Monte Carlo simulation and molecular theory of tethered polyelectrolytes (original) (raw)
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Journal of Polymer Science Part B: Polymer Physics, 2006
The structural and thermodynamical properties of weak polyelectrolytes end-tethered to surfaces of arbitrary geometry are studied using a molecular theory. The theory is based on writing down the free energy functional of the system including all the basic interactions and the explicit acid-base equilibrium for the chargeable groups of the polymer. The theory explicitly includes the size, shape, conformations, and charge distribution of all the molecular species. The electrostatic interactions include a density-dependent dielectric function, modeled with the Maxwell-Garnett mixing formula, to account for the composition-dependent permittivity. The minimization of the free energy leads to the distribution of all molecular species and their dependence on bulk pH and salt concentration. We apply the theory to polymer chains end-tethered to planar, cylindrical, and spherical surfaces. The radius of the curved surfaces is small to enhance the curvature effect. We find that when the grafting surfaces are uncharged, the approximation of a constant dielectric function works very well for both structural and thermodynamic properties. The structure of weak polyelectrolytes tethered on cylindrical and spherical surfaces is different from that of polymers tethered on planar surfaces due to the available volume as a function of the distance from the surface. Specifically, the degree of dissociation increases with increasing curvature of the surface. This is a manifestation of the coupling between the local density of protons, counterions, and polymer segments. The results can be interpreted in terms of the local Le Chatelier principle for the acid-base equilibrium, with proper account of the three local contributions: counterions, protons, and chargeable groups. We find that one can achieve local changes of pH between one to two units within 1-2 nm. The thickness of the tethered layers as a function of bulk pH shows a large increase when the pH is equal to the bulk pK. However, the variation with salt concentration is different for the different geometries. The largest swelling is found for cylindrical surfaces. The predictions from scaling theories of a maximum in the thickness of the film as a function of salt concentration is found for planar films, but not for curved surfaces. Finally, the interactions between cylinders with tethered polyelectrolytes is very different from the equivalent planar surfaces. These results are important for the interpretation of force measurements with nanoscale AFM tips. The implications of the results for the rational design of responsive tethered polymer layers is discussed together with the limitations of the theoretical approach.
Phase Behavior and Charge Regulation of Weak Polyelectrolyte Grafted Layers
Physical Review Letters, 2007
The stability of weak polyelectrolytes end grafted to a planar surface has been studied with a molecular theory. The effective quality of the solvent is found to depend on the interplay between polymer grafting density, acid-base equilibrium, and salt concentration. Our results reveal that increasing salt concentration results in a thermodynamically more stable layer. This reverse salt effect is due to the competition between the solvent quality and the dual role of the ionic strength in screening the electrostatic interactions (reducing stability with increasing salt concentration), and regulating the charge on the polymer (increasing charge with increasing salt concentration). Grafted weak polyelectrolyte layers are found to be thermodynamically unstable at intermediate surface coverages. Additionally, it is established that the increased solubility of the layer at low surface coverage is due to the relatively large charge of the grafted polymers. The range of stability of the film with regard to polymer surface coverage, temperature, bulk pH and salt concentration is demonstrated.
Polyelectrolytes tethered to a free surface
The European Physical Journal E, 2001
Several attempts have been already carried out in order to tether charged chains by an end at a free fluctuating surface. We review here most of these attempts and focus on how close the physics of charged brushes can be investigated by such an approach. We first describe results about films of chargedneutral diblock copolymers spread at the surface of water. Results can be mostly rationalized in terms of charged brushes although additional structurations and fluctuations of the interface can be observed. The latter deformations are also observed when adsorbed layers of charged-neutral diblock copolymers are considered. At last, we examine how free suspended films of charged-neutral diblock copolymers can be viewed as two opposing charged brushes, both in terms of thickness and pressure.
On the Monomer Density of Grafted Polyelectrolyte Brushes and Their Interactions
Langmuir, 2004
Most of the modern theories of grafted polyelectrolyte brushes are valid only for moderate stretching of the polyelectrolyte. However, particularly at low ionic strength and high grafting densities, even a moderate charge of the polyelectrolyte can generate a strong stretching. A simple mean field model for strongly stretched grafted polyelectrolyte brushes is suggested, based on an approximate calculation of the partition function of a polyelectrolyte chain. It is shown that the average Boltzmann factor of a possible chain configuration can be approximated by the Boltzmann factor of a configuration with a constant monomer distribution, for which the free energy can be readily obtained. The monomer density in the brush and the interaction between two surfaces with grafted polyelectrolyte brushes could be calculated as a statistical average over all possible configurations. Some simple analytical results are derived, and their accuracy is examined. The dependence of the brush thickness on the electrolyte concentration is investigated, and it is shown that the trapping of a fraction of counterions in the brush influences strongly the thickness of the brush. When two surfaces with grafted polyelectrolyte brushes approach each other more rapidly than the ion diffusion parallel to the surface, the trapping of the counterions between the brushes can affect the interactions by orders of magnitude.
Specific Ion versus Electrostatic Effects on the Construction of Polyelectrolyte Multilayers †
Langmuir, 2009
Self-assembled multilayers of a strong polyanion, poly(sodium 4-styrenesulfonate) (PSS), and a strong polycation, poly[(diallyl-dimethyl-ammonium chloride)-stat-(N-methyl-N-vinyl acetamide)] (P(DADMAC-stat-NMVA)), are fabricated on silicon substrates. This article addresses the effect of electrostatics versus ion specificity. Therefore, multilayer formation and growth are investigated as a function of the charge density of the polycation, the type of salt in the polyelectrolyte dipping solution, and its ionic strength. This study focuses on monovalent ions (Li + , Na + , K + , Cs + , Rb + , F -, Cl -, Br -, and ClO 3 -). Ellipsometry and X-ray reflectometry data indicate that anions have a significantly larger effect on the thickness of the multilayer, but contrary to other studies on ion-specific effects, the influence of the type of cation is not negligible at higher salt concentrations. Larger ions, with smaller hydration shells, are highly polarizable and consequently interact strongly with charged polyelectrolytes, resulting in thicker and rougher multilayers. AFM studies confirm a higher roughness of the multilayer prepared from larger anions. The substrate can mask ion-specific effects over a distance of about 10 nm. Ion-specific effects become important above an ionic strength of 0.1 M in the case of anions and above an ionic strength of 0.25 M for cations. At lower ionic strengths, electrostatic interactions between and within the polyelectrolyte chains are dominating. Reducing the degree of polymer charge down to 75% does not shift this threshold of ionic strength. It is shown that a combination of ionic strength, polymer charge, and type of ion is a suitable tool for tuning the mobility and stability of polyelectrolyte multilayers.
Macromolecules, 2008
On basis of a coarse-grained model, we investigate the conformational behavior of a spherical polyelectrolyte brush (SPB) in a solution containing oppositely charged linear polyelectrolytes. Our results obtained from Brownian dynamics (BD) simulations show that with increasing amount of linear polyelectrolytes the SPB undergoes the process of swelling f collapse f reswelling. The collapse of the SPB is due to the replacement of confined counterions by linear polyelectrolytes and is well described within a theoretical mean field approach. This replacement and a strong correlation between linear chains and SPB chains lead to a drop in the osmotic pressure inside the SPB. The reswelling is caused by further adsorption of linear chains and counterions. This in turn results in an enhanced excluded volume effect within SPB. A weak charge inversion of the SPB complex is observed. With increasing length of linear polyelectrolytes the collapse of the SPB and its reswelling is shifted toward lower concentrations of linear chains at which both effects occur. An increasing grafting density induces a multilayer structure of adsorbed linear chains and SPB chain segments. The packing process in turn increases the thickness of the SPB. We find that adsorbed linear polyelectrolytes are significantly denatured compared to the free ones in the solution.
MRS Advances, 2016
ABSTRACTWe explore the impact of monovalent counter-ions on the molecular conformation of highly charged flexible polyelectrolytes for a range of molecular topologies (linear chains, stars, and unknotted and trefoil rings) by molecular dynamics simulations that include an explicit solvent having short range interaction with the polyelectrolyte. In particular, we investigate how the counter-ions near the polyelectrolytes with variable mass influence the average molecular shape. We also characterize the interfacially “bound” counter-ions by calculating the time-averaged number of interfacial counter-ions, as well as the degree to which the polyelectrolytes wrap around the counter-ions by calculating the number of contacts between the counter-ions and the polyelectrolyte.