A three‐state model for counterions in a dilute solution of weakly charged polyelectrolytes

In this paper we consider the influence of counterion distribution on the behavior of polyelectrolyte systems. We propose the unified model to describe and to compare the swelling and collapse properties of single polyelectrolyte chains in dilute solutions, microgel particles of various molecular masses, and (as a limiting case) macroscopic gels. A novel feature of the new approach is that we distinguish three possible states of counterions: free counterions inside and outside the polymer macromolecule and a bound state of counterions forming ion pairs with corresponding ions of polymer chains. The latter possibility becomes progressively important when macromolecules or gels shrink. In this case the formation of a supercollapsed state is possible, when all couterions are trapped and form ion pairs. On the other hand, the fact that counterions can float in the outer solution affects essentially the conformation of polyelectrolyte chains in dilute solutions of good quality where practically all counter ions can escape the space inside polymer coils and the repulsion between uncompensated charges plays an important role in the chain behavior.     

Correlation between conformation change of polyelectrolyte brushes and lubrication

We directly monitor the absolute separation profiles that function as film thickness between a single glass disk and the charged polyelectrolyte brushes decorated steel slider in water using a home-made slider-on-disk apparatus, which reflects the structural conformation variations and interactions of polymer brushes under externally applied pressure, in addition to probing the relative variation of friction forces under different applied loads and sliding velocities. We find that the polyelectrolyte brushes modified surfaces can sustain high pressure and have extremely low friction coefficients(around 0.006 at pressures of 0.13 MPa; 0.5-0.6 without brushes). The water-lubrication characteristics are correlated to the structural conformation changes of the polyelectrolyte brushes that are mainly governed by electrostatic interactions and the osmotic pressure of counterions inside the polymer chains, which can be used to support and distribute the normal pressure. The apparent thickness of the brush decreases with the increase of loading forces, an increase in the ionic strength causes the polymer chains collapse, and the friction forces increase. This fundamental research is of great importance to understand the mechanical and structural properties of polyelectrolyte brushes and their influences on the tribological behaviors, and helps to design friction/lubrication-controlled surface/interface by taking advantage of polyelectrolyte brushes.     

Electrochemical Quantitative Evaluation of the Surface Charge of a Poly(1-Vinylimidazole) Multilayer Film and Application to Nanopore pH Sensor

Nanopore pH sensing is based on the interaction between the surface charge of the nanopore and ions passing through the nanopore. The nanopore surface charge can be derived from the acid-base dissociation equilibrium of the modified polyelectrolyte. Various polyelectrolytes have been selected based on the acid dissociation constant of the monomer units, and various techniques have been applied to modify nanopores. However, they have been developed without clear guidelines for characterizing the surface modification status or surface charge. One reason has been the difficulty in accurately estimating the surface charge of nanopores in solution. Thus, in this study, the dissociation constant (pKa_app) of the surface charge of a modified polyelectrolyte nanopore was quantitatively estimated via electrochemical measurements. Previously, the modification status of nanopores has been evaluated using the ion current response. In addition, we monitored in real-time the polyelectrolyte modification status using a quartz crystal microbalance (QCM). Some polyelectrolytes were difficult to immobilize directly on the nanopore surface, and those polymers could be effectively modified by the layer-by-layer (LbL) technique. Therefore, we produced a guideline for the fabrication of a nanopore sensor for pH measurements under physiological conditions by quantitative evaluation of the pKa_app via electrochemical methods, the monitoring of the modification status by QCM, and the development of an effective modification method via the LbL technique.     

Flexible polyelectrolyte simulations at the Poisson-Boltzmann level: a comparison of the kink-jump and multigrid configurational-bias Monte Carlo methods

We present a new approach for simulating the motions of flexible polyelectrolyte chains based on the continuous kink-jump Monte Carlo technique coupled to a lattice field theory based calculation of the Poisson-Boltzmann (PB) electrostatic free energy "on the fly." This approach is compared to the configurational-bias Monte Carlo technique, in which the chains are grown on a lattice and the PB equation is solved for each configuration with a linear scaling multigrid method to obtain the many-body free energy. The two approaches are used to calculate end-to-end distances of charged polymer chains in solutions with varying ionic strengths and give similar numerical results. The configurational-bias Monte Carlo/multigrid PB method is found to be more efficient, while the kink-jump Monte Carlo method shows potential utility for simulating nonequilibrium polyelectrolyte dynamics.     

The Influence of Ion Pair Formation on the Phase Behavior of Polyelectrolyte Solutions

In this paper we calculate the phase diagrams of polyelectrolyte solutions taking into account the possibility of ion pair formation between counterions and ions on polymer chains with their subsequent aggregation in multiplets. Multiplets play a role of reversible physical crosslinks between different polymer chains. Furthermore, we assume that the dielectric constant, and hence the binding energy of ion pairs and multiplets, depends on the volume fraction of polymer in the solution. We have shown that ion pairing and multiplet formation leads to instability of the homogeneous phase, so that at some conditions the phase separation can proceed even in good solvent. Another qualitatively new feature of the behavior of polyelectrolyte solutions is the emergence of a triple point on the phase diagram. The effect of the solvent polarity and the polarity of the dry polymer on the general form of the phase diagram is studied in detail.     

Coupling Effects of Electrostatic Interactions and Salt Concentration Gradient in Polymer Translocation through a Nanopore: A Coarse-Grained Molecular Dynamics Simulations Study

We study the influence of polymer pore interactions and focus on the role played by the concentration gradient of salt in the translocation of polyelectrolytes (PE) through nanopores explicitly using coarse-grained Langevin dynamics simulations. The mean translocation time is calculated by varying the applied voltage, the pH, and the salt concentration gradient. Changing the pH can alter the electrostatic interaction between the protein pore and the polyelectrolyte chain. The polymer pore interaction is weakened by the increase in the strength of the externally applied electric field that drives translocation. Additionally, the screening effect of the salt can reduce the strong charge-charge repulsion between the PE beads which can make translocation faster. The simulation results show there can be antagonistic or synergistic coupling between the salt concentration-induced screening effect and the drift force originating from the salt concentration gradient thereby affecting the translocation time. Our simulation results are explained qualitatively with free energy calculations.     

ac response of a carbon chain under a finite frequency bias

Based on nonequilibrium Green's function approach and density functional theory, we report first principles investigation on ac transport of four carbon atom chain connected by two semi-infinite aluminum leads Al-C(4)-Al. For small alternating external bias voltage, we expanded nonequilibrium Green's function to the first order in the external voltage and calculated the dynamical conductance. The suppression of the dynamic conductance was obtained near the resonant level while far away from the resonance the giant enhancement of the dynamic conductance was also observed. These behaviors can be well understood under the wide-band limit. By changing the coupling distance between the carbon atom and aluminum leads, the system could change its transport response between capacitivelike and inductivelike.     

Corrected Article: "ac response of a carbon chain under a finite frequency bias" [J. Chem. Phys. 127, 104701 (2007)

Based on nonequilibrium Green's function approach and density functional theory, we report first principles investigation on ac transport of four carbon atomic chain connected by two semi-infinite aluminum leads, Al-C(4)-Al. For small alternating external bias voltage, we expanded nonequilibrium Green's function to the first order in the external voltage and calculated the dynamical conductance. The suppression of the dynamic conductance was obtained near the resonant level, while far away from the resonance, the large enhancement of the dynamic conductance was observed. These behaviors can be understood well under the wide-band limit. By changing the coupling distance between the carbon atom and the aluminum leads, the system could change its transport response between capacitivelike and inductivelike.     

Thermodynamics for nonequilibrium solvation and numerical evaluation of solvent reorganization energy

This work presents a thermodynamic method for treating nonequilibrium solvation. By imposing an extra electric field onto the nonequilibrium solvation system, a virtual constrained equilibrium state is prepared. In this way, the free energy difference between the real nonequilibrium state and the con-strained equilibrium one is simply the potential energy of the nonequilibrium polarization in the extra electronic field, according to thermodynamics. Further, new expressions of nonequilibrium solvation energy and solvent reorganization energy have been formulated. Analysis shows that the present formulations will give a value of reorganization energy about one half of the traditional Marcus theory in polar solvents, thus the explanation on why the traditional theory tends to overestimate this quantity has been found out. For the purpose of numerical determination of solvent reorganization energy, we have modified Gamess program on the basis of dielectric polarizable continuum model. Applying the procedure to the well-investigated intramolecular electron transfer in biphenyl-androstane-naphthyl and biphenyl-androstane-phenanthryl systems, the numerical results of solvent reorganization energy have been found to be in good agreement with the experimental fittings.     

Redox and acid-base coupling in ultrathin polyelectrolyte films

A single layer of poly(allylamine) with a covalently attached osmium pyridine-bipyridine complex adsorbed onto a Au surface modified by mercaptopropanesulfonate has been studied theoretically with a molecular approach and experimentally by cyclic voltammetry. These investigations have been carried out at different pHs and ionic strengths of the electrolyte solution in contact with the redox polyelectrolyte modified electrode. The theory predicts strong coupling between the acid-base and redox equilibria, particularly for low ionic strength, pH close to the pKa, and high concentration of redox sites. The coupling leads to a decrease in the peak potential at pH values above the apparent pKa of the weak polyelectrolyte, in good agreement with the experimental pH dependence at 4 mM NaNO3. Theoretical calculations suggest that the inflection point in the peak position versus pH curves can be used to estimate the apparent pKa of the amino groups in the polymer. Comparison of the apparent pKa for PAH-Os in the film with that of poly(allylamine) reported in the literature shows that the underlying charged thiol strongly influences charge regulation in the film. A systematic study of the film thickness and the degree of protonation in sulfonate and amino groups for solutions of different pH and ionic strength shows the coupling between the different interactions. It is found that the variation of the film properties has a non-monotonic dependence on bulk pH and salt concentration. For example, the film thickness shows a maximum with electrolyte ionic strength, whose origin is attributed to the balance between electrostatic amino-amino repulsions and amino-sulfonate attractions.     

Combined depletion and electrostatic forces in polymer-induced membrane adhesion: a theoretical model

We develop a semi-quantitative analytical theory to describe adhesion between two identical planar charged surfaces embedded in a polymer-containing electrolyte solution. Polymer chains are uncharged and differ from the solvent by their lower dielectric permittivity. The solution mimics physiological fluids: It contains 0.1 M of monovalent ions and a small number of divalent cations that form tight bonds with the headgroups of charged lipids. The components have heterogeneous spatial distributions. The model was derived self-consistently by combining: (a) a Poisson-Boltzmann like equation for the charge densities, (b) a continuum mean-field theory for the polymer profile, (c) a solvation energy forcing the ions toward the polymer-poor regions, and (d) surface interactions of polymers and electrolytes. We validated the theory via extensive coarse-grained Molecular Dynamics (MD) simulations. The results confirm our analytical model and reveal interesting details not detected by the theory. At high surface charges, polymer chains are mainly excluded from the gap region, while the concentration of ions increases. The model shows a strong coupling between osmotic forces, surface potential and salting-out effects of the slightly polar polymer chains. It highlights some of the key differences in the behaviour of monomeric and polymeric mixed solvents and their responses to Coulomb interactions. Our main findings are: (a) the onset of long-ranged ion-induced polymer depletion force that increases with surface charge density and (b) a polymer-modified repulsive Coulomb force that increases with surface charge density. Overall, the system exhibits homeostatic behaviour, resulting in robustness against variations in the amount of charges. Applications and extensions of the model are briefly discussed.     

Transmembrane potential across single conical nanopores and resulting memristive and memcapacitive ion transport

Memristive and memcapacitive behaviors are observed from ion transport through single conical nanopores in SiO(2) substrate. In i-V measurements, current is found to depend on not just the applied bias potential but also previous conditions in the transport-limiting region inside the nanopore (history-dependent, or memory effect). At different scan rates, a constant cross-point potential separates normal and negative hysteresis loops at low and high conductivity states, respectively. Memory effects are attributed to the finite mobility of ions as they redistribute within the negatively charged nanopore under applied potentials. A quantative correlation between the cross-point potential and electrolyte concentration is established.     

Electrokinetic transport of nanoparticles in functional group modified nanopores

Nanopore detection is a hot issue in current research. One of the challenges is how to slow down the transport velocity of nanoparticles in nanopores. In this paper, we propose a functional group modified nanopore. That means a polyelectrolyte brush layer is grafted on the surface of the nanopore to change the surface charge properties. The existing studies generally set the charge density of the brush layer to a fixed value. On the contrary, in this paper, we consider an essential property of the brush layer: the volume charge density is adjustable with pH. Thus, the charge property of the brush layer will change with the local H⁺ concentration. Based on this, we established a mathematical model to study the transport of nanoparticles in polyelectrolyte brush layer modified nanopores. We found that pH can effectively adjust the charge density and even the polarity of the brush layer. A larger pH can reduce the transport velocity of nanoparticles and improve the blockade degree of ion current. The grafting density does not change the polarity of the brush charge. The larger the grafting density, the greater the charge density of the brush layer, and the blockade degree of ion current is also more obvious. The polyelectrolyte brush layer modified nanopores in this paper can effectively reduce the nanoparticle transport velocity and retain the essential ion current characteristics, such as ion current blockade and enhancement.     

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.     

The role of disorder on the electronic structure of conjugated polymers. The case of poly-2,5-bis(phenylethynyl)-1,3,4-thiadiazole

Insight into the electronic structure of disordered poly-2,5-bis(phenylethynyl)-1,3,4-thiadiazole in an amorphous region, in comparison to an ideal two-planar cofacial oligomer system, is pursued. The atomic structure of the amorphous polymer was obtained from classical molecular dynamics. It was subsequently used to calculate the electronic states and inter- and intrachain electronic coupling integrals using the density functional theory based charge patching method. The interchain electronic coupling integrals in the amorphous system were found to be an order of magnitude smaller than in the ordered system with similar distances between the chains. The results also suggest that the electronic structure of the whole system cannot be understood as a collection of the electronic structures of individual chains. The band gap of the whole system is significantly smaller than the band gaps of individual chains. This decrease originates from the disordered long range electrostatic potential created by the dipole moments of polymer repeat units, which should be minimized if one seeks good transport properties.     

环状RGDs修饰的分子刷型共聚物在成像及药物运输中的应用

以具有丰富接枝侧链的阴离子型共轭聚合物分子刷PFPANa为材料,通过简单的一步修饰法在聚合物的部分接枝侧链上引入靶向配体分子c(RGDyK),并利用分子刷侧链上未修饰配体分子的羧基负离子与抗癌药物DOX静电结合,制备了基于分子刷型共轭聚合物的靶向细胞成像和载药系统.研究结果表明载药系统对DOX药物的载药量可达13.3 wt%,体外细胞实验研究结果表明该载药系统可实现对肿瘤细胞的靶向选择性成像,并显著促进了肿瘤细胞对DOX药物的摄取,具有良好的抗肿瘤细胞生长效果,显著提高了药物运输效率.     

压力对带有pH值可调聚电解质刷的仿生纳米孔中离子选择性的影响

具有pH值可调聚电解质（Polyelectrolyte,PE）刷的合成纳米孔的仿生离子通道在纳米尺度下离子、流体和生物粒子的主动运输控制方面具有重大应用潜力. 离子选择性是纳流体设备中离子传输的重要现象,具有很大的现实意义和实用价值. 本文提出了施加压力控制纳米孔中离子选择度的方法,综合研究了溶液pH值、浓度、外加电压和压力对离子选择度的影响. 仿真结果表明,离子选择度对压力的刺激是敏感的,且不像电压对离子选择度的影响会受到溶液pH值和浓度的制约,且方向不定,速度不可控;压力对离子选择度的影响不受溶液性质制约,并且灵活可控. 该结果对设计带pH值可调聚电解质刷的纳米孔有重要的启发作用.     

Statistics of polymer chains in orienting fields

The theory of a freely jointed polymer chain is modified by introduction of interactions between dipole chain segments and an orienting field. Such a field results either from external forces (e.g. external electric or magnetic fields) or represents interactions between dipole segments of chains (molecular mean-field). The distribution of orientations of chain segments and the free energy of a chain in such orienting fields are calculated and discussed.     

Reverse nonequilibrium molecular dynamics simulation of thermal conductivity in nanoconfined polyamide-6,6

A new molecular dynamics simulation method, with coupling to external baths, is used to perform equilibrium simulations on polyamide-6,6 trimers nanoconfined between graphene surfaces, in equilibrium with the bulk polymer. The method is coupled with the reverse nonequilibrium molecular dynamics simulation technique to exchange heat in the direction normal to the surfaces. To be able to study the effect of confinement on the heat conductance in nanoconfined pores, in this work a number of simulations on systems with different pore sizes are done. It is concluded that the coefficient of heat conductivity depends on the degree of polymer layering between the surfaces and on the pore width. Our results further indicate a considerable temperature drop at the interface between the surfaces and polymer. The calculated Kapitza lengths depend on the intersurface distance and on the layering of the polymer nanoconfined between the surfaces.