The structure of polyelectrolytes is highly sensitive to small changes in the interactions between its monomers. In particular, interactions mediated by counterions play a significant role, and are affected by both specific molecular effects and generic concentration effects. The ability of coarse-grained models to reproduce the structural properties of an atomic model is thus a challenging task. Our present study compares the ability of different kinds of coarse-grained models: (i)~to reproduce the structure of an atomistic model of a polyelectrolyte (the sodium polyacrylate), (ii)~to reproduce the variations of this structure with the number of monomers and with the concentration of the different species. We show that the adequate scalings of the gyration radius of the polymer~$R_{\rm g}$ with the number of monomers~$N$ and with the box size~$L_{\rm box}$ are only obtained, first, if the monomer charges and the counterions are explicitely described, and second, if an attractive Lennard-Jones contribution is added to the interaction between distant monomers. Also, we show that implicit ion models are relevant only to the high electrostatic screening regime.
We use the recently developed soft-potential-enhanced Poisson-Boltzmann (SPB) theory to study the interaction between two parallel polyelectrolytes (PEs) in monovalent ionic solutions in the weak-coupling regime. The SPB theory is fitted to ion distributions from coarse-grained molecular dynamics (MD) simulations and benchmarked against all-atom MD modelling for poly(diallyldimethylammonium) (PDADMA). We show that the SPB theory is able to accurately capture the interactions between two PEs at distances beyond the PE radius. For PDADMA positional correlations between the charged groups lead to…
The low-frequency limit of the electrical conductivity (d.c. conductivity) of differently flexible polyions in aqueous solutions has been measured over an extended polyion concentration range, covering both the dilute and semidilute (entangled and unentangled) regime, up to the concentrated regime. The data have been analyzed taking into account the different flexibility of the polymer chains according to the scaling theory of polyion solutions, in the case of flexible polyions, and according to the Manning model, in the case of rigid polyions. In both cases, the fraction f of free counterions…
A series of well-defined hydrophilic and hydrophobic polyelectrolytes of various chain lengths $N$ and effective charge fractions $f_{eff}$ have been adsorbed onto oppositely charged solid surfaces immersed in aqueous solutions. \emph{In situ} high energy X-ray reflectivity has provided the thickness $h$, the electron density and the roughness of the adsorbed layer in its aqueous environment. In the case of hydrophobic polyelectrolytes, we have found $h\propto N^0 f_{eff}^{-2/3}$, in agreement with a pearl-necklace conformation for the chains induced by a Rayleigh-like instability.
In this communication we illustrate the occurrence of a recently reported new phenomenon of surface-charge amplification, SCA, (originally dubbed overcharging, OC), [Jimenez-Angeles F. and Lozada-Cassou M., J. Phys. Chem. B, 2004, 108, 7286] by means of molecular dynamics simulation of aqueous electrolytes solutions involving multivalent cations in contact with charged graphene walls and the presence of short-chain lithium polystyrene sulfonates where the solvent water is described explicitly with a realistic molecular model. We show that the occurrence of SCA in these systems, in contrast to …
We demonstrate in this paper the influence of solvent quality on the structure of the semi-dilute solution of a hydrophobic polyelectrolyte, partially sulfonated Poly-Styrene Sulfonate. Two solvents are used: (i) one mixture of water and an organic solvent: THF, which is also slightly polar; (ii) DMSO, a polar organic solvent. In case (i), it is shown by SAXS study that the structure - namely the scattering from all chains, characterised by a maximum ("polyelectrolyte peak"), of the aqueous hydrophobic polyelectrolyte solutions (PSS) depends on the solvent quality through the added amount of o…
We theoretically investigate electrostatic properties between two charged surfaces with a grafted polyelectrolyte layer in an aqueous electrolyte solution by using the Poisson-Boltzmann approach accounting for ion partitioning. In order to consider the ion partitioning effect, we focus on changes of electrostatic properties due to the difference in dielectric permittivity of the polyelectrolyte layer and the aqueous electrolyte solution. We find that ion partitioning enhances electrostatic potential in the region between two charged soft surfaces and hence increases the electrostatic interacti…
The combination of two techniques (Small Angle X-ray Scattering and Atomic Force Microscopy) has allowed us to measure in reciprocal and real space the correlation length $ξ$ of salt-free aqueous solutions of highly charged hydrophobic polyelectrolyte as a function of the polymer concentration $C_p$, charge fraction $f$ and chain length $N$. Contrary to the classical behaviour of hydrophilic polyelectrolytes in the strong coupling limit, $ξ$ is strongly dependent on $f$. In particular a continuous transition has been observed from $ξ\sim C_p^{-1/2}$ to $ξ\sim C_p^{-1/3}$ when $f$ decreased fro…
The dynamic behavior of polyelectrolyte chains in the oligomer range is investigated with coarse-grained molecular dynamics simulation and compared to data obtained by two different experimental methods, namely capillary electrophoresis and electrophoresis NMR. We find excellent agreement of experiments and simulations when hydrodynamic interactions are accounted for in the simulations. We show that the electrophoretic mobility exhibits a maximum in the oligomer range and for the first time illustrate that this maximum is due to the hydrodynamical shielding between the chain monomers. Our find…
We use a coarse-grained molecular dynamics model to study the electrophoretic behaviour of flexible polyelectrolyte chains. We first characterize the static properties of the model with respect to the chain length, the polyelectrolyte concentration, additional salt and the influence of an applied external field. Next we investigate the dynamic behaviour in the oligomer range and compare to data obtained by two different experimental methods, namely capillary electrophoresis and PFG-NMR. We find excellent agreement of experiments and simulations when hydrodynamic interactions are accounted for …
We provide numerical evidence that hydrodynamic interactions are screened for charged polymers in salt solution on time scales below the Zimm time. At very short times, a crossover to hydrodynamic behavior is observed. Our conclusions are drawn from extensive coarse-grained computer simulations of polyelectrolytes in explicit solvent and explicit salt, and discussed in terms of analytical arguments based on the Debye-Hueckel approximation.
We investigate electro-osmosis in aqueous solutions of polyelectrolytes using mean-field equations. A solution of positively charged polyelectrolytes is confined between two negatively charged planar surfaces, and an electric field is applied parallel to the surfaces. When electrostatic attraction between the polymer and the surface is strong, the polymers adhere to the surface, forming a highly viscous adsorption layer that greatly suppresses the electro-osmosis. Conversely, electro-osmosis is enhanced by depleting the polymers from the surfaces. We also found that the electro-osmotic flow is…
Complexation between anionic and cationic polyelectrolytes results in solid-like precipitates or liquid-like coacervate depending on the added salt in the aqueous medium. However, the boundary between these polymer-rich phases is quite broad and the associated changes in the polymer relaxation in the complexes across the transition regime are poorly understood. In this work, the relaxation dynamics of complexes across this transition is probed over a wide timescale by measuring viscoelastic spectra and zero-shear viscosities at varying temperatures and salt concentrations for two different sal…
Macromolecules based on dendritic or hyperbranched polyelectrolytes have been emerging as high potential candidates for biomedical applications. Here we study the charge and solvation structure of dendritic polyglycerol sulphate (dPGS) of generations 0 to 3 in aqueous sodium chloride solution by explicit-solvent molecular dynamics computer simulations. We characterize dPGS by calculating several important properties such as relevant dPGS radii, molecular distributions, the solvent accessible surface area, and the partial molecular volume. In particular, as the dPGS exhibits high charge renorma…
Structural and thermodynamic properties of the model solution containing charged oligomers and the equivalent number of counterions were studied by means of the canonical Monte Carlo simulation technique. The oligomers are represented as (flexible) freely jointed chains or as a linear (rigid) array of charged hard spheres. In accordance with the primitive model of electrolyte solutions, the counterions are modeled as charged hard spheres and the solvent as dielectric continuum. Significant differences in the pair distribution functions, obtained for the rigid (rod-like) and flexible model are …
Hydrophobic polyelectrolytes have been predicted to adopt an unique pearl-necklace conformation in aqueous solvents. We present in this Letter an attempt to characterise quantitatively this conformation with a focus on $D_p$, the pearl size. For this purpose polystyrenesulfonate (PSS) of various effective charge fractions $f_{eff}$ and chain lengths $N$ has been adsorbed onto oppositely charged surfaces immersed in water in condition where the bulk structure is expected to persist in the adsorbed state. \emph{In situ} ellipsometry has provided an apparent thickness $h_{app}$ of the PSS layer. …
The effect of hydrodynamic interactions on the free-solution electrophoresis of polyelectrolytes is investigated with coarse-grained molecular dynamics simulations. By comparing the results to simulations with switched-off hydrodynamic interactions, we demonstrate their importance in modelling the experimentally observed behaviour. In order to quantify the hydrodynamic interactions between the polyelectrolyte and the solution, we present a novel way to estimate its effective charge. We obtain an effective friction that is different from the hydrodynamic friction obtained from diffusion measure…
The role of electrostatics on the interfacial properties of polyelectrolyte microgels has been discussed controversially in the literature. It is not yet clear if, or how, Coulomb interactions affect their behavior under interfacial confinement. In this work, we combine compression isotherms, atomic force microscopy imaging, and computer simulations to further investigate the behavior of pH-responsive microgels at oil-water interfaces. At low compression, charged microgels can be compressed more than uncharged microgels. The in-plane effective area of charged microgels is found to be smaller i…
The electrostatic complexation between DOTAP-DOPC unilamellar liposomes and an oppositely charged polyelectrolyte (NaPA) has been investigated in a wide range of the liposome surface charge density. We systematically characterized the "reentrant condensation" and the charge inversion of polyelectrolyte-decorated liposomes by means of dynamic light scattering and electrophoresis. We explored the stability of this model polyelectrolyte/colloid system by fixing each time the charge of the bare liposomes and by changing two independent control parameters of the suspensions: the polyelectrolyte/col…
We investigate the complexation of a highly charged sphere with a long flexible polyelectrolyte, \textit{both negatively charged} in salt free environment. Electroneutrality is insured by the presence of divalent counterions. Using molecular dynamics (MD) within the framework of the primitive model, we consider different Coulomb coupling regimes. At strong Coulomb coupling we find that the adsorbed chain is always confined to the colloidal surface but forms different conformations that depend on the linear charge density of the chain. A mechanism involving the polyelectrolyte \textit{overcharg…
Polyelectrolyte-surfactant complexes (PESCs) have long been employed as oil-in-water (o/w) emulsions stabilizers, but never in the structure of colloidal complex coacervates providing a Pickering effect. The complexed state of PESCs could make them unsuitable o/w Pickering emulsifiers, which instead require a balance between colloidal structure and stability, amphiphilicity and wettability. Here we hypothesize that PESCs coacervates are efficient Pickering stabilizers. Instead of classical surfactants, we employ sophorolipid (SL) biosurfactants, atypical anionic/neutral stimuli-responsive bios…
We utilize total-internal reflection to isolate the two-dimensional `surface foam' formed at the planar boundary of a three-dimensional sample. The resulting images of surface Plateau borders are consistent with Plateau's laws for a truly two-dimensional foam. Samples are allowed to coarsen into a self-similar scaling state where statistical distributions are independent of time, except for an overall scale factor. There we find that statistical measures of side number distributions, size-topology correlations, and bubble shapes, are all very similar to those for two-dimensional foams. However…
Electrostatic interactions between macroions largely govern the equilibrium thermodynamic and dynamical properties of charge-stabilized colloidal suspensions and polyelectrolyte solutions. Predicting the properties of such complex, multicomponent systems with accuracy sufficient to guide and interpret experiments requires realistic modeling of the interparticle interactions and collective behavior of many-particle systems. While the fundamental interactions may be simple, the sheer number of particles and the broad ranges of length and time scales confront the modeler with significant computat…
The nature of electrostatic interactions involving polyanions modulate the properties of both synthetic and biological macromolecules. Although intensely studied for decades the interplay of many length scales has prevented a complete resolution of some of the basic questions such as how the electrostatic persistence length ($l_e$) varies with ionic strength ($I$). In this review we describe certain characteristics of polyelectrolytes (PAs) and polyampholytes (PAs), which are polymers whose monomers have a random distribution of opposite charges. After reviewing the current theoretical underst…
The association between polyelectrolytes (PEs) of the same size but opposite charge is systematically studied in terms of the potential of mean force (PMF) along their center-of-mass reaction coordinate via coarse-grained, implicit-solvent, explicit-salt computer simulations. The focus is set on the onset and the intermediate, transient stages of complexation. At conditions above the counterion-condensation threshold, the PE association process exhibits a distinct sliding-rod-like behavior where the polymer chains approach each other by first stretching out at a critical distance close to thei…
We present a comprehensive study of the interaction of human serum albumin (HSA) with poly(acrylic acid) (PAA; number average degree of polymerization: 25) in aqueous solution. The interaction of HSA with PAA is studied in dilute solution as the function of the concentration of added salt (20 - 100 mM) and temperature (25 - 37$^{\circ}$C). Isothermal titration calorimetry (ITC) is used to analyze the interaction and to determine the binding constant and related thermodynamic data. It is found that only one PAA chain is bound per HSA molecule. The free energy of binding $ΔG_b$ increases with te…
Properties of polyelectrolytes in tetravalent salt solutions are intensively investigated by a coarse-grained model. The concentration of salt and the size of tetravalent counterions are found playing a decisive role on chain properties. If the size of tetravalent counterions is compatible with the one of monomers, the chains show extended structures at low and at high salt concentrations, whereas at intermediate salt concentrations, they acquire compact and prolate structures. The swelling exponent of a chain against salt concentration behaves in an analogous way as the morphological quantiti…
When polyelectrolyte-neutral block copolymers are mixed in solutions to oppositely charged species (e.g. surfactant micelles, macromolecules, proteins etc), there is the formation of stable supermicellar aggregates combining both components. The resulting colloidal complexes exhibit a core-shell structure and the mechanism yielding to their formation is electrostatic self-assembly. In this contribution, we report on the structural properties of supermicellar aggregates made from yttrium-based inorganic nanoparticles (radius 2 nm) and polyelectrolyte-neutral block copolymers in aqueous solution…
The article presents a comprehensive study of counterion dynamics around a generic linear polyelectrolyte (PE) chain with the help of coarse-grained computer simulations. The ion-chain coupling is discussed in the form of binding time, mean-square-displacement (MSD) relative to the chain, local ion transport coefficient, and spatio-temporal correlations in the effective charge. We have shown that a counterion exhibits sub-diffusive behavior $\langle δR^2 \rangle \sim t^δ$, $δ\approx0.9$ w.r.t. chain's centre of mass (COM). The MSD of ions perpendicularly outwards from the chain segment exhibit…
Size Effect of Monovalent Ions on Polyelectrolyte Brushes
South China Advanced Institute for Soft Matter Science and Technology, School of Emergent Soft Matter, South China University of Technology（华南软物质科学与技术高等研究院， emergent soft matter 学院，华南理工大学）
Conformation of single polyelectrolytes in tetravalent salt solutions is investigated under the framework of a coarse-grained model, using Langevin dynamics simulations. The chain size, studied by the radius of gyration, shows three different variational behaviors with salt concentration, depending on the chain stiffness. According to these behaviors, polyelectrolytes of fixed chain length are classified into three categories: flexible chain, semiflexible chain, and rigid chain. The worm-like chain model with persistence length predicted by the Odijk-Skolnick-Fixman theory is found to be able …
Understanding the behavior of charged complex fluids is crucial for a plethora of important industrial, technological, and medical applications. Using coarse-grained molecular dynamics simulations, here we investigate the properties of a polyelectrolyte solution, with explicit counterions and implicit solvent, that is driven by a steady electric field. By properly tuning the interplay between interparticle electrostatics and the applied electric field, we uncover two nonequilibrium continuous phase transitions as a function of the driving field. The first transition occurs from a homogeneously…
We study the complex formation between one long polyanion chain and many short oligocation chains by computer simulations. We employ a coarse-grained bead-spring model for the polyelectrolyte chains, and model explicitly the small salt ions. We systematically vary the concentration and the length of the oligocation, and examine how the oligocations affects the chain conformation, the static structure factor, the radial and axial distribution of various charged species, and the number of bound ions in the complex. At low oligocation concentration, the polyanion has an extended structure. Upon i…
Interactions between actin, an anionic polyelectrolyte, and lysozyme, a cationic globular protein, have been examined using a combination of synchrotron small-angle x-ray scattering and molecular dynamics simulations. Lysozyme initially bridges pairs of actin filaments, which relax into hexagonally-coordinated columnar complexes comprised of actin held together by incommensurate one-dimensional close-packed arrays of lysozyme macroions. These complexes are found to be stable even in the presence of significant concentrations of monovalent salt, which is quantitatively explained from a redistri…
A temperature (T)-dependent coarse-grained (CG) Hamiltonian of polyethylene glycol/oxide (PEG/PEO) in aqueous solution is reported to be used in implicit-solvent material models in a wide temperature (i.e., solvent quality) range. The T-dependent nonbonded CG interactions are derived from a combined "bottom-up" and "top-down" approach. The pair potentials calculated from atomistic replica-exchange molecular dynamics simulations in combination with the iterative Boltzmann inversion are post-refined by benchmarking to experimental data of the radius of gyration. For better handling and a fully c…
We study swelling and structural properties of ionic microgel suspensions within a comprehensive coarse-grained model that combines the polymeric and colloidal natures of microgels as permeable, compressible, charged spheres governed by effective interparticle interactions. The model synthesizes the Flory-Rehner theory of cross-linked polymer gels, the Hertz continuum theory of effective elastic interactions, and a theory of density-dependent effective electrostatic interactions. Implementing the model using Monte Carlo simulation and thermodynamic perturbation theory, we compute equilibrium p…
We show how to implement stick boundary conditions for a spherical colloid in a solvent that is coarse-grained by the method of stochastic rotation dynamics. This allows us to measure colloidal rotational velocity auto-correlation functions by direct computer simulation. We find quantitative agreement with Enskog theory for short times and with hydrodynamic mode-coupling theory for longer times. For aqueous colloidal suspensions, the Enskog contribution to the rotational friction is larger than the hydrodynamic one when the colloidal radius drops below 35nm.
A versatile and transferable coarse-grained (CG) model was developed to investigate the self-assembly of two ubiquitous methacrylate-based copolymers: poly(ethylene oxide-b-methylmethacrylate) (PEO-b-PMMA) and poly(ethylene oxide-b-butylmethacrylate) (PEO-b-PBMA). We derive effective CG potentials that can reproduce their behaviour in aqueous and organic polymer solutions, pure copolymer systems, and at the air-water interface following a hybrid structural-thermodynamic approach, which incorporates macroscopic and atomistic-level information. The parameterization of the intramolecular CG poten…
Recently, Maassen et al. measured an appreciable pH difference between the bulk solution and the solution in the lumen of virus-like particles, self-assembled in an aqueous buffer solution containing the coat proteins of a simple plant virus and polyanions. [Maassen, S. J.; et al. Small 2018, 14, 1802081] They attribute this to the Donnan effect, caused by an imbalance between the number of negative charges on the encapsulated polyelectrolyte molecules and the number of positive charges on the RNA binding domains of the coat proteins that make up the virus shell or capsid. By applying Poisson-…
Conformational characteristics of polyzwitterionic molecules in aqueous solutions are investigated using the variational method. Analytical relations are derived for the radius of gyration of a single polyzwitterionic chain as a function of the chain length, electrostatic interaction strength, added salt concentration, dipole moment and degree of ionization of the zwitterionic monomers. In the absence of the small ions (counterions and coions) near the polyzwitterionic chain, attractive dipole-dipole interactions are shown to induce a collapse of the polyzwitterionic chain. However, in the pre…
The interaction between charged objects in solution is generally expected to recapitulate two central principles of electromagnetics: (i) like-charged objects repel, and (ii) they do so regardless of the sign of their electrical charge. Here we demonstrate experimentally that the solvent plays a hitherto unforeseen but crucial role in interparticle interactions, and importantly, that interactions in the fluid phase can break charge-reversal symmetry. We show that in aqueous solution, negatively charged particles can attract at long range while positively charged particles repel. In solvents th…
To evaluate shear viscosity of ethylene glycol oligomers (EGO)/water binary mixture by means of coarse-grained molecular dynamics (CG-MD) simulations, we proposed the self-diffusion-coefficient-based parameterization of non-bonded interactions among CG particles. Our parameterization procedure consists of three steps: 1) determination of bonded potentials, 2) scaling for time and solvent diffusivity, and 3) optimization of Lennard-Jones parameters to reproduce experimental self-diffusion coefficient and density data. With the determined parameters and the scaling relations, we evaluated shear …
GCMe: Efficient implementation of the Gaussian core model with smeared electrostatic interactions for molecular dynamics simulations of soft matter systems
We develop coarse-grained force fields for poly (vinyl alcohol) and poly (acrylic acid) oligomers. In both cases, one monomer is mapped onto a coarse-grained bead. The new force fields are designed to match structural properties such as radial distribution functions of various kinds derived by atomistic simulations of these polymers. The mapping is therefore constructed in a way to take into account as much atomistic information as possible. On the technical side, our approach consists of a simplex algorithm which is used to optimize automatically non-bonded parameters as well as bonded parame…
