Electrophoretic (EP) mobility reversal is commonly observed for strongly charged macromolecules in multivalent salt solutions. This curious effect takes place, e.g., when a charged polymer, such as DNA, adsorbs excess counterions so that the counterion-dressed surface charge reverses its sign, leading to the inversion of the polymer drift driven by an external electric field. In order to characterize this seemingly counterintuitive phenomenon that cannot be captured by electrostatic mean-field theories, we adapt here a previously developed strong-coupling-dressed Poisson-Boltzmann approach to the cylindrical geometry of the polyelectrolyte-salt system. Within the framework of this formalism, we derive an analytical polymer mobility formula dressed by charge correlations. In qualitative agreement with polymer transport experiments, this mobility formula predicts that the increment of the monovalent salt, the decrease of the multivalent counterion valency, and the increase of the dielectric permittivity of the background solvent, suppress charge correlations and increase the multivalent bulk counterion concentration required for EP mobility reversal. These results are corroborated by coarse-grained molecular dynamics simulations showing how multivalent counterions induce mobility inversion at dilute concentrations and suppress the inversion effect at large concentrations. This re-entrant behavior, previously observed in the aggregation of like-charged polymer solutions, calls for verification by polymer transport experiments.
We present a numerical study of polyelectrolytes electrophoresing in free solution while squeezed by an axisymmetric confinement force transverse to their net displacement. Hybrid multi-particle collision dynamics and molecular dynamics simulations with mean-field finite Debye layers show that even though the polyelectrolyte chains remain "free-draining", their electrophoretic mobility increases with confinement in nanoconfining potential wells. The primary mechanism leading to the increase in mobility above the free-solution value, despite long-range hydrodynamic screening by counterion layer…
We study the mobility of a charged colloidal particle in a constant homogeneous electric field by means of computer simulations. The simulation method combines a lattice Boltzmann scheme for the fluid with standard Langevin dynamics for the colloidal particle, which is built up from a net of bonded particles forming the surface of the colloid. The coupling between the two subsystems is introduced via friction forces. In addition explicit counterions, also coupled to the fluid, are present. We observe a non-monotonous dependence of the electrophoretic mobility on the bare colloidal charge. At l…
We present (asymptotically) exact expressions for the mobility and electrophoretic mobility of a weakly charged spherical particle in an $1:1$ electrolyte solution. This is done by analytically solving the electro and hydrodynamic equations governing the electric potential and fluid flow with respect to an electric field and a nonelectric force. The resulting formulae are cumbersome, but fully explicit and trivial for computation. In the case of a very small particle compared to the Debye screening length ($R \ll r_D$) our results reproduce proper limits of the classical Debye and Onsager theo…
Critical coagulation concentration (CCC) is a key parameter of particle dispersions, since it provides the threshold limit of electrolyte concentrations, above which the dispersions are destabilized due to rapid particle aggregation. A computational method is proposed to predict CCC values using solely electrophoretic mobility data without the need to measure aggregation rates of the particles. The model relies on the DLVO theory; contributions from repulsive double-layer forces and attractive van der Waals forces are included. Comparison between the calculated and previously reported experime…
We study the electrophoretic flow of suspensions of charged colloids with a mesoscopic method that allows to model generic experimental conditions. We show that for highly charged colloids their electrophoretic mobility increases significantly and displays a mobility maximum on increasing the colloidal charge for all salt concentrations. The electrophoretic mobility of highly charged colloids is also enhanced significantly when ion advection is dominant, leading to a strong heterogeneity in the local electrophoretic response especially at low salt concentration, when ion diffuse layers overlap…
Capillary electrophoresis has long been been recognized as a powerful analytic tool. Here it is demonstrated that the same capillary electrophoretic experiments also reveal dynamic properties of the polymer solutions being used as the support medium. The dependence of the electrophoretic mobility on the size of the probe and the properties of the matrix polymers shows a unity of behavior between electrophoresis and other methods of studying polymer properties.
Thermal scaling and relaxation of the interface width in an electrophoretic deposition of polymer chains is examined by a three-dimensional Monte Carlo simulation on a discrete lattice. Variation of the equilibrium interface width $W_r$ with the temperature $T$ shows deroughening $W_r \propto T^{-δ}$, with $δ\sim 1/4$, at low temperatures and roughening $W_r \propto T^ν$, with $ν\sim 0.4$ at high temperatures. The roughening-deroughening transition temperature $T_t$ increases with longer chain lengths and is reduced by using the slower segmental dynamics.
Growth and roughness of the interface of deposited polymer chains driven by a field onto an impenetrable adsorbing surface are studied by computer simulations in (2+1) dimensions. The evolution of the interface width W shows a crossover from short-time growth described by the exponent beta1 to a long-time growth with exponent beta2 (>beta1). The saturated width increases, i.e., the interface roughens, with the molecular weight Lc, but the roughness exponent alpha (from Ws~L^alpha) becomes negative in contrast to models for particle deposition; alpha depends on the chain length--a nonuniversal …
Using different segmental dynamics and relaxation, characteristics of the interface growth is examined in an electrophoretic deposition of polymer chains on a three (2+1) dimensional discrete lattice with a Monte Carlo simulation. Incorporation of faster modes such as crankshaft and reptation movements along with the relatively slow kink-jump dynamics seems crucial in relaxing the interface width. As the continuously released polymer chains are driven (via segmental movements) and deposited, the interface width $W$ grows with the number of time steps $t$, $W \propto t^β,$ ($β\sim 0.4$--$0.8)$,…
Polarization of the interface, spontaneously occurring when water is in contact with hydrophobic solutes or air, couples with the uniform external field to produce a non-zero force acting on a suspended particle. This force exists even in the absence of a net particle charge, and its direction is affected by the first-order, dipolar and the second-order, qudrupolar orientational order parameters of the interfacial water. The quadrupolar polarization gives rise to an effectively negative charge. The corresponding surface charge density is inversely proportional to the area of the shear surface.…
Characteristics of relaxed density profile and conformation of polymer chains are studied by a Monte Carlo simulation on a discrete lattice in three dimensions using different segmental (kink-jump $K$, crank-shaft $C$, reptation $R$) dynamics. Three distinct density regimes, substrate, bulk, and interface, are identified. With the $KC$ segmental dynamics we find that the substrate coverage grows with a power-law, $d_s \propto t^γ$ with a field dependent nonuniversal exponent $γ= 0.23 + 0.7 E$. The bulk volume fraction $d_b$ and the substrate polymer density ($d_s$) increases exponentially with…
We study the electrophoretic mobility of spherical charged colloids in a low-salt suspension as a function of the colloidal concentration. Using an effective particle charge and a reduced screening parameter, we map the data for systems with different particle charges and sizes, including numerical simulation data with full electrostatics and hydrodynamics and experimental data for latex dispersions, on a single master curve. We observe two different volume fraction-dependent regimes for the electrophoretic mobility that can be explained in terms of the static properties of the ionic double la…
Numerical solutions of the standard electrokinetic model provide a basis for interpreting a variety of electrokinetic phenomena involving `bare' colloids. However, the model rests on the classical notion of a shear or slipping plane, whose location is unknown when surfaces are coated with permeable polymer. Consequently, an electrokinetic model for `soft', `hairy' or `fuzzy' colloids has been developed, but until recently solutions were available only for several restricted cases, most notably for particles with thin, uniform layers, and without polarization and relaxation. Here we present num…
In this work, we use Molecular Dynamics and Lattice-Boltzmann simulations to study the properties of charged Janus particles in an electric field. We show that for relatively small net charge and thick electrostatic diffuse layer mobilities of Janus particles and uniformly charged colloids of the same net charge are identical. However, for higher charges and thinner diffuse layers Janus particles always show lower electrophoretic mobility. We also demonstrate that Janus particles align with the electric field and the angular deviation from the field's direction are related to their dipole mome…
We study electrophoretic mobility of metal-dielectric Janus particles with dipolar director profile in two nematic liquid crystals (LCs) having same (positive) conductivity anisotropy and opposite dielectric anisotropy. The applied ac electric field is parallel and perpendicular to the director for the positive and negative dielectric anisotropy LCs, respectively. The velocity of the Janus particles in both LCs is significantly higher than that of the non-Janus particles. We map the electroosmotic flow fields surrounding the particles using microparticle image velocimetry ($μ$-PIV) and show th…
We formulate a numerical method for predicting the tensorial linear response of a rigid, asymmetrically charged body to an applied electric field. This prediction requires calculating the response of the fluid to the Stokes drag forces on the moving body and on the countercharges near its surface. To determine the fluid's motion, we represent both the body and the countercharges using many point sources of drag known as stokeslets. Finding the correct flow field amounts to finding the set of drag forces on the stokeslets that is consistent with the relative velocities experienced by each stoke…
A new lattice method is presented in order to efficiently solve the electrokinetic equations, which describe the structure and dynamics of the charge cloud and the flow field surrounding a single charged colloidal sphere, or a fixed array of such objects. We focus on calculating the electrophoretic mobility in the limit of small driving field, and systematically linearise the equations with respect to the latter. This gives rise to several subproblems, each of which is solved by a specialised numerical algorithm. For the total problem we combine these solvers in an iterative procedure. Applyin…
The charge inversion phenomenon is studied by molecular dynamics simulations, focusing on size and valence asymmetric salts, and a threshold of surface charge density for charge inversion. The charge inversion criteria by the electrophoretic mobility and the radial distribution functions of ions coincide except around the charge inversion threshold. The reversed electrophoretic mobility increases with the ratio of coion to counterion radii, while it decreases with the ratio of coion to counterion valences. The monovalent salt enhances charge inversion of a strongly charged macroion at small io…
The transient electric current of surfactants dissolved in a nonpolar solvent is investigated both experimentally and theoretically in the parallel-plate geometry. Due to a low concentration of free charges the cell can be completely polarized by an external voltage of several volts. In this state, all the charged micelles are compacted against the electrodes. After the voltage is set to zero the reverse current features a sharp discharge spike and a broad peak. This shape and its variation with the compacting voltage are reproduced in a one-dimensional drift-diffusion model. The model reveals…
We propose a new method for electrophoretic separation of DNA in which adsorbed polymers are driven over a disordered two-dimensional substrate which contains attractive sites for the polymers. Using simulations of a model for long polymer chains, we show that the mobility increases with polymer length, in contrast to gel electrophoresis techniques, and that separation can be achieved for a range of length scales. We demonstrate that the separation mechanism relies on steric interactions between polymer segments, which prevent substrate disorder sites from trapping more than one DNA segment ea…
Polymer translocation experiments typically involve anionic polyelectrolytes such as DNA molecules driven through negatively charged nanopores. Quantitative modelling of polymer capture to the nanopore followed by translocation therefore necessitates the consideration of the electrostatic barrier resulting from like-charge polymer-pore interactions. To this end, in this work we couple mean-field level electrohydrodynamic equations with the Smoluchowski formalism to characterize the interplay between the electrostatic barrier, the electrophoretic drift, and the electro-osmotic liquid flow. In p…
We propose a simple dynamic model of polymers under shear with an anisotropic mobility tensor. We calculate the shear viscosity, the rheo-dielectric response function, and the parallel relaxation modulus under shear flow deduced from our model. We utilize recently developed linear response theories for nonequilibrium systems to calculate linear response functions. Our results are qualitatively consistent with experimental results. We show that our anisotropic mobility model can reproduce essential dynamical nature of polymers under shear qualitatively. We compare our model with other models or…
Using computer simulations, the electrophoretic motion of a positively charged colloid (macroion) in an electrolyte solution is studied in the framework of the primitive model. Hydrodynamic interactions are fully taken into account by applying a hybrid simulation scheme, where the charged ions (i.e. macroion and electrolyte), propagated via molecular dynamics (MD), are coupled to a Lattice Boltzmann (LB) fluid. In a recent experiment it was shown that, for multivalent salt ions, the mobility $μ$ initially increases with charge density $σ$, reaches a maximum and then decreases with further incr…
We propose a dynamic coarse-graining (CG) scheme for mapping heterogeneous polymer fluids onto extremely CG models in a dynamically consistent manner. The idea is to use as target function for the mapping a wave-vector dependent mobility function derived from the single-chain dynamic structure factor, which is calculated in the microscopic reference system. In previous work, we have shown that dynamic density functional calculations based on this mobility function can accurately reproduce the order/disorder kinetics in polymer melts, thus it is a suitable starting point for dynamic mapping. To…
Free surfaces in glassy polymer films are known to induce surface mobile layers with enhanced dynamics. Using molecular dynamics simulations of a bead-spring model, we study a wide variety of layer-resolved structural and dynamical properties of polymer films equilibrated at a low temperature. Surface enhancement on thermally induced particle hopping rate is found to terminate abruptly only about 5 particle diameters from the free surface. In contrast, enhancement on the net motions of particles measured at longer time scales penetrates at least 2 particle diameters deeper. The diverse penetra…
The alteration of the dielectric membrane properties by membrane engineering techniques such as carbon nanotube (CNT) coating opens the way to novel molecular transport strategies for biosensing purposes. In this article, we predict a macromolecular transport mechanism enabling the dielectric manipulation of the polymer translocation dynamics in dielectric membrane pores confining mixed electrolytes. In the giant permittivity regime of these engineered membranes governed by attractive polarization forces, multivalent ions adsorbed by the membrane nanopore trigger a monovalent ion separation an…
A highly-charged spherical colloid in a salt-free environment exerts such a powerful attraction on its counterions that a certain fraction condenses onto the surface of a particle. The degree of condensation depends on the curvature of the surface. So, for instance, condensation is triggered on a highly-charged sphere only if the radius exceeds a certain critical radius $\collrad^{*}$. $\collrad^{*}$ is expected to be a simple function of the volume fraction of particles. To test these predictions, we prepare spherical particles which contain a covalently-bound ionic liquid, which is engineere…
We present an extensive molecular dynamics (MD) simulation study of the lithium ion transport in ternary polymer electrolytes consisting of poly(ethylene oxide) (PEO), lithium-bis(trifluoromethane)sulfonimide (LiTFSI) and the ionic liquid N-methyl-N-propylpyrrolidinium bis(trifluoromethane)sulfonimide (PYR13TFSI). In particular, we focus on two different strategies by which the ternary electrolytes can be devised, namely by (a) adding the ionic liquid to PEO20LiTFSI, and (b) substituting the PEO chains in PEO20LiTFSI by the ionic liquid. In order to grasp the changes of the overall lithium tra…
The hydrodynamic forces between Brownian spheres are determined from a measurement of the correlated thermal fluctuations in particle position using a new method, two-particle cross-correlation spectroscopy (TCS). A pair of 1.3 um diameter polymer-coated poly(methyl methacrylate) were held at separations of between 2 um and 20 um using optical traps. The mobility tensor is determined directly from the statistically-averaged Brownian fluctuations of the two spheres. The observed distance dependence of the mobility tensor is in quantitative agreement with low-Reynolds number calculations.
We analyze the influence of finite ion size effects in the response of a salt-free concentrated suspension of spherical particles to an oscillating electric field. Salt-free suspensions are just composed of charged colloidal particles and the added counterions released by the particles to the solution, that counterbalance their surface charge. In the frequency domain, we study the dynamic electrophoretic mobility of the particles and the dielectric response of the suspension. We find that the Maxwell-Wagner-O'Konski process associated with the counterions condensation layer, is enhanced for mo…
The influence of substrate treatment with self-assembled monolayers and thermal annealing was analysed by electrical and structural measurements on field-effect transistors (FETs) and metal-insulator-semiconductor (MIS) diodes using poly(3-hexylthiophene) (P3HT) as a semiconducting polymer and Si/SiO2 wafers as a substrate. It is found that surface treatment using silanising agents like hexamethyldisilazane (HMDS) and octadecyltrichlorosi-lane (OTS) can increase the field-effect mobility by up to a factor of 50, reaching values in saturation of more than 4E-2 cm^2/Vs at room temperature. While…
We consider electrophoresis of a single charged colloidal particle in a finite box with periodic boundary conditions, where added counterions and salt ions ensure charge neutrality. A systematic rescaling of the electrokinetic equations allows us to identify a minimum set of suitable dimensionless parameters, which, within this theoretical framework, determine the reduced electrophoretic mobility. It turns out that the salt-free case can, on the Mean Field level, be described in terms of just three parameters. A fourth parameter, which had previously been identified on the basis of straightfor…
Diffusive transport of small molecules within the internal structures of biological and synthetic material systems is complex because the crowded environment presents chemical and physical barriers to mobility. We explored this mobility using a synthetic experimental system of small dye molecules diffusing within a polymer network at short time scales. We find that the diffusion of inert molecules is inhibited by the presence of the polymers. Counter-intuitively, small, hydrophobic molecules display smaller reduction in mobility and also able to diffuse faster through the system by leveraging …
We describe a series of surface levelling experiments in glassy polystyrene (PS) of varying molecular weight. The evolution through a mobile surface layer is described by the glassy thin film equation that was introduced and used in a previous work. Excellent agreement with the data is achieved, with surface mobility as the single free parameter. Different molecular-weight dependencies in mobility are then observed above and below the glass transition. The results are discussed in terms of surface-chain anchoring in the bulk matrix, and the length scale for surface mobility.
While nearly all theoretical and computational studies of entangled polymer melts have focused on uniform samples, polymer synthesis routes always result in some dispersity, albeit narrow, of distribution of molecular weights (D_M=M_w/M_n ~ 1.02-1.04). Here the effects of dispersity on chain mobility are studied for entangled, disperse melts using a coarse-grained model for polyethylene. Polymer melts with chain lengths set to follow a Schulz-Zimm distribution for the same average M_w = 36 kg/mol with D_M = 1.0 to 1.16, were studied for times of $600-800$ $μ$s using molecular dynamics simulati…
Transient networks comprised of polymers connected by short-lived bonds are a common design theme for both biological and synthetic materials. Transient bonds can provide mechanical rigidity, while still allowing for visco-elastic flows on timescales longer than the bond lifetime. In many biological polymer networks such as the actin cytoskeleton, the short-lived bonds are formed by accessory proteins that diffuse away after unbinding. By contrast, bonds in synthetic networks, such as the pendant groups of telechelic polymers, can only rebind in the same location. Using a recently developed th…
We propose and compare different strategies to construct dynamic density functional theories (DDFTs) for inhomogeneous polymer systems close to equilibrium from microscopic simulation trajectories. We focus on the systematic construction of the mobility coefficient, $Λ(r,r')$, which relates the thermodynamic driving force on monomers at position $r'$ to the motion of monomers at position $r$. A first approach based on the Green-Kubo formalism turns out to be impractical because of a severe plateau problem. Instead, we propose to extract the mobility coefficient from an effective characteristic…
We investigate the possibility that electrically neutral porous spheres electrophorese in electrolyte solutions with asymmetric affinity of ions to spheres on the basis of electrohydrodynamics and the Poisson-Boltzmann and Debye-Bueche-Brinkman theories. Assuming a weak electric field and ignoring the double-layer polarization, we obtain analytical expressions for electrostatic potential, electrophoretic mobility, and flow field. In the equilibrium state, the Galvani potential forms across the interface of the spheres. Under a weak electric field, the spheres show finite mobility with the same…
Self-consistent solution of charge injection and transport in low mobility LEDs is reported . We show that explicit description of the contact region under the same premise as transport equation is needed to accurately evaluate the current-voltage characteristics of polymer or small-molecule based LEDs . The result is compared to widely used models, which treat the contact region in implicit manner .
Physico-chemical study of polymer mixtures formed by a polycation and a zwitterionic copolymer in aqueous solution and upon adsorption onto negatively charged surfaces
The mobility of polymer chains in perfect polyethylene (PE) crystal was calculated as a function of temperature and chain length through Molecular dynamics (MD) in united atom approximation. The results demonstrate that the chain mobility drastically increases in the vicinity of the phase transition from the orthorhombic to quasi-hexagonal phase. In the quasi-hexagonal phase, the chain mobility is almost independent on temperature and inversely proportional to the chain length.
Measuring the electrophoretic mobility of molecules is a powerful experimental approach for investigating biomolecular processes. A frequent challenge in the context of single-particle measurements is throughput, limiting the obtainable statistics. Here, we present a molecular force sensor and charge detector based on parallelised imaging and tracking of tethered double-stranded DNA functionalised with charged nanoparticles interacting with an externally applied electric field. Tracking the position of the tethered particle with simultaneous nanometre precision and microsecond temporal resolut…
Processes on different length scales affect the dynamics of chain molecules. In this work, we focus on structures on the scale of a monomer and investigate polyolefins, i.e. hydrocarbon chains with different small scale architectures. We present an exact enumeration scheme for the simulation of interactions and relative motion of two short chain sections on a lattice and employ it to deduce the probability for segmental motion for polymers of four different architectures in the melt. The probability for segmental motion is inversely proportional to the monomeric friction coefficient and hence …
Structure, Dynamics and Hydrogen Transport in Amorphous Polymers: An Analysis of the Interplay Between Free Volume Element Distribution and Local Segmental Dynamics from Molecular Dynamics Simulations
Half-integer Topological Defects Paired via String Micelles in Polar Liquids
Southern University of Science and Technology（南方科技大学）；Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology（广东省功能性与智能杂化材料器件重点实验室，华南理工大学）
Charge-carrier transport in a paradigmatic semicrystalline polymer semiconductor (P3HT) is important for both fundamental understanding and applications. In samples with enhanced structural disorder due to ad-hoc point defects, the mobility displays rich behavior as a function of electric field (F) and temperature (T). At low T, the mobility increases with the applied field, but upon further increasing T, the field-dependence becomes shallower. Eventually, at the highest T considered, the slope changes sign and the mobility then decreases with the field. This phenomenon can be interpreted with…
Thin polymer films have striking dynamical properties that differ from their bulk counterparts. With the simple geometry of a stepped polymer film on a substrate, we probe mobility above and below the glass transition temperature $T_{\textrm{g}}$. Above $T_{\textrm{g}}$ the entire film flows, while below $T_{\textrm{g}}$ only the near surface region responds to the excess interfacial energy. An analytical thin film model for flow limited to the free surface region shows excellent agreement with sub-$T_{\textrm{g}}$ data. The system transitions from whole film flow to surface localized flow ove…
We study the dynamics of local bond orientation in regular hyperbranched polymers modeled by Vicsek fractals. The local dynamics is investigated through the temporal autocorrelation functions of single bonds and the corresponding relaxation forms of the complex dielectric susceptibility. We show that the dynamic behavior of single segments depends on their remoteness from the periphery rather than on the size of the whole macromolecule. Remarkably, the dynamics of the core segments (which are most remote from the periphery) shows a scaling behavior that differs from the dynamics obtained after…
In this paper we study the role of topology in DNA gel electrophoresis experiments via molecular dynamics simulations. The gel is modelled as a 3D array of obstacles from which half edges are removed at random with probability p, thereby generating a disordered environment. Changes in the microscopic structure of the gel are captured by measuring the electrophoretic mobility of ring polymers moving through the medium, while their linear counterparts provide a control system as we show they are insensitive to these changes. We show that ring polymers provide a novel non-invasive way of exploiti…
We consider single particle and polymer translocation where the frictional properties experienced from the environment are changing in time. This work is motivated by the interesting frequency responsive behaviour observed when a polymer is passing through a pore with an oscillating width. In order to explain this better we construct general diffusive and non-diffusive frequency response of the gain in translocation time for a single particle in changing environments and look at some specific variations. For two state confinement, where the particle either has constant drift velocity or is sta…
