Molecular dynamics simulations of end‐grafted polymers with charged side chains

We report molecular dynamics simulations on bottle‐brush polyelectrolytes end‐grafted to a planar surface. For each bottle‐brush polyelectrolyte, flexible charged side chains are anchored to one neutral main chain. The effects of the counterion valence and the grafting density on the density profiles and the structural characteristics of the brush were studied in this work. It is found that the electrostatic repulsion between charged monomers in the side chains leads an extended conformation of the brush in a solution containing monovalent counterions, while strong electrostatic binding of multivalent counterions to the side chains has a significant contribution to the collapse of the brush. For the trivalent case, the distribution of end monomers in the main chains becomes broader upon decreasing the grafting density, as compared with the monovalent case. However, the position of the distribution for the monovalent case is relatively insensitive to the change of the grafting density. Additionally, with increased counterion valence, enhanced electrostatic correlation between counterions and charged side chains also weakens the diffusive ability of counterions. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Chain stiffness, salt valency, and concentration influences on titration curves of polyelectrolytes: Monte Carlo simulations

Monte Carlo simulations have been used to study two different models of a weak linear polyelectrolyte surrounded by explicit counterions and salt particles: (i) a rigid rod and (ii) a flexible chain. We focused on the influence of the pH, chain stiffness, salt concentration, and valency on the polyelectrolyte titration process and conformational properties. It is shown that chain acid-base properties and conformational properties are strongly modified when multivalent salt concentration variation ranges below the charge equivalence. Increasing chain stiffness allows to minimize intramolecular electrostatic monomer interactions hence improving the deprotonation process. The presence of di and trivalent salt cations clearly promotes the chain degree of ionization but has only a limited effect at very low salt concentration ranges. Moreover, folded structures of fully charged chains are only observed when multivalent salt at a concentration equal or above charge equivalence is considered. Long-range electrostatic potential is found to influence the distribution of charges along and around the polyelectrolyte backbones hence resulting in a higher degree of ionization and a lower attraction of counterions and salt particles at the chain extremities.     

Response of Bi-disperse Polyelectrolyte Brushes to External Electric Fields——A Numerical Self-consistent Field Theory Study

The self-consistent field theory has been employed to numerically study the response of bi-disperse flexible polyelectrolyte (PE) brushes grafted on an electrode to electric fields generated by opposite surface charges on the PE-grafted electrode and a second parallel electrode. The numerical study reveals that, under a positive external electric field, the shorter and negatively charged PE chains are more responsive than the longer PE chains in terms of the relative changes in their respective brush heights. Whereas under a negative external electric field, the opposite was observed. The total electric force on the grafted PE chains was calculated and it was found that, under a positive external electric field, the magnitude of the total electric force acting on one shorter PE chain is larger than that on one longer PE chain, or vice versa. The underlying mechanism was unraveled through analyzing the total electric field across the two oppositely charged electrodes.     

Complexes of polyelectrolyte hydrogels with organic dyes: Effect of charge density on the complex stability and intragel dye aggregation

The swelling behavior of polyelectrolyte gels based on poly(diallyldimethylammonium chloride) (copolymers of diallyldimethylammonium chloride and acrylamide with the variable composition) and poly(methacrylic acid, sodium salt) in the presence of organic water soluble dyes (alizarin, naphthol blue black, rhodamine) was studied. The collapse of the polyelectrolyte gels in the presence of oppositely charged dyes together with the effective absorption of dyes was observed. The shrinking degree and the dye absorption by the gel depend on the charges of the polymer network and the dye, and also on the dye concentration. Stability of the gel–dye complexes in a salt solution of NaCl and Al₂(SO₄)₃ was studied. It was shown that the complex stability in the salt solution depends on the charge density of the polymer chains forming the gel. The increase of charge density of polymer generally leads to the enhancement of the complex stability. For the systems with the fraction of charged poly(diallyldimethylammonium chloride) monomer units above 0.5 the release of alizarin to the external solution of Al₂(SO₄)₃ reservoir is practically completely suppressed. The obtained results show that oppositely charged dyes are generally from stable complexes with polyelectrolyte gels. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1209–1217, 1999     

Interactions of polyelectrolyte brushes with oppositely charged surfactants

Using Brownian dynamics simulations, we study the effect of the charge ratio, the surfactant length, and the grafting density on the conformational behavior of the complex formed by the polyelectrolyte brush with oppositely charged surfactants. In our simulations, the polyelectrolyte chains and surfactants are represented by a coarse-grained bead-spring model, and the solvent is treated implicitly. It is found that varying the charge ratio induces different morphologies of surfactant aggregates adsorbed onto the brush. At high charge ratios, the density profiles of surfactant monomers indicate that surfactant aggregates exhibit a layer-by-layer arrangement. The surfactant length has a strong effect on the adsorption behavior of surfactants. The lengthening of surfactant leads to a collapsed brush configuration, but a reswelling of the brush with further increasing the surfactant length is observed. The collapse of the brush is attributed to the enhancement of surfactants binding to polyelectrolyte chains. The reswelling is due to an increase in the volume of adsorbed surfactant aggregates. At the largest grafting density investigated, enhanced excluded volume interactions limit the adsorption of surfactant within the polyelectrolyte brush. We also find that end monomers in polyelectrolyte chains exhibit a bimodal distribution in cases of large surfactant lengths and high charge ratios.     

Mixed brushes consisting of oppositely charged Y-shaped polymers in salt free,monovalent, and divalent salt solutions

The conformation and the internal stratification of mixed brushes formed from oppositely charged Y(−) and Y(+)-shaped chains in salt free, monovalent, and divalent salt solutions were studied by means of molecular dynamics simulations using the primitive model. Scaling relations of mixed brush height with respect to the grafting surface per chain, the ratio of the total positive to the total negative charge of polyelectrolyte chains, and salt concentrations were obtained. The simulations predicted that mixed brushes show a unique response to divalent salt (1:2) solutions. For symmetric brushes having the same spacer lengths, number of chains and charged units fractions the increase of the salt concentration leads to the enrichment of the outer brush surface with Y(+) units and the lamella microphase separation. For asymmetric brushes in high salt concentration cylindrical domain microphases are formed.     

Diblock polyampholytes grafted onto spherical particles: effect of stiffness, charge density, and grafting density

The structure of spherical brushes formed by symmetric diblock polyampholytes end-grafted onto small spherical particles in aqueous solution is examined within the framework of the so-called primitive model using Monte Carlo simulations. The properties of the two blocks are identical except for the sign of their charges. Three different chain flexibilities corresponding to flexible, semiflexible, and stiff blocks are considered at various polyampholyte linear charge densities and grafting densities. The link between the two blocks is flexible at all conditions, and the grafted segments are laterally mobile. Radial and lateral spatial distribution functions of different types and single-chain properties are analyzed. The brush structure strongly depends on the chain flexibility. With flexible chains, a disordered polyelectrolyte complex is formed at the surface of the particle, the complex becoming more compact at increasing linear charge density. With stiff blocks, the inner blocks are radially oriented. At low linear charged density, the outer blocks are orientationally disordered, whereas at increasing electrostatic interaction the two blocks of a polyampholyte are parallel and close to each other, leading to an ordered structure referred to as a polyampholyte star. As the grafting density is increased, the brush thickness responds differently for flexible and nonflexible chains, depending on a different balance between electrostatic interactions and excluded volume effects.     

Directed motion of a polyelectrolyte micelle along tethered chains of oppositely charged polyelectrolyte brush

The complexation of different single polyelectrolyte (PE) micelles formed by linear diblock copolymers with oppositely charged brushes with varying grafting densities and charge content was studied by means of molecular dynamics simulations using the primitive model. We found that all micelles perform a directed motion along the vertical z axis on the grafted surface where they trapped while on the other axes the motion is restricted in a circle in which the diameter decreases with the increase of the hydrophilic length of the linear diblock copolymer. The motion of micelles is characterized as super diffusion inside brushes with low densities and low charge content. At high grafting densities and charge content the diffusion becomes Fickian or slightly subdiffusive. The number of the absorbed brush chains on the micelle corona increases almost monotonically with the increase of brush grafting density or with the decrease of charge content. The distance from the surface in which the micelle is trapped can be controlled by the charge density along the grafted PE chain. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 621–631     

良溶剂中接枝型聚两性电解质单链构象的布朗动力学模拟

采用布朗动力学研究了在良溶剂中荷电平衡的接枝聚两性电解质(GPA)的单链构象转变行为,讨论了主链链长、支链数及电荷密度对GPA分子链构象转变的影响.研究发现,随着静电相互作用的增强,GPA分子链构象转变过程由线团、主链与支链间的折叠、链段塌缩和电荷配对形成偶极子与四极子等4个阶段构成.与线型聚两性电解质不同,GPA存在的额外支链间空间排斥与静电排斥作用随着分子结构的变化而改变,并影响构象转变行为.在强静电相互作用下,良溶剂中的GPA链由于溶剂化作用会再伸展,以保证偶极子完全配对成四极子.减小主链长度或电荷密度或增加支链数目都会增大体系的排斥力和主链的刚性,阻滞分子链的塌缩,并使得分子链再伸展的幅度增大.     

Surface potential of spherical polyelectrolyte brushes in the presence of trivalent counterions

We consider the ζ-potential and the effective charge of spherical polyelectrolyte brushes (SPBs) in aqueous solution in the presence of trivalent europium ions. The SPB consists of a polystyrene core of ca. 250 nm diameter onto which long chains of the strong polyelectrolyte poly(styrene sulfonate) are grafted (contour length: 82 nm). At low concentration of EuCl₃ the chains are stretched to nearly full length. If the concentration of the trivalent ions is raised, the surface layer of the polyelectrolyte chains collapses. The ζ-potential of the SPB is calculated from the electrophoretic mobilities measured at different concentrations of EuCl₃. At the collapse, ζ decreases by the partial neutralization of the charges by the trivalent ions. The experimental ζ-potential thus obtained agrees with the theoretical surface potential Ψ_theo calculated for the effective shear plane by a variational free energy model of the SPB.     

Simulation Study of the Conformational Properties of Diblock Polyelectrolytes in Salt Solutions

Coarse-grained molecular dynamics simulations are performed to understand the behavior of diblock polyelectrolytes in solutions of divalent salt by studying the conformations of chains over a wide range of salt concentrations. The polymer molecules are modeled as bead spring chains with different charged fractions and the counterions and salt ions are incorporated explicitly. Upon addition of a divalent salt, the salt cations replace the monovalent counterions, and the condensation of divalent salt cations onto the polyelectrolyte increases, and the chains favor to collapse. The condensation of ions changes with the salt concentration and depends on the charged fraction. Also, the degree of collapse at a given salt concentration changes with the increasing valency of the counterion due to the bridging effect. As a quantitative measure of the distribution of counterions around the polyelectrolyte chain, we study the radial distribution function between monomers on different polyelectrolytes and the counterions inside the counterion worm surrounding a polymer chain at different concentrations of the divalent salt. Our simulation results show a strong dependence of salt concentration on the conformational properties of diblock copolymers and indicate that it can tune the self-assembly behaviors of such charged polyelectrolyte block copolymers.     

Explicit ions condensation around strongly charged polyelectrolytes and spherical macroions: the influence of salt concentration and chain linear charge density. Monte Carlo simulations

The condensation of monovalent counterions and trivalent salt particles around strong rigid and flexible polyelectrolyte chains as well as spherical macroions is investigated by Monte Carlo simulations. The results are compared with the condensation theory proposed by Manning. Considering flexible polyelectrolyte chains, the presence of trivalent salt is found to play an important role by promoting chain collapse. The attraction of counterions and salt particles near the polyelectrolyte chains is found to be strongly dependent on the chain linear charge density with a more important condensation at high values. When trivalent salt is added in a solution containing monovalent salt, the trivalent cations progressively replace the monovalent counterions. Ion condensation around flexible chains is also found to be more efficient compared with rigid rods due to monomer rearrangement around counterions and salt cations. In the case of spherical macroions, it is found that a fraction of their bare charge is neutralized by counterions and salt cations. The decrease of the Debye length, and thus the increase of salt concentration, promotes the attraction of counterions and salt particles at the macroion surface. Excluded volume effects are also found to significantly influence the condensation process, which is found to be more important by decreasing the ion size.     

Adsorption of polyelectrolyte versus surface charge: in situ single-molecule atomic force microscopy experiments on similarly, oppositely, and heterogeneously charged surfaces

We have studied the effect of the pH and surface charge of mica on the adsorption of the positively charged weak polyelectrolyte (PE) poly(2-vinylpyridine) (P2VP) using atomic force microscopy (AFM) single-molecule experiments. These AFM experiments were performed in situ directly under aqueous media. If the mica's surface and the PE are oppositely charged (pH > 3), the PE forms a flat adsorbed layer of two-dimensionally (2D) equilibrated self-avoiding random walk coils. The adsorbed layer's structure remains almost unchanged if the pH is decreased to pH 3 (the mica's surface is weakly charged). At pH 2 (the mica surface is decorated by spots of different electrical charges), the polyelectrolyte chains take the form of a 2D compressed coil. In this pH range, at an increased P2VP concentration in solution, the PE segments preferentially adsorb onto the top of previously adsorbed segments, rather than onto an unoccupied surface. We explain this behavior as being caused by the heterogeneous character of the charged surface and the competitive adsorption of hydronium ions. The further increase of polymer concentration results in a complete coverage of the mica substrate and the charge overcompensation by P2VP chains adsorbed on the similarly charged substrate, due to van der Waals forces.     

Diblock polyampholytes grafted onto spherical particles: Monte Carlo simulation and lattice mean-field theory

Spherical brushes composed of diblock polyampholytes (diblock copolymers with oppositely charged blocks) grafted onto solid spherical particles in aqueous solution are investigated by using the primitive model solved with Monte Carlo simulations and by lattice mean-field theory. Polyampholyte chains of two compositions are considered: a copolymer with a long and a short block, A100B10, and a copolymer with two blocks of equal length, A50B50. The B block is end-grafted onto the surface, and its charge is varied, whereas the charge of the A block is fixed. Single-chain properties, radial and lateral spatial distributions of different types, and structure factors are analyzed. The brush structure strongly depends on the charge of the B block. In the limit of an uncharged B block, the chains are stretched and form an extended polyelectrolyte brush. In the other limit with the charges of the blocks compensating each other, the chains are collapsed and form a polyelectrolyte complex surrounding the particles. At intermediate charge conditions, a polyelectrolyte brush and a polyelectrolyte complex coexist and constitute two substructures of the spherical brush. The differences of the brush structures formed by the A100B10 and A50B50 polyampholytes are also analyzed. Finally, a comparison of the predictions of the two theoretical approaches is made.     

Surface Patterns of a Tetrahedral Polyelectrolyte Brush Induced by Grafting Density and Charge Fraction

A tetrahedral polyelectrolyte brush in the presence of trivalent counterions is researched under the condition of good solution by mea ns of molecular dynamics simulati ons.Grafting density and charge fraction are varied to gen erate a series of surface patter ns.Lateral microphase separation happens and various interesting pinned patches appear at appropriate charge fraction and grafting density.Through a careful analysis on the brush thickness,the pair correlation functions,the distributions of net charge,and the four states of trivalent counterions in the brush,we find that the ordered surface patterns and special properties are induced by the pure electrostatic correlation effect of trivalent ions even in the good solvent.Furthermore,the dependences of electrostatic correlation on the charge fraction of tethered chains are evaluated for fixed grafting den sity.Also,our results can serve as a guide for precise control over the stimuli-responsive materials rational and self-assembly of nanoparticles.     

Molecular dynamics simulations of polyelectrolyte multilayering on a charged particle

Molecular dynamics simulations of polyelectrolyte multilayering on a charged spherical particle revealed that the sequential adsorption of oppositely charged flexible polyelectrolytes proceeds with surface charge reversal and highlighted electrostatic interactions as the major driving force of layer deposition. Far from being completely immobilized, multilayers feature a constant surge of chain intermixing during the deposition process, consistent with experimental observations of extensive interlayer mixing in these films. The formation of multilayers as well as the extent of layer intermixing depends on the degree of polymerization of the polyelectrolyte chains and the fraction of charge on its backbone. The presence of ionic pairs between oppositely charged macromolecules forming layers seems to play an important role in stabilizing the multilayer film.     

Hydrophilic/hydrophobic character of grafted cellulose

Vinyl monomers with long paraffin chains were grafted onto two kinds of cellulose (cotton and cotton linter) by direct irradiation grafting technique. The effect of dose, monomer structure and concentration, as well as homopolymer suppressor (styrene) concentration on the grafting yield was studied and the optimal grafting conditions were established. Grafting decreased the swelling of the samples in water and increased their polymer compatibility in polypropylene matrix.     

Phase behavior of aqueous polyion-surfactant ion complex salts: effects of polyion charge density

The effect of varying the fraction of charged monomer units of the polyion in aqueous polyion-oppositely charged surfactant complex salts has been investigated. The complex salts used were based on cetyltrimethylammonium (C16TA+) with three different polymeric counterions: poly(acrylate) (PA-) or poly(acrylate) copolymerized with either dimethylacrylamide (PA-/DAM) or N-isopropylamide (PA-/NIPAM). The charge density of the polyion was varied by either adding poly(acrylic) acid (PAA) to the C16TAPA complex salt (annealed charges) or by varying the fraction of uncharged units in the C16TAPA/DAM or C16TAPA/NIPAM complex salts (quenched charges). The formed phases were studied visually between crossed polarizers and by small angle X-ray scattering (SAXS). Both types of complex salts (annealed and quenched) formed hexagonal phases at high fractions of charged monomers and low water contents. Upon increasing the water content, a cubic phase of the Pm3n space group was found. Upon further addition of water, a miscibility gap with the cubic phase in equilibrium with pure water was found. Decreasing the fraction of charged monomers in the annealed complex salt resulted in an increase of the curvature of the surfactant aggregates. Only at very low (<0.05) fractions of charged monomers did the packing of the surfactant aggregates lose long-range order, and eventually, the miscibility gap disappeared. For the quenched complex salts, the changes upon decreasing the fraction of charged monomers in the polyion were similar, but the loss of long-range order occurred at much higher fractions of charged monomers. The average surfactant aggregation number in the surfactant aggregates, which was similar for the annealed and quenched systems, decreased when the fraction of charged monomers was decreased.     

Grafting of poly(sodium styrenesulfonate) onto gold surface from NaNO<Subscript>3</Subscript> solution

The chemical grafting of thiol terminated poly(sodium styrenesulfonate)(HS-PSSS) chains from sodium nitrate (NaNO_3) salt solution to a gold surface was investigated with a quartz crystal microbalance with dissipation monitoring (QCM-D) in different salt concentrations.It was found that at low salt concentration grafting density of HS-PSSS was low and the grafted chains adopted a mushroom conformation.With the increase of salt concentration polyelectrolyte chains underwent a transition toward coiled stat...