Neutral Polymer Solutions Research Articles

Field‐theoretic simulations of polyelectrolyte complexation

Field‐theoretic simulations of polyelectrolyte complexation

Challenging scaling laws of flexible polyelectrolyte solutions with effective renormalization concepts

Recasting a many-particle problem in a field-theoretic formalism is nowadays a well-established theoretical tool used by scientists across a wide spectrum of research areas, ranging from polymer physics to molecular electronic structure theory. It has shown to provide useful results in many complex situations, where the physics of the system involves many degrees of freedom and a multitude of different length scales, generally rendering its numerical treatment on a detailed level computationally intractable. To reduce the computational burden, field-theoretic methodologies usually take advantage of the mean-field approximation. This approximation technique is known to give reliable information about the system in the high concentration regime, where the interactions are highly screened. However, it is well established that the ranges of physical interest in most biological and technological applications lie in the intermediate to low concentration regimes, where fluctuations beyond the mean-field level of approximation become important and dominate the overall physical behavior. In this work we introduce a new self-consistent field theory for flexible polyelectrolyte chains, in which the monomers interact via a pair potential of screened Coulomb type, and derive suitable thermodynamic expressions for all concentration regimes. Our approach combines the renormalization concepts of tadpole renormalization, which has recently been successfully employed in calculations of prototypical neutral polymer and polyelectrolyte solutions, with the Hartree renormalization procedure. By comparing our approach to experimental measurements as well as alternative theoretical approaches, we demonstrate that it provides useful osmotic pressure results for polyelectrolyte systems composed of sodium poly(styrene-sulfonate) without and with added salt over the whole range of monomer concentrations.

Solution Rheological Behavior and Electrospinning of Cationic Polyelectrolytes

The influence of polyelectrolyte rheological behavior on the electrospinning process was determined for a series of poly(2-(dimethylamino)ethyl methacrylate hydrochloride) (PDMAEMA·HCl) aqueous solutions in the presence of added NaCl. Solution rheological studies revealed that PDMAEMA·HCl in an 80/20 w/w water/methanol cosolvent displayed polyelectrolyte behavior based on the scaling relationship between specific viscosity (ηsp) and concentration in the semidilute unentangled and semidilute entangled regimes. The entanglement concentration (Ce) increased with NaCl concentration due to screening of the electrostatic repulsive forces along the PDMAEMA·HCl backbone, which enabled the PDMAEMA·HCl chains to adopt a flexible, coillike conformation. Moreover, the scaling behavior in the semidilute entangled regime shifted from polyelectrolyte (ηsp ∼ C1.5) to neutral polymer behavior (ηsp ∼ C3.75) in the high salt limit. The electrospinning performance of PDMAEMA·HCl solutions was also dependent on NaCl concentration, and NaCl-free PDMAEMA·HCl solutions did not form fibers at concentrations less than 8Ce. The minimum concentration for fiber formation decreased as the level of NaCl was increased due to screening of the repulsive, electrostatic interactions between charged repeating units that served to stabilize the electrospinning jet. Moreover, because of the high electrical conductivity of the polyelectrolyte solutions, the electrospun polyelectrolyte fibers were 2−3 orders of magnitude smaller in diameter compared to fibers that were electrospun from solutions of neutral polymers of equal zero shear viscosity (η0) and normalized concentration (C/Ce).

Studies on the viscosity behavior of polymer solutions at low concentrations

Viscosity measurements had been made on poly(vinyl alcohol) (PVA), poly( N-vinyl-2-pyrrolidone) (PVP) and poly(ethylene oxide) (PEO) solutions down to low concentrations. It was found that t 0 ∗ defined as the flow time of the pure solvent in ideal conditions and obtained practically by extrapolating the flow time of polymer solution t to zero concentration, was not equal to the flow time of the pure solvent t 0 measured. The reduced viscosity η sp/ C determined by ( t / t 0 - 1 ) / C exhibited either a drastic increase or a significant decrease with dilution, depending upon the polymer solution investigated. On the other hand, η sp/ C determined by ( t / t 0 ∗ - 1 ) / C was proportional to C even at low concentrations. The anomalous viscosity behavior of neutral polymer solutions at low concentrations, therefore, was due to the incorrect method by which η sp/ C was determined. The detailed experiments indicated that the effective diameter of the viscometer capillary, the surface property of the capillary wall and the additional pressure corresponding to the measurement of t and t 0 for PVA, PVP and PEO solutions were not the same. Taking into account the contact anger and the surface tension of the liquid, together with the geometric parameter of the viscometer, the influence of the additional pressure upon the flow time measurement could be studied quantitatively. The calculation was in a good agreement with the experimental result. According to the method presented in this paper, the thickness of the adsorbed polymer layers on the capillary walls could be determined. It was noted that the thickness of the adsorbed polymer layers on the capillary walls was closely related to the solvent in which the polymer molecules were dissolved. The polymer molecular weight, however, had little or no effect on the thickness of the adsorbed polymer layers on the walls of the viscometer capillary.

Rheology and Ultrasound Scattering from Aggregated Red Cell Suspensions in Shear Flow

The shear flow dynamics of reversible red cell aggregates in dense suspensions were investigated by ultrasound scattering, to study the shear disruption processes of Rayleigh clusters and examine the effective mean field approximation used in microrheological models. In a first section, a rheo-acoustical model, in the Rayleigh scattering regime, is proposed to describe the shear stress dependence of the low frequency scattered power in relation to structural parameters. The fractal scattering regime characterizing the anisotropic scattering from flocs of size larger than the ultrasound wavelength is further discussed. In the second section, we report flow-dependent changes in the low-frequency scattering coefficient in a plane-plane flow geometry to analyze the shear disruption processes of hardened or deformable red cell aggregates in neutral dextran polymer solution. Rheo-acoustical experiments are examined on the basis of the rheo-acoustical model and the effective medium approximation. The ability of ultrasound scattering technique to determine the critical disaggregation shear stress and to give quantitative information on particle surface adhesive energy is analyzed. Lastly, the shear-thinning behavior of weakly aggregated hardened or deformable red cells is described.

Neutral polymer slow mode may signify an incipient growth-frustrated domain-forming glass.

Kivelson, et al. [J. Chem. Phys. 101, 2391 (1994)] propose a model for glass-forming liquids based on the potential existence of frustration-limited structures. Frustration-limited structures are equilibrium supramolecular assemblages. The maximum size of an assemblage is limited by geometric constraints. Here I propose that the "slow mode" found in the quasielastic light scattering spectra of some but not all neutral polymer solutions corresponds to the presence of an incipient growth-frustrated domain-forming glass in these solutions. A physical picture is proposed for the origin of frustration in polymer solutions.

Dynamic charge-density correlation function in weakly charged polyampholyte globules.

We study solutions of statistically neutral polyampholyte chains containing a large fraction of neutral monomers. It is known that such solutions phase separate at very low concentrations, even if the quality of the solvent with respect to the neutral monomers is good. The precipitate is semidilute if the chains are weakly charged. This paper considers straight theta solvents and good solvents, and we calculate the dynamic charge density correlation function g(k,t) in the precipitate, using the quadratic approximation to the Martin-Siggia-Rose generating functional. It is convenient to express the results in terms of dimensionless space and time variables. Let xi be the blob size, and let tau be the characteristic time scale at the blob level. Define the dimensionless wave vector q=xik, and the dimensionless time s=t/tau. In the regime q<1, corresponding to length scales larger than the blob size, and 1<s<q(-4), corresponding to time scales in between the blob relaxation time and the relaxation time at scale q(-1), we find that the charge density fluctuations relax according to the power law g(q,s) approximately q(2)s(-1/2). This relaxation is qualitatively different from that of a neutral semidilute polymer solution. We expect our results to be valid for wave vectors q>0.1, where entanglements are unimportant.

Test of the des Cloiseaux Law by Membrane Osmometry on Pullulan

The des Cloiseaux law Π ∼ C 9/4 describing the scaling relation between osmotic pressure and concentration in semi-dilute solutions of neutral polymers in athermal solvent (good solvent) was tested on pullulan, which is a linear polysaccharide, using membrane osmometry. The experimentally determined exponent is 2.2865 ± 0.026, which agrees well with this power law and disagrees with the theoretical value of 2 based on the mean field approximation.

Polymer solution film formation process in spin coating

The results of numerical modeling of polymeric films formation under mass forces action are presented. The rheology laws of neutral and charged polymer solutions are discussed The instability of non-Newtonian liquid front edge at the initial stage of flow over disk is studied. Quasistationary shapes of the liquid film spreading over surface with some rheology laws in front edge vicinity are determined. For modeling of the second stage of coating flow a special attention was paid to the effects connected with two-dimensional character of the flow. Using complex codes that calculate two-dimensional non-stationary flow of non-Newtonian liquid the impact of rheological properties of a liquid to free surface shape was studied. The factors that determine final shape of polymeric coating free surface are discussed.

Polyelectrolyte Electrophoresis in a Dilute Solution of Neutral Polymers: Model Studies

Dilute neutral polymer solutions provide an effective environment for the electrophoretic separation of polyelectrolytes by molecular weight. To better understand the mechanisms responsible, this study examines how the molecular weight dependent mobility μ of poly(styrenesulfonate), termed the probe chain, depends on the molecular weight and concentration of various dilute pullulans, termed the host chains. Available for this system are nearly monodisperse probes and hosts. Carefully performed capillary electrophoresis experiments measure absolute values of μ and its distribution. Below the overlap concentration, hosts reduce μ from its free solution value in proportion to concentration. The strongest dependence of μ on probe molecular weight occurs at nearly equal probe and host chain lengths. The influence of host and probe chain lengths on μ can be understood in terms of pairwise probe−host configurational interactions. Three parametersentanglement probability, average entanglement duration, and averag...

Monte Carlo Simulations of Probe−Host Chain Entanglement: Influence of Host Mobility and Size on Probe Electrophoretic Motion

A Monte Carlo method simulates chain trajectories during the pairwise configurational interactions of a single field-driven polyelectrolyte probe chain and a single neutral host chain. The goal is to understand how the mobility and chain length of dilute, neutral polymers affect the separation of dilute polyelectrolytes during capillary electrophoresis in a neutral polymer solution. The simulations fix probe charge density, Debye-Huckel screening length, and probe-host starting displacement, but vary chain length from 50 to 200 and 70 to 200 Kuhn steps, respectively, for flexible probe and hosts. Many trajectories lead to probe-host chain entanglement, an event believed responsible for the polyelectrolyte size discrimination observed in actual experiments. Chain distortions in response to such entanglement frequently produce double hairpin configurations that persist until the shortest hairpin arm slides past the locus of entanglement. Average probe velocity exhibits a minimum when probe and host chain lengths are nearly equal. The minimum reflects an interplay of two effects: the average duration of entanglement, which by increasing with probe length reduces mobility, and the average displacement of an entanglement, which by increasing with probe length raises mobility.

Transport of Probe Particles in Semidilute Polymer Solutions

Dynamic light scattering and sedimentation measurements are carried out to study the motion of probe particles in neutral and adsorbing polymer solutions. By varying the microscopic interaction between the colloidal particle and the polymer molecule, we observe three different behaviors to the Stokes−Einstein (SE) equation in the same colloid−polymer system. The measurements clearly delineate the sample conditions under which the three different behaviors are observed, respectively. It is shown that the three different behaviors can be explained consistently in terms of the microstructures formed in the colloid−polymer mixture. The experiment demonstrates the importance of restraining the particle−medium interaction in the measurement of the microrheological properties of complex fluids.

Thermodynamic Properties of CTAB in Aqueous Solutions of Neutral Polymers at 25°C

Interactions of polyethylene glycols (PEGs) and polypropylene glycols (PPOs) in aqueous solutions of hexadecyltrimethylammonium bromide (CTAB) were investigated through thermodynamic properties at 25°C. The densities and heat capacities of the solutions were measured with a vibrating tube densimeter and a Picker flow microcalorimeter, respectively. The variations in the apparent molar volumes and heat capacities of both solutes, calculated from the densities and heat capacities of the solutions, are unusually large in the vicinity of the CMC, reflecting the existence of very strong interactions between CTAB and PPOs. With the more hydrophilic polymers, PEGs, the apparent properties of CTAB are less affected by the presence of the polymer, indicating that PEGs interact only weakly with CTAB.

Theory of electrophoretic mobility of a polyelectrolyte in semidilute solutions of neutral polymers.

An explicit formula is derived for the electrophoretic mobility of a polyelectrolyte molecule in a semidilute solution of neutral polymers in terms of the molecular weight N of a polyelectrolyte, concentration c of neutral polymers, Debye length and solvent quality. The nature of the crossover between different regimes, as c, N, and the salt concentration are varied, is presented. The calculations show that one progressively enters into regimes of no-separation, separation, and no-separation in the electrophoresis of polyelectrolytes as c is increased. If c is very high, one returns to the mechanism of separation in gel electrophoresis.

Scaling Theory of Polyelectrolyte Solutions

We extend and generalize the scaling picture of de Gennes et al. and Pfeuty to both unentangled and entangled regimes of intrinsically flexible polyelectrolyte solutions. In semidilute solution the electrostatic persistence length of a polyelectrolyte is assumed to be proportional to the Debye screening length. If the salt concentration is low, the unentangled semidilute concentration regime spans three to four decades in polymer concentration. In this regime the dynamics of the chain is Rouse-like with viscosity weakly increasing with concentration η∼c 1/2 (Fuoss law), relaxation time decreasing with concentration τ Rouse ∼c -1/2 , and diffusion coefficient independent of concentration. Polyelectrolytes should form entanglements at the same relative viscosity as neutral polymer solutions (η≅50η s ). In the entangled regime of salt-free polyelectrolytes we predict the viscosity η∼c 3/2 , relaxation time to be independent of concentration, and diffusion coefficient D self ∼c -1/2 . Our predictions are found to compare favorably with experiments

The mobility minima in pulsed-field capillary electrophoresis of large DNA.

Pulsed-field capillary electrophoresis represents a new tool for rapid and highly efficient separations of large biopolymers. The method has been utilized here to study dependencies of the electrophoretic mobility upon the frequency and pulse shape of applied voltage for large, double-stranded DNA molecules (5-100 kb) migrating in neutral polymer solutions. Two different shapes of alternating electric field (sine- and square-wave impulses) were examined with the frequency values ranging from 1 to 30 Hz. The linear dependence between duration of the forward pulse (at which the DNA molecule experiences a minimum mobility) and the product N.In(N) (where N is the number of base pairs) was experienced in field-inversion gel electrophoresis, while exponential dependence was found with the sinusoidal electric field. The mobility minima were lower in field-inversion electrophoresis than with the biased sinusoidal-field technique. The DNA (5 kb concatamers) was adequately separated using a ramp of frequency in the square-wave electric field, in approximately 1 h. The migration order of DNA fragments was referenced through adding a monodisperse DNA (48.5 kb) into the sample. The band inversion phenomena were not observed under any experimental conditions used in this work.

Electrostatic Persistence Length of a Polyelectrolyte Chain

We calculate the electrostatic persistence length I, both for flexible and for stiff polyelec- trolytes using a self-consistent variational theory. For the case of intrinsically rigid polyelectrolytes we recover the classical results due to Odijk, Skolnick, and Fixman (OSF), namely, 1, = K-~ where K-~ is the Debye screening length. In contrast, 1, for intrinsically flexible polyelectrolytes is found to be proportional to K-~ in the limit of large screening. This is in accord with simulations, experiments, and numerical estimates. We also provide a criterion for the crossover from the OSF result to the behavior observed for intrinsically flexible polyelectrolytes. Despite numerous theoretical studies of charged polymers,l-1° a theory for the description of their conformations, at the level comparable to that for neutral polymer solutions,ll does not exist. The pres- ence of multiple length scales (six) makes a scaling description of polyelectrolytes difficult to construct. The behavior of a dilute polyelectrolyte solution has been largely analyzed in terms of the electrostatic persistence length advanced by Odijk3 and independently by Skolnick and Fi~man.~ In the Odijk-Skonick-Fixman (hereaf- ter called OSF) theories, the polyion is described by a semiflexible chain near the rod limit having N charged monomers separated by a distance A along its contour. The electrostatic interaction between the charged seg- ments is assumed to be given the Debye-Huckel potential, u(r) = ZBe-Vr. The strength of the interaction is measured in terms of the Bjerrum length Ig = e2/4mkT where e is the charge per segment, and E is the dielectric constant of the solvent. The Debye screening length, r~ = K-~, is roughly the distance beyond which the electrostatic interaction is screened. It depends on the total concentration, n, of the count- erions (assumed to be monovalent) and any added electrolytes through the relation K~ = 4nZgn. OSF calculated the increase in free energy due to electrostatic interaction and elastic bending energy for a slightly bent configuration with reference to a rodlike configuration. This was used to analyze the effect of the charges on the chain stiffness, leading naturally to the crucial concept of the electrostatic persistence length, I,. Following Odijk, the configuration of the polyion is described by the unit tangent vector u(s) = &/as, 0 I s 5 L, where rb) is the radius vector of a segment of the chain at the curvilinear position s, and L is the contour length of the chain. If the chain is near the rod limit, only those paths which minimize the elastic free energy, Le., paths for which the angle 8 defined by cos(B(s)) = u(s).u(O) varies linearly with s, contribute significantly to the partition function.12 The electrostatic contribution to the chain stiffness due to the departure from the rod limit allows for the calcula- tion of I, which in the limit of KL >> 1 is given by3~4 Abstract published in Advance ACS Abstracts, December 15, 1994. 0024-9297/95/2228-0577$09.0Qf0 The configurational properties of the chain are deter- mined by the total persistance length which is the sum of ZOSF and the bare persistence length IO. Odijk's result is based on the assumption that 8(s) is small, which is appropriate for stiff chains. However, this approximation is expected to break down for intrinsically flexible chains. In this case fluctuations in chain configurations could make a substantial con- tribution to the free energy, which in turn may result in the alteration of the electrostatic persistence length. Recently, Barrat and Joanny13 argued that these fluc- tuations contribute to (8(s)2) where (. 0) indicates the average over all paths weighted by the appropriate Boltzmann factor. The criterion for the validity of Odijk's theory can be established by examining the behavior of (8(s)2) as a function of s. Barrat and Joanny (BJ) noted that Odijk's estimate for los~ is valid at length scales larger than a certain crossover length sc given by13

Computer simulations for polymer solutions

Abstract The properties of charged and neutral polymer solutions are investigated by molecular dynamics (MD) simulations. In the case of the neutral polymers the dynamics of a single chain (length between 30 and 60 monomers) immersed in a large number of solvent particles was studied, in order to test the predictions of the Zimm model. For the case of charged polymers the complete Coulomb interactions were explicitly taken into account. This allows to study the static chain properties as a function of density for systems of up to 2048 ions without the usual mean field approximations.

Cooperative diffusion in weakly charged polyelectrolyte solutions

We study the dynamics of concentration fluctuations of a weakly charged polyelectrolyte solution in the limit where they are controlled by hydrodynamic interactions. We find three relaxation modes: a plasmon mode corresponding to the fast relaxation of charge fluctuations; a diffusive mode involving mainly the motion of the small ions (salt and counterions) to restore the ‘‘Donnan equilibrium,’’ and a slower cooperative diffusion mode corresponding to the breathing motion of the polyelectrolyte chains and ions. In the limit where the electrostatic effects are dominant, at zero wave vector, the cooperative diffusion constant has a nonmonotonic variation with the monomer concentration. Contrary to what happens in neutral polymer solutions, in the limit of low ionic strength, it decreases with the monomer concentration in agreement with recent experimental observations of Schosseler et al. on gels.The cooperative diffusion constant as a function of wave vector shows a minimum for a wave vector corresponding approximately to the peak in the structure factor.

The liquid–gas transition and the polymer–magnet analogy

We propose a new unified field-theoretic path integral treatment of liquid–gas transition occurring in simple neutral fluids and neutral monodisperse polymer solutions. Obtained theoretical results indicate that both systems belong to the same Ising-type universality class which is strongly supported by the most recent experimental results on the liquid–gas transitions.