Implicit method for simulating electrohydrodynamics of polyelectrolytes

Conformation and Dynamics of Long-Chain End-Tethered Polymers in Microchannels

Polyelectrolytes constitute an important group of materials, used for such different purposes as the stabilization of emulsions and suspensions or oil recovery. They are also studied and utilized in the field of microfluidics. With respect to the latter, a part of the interest in polyelectrolytes inside microchannels stems from genetic analysis, considering that deoxyribonucleic acid (DNA) molecules are polyelectrolytes. This review summarizes the single-molecule experimental and molecular dynamics simulation-based studies of end-tethered polyelectrolytes, especially addressing their relaxation dynamics and deformation characteristics under various external forces in micro-confined environments. In most of these studies, DNA is considered as a model polyelectrolyte. Apart from summarizing the results obtained in that area, the most important experimental and simulation techniques are explained.

Influence of weak groups on polyelectrolyte mobilities

The ionization of dissociable groups in weak polyelectrolytes does not occur in a homogenous fashion. Monomer connectivity imposes constraints on the localization of the dissociated (charged) monomers that affect the local electric potential. As a result, the mean bare charge along a weak polyelectrolyte can vary depending on the proximity to topological features (e.g. presence of crosslinks or dangling ends). Using reaction-ensemble Monte-Carlo simulations we calculate the dissociation inhomogeneities for a few selected PE configurations, linear, rod-like, flexible four-arm star, and a star with stiff arms. An ensemble preaverage is used to obtain the annealed bare charge profile for these different polymer configurations. Using molecular dynamics simulations within a Lattice-Boltzman fluid, we investigate how the electrophoretic mobility is affected by the bare charge inhomogeneities arising from the annealed weak polyelectrolytes. Surprisingly, the mobility obtained for the situations corresponding to the predicted charge profile for annealed weak polyelectrolytes are not significantly different than the mobility obtained when all the monomers have an identical charge (under the constraint that the total polyelectrolyte bare charge is the same). This is also true for the stiff rod-like variants where conformational changes induced from the localization of the monomer charges are negligible. In salty solutions, we find that counterions are affected by the electric potential modulations induced by the topological features. Since the counterions crowd in regions where the electric potential caused by the dissociated monomers is highest, they wash-out the bare charge inhomogeneities and contribute to a more uniform effective backbone charge.

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.

Electric-field-induced stretching of surface-tethered polyelectrolytes in a microchannel

We study the stretching of a surface-tethered polyelectrolyte confined between parallel surfaces under the application of a dc electric field. We explore the influence of the electric-field strength, the length of the polyelectrolyte, and the degree of confinement on the conformation of the polyelectrolyte by single-molecule experiments and coarse-grained coupled lattice-Boltzmann molecular-dynamics simulations. The fractional extension of the polyelectrolyte is found to be a universal function of the product of the applied electric field and the molecular contour length, which is explained by simple scaling arguments. The degree of confinement does not have any significant influence on the stretching. We also confirm that an electrohydrodynamic equivalence principle relating the stretching in an electric field to that in a flow field is applicable.

A coarse-grained DNA model for the prediction of current signals in DNA translocation experiments

We present an implicit solvent coarse-grained double-stranded DNA (dsDNA) model confined to an infinite cylindrical pore that reproduces the experimentally observed current modulations of a KaCl solution at various concentrations. Our model extends previous coarse-grained and mean-field approaches by incorporating a position dependent friction term on the ions, which Kesselheim et al. [Phys. Rev. Lett. 112, 018101 (2014)] identified as an essential ingredient to correctly reproduce the experimental data of Smeets et al. [Nano Lett. 6, 89 (2006)]. Our approach reduces the computational effort by orders of magnitude compared with all-atom simulations and serves as a promising starting point for modeling the entire translocation process of dsDNA. We achieve a consistent description of the system's electrokinetics by using explicitly parameterized ions, a friction term between the DNA beads and the ions, and a lattice-Boltzmann model for the solvent.

Influence of concentration polarization on DNA translocation through a nanopore

Concentration polarization can be induced by the unique ion-perm selectivity of small nanopores, leading to a salt concentration gradient across nanopores. This concentration gradient can create diffusio-osmosis and induce an electric field, affecting ionic currents on DNA that translocates through a nanopore. Here this influence is theoretically investigated by solving the continuum Poisson-Nernst-Planck model for different salt concentrations, DNA surface charge densities, and pore properties. By implementing the perturbation method, we can explicitly compute the contribution of concentration polarization to the ionic current. The induced electric field by concentration polarization is opposite to the imposed electric field and decreases the migration current, and the induced diffusio-osmosis can decrease the convection current as well. Our studies suggest that the importance of the concentration polarization can be determined by the parameter λ/G where λ is the double-layer thickness and G is the gap size. When λ/G is larger than a critical value, the influence of concentration polarization becomes more prominent. This conclusion is supported by the studies on the dependence of the ionic current on salt concentration and pore properties, showing that the difference between two models with and without accounting for concentration polarization is larger for low salts and small pores, which correspond to larger λ/G.

Computer simulations of single particles in external electric fields

Applying electric fields is an attractive way to control and manipulate single particles or molecules, e.g., in lab-on-a-chip devices. However, the response of nanosize objects in electrolyte solution to external fields is far from trivial. It is the result of a variety of dynamical processes taking place in the ion cloud surrounding charged particles and in the bulk electrolyte, and it is governed by an intricate interplay of electrostatic and hydrodynamic interactions. Already systems composed of one single particle in electrolyte solution exhibit a complex dynamical behaviour. In this review, we discuss recent coarse-grained simulations that have been performed to obtain a molecular-level understanding of the dynamic and dielectric response of single particles and single macromolecules to external electric fields. We address both the response of charged particles to constant fields (DC fields), which can be characterized by an electrophoretic mobility, and the dielectric response of both uncharged and charged particles to alternating fields (AC fields), which is described by a complex polarizability. Furthermore, we give a brief survey of simulation algorithms and highlight some recent developments.

Theory of end-labeled free-solution electrophoresis: is the end effect important?

In the theory of free-solution electrophoresis of a polyelectrolyte (such as the DNA) conjugated with a "drag-tag," the conjugate is divided into segments of equal hydrodynamic friction and its electrophoretic mobility is calculated as a weighted average of the mobilities of individual segments. If all the weights are assumed equal, then for an electrically neutral drag-tag, the elution time t is predicted to depend linearly on the inverse DNA length 1/M. While it is well-known that the equal-weights assumption is approximate and in reality the weights increase toward the ends, this "end effect" has been assumed to be small, since in experiments the t(1/M) dependence seems to be nearly perfectly linear. We challenge this assumption pointing out that some experimental linear fits do not extrapolate to the free (i.e. untagged) DNA elution time in the limit 1/M→0, indicating nonlinearity outside the fitting range. We show that a theory for a flexible polymer taking the end effect into account produces a nonlinear curve that, however, can be fitted with a straight line over a limited range of 1/M typical of experiments, but with a "wrong" intercept, which explains the experimental results without additional assumptions. We also study the influence of the flexibilities of the charged and neutral parts.

Electrophoretic mobility reversal of polyampholytes induced by strong electric fields or confinement

We investigate the mobility of polyampholytes consisting of both negatively and positively charged sections. The simulations are carried out using molecular dynamics simulations with electrohydrodynamical effects taken into account via a simple coupling scheme to a lattice-Boltzmann fluid. Our results show a previously predicted mobility reversal of the polyampholytes as the applied electric field is increased due to stretching of the polyampholytes. Further, we show that a similar mobility reversal can be induced due to confinement between parallel plates. At high electric field strengths, the polyampholytes' electrophoretic mobility is a non-monotonic function of the distance between the plates. These results help to clarify the role of deformation and confinement on the electrophoretic mobility of polyampholytes.

Translocation of nanoparticles through a polymer brush-modified nanochannel

A basic understanding of the transport mechanisms of nanostructures in a polymer brush-modified nanochannel as well as the brush-nanostructure interactions at molecular level is important to design and fabricate emerging smart nano/microfluidic channels. In this work, we report coarse-grained molecular dynamics simulations of the translocation of nanoparticles through a cylindrical nanochannel coated with the polymer brush. The effects of the interparticle interaction and grafting density on the distribution and electrokinetic transport of nanoparticles are addressed in detail. Analysis of the distribution and velocity profiles of nanoparticles from the simulations indicate that the location of nanoparticles along the radial direction and their migration velocity are very sensitive to the change of interparticle interaction. We find complicated transport dynamics of nanoparticles under the influence of various grafting densities. The nanoparticles show markedly different translocation behavior upon increasing the grafting density, which depends on the counterion distribution, free room within the brush, nanoparticle-polymer friction, and brush configuration. Our results may serve as a useful starting point for the transport of nanostructures in polymer-modified channels and help to guide the design of novel smart nanofluidic channels for controlling the migration behavior of nanostructures.

Simulations of free-solution electrophoresis of polyelectrolytes with a finite Debye length using the Debye-Hückel approximation

We introduce a mesoscale simulation method based on multiparticle collision dynamics (MPCD) for the electrohydrodynamics of polyelectrolytes with finite Debye lengths. By applying the Debye-Hückel approximation to assign an effective charge to MPCD particles near charged monomers, our simulations are able to reproduce the rapid rise in the electrophoretic mobility with respect to the degree of polymerization for the shortest polymer lengths followed by a small decrease for longer polymers due to charge condensation. Moreover, these simulations demonstrate the importance of a finite Debye length in accurately determining the mobility of uniformly charged polyelectrolytes and net neutral polyampholytes.