In this work we investigated the question of how the molecular nature of the dielectric media and the polymer-solvent dielectric mismatch affect the collapse of a polyelectrolyte chain in solution by means of dissipative particle dynamics simulations. First, we studied whether the explicit treatment of dielectric media as polar beads instead of homogeneous dielectric background results in a different system behavior. We showed that the explicit treatment of polar beads facilitates the chain collapse, i.e. it occurs at smaller values of the electrostatic strength parameter values $λ^2 \sim Q^2/(εkT)$. We believe that the main reason for such behavior is that the dielectric response is in fact a collective effect, and the "effective" dielectric permittivity is different from the bulk value when the charges are close to each other and/or the density of the charges is high enough. This implies that the value of $λ$ does not have a universal meaning due to the small-scale effects related to the presence of polar species; therefore, changing the total unit charge $Q$ or the temperature $kT$ is not equivalent to changing $ε$. Next, we investigated how the difference of the dielectric permittivities of the polymer chain and solvent affects the collapse. We showed the polar chain adapts less swollen conformations in the polyelectrolyte regime and collapses easier compared to the case of non-polar chain; the possible reasons for such behavior are discussed.
In this paper, we present a self-consistent field theory of macroscopic forces in spatially inhomogeneous flexible chain polyelectrolyte solutions. We derive an analytical expression for a stress tensor which consists of three terms: isotropic hydrostatic stress, electrostatic (Maxwell) stress, and stress rising from conformational entropy of polymer chains -- conformational stress. We apply our theory to the description of polyelectrolyte solutions confined in a conductive slit nanopore and observe anomalous behavior of disjoining pressure and electric differential capacitance.
The effective elasticity of highly charged stiff polyelectrolytes is studied in the presence of counterions, with and without added salt. The rigid polymer conformations may become unstable due to an effective attraction induced by counterion density fluctuations. Instabilities at the longest, or intermediate length scales may signal collapse to globule, or necklace states, respectively. In the presence of added-salt, a generalized electrostatic persistence length is obtained, which has a nontrivial dependence on the Debye screening length. It is also found that the onset of conformational ins…
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-i…
Hydrophobic polyelectrolytes (HPE) can solubilize bilayer membranes, form micelles or can reversibly aggregate as a function of pH. The transitions are often remarkably sharp. We show that these cooperative transitions occur by a competition between two or more conformational states and can be explained within the framework of Monod - Wymann - Changeux (MWC) theory that was originally formulated for allosteric interactions. Here we focus on the pH-dependent destabilization and permeation of bilayer membranes by HPE. We formulate the general conditions that lead to sharp conformational transiti…
For single-file translocations of a charged macromolecule through a narrow pore, the crucial step of arrival of an end at the pore suffers from free energy barriers, arising from changes in intrachain electrostatic interaction, distribution of ionic clouds and solvent molecules, and conformational entropy of the chain. All contributing factors to the barrier in the initial stage of translocation are evaluated by using the self-consistent field theory for the polyelectrolyte and the coupled Poisson-Boltzmann description for ions, without radial symmetry. The barrier is found to be essentially e…
We present a systematic statistical mechanical analysis of the conformational properties of a stiff polyelectrolyte chain with intrachain attractions that are due to counterion correlations. We show that the mean-field solution corresponds to an Euler-like buckling instability. The effect of the conformational fluctuations on the buckling instability is investigated, first, qualitatively, within the harmonic (``semiclassical'') theory, then, systematically, within a 1/d-expansion, where d denotes the dimension of embedding space. Within the ``semiclassical'' approximation, we predict that the …
Using molecular dynamics simulations we study the behavior of a dilute solution of strongly charged polyelectrolytes in poor solvents, where we take counterions explicitly into account. We focus on the chain conformational properties under conditions where chain-chain interactions can be neglected, but the counterion concentration remains finite. We investigate the conformations with regard to the parameters chain length, Coulomb interaction strength, and solvent quality, and explore in which regime the competition between short range hydrophobic interactions and long range Coulomb interaction…
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 apply extensive Molecular Dynamics simulations and analytical considerations in order to study the conformations and the effective interactions between weakly charged, flexible polyelectrolyte chains in salt-free conditions. We focus on charging fractions lying below 20%, for which case there is no Manning condensation of counterions and the latter can be thus partitioned in two states: those that are trapped within the region of the flexible chain and the ones that are free in the solution. We examine the partition of counterions in these two states, the chain sizes and the monomer distrib…
We study the properties of polyelectrolyte chains under different solvent conditions, using a variational technique. The free energy and the conformational properties of a polyelectrolyte chain are studied minimizing the free energy $F_N$, depending on $N(N-1)/2$ trial probabilities that characterize the conformation of the chain. The Gaussian approximation is considered for a ring of length $2^4<N<2^{16}$ and for an open chain of length $2^4<N<2^9$ in poor and theta solvent conditions, including a Coulomb repulsion between the monomers. In theta solvent conditions the blob size is measured an…
Conformational properties of a single flexible polyelectrolyte chain in a poor solvent are studied using constant temperature molecular dynamics simulation. The effects of counterions are explicitly taken in to account. Structural properties of various phases and the transition between these phases are studied by tracking the values of asphericity, radius of gyration, fraction of condensed counterions, number of non-bonded neighbours and Coulomb interaction energies. From our simulations, we find strong evidence for a first-order phase transition from extended to collapsed phase consistent wit…
We theoretically study the polarizability and the interactions of neutral complexes consisting of a semi-flexible polyelectrolyte adsorbed onto an oppositely charged spherical colloid. In the systems we studied, the bending energy of the chain is small compared to the Coulomb energy and the chains are always adsorbed on the colloid. We observe that the polarizability is large for short chains and small electrical fields and shows a non-monotonic behavior with the chain length at fixed charge density. The polarizability has a maximum for a chain length equal to half of the circumference of the …
We demonstrate that a highly charged polyelectrolyte confined in a spherical cavity undergoes reversible transformations between amorphous conformations to a four-fold symmetry morphology as a function of dielectric mismatch between the media inside and outside the cavity. Surface polarization due to dielectric mismatch exhibits an extra "confinement" effect, which are most pronounced within a certain range of the cavity radius and the electrostatic strength between the monomers and counterions and multivalent counterions. For cavities with a charged surface, surface polarization leads to an i…
We reconsider the electrostatic contribution to the persistence length, $\ell_e$, of a single, infinitely long charged polymer in the presence of screening. A Gaussian variational method is employed, taking $\ell_e$ as the only variational parameter. For weakly charged and flexible chains, crumpling occurs at small length scales because conformational fluctuations overcome electrostatic repulsion. The electrostatic persistence length depends on the square of the screening length, $\ell_e\simκ^{-2}$, as first argued by Khokhlov and Khachaturian by applying the Odijk-Skolnick-Fixman (OSF) theory…
Polyelectrolytes under confinement are crucial for energy storage and for understanding biomolecular functions. Using molecular dynamics simulations, we analyze a polyelectrolyte solution confined between two oppositely charged planar dielectric surfaces and include surface polarization effects due to dielectric mismatch at the two electrodes. Although the effect of polarization on the charge distribution seems minor, we find that surface polarization enhances energy storage and also leads to the emergence of negative differential capacitance in confined polyelectrolyte solutions.
A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain in $d$ dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when screening is not present, in order to compute the end-to-end distance and the asymptotic properties of the chain as a function of the polymer chain length $N$. We find $R \simeq N^ν(\log N)^γ$ where $ν= \frac{3}{λ+2}$ and $λ$ is the exponent which characterize the long-range interaction $U \propto 1/r^λ$. The exponent $γ$ is shown to be non-universal, depending o…
The transport of polyelectrolytes confined by oppositely charged surfaces and driven by a constant electric field is of interest in studies of DNA separation according to size. Using molecular dynamics simulations that include surface polarization effect, we find that the mobilities of the polyelectrolytes and their counterions change non-monotonically with the confinement surface charge density. For an optimum value of the confinement charge density, efficient separation of polyelectrolytes can be achieved over a wide range of polyelectrolyte charge due to the differential friction imparted b…
The physical chemistry of liquid-liquid phase separation (LLPS) of polymer solutions bears directly on the assembly of biologically functional droplet-like bodies from proteins and nucleic acids. These biomolecular condensates include certain extracellular materials, and intracellular compartments that are characterized as "membraneless organelles". Analytical theories are a valuable, computationally efficient tool for addressing general principles. LLPS of neutral homopolymers are quite well described by theory; but it has been a challenge to develop general theories for the LLPS of heteropol…
Understanding the effect of inhomogeneity on the charge regulation and dielectric properties, and how it depends on the conformational characteristics of the macromolecules is a long-standing problem. In order to address this problem, we have developed a field-theory to study charge regulation and local dielectric function in planar polyelectrolyte brushes. The theory is used to study a polyacid brush, which is comprised of chains end-grafted at the solid-fluid interface, in equilibrium with a bulk solution containing monovalent salt ions, solvent molecules and pH controlling acid. In particul…
A weakly charged flexible polyelectrolyte chain in a neutral spherical cavity is analyzed using self-consistent field theory (SCFT) within an explicit solvent model. Assuming the radial symmetry for the system, it is found that the confinement of the chain leads to creation of a charge density wave along with the development of a potential difference across the center of cavity and the surface. We show that the solvent entropy plays an important role in the free energy of the confined system. For a given radius of the spherical cavity and fixed charge density along the backbone of the chain, s…
We present a field-theoretic renormalization group (RG) analysis of a dilute solution of flexible, screened polyelectrolyte chains (Debye-Hueckel chains) in a polar solvent. We perform a virial expansion to calculate the scaling dependence of the Osmotic pressure on the chain density, chain size and screening length. The formalism is developed for general chain distributions and we give explicit forms for a monodisperse chain size distribution. We utilize the fact that a Debye-Hueckel chain may be mapped to a local field theory with TWO length-scales requiring the calculation of scaling functi…
We study conformational and electrophoretic properties of polyelectrolytes (PEs) in tetravalent salt solutions under the action of electric fields by means of molecular dynamics simulations. Chain conformations are found to have a sensitive dependence on salt concentration $C_s$. As $C_s$ is increased, the chains first shrink to a globular structure and subsequently reexpand above a critical concentration $C_s^*$. An external electric field can further alter the chain conformation. If the field strength $E$ is larger than a critical value $E^*$, the chains are elongated. $E^*$ is shown to be a…
We study the behavior of single linear polyelectrolytes condensed by trivalent salt under the action of electric fields through computer simulations. The chain is unfolded when the strength of the electric field is stronger than a critical value. This critical electric field follows a scaling law against chain length and the exponent of the scaling law is $-0.77(1)$, smaller than the theoretical prediction, $-3ν/2$ [Netz, Phys. Rev. Lett. 90 (2003) 128104], and the one obtained by simulations in tetravalent salt solutions, $-0.453(3)$ [Hsiao and Wu, J. Phys. Chem. B 112 (2008) 13179]. It demon…
We present a field-theoretic renormalization group (RG) analysis of a single flexible, screened polyelectrolyte chain (a Debye-Hückel chain) in a polar solvent. We point out that the Debye-Hückel chain may be mapped onto a local field theory which has the same fixed point as a generalised $n \to 1$ Potts model. Systematic analysis of the field theory shows that the system is one with two interplaying length-scales requiring the calculation of scaling functions as well as exponents to fully describe its physical behaviour. To illustrate this, we solve the RG equation and explicitly calculate th…
We applied the mean-field approach to a columnar bundle assembled by the parallel arrangement of stiff polyelectrolyte rods in a salt bath. The electrostatic potential can be divided into two regions: inside the bundle for condensed counter-ions, and outside the bundle for free small ions. To determine the distribution of condensed counter-ions inside the bundle, we use a local self-consistent condition that depends on the charge density, the electrostatic potential, and the net polarization. The results showed that, upon bundle formation, the electric charge of polyelectrolytes, even those in…
The precise sequence of aminoacids plays a central role in the tertiary structure of proteins and their functional properties. The Hydrophobic-Polar lattice models have provided valuable insights regarding the energy landscape. We demonstrate here the isomorphism between the protein sequences and designable structures for two and three dimensional lattice proteins of very long aminoacid chains using exact enumerations and intuitive considerations.We emphasize that the topological arrangement of the aminoacid residues alone is adequate to deduce the designable and non-designable sequences witho…
Applying the contact density chain-growth algorithm to lattice heteropolymers, we identify the conformational transitions of a nongrafted hydrophobic-polar heteropolymer with 103 residues in the vicinity of a polar, a hydrophobic, and a uniformly attractive substrate. Introducing only two system parameters, the numbers of surface contacts and intrinsic hydrophobic contacts, respectively, we obtain surprisingly complex temperature and solvent dependent, substrate-specific pseudo-phase diagrams.
We propose a simple phenomenological model for describing the conformational dynamics of biopolymers via the nonlinearity-induced buckling and collapse (i.e. coiling up) instabilities. Taking into account the coupling between the internal and mechanical degrees of freedom of a semiflexible biopolymer chain, we show that self-trapped internal excitations (such as amide-I vibrations in proteins, base-pair vibrations in DNA, or polarons in proteins) may produce the buckling and collapse instabilities of an initially straight chain. These instabilities remain latent in a straight infinitely long c…
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…
Random polyampholytes (PAs) contain positively and negatively charged monomers that are distributed randomly along the polymer chain. The interaction between charges is assumed to be given by the Debye-Huckel potential. We show that the size of the PA is determined by an interplay between electrostatic interactions, giving rise to the polyelectrolyte (PE) effect due to net charge per monomer ($σ$), and an effective attractive PA interaction due to charge fluctuations, $δσ$. The interplay between these terms gives rise to non-monotonic dependence of the radius of gyration, $R_g$ on the inverse …
In the present work, we provide a dielectric study on two differently concentrated aqueous lysozyme solutions in the frequency range from 1 MHz to 40 GHz and for temperatures from 275 to 330 K. We analyze the three dispersion regions, commonly found in protein solutions, usually termed beta-, gamma-, and delta-relaxation. The beta-relaxation, occurring in the frequency range around 10 MHz and the gamma-relaxation around 20 GHz (at room temperature) can be attributed to the rotation of the polar protein molecules in their aqueous medium and the reorientational motion of the free water molecules…
