuity, and/or (iii) the change in the attractive Coulomb correlations.