Non-equilibrium effects of molecular motors on polymers.

We present a generic coarse-grained model to describe molecular motors acting on polymer substrates, mimicking, for example, RNA polymerase on DNA or kinesin on microtubules. The polymer is modeled as a connected chain of beads; motors are represented as freely diffusing beads which, upon encountering the substrate, bind to it through a short-ranged attractive potential. When bound, motors and polymer beads experience an equal and opposite active force, directed tangential to the polymer; this leads to motion of the motors along the polymer contour. The inclusion of explicit motors differentiates our model from other recent active polymer models. We study, by means of Langevin dynamics simulations, the effect of the motor activity on both the conformational and dynamical properties of the substrate. We find that activity leads, in addition to the expected enhancement of polymer diffusion, to an effective reduction of its persistence length. We discover that this effective "softening" is a consequence of the emergence of double-folded branches, or hairpins, and that it can be tuned by changing the number of motors or the force they generate. Finally, we investigate the effect of the motors on the probability of knot formation. Counter-intuitively our simulations reveal that, even though at equilibrium a more flexible substrate would show an increased knotting probability, motor activity leads to a marked decrease in the occurrence of knotted conformations with respect to equilibrium.

Structure formation in soft nanocolloids: liquid-drop model.

Using a model where soft nanocolloids such as spherical polymer brushes and star polymers are viewed as compressible liquid drops, we theoretically explore contact interactions between such particles. By numerically minimizing the phenomenological free energy consisting of bulk and surface terms, we find that at small deformations the drop-drop interaction is pairwise additive and described by a power law. We also propose a theory to describe the small-deformation regime, and the agreement is very good at all drop compressibilities. The large-deformation regime, which is dominated by many-body interactions, is marked by a rich phase diagram which includes the face- and body-centered-cubic, σ, A15, and simple hexagonal lattice as well as isostructural and re-entrant transitions. Most of these features are directly related to the non-convex deformation free energy emerging from many-body effects in the partial-faceting regime. The phase diagram, which depends on just two model parameters, contains many of the condensed phases observed in experiments. We also provide statistical-mechanical arguments that relate the two model parameters to the molecular architecture of the polymeric nanocolloids, chain rigidity, and solvent quality. The model represents a generic framework for the overarching features of the phase behavior of polymeric nanocolloids at high compressions.

Ultrasoft colloid-polymer mixtures: structure and phase diagram.

Binary mixtures of ultrasoft colloids and linear polymer chains were investigated by small-angle neutron scattering and liquid state theory. We show that experimental data can be described by employing recently developed effective interactions between the colloid and the polymer chains, in which both components are modeled as point particles in a coarse-grained approach, in which the monomers have been traced out. Quantitative, parameter-free agreement between experiment and theory for the pair correlations, the phase behavior and the concentration dependence of the interaction length is achieved.

Osmotic shrinkage in star/linear polymer mixtures.

Multiarm star polymers were used as model grafted colloidal particles with long hairs, to study their size variation due to osmotic forces arising from added linear homopolymers of smaller size. This is the origin of the depletion phenomenon that has been exploited in the past as a means to melt soft colloidal glasses by adding linear chains and analyzed using dynamic light scattering experiments and an effective interactions analysis yielding the depletion potential. Shrinkage is a generic phenomenon for hairy particles, which affects macroscopic properties and state transitions at high concentrations. In this work we present a small-angle neutron scattering study of star/linear polymer mixtures with different size ratios (varying the linear polymer molar mass) and confirm the depletion picture, i.e., osmotic star shrinkage. Moreover, we find that as the linear/star polymer size ratio increases for the same effective linear volume fraction (c/c* with c* the overlapping concentration), the star shrinkage is reduced whereas the onset of shrinkage appears to take place at higher linear polymer volume fractions. A theoretical description of the force balance on a star polymer in solution, accounting for the classic Flory contributions, i.e. elastic and excluded volume, as well as the osmotic force due to the linear chains, accurately predicts the experimental findings of reduced star size as a function of linear polymer concentration. This is done in a parameter-free fashion, in which the size of the cavity created by the star, and from which the chains are excluded, is related to the radius of the former from first principles.

Asymmetric caging in soft colloidal mixtures.

The long-standing observations that different amorphous materials exhibit a pronounced enhancement of viscosity and eventually vitrify on compression or cooling continue to fascinate and challenge scientists, on the ground of their physical origin and practical implications. Glass formation is a generic phenomenon, observed in physically quite distinct systems that encompass hard and soft particles. It is believed that a common underlying scenario, namely cage formation, drives dynamical arrest, especially at high concentrations. Here, we identify a novel, asymmetric glassy state in soft colloidal mixtures, which is characterized by strongly anisotropically distorted cages, bearing similarities to those of hard-sphere glasses under shear. The anisotropy is induced by the presence of soft additives. This phenomenon seems to be generic to soft colloids and its origins lie in the penetrability of the constituent particles. The resulting phase diagram for mixtures of soft particles is clearly distinct from that of hard-sphere mixtures and brings forward a rich variety of vitrified states that delineate an ergodic lake in the parameter space spanned by the size ratio between the two components and by the concentration of the additives. Thus, a new route opens for the rational design of soft particles with desired tunable rheological properties.

Structure, phase behavior, and inhomogeneous fluid properties of binary dendrimer mixtures.

The effective pair potentials between different kinds of dendrimers in solution can be well approximated by appropriate Gaussian functions. We find that in binary dendrimer mixtures the range and strength of the effective interactions depend strongly upon the specific dendrimer architecture. We consider two different types of dendrimer mixtures, employing the Gaussian effective pair potentials, to determine the bulk fluid structure and phase behavior. Using a simple mean field density functional theory (DFT) we find good agreement between theory and simulation results for the bulk fluid structure. Depending on the mixture, we find bulk fluid-fluid phase separation (macrophase separation) or microphase separation, i.e., a transition to a state characterized by undamped periodic concentration fluctuations. We also determine the inhomogeneous fluid structure for confinement in spherical cavities. Again, we find good agreement between the DFT and simulation results. For the dendrimer mixture exhibiting microphase separation, we observe a rather striking pattern formation under confinement.

Bulk and interfacial properties in colloid-polymer mixtures.

Large-scale Monte Carlo simulations of a phase-separating colloid-polymer mixture are performed and compared to recent experiments. The approach is based on effective interaction potentials in which the central monomers of self-avoiding polymer chains are used as effective coordinates. By incorporating polymer nonideality together with soft colloid-polymer repulsion, the predicted binodal is in excellent agreement with recent experiments. In addition, the interfacial tension as well as the capillary length are in quantitative agreement with experimental results obtained at a number of points in the phase-coexistence region, without the use of any fit parameters.

Soft colloids driven and sheared by traveling wave fields.

We study the dynamics of soft colloids interacting via a Gaussian pair potential in an external moving potential which is periodic in the spatial coordinate of the direction of motion. Both dynamical density functional theory and Brownian dynamics computer simulations are used to predict the steady-state density profiles. Two different situations are investigated: the first corresponds to a light wave that travels with a constant velocity v through the quiescent solvent containing the colloidal suspension. The second setup consists of two parallel repulsive walls with a periodic topographical substructure. One of the walls is at rest relative to the solvent while the other is in motion, inducing a shearing of the suspension. In the first case, we find that the amplitude of the steady-state density behaves nonmonotonically with the traveling speed v of the wave if the shape of the wave contains an edge: for increasing v , it first grows and then decreases. In the second setup we show that a strongly confined suspension induces a shear resistance which is a nonmonotonic function of the wall velocity. These effects are verifiable in real-space experiments on colloidal suspensions exposed to external laser-optical fields. In both situations, the dynamical density functional theory is in good agreement with the Brownian dynamics simulation data.

Anisotropic mean-square displacements in two-dimensional colloidal crystals of tilted dipoles.

Superparamagnetic colloidal particles confined to a flat horizontal air-water interface in an external magnetic field, which is tilted relative to the interface, form anisotropic two-dimensional crystals resulting from their mutual dipole-dipole interactions. Using real-space experiments and harmonic lattice theory we explore the mean-square displacements of the particles in the directions parallel and perpendicular to the in-plane component of the external magnetic field as a function of the tilt angle. We find that the anisotropy of the mean-square displacement behaves nonmonotonically as a function of the tilt angle and does not correlate with the structural anisotropy of the crystal.

Ionic microgels as model systems for colloids with an ultrasoft electrosteric repulsion: structure and thermodynamics.

We present a theoretical analysis of the structural properties and phase behavior of spherical, loosely cross-linked ionic microgels that possess a low monomer concentration. The analysis is based on the recently derived effective interaction potential between such particles [A. R. Denton, Phys. Rev. E 67, 011804 (2003)]. By employing standard tools from the theory of the liquid state, we quantitatively analyze the pair correlations in the fluid and find anomalous behavior above the overlap concentration, similar to the cases of star-branched neutral and charged polymers. We also employ an evolutionary algorithm in order to predict the crystalline phases of the system without any a priori assumptions regarding their symmetry class. A very rich phase diagram is obtained, featuring two reentrant melting transitions and a number of unusual crystal structures. At high densities, both the Hansen-Verlet freezing criterion [J.-P. Hansen and L. Verlet, Phys. Rev. 184, 151 (1969)] and the Lindemann melting criterion [F. A. Lindemann, Phys. Z. 11, 609 (1910)] lose their validity. The topology of the phase diagram is altered when the steric interactions between the polymer segments become strong enough, in which case the lower-density reentrant melting disappears and the region of stability of the fluid is split into two disconnected domains, separated by intervening fcc and bcc regions.

Tailoring the flow of soft glasses by soft additives.

We examine the vitrification and melting of asymmetric star polymer mixtures by combining rheological measurements with mode coupling theory. We identify two types of glassy states, a single glass, in which the small component is fluid in the glassy matrix of the big one, and a double glass, in which both components are vitrified. Addition of small-star polymers leads to melting of both glasses, and the melting curve has a nonmonotonic dependence on the star-star size ratio. The phenomenon opens new ways for externally steering the rheological behavior of soft matter systems.

Soft effective interactions between weakly charged polyelectrolyte chains.

We apply extensive molecular dynamics simulations and analytical considerations in order to study the conformations and the effective interactions between weakly charged, flexible polyelectrolyte chains in salt-free conditions. We focus on charging fractions lying below 20%, for which case there is no Manning condensation of counterions and the latter can be thus partitioned in two states: those that are trapped within the region of the flexible chain and the ones that are free in the solution. We examine the partition of counterions in these two states, the chain sizes and the monomer distributions for various chain lengths, finding that the monomer density follows a Gaussian shape. We calculate the effective interaction between the centers of mass of two interacting chains, under the assumption that the chains can be modeled as two overlapping Gaussian charge profiles. The analytical calculations are compared with measurements from molecular dynamics simulations. Good quantitative agreement is found for charging fractions below 10%, where the chains assume coil-like configurations, whereas deviations develop for charge fraction of 20%, in which case a conformational transition of the chain towards a rodlike configuration starts to take place.

Tunable effective interactions between dendritic macromolecules.

We employ extensive Monte Carlo and molecular-dynamics simulations to investigate the effective interactions between the centers of mass of dendritic macromolecules of variable flexibility and generation number. Two different models for the connectivity and steric interactions between the monomers are employed, the first one being purely entropic in nature and the second explicitly involving energetic interactions. We find that the effective potentials have a generic Gaussian shape, whose range and strength can be tuned via modifications in the generation number and flexibility of the spacers. We supplement our simulation analysis by a density-functional approach in which the connectivity between the monomers is approximated by an external confining potential that holds the monomer beads together. Using a simple density functional for the interactions between the monomers, we find semiquantitative agreement between theory and simulation. The implications of our findings for the interpretation of scattering data from concentrated dendrimer solutions are also discussed.

Is there a reentrant glass in binary mixtures?

By employing computer simulations for a model binary mixture, we show that a reentrant glass transition upon adding a second component occurs only if the ratio alpha of the short-time mobilities between the glass-forming component and the additive is sufficiently small. For alpha approximately 1, there is no reentrant glass, even if the size asymmetry between the two components is large, in accordance with the two-component mode-coupling theory. For alpha<<1, on the other hand, the reentrant glass is observed and reproduced only by an effective one-component mode-coupling theory.

Phase behavior of ionic microgels.

We employ effective interaction potentials between spherical polyelectrolyte microgels in order to investigate theoretically the structure, thermodynamics, and phase behavior of ionic microgel solutions. Combining a genetic algorithm with accurate free energy calculations we are able to perform an unrestricted search of candidate crystal structures. Hexagonal, body-centered orthogonal, and trigonal crystals are found to be stable at high concentrations and charges of the microgels, accompanied by reentrant melting behavior and fluid-fcc-bcc transitions below the overlap concentration.

Depletion forces in nonequilibrium.

The concept of effective depletion forces between two fixed big colloidal particles in a bath of small particles is generalized to a nonequilibrium situation where the bath of small Brownian particles is flowing around the big particles with a prescribed velocity. In striking contrast to the equilibrium case, the nonequilibrium forces violate Newton's third law; they are nonconservative and strongly anisotropic, featuring both strong attractive and repulsive domains.

Structural arrest in dense star-polymer solutions.

The dynamics of star polymers is investigated via extensive molecular and Brownian dynamics simulations for a large range of functionality f and packing fraction eta. The calculated isodiffusivity curves display both minima and maxima as a function of eta and minima as a function of f. Simulation results are compared with theoretical predictions based on different approximations for the structure factor. In particular, the ideal glass transition line predicted by mode-coupling theory is shown to exactly track the isodiffusivity curves, offering a theoretical understanding for the observation of disordered arrested states in star-polymer solutions.

Azimuthal frustration and bundling in columnar DNA aggregates.

The interaction between two stiff parallel DNA molecules is discussed using linear Debye-Hückel screening theory with and without inclusion of the dielectric discontinuity at the DNA surface, taking into account the helical symmetry of DNA. The pair potential furthermore includes the amount and distribution of counterions adsorbed on the DNA surface. The interaction does not only depend on the interaxial separation of two DNA molecules, but also on their azimuthal orientation. The optimal mutual azimuthal angle is a function of the DNA-DNA interaxial separation, which leads to azimuthal frustrations in an aggregate. On the basis of the pair potential, the positional and orientational order in columnar B-DNA assemblies in solution is investigated. Phase diagrams are calculated using lattice sums supplemented with the entropic contributions of the counterions in solution. A variety of positionally and azimuthally ordered phases and bundling transitions is predicted, which strongly depend on the counterion adsorption patterns.

Crystal structures of two-dimensional magnetic colloids in tilted external magnetic fields.

The stability of different crystal lattices of two-dimensional superparamagnetic suspensions that are confined to a planar liquid-gas interface and exposed to a tilted external magnetic field is studied theoretically by lattice sum minimizations. The magnetic field induces magnetic dipoles onto the colloidal particles along its direction, whose strength can be controlled by the amplitude of the external field. The mutual interaction between the colloids is governed by dipole-dipole forces and a short-ranged repulsion having its physical origin at the presence of the colloidal cores. If the direction of the magnetic field is perpendicular to the liquid-gas interface, there is a purely repulsive interaction leading to stable triangular crystals. By tilting the external field, the interaction becomes anisotropic and a mutual attraction appears upon a threshold tilt angle. We have calculated the full phase diagram at zero temperature varying the tilt angle, the colloidal density, and the strength of the magnetic field. Apart from the triangular lattice we find a variety of stable crystal lattices including rectangular, oblique, chainlike oblique, and rhombic structures. We also present the accurate derivation of the Hamiltonian of two polarizable particles of finite arbitrary geometries in external magnetic and electric fields.

Polymer-mediated melting in ultrasoft colloidal gels.

Star polymers with a high number of arms, f=263, become kinetically trapped when dispersed in an athermal solvent at concentrations above the overlapping one, forming physical gels. We show that the addition of linear chains at different concentrations and molecular weights reduces the modulus of the gel, eventually melting it. We explain this linear polymer-induced gel-liquid transition in terms of effective interactions and star depletion. In the limit of very high linear-chain molecular weight a "reentrant gelation" is detected and attributed to bridging flocculation, analogous to that observed in colloidal dispersions.