Entropic stochastic resonance of a flexible polymer chain in a confined system

We have studied the dynamics of a flexible polymer chain in constrained dumb-bell-shape geometry subject to a periodic force and external noise along the longitudinal direction. It is found that the system exhibits a feature of entropic stochastic resonance (ESR), i.e., the temporal coherence of the polymer motion can reach a maximum level for an optimal noise intensity. We demonstrate that the occurrence of ESR is robust to the change of chain length, while the bottleneck width should be properly chosen. A gravity force in the vertical direction is not necessary for the ESR here, however, the elastic coupling between polymer beads is crucial.     

Polymer translocation: the effect of backflow

We investigate the effect of backflow on the translocation dynamics of short, flexible polymer chains threading through a small hole in a wall. We find that hydrodynamic interactions between polymer beads play an important role in determining the translocation time distribution: as a monomer moves through the hole it sets up a flow field which transfers momentum to neighboring monomers, thus helping them to move in the same direction. Translocation times are calculated by using the velocity-Verlet algorithm to solve the equations of motion of a polymer which moves in a fluid described by the stochastic rotation algorithm, a particle-based Navier-Stokes solver.     

Numerical and theoretical study on the mechanism of biopolymer translocation process through a nano-pore

We conducted a numerical study on the translocation of a biopolymer from the cis side to the trans side of a membrane through a synthetic nano-pore driven by an external electric field in the presence of hydrodynamic interactions (HIs). The motion of the polymer is simulated by 3D Langevin dynamics technique using a worm-like chain model of N identical beads, while HI between the polymer and fluid are incorporated by the lattice Boltzmann equation. The translocation process is induced by electrophoretic force, which sequentially straightens out the folds of the initial random configuration of the polymer chain on the cis side. Our simulation results on translocation time and velocity are in good quantitative agreement with the corresponding experimental ones when the surface charge on the nano-pore and the HI effect are considered explicitly. We found that the translocation velocity of each bead inside the nano-pore mainly depends upon the length of the straightened portion of the polymer in forced motion near the pore. We confirmed this by a theoretical formula. After performing simulations with different pore lengths, we observed that translocation velocity mainly depends upon the applied potential difference rather than upon the electric field inside the nano-pore.     

Effect of Hydrodynamic Interaction on Flow-induced Polymer Translocation Through a Nanotube

We investigated the effect of hydrodynamic interaction(HI) on flow-induced polymer translocation through a nanotube by Brownian dynamics simulations. Whether there is HI in the simulation system is separately controlled by using different diffusion tensors. It is found that HI has no effect on critical velocity flux for long polymer chains due to the competition between more drag force and the hindrance of chain stretching from HI, however, HI broadens the transition interval. In addition, for flow-induced polymer translocation with HI, the critical velocity flux firstly slowly decreases with the increase of chain length and then becomes identical to that of it without HI, that is, the critical velocity flux is independent of chain length. At the same time, HI also accelerates the translocation process and makes the relative variation amplitude of single bead translocation time smaller. In fact, HI can enhance the intrachain cooperativity to make the whole chain obtain more drag force from fluid field and hinder chain stretching, both of which play an important role in translocation process.     

Deformation and motion of a charged conducting drop in a dielectric liquid under a nonuniform electric field

As a tool for transporting a drop inside another fluid, a charged conducting drop driven by Coulombic force is considered. Specifically, deformation and motion of a charged conducting drop under nonuniform electric fields are studied using the perturbation method. For simplicity in analysis, the applied electric field is assumed to be expressed as the sum of a uniform field and a linear field and the flow is assumed to be in the Stokes flow range. The deformed drop shape due to electrical stress is computed to the first order of the electrical Weber number (W). Then the electric force and the hydrodynamic drag are computed to derive the formula of the translation velocity, which is valid up to O(W). Several important results have also been obtained for the effect of drop deformation on the electric and hydrodynamic forces exerted on the drop.     

Role of Hydrodynamic Interactions in the Deformation of Star Polymers in Poiseuille Flow

Stretching polymer in fluid flow is a vital process for studying and utilizing the physical properties of these molecules,such as DNA linearization in nanofluidic channels.We studied the role of hydrodynamic interactions(His)in stretching a free star polymer in Poiseuille flow through a tube using mesoscale hydrodynamic simulations.As increasing the flow strength,star polymers migrate toward the centerline of tube due to His,whereas toward the tube wall in the absence of His.By analyzing the end monomer distribution and the perturbed flow around the star polymer,we found that the polymer acts like a shield against the flow,leading to additional hydrodynamic drag forces that compress the arm chains in the front of the star center toward the tube axis and lift the arm chai ns at the back toward the tube wall.The balanced hydrodynamic forces freeze the polymer into a trumpet structure,where the arm chains maintain a steady strongly stretched state at high flow strength.In contrast,the polymer displays remarkably large conformational change when switching off His.Our simulation results explained the coupling between His and the structure of star polymers in Poiseuille flow.     

Conformation and diffusion behavior of ring polymers in solution: a comparison between molecular dynamics, multiparticle collision dynamics, and lattice Boltzmann simulations

We have studied the effect of chain topology on the structural properties and diffusion of polymers in a dilute solution in a good solvent. Specifically, we have used three different simulation techniques to compare the chain size and diffusion coefficient of linear and ring polymers in solution. The polymer chain is modeled using a bead-spring representation. The solvent is modeled using three different techniques: molecular dynamics (MD) simulations with a particulate solvent in which hydrodynamic interactions are accounted through the intermolecular interactions, multiparticle collision dynamics (MPCD) with a point particle solvent which has stochastic interactions with the polymer, and the lattice Boltzmann method in which the polymer chains are coupled to the lattice fluid through friction. Our results show that the three methods give quantitatively similar results for the effect of chain topology on the conformation and diffusion behavior of the polymer chain in a good solvent. The ratio of diffusivities of ring and linear polymers is observed to be close to that predicted by perturbation calculations based on the Kirkwood hydrodynamic theory.     

Electromechanical Responses of a Crosslinked Polydimethylsiloxane

A high molecular weight polydimethylsiloxane, PDMS, gel was prepared and investigated as an electroactive polymer actuator. Electromechanical properties of the PDMS gels were measured under an oscillatory shear mode at the temperature of 27 °C to determine the effects of crosslink ratio and electric field strength. The storage modulus, G′, of PDMS gel increases linearly with crosslink density but nonlinearly with electric field. The increase in the storage modulus with crosslink density is due to the increase in the number of junction points and strands. With increasing electric field strength, the storage modulus increases as the electric field induces dipole moments generating the electrostatic forces within the matrices. The gel with the crosslink ratio of 0.01 possesses the highest G′ sensitivity of 41% at 2 kV/mm. The temporal response of PDMS gels upon repeated applications of electric field strength of 2 kV/mm was investigated. For the crosslink PDMS (N_c/N_m = 0.01) system, at the electric field of 2 kV/mm, G′ immediately increases and rapidly reaches a steady-state value. With electric field off, G′ decreases and nearly recovers its original value. The crosslinked PDMS (N_c/N_m = 0.01) is nearly a reversible system. Finally, we investigated the bending response of the PDMS films, suspended in silicone oil between copper electrodes. From the deformation data, we estimated the dielectrophoresis force, F_D, to be a linear function of electric field strength.     

Electrohydrodynamics of spherical polyampholyte‐grafted nanoparticles: Multiscale simulations by coupling of molecular dynamics and lattice‐boltzmann method

We perform multiscale simulations based on the coupling of molecular dynamics and lattice‐Boltzmann (LB) method to study the electrohydrodynamics of a polyampholyte‐grafted spherical nanoparticle. The long‐range hydrodynamic interactions are modeled by coupling the movement of particles to a LB fluid. Our results indicate that the net‐neutral soft particle moves with a nonzero mobility under applied electric fields. We systematically explore the effects of different parameters, including the chain length, grafting density, electric field, and charge sequence, on the structures of the polymer layer and the electrophoretic mobility of the soft particle. It shows that the mobility of nanoparticles has remarkable dependence on these parameters. We find that the deformation of the polyampholyte chains and the ion distribution play dominant roles in modulating the electrokinetic behavior of the polyampholyte‐grafted particle. The enhancement or reduction in the accumulation of counterions around monomers can be attributed to the polymer layer structure and the conformational transition of the chains in the electric field. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1435–1447     

Polymer capture by electro-osmotic flow of oppositely charged nanopores

The authors have addressed theoretically the hydrodynamic effect on the translocation of DNA through nanopores. They consider the cases of nanopore surface charge being opposite to the charge of the translocating polymer. The authors show that, because of the high electric field across the nanopore in DNA translocation experiments, electro-osmotic flow is able to create an absorbing region comparable to the size of the polymer around the nanopore. Within this capturing region, the velocity gradient of the fluid flow is high enough for the polymer to undergo coil-stretch transition. The stretched conformation reduces the entropic barrier of translocation. The diffusion limited translocation rate is found to be proportional to the applied voltage. In the authors' theory, many experimental variables (electric field, surface potential, pore radius, dielectric constant, temperature, and salt concentration) appear through a single universal parameter. They have made quantitative predictions on the size of the adsorption region near the pore for the polymer and on the rate of translocation.     

Force acting on a dielectric particle in a concentration gradient by ionic concentration polarization under an externally applied DC electric field

There is a concentration-polarization (CP) force acting on a particle submerged in an electrolyte solution with a concentration (conductivity) gradient under an externally applied DC electric field. This force originates from the two mechanisms: (i) gradient of electrohydrodynamic pressure around the particle developed by the Coulombic force acting on induced free charges by the concentration polarization, and (ii) dielectric force due to nonuniform electric field induced by the conductivity gradient. A perturbation analysis is performed for the electric field, the concentration field, and the hydrodynamic field, under the assumptions of creeping flow and small concentration gradient. The leading order component of this force acting on a dielectric spherical particle is obtained by integrating the Maxwell and the hydrodynamic stress tensors. The analytical results are validated by comparing the surface pressure and the skin friction to those of a numerical analysis. The CP force is proportional to square of the applied electric field, effective for electrically neutral particles, and always directs towards the region of higher ionic concentration. The magnitude of the CP force is compared to that of the electrophoretic and the conventional dielectrophoretic forces.     

Transport and deformation of droplets in a microdevice using dielectrophoresis

In microfluidic devices the fluid can be manipulated either as continuous streams or droplets. The latter is particularly attractive as individual droplets can not only move but also split and fuse, thus offering great flexibility for applications such as laboratory-on-a-chip. We consider the transport of liquid drops immersed in a surrounding liquid by means of the dielectrophoretic force generated by electrodes mounted at the bottom of a microdevice. The direct numerical simulation (DNS) approach is used to study the motion of droplets subjected to both hydrodynamic and electrostatic forces. Our technique is based on a finite element scheme using the fundamental equations of motion for both the droplets and surrounding fluid. The interface is tracked by the level set method and the electrostatic forces are computed using the Maxwell stress tensor. The DNS results show that the droplets move, and deform, under the action of nonuniform electric stresses on their surfaces. The deformation increases as the drop moves closer to the electrodes. The extent to which the isolated drops deform depends on the electric Weber number. When the electric Weber number is small, the drops remain spherical; otherwise, the drops stretch. Two droplets, however, that are sufficiently close to each other, can deform and coalesce, even if the electric Weber number is small. This phenomenon does not rely on the magnitude of the electric stresses generated by the bulk electric field, but instead is due to the attractive electrostatic drop-drop interaction overcoming the surface tension force. Experimental results are also presented and found to be in agreement with the DNS results.     

Elastic Behavior of Polymer Chains

The elastic behavior of the polymer chain was investigated in a three-dimensional off-lattice model. We sample more than 109 conformations of each kind of polymer chain by using a Monte Carlo algorithm, then analyze them with the non-Gaussian theory of rubberlike elasticity, and end with a statistical study. Through observing the effect of the chain flexibility and the stretching ratio on the mean-square end-to-end distance, the average energy, the average Helmholtz free energy, the elastic force, the contribution of energy to the elastic force, and the entropy contribution to elastic force of the polymer chain, we find that a rigid polymer chain is much easier to stretch than a flexible polymer chain. Also, a rigid polymer chain will become difficult to stretch only at a quite high stretching ratio because of the effect of the entropy contribution. These results of our simulation calculation may explain some of the macroscopic phenomena of polymer and biomacromolecular elasticity.     

Effect of charge distribution on the translocation of an inhomogeneously charged polymer through a nanopore

We investigate the voltage-driven translocation of an inhomogeneously charged polymer through a nanopore by utilizing discrete and continuous stochastic models. As a simplified illustration of the effect of charge distribution on translocation, we consider the translocation of a polymer with a single charged site in the presence and absence of interactions between the charge and the pore. We find that the position of the charge that minimizes the translocation time in the absence of pore-polymer interactions is determined by the entropic cost of translocation, with the optimum charge position being at the midpoint of the chain for a rodlike polymer and close to the leading chain end for an ideal chain. The presence of attractive and repulsive pore-charge interactions yields a shift in the optimum charge position toward the trailing end and the leading end of the chain, respectively. Moreover, our results show that strong attractive or repulsive interactions between the charge and the pore lengthen the translocation time relative to translocation through an inert pore. We generalize our results to accommodate the presence of multiple charged sites on the polymer. Our results provide insight into the effect of charge inhomogeneity on protein translocation through biological membranes.     

Hydrodynamic,optical, and electrooptical properties of macromolecules of third-generation cylindrical dendrimers in chloroform and dichloroacetic acid

Acrylic polymers containing side dendrons of the third generation based on L-aspartic acid have been studied via the methods of molecular hydrodynamics, dynamic and static light-scattering, optics, and electrooptics. There are marked differences in hydrodynamic and optical properties of the macromolecules under study and previously examined polymers with side dendrons of first and second generations. In the range of degrees of polymerization from 10 to 40, these macromolecules possess an extremely low shape asymmetry. Experiments demonstrate the predominant orientation of end side dendrons along the main molecular chain. In chloroform solutions, the orientation of macromolecules in hydrodynamic and electric fields occurs according to the large-scale mechanism. In dichloroacetic acid, the hydrodynamic dimensions of macromolecules decrease, an effect that is accompanied by an increase in the kinetic flexibility of polymer chains.     

Design of a microfabricated magnetic cell separator.

A new magnetic separation idea utilizing several ideas from microfabrication and nanomagnetics is presented. The basic idea comes from our earlier work using asymmetry in obstacles and Brownian motion to effect separation of objetcs [10] by moving them in streams whose angle to the hydrodynamic average velocity is a function of the diffusion coefficient of the object. The device we propose here is not technically a Brownian ratchet device but uses the idea of force which acts at angle to the hydrodynamic flow. In our case, the force is generated by a magnetic field gradient which comes from an array of magnetized wires which lie at an angle 0 to a hydrodynamic field flow. The sum of the hydrodynamic force and the magnetic force create a new vector which as in the case of the Brownian ratchet moves the cell out of the main stream direction.     

Electrophoretic motion of a spherical particle with a symmetric nonuniform surface charge distribution in a nanotube

The electrophoretic motion of a spherical nanoparticle, subject to an axial electric field in a nanotube filled with an electrolyte solution, has been investigated using a continuum theory, which consists of the Nernst-Planck equations for the ionic concentrations, the Poisson equation for the electric potential in the solution, and the Stokes equation for the hydrodynamic field. In particular, the effects of nonuniform surface charge distributions around the nanoparticle on its axial electrophoretic motion are examined with changes in the bulk electrolyte concentration and the surface charge of the tube's wall. A particle with a nonuniform charge distribution is shown to induce a corresponding complex ionic concentration field, which in turn influences the electric field and the fluid motion surrounding the particle and thus its electrophoretic velocity. As a result, contrary to the relatively simple dynamics of a particle with a uniform surface charge, dominated by the irradiating electrostatic force, that with a nonuniform surface charge distribution shows various intriguing behaviors due to the additional interplay of the nonuniform electro-osmotic effects.     

On the effect of induced electro-osmosis on a cylindrical particle next to a surface

The effect of induced electro-osmosis on a cylindrical particle positioned next to a planar surface (wall) is studied theoretically both under the thin double layer approximation utilizing the Smoluchowski slip velocity approximation and under thick electric double layer conditions by solving the Poisson-Nernst-Planck (PNP) equations. The imposed, undisturbed electric field is parallel to the planar surface. The induced hydrodynamic and electrostatic forces are calculated as functions of the particle's and the medium's dielectric constants and the distance between the particle and the surface. The resultant force acting on the particle is directed normal to and away from the wall. The presence of such a repulsive force may adversely affect the interactions between macromolecules suspended in solution and wall-immobilized molecules and may be significant to near-wall particle imaging velocimetry (PIV) in electrokinetic flows.     

Computer Simulation of High-Frequency Heating of a Protonated Poly(ethylene oxide) Chain in a Vacuum

Heating of an isolated protonated poly(ethylene oxide) chain by high-frequency electric field was simulated using molecular dynamics. Simulations were performed at the field strength of about 10⁸ V/m and frequencies from 1 to 100 GHz. At initial temperature (500 K), the chain is a globule. Absorption of the field energy heats the chain and leads to a growth in its size. In some frequency ranges, the field causes the chain to rotate as a whole. The rotation leads to a sharp increase in the heating rate and the rate of stretching the chain. The rotating chain has larger size than its non rotating counterpart at the same temperature. Contrary to the non rotating chain, this chain can be in a two-phase state in which the globular and the stretched microphases coexist. The absorption spectrum of the chain is temperature dependent and, at high temperatures, contains two distinctly expressed peaks. In the vicinity of these peaks, the chain rotates with a frequency equal to the field frequency or about half the field frequency. The results obtained are explained using the model of a spatial damped oscillator in which, together with the usual resonance, the subharmonic resonances typical for nonlinear systems arise.     

Combining molecular dynamics with Lattice Boltzmann: a hybrid method for the simulation of (charged) colloidal systems

We present a hybrid method for the simulation of colloidal systems that combines molecular dynamics (MD) with the Lattice Boltzmann (LB) scheme. The LB method is used as a model for the solvent in order to take into account the hydrodynamic mass and momentum transport through the solvent. The colloidal particles are propagated via MD and they are coupled to the LB fluid by viscous forces. With respect to the LB fluid, the colloids are represented by uniformly distributed points on a sphere. Each such point [with a velocity V(r) at any off-lattice position r] is interacting with the neighboring eight LB nodes by a frictional force F = xi0(V(r)-u(r)), with xi0 being a friction coefficient and u(r) being the velocity of the fluid at the position r. Thermal fluctuations are introduced in the framework of fluctuating hydrodynamics. This coupling scheme has been proposed recently for polymer systems by Ahlrichs and Dunweg [J. Chem. Phys. 111, 8225 (1999)]. We investigate several properties of a single colloidal particle in a LB fluid, namely, the effective Stokes friction and long-time tails in the autocorrelation functions for the translational and rotational velocity. Moreover, a charged colloidal system is considered consisting of a macroion, counterions, and coions that are coupled to a LB fluid. We study the behavior of the ions in a constant electric field. In particular, an estimate of the effective charge of the macroion is yielded from the number of counterions that move with the macroion in the direction of the electric field.