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The swelling of polyelectrolyte hydrogels has been often explained using simple models derived from the Flory-Rehner model. While these models qualitatively predict the experimentally observed trends, they also introduce strong approximations and neglect some important contributions. Consequently, they sometimes incorrectly ascribe the observed trends to contributions which are of minor importance under the given conditions. In this work, we investigate the swelling properties of weak (pH-responsive) polyelectrolyte gels at various pH and salt concentrations, using a hierarchy of models, gradually introducing various approximations. For the first time, we introduce a three-dimensional particle-based model which accounts for the topology of the hydrogel network, for electrostatic interactions between gel segments and small ions and for acid-base equilibrium coupled to the Donnan partitioning of small ions. This model is the most accurate one, therefore, we use it as a reference when assessing the effect of various approximations. As the first approximation, we introduce the affine deformation, which allows us to replace the network of many chains by a single chain, while retaining the particle-based representation. In the next step, we use the mean-field approximation to replace particles by density fields, combining the Poisson-Boltzmann equation with elastic stretching of the chain. Finally, we introduce an ideal gel model by neglecting the electrostatics while retaining all other features of the previous model. Comparing predictions from all four models allows us to understand which contributions dominate at high or low pH or salt concentrations. We observe that the field-based models overestimate the ionization degree of the gel because they underestimate the electrostatic interactions. Nevertheless, a cancellation of effects on the electrostatic interactions and Donnan partitioning causes that both particle-based and field-based models consistently predict the swelling of the gels as a function of pH and salt concentration. Thus, we can conclude that any of the employed models can rationalize the known experimental trends in gel swelling, however, only the particle-based models fully account for the true effects causing these trends. The full understanding of differences between various models is important when interpreting experimental results in the framework of existing theories and for ascribing the observed trends to particular contributions, such as the Donnan partitioning of ions, osmotic pressure or electrostatic interactions.

Mixing of oppositely charged macromolecules can, under certain conditions, lead to the formation of electrostatically cross-linked coacervate gels. In this simulation study, we determine the condit...

We use hybrid molecular dynamics/Monte Carlo simulations and coarse-grained polymer models to study the swelling of polyelectrolyte gels in salt solutions. Besides existing industrial applications, such gels have been recently proposed as a promising agent for water desalination. We employ the semi-grand canonical ensemble to investigate partitioning of the salt between the bulk solution and the gel and the salt-induced deswelling of the gels under free swelling equilibrium and under compression. We compare our findings to the analytic model of Katchalsky and Michaeli which explicitly accounts for electrostatic effects. The partitioning of small ions predicted by the model well captures the deviations from the simple Donnan approximation observed in the simulation data. In contrast, the original model highly overestimates the gel swelling, predicting even chain stretching beyond contour length. With a modified model, where we replace the Gaussian elasticity with the Langevin function for finite extensibil...

We study the electrophoresis of a polyelectrolyte-grafted colloid immersed in monovalent salt solution by means of explicit-ion molecular dynamics simulations including long-ranged hydrodynamic interactions via a lattice-Boltzmann fluid. We expand on our previous work on the subject by investigating the effect of charges and the salt concentration on both net-neutral and net-charged composites. We show that the dominant role of the polyelectrolytes at higher salt concentrations prevents a net-negative soft colloid to reverse mobility with respect to net charge except at extremely high net charges. We explain all our simulation results by examining in detail the ion and monomer density profiles around the colloid and the ratio of the Debye length to the brush height. Our simulation results show good agreement with both approximate analytic expressions and numerical solutions based on an extended standard electrokinetic model for polymer-grafted spherical colloids.

We employ fluorescence correlation spectroscopy (FCS) to study the translational mobility of molecular tracers in stimuli-responsive grafted poly(N-isopropylacrylamide) (PNiPAAm) hydrogels, under variable solvency conditions. Tracer–matrix interactions were tuned by selecting three different molecular tracers. In contrast to a noninteracting tracer (Alexa 647), the mobility of a weakly (Alexa 488) and a strongly interacting (Rhodamine 6G) tracer deviates from a simple single Fickian diffusion. In addition to pure crowding effects, the mobility of both Alexa488 and Rhodamine 6G is influenced by tracer–polymer interactions. We interpret the observed trends in tracer mobility in terms of the interplay between Coulombic repulsions and short-range attractions. Although tracer dynamics and hydrogel swelling ratio are interdependent properties, their relation turns out to be nontrivial and does not allow predictions of tracer dynamics on the basis of polymer structural information. Hence, a universal scaling beh...

Electro-osmotic flow (EOF) plays a crucial role in the functioning of devices in micro- and nanofluidics. In order to optimize the operation of a device, polymer coatings are often used to control ...

Extensive all-atom molecular dynamics simulations have been performed to investigate the effect of surface features on the adsorption of poly(styrenesulfonate) (PSS) oligomers on top of a modified ...

Explicit solvent all-atom molecular dynamics simulations of mixtures of poly(styrenesulfonate)(PSS) and poly(diallyldimethylammonium) (PDADMA) polyelectrolytes at various salt (NaCl) concentrations are performed. We characterize the formed polyelectrolyte complexes (PECs) and relate the observed physical properties of PSS−PDADMA PECs to the properties found in polyelectrolyte multilayers (PEMs) made of the same compositions. Our results reveal a change in the way charges are compensated upon the addition of salt, namely from an intrinsic mechanism (polyanions pair with polycations) toward an extrinsic one (polyions pair with salt ions). The probability of the intrinsic compensating mechanism decreases from about 90% to about 60% when the salt concentration increases from 0.168 to 1 mol/L. The interaction energies of the ion-pairing follow the order of Na−Cl > PSS−Na > PDADMA−Cl ≅ PSS−PDADMA. Furthermore, we investigate thoroughly the water distribution and study the hydration mechanisms in our system. Wat...

The bundle formation in solution of hydrophobically modified sulfonated poly(p-phenylene) oligomers (PPP) is studied by molecular dynamics simulations. These oligomers form cylindrical micelles in water. Light scattering experiments suggest that the number of PPP oligomers in the cross section is around 10−19 when monovalent Na+ is used as counterion. On the other hand, if divalent Ca2+ counterions are used, this number dramatically increases to 60 oligomers. Here, we show that the basic packing of the PPP oligomers does not change upon increase of the counterion valency. However, the interaction among bundles goes from repulsive to attractive as the counterions are changed from Na+ to Ca2+. We propose that the observed aggregate size of 60 oligomers could be explained by aggregation of several bundles (i.e., bundle of bundles).

Osmotic properties of dilute salt-free solutions of stiff-chain polyelectrolytes are studied using computer simulations. A number of factors affecting the charge distribution around the macroions are analyzed quantitatively for parameters of an aqueous solution of a typical synthetic strongly charged rodlike polyelectrolyte. Departing from a mean-field treatment of an infinitely long linear charged rod, we significantly refine the model description. We found that incorporation of effects such as electrostatic correlations between counterions, chain flexibility, and addition of salt decreases the osmotic coefficient slightly. On the other hand, a model of a finite macroion with a noncentral charge distribution predicted significantly higher pressure. We quantify all these contributions separately and show what deviation one should expect from the prediction of the Poisson-Boltzmann solution of the infinite rod cell model. We further comment on the discrepancy between our simulation results and experimentally measured values.

We use Molecular Dynamics simulations to study attractive interactions and the underlying ionic correlations between parallel like-charged rods in the absence of additional salt. For a generic bulk system of rods we identify a reduction of short range repulsions as the origin of a negative osmotic coefficient. The counterions show signs of a weak three-dimensional order in the attractive regime only once the rod-imposed charge-inhomogeneities are divided out. We also treat the case of attraction between a single pair of rods for a few selected line charge densities and rod radii. Measurements of the individual contributions to the force between close rods are studied as a function of Bjerrum length. We find that even though the total force is always attractive at sufficiently high Bjerrum length, the electrostatic contribution can ultimately become repulsive. We also measure azimuthal and longitudinal correlation functions to answer the question how condensed ions are distributed with respect to each other and to the neighboring rod. For instance, we show that the prevalent image of mutually interlocked ions is qualitatively correct, even though modifications due to thermal fluctuations are usually strong., 14 pages, 14 figures, REVTeX4 style