Polyelectrolytes In Salt Solutions Research Articles

Stable Vesicles Formed by a Single Polyelectrolyte in Salt Solutions

The conformation of polyelectrolyte (PE) affects a wealth of structural and dynamic properties of PE solutions and is also fundamental to the study of the folding and aggregation of proteins. Here, we theoretically investigate the classical problem of the conformation of a single homogeneous PE in salt solutions. We predict the formation of a stable vesicle structure at intermediate salt concentrations which is beyond the well-accepted framework of globule to pearl-necklace transition. The vesicle formed by a single PE is electrostatic in origin where salt ions play the role of surfactant. We demonstrate that the transitions from vesicle to both spherical globule and pearl-necklace are discontinuous; the latter involves a two-step nucleation with an intermediate vesicle-necklace state. We also calculate the full diagram of state and show the existence of a critical quadruple point that is uniquely determined for PE with a given chain length. The vesicle structure can be well-controlled by the external salt concentration, which facilitates the design of ionic-responsive single-chain nanoparticles.

Association of two polyelectrolytes in salt solutions.

The association of polyelectrolytes (PEs) in solution affects a wealth of structural and dynamic behaviors, and is also fundamentally important for an understanding of protein association and aggregation. Here, we theoretically study the association of two PE chains by addressing the stability and morphology of the non-spherical associates. Our theory predicts that an elongated pearl-necklace (PN) associate can be stable at high salt concentrations due to the screened electrostatic repulsion. This contradicts the implication of scaling theory. In addition, there is no one-to-one correspondence between the morphology of the associate and its constituting unimers, which is demonstrated by the existence of different association modes.

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.

Polyelectrolytes in Salt Solutions: Molecular Dynamics Simulations

We present results of the molecular dynamics simulations of salt solutions of polyelectrolyte chains with number of monomers N = 300. Polyelectrolyte solutions are modeled as an ensemble of bead–spring chains of charged Lennard-Jones particles with explicit counterions and salt ions. Our simulations show that in dilute and semidilute polyelectrolyte solutions the electrostatic induced chain persistence length scales with the solution ionic strength as I–1/2. This dependence of the chain persistence length is due to counterion condensation on the polymer backbone. In dilute polyelectrolyte solutions the chain size decreases with increasing the salt concentration as R ∝ I–1/5. This is in agreement with the scaling of the chain persistence length on the solution ionic strength, lp ∝ I–1/2. In semidilute solution regime at low salt concentrations the chain size decreases with increasing polymer concentration, R ∝ cp–1/4, while at high salt concentrations we observed a weaker dependence of the chain size on th...

Swelling of biological and semiflexible polyelectrolytes

We have developed a theoretical model of swelling of semiflexible (biological)polyelectrolytes in salt solutions. Our approach is based on separation of length scaleswhich allowed us to split a chain’s electrostatic energy into two parts that describe localand remote electrostatic interactions along the polymer backbone. The local part takes intoaccount interactions between charged monomers that are separated by distances along thepolymer backbone shorter than the chain’s persistence length. These electrostaticinteractions renormalize chain persistence length. The second part includes electrostaticinteractions between remote charged pairs along the polymer backbone located at distanceslarger than the chain persistence length. These interactions are responsible forchain swelling. In the framework of this approach we calculated effective chainpersistence length and chain size as a function of the Debye screening length, chaindegree of ionization, bare persistence length and chain degree of polymerization.Our crossover expression for the effective chain’s persistence length is in goodquantitative agreement with the experimental data on DNA. We have been able to fitexperimental datasets by using two adjustable parameters: DNA ionization degree (α = 0.15–0.17) and a barepersistence length (lp = 40–44 nm).

Role of chain stiffness on the conformation of single polyelectrolytes in salt solutions

Conformation of single polyelectrolytes in tetravalent salt solutions is investigated under the framework of a coarse-grained model, using Langevin dynamics simulations. The chain size, studied by the radius of gyration, shows three different variational behaviors with salt concentration, depending on the chain stiffness. According to the size variations, polyelectrolytes of fixed chain length are classified into three categories: (1) flexible chain, for which the variation shows a curve similar to a tilted L, (2) semiflexible chain, whose curve resembles U, and (3) rigid chain, for which the curve is a straight line. The wormlike chain model with persistence length predicted by the Odijk-Skolnick-Fixman theory is found to be able to qualitatively describe the end-to-end distance at low salt concentration not only for semiflexible and rigid chains but also for flexible chain. In a low salt region, a flexible polyelectrolyte extends more significantly than a semiflexible chain, in reference of the size of their uncharged counterparts, and in a high salt region, regardless of chain stiffness, a chain attains a dimension comparable to that of its neutral polymer. The chain stiffness influences both the local and the global chain structures. A flexible chain exhibits a zigzagged local structure in the presence of salt ions, and the condensed structure is a disordered, random globule. A semiflexible chain is locally smooth, and the condensed structure is orderly packed, taking a form such as hairpin or toroid. Moreover, the chain stiffness can also affect the nature of the coil-globule transition. The transition occurred in a discrete manner for semiflexible chain, whereas it occurred in a continuous way for flexible chain. This discrete feature happened not only at low salt concentration when a semiflexible chain collapsed but also at high salt concentration when the collapsed chain is reexpanded. At the end, the effects of chain stiffness and salt concentration on the conformation of single polyelectrolytes are summarized in a schematic state diagram.

Electrostatic interactions in dissipative particle dynamics using the Ewald sums

The electrostatic interactions in dissipative particle dynamics (DPD) simulations are calculated using the standard Ewald [Ann. Phys. 64, 253 (1921)] sum method. Charge distributions on DPD particles are included to prevent artificial ionic pair formation. This proposal is an alternative method to that introduced recently by Groot [J. Chem. Phys. 118, 11265 (2003)] where the electrostatic field was solved locally on a lattice. The Ewald method is applied to study a bulk electrolyte and polyelectrolyte-surfactant solutions. The structure of the fluid is analyzed through the radial distribution function between charged particles. The results are in good agreement with those reported by Groot for the same systems. We also calculated the radius of gyration of a polyelectrolyte in salt solution as a function of solution pH and degree of ionization of the chain. The radius of gyration increases with the net charge of the polymer in agreement with the trend found in static light scattering experiments of polystyrene sulfonate solutions.

Precipitation of oppositely charged polyelectrolytes in salt solutions.

We study phase separation in symmetric solutions of weakly charged flexible chains of opposite sign. Precipitation is caused by effective attractions due to charge fluctuations and by short-range attractions between monomers. The contribution from charge fluctuations is computed within the random phase approximation (RPA), which takes into account the connectivity of charges in the polyions. The impenetrability of the ions is accounted for by using a modified Coulomb potential in the RPA. In good solvent conditions the precipitate monotonically swells and eventually dissolves upon addition of salt. However, near the theta-solvent condition, but still in the good solvent, the precipitate can be stable at any salt concentration. Moreover, the density of the precipitate after initial decrease can increase with addition of salt. This effect is a result of redistribution of salt between the precipitate and the supernatant, which is due to an interplay of electrostatic and hardcore interactions. For not too weakly charged polyions the precipitate properties become strongly dependent on temperature even in good solvent conditions.

Comparison of the Poisson–Boltzmann Model and the Donnan Equilibrium of a Polyelectrolyte in Salt Solution

A sequence of charged parallel flat plates immersed in a salt solution is used to model the swelling behavior of a polyelectrolyte. The solution of the nonlinear Poisson–Boltzmann equation gives rise to an analytical expression of the plate distance as a function of swelling pressure (p), plate charge density (ς), and salt concentration (n). The exact treatment of the system also yields the connection between polyelectrolyte concentration nP, p, ς, and n. A formula for the electric potential difference between polyelectrolyte and salt solutions is derived. On the other hand, the relation between nP, p, and n is known from the Donnan equilibrium. It is shown that the Donnan potential, UD(nP, n), and swelling pressure, pD(nP, n), are always larger than the equivalent quantities in the Poisson–Boltzmann theory (UPB(ς, nP, n) and pPB(ς, nP, n), respectively). The transition from the Poisson–Boltzmann theory to the Donnan model is achieved by the limiting process ς → 0 which reveals the intrinsic linkage between the two theories. pD(nP, n) = limς→0pPB(ς, nP, n) and UD(nP, n) = limς→0UPB(ς, nP, n).

Very large thermal separations for polyelectrolytes in salt solutions

A conductivity method is used to measure the Soret coefficient and heat of transport of aqueous sodium poly(styrenesulfonate)(NanPSSA). The data are used to calculate thermal separation factors for NanPSSA dissolved in aqueous sodium chloride solutions. The calculations show that large steady-state concentration gradients in the polyelectrolyte will be established when a temperature gradient is applied to mixed NanPSSA–NaCl solutions, ranging up to 80% change in concentration per degree as the polyelectrolyte concentration approaches zero. The Soret coefficient and heat of transport of aqueous sodium benzenesulfonate are measured and compared with the corresponding values for NanPSSA.

Influence of charge mobility on the equilibrium properties of polyelectrolytes in salt solutions: a Monte Carlo study

Using a Metropolis algorithm, various average properties of 'lattice were calculated, i.e. the squared end-to-end distance, the squared radius of gyration, the apparent persistence length, the charge distribution over the segments, the average distance between the charges and the center of mass, and the eccentricities of the mass and charge distributions. Lattice polyelectrolytes are self-avoiding random walks on a (3-dimensional) cubic lattice, bearing either equidistantly fixed or mobile, discrete charges. For the electrostatic interaction a Debye-Huckel potential is used. Differences due to charge mobility along the chain are analyzed. It is found that most of these differences can be explained in terms of a more uniform average charge distribution in the mobile case, and a charge accumulation of the mobile charges near the ends of the chain. Furthermore, the mobile charges will tend to preferentially localize themselves away from bends in the chain, thus enhancing its flexibility. Our results for the end-to-end distance and chain stiffness for increasing charge density are compared with the theoretical results given by Katchalsky, Odijk, Schmidt, Skolnick and Fixman, and also with (other) simulation results by Carnie, Christos, and Creamer.

Monte Carlo and mean field studies of a polyelectrolyte in salt solution

A single flexible polyelectrolyte chain in salt solution is studied by means of Monte Carlo simulations and within a mean field theory. The effect of salt has been treated both explicitly and in an approximate way using the screened Coulomb potential. The general conclusion is that the latter approximation is an excellent one for low and moderate salt concentrations of 1 : 1 electrolyte. The introduction of divalent ions requires a more stringent treatment in the theory including both nonlinear effects and possibly also ion-ion correlations. The mean field theory, incorporating nearest-neighbour interactions within the chain, is qualitatively correct, although it fails in the quantitative comparisons. Further extensions of the mean field theory, incorporating more explicit interactions within the polyelectrolyte chain, are discussed and it is concluded that these extensions are not likely to give a general improvement.

Chain conformation of linear polyelectrolyte in salt solutions: sodium poly(styrenesulfonate) in potassium chloride and sodium chloride

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTChain conformation of linear polyelectrolyte in salt solutions: sodium poly(styrenesulfonate) in potassium chloride and sodium chlorideLixiao Wang and Hyuk YuCite this: Macromolecules 1988, 21, 12, 3498–3501Publication Date (Print):December 1, 1988Publication History Published online1 May 2002Published inissue 1 December 1988https://doi.org/10.1021/ma00190a026RIGHTS & PERMISSIONSArticle Views688Altmetric-Citations77LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (545 KB) Get e-Alerts Get e-Alerts

Intrinsic Viscosity of Polyelectrolytes in Salt Solutions

A theory is given for the inverse square-root dependence of the intrinsic viscosity of polyelectrolytes on the concentration of added salt. The results agree with the data by Noda, Tsuge, and Nagasawa. The existence of at least a partial drainage effect in polyelectrolytes is discussed.

Excluded volume study of a sulfonate‐containing polyelectrolyte in salt solutions

AbstractChain characteristics of a linear sulfonate‐containing homopolymer, sodium poly(3‐methacryloyloxypropane‐1‐sulfonate), in aqueous salt solutions (ionic strength, Cs = 0.01N to 5N NaCl) have been investigated by light scattering and intrinsic viscosity. The molecular weight (M̄w)–viscosity relation can be well described by the Mark–Houwink and the Stockmayer–Fixman equations. The coil is highly expanded even in the most concentrated NaCl solution (6N), and no 1:1 electrolyte was found to precipitate this polymer.A linear relation was observed between the viscosity expansion factor, α3η, and (M̄w/Cs)1/2. Examination of the data in terms of theories for excluded volume and hydrodynamic interaction suggests that the coil experiences dominant hydrodynamic interaction, corresponding to a nondraining coil, and the second virial coefficient and coil expansion at high Cs can be correlated by the Flory–Krigbaum–Orofino equation. Results for this polymer are compared with those for other polyelectrolytes, and are discussed in terms of chain structure, flexibility, and hydrophobicity.

Intrinsic viscosity of polyelectrolytes in salt solutions

AbstractThe dependence of the intrinsic viscosity of polyelectrolytes on the concentration of added salt is given satisfactorily by a formula obtained recently. A new viscosity—molecular weight relation gives satisfactory agreement with experiments.

Electrophoresis of a rod-like polyelectrolyte in salt solution

Electrophoresis of a rod-like polyelectrolyte in salt solution

Effect of Excluded Volume on Polyelectrolytes in Salt Solutions

A recently developed theory of excluded volume, relating α to z ∝ M½βL−3 by means of an integral equation, is applied to polyelectrolytes. The line describing α(M½) is the same for all polymers; the dependence of α on the polyelectrolyte parameters (ionic strength and charge density) requires, however, further elaboration. Thus, the excluded volume β is summarily identified with the high-potential shell coaxially surrounding the charged filament, as treated in a polyelectrolyte theory presented some time ago. Distinction is made between two cases: (a) When the shell radius is smaller than the link length L characterizing the polymer and (b) when the converse holds—so that the length of free hinged links becomes determined by the shell radius. The predicted dependence of α on the molecular weight and on the ionic strength is found to agree satisfactorily with the extensive viscosity data reported by Takahashi and Nagasawa. Additional aspects of investigating α(z) are also discussed.

Polyelectrolytes in salt solutions

AbstractIt is shown that the exceptionally low expansion values expected by Kimball, Cutler, and Samuelson's theory result from their interpretation of the Gaussian distribution function for polymer chain segments rather than a statistical mechanical additivity problem.

Excluded Volume of Polyelectrolyte in Salt Solutions

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTExcluded Volume of Polyelectrolyte in Salt SolutionsAkira. Takahashi and Mitsuru. NagasawaCite this: J. Am. Chem. Soc. 1964, 86, 4, 543–548Publication Date (Print):February 1, 1964Publication History Published online1 May 2002Published inissue 1 February 1964https://doi.org/10.1021/ja01058a003RIGHTS & PERMISSIONSArticle Views380Altmetric-Citations131LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (671 KB) Get e-Alerts Get e-Alerts