Directed Self-Assembly of Polarizable Ellipsoids in an External Electric Field.

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.

Depletion controlled surface deposition of uncharged colloidal spheres from stable bulk dispersions.

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.

Anisotropic magnetic particles in a magnetic field.

We characterize the structural properties of magnetic ellipsoidal hematite colloids with an aspect ratio ρ ≈ 2.3 using a combination of small-angle X-ray scattering and computer simulations. The evolution of the phase diagram with packing fraction ϕ and the strength of an applied magnetic field B is described, and the coupling between orientational order of magnetic ellipsoids and the bulk magnetic behavior of their suspension addressed. We establish quantitative structural criteria for the different phase and arrest transitions and map distinct isotropic, polarized non-nematic, and nematic phases over an extended range in the ϕ-B coordinates. We show that upon a rotational arrest of the ellipsoids around ϕ = 0.59, the bulk magnetic behavior of their suspension switches from superparamagnetic to ordered weakly ferromagnetic. If densely packed and arrested, these magnetic particles thus provide persisting remanent magnetization of the suspension. By exploring structural and magnetic properties together, we extend the often used colloid-atom analogy to the case of magnetic spins.

Tethered poly(2-isopropyl-2-oxazoline) chains: temperature effects on layer structure and interactions probed by AFM experiments and modeling.

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.

Quasi-2d fluids of dipolar superballs in an external field.

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.

Ions confined in spherical dielectric cavities modeled by a splitting field-theory.

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.

Lateral interactions in brush layers of bottle-brush polymers.

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.

Branched-linear polyion complexes investigated by Monte Carlo simulations.

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.

Tuning the smooth particle mesh Ewald sum: application on ionic solutions and dipolar fluids.

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.

Green's function for a spherical dielectric discontinuity and its application to simulation.

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.

Topological effects on capsomer-polyion co-assembly.

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.

Spreading and brush formation by end-grafted bottle-brush polymers with adsorbing side chains.

We investigate structural and thermodynamic properties of surface-grafted layers of model "bottle-brush" polymers by Monte Carlo simulation. The polymers consist of a longer main chain densely grafted with shorter side chains, of which the latter have some degree of affinity to the surface. Our focus is on the effect of the side-chain surface affinity on the brush properties, which we study in terms of compression isotherms spanning a broad range of grafting densities. For low grafting densities, side-chain adsorption causes the polymers to spread on the surface. As the grafting density is increased, the layer goes through a "pancake-to-brush" transition to form a brush with the main chains aligned perpendicular to the surface. We find that side-chain adsorption is decisive for the structure of dilute layers and in the transition region but has little influence on the properties of dense brushes. The close relation between compression and adsorption isotherms is discussed, and the implications of side-chain adsorption for the ability of the polymer to form a dense brush are investigated. This analysis suggests that side-chain surface affinity alone will not give rise to "brush of bottle-brushes" layers by adsorption of polymers from solution, in agreement with recent experimental results.

Icosahedral capsid formation by capsomers and short polyions.

Kinetical and structural aspects of the capsomer-polyion co-assembly into icosahedral viruses have been simulated by molecular dynamics using a coarse-grained model comprising cationic capsomers and short anionic polyions. Conditions were found at which the presence of polyions of a minimum length was necessary for capsomer formation. The largest yield of correctly formed capsids was obtained at which the driving force for capsid formation was relatively weak. Relatively stronger driving forces, i.e., stronger capsomer-capsomer short-range attraction and∕or stronger electrostatic interaction, lead to larger fraction of kinetically trapped structures and aberrant capsids. The intermediate formation was investigated and different evolving scenarios were found by just varying the polyion length.

Cationic poly(N-isopropylacrylamide) block copolymer adsorption investigated by dual polarization interferometry and lattice mean-field theory.

A series of cationic diblock copolymers, poly(N-isopropylacrylamide)(48)-block-poly((3-acrylamidopropyl)trimethylammonium chloride)(X), abbreviated as PNIPAAM(48)-b-PAMPTMA(+)(X) (X = 0, 6, 10, 14, and 20), has been synthesized, and their adsorption onto silicon oxynitride from aqueous solution has been investigated using dual polarization interferometry. The polymer adsorption was modeled by using a lattice mean-field theory, and a satisfactory consistency between theory and experiments was found in terms of surface excess and layer thickness. Both theory and experiments show that the adsorption is limited by steric repulsion for X < X(max) and by electrostatic interactions for X > X(max). Modeling demonstrates that significant surface charge regulation occurs due to adsorption. Both the nonionic and cationic block exhibit nonelectrostatic affinity to silicon oxynitride and thus contribute to the driving force for adsorption, and modeling is used for clarifying how changes in the nonelectrostatic affinity affects the surface excess. The segments of the nonionic and cationic blocks seem less segregated when both have a nonelectrostatic affinity for the surface compared to the case where the segments had no surface affinity. Adsorption kinetics was investigated experimentally. Two kinetic regimes were observed: the adsorption rate is initially controlled by the mass transfer rate to the surface and at higher coverage is limited by the attachment rate.

When do water-insoluble polyion-surfactant ion complex salts "redissolve" by added excess surfactant?

The redissolution of water-insoluble polyion-surfactant ion complexes by added excess of surfactant has systematically been investigated in experimental and theoretical phase equilibrium studies. A number of stoichiometric polyion-surfactant ion "complex salts" were synthesized and they consisted of akyltrimethylammonium surfactant ions of two different alkyl chain lengths (C(12)TA(+) and C(16)TA(+)) combined with homopolyions of polyacrylate of two different lengths (PA(-)(25) and PA(-)(6000)) or copolyions of acrylate and the slightly hydrophobic nonionic comonomers N-isopropylacrylamide (PA(-)-co-NIPAM) or N,N-dimethylacrylamide (PA(-)-co-DAM). The complex salts were mixed with water and excess alkyltrimethylammonium surfactant with either bromide or acetate counterions (C(n)TABr or C(n)TAAc). Factors promoting efficient redissolution were (i) very short polyions, (ii) a large fraction of NIPAM or DAM comonomers, and (iii) acetate, rather than bromide, as the surfactant counterion. Added C(12)TAAc gave an efficient redissolution of C(12)TAPA(25) but virtually no redissolution of C(12)TAPA(6000). A very efficient redissolution by added C(12)TAAc was obtained for PA(-)-co-NIPAM with 82 mol % of NIPAM. The C(12)TAPA-co-NIPAM/C(12)TAAc/H(2)O ternary phase diagram closely resembled the corresponding diagram for the much-studied pair cationic hydroxyethyl cellulose-(sodium) dodecyl sulfate. The simple Flory-Huggins theory adopted for polyelectrolyte systems successfully reproduced the main features of the experimental phase diagrams for the homopolyion systems, including the effect of the surfactant counterion. The efficient redissolution found for certain copolyion systems was explained by the formation of soluble polyion-surfactant ion complexes carrying an excess of surfactant ions through an additional hydrophobic attraction.

Adsorption of branched-linear polyethyleneimine-ethylene oxide conjugate on hydrophilic silica investigated by ellipsometry and Monte Carlo simulations.

The adsorption of and conformation adopted by a branched-linear polymer conjugate to the hydrophilic silica-aqueous solution interface have been studied by in situ null ellipsometry and Monte Carlo simulations. The conjugate is a highly branched polyethyleneimine structure with ethyleneoxide chains grafted to its primary and secondary amino groups. In situ null ellipsometry demonstrated that the polymer conjugate adsorbs to the silica surface from water and aqueous solution of 1 mM asymmetric divalent salt (calcium and magnesium chloride to emulate hard water) over a large pH range. The adsorbed amount is hardly affected by pH and large charge reversal on the negatively charged silica surface occurred at pH = 4.0, due to the adsorption of the cationic polyelectrolyte. The Monte Carlo simulations using an appropriate coarse-grained model of the polymer in solution predicted a core-shell structure with no sharp boundary between the ethyleneimine and ethyleneoxide moieties. The structure at the interface is similar to that in solution when the polymer degree of protonation is low or moderate while at high degree of protonation the strong electrostatic attraction between the ethyleneimine core and oppositely charged silica surface distorts the ethyleneoxide shell so that an "anemone"-like configuration is adopted. The adsorption of alkyl benzene sulfonic acid (LAS) to a preadsorbed polymer layer was also investigated by null ellipsometry. The adsorption data brought additional support for the existence of a strong polymer adsorption and showed the presence of a binding which was further enhanced by the decreased solvency of the surfactant in the salt solution and confirmed the surface charge reversal by the polymer adsorption at pH = 4.0.

Macroion solutions in the cell model studied by field theory and Monte Carlo simulations.

Aqueous solutions of charged spherical macroions with variable dielectric permittivity and their associated counterions are examined within the cell model using a field theory and Monte Carlo simulations. The field theory is based on separation of fields into short- and long-wavelength terms, which are subjected to different statistical-mechanical treatments. The simulations were performed by using a new, accurate, and fast algorithm for numerical evaluation of the electrostatic polarization interaction. The field theory provides counterion distributions outside a macroion in good agreement with the simulation results over the full range from weak to strong electrostatic coupling. A low-dielectric macroion leads to a displacement of the counterions away from the macroion.

Some comments and corrections regarding the calculation of electrostatic potential derivatives using the Ewald summation technique.

A review of the literature on the calculation of electrostatic potentials, fields, and field gradients in systems consisting of charges and dipoles using the Ewald summation technique is presented. Discrepancies between the previous formulas are highlighted, and an error in the derivation of the reciprocal contributions to the electrostatic field and field gradient is corrected. The new formulas for the field and field gradient are shown to exhibit a termwise identity with the ones for the electrostatic energy.

Communication: Delayed asymmetric Coulomb fission of molecular clusters: application of a dielectric liquid-drop model.

Delayed asymmetric Coulomb fission in size-selected molecular dication clusters has been recorded for the first time. Observations on (NH(3))(n)(2+) clusters show that fragmentation accompanied by charge separation can occur on a microsecond time scale, exhibits considerable asymmetry, and involves a kinetic energy release of ∼0.9 eV. The fission process has been modeled by representing the fragments as charged dielectric spheres and the calculated maximum in the electrostatic interaction energy between the fragments gives a good account of the measured kinetic energy release. A simple kinetic model shows that instrumental factors may contribute to the observation of asymmetric fragmentation.

Retardation effects breaking long-range orientational ordering in dipolar fluids.

A strongly coupled dipolar fluid confined in a sphere has been examined by Monte Carlo simulations using a modified distance-dependent pair interaction to emulate retardation effects. The effective dipole-dipole interaction and a property closely related to Kirkwood's g-factor have been analyzed for potentials with different distances at which the retardation effects became effective. The retardation effects were found to break the otherwise long-range structural ordering occurring in strongly coupled dipolar fluids.