Molecular simulation of the swelling of polyelectrolyte gels by monovalent and divalent counterions (original) (raw)
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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 beadÀspring 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 À1/2 . 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 µ I À1/5 . This is in agreement with the scaling of the chain persistence length on the solution ionic strength, l p µ I À1/2 . In semidilute solution regime at low salt concentrations the chain size decreases with increasing polymer concentration, R µ c p À1/4 , while at high salt concentrations we observed a weaker dependence of the chain size on the solution ionic strength, R µ I À1/8 . Our simulations also confirmed that the peak position in the polymer scattering function scales with the polymer concentration in dilute polyelectrolyte solutions as c p 1/3 . In semidilute polyelectrolyte solutions at low salt concentrations the location of the peak in the scattering function shifts toward the large values of q* µ c p 1/2 while at high salt concentrations the peak location depends on the solution ionic strength as I À1/4 . Analysis of the simulation data throughout the studied salt and polymer concentration ranges shows that there exist general scaling relations between multiple quantities X(I) in salt solutions and corresponding quantities X(I 0 ) in salt-free solutions, X(I) = X(I 0 )(I/I 0 ) β . The exponent β = À1/2 for chain persistence length l p , β = 1/4 for solution correlation length ξ, and β = À1/5 and β = À1/8 for chain size R in dilute and semidilute solution regimes, respectively.
Competitive Solvation Effects in Polyelectrolyte Solutions
ACS Symposium Series, 2018
An understanding of the solution properties and phase behavior of natural and synthetic polyelectrolytes requires an understanding of the competitive association of water ("hydration") and ion association to the polymer backbone and the consequences of large scale clustering of counter-ions around highly charged polymers and associated chain clustering due to the high polarizability of this diffuse counter-ion cloud. We investigate the influence of counter-ion affinity for polyelectrolyte segments on the conformational properties of individual highly charged flexible polyelectrolyte chain using molecular dynamics simulations that include both ions and an explicit solvent. We find that an increase in the affinity of the counter-ions for polyelectrolyte segments leads to a significant increase in the average number of interfacial counter-ions. For a constant charge interaction defined by a fixed Bjerrum length and Debye screening length, this increase in the number of interfacial counter-ions with an increased strength in counter-ion affinity for the polyelectrolyte segments decreases the size of the polyelectrolyte chain and the average polyelectrolyte shape becomes less extended. We also calculate and quantify the distribution of counter-ions around solvated polyelectrolyte chains, where we find that a strong affinity of the counter-ions for the polyelectrolyte segments results in a decrease in the spatial extent of the diffuse counter-ion cloud around highly charged polymers.
Macromolecules, 1998
Monte Carlo simulations of linear polyelectrolytes together with explicit ions have been performed in a spherical cell model to study conformational changes and activity coefficients in relation to the isoionic dilution method used in viscosity measurements. The results show that it is possible to define an effective ionic strength that will keep the average chain conformation constant on isoionic dilution and that this ionic strength can be predicted from the activity of the counterions, as has been suggested experimentally. Activity coefficients have been calculated from the simulations and compared with theoretical estimates based on various applications of the Debye-Hü ckel approximation, including Manning theory and an expression for a rigid rod with discrete charges. Manning theory generally gives poor agreement with the simulations, while the rigid-rod expression, which includes an ion-ion term, is able to predict the mean activity coefficient at not too high charge densities. Assuming that the co-ions are completely inert, the rigid-rod expression also leads to a reasonable approximation for the counterion activity. The simulation results have been used as input for two theoretical expressions for the reduced viscosity. The first, which is only based on the average chain conformation, does not reproduce the qualitative features of experimental curves. Our chains, with only 80 monomers, do not display large conformational changes upon dilution with salt solutions of varying ionic strength. In contrast, the second viscosity expression, which takes intermolecular electrostatic interactions into account, gives a correct qualitative behavior.
Discover chemical engineering, 2024
A complex overlay of interactions governs the conformations of polymers in solution. Among them, electrostatic interactions are the dominating factor for governing the dynamics of charged macromolecules. Salt ions further impact the conformations by inducing screening of the electrostatic interactions of the polymers. Polyelectrolytes and polyampholytes are two majorly used charged polymers for engineering hydrogels. These polymers form a complex when added together in a solution. This article emphasises the effect of salts on the polyelectrolyte-polyampholyte complex. The interactions have been analysed through the viscosity and diffusivity measurements. The in-depth analysis of the specific ion effect along with the viscous effect induced by the polymer has been carried out. It was concluded that the viscous effect tends to reverse the impact of salts on the electrostatic-dominated conformations of the polymers. The 'Shear Dependent Generalised Intrinsic Viscosity' (SDGIV) have been used to gain insights into the interactions between the polymers. Finally, the scaling of the viscosity with respect to the polymer concentration and the impact of the salts on the same has also been studied. It is concluded that the viscous effect of the polymers should also be considered for analysing the specific ion effects of the salts on the charged polymers. Sunetra V. Chituru and Sougat Das contributed equally.
Molecular Dynamics Simulations of Polyampholyte−Polyelectrolyte Complexes in Solutions
Macromolecules, 2005
We have studied how the charge distribution along a polyampholyte backbone influences aggregation of polyampholyte and polyelectrolyte chains in dilute and semidilute solutions. Using molecular dynamics (MD) simulations, we have shown that the complexation between polyampholyte and polyelectrolyte chains is due to polarization-induced attractive interactions between molecules. A polyampholyte chain binds to a polyelectrolyte in such a way to maximize the electrostatic attraction between oppositely charged ionic groups and minimize the electrostatic repulsion between similarly charged ones. The charge sequence along the polyampholyte backbone has a profound effect on the complex structure. In dilute solutions, a diblock polyampholyte could form a three-arm starlike complex in which the longest branches of the star are formed either by two sections of the polyelectrolyte chain or by a negatively charged block of the polyampholyte and by a section of the polyelectrolyte chain. There are no such complexes in solutions of random polyampholytes and polyampholytes with short blocky charge sequences. In dilute solutions of moderate polymer concentration polyampholytes with long blocky charge sequences form mixed micellar aggregates containing both polyampholyte and polyelectrolyte chains. In semidilute solutions diblock polyampholytes form a network of micelles spanning the entire system. On the contrary, the structure of multichain aggregates formed by random polyampholytes and polyelectrolytes resembles that of branched polymers with polyampholyte chains cross-linking polyelectrolytes together. The osmotic coefficients of polyampholyte polyelectrolyte mixtures show no dependence on the charge sequence along the polymer backbone, confirming the leading contribution of small ions to osmotic pressure of ionic systems.
Ion binding in polyelectrolyte solutions. An account for noncoulombic interactions
Berichte der Bunsengesellschaft für physikalische Chemie, 1996
method is used to study a refined model of polyelectrolyte solution. The discrete charges on a polyion are located periodically along the helix. The ion-ion and ion-polyion interactions are described by a solvent-averaged potential which accounts for the desolvation of ions. The major parameters of the short-range potential function are Gurney coefficients for the countenon-countenon (A,) and the charged group-counterion interaction (A,). From simulations, the self-diffusion coefficient for counterions, D/D,, was calculated. This quantity is rather sensitive to the value of A, and much less to the choice of the counterion-counterion coefficient. The refined model is used to analyze a fraction of apparently free counterions, a (=D/Da), as obtained from recent measurements of transport properties in aqueous solutions of lithium and cesium poly(styrenesu1fonate). The values of Gurney parameters, which fit experimental results, are determined: for a good agreement with experimental data an additional repulsive interaction A,= 3900 J/mol is required for lithium poly(styrenesulfonate) at 5 "C. This value is smaller (= 1500 J/mol) for lithium salt at 35 "C, and negative, =-130 J/mol, for cesium salt of poly(styrenesu1fonic) acid.
Polyelectrolytes in Solution-Recent Computer Simulations
Arxiv preprint cond-mat/9812152, 1998
We present a short overview over recent MD simulations of systems of fully flexible polyelectrolyte chains with explicitly treated counter ions using the full Coulomb potential. The main emphasis is given on the conformational properties of the polymers, with a short discussion on counter ion condensation.
Polym. Sci. Ser. A 48, 859–869 (2006) , 2006
A self-consistent integral equation theory in the form of a hybrid Monte Carlo/PRISM computation scheme was used to study a polyelectrolyte solution. The static conformational and structural properties of polyions of different rigidities in a good solvent were studied with explicit allowance for counterions over a wide concentration range. An analysis of the calculated effective potentials and correlation functions confirms the presence of effective attraction between units of the charged polymer in semidilute and concentrated solutions; this attraction leads to the collapse of polyions under certain conditions. It was shown that the cause of effective attraction is the dipole–dipole interaction of ion pairs. For the region of polyelectrolyte transition from the semidilute to the concentrated state of solution, the results qualitatively agree with experimental data and theoretical predictions. Visualized images of conformations in the test range of parameters are given.
A Model for Ion Binding and Exchange in Polyelectrolyte Solutions and Gels
The Journal of Physical Chemistry, 1957
A molecular model for linear and cross-linked polyelectrolytes is described. The model emphasizes the effect of interactions between neighboring charged groups upon both configurational and thermodynamic properties of the polymeric systems. Ion binding is introduced in a ,phenomenological manner, and it is shown that the model predicts far larger amounts of binding to polymers than to small molecules containing similar functional groups. It is found that ion binding is necessary to explain the configurational properties and titration curves of linear polyelectrolytes. Moreover, equilibria among ion pairs and unbound ions are shown to provide a means for understanding of the variation of ion-exchange resin selectivity with cross-linking, exchange capacity and the composition of the solution in contact with the resin.