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We consider polymer brushes in poor solvent that are grafted onto planar substrates and onto the internal and external surfaces of a cylinder using molecular dynamics simulation, self-consistent field (SCF), and mean-field theory. We derive a unified expression for the mean field free energy for the three geometrical classes. While for low grafting densities, the effect of chain elasticity can be neglected in poor solvent conditions, it becomes relevant at higher grafting densities and, in particular, for concave geometries. Based on the analysis of the end monomer distribution, we introduce an analytical term that describes the elasticity as a function of grafting density. The accuracy of the model is validated with molecular dynamics simulations as well as SCF computations and shown to yield precise values for the layer thickness over a wide range of system parameters. We further apply this model to analyze the gating behavior of switchable brushes inside nanochannels. [ABSTRACT FROM AUTHOR]

Using a variant of the Bond Fluctuation Model which improves its parallel efficiency in particular running on graphic cards we perform large scale simulations of polymer brushes in poor explicit solvent. Grafting density, solvent quality, and chain length are varied. Different morphological structures in particular octopus micelles are observed for low grafting densities. We reconsider the theoretical model for octopus micelles proposed by Williams using scaling arguments with the relevant scaling variable being a c, and with the characteristic grafting density given by ac - N-4/3. We find that octopus micelles only grow laterally, but not in height and we propose an extension of the model by assuming a cylindrical shape instead of a spherical geometry for the micelle-core. We show that the scaling variable ac can be applied to master plots for the averaged height of the brush, the size of the micelles, and the number of chains per micelle. The exponents in the corresponding power law relations for the grafting density and chain length are in agreement with the model for flat cylindrical micelles. We also investigate the surface roughness and find that polymer brushes in explicit poor solvent at grafting densities higher than the stretching transition are flat and surface rippling can only be observed close to the stretching transition. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations are applied to investigate salt-free planar polyelectrolyte brushes under poor solvent conditions. Starting above the -point with a homogeneous brush and then gradually reducing the temperature, the polymers initially display a lateral structure formation, forming vertical bundles of chains. A further reduction of the temperature (or solvent quality) leads to a vertical collapse of the brush. By varying the size and selectivity of the counterions, we show that lateral structure formation persists and therefore demonstrate that the entropy of counterions being the dominant factor for the formation of the bundle phase. By applying an external compression force on the brush we calculate the minimal work done on the polymer phase only and prove that the entropy gain of counterions in the bundle state, as compared to the homogeneously collapsed state at the same temperature, is responsible for the lateral microphase segregation. As a consequence, the observed lateral structure formation has to be regarded universal for osmotic polymer brushes below the -point. [ABSTRACT FROM AUTHOR]

We study the dynamics of tethered chains of length N on adsorbing surfaces, considering the dilute case; for this we use the bond fluctuation model and scaling concepts. In particular, we focus on the mean-square displacement of single monomers and of the center of mass of the chains. The characteristic time τ of the fluctuations of a free chain in a good solvent grows as τ∼Na, where the coefficient a obeys a=2ν+1. We show that the same coefficient also holds at the critical point of adsorption. At intermediate time scales single monomers show subdiffusive behavior; this concurs with the behavior calculated from scaling arguments based on the dynamical exponent a. In the adsorbed state τ⊥, the time scale for the relaxation in the direction perpendicular to the surface, becomes independent of N; τ⊥ is then the relaxation time of an adsorption blob. In the direction parallel to the surface the motion is similar to that of a two-dimensional chain and is controlled by a time scale given by τ∥∼N2ν2+1L-2Δν/ν, where ν2 is the Flory exponent in two dimensions, ν is the Flory exponent in three dimensions, and Δν=ν2-ν. For the motion parallel to the surface we find dynamical scaling over a range of about four decades in time. [ABSTRACT FROM AUTHOR]

We present extensive Monte Carlo simulations of tethered chains of length N on adsorbing surfaces, considering the dilute case in good solvents, and analyze our results using scaling arguments. We focus on the mean number M of chain contacts with the adsorbing wall, on the chain’s extension (the radius of gyration) perpendicular and parallel to the adsorbing surface, on the probability distribution of the free end and on the density profile for all monomers. At the critical adsorption strength εc one has Mc∼N[lowercase_phi_synonym], and we find (using the above results) as best candidate [lowercase_phi_synonym] to equal 0.59. However, slight changes in the estimation of εc lead to large deviations in the resulting [lowercase_phi_synonym]; this might be a possible reason for the difference in the [lowercase_phi_synonym] values reported in the literature. We also investigate the dynamical scaling behavior at εc, by focusing on the end-to-end correlation function and on the correlation function of monomers adsorbed at the wall. We find that at εc the dynamic scaling exponent a (which describes the relaxation time of the chain as a function of N) is the same as that of free chains. Furthermore, we find that for tethered chains the modes perpendicular to the surface relax quicker than those parallel to it, which may be seen as a splitting in the relaxation spectrum. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A theoretical concept for phase segregation of polymers in the presence of multicomponent selective solvents is presented. Phase separation is caused by nonspecific attractive interactions between the polymers and a smaller component in the solution instead of repulsion between monomers and solvent molecules. We call the component that adsorbs on the polymers and thus causes condensation "gluonic". It is shown that a discontinuous phase transition from a diluted or semidiluted state to the condensed state takes place if the fraction of the gluonic component is increased. The location of the phase coexistence can be shifted by influencing the binding efficiency of the gluonic component. This can be achieved by adding a regulator component to the solution. The latter is assumed to bind specifically to the polymer and interferes with the gluonic component. In this way a switching of the state of the polymer from dissolved to condensed can be achieved without changing the chemical properties of the system. Applications of this model range from co-nonsolvency in synthetic polymers, over polymer-nanoparticle systems, to biological systems such as the formation of protein-RNA droplets. [ABSTRACT FROM AUTHOR]

We study the properties of a polymer brush exposed to a mixture of two solvents where one component, called the co-nonsolvent (CNS), has a stronger preference with respect to the polymer. The concept of preferential adsorption of CNS onto the polymer, as recently proposed by Mukherhi, Kremer, and Marques [Nat. Commun. 2014, 5, 4882], is combined with the mean-field Alexander-de Gennes approach for the polymer brush. The key assumption is that CNS can form bridges between two monomers which is associated with a further gain in free energy, thus leading to an effective monomer-monomer attraction. The adsorption equilibrium of CNS at a given value of the monomer concentration results in a concentration-dependent χ-function for the polymer brush which describes the effective interactions between the monomers in the mixed solvent. This in turn can lead to a discontinuous collapse transition and to a corresponding reentry transition at higher CNS concentrations. The problem can be analytically treated for a minimal model where the increase of self-volume of the monomers due to adsorption of CNS is neglected. In this case the collapse and the reswelling transition have the same signature. For low brush densities in the noncollapsed state we give an analytic approximation for the spinodal of the collapse. This also allows to define two scaling variables instead of the three control parameters which are the grafting density, the CNS-monomer selectivity, and the volume faction of CNS. The proposed effective free energy contribution resulting from the CNS adsorption equilibrium can be transferred to other systems such as to gels or dendrimers. [ABSTRACT FROM AUTHOR]

We use the bond fluctuation model with explicit solvent to study single polymer chains under poor solvent conditions. Static and dynamic properties of the bond fluctuation model with explicit solvent are compared with the implicit solvent model, and the Θ-temperatures are determined for both solvent models. We show that even in the very poor solvent regime, dynamics is not frozen for the explicit solvent model. We investigate some aspects of the structure of a single collapsed globule and show that rather large chain lengths are necessary to reach the scaling regime of a dense sphere. The force-extension curve of a single polymer chain under poor solvent conditions in the fixed end-to-end distance ensemble is analyzed. We find that the transition of the tadpole conformation to the stretched chain conformation is rather smooth because of fluctuation effects, which is in agreement with recent experimental results. [ABSTRACT FROM AUTHOR]

We reconsider the isothermal equation of state (EOS) for linear homopolymers in good solvents, p=p(c,T), which relates the osmotic pressure p of polymers with the bulk concentration c and the temperature T. The classical scaling theory predicts the EOS in dilute and semidilute regimes. We suggest a generalized EOS that extends the universal behavior of polymer solutions up to the highly concentrated state and confirm it by molecular dynamics simulations and available experimental data. Our conjecture implies that properties of polymer chains dominate the EOS in the presence of many-body interactions. Our theoretical approach is based on a viral expansion in terms of concentration blobs leading to a superposition of two power laws in the regime of concentrated solutions. [ABSTRACT FROM AUTHOR]

Cross-linking a single polymer chain with itself leads to soft nanoparticles with well-defined properties. We study such single-chain nanoparticles (SCNP) obtained by cross-linking in good and in poor solvents using Monte Carlo simulations and theoretical models. We show that SCNP obtained by cross-linking in poor solvents preserve their shape during swelling in good solvents only if the precursor chain is very long. In this case the Flory-Rehner model describes the swelling of SCNP. Shorter chains and SCNPs cross-linked in good solvent generate noncompact structures. Here we obtain a good theoretical description of the simulated swelling properties using a mean-field model by taking into account the cross-linking topology using the connectivity matrix of the cross-linked chain. The crossover between the two regimes can consistently be described using a scaling argument. We further show that the distances between cross-links along the chain contour follows the distribution for Gaussian chains after cross-linking under poor solvent conditions. [ABSTRACT FROM AUTHOR]

Modifying material properties in simple macromolecules such as polyethylene (PE) is achieved by different connection modes of ethylene monomers resulting in a plurality of possible topologies-from highly linear to dendritic species. However, the challenge still lies within the experimental identification of the topology and conformation of the isolated macromolecules because of their low solubility, which demands methods with specific solvents and high operating temperatures. Additionally, a separation technique has to be coupled to different detection methods to meet the specific demands of the respective characterization goal. In this work, we report a quadruple-detector high temperature size exclusion chromatography (HT-SEC) system which contains online multiangle laser light scattering, dynamic light scattering, differential viscometry, and differential refractometry detectors. Quadruple-detector HT-SEC was successfully applied to explore the full range of physical parameters of various PE samples with different branching topologies ranging from highly linear macromolecules, polymers with moderate level of branching, to highly branched PEs with hyperbranched structure. This method is a useful tool not only to investigate molecular weight, mass distribution, and size but also to enable access to important factors which describe the conformation in dilute solution and branching density. [ABSTRACT FROM AUTHOR]

A continuum-space mean-field model for brushes made of starlike polymers in Θ-solvent is developed. The model accounts for the segregation of molecules into two vertical layers and predicts the population fractions of these layers. It reproduces recently reported deviations of the brush heights from scaling theory at moderate and high grafting densities. In the regime of very low monomer densities, the scaling of its brush heights is crossing over to the classical scaling prediction. During our analysis, we modify the elastic properties of the molecules, as well as their volumetric interactions, in order to study the impact of these model parameters on the resulting brush properties. Comparisons with another, recently published mean-field model of brushes on a lattice and with molecular dynamic simulations are carried out. It is demonstrated that most variants of the mean-field models are generating brush heights in reasonable agreement with the simulation data. The partition of molecules into the two populations, however, exhibits a significant model dependence. [ABSTRACT FROM AUTHOR]

Abstract: The properties of starlike polymer brushes in Θ-solvent are investigated using molecular dynamics simulations, scaling- and mean-field theory. Deviations of layer thickness and monomer density from predictions of scaling theory are analyzed and explained. Contrary to common believes, we conclude that the Alexander-deGennes scaling theory is not valid for starlike polymer brushes in Θ-solvent, unless the grafting density is extremely low. A comparison with structural and dynamical properties of starlike polymer brushes in good solvent is carried out. Previous studies in good solvent reported about the dual-population structure of these branched polymer brushes, with coexisting phases of stretched and retracted molecules; the same separation emerges in Θ-solvent, though at higher grafting densities. Molecular tension and population fractions are shown to be solvent-dependent, and a reduced dynamical flip-rate between the two populations is observed for the case of the Θ-brush. [Copyright &y& Elsevier]