Diffusiophoretic Behavior Research Articles

Diffusiophoresis in Polymer and Nanoparticle Gradients.

Diffusiophoresis is the movement of the colloidal particles in response to a concentration gradient and can be observed for both electrolyte (e.g., salt) and nonelectrolyte (e.g., glucose) solutes. Here, we investigated the diffusiophoretic behavior of polystyrene (PS-carboxylate surface) microparticles in nonadsorbing charged and uncharged solute gradients [sodium polystyrenesulfonate (NaPSS), polyethylene glycol (PEG), and nanoscale colloidal silica (SiO2)] using a dead-end channel setup. We compared the diffusiophoretic motion in these gradient types with each other and to the case of using a monovalent salt gradient. In each of the nonadsorbing gradient systems (NaPSS, PEG, and SiO2 nanoparticles), the PS particles migrated toward the lower solute concentration. The exclusion distance values (from the initial position) of particles were recorded within the dead-end channel, and it was found that an increase in solute concentration increases exclusion from the main channel. In the polyelectrolyte case, the motion of PS microparticles was reduced by the addition of a background salt due to reduced electrostatic interaction, whereas it remained constant when using the neutral polymer. Particle diffusiophoresis in gradients of polyelectrolytes (charged macromolecules) is quite similar to the behavior when using a PEG gradient (uncharged macromolecule) in the presence of a background electrolyte. Moreover, we observed PS microparticles under different concentrations and molecular weights of PEG gradients. By combining the simulations, we estimated the exclusion length, which was previously proposed to be the order of the polymer radius. Furthermore, the movement of PS microparticles was analyzed in the gradient of silica nanoparticles. The exclusion distance was higher in silica nanoparticle gradients compared to similar-size PEG gradients because silica nanoparticles are charged. The diffusiophoretic transport of the PS microparticles could be simulated by considering the interaction between the PS microparticles and silica nanoparticles.

Diffusiophoretic Behavior of Polyelectrolyte-Coated Particles.

Diffusiophoresis, the movement of particles under a solute concentration gradient, has practical implications in a number of applications, such as particle sorting, focusing, and sensing. For diffusiophoresis in an electrolyte solution, the particle velocity is described by the electrolyte relative concentration gradient and the diffusiophoretic mobility of the particle. The electrolyte concentration, which typically varies throughout the system in space and time, can also influence the zeta potential of particles in space and time. This variation affects the diffusiophoretic behavior, especially when the zeta potential is highly dependent on the electrolyte concentration. In this work, we show that adsorbing a single bilayer (or 4 bilayers) of a polyelectrolyte pair (PDADMAC/PSS) on the surface of microparticles resulted in effectively constant zeta potential values with respect to salt concentration throughout the experimental range of salt concentrations. This allowed a constant potential model for diffusiophoretic transport to describe the experimental observations, which was not the case for uncoated particles in the same electrolyte system. This work highlights the use of simple polyelectrolyte pairs to tune the zeta potential and maintain constant values for precise control of diffusiophoretic transport.

Diffusiophoresis of a pH-regulated polyelectrolyte in a pH-regulated nanochannel

Considering its potential application in improving the performance of a single-molecule biosensing device, the diffusiophoresis of a polyelectrolyte sphere in a charged cylindrical nanochannel is studied taking account of the effect of diffusioosmosis flow. The interaction of the double layers in the present system is expected to influence significantly the relevant fields, yielding profound diffusiophoretic behaviors. Adopting a zwitterionic, pH-regulated polyelectrolyte in a silicon dioxide nanochannel as an example, these behaviors are simulated by varying the pH and the bulk salt concentration of the liquid phase, and the nanochannel radius. We show that the charged nanochannel could influence significantly both the quantitative and the qualitative behavior of the polyelectrolyte. The underlying mechanisms leading to this observation are discussed in detail.

Diffusiophoresis of a pH-regulated toroidal polyelectrolyte in a solution containing multiple ionic species

Extending previous analysis for the diffusiophoresis of a toroidal PE having a fixed charge density, we consider the case where it is pH-regulated and the liquid phase contains multiple ionic species so that the underlying assumptions are more realistic. The diffusiophoretic behaviors of the toroidal PE considered under various conditions are examined by varying its functional group density, size, and softness, and the solution pH and bulk salt concentration. We show that the behavior of a toroidal PE can be different both quantitatively and qualitatively from the corresponding spherical PE. The effective charge of the present PE is also different both quantitatively and qualitatively from the corresponding PE having fixed charge density. In particular, both the magnitude and the direction of diffusiophoretic velocity depend highly on the conditions assumed, implying that an efficient separation process can be designed. A three-dimensional velocity-pH-Debye length plot is constructed for that purpose.

Diffusiophoresis of polyelectrolytes: Effects of temperature, pH, type of ionic species and bulk concentration

Extending previous analyses on rigid particles to non-rigid ones, we model the diffusiophoresis of a pH-regulated polyelectrolyte (PE) in a solution containing multiple ionic species. For the first time, the effects of temperature, pH, type of ionic species and bulk concentration are taken into account, and therefore, the conditions considered are more comprehensive and closer to reality than those of the available results in the literature. Numerical simulation is conducted to examine the diffusiophoretic behaviors of a PE under various conditions, and empirical relationships are developed for the dependence of its mobility on the factors mentioned above. We show that temperature and pH influence appreciably the charged conditions of a PE, the ionic diffusivities, and the fluid viscosity, yielding complicated and interesting behaviors that are informative to device design.

Influence of double-layer polarization and chemiosmosis on the diffusiophoresis of a non-spherical polyelectrolyte

The diffusiophoresis of a non-spherical polyelectrolyte (PE) is modeled theoretically by considering an ellipsoidal PE of fixed volume and varying aspect ratio, capable of simulating porous entities such as DNAs, proteins, and synthetic polymeric particles. A continuum model comprising coupled Poisson–Nernst–Planck equations and Stokes equations is adopted. Parameters including the physicochemical properties of a PE, the degree of deformation, and the bulk ionic concentration are examined in detail for their influence on the diffusiophoretic behavior of the PE. We show that the effects of double-layer polarization, polarization of the condensed counterions inside a PE, and the chemiosmotic retardation flow inside it yield complicated diffusiophoretic behavior. In particular, the mobility of an elliptic PE can differ both quantitatively and qualitatively from that of a spherical PE. This phenomenon, which has not been reported previously, provides valuable information for both experimental data interpretation and device design.

Diffusiophoresis of a soft, pH-regulated particle in a solution containing multiple ionic species

The diffusiophoresis of a soft, pH-regulated particle comprising a rigid core and a polyelectrolyte (PE) layer in an aqueous salt solution containing multiple ionic species is modeled theoretically. We show that the diffusiophoretic behavior of a soft particle can be different appreciably from that of a rigid one. In particular, both the sign and the magnitude of the mobility of a soft particle can vary with the friction coefficient of its PE layer. In an aqueous KCl solution, if that coefficient is sufficiently large, the particle always moves towards the opposite direction as that of the applied concentration gradient, regardless of the pH level, an interesting observation which has not been reported previously. In an aqueous NaCl solution, if pH is sufficiently low, the particle mobility increases with increasing friction coefficient, an interesting and unexpected finding. The results obtained provide valuable and necessary information for both interpreting experimental data and design diffusiophoresis devices.

Diffusiophoresis of a pH-regulated, zwitterionic polyelectrolyte in a solution containing multiple ionic species

The diffusiophoresis of a pH-regulated, zwitterionic polyelectrolyte (PE) simulating entities such as DNAs, proteins, and synthetic polymeric particles in a solution containing multiple ionic species is modeled theoretically. The results of numerical simulation reveal that the diffusiophoretic behavior of the PE is influenced significantly by its physicochemical properties, the solution pH, the bulk salt concentration, and the types of ionic species. In particular, both the magnitude and the sign of the PE mobility are influenced appreciably by the bulk salt concentration and the types of ionic species. We show that the induced electric field coming from the applied concentration gradient is weakened by the movement of H+ and OH−. This phenomenon is more appreciable when pH is away from the isoelectric point of a PE. The results obtained provide valuable and necessary information for the design of diffusiophoresis devices.

Diffusiophoresis of a Charged Sphere in a Necked Nanopore

In an attempt to improve the performance of single-molecule nanopore based biosensors, we study theoretically the diffusiophoresis of a particle along the axis of a charged, necked nanopore, and the mechanisms involved. Numerical simulation is conducted by varying the geometry of the nanopore and its charged status, the particle position, and the background salt concentration to examine the particle behavior under various conditions and to gather necessary information for future device design. We show that the strength of the local concentration gradient, the charge density of the nanopore, and the presence of the nanopore wall yield complicated and interesting diffusiophoretic behaviors, which are informative to potential applications.

Diffusiophoresis of Polyelectrolytes in Nanodevices: Importance of Boundary

Considering the potential applications of diffusiophoresis conducted in nanodevices, a thorough theoretical analysis is performed for the first time on the diffusiophoresis of a polyelectrolyte (PE) in the presence of two representative types of boundaries: the direction of diffusiophoresis is either normal (type I) or parallel (type II) to a boundary, using two large parallel disks and a cylindrical pore as an example, respectively. It is interesting to observe that due to the effects of double-layer polarization, counterion condensation, polarization of condensed counterions, and diffusion of co-ions across a PE, its diffusiophoretic behavior can be influenced both quantitatively (magnitude of mobility) and qualitatively (direction of diffusiophoresis) by a boundary. In general, type I (II) boundary raises the diffusiophoretic mobility of a PE toward the high (low) salt concentration side. The results gathered provide necessary information for applications in, for example, designing catalytic swimmers and nanopore-based biosensor devices.

Importance of temperature on the diffusiophoretic behavior of a charge-regulated zwitterionic particle

Previous theoretical diffusiophoresis analyses were usually based on a fixed temperature, and its influence on the diffusiophoresis behavior of a particle was seldom discussed. Because both the physicochemical properties of the liquid phase and the charged conditions of a particle can be influenced appreciably by the temperature, so is diffusiophoresis behavior. This effect is taken into account in the present study for the first time, along with the possible presence of multiple ionic species in the liquid phase, a factor of practical significance if reactions occur on the particle surface and/or the solution pH is adjusted. Taking an aqueous dispersion of SiO2 particles as an example, a thorough numerical simulation is conducted to examine the behavior of a charge-regulated, zwitterionic particle subject to an applied salt concentration gradient under various conditions. Considering the potential applications of diffusiophoresis, the results gathered provide necessary information for the design of diffusiophoresis devices, and empirical relationships that correlate the scaled particle mobility with key parameters are developed for that purpose.

Diffusiophoresis of a polyelectrolyte in a salt concentration gradient

The diffusiophoresis of a polyelectrolyte subject to an applied salt concentration gradient is modeled theoretically. The entirely porous type of particle is capable of simulating entities such as DNA, protein, and synthetic polymeric particles. The dependence of the diffusiophoretic behavior of the polyelectrolyte on its physical properties, and the types of ionic species and their bulk concentrations are discussed in detail. We show that in addition to the effects coming from the polarization of double layer and the difference in the ionic diffusivities, the polarization of the condensed counterions inside the polyelectrolyte might also be significant. The last effect, which has not been reported previously, reduces both the electric force and the hydrodynamic force acting on the polyelectrolyte. Both the direction and the magnitude of the diffusiophoretic velocity of the polyelectrolyte are found to highly depend upon its physical properties. These results provide valuable references for applications such as DNA sequencing and catalytic nano- or micromotors.

Importance of Boundary Effect on the Diffusiophoretic Behavior of a Charged Particle in an Electrolyte Medium

The presence of a boundary on the diffusiophoretic behavior of a particle is analyzed by considering the diffusiophoresis of a charged, finite cylindrical particle along the axis of an uncharged cylindrical pore filled with an electrolyte solution. Compared with the other similar geometries considered in the literature, the boundary effect is the most significant in the present geometry, thereby highlighting its importance. The influence of chemiphoresis arising from two types of double-layer polarization (DLP) and that of the electrophoresis effect coming from the difference in the ionic diffusivities on the diffusiophoretic behavior of a particle are discussed. We show that this behavior can be influenced both quantitatively and qualitatively by the boundary. This is because all of the relevant factors, including the DLP effect, the electrophoresis effect, the electric repulsive force between the particle and the co-ions outside its double layer, and the hydrodynamic drag all depend highly on the degree...

Diffusiophoresis of a Nonuniformly Charged Sphere in a Narrow Cylindrical Pore

The influences of the boundary effect and the charged conditions of a particle on its diffusiophoretic behavior are studied by considering the diffusiophoresis of a nonuniformly charged sphere along the axis of a narrow cylindrical pore. We show that the surface charge distribution of the particle is capable of yielding the complicated phenomenon of double-layer polarization and, together with the presence of the pore, leads to profound and interesting diffusiophoretic behaviors. For example, if the electrophoresis effect coming from the difference in the ionic diffusivities is absent, then the diffusiophoretic velocity of a particle with the sign of the surface charge on its middle part different from that on its left- and right-hand parts has both a local maximum and a local minimum as the fraction of the middle varies; that velocity has only a local minimum if the whole particle is charged with the same sign. If the electrophoresis effect is significant, then the diffusiophoretic behavior of the particle depends mainly on its averaged surface charge density.

Diffusiophoresis of a soft spherical particle along the axis of a cylindrical microchannel

The diffusiophoresis of a soft particle is modeled theoretically by considering a soft sphere moving along the axis of a cylindrical microchannel. This geometry allows us to examine simultaneously the boundary effect and the nature of a particle on its diffusiophoretic behavior. The soft particle, which comprises a rigid core and an ion-penetrable layer, is capable of simulating biocolloids such as cells and particles covered by an artificial membrane layer. The results of numerical simulation reveal that due to its specific structure, the diffusiophoretic behavior of a soft particle is quite different from that of a rigid particle. The influence of the cylindrical microchannel on the diffusiophoretic behavior of the particle is also very different from that of other geometries considered in the literature. We show that, in addition to the effect of double-layer polarization, the effect of electrophoresis, and the electrical interaction between the coions outside the double layer and the particle, the nature of the soft particle can also influence both quantitatively and qualitatively its diffusiophoretic behavior. Several interesting results are observed, providing valuable reference for both the design of a diffusiophoresis device and the interpretation of the relevant experimental data.

Diffusiophoresis of a nonuniformly charged sphere in an electrolyte solution

The diffusiophoresis of a rigid, nonuniformly charged spherical particle in an electrolyte solution is analyzed theoretically focusing on the influences of the thickness of double layer, the surface charge distribution, the effect of electrophoresis, and the effect of double-layer polarization. We show that the nonuniform charge distribution on the particle surface yields complicated effect of double-layer polarization, leading to interesting diffusiophoretic behaviors. For example, if the sign of the middle part of the particle is different from that of its left- and right-hand parts, then depending upon the charge density and the fraction of the middle part, the particle can move either to the high-concentration side or to the low-concentration side. Both the diffusiophoretic velocity and its direction can be manipulated by the distribution of the surface charge density. In particular, if the electrophoresis effect is significant, then those properties are governed by the averaged surface charge density of the particle. A dipolelike particle, where its left- (right-) hand half is negatively (positively) charged, always migrates toward the low-concentration (left-hand) side, that is, it has a negative diffusiophoretic velocity. In addition, that diffusiophoretic velocity has a negative local minimum as the thickness of double layer varies.

Diffusiophoresis of a Soft Sphere Normal to Two Parallel Disks

The diffusiophoresis of a soft spherical particle normal to two parallel disks subject to an applied ionic concentration gradient is modeled theoretically. The soft particle, which comprises a rigid core and a porous membrane layer, is capable of simulating a wide class of particles such as biocolloids and particles covered by an artificial membrane layer; a rigid particle can also be recovered as the limiting case where the membrane layer is infinitely thin. The problem considered simulates, for example, the chemotaxis of cells or microorganisms. We show that the presence of the membrane layer is capable of yielding complicated diffusiophoretic behavior when the sign of the charge carried by that layer is different from that on the surface of the rigid core of the particle. Both the sign and the magnitude of the diffusiophoretic velocity of a particle can be adjusted through varying the friction coefficient of its membrane layer. These results are of practical significance, for example, in the case where diffusiophoresis is adopted as a separation operation or as a tool to carry and/or control the rate of drug release.

Diffusiophoresis of an Ellipsoid along the Axis of a Cylindrical Pore

The influences of a boundary and the shape of a particle on its diffusiophoretic behavior are examined by considering the diffusiophoresis of a charged ellipsoid along the axis of an uncharged cylindrical pore filled with electrolyte solutions. The diffusiophoretic mobility of the particle under various conditions is evaluated through varying the particle aspect ratio, the size of the particle, the thickness of the double layer, the diffusivities of co-ions and counterions, and the level of the surface potential. Because the double-layer polarization, the electrophoresis effect, the boundary effect, and the electrical interaction between the particle and the co-ions outside the double layer all play a role, the diffusiophoretic behavior of the particle is complicated. For a fixed particle volume, the relative magnitude of the diffusiophoretic mobilities of particles of various shapes depends highly on the degree of the boundary effect. It is possible for a particle to migrate toward the low-concentration side, regardless of the level of the surface potential, which is not observed in the case of a sphere in a planar slit or in a spherical cavity.

Diffusiophoretic Motion of a Charged Spherical Particle in a Nanopore

The diffusiophoretic motion of a charged spherical particle in a nanopore, subjected to an axial electrolyte concentration gradient, is investigated using a continuum theory, which consists of the ionic mass conservation equations for the ionic concentrations, the Poisson equation for the electric potential in the solution, and the Stokes equations for the hydrodynamic field. With the concentration gradient imposed, the particle motion is induced by two different mechanisms: an electrophoresis generated by the induced electric field arising from the difference of ionic diffusivities and the double layer polarization (DLP) and a chemiphoresis by the resulting osmotic pressure gradient induced by the solute gradient in the electrical double layer around the particle. The particle diffusiophoretic velocity along the axis of the nanopore is computed as functions of the ratio of the particle size to the thickness of the electrical double layer, the ratio of the nanopore size to the particle size, the particle surface charge density, and the properties of the salt solution. The diffusiophoretic behavior of a particle comparable to the nanopore size is governed predominantly by the induced electrophoresis generated by the DLP-induced electric field, caused by the imposed concentration gradient and the double layer compression due to the presence of the impervious nanopore wall.

Diffusiophoresis of a Charge-Regulated Sphere along the Axis of an Uncharged Cylindrical Pore

The diffusiophoresis of a charge-regulated spherical particle along the axis of a cylindrical pore is modeled. The problem considered allows us to examine simultaneously the effects of the presence of a boundary, the charge conditions on the particle surface, the thickness of the double layer, and the nature of a dispersion medium including its pH value and the diffusivities of the ionic species with respect to the diffusiophoretic behavior of a particle. We show that, in addition to the factors of double-layer polarization, electrophoresis, and the osmotic flow of solvent, the diffusiophoretic behavior of the particle can also be affected significantly by the electrical repulsive interaction between the particle and the co-ions immediately outside the double layer as they diffuse through the gap between the double layer and the pore. The last effect, which can influence the diffusiophoretic behavior of a particle both quantitatively and qualitatively, is absent in the diffusiophresis of a sphere in a spherical cavity. The competition of those effects yields many interesting results that are of practical significance in the design of a diffusiophoretic apparatus and/or the interpretation of experimental data.