# Structure and dynamics of atactic Na+-poly(acrylic) acid (PAA) polyelectrolyte in aqueous solution in dilute, semi-dilute and concentrated regimes

Abstract: Structural and dynamic properties of aqueous solution of atactic poly(acrylic) acid (PAA) in dilute, semi-dilute and concentrated regimes were studied by fully atomistic molecular dynamics simulati...

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01 Jan 1990

812 citations

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TL;DR: It is observed that at low polymer concentrations PDMAEMA chains adopt a stiffer and slightly extended conformation due to excluded-volume effects and electrostatic repulsions within the polymer chains, as the polymer concentration increases above 20 wt %, and adopt more flexible conformations.

Abstract: A combined experimental and molecular dynamics (MD) study is performed to investigate the effect of polymer concentration on the zero shear rate viscosity η0 of a salt-free aqueous solution of poly(N,N-dimethylaminoethyl methacrylate) (PDMAEMA), a flexible thermoresponsive weak polyelectrolyte with a bulky 3-methyl-1,1-diphenylpentyl unit as the terminal group. The study is carried out at room temperature (T = 298 K) with relatively short PDMAEMA chains (each containing N = 20 monomers or repeat units) at a fixed degree of ionization (α+ = 100%). For the MD simulations, a thorough validation of several molecular mechanics force fields is first undertaken for assessing their capability to accurately reproduce the experimental observations and established theoretical laws. The generalized Amber force field in combination with the restrained electrostatic potential charge fitting method is eventually adopted. Three characteristic concentration regimes are considered: the dilute (from 5 to 10 wt %), the semidilute (from 10 to 20 wt %), and the concentrated (from 20 to 29 wt %); the latter two are characterized by polymer concentrations cp higher than the characteristic overlap concentration cp*. The structural behavior of the PDMAEMA chains in the solution is assessed by calculating the square root of their mean-square radius of gyration «Rg 2»0.5, the square root of the average square chain end-to-end distance «Ree 2»0.5, the ratio «Ree 2»/«Rg 2», and the persistence length Lp. It is observed that at low polymer concentrations, PDMAEMA chains adopt a stiffer and slightly extended conformation because of excluded-volume effects (a good solvent is considered in this study) and electrostatic repulsions within the polymer chains. As the polymer concentration increases above 20 wt %, the PDMAEMA chains adopt more flexible conformations, as the excluded-volume effects seize and the charge repulsion within the polymer chains subsides. The effect of total polymer concentration on PDMAEMA chain dynamics in the solution is assessed by calculating the orientational relaxation time τc of the chain, the center-of-mass diffusion coefficient D, and the zero shear rate viscosity η0; the latter is also measured experimentally here and found to be in excellent agreement with the MD predictions.

11 citations

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Abstract: We investigate theoretically charge regulation of weakly dissociating polyacids by potentiometric titration of their aqueous solutions. By treating deprotonation and cation binding to the polyacids as reversible reactions in our model, the ionization constant of acid groups along the polyacid chain is adjusted from its intrinsic value by electrostatic correlations. If electrostatic correlations are modeled with a Debye-Huckel electrostatic free energy that ignores the connectivity of acid groups, the theory follows Henderson-Hasselbalch behavior for monoacids at low polyacid concentrations, and does not capture the shift of the ionization constant from its intrinsic value with increasing pH. Using a random phase approximation (RPA) that captures the chain connectivity, the shift of the ionization constant is predicted, which is found to directly originate from the electrostatic repulsions along the polyacid chain. We make predictions for titration of rodlike and Gaussian coil polyacids, and find that the former is followed by hydrophilic poly(acrylic acid), while the latter is followed more closely by hydrophobic poly(acrylamido-2-methyl-1-propanesulfonic acid). The results suggest that development of more advanced free energy models that allow chain configurations to self-adjust with changing pH and chain hydrophobicity could provide accurate a priori modeling of charge regulation of polyacids.

10 citations

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Abstract: We report chain self-diffusion and viscosity data for sodium polystyrene sulfonate (NaPSS) in semidilute salt-free aqueous solutions measured by pulsed field gradient NMR and rotational rheometry respectively. The observed concentration dependence of $\eta$ and $D$ are consistent with the Rouse-Zimm scaling model with a concentration dependent monomeric friction coefficient. The concentration dependence of the monomeric friction coefficient exceeds that expected from free-volume models of diffusion, and its origin remains unclear. Correlation blobs and dilute chains with equivalent end-to-end distances exhibit nearly equal friction coefficients, in agreement with scaling. The viscosity and diffusion data are combined using the Rouse model to calculate the chain dimensions of NaPSS in salt-free solution, these agree quantitatively with SANS measurements.

6 citations

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Abstract: Molecular dynamics simulations are used to study structure and dynamics of poly(vinyl alcohol) and water in aqueous solution as a function ofconcentration at different temperatures in the range 278...

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Abstract: In molecular dynamics (MD) simulations the need often arises to maintain such parameters as temperature or pressure rather than energy and volume, or to impose gradients for studying transport properties in nonequilibrium MD A method is described to realize coupling to an external bath with constant temperature or pressure with adjustable time constants for the coupling The method is easily extendable to other variables and to gradients, and can be applied also to polyatomic molecules involving internal constraints The influence of coupling time constants on dynamical variables is evaluated A leap‐frog algorithm is presented for the general case involving constraints with coupling to both a constant temperature and a constant pressure bath

22,197 citations

### "Structure and dynamics of atactic N..." refers methods in this paper

...V–Rescale (velocity rescaling) and Berendsen algorithms were used for coupling to the temperature and pressure baths[59]....

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TL;DR: An N⋅log(N) method for evaluating electrostatic energies and forces of large periodic systems is presented based on interpolation of the reciprocal space Ewald sums and evaluation of the resulting convolutions using fast Fourier transforms.

Abstract: An N⋅log(N) method for evaluating electrostatic energies and forces of large periodic systems is presented. The method is based on interpolation of the reciprocal space Ewald sums and evaluation of the resulting convolutions using fast Fourier transforms. Timings and accuracies are presented for three large crystalline ionic systems.

20,639 citations

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TL;DR: It is demonstrated that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N), which is comparable to that of a simple truncation method of 10 A or less.

Abstract: The previously developed particle mesh Ewald method is reformulated in terms of efficient B‐spline interpolation of the structure factors This reformulation allows a natural extension of the method to potentials of the form 1/rp with p≥1 Furthermore, efficient calculation of the virial tensor follows Use of B‐splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy We demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N) For biomolecular systems with many thousands of atoms this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 A or less

15,288 citations

### "Structure and dynamics of atactic N..." refers methods in this paper

...The cross-correlation function [65] between the backbone and side dihedral angles of the PAA chain was calculated using the expression...

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TL;DR: A new implementation of the molecular simulation toolkit GROMACS is presented which now both achieves extremely high performance on single processors from algorithmic optimizations and hand-coded routines and simultaneously scales very well on parallel machines.

Abstract: Molecular simulation is an extremely useful, but computationally very expensive tool for studies of chemical and biomolecular systems Here, we present a new implementation of our molecular simulation toolkit GROMACS which now both achieves extremely high performance on single processors from algorithmic optimizations and hand-coded routines and simultaneously scales very well on parallel machines The code encompasses a minimal-communication domain decomposition algorithm, full dynamic load balancing, a state-of-the-art parallel constraint solver, and efficient virtual site algorithms that allow removal of hydrogen atom degrees of freedom to enable integration time steps up to 5 fs for atomistic simulations also in parallel To improve the scaling properties of the common particle mesh Ewald electrostatics algorithms, we have in addition used a Multiple-Program, Multiple-Data approach, with separate node domains responsible for direct and reciprocal space interactions Not only does this combination of a

12,609 citations

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Uppsala University

^{1}, Stockholm University^{2}, Max Planck Society^{3}, University of Groningen^{4}TL;DR: The software suite GROMACS (Groningen MAchine for Chemical Simulation) that was developed at the University of Groningen, The Netherlands, in the early 1990s is described, which is a very fast program for molecular dynamics simulation.

Abstract: This article describes the software suite GROMACS (Groningen MAchine for Chemical Simulation) that was developed at the University of Groningen, The Netherlands, in the early 1990s. The software, written in ANSI C, originates from a parallel hardware project, and is well suited for parallelization on processor clusters. By careful optimization of neighbor searching and of inner loop performance, GROMACS is a very fast program for molecular dynamics simulation. It does not have a force field of its own, but is compatible with GROMOS, OPLS, AMBER, and ENCAD force fields. In addition, it can handle polarizable shell models and flexible constraints. The program is versatile, as force routines can be added by the user, tabulated functions can be specified, and analyses can be easily customized. Nonequilibrium dynamics and free energy determinations are incorporated. Interfaces with popular quantum-chemical packages (MOPAC, GAMES-UK, GAUSSIAN) are provided to perform mixed MM/QM simulations. The package includes about 100 utility and analysis programs. GROMACS is in the public domain and distributed (with source code and documentation) under the GNU General Public License. It is maintained by a group of developers from the Universities of Groningen, Uppsala, and Stockholm, and the Max Planck Institute for Polymer Research in Mainz. Its Web site is http://www.gromacs.org.

10,642 citations