Counterion-Correlation-Induced Attraction and Necklace Formation in Polyelectrolyte Solutions: Theory and Simulations (original) (raw)
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Single-Chain Properties of Polyelectrolytes in Poor Solvent †
The Journal of Physical Chemistry B, 2003
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 interactions leads to pearl-necklace like structures. We observe that large number and size fluctuations in the pearls and strings lead to only small direct signatures in experimental observables like the single chain form factor. Furthermore we do not observe the predicted first order collapse of the necklace into a globular structure when counterion condensation sets in. We will also show that the pearlnecklace regime is rather small for strongly charged polyelectrolytes at finite densities. Even small changes in the charge fraction of the chain can have a large impact on the conformation due to the delicate interplay between counterion distribution and chain conformation.
Necklace Globule and Counterion Condensation
Macromolecules, 2007
We have developed a necklace model of polyelectrolyte chain in which the necklace structure appears as a result of the counterion condensation on the polyelectrolyte backbone. This necklace structure optimizes the correlation-induced attraction of the condensed counterions and charged monomers and electrostatic repulsion between uncompensated charges. The new feature of this necklace globule is that it can be formed even in good solvent conditions for the polymer backbone. By using the scaling analysis, we have calculated the diagram of state of polyelectrolyte chain as a function of the solvent quality for the polymer backbone and value of the Bjerrum length. To test the predictions of a scaling model, we have performed molecular dynamics simulations of polyelectrolyte chains with the degrees of polymerizations N ) 124-304 and fraction of charged monomers f ) 1 / 3 in good, θ, and poor solvent conditions for the polymer backbone. We have identified the range of parameters in which the necklace globule is formed due to correlation-induced attractive interactions in the good solvent conditions for the polymer backbone. The results of the molecular dynamics simulations are in qualitative agreement with the predictions of a scaling model.
Polymer, 1993
Monte Carlo simulations on the cubic lattice were used to investigate how the functions describing the concentration-dependent size of macromolecular solutes are affected when the usual, low-molecular-weight ('monomeric') solvent is replaced by a chain-like 'polymeric' solvent. The simulations confirm the expected trend of coil shrinkage with the increase of solute volume fraction qk Remarkably, however, only a minor difference was found between the monomeric and polymeric solvents in the concentration dependence of the expansion coefficient ct. The double logarithmic plot of the function ~2 versus & in the range of semidilute solutions gives a value of exponent y ~ -0.24 for both types of solvents, which is in good accord with the arguments of the mean-field and scaling theories. In contrast to the concentration dependence of ~, the chain-like character of the solvent has a considerable effect on the variation of the expansion coefficient with the solvent quality given, for example, by the Z parameter.
Statistical Properties of a Polymer Chain in the Environment with Low Concentration of Nanoparticles
Acta Physica Polonica A
We have investigated the statistical properties of polymer in the environment with low concentration of nanoparticles by using large-scale molecular dynamics simulations. The scaling law for the mean square radius of gyration was examined and simulation results for the polymer lengths 64 ≤ N ≤ 144 yielding a reasonably accurate value of the Flory exponent ν = 0.58 at weak polymer-nanoparticle interaction εPN. Within the same range of N , the mean asphericity of the chain is independent of N. We found that the polymer behaves like a self-avoiding walk chain at small εPN and a compact sphere at large εPN. The results are attributed to the increase in the contact between polymer and nanoparticles with increasing εPN. Normal diffusions of polymer are always observed at whatever εPN and size and concentration of nanoparticles. Our result shows that the normal diffusion behavior of polymer is independent of polymer's state even though there is a phase transition from a desorbed polymer phase at small εPN to an adsorbed polymer phase at large εPN.
Computer Simulation Studies of a Single Polyelectrolyte Chain in Poor Solvent
Macromolecules, 1999
The conformational behavior of a single, intrinsically exible, weakly charged polyelectrolyte chain in poor solvent is analyzed by extensive computer simulations combining Monte Carlo and Molecular Dynamics techniques. After determining the point for the charge{free case, we focus on the weak screening limit, corresponding to low salt concentration in the solution. We study the dependence on both the solvent strength, characterized by the relative deviation from the point, , and the fraction of charged monomers in the chain, which is e ectively tuned by varying the Coulomb interaction parameter. The conformations are discussed in terms of global properties (like the end{to{end distance, the inertia tensor components, etc.), and functions revealing more detailed information, like the density distribution around the center of mass, and the structure factor. For chains in the regime our data con rm the picture of a string of electrostatic blobs. For poorer solvents (up to = 0:4) we observe, upon increasing the intra{chain Coulomb repulsion, a splitting of the spherical globule into a dumbbell{type structure, accompanied by a sharp increase in the chain's gyration radius. For su ciently large , a further splitting is observed as well. Such a \necklace globule" (a sequence of transitions) had been predicted by Dobrynin, Obukhov (Macromolecules 1996, v. 29, p. 2974), with a nontrivial scaling of the gyration radius with chain length and interaction parameters, which is con rmed by our data. By means of a scaling analysis we argue that the transitions can be interpreted as thermodynamic rst{ order phase transformations, when taking the appropriate thermodynamic limit, which implies a scaling of the electrostatic coupling with inverse chain length.
Cascade of Transitions of Polyelectrolytes in Poor Solvents
Macromolecules, 1996
We develop a scaling model for the dilute solution conformation of a uniformly charged polymer in a poor solvent. We find that there is a range of temperatures and charge densities for which the polymer has a necklace-like shape with compact beads joined by narrow strings. The free energy of a polyelectrolyte in this conformation is lower than in a cylindrical globule because the length of the necklace is larger than that of a cylinder and is proportional to the total charge on the chain. With changing charge on the chain or temperature, the polyelectrolyte undergoes a cascade of abrupt transitions between necklaces with different numbers of beads.
Polymer, 1999
The isoionic dilution method was used to measure the intrinsic viscosity, [h], and the Huggins coefficient, K H , of two poly(acrylic acid) samples, 50% neutralized with NaOH, with molecular weights 5.0 × 10 3 (Na50PA5) and 4.8 × 10 4 (Na50PA48) at different ionic strengths. For Na50PA5 at low ionic strength, [h] is higher than the value predicted by a rigid-rod model. Assuming that the chain has reached its maximum extension, we have combined the rigid-rod model with the idea of effective dimensions that depend linearly on the Debye-Hückel screening length, k Ϫ1 , to account for a primary electroviscous effect, as a means to describe the observed behavior. As a consistent approach, we have also combined the effective dimensions with the wormlike chain model to calculate the persistence length of the higher molecular weight sample, Na50PA48. The result is that the electrostatic persistence length, l e , is proportional to k Ϫ1 , in the region of high to moderate ionic strength, as is usually observed experimentally for flexible polyelectrolytes, while at the lowest ionic strengths, l e tends to level off, which was predicted theoretically. Both the samples show a considerable increase in the Huggins coefficient as the ionic strength is lowered, with the sample having the lowest molecular weight giving the highest value at any particular ionic strength. This is attributed to the increasing intermolecular electrostatic interactions, which have a relatively larger importance in the case of Na50PA5, because the dimensions of the chain are smaller when compared with the range of the electrostatic interactions, as measured by k Ϫ1 , than for Na50PA48.
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.
Macromolecules, 2008
according to the journal that you are submitting your paper to) 2 ABSTRACT: In order to better understand the collapse of polyions in poor solvent conditions the effective charge and the solvent quality of the hypothetically uncharged polymer backbone need to be known. In the present work this is achieved by utilizing poly-2-vinylpyridine quaternized to 4.3% with ethylbromide. Conductivity and light scattering measurements were utilized to study the polyion collapse in isorefractive solvent/non-solvent mixtures consisting of 1-propanol and 2-pentanone, respectively, at nearly constant dielectric constant. The solvent quality of the uncharged polyion could be quantified which, for the first time, allowed the experimental investigation of the effect of the electrostatic interaction prior and during polyion collapse, by comparing to a newly developed theory.