Static structure of sodium polystyrene sulfonate solutions obtained through a coarse-grained model

We present a model based on effective pair interactions to describe the arrangement of sodium polystyrene sulfonate chains in suspension. The potential functions are obtained from the analysis of all-atom simulations and they are the main ingredient of a Brownian dynamics simulation. The resulting configurations are used to reconstruct the corresponding scattering intensity spectra that have the main features of experimental patterns. This coarse-grained model in conjunction with the reconstruction scheme allows us to gain some insights on the structural properties of a polyelectrolyte in solution.     

Salt-induced counterion-mobility anomaly in polyelectrolyte electrophoresis

We study the electrokinetics of a single polyelectrolyte chain in salt solution using hydrodynamic simulations. The salt-dependent chain mobility compares well with experimental DNA data. The mobility of condensed counterions exhibits a salt-dependent change of sign, an anomaly that is also reflected in the counterion excess conductivity. Using Green's function techniques this anomaly is explained by electrostatic screening of the hydrodynamic interactions between the chain and counterions.     

New considerations on the role of covalency in ferroelectric niobates and tantalates

We consider the interaction of an homogeneous polyelectrolyte with an obstacle during electrophoretic drift. We explicitly take into account the hydrodynamic interactions generated by this mechanical trapping, and we evaluate their influence on the unhooking process. Important qualitative effects are pointed out in low and moderate field regimes. However, numerical simulations indicate that, in strong field, the existing simpler local force models, which neglect these hydrodynamic interactions, are quantitatively acceptable. Received: 18 March 1998 / Received in final form and accepted: 20 May 1998     

Monte Carlo simulation of a coarse-grained model of polyelectrolyte networks

The structure and properties of a coarse-grained model of a polyelectrolyte network is studied by means of Monte Carlo simulations. Counterions are treated explicitly, and permanent tetrafunctional cross-linking sites are annealed. The resulting pressure-density relationships exhibit a strong dependence on the strength of electrostatic interactions. A discontinuous volume change is observed when electrostatic interactions are strong. The structure of the model networks is examined at various conditions, and it is found to be considerably different from that of noncross-linked polyelectrolytes.     

Non-linear osmotic brush regime: Simulations and mean-field theory

We investigate polyelectrolyte brushes in the osmotic regime using both theoretical analysis and molecular dynamics simulation techniques. In the simulations at moderate Bjerrum length, we observe that the brush height varies weakly with grafting density, in contrast to the accepted scaling law, which predicts a brush thickness independent of the grafting density. We show that such behavior can be explained by considering lateral electrostatic effects (within the non-linear Poisson-Boltzmann theory) combined with the coupling between lateral and longitudinal degrees of freedom due to the conserved polymer volume (which are neglected in scaling arguments). We also take the non-linear elasticity of polyelectrolyte chains into consideration, which makes significant effects as chains are almost fully stretched in the osmotic regime. It is shown that all these factors lead to a non-monotonic behavior for the brush height as a function of the grafting density. At large grafting densities, the brush height increases with increasing the grafting density due to the volume constraint. At small grafting densities, we obtain a re-stretching of the chains for decreasing grafting density, which is caused by lateral electrostatic contributions and is controlled by the counterion-condensation process around polyelectrolyte chains. These results are obtained assuming all counterions to be trapped within the brush, which is valid for sufficiently long chains of large charge fraction.Received: 14 May 2003, Published online: 11 November 2003PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 36.20.-r Macromolecules and polymer molecules - 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc.     

Molecular dynamics simulations of end-grafted centipede-like polymers with stiff charged side chains

We use molecular dynamics simulations to investigate centipede-like polymers with stiff charged side chains, end-grafted to a planar wall. The effect of the grafting density and the Bjerrum length on the conformational behaviour of the brush is examined in detail. In addition, we make a comparison of centipede-like polyelectrolyte (CPE) brushes with neutral centipede-like polymer (NCP) and linear polyelectrolyte (LPE) brushes. At weak electrostatic interaction, the main chains of the CPE chains adopt a strongly stretched conformation, and the monomer density profiles of side chains exhibit a clear oscillatory behaviour. With increasing Bjerrum length, the CPE brush undergoes a collapse transition. Compared to the CPE brushes, the counterion condensation effect is stronger for the LPE brushes, regardless of whether the electrostatic interaction is weak or strong and of whether the grafting density is low or high. Additionally, it is shown that the architecture of the grafted chains makes a weak contribution to the counterion condensation at strong electrostatic interaction. We also find that the electrostatic repulsion between charged side chains can enhance the stiffness of the main chains and thus limit the range of movement of the free-end monomers.     

Structure of bottle-brush brushes under good solvent conditions: a molecular dynamics study

We report a simulation study for bottle-brush polymers grafted on a rigid backbone. Using a standard coarse-grained bead-spring model extensive molecular dynamics simulations for such macromolecules under good solvent conditions are performed. We consider a broad range of parameters and present numerical results for the monomer density profile, density of the untethered ends of the grafted flexible backbones and the correlation function describing the range that neighboring grafted bottle-brushes are affected by the presence of the others due to the excluded-volume interactions. The end beads of the flexible backbones of the grafted bottle-brushes do not access the region close to the rigid backbone due to the presence of the side chains of the grafted bottle-brush polymers, which stretch the chains further in the radial directions. Although a number of different correlation lengths exist as a result of the complex structure of these macromolecules, their properties can be tuned with high accuracy in good solvents. Moreover, qualitative differences with 'typical' bottle-brushes are discussed. Our results provide a first approach to characterizing such complex macromolecules with a standard bead-spring model.     

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.     

Effect of counterions on the swelling of spherical polyelectrolyte brushes

We investigate the swelling of colloidal spherical polyelectrolyte brushes in the presence of different counterions. The colloidal particles consist of a solid poly(styrene) core of ca. 100 nm diameter onto which linear polyelectrolyte chains are chemically grafted. Two types of polyelectrolyte chains have been used here: The cationic polyelectrolyte poly(2-(acryloyl)ethyltrimethylammonium chloride)) (PATAC) and the anionic poly(styrenesulfonate) (PSS). Both systems are dispersed in water and the degree of swelling of the surface layer is studied by dynamic light scattering. Adding more and more salt leads to a strong shrinking of the surface layer as expected for polyelectrolyte brushes. It is shown that data obtained at low ionic strength can be collapsed on suitable master curves for monovalent and divalent counterions, respectively. For some ions, however, high salt concentrations may lead to a re-swelling of the brush layer in case of the cationic systems. This points to specific interactions of the counterions with the PATAC chains. This strong specific interaction between the counterions and the attached polyelectrolyte may even lead to flocculation of the particles at intermediate salt concentration. Surprisingly, for iodide and magnesium counterions the solubility increases again if the salt concentration is raised to 1 mol/l. Hence, specific interaction leads to salting-out effects as well as to salting-in effects for these colloidal particles. All specific effects seen at high concentrations of added salt can be explained by the increase of the reduced excluded-volume parameter which is due to the adsorption of salt ions.     

Deformation of a tethered polymer in uniform flow

Static properties of a single polymer fixed at one end and subjected to a uniform flow field are investigated for several polymer models: the Gaussian chain, the freely jointed chain, and the FENE (Finitely Extensible Nonlinear Elastic) chain. By taking into account first the excluded-volume interaction and subsequently also the hydrodynamic interaction, the polymer models are gradually completed and the relevance of each effect for the polymer deformation can be identified. Results from computer simulations of these bead spring chains are compared with analytical calculations using either the conformational distribution function or blob models. To this end, in contrast to the blob model with non-draining blobs introduced for a tethered polymer by Brochard-Wyart, we here develop also a model with free-draining blobs. It turns out that a limited extensibility of the polymer – described by nonlinear spring forces in the model – leads to a flow velocity dependence of the end-to-end distance, segment density, etc. which agrees with the power law predictions of the blob model only for very long chains and in a narrow range of flow velocities. This result is important for comparison with recent experiments on DNA molecules which turn out to be still rather short in this respect. The relative importance of finite extensibility, the excluded-volume effect, and hydrodynamic interactions for polymers in flow is not fully understood at present. The simulation of reasonably long chains becomes possible even when fluctuating hydrodynamic interactions are taken into account without employing averaging procedures by introducing efficient numerical approximation schemes. At medium velocity of the uniform flow the polymer is partially uncoiled and simulations show that the effects of excluded-volume and hydrodynamic interactions are position-dependent. Both are stronger near the free end than near the tethered end of the polymer. A crossover from a nearly non-draining polymer at small flow velocities to a free-draining almost uncoiled chain at large velocities is found in the simulations. Accordingly, models assuming the polymer to be composed of either free- or non-draining subunits, like the two blob models, cannot correctly describe the extension and shape of a tethered polymer in flow, and simple power laws for the polymer extension, etc. cannot be expected. Received 21 June 1999     

Salt-induced collapse and reexpansion of highly charged flexible polyelectrolytes

We study the salt-dependent conformations of dilute flexible polyelectrolytes in solution via computer simulations. Low concentrations of multivalent salt induce the known conformational collapse of individual polyelectrolyte chains, but as the salt concentration is increased further this is followed by a reexpansion. We explicitly demonstrate that multivalent counterions can overcompensate the bare charge of the chain in the reexpansion regime. Both the degree of reexpansion and the occurrence of overcharging sensitively depend on ion size. Our findings are relevant for a wide range of salt-induced complexation phenomena.     

Influence of hydrodynamic interactions on lane formation in oppositely charged driven colloids

The influence of hydrodynamic interactions on lane formation of oppositely charged driven colloidal suspensions is investigated using Brownian dynamics computer simulations performed on the Rotne-Prager level of the mobility tensor. Two cases are considered, namely sedimentation and electrophoresis. In the latter case the Oseen contribution to the mobility tensor is screened due to the opposite motion of counterions. The simulation results are compared to that resulting from simple Brownian dynamics where hydrodynamic interactions are neglected. For sedimentation, we find that hydrodynamic interactions strongly disfavor laning. In the steady state of lanes, a macroscopic phase separation of lanes is observed. This is in marked contrast to the simple Brownian case where a finite size of lanes was obtained in the steady state. For strong Coulomb interactions between the colloidal particles a lateral square lattice of oppositely driven lanes is stable similar to the simple Brownian dynamics. In an electric field, on the other hand, the behavior is found in qualitative and quantitative accordance with the case of neglected hydrodynamics.     

Counterion-mediated, non-pairwise-additive attractions in bundles of like-charged rods

Stiff polyelectrolyte chains, such as DNA, can attract each other in solution even though they have the same sign of charge. The attractions are mediated by multivalent counterions, which lead to an effective interaction at the two-chain level that is attractive at short range and repulsive at long range. However, the effective interchain interactions are not pairwise additive. We present a formulation that allows theoretical treatment of the many-chain problem without assuming pairwise additivity. We show that a bundle of chains held together by counterion-mediated attractions can be described in terms of a bulk and surface free energy, and discuss the temperature dependence of the attraction.     

Hydrodynamics of the Zero-Range Process in the Condensation Regime

We argue that the coarse-grained dynamics of the zero-range process in the condensation regime can be described by an extension of the standard hydrodynamic equation obtained from Eulerian scaling even though the system is not locally stationary. Our result is supported by Monte Carlo simulations.     

OxDNA to Study Species Interactions

Molecular ecology uses molecular genetic data to answer traditional ecological questions in biogeography and biodiversity, among others. Several ecological principles, such as the niche hypothesis and the competitive exclusions, are based on the fact that species compete for resources. More in generally, it is now recognized that species interactions play a crucial role in determining the coexistence and abundance of species. However, experimentally controllable platforms, which allow us to study and measure competitions among species, are rare and difficult to implement. In this work, we suggest exploiting a Molecular Dynamics coarse-grained model to study interactions among single strands of DNA, representing individuals of different species, which compete for binding to other oligomers considered as resources. In particular, the well-established knowledge of DNA–DNA interactions at the nanoscale allows us to test the hypothesis that the maximum consecutive overlap between pairs of oligomers measure the species’ competitive advantages. However, we suggest that a more complex structure also plays a role in the ability of the species to successfully bind to the target resource oligomer. We complement the simulations with experiments on populations of DNA strands which qualitatively confirm our hypotheses. These tools constitute a promising starting point for further developments concerning the study of controlled, DNA-based, artificial ecosystems.     

Phase behaviour and interfacial properties of ternary system CO2 + n-butane + n-decane: coarse-grained theoretical modelling and molecular simulations

ABSTRACT

This work illustrates the application of a three-party approach based on theoretical modelling, molecular dynamic (MD) simulations and available experimental data for describing the phase equilibrium and interfacial properties for the ternary system: carbon dioxide + n-butane + n-decane and its corresponding binary sub-systems at 344.3 K. Specifically, a coarse-grained force field is employed for both theoretical predictions and MD. The interfacial region is described by the square gradient theory where the homogenous Helmholtz energy density contribution is provided by the Statistical Associated Fluid Theory equation of state for potentials of variable range for molecules conformed of segments interacting through the Mie potential (SAFT-VR Mie) and MD simulations in the canonical ensemble where the molecules are represented by a coarse-grained Mie force field. The novelty here is that both the theory and the simulations uniquely share the same underlying intermolecular potentials; hence, the experimental data are employed to verify both the theory and simulations. In this schema, the ternary mixture is full predictive as its parameters are only based on pure fluids parameters and binary interactions. It is observed that the phase equilibria and the interfacial properties are equally well represented by the used approach.     

Hydrodynamic boundary conditions: An emergent behavior of fluid–solid interactions

By using the Onsager principle of minimum energy dissipation, the hydrodynamic boundary conditions at the fluid–solid interface are shown to be the natural emergent behavior of microscopic interactions that lead to the interfacial tension and the tangential friction at the fluid–solid interface [T. Qian, C. Qiu, P. Sheng, J. Fluid Mech. 611 (2008) 333]. This is satisfying because the equations of motion, e.g., the Stokes equation, and the hydrodynamic boundary conditions can now be derived from a unified framework. The resulting continuum hydrodynamic formulation yields predictions for immiscible two-phase flows that are in quantitative agreement with molecular dynamic simulations. In particular, the classical problem of the moving contact line is resolved. We also show results on the moving contact line over chemically patterned surfaces which exhibit striking nanoscale characteristics as well as sub-quadratic dependence of the moving contact line dissipation on its average velocity.     

水合作用与pH调控聚电解质刷的构象转变

我们基于Flory-Huggins理论,建立理论模型研究水合作用与pH调控聚电解质刷的构象转变.理论模型考虑聚电解质链与水分子间的作用(聚电解质链的水合作用)、体系中的静电作用.研究发现,随着水合作用的改变,聚电解质刷出现由溶胀到塌缩的构象转变.由此表明了水合作用可在很大程度调节聚电解质刷的相变.通过分析pH的调控效应我们还发现,在碱性环境中(pH=8),聚电解质链单体的解离度增大,静电排斥会使得聚电解质刷溶胀.由此表明,聚电解质刷内水合作用与静电效应的耦合,将会共同决定聚电解质刷的构象转变特性.理论结果深刻揭示了水合作用的改变,会使得聚电解质刷体系发生相变,pH可在很大程度上改变其相变特性.