Salt-modulated structure of polyelectrolyte-macroion complex fibers

The structure and stability of strongly charged complex fibers, formed by complexation of a single long semi-flexible polyelectrolyte chain and many oppositely charged spherical macroions, are investigated numerically at the ground-state level using a chain-sphere cell model. The model takes into account chain elasticity as well as electrostatic interactions between charged spheres and chain segments. Using a numerical optimization method based on a periodically repeated unit cell, we obtain fiber configurations that minimize the total energy. The optimal fiber configurations exhibit a variety of helical structures for the arrangement of macroions including zig-zag, solenoidal and beads-on-a-string patterns. These structures result from the competition between attraction between spheres and the polyelectrolyte chain (which favors chain wrapping around the spheres), chain bending rigidity and electrostatic repulsion between chain segments (which favor unwrapping of the chain), and the interactions between neighboring sphere-chain complexes which can be attractive or repulsive depending on the system parameters such as salt concentration, macroion charge and chain length per macroion (linker size). At about physiological salt concentration, dense zig-zag patterns are found to be energetically most stable when parameters appropriate for the DNA-histone system in the chromatin fiber are adopted. In fact, the predicted fiber diameter in this regime is found to be around 30 nanometers, which roughly agrees with the thickness observed in in vitro experiments on chromatin. We also find a macroion (histone) density of 5–6 per 11nm which agrees with results from the zig-zag or cross-linker models of chromatin. Since our study deals primarily with a generic chain-sphere model, these findings suggest that structures similar to those found for chromatin should also be observable for polyelectrolyte-macroion complexes formed in solutions of DNA and synthetic nano-colloids of opposite charge. In the ensemble where the mean linear density of spheres on the chain is fixed, the present model predicts a phase separation at intermediate salt concentrations into a densely packed complex phase and a dilute phase.     

Complexation between oppositely charged polyelectrolytes: Beyond the Random Phase Approximation

: We consider the phase behavior of polymeric systems by calculating the structure factors beyond the Random Phase Approximation. The effect of this correction to the mean-field RPA structure factor is shown to be important in the case of Coulombic systems. Two examples are given: simple electrolytes and mixtures of incompatible oppositely charged polyelectrolytes. In this last case, all former studies predicted an enhancement of compatibility for increasing charge densities; we also describe the complexation transition between the polyelectrolytes. We determine a phase diagram of the polyelectrolyte mixture that includes both complexation and incompatibility.     

半刚性聚电解质链与带相反电荷颗粒复合体系的动力学模拟

用Langevin动力学研究了半刚性聚电解质链与带相反电荷球状颗粒在溶液中的复合体系，并研究了链的拉伸性质.具体考察了带电颗粒的电量以及溶液中盐离子浓度对复合体系的影响.链两端没有施加外力的情况下，当溶液中盐离子浓度较低时，复合体系呈现一种串珠状结构；当溶液中盐离子浓度较高时，复合体系转变为一种聚集态结构.链的两端施加外力的情况下，带电颗粒从链上脱落的过程可以分为两步. 关键词： 聚电解质链 Langevin动力学 Debye-Hückel长度     

Water-Soluble Polyelectrolyte Complexes of Oppositely Charged Polysaccharides

The article is an overview of our recent study on some particular aspects of polyelectrolyte complex (PEC) formation by oppositely charged polysaccharides when they are brought into contact in aqueous solutions. This type of complexation can lead to the thickening effect, jellification or PEC precipitation that find numerous applications in a variety of fields from the regulation of rheological characteristics of solutions to fabrication of functional materials by the layer-by-layer technique. Our focus was on the rheological aspects of water-soluble PEC formation and jellification, but to gain an insight into the mechanisms of the processes involved, atomic force microscopy, scanning electron microscopy and differential scanning calorimetry were also applied. As cationic polysaccharides, chitosan and cationic derivatives of hydroxypropylcellulose including hydrophobically modified samples were taken and, as their anionic counterparts, alginates, carrageenans, xanthans and fucoidans were used. Their combination allowed us to consider the influence of charge density, hydrophobicity and flexibility–stiffness of macromolecules on the association of oppositely charged polysaccharides, the formation of temperature sensitive hydrogels and some PEC morphological features.     

Lysozyme complexes with thermo- and pH-responsive PNIPAM-<Emphasis Type="Italic">b</Emphasis>-PAA block copolymer

Lysozyme is an enzyme responsible for the damage of bacterial cell walls and is abundant in a number of secretions such as tears and human milk. In the present study, we investigated the structure, the physicochemical characteristics, and the temperature-responsiveness of lysozyme complexes with poly(N-isopropylacrylamide)-b-poly(acrylic acid) block polyelectrolyte in aqueous media. A gamut of light-scattering techniques and fluorescence spectroscopy were used in order to examine the complexation process, as well as the structure, solution behavior, and temperature response of the nanosized complexes. The concentration of copolymer polyelectrolyte was kept constant. The values of the scattering intensity, I ₉₀, which is proportional to the mass of the species in solution, increased gradually as a function of C _LYS, providing proof of the occurring complexation, while the size of the nanostructures decreased. The structure of the complexes became more open as the C _LYS increased. The increase of the salinity did not affect the structural characteristics of the supramolecular nanoparticulate aggregates. On the other hand, the physicochemical and structural characteristics of the complexes changed upon increasing temperature, and the changes depended on the initial ratio block polyelectrolyte/lysozyme. The knowledge on developing block polyelectrolyte/protein complexes through electrostatic interactions, obtained from this investigation, may be applied to the design of nutraceuticals.     

Thermodynamic Properties of a Simple Model of Like-Charged Attracting Rods

We study the thermodynamic properties of a simple model for the possible mechanism of attraction between like charged rod-like polyions inside a polyelectrolyte solution. We consider two polyions in parallel planes, with Z charges each, in a solution containing multivalent counterion of valence . The model is solved exactly for Z13 for a general angle between the rods and supposing that n counterions are condensed onto each polyion. The free energy has two minima, one at =0 (parallel rods) and another at =/2 (perpendicular rods). The stability of the parallel and perpendicular configurations is analyzed.     

Self-consistent field theory of adsorption of flexible polyelectrolytes onto an oppositely charged sphere

The adsorption of flexible polyelectrolyte （PE） with the smeared charge distribution onto an oppositely charged sphere immersed in a PE solution is studied numerically with the continuum self-consistent field theory. The power law scaling relationships between the boundary layer thickness and the surface charge density and the charge fraction of PE chains revealed in the study are in good agreement with the existing analytical result. The curvature effect on the degree of charge compensation of the total amount of charges on the adsorbed PE chains over the surface charges is examined, and a clear understanding of it based on the dependences of the degree of charge compensation on the surface charge density and the charge fraction of PE chains is established.     

Dynamical conductivity of the two-dimensional Bose condensate: Superfluid-insulator transition for a long-range random potential

We calculate the dynamical conductivity of a disordered charged Bose condensate in two dimensions with a long-range random potential due to charged impurities with a large spacer width . Analytical results for the frequency-dependent conductivity for weak disorder are derived. For strong disorder the frequency-dependent conductivity is given in terms of a transcendental equation. The disorder-induced transition from a superfluid phase to an insulator phase is discussed. The density-density relaxation function and the screening properties of the disordered Bose gas are calculated. Experimental results for high-T _c superconductors are discussed.     

Direct observation of counterion organization in F-actin polyelectrolyte bundles

Attractions between like-charged polyelectrolytes have been observed in a variety of systems (W.M. Gelbart, R.F. Bruinsma, P.A. Pincus, V.A. Parsegian, Phys. Today 53, September issue, 38 (2000)). Recent biological examples include DNA, filamentous viruses, and F-actin. Theoretical investigations on idealized systems indicate that counterion correlations play a central role, but no experiments that specifically probe such correlations have been performed. Using synchrotron X-ray diffraction, we have directly observed the organization of multivalent ions on cytoskeletal filamentous actin (a well-defined biological polyelectrolyte) and found an unanticipated symmetry-breaking collective counterion mechanism for generating attractions. Surprisingly, the counterions do not form a lattice that simply follows actins helical symmetry; rather, the counterions organize into frozen ripples parallel to the actin filaments and form structures reminiscent of charge density waves. Moreover, these 1D counterion charge density waves form a coupled mode with twist deformations of the oppositely charged actin filaments. This counterion organization is not sensitive to thermal fluctuations in temperature range accessible to protein-based polyelectrolyte systems. Moreover, the counterion density waves are pinned to the spatial periodicity of charges on the actin filament even if the global filament charge density is varied, indicating the importance of charge periodicity on the polyelectrolyte substrate.     

Annealing polyelectrolytes at charged interfaces

The conformation of a weakly dissociating (annealing) polyelectrolyte chain end-tethered to a similarly or oppositely charged planar surface is analyzed in the framework of scaling arguments. For a similarly charged interface an analytical model is also utilized. We demonstrate that at low salt concentration in bulk solution there is a strong coupling between the polyelectrolyte conformation and its degree of ionization. In the case of an oppositely charged (adsorbing) surface, adsorption promotes ionization of the annealing polyelectrolyte. As a result, the adsorbed layer thickness decreases as a function of surface charge density more rapidly for an annealing polyelectrolyte than for a quenched one. In the case of a similarly charged (repulsive) surface the chain ionization is suppressed, and the annealing polyelectrolyte chain is less extended than the quenched one. Moreover, an increase in surface charge density leads to non-monotonous extension of the tethered polyelectrolyte.Received: 16 September 2003, Published online: 5 February 2004PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 82.35.Gh Polymers on surfaces; adhesion - 82.35.Rs Polyelectrolytes     

Thermal fluctuation electromagnetic field as a reason for the sensitivity of a condensed diamagnetic medium to weak actions

Interaction between the thermal fluctuation electromagnetic field of a condensed medium and a weak external factor, say, a weak effective magnetic field including an external magnetic field, rigid rotation of the medium, and Coriolis force, imparts a torque to any charged free or bound particles (atoms, molecules, etc.). which indicates that the medium is sensitive to weak actions. The torque is proportional to thermal energy kT and may increase substantially under the cyclotron resonance conditions. The so-called kT problem is solved, so that many observations having to do with the field of physics that can be called the physics of weak actions (?kT) can now be theoretically explained.     

Symmetry properties of a charged fluid in the general theory of relativity

The problem of specifying the symmetry properties of a charged fluid in space-time V₄, which has a definite group of motions, is considered. It is shown that if nonempty spacetime V₄ with an energy-momentum tensor for the charged fluid has symmetry (i.e., admits a group of motions), then the mass density, the pressure, and the four-velocity of the fluid inherits this symmetry, and for an electromagnetic field the relationL f _ij =7.*f _ij is satisfied. The necessary and sufficient conditions are found so that =0 in the case of a one-parameter group. Then additional relationships between and the structure constants are obtained in the case of an r-parameter group. It is shown that under certain conditions the symmetry properties obtained for charged matter are necessary and sufficient conditions for the symmetry of space-time V₄.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 113–117, November, 1978.     

Complexation and overcharging of polyelectrolyte stars and charged colloids

We examine the complexation behavior of polyelectrolyte stars on oppositely charged colloidal particles with similar sizes by means of computer simulations employing the molecular dynamics approach. In particular the overcharging phenomenon is considered and its dependence on the charge and functionality of the stars. The complexes thus formed are a realization of inverse patchy particles (Bianchi et?al 2011 Soft Matter 7 8313) for which both the number of patches and the total charge can be tuned.     

Problems of Dust Grains Charging to Negative Potentials

The presence of dust grains is a common phenomenon in the space environment. Grains can be charged by many different processes (e.g., photoemission, attachment of electrons/ions, the secondary emission, etc.). If the grain's surface potential becomes high enough, one can observe field emission of ions or electrons. We are trapping a single dust grain in a Paul trap, expose it to a low-energy electron beam, and investigate the evolution of its charge-to-mass ratio with respect to the energy of primary electron beam. We use micron-sized (D = 2–11 m) glass grains and charge them up to -300 V of surface potentials; it corresponds to the electric field strength of about 10⁸ V/m. Analysis of the charging/discharging processes has shown that (1) the effect of the field enhanced secondary emission is negligible in the case of insulators and (2) the effective work function for electron field emission from charged insulators is as low as 1 eV.     

Optimisation of the self-assembly process: production of stable,alginate-based polyelectrolyte nanocomplexes with protamine

The aim of this work was to investigate the possibility of covalent cross-linker-free, polyelectrolyte complex formation at the nanoscale between alginic acid (as sodium alginate, ALG) and protamine (PROT). Optimisation of the self-assembly conditions was performed by varying the type of polymer used, pH of component solutions, mass mixing ratio of the components and the speed and order of component addition on the properties of complexes. Homogenous particles with nanometric sizes resulted when an aqueous dispersion of ALG was rapidly mixed with a solution of PROT. The polyelectrolyte complex between ALG and PROT was confirmed by infrared spectroscopy. To facilitate incorporation of drugs soluble at low pH, pH of ALG dispersion was decreased to 2; however, no nanoparticles (NPs) were formed upon complexation with PROT. Adjusting pH of PROT solution to 3 resulted in the formation of cationic or anionic NPs with a size range 70–300 nm. Colloidal stability of selected alginic acid low/PROT formulations was determined upon storage at room temperature and in liquid media at various pH. Physical stability of NPs correlated with the initial surface charge of particles and was time- and pH-dependent. Generally, better stability was observed for anionic NPs stored as native dispersions and in liquids covering a range of pH.

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Schematic presenting the formation and size of alginate/protamine nanoparticles

     

Structure and switching of single-stranded DNA tethered to a charged nanoparticle surface

Using a molecular theory, we investigate the temperature-dependent self-assembly of single-stranded DNA(ss DNA)tethered to a charged nanoparticle surface. Here the size, conformations, and charge properties of ss DNA are taken into account. The main results are as follows: i) when the temperature is lower than the critical switching temperature, the ss DNA will collapse due to the existence of electrostatic interaction between ss DNA and charged nanoparticle surface; ii)for the short ss DNA chains with the number of bases less than 10, the switching of ss DNA cannot happen, and the critical temperature does not exist; iii) when the temperature increases, the electrostatic attractive interaction between ss DNA and charged nanoparticle surface becomes weak dramatically, and ss DNA chains will stretch if the electrostatic attractive interaction is insufficient to overcome the elastic energy of ss DNA and the electrostatic repulsion energy. These findings accord well with the experimental observations. It is predicted that the switching of ss DNA will not happen if the grafting densities are too high.     

Effect of nonequilibrium charge screening in A + B → 0 bimolecular reactions in condensed matter

The formalism of many-particle densities developed earlier by the present authors is applied to the study of the cooperative effects in the kinetics of bimolecular A + B 0 reactions between oppositely charged particles (reactants). It is shown that unlike the Debye-Hückel theory in statistical physics, here charge screening has essentially a nonequilibrium character. For the asymmetric mobility of reactants (D _A = 0,D _B 0 the joint spatial distribution of similar immobile reactants A reveals at short distances a singular character associated with their aggregation. The relevant reaction rate does not approach a steady state (as it does in the symmetric case,D _A =D _B, but increases infinitely in time, thus leading to a concentration decay which is quicker than the algebraic law generally accepted in chemical kinetics,n t _–1.     

Colour gluons and scaling in a unified gauge model

Deep inelastic weak and electromagnetic processes are considered within the parton framework taking the partons to be integrally charged quarks and coloured gluons. Despite the participation of the spin-one gluons in these processes, scaling is shown to be maintained by treating the problem in a unified gauge model based on the groupSU (3)_colour⊗SU _L (2)⊗U(1). This is a consequence of the vector-dominance type of couplings between the gluons and the weak or electromagnetic vector bosons which are induced by the spontaneous breakdown of gauge symmetry. As a further consequence it is found that in the asymptotic region far above the gluon masses the colour octet parts of the weak and electromagnetic currents of the quarks are damped so that, in particular, the integrally charged quarks behave as fractionally charged quarks in this region.     

Heavy top quark decay into a charged Higgs scalar and a photon (gluon)

We consider the decay of a heavy top quark into a charged Higgs scalar and a hard photon (gluon)tH ⁺ b(g). We give the general result for fermions of arbitrary mass. Our results for the differential decay rate for these two processes are remarkably simple. The radiation amplitude zero (RAZ) factorization is explicit but there is no RAZ for these processes because of the presence of opposite-sign charges. We obtain a branching ratio of 0.063% for bH⁺ and 5.6% for bH⁺g. Thus both decays should be relatively easy to see at the SSC.