Simulation of weak polyelectrolytes: A comparison between the constant pH and the reaction ensemble method

The reaction ensemble and the constant pH method are well-known chemical equilibrium approaches to simulate protonation and deprotonation reactions in classical molecular dynamics and Monte Carlo simulations. In this article, we show similarity between both methods {under certain conditions}. We perform molecular dynamics simulations of a weak polyelectrolyte in order to compare the titration curves obtained by both approaches. Our findings reveal a good agreement between the methods when the reaction ensemble is used to sweep the reaction constant. Pronounced differences between the reaction ensemble and the constant pH method can be observed for stronger acids and bases in terms of adaptive pH values. These deviations are due to the presence of explicit protons in the reaction ensemble method which induce a screening of electrostatic interactions between the charged titrable groups of the polyelectrolyte. The outcomes of our simulation hint to a better applicability of the reaction ensemble method for systems in confined geometries and titrable groups in polyelectrolytes with different pK$_\text{a}$ values.Comment: 3 figure

Simulation und Modellierung von Polyelektrolytgelen

Diese Dissertation behandelt die Entwicklung von Computermodellen zur Beschreibung von Polyelektrolytnetzwerken. Basierend auf dem periodische Gelmodell entwickeln wir zwei aufeinander aufbauende Computermodelle, welche zur Beschreibung der elastischen Eigenschaften von Polyelektrolytgelen dienen: das Einzelketten-Zellen-Gelmodell (ZGM) und das Poisson-Boltzmann Zellen-Gelmodell (PB ZGM). Da viele Polyelektrolytgele aus Bausteinen bestehen, welche chemisch reaktiv sind, ist es wichtig diese Eigenschaft korrekt in Computermodellen abzubilden. Zur Untersuchung dieser schwachen Polyelektrolytgele führen wir eine Methode zur Simulation von Ionisationsgleichgewichten in solchen Systemen ein. Der pH-Wert und die Salzkonzentration werden durch die Zusammensetzung der Überstandslösung definiert. Unsere Implementierung des Teilchenaustausches mit der Überstandslösung vermeidet bekannte Artefakte und unphysikalische Parameterkombinationen

Computer Simulations of Static and Dynamical Properties of Weak Polyelectrolyte Nanogels in Salty Solutions

We investigate the chemical equilibria of weak polyelectrolyte nanogels with reaction ensemble Monte Carlo simulations. With this method, the chemical identity of the nanogel monomers can change between neutral or charged following the acid-base equilibrium reaction HA ⇌ A− + H+. We investigate the effect of changing the chemical equilibria by modifying the dissociation constant K a . These simulations allow for the extraction of static properties like swelling equilibria and the way in which charge—both monomer and ionic—is distributed inside the nanogel. Our findings reveal that, depending on the value of K a , added salt can either increase or decrease the gel size. Using the calculated mean-charge configurations of the nanogel from the reaction ensemble simulation as a quenched input to coupled lattice-Boltzmann molecular dynamics simulations, we investigate dynamical nanogel properties such as the electrophoretic mobility μ and the diffusion coefficient D

Modeling the current modulation of dsDNA in nanopores – from mean-field to atomistic and back

All-atom molecular dynamics (MD) simulations of double stranded DNA (dsDNA) translocating through a cylindrical nanopore by Kesselheim et al. [Phys. Rev. Lett. 112, 018101 (2014)] have revealed that ions close to the surface of the DNA experience an additional friction contribution when compared to their bulk value. This friction is a key ingredient in reproducing the 2006 experimentally observed current modifications by Smeets and coworkers. While these findings were already incorporated into a coarse-grained model by Weik et al. [J. Chem. Phys. 145, 194106 (2016)], we now present an extended mean-field model for solving the electrokinetic equations of a dsDNA confined to a structureless cylindrical pore. This is done by incorporating a suitably constructed friction term into the Nernst-Planck equation. Solving the modified electrokinetic equations using a finite element method, we demonstrate that this model is able to reproduce experimental and atomistic MD results for dsDNA current modulations. The advantage of our model is that it allows a fast evaluation of new geometric arrangements of the DNA within the cylinder

Wang–Landau Reaction Ensemble Method: Simulation of Weak Polyelectrolytes and General Acid–Base Reactions

We present a novel method for the study of weak polyelectrolytes and general acid–base reactions in molecular dynamics and Monte Carlo simulations. The approach combines the advantages of the reaction ensemble and the Wang–Landau sampling method. Deprotonation and protonation reactions are simulated explicitly with the help of the reaction ensemble method, while the accurate sampling of the corresponding phase space is achieved by the Wang–Landau approach. The combination of both techniques provides a sufficient statistical accuracy such that meaningful estimates for the density of states and the partition sum can be obtained. With regard to these estimates, several thermodynamic observables like the heat capacity or reaction free energies can be calculated. We demonstrate that the computation times for the calculation of titration curves with a high statistical accuracy can be significantly decreased when compared to the original reaction ensemble method. The applicability of our approach is validated by the study of weak polyelectrolytes and their thermodynamic properties

Grand-reaction method for simulations of ionization equilibria coupled to ion partitioning

We developed a new method for coarse-grained simulations of acid-base equilibria in a system coupled to a reservoir at a given pH and concentration of added salt, that we term the Grand-reaction method. More generally, it can be used for simulations of any reactive system coupled to a reservoir of a known composition. Conceptually, it can be regarded as an extension of the reaction ensemble, combining explicit simulations of reactions within the system and Grand-canonical exchange of particles with the reservoir. To demonstrate its strength, we applied our method to a solution of weak polyelectrolytes in equilibrium with a reservoir. Our results show that the ionization and swelling of a weak polyelectrolyte are affected by the Donnan effect due to the partitioning of ions and by the polyelectrolyte effect due to electrostatic repulsion along the chain. Both effects lead to a similar shift in ionization and swelling as a function of pH; albeit for different physical reasons. By comparison with published results, we showed that neglecting one or the other effect may lead to erroneous predictions or misinterpretations of results. In contrast, the Grand-reaction method accounts for both effects on the results and allows us to quantify them. Finally, we outline possible extensions and generalizations of the method and provide a set of guidelines for its safe application by a broad community of users.</div