Electrostatic repulsions can drive crystallization in many-particle systems. For charged colloida... more Electrostatic repulsions can drive crystallization in many-particle systems. For charged colloidal systems, the phase boundaries as well as crystal structure are highly tunable by experimental parameters such as salt concentration and pH. By using projections of the colloid-ion mixture to a system of (soft) repulsive spheres and the one-component plasma (OCP), we study the hitherto unexplained experimentally observed reentrant melting of electrostatically repelling colloids upon increasing the colloid density. Our study shows that the surface chemistry should involve a competition between adsorption of cations and anions to explain the observed density-induced reentrant melting.
We introduce the Poisson-Boltzmann cell model for spherical colloidal particles with a heterogene... more We introduce the Poisson-Boltzmann cell model for spherical colloidal particles with a heterogeneous surface charge distribution. This model is obtained by generalizing existing cell models for mixtures of homogeneously charged colloidal spheres. Our new model has similar features as Onsager's second-virial theory for liquid crystals, but it predicts no orientational ordering if there is no positional ordering. This implies that all phases of heterogeneously charged colloids that are liquid-like with respect to translational degrees of freedom are also isotropic with respect to particle orientation.
We theoretically study sedimentation-diffusion equilibrium of dilute binary, ternary, and polydis... more We theoretically study sedimentation-diffusion equilibrium of dilute binary, ternary, and polydisperse mixtures of colloidal particles with different buoyant masses and/or charges. We focus on the low-salt regime, where the entropy of the screening ions drives spontaneous charge separation and the formation of an inhomogeneous macroscopic electric field. The resulting electric force lifts the colloids against gravity, yielding highly nonbarometric and even nonmonotonic colloidal density profiles. The most profound effect is the phenomenon of segregation into layers of colloids with equal mass-per-charge, including the possibility that heavy colloidal species float onto lighter ones.
In this work we theoretically study the differential capacitance of an aqueous electrolyte in con... more In this work we theoretically study the differential capacitance of an aqueous electrolyte in contact with a planar electrode, using classical Density Functional Theory, and show how this measurable quantity can be used as a probe to better understand the structure and composition of the electric double layer at play. Specifically, we show how small trace amounts of divalent ions can influence the differential capacitance greatly, and also how small ions dominate its behaviour for high electrode potentials. In this study, we consider primitive model electrolytes, and not only use the standard definition of the differential capacitance, but also derive a new expression from mechanical equilibrium in a planar geometry. This expression reveals explicitly that the first layer of ions near the charged surface is key to its understanding. Our insights might be used as a guide in experiments to better understand the electrolyte-electrode interface as well as the (composition of the) bulk electrolyte.
Using a grand-canonical Landau-de Gennes theory for colloidal suspensions of bent (banana-shaped)... more Using a grand-canonical Landau-de Gennes theory for colloidal suspensions of bent (banana-shaped) rods, we investigate how spatial deformations in the nematic director field affect the local density of twist-bend and splay-bend nematic phases. The grand-canonical character of the theory naturally relates the local density to the local nematic order parameter S. In the splay-bend phase, we find S and hence the local density to modulate periodically along one spatial direction. As a consequence the splay-bend phase has the key symmetries of a smectic rather than a nematic phase. By contrast we find that S and hence the local density do not vary in space in the twist-bend phase, which is therefore a proper nematic phase. The theoretically predicted one-dimensional density modulations in splay-bend phases are in agreement with recent simulations.
Using simulations we study the phase behavior of a family of hard spherotetrahedra, a shape that ... more Using simulations we study the phase behavior of a family of hard spherotetrahedra, a shape that interpolates between tetrahedra and spheres. We identify 13 close-packed structures, some with packings that are significantly denser than previously reported. Twelve of these are crystals with unit cells of N = 2 or N = 4 particles, but in the shape regime of slightly rounded tetrahedra we find that the densest structure is a quasicrystal approximant with a unit cell of N = 82 particles. All 13 structures are also stable below close packing, together with an additional 14th plastic crystal phase at the sphere side of the phase diagram, and upon sufficient dilution to packing fractions below 50-60% all structures melt. Interestingly, however, upon compressing the fluid phase, self-assembly takes place spontaneously only at the tetrahedron and the sphere side of the family but not in an intermediate regime of tetrahedra with rounded edges. We describe the local environment of each particle by a set of l-fold bond orientational order parameters q ̅ l , which we use in an extensive principal component analysis. We find that the total packing fraction as well as several particular linear combinations of q ̅ l rather than individual q ̅ l 's are optimally distinctive, specifically the differences q ̅ 4 -q ̅ 6 for separating tetragonal from hexagonal structures and q ̅ 4 -q ̅ 8 for distinguishing tetragonal structures. We argue that these characteristic combinations are also useful as reliable order parameters in nucleation studies, enhanced sampling techniques, or inversedesign methods involving odd-shaped particles in general.
We derive a microscopic expression for the chemical potential of active Brownian spheres in stead... more We derive a microscopic expression for the chemical potential of active Brownian spheres in steady state. We show that the local chemical potential consists of (i) an intrinsic chemical potential similar to passive systems, which depends on density and self-propulsion speed, but not on the external potential, (ii) the external potential, and (iii) a newly derived one-body swim potential due to the activity of the particles. Our simulations on active Brownian particles show good agreement with our Fokker-Planck calculations, and confirm that the chemical potential is spatially constant for several inhomogeneous active fluids in their steady states. Finally, we show that gas-liquid coexistence of active particles with a planar interface satisfies not only mechanical but also diffusive equilibrium, which is well-described by equating the bulk chemical potential and bulk pressure obtained from bulk simulations.
We present a study of the structure and differential capacitance of electric double layers of aqu... more We present a study of the structure and differential capacitance of electric double layers of aqueous electrolytes. We consider electric double layer capacitors (EDLC) composed of spherical cations and anions in a dielectric continuum confined between a planar cathode and anode. The model system includes steric as well as Coulombic ion-ion and ion-electrode interactions. We compare results of computationally expensive, but “exact” , Brownian Dynamics (BD) simulations with approximate, but cheap, calculations based on classical Density Functional Theory (DFT). Excellent overall agreement is found for a large set of system parameters, including variations in concentration, ionic size- and valency-asymmetries, applied voltages and electrode separation, provided the differences between the canonical ensemble of the BD simulations and the grand-canonical ensemble of DFT are properly taken into account. In particular, a careful distinction is made between the differential capacitance $$C_...
In this work, we theoretically study the differential capacitance of an aqueous electrolyte in co... more In this work, we theoretically study the differential capacitance of an aqueous electrolyte in contact with a planar electrode, using classical density functional theory, and show how this measurable quantity can be used as a probe to better understand the structure and composition of the electric double layer at play. Specifically, we show how small trace amounts of divalent ions can influence the differential capacitance greatly and also how small ions dominate its behavior for high electrode potentials. In this study, we consider primitive model electrolytes and not only use the standard definition of the differential capacitance but also derive a new expression from mechanical equilibrium in a planar geometry. This expression reveals explicitly that the first layer of ions near the charged surface is key to its understanding. Our insights might be used as a guide in experiments to better understand the electrolyte–electrode interface as well as the (composition of the) bulk elec...
We develop a phenomenological Landau–de Gennes (LdG) theory for lyotropic colloidal suspensions o... more We develop a phenomenological Landau–de Gennes (LdG) theory for lyotropic colloidal suspensions of bent rods using a Q-tensor expansion of the chemical-potential dependent grand potential. In addition, we introduce a bend flexoelectric term, coupling the polarization and the divergence of the Q-tensor, to study the stability of uniaxial (N), twist-bend (NTB), and splay-bend (NSB) nematic phases of colloidal bent rods. We first show that a mapping can be found between the LdG theory and the Oseen–Frank theory. By breaking the degeneracy between the splay and bend elastic constants, we find that the LdG theory predicts either an N–NTB–NSB or an N–NSB–NTB phase sequence upon increasing the particle concentration. Finally, we employ our theory to study the first-order N–NTB phase transition, for which we find that K33 as well as its renormalized version K33eff remain positive at the transition, whereas K33eff vanishes at the nematic spinodal. We connect these findings to recent simulati...
We study the effect of flexibility and bend angle on systems of hard semiflexible boomerangs. The... more We study the effect of flexibility and bend angle on systems of hard semiflexible boomerangs. These are modelled as two rodlike segments joined at one end with an angle that can fluctuate about a preferred angle. We use a second-virial theory for semiflexible chains with two segments, and numerically solve for the full orientation distribution function as a function of the four angles that determine the boomerang's orientation. We plot the single segment distributions as a function of two angles as well as the interarm angle distribution. For stiff boomerangs, we find prolate, oblate and biaxial nematic phases depending on the bend angle and density, in partial agreement with previous results on rigid boomerangs. For the case that the preferred interarm angle is 90 • , however, we find that the biaxial nematic phase has four-fold rather than two-fold rotational symmetry, and thus requires fourth-rank order parameters to describe it. In addition, we find that flexibility drastically reduces the region of stability for the biaxial nematic phase, with the prolate nematic becoming more favourable.
To study the role of torque in motility-induced phase separation (MIPS), we simulate a system of ... more To study the role of torque in motility-induced phase separation (MIPS), we simulate a system of self-propelled particles whose shape varies smoothly from isotropic (disks/spheres) to weakly elongated (rods). We construct the phase diagrams of 2D active disks, 3D active spheres, and 2D/3D active rods of aspect ratio l/σ = 2. A stability analysis of the homogeneous isotropic phase allows us to predict the onset of MIPS based on the effective swimming speed and rotational diffusion of the particles. Both methods find suppression of MIPS as the particle shape is elongated. We propose a suppression mechanism based on the duration of collisions and argue that this mechanism can explain both the suppression of MIPS found here for rodlike particles and the enhancement of MIPS found for particles with Vicsek interactions.
We revisit the classical problem of flow of electrolyte solutions through charged capillary nanop... more We revisit the classical problem of flow of electrolyte solutions through charged capillary nanopores or nanotubes as described by the capillary pore model (also called "space charge" theory). This theory assumes very long and thin pores and uses a one-dimensional flux-force formalism which relates fluxes (electrical current, salt flux, fluid velocity) and driving forces (difference in electric potential, salt concentration, pressure). We analyze the general case with overlapping electric double layers in the pore and a nonzero axial salt concentration gradient. The 3 × 3 matrix relating these quantities exhibits Onsager symmetry and we report a significant new simplification for the diagonal element relating axial salt flux to the gradient in chemical potential. We prove that Onsager symmetry is preserved under changes of variables, which we illustrate by transformation to a different flux-force matrix given by Gross and Osterle (1968). The capillary pore model is well-suited to describe the nonlinear response of charged membranes or nanofluidic devices for electrokinetic energy conversion and water desalination, as long as the transverse ion profiles remain in local quasi-equilibrium. As an example, we evaluate electrical power production from a salt concentration difference by reverse electrodialysis, using an efficiency vs. power diagram. We show that since the capillary pore model allows for axial gradients in salt concentration, partial loops in current, salt flux or fluid flow can develop in the pore. Predictions for macroscopic transport properties using a reduced model where the potential and concentration are assumed to be invariant with radial coordinate ("uniform potential" or "fine capillary pore" model), are close to results of the full model.
We combine a general formulation of microswimmer equations of motion with a numerical bead-shell ... more We combine a general formulation of microswimmer equations of motion with a numerical bead-shell model to calculate the hydrodynamic interactions with the fluid, from which the swimming speed, power, and efficiency are extracted. From this framework, a generalized Scallop theorem emerges. The applicability to arbitrary shapes allows for the optimization of the efficiency with respect to the swimmer geometry. We apply this scheme to “three-body swimmers” of various shapes and find that the efficiency is characterized by the single-body friction coefficient in the long-arm regime, while in the short-arm regime the minimal approachable distance becomes the determining factor. Next, we apply this scheme to a biologically inspired set of swimmers that propel using a rotating helical flagellum. Interestingly, we find two distinct optimal shapes, one of which is fundamentally different from the shapes observed in nature (e.g., bacteria).
Manipulation of the charge of the dielectric interface between two bulk liquids not only enables ... more Manipulation of the charge of the dielectric interface between two bulk liquids not only enables the adjustment of the interfacial tension, but also controls the storage capacity of ions in the ionic double layers adjacent to each side of the interface.
We explore the crystallization of charged colloidal particles in a nonpolar solvent mixture. We s... more We explore the crystallization of charged colloidal particles in a nonpolar solvent mixture. We simultaneously charge the particles and add counterions to the solution with aerosol-OT (AOT) reverse-micelles. At low AOT concentrations, the charged particles crystallize into body-centered cubic (BCC) or face-centered cubic (FCC) Wigner crystals; at high AOT concentrations, the increased screening drives a thus far unobserved re-entrant melting transition. We observe an unexpected scaling of the data with particle size, and account for all behavior with a model that quantitatively predicts both the re-entrant melting and the data collapse.
We study numerically the effect of attractive triplet interactions on the phase behavior of suspe... more We study numerically the effect of attractive triplet interactions on the phase behavior of suspensions of highly charged colloidal particles at low salinity. In our computer simulations, we employ the pair and triplet potentials that were obtained from a numerical Poisson-Boltzmann study [C. Russ et al., Phys. Rev. E 66, 011402 (2002)]. On the basis of free energy calculations, we determine the phase diagram of an aqueous suspension of identical spheres of diameter = 32 nm and charge Z = 80 as a function of colloid concentration and salinity, both for the purely pairwise additive system and for the system with pair and triplet interactions. The main effect of including the triplet interactions is a destabilization of the body-centered-cubic (bcc) crystal phase in favor of the face-centered-cubic (fcc) crystal phase. As a consequence the phase diagram features the coexistence of a rather dilute fluid with an almost-close-packed fcc phase at low salinity and bcc-fcc coexistence with a big density jump at intermediate salinity. The triplet attractions do not affect the phase behavior at sufficiently high salinity; under these conditions the system is well described by the pairwise potential.
Electrostatic repulsions can drive crystallization in many-particle systems. For charged colloida... more Electrostatic repulsions can drive crystallization in many-particle systems. For charged colloidal systems, the phase boundaries as well as crystal structure are highly tunable by experimental parameters such as salt concentration and pH. By using projections of the colloid-ion mixture to a system of (soft) repulsive spheres and the one-component plasma (OCP), we study the hitherto unexplained experimentally observed reentrant melting of electrostatically repelling colloids upon increasing the colloid density. Our study shows that the surface chemistry should involve a competition between adsorption of cations and anions to explain the observed density-induced reentrant melting.
We introduce the Poisson-Boltzmann cell model for spherical colloidal particles with a heterogene... more We introduce the Poisson-Boltzmann cell model for spherical colloidal particles with a heterogeneous surface charge distribution. This model is obtained by generalizing existing cell models for mixtures of homogeneously charged colloidal spheres. Our new model has similar features as Onsager's second-virial theory for liquid crystals, but it predicts no orientational ordering if there is no positional ordering. This implies that all phases of heterogeneously charged colloids that are liquid-like with respect to translational degrees of freedom are also isotropic with respect to particle orientation.
We theoretically study sedimentation-diffusion equilibrium of dilute binary, ternary, and polydis... more We theoretically study sedimentation-diffusion equilibrium of dilute binary, ternary, and polydisperse mixtures of colloidal particles with different buoyant masses and/or charges. We focus on the low-salt regime, where the entropy of the screening ions drives spontaneous charge separation and the formation of an inhomogeneous macroscopic electric field. The resulting electric force lifts the colloids against gravity, yielding highly nonbarometric and even nonmonotonic colloidal density profiles. The most profound effect is the phenomenon of segregation into layers of colloids with equal mass-per-charge, including the possibility that heavy colloidal species float onto lighter ones.
In this work we theoretically study the differential capacitance of an aqueous electrolyte in con... more In this work we theoretically study the differential capacitance of an aqueous electrolyte in contact with a planar electrode, using classical Density Functional Theory, and show how this measurable quantity can be used as a probe to better understand the structure and composition of the electric double layer at play. Specifically, we show how small trace amounts of divalent ions can influence the differential capacitance greatly, and also how small ions dominate its behaviour for high electrode potentials. In this study, we consider primitive model electrolytes, and not only use the standard definition of the differential capacitance, but also derive a new expression from mechanical equilibrium in a planar geometry. This expression reveals explicitly that the first layer of ions near the charged surface is key to its understanding. Our insights might be used as a guide in experiments to better understand the electrolyte-electrode interface as well as the (composition of the) bulk electrolyte.
Using a grand-canonical Landau-de Gennes theory for colloidal suspensions of bent (banana-shaped)... more Using a grand-canonical Landau-de Gennes theory for colloidal suspensions of bent (banana-shaped) rods, we investigate how spatial deformations in the nematic director field affect the local density of twist-bend and splay-bend nematic phases. The grand-canonical character of the theory naturally relates the local density to the local nematic order parameter S. In the splay-bend phase, we find S and hence the local density to modulate periodically along one spatial direction. As a consequence the splay-bend phase has the key symmetries of a smectic rather than a nematic phase. By contrast we find that S and hence the local density do not vary in space in the twist-bend phase, which is therefore a proper nematic phase. The theoretically predicted one-dimensional density modulations in splay-bend phases are in agreement with recent simulations.
Using simulations we study the phase behavior of a family of hard spherotetrahedra, a shape that ... more Using simulations we study the phase behavior of a family of hard spherotetrahedra, a shape that interpolates between tetrahedra and spheres. We identify 13 close-packed structures, some with packings that are significantly denser than previously reported. Twelve of these are crystals with unit cells of N = 2 or N = 4 particles, but in the shape regime of slightly rounded tetrahedra we find that the densest structure is a quasicrystal approximant with a unit cell of N = 82 particles. All 13 structures are also stable below close packing, together with an additional 14th plastic crystal phase at the sphere side of the phase diagram, and upon sufficient dilution to packing fractions below 50-60% all structures melt. Interestingly, however, upon compressing the fluid phase, self-assembly takes place spontaneously only at the tetrahedron and the sphere side of the family but not in an intermediate regime of tetrahedra with rounded edges. We describe the local environment of each particle by a set of l-fold bond orientational order parameters q ̅ l , which we use in an extensive principal component analysis. We find that the total packing fraction as well as several particular linear combinations of q ̅ l rather than individual q ̅ l 's are optimally distinctive, specifically the differences q ̅ 4 -q ̅ 6 for separating tetragonal from hexagonal structures and q ̅ 4 -q ̅ 8 for distinguishing tetragonal structures. We argue that these characteristic combinations are also useful as reliable order parameters in nucleation studies, enhanced sampling techniques, or inversedesign methods involving odd-shaped particles in general.
We derive a microscopic expression for the chemical potential of active Brownian spheres in stead... more We derive a microscopic expression for the chemical potential of active Brownian spheres in steady state. We show that the local chemical potential consists of (i) an intrinsic chemical potential similar to passive systems, which depends on density and self-propulsion speed, but not on the external potential, (ii) the external potential, and (iii) a newly derived one-body swim potential due to the activity of the particles. Our simulations on active Brownian particles show good agreement with our Fokker-Planck calculations, and confirm that the chemical potential is spatially constant for several inhomogeneous active fluids in their steady states. Finally, we show that gas-liquid coexistence of active particles with a planar interface satisfies not only mechanical but also diffusive equilibrium, which is well-described by equating the bulk chemical potential and bulk pressure obtained from bulk simulations.
We present a study of the structure and differential capacitance of electric double layers of aqu... more We present a study of the structure and differential capacitance of electric double layers of aqueous electrolytes. We consider electric double layer capacitors (EDLC) composed of spherical cations and anions in a dielectric continuum confined between a planar cathode and anode. The model system includes steric as well as Coulombic ion-ion and ion-electrode interactions. We compare results of computationally expensive, but “exact” , Brownian Dynamics (BD) simulations with approximate, but cheap, calculations based on classical Density Functional Theory (DFT). Excellent overall agreement is found for a large set of system parameters, including variations in concentration, ionic size- and valency-asymmetries, applied voltages and electrode separation, provided the differences between the canonical ensemble of the BD simulations and the grand-canonical ensemble of DFT are properly taken into account. In particular, a careful distinction is made between the differential capacitance $$C_...
In this work, we theoretically study the differential capacitance of an aqueous electrolyte in co... more In this work, we theoretically study the differential capacitance of an aqueous electrolyte in contact with a planar electrode, using classical density functional theory, and show how this measurable quantity can be used as a probe to better understand the structure and composition of the electric double layer at play. Specifically, we show how small trace amounts of divalent ions can influence the differential capacitance greatly and also how small ions dominate its behavior for high electrode potentials. In this study, we consider primitive model electrolytes and not only use the standard definition of the differential capacitance but also derive a new expression from mechanical equilibrium in a planar geometry. This expression reveals explicitly that the first layer of ions near the charged surface is key to its understanding. Our insights might be used as a guide in experiments to better understand the electrolyte–electrode interface as well as the (composition of the) bulk elec...
We develop a phenomenological Landau–de Gennes (LdG) theory for lyotropic colloidal suspensions o... more We develop a phenomenological Landau–de Gennes (LdG) theory for lyotropic colloidal suspensions of bent rods using a Q-tensor expansion of the chemical-potential dependent grand potential. In addition, we introduce a bend flexoelectric term, coupling the polarization and the divergence of the Q-tensor, to study the stability of uniaxial (N), twist-bend (NTB), and splay-bend (NSB) nematic phases of colloidal bent rods. We first show that a mapping can be found between the LdG theory and the Oseen–Frank theory. By breaking the degeneracy between the splay and bend elastic constants, we find that the LdG theory predicts either an N–NTB–NSB or an N–NSB–NTB phase sequence upon increasing the particle concentration. Finally, we employ our theory to study the first-order N–NTB phase transition, for which we find that K33 as well as its renormalized version K33eff remain positive at the transition, whereas K33eff vanishes at the nematic spinodal. We connect these findings to recent simulati...
We study the effect of flexibility and bend angle on systems of hard semiflexible boomerangs. The... more We study the effect of flexibility and bend angle on systems of hard semiflexible boomerangs. These are modelled as two rodlike segments joined at one end with an angle that can fluctuate about a preferred angle. We use a second-virial theory for semiflexible chains with two segments, and numerically solve for the full orientation distribution function as a function of the four angles that determine the boomerang's orientation. We plot the single segment distributions as a function of two angles as well as the interarm angle distribution. For stiff boomerangs, we find prolate, oblate and biaxial nematic phases depending on the bend angle and density, in partial agreement with previous results on rigid boomerangs. For the case that the preferred interarm angle is 90 • , however, we find that the biaxial nematic phase has four-fold rather than two-fold rotational symmetry, and thus requires fourth-rank order parameters to describe it. In addition, we find that flexibility drastically reduces the region of stability for the biaxial nematic phase, with the prolate nematic becoming more favourable.
To study the role of torque in motility-induced phase separation (MIPS), we simulate a system of ... more To study the role of torque in motility-induced phase separation (MIPS), we simulate a system of self-propelled particles whose shape varies smoothly from isotropic (disks/spheres) to weakly elongated (rods). We construct the phase diagrams of 2D active disks, 3D active spheres, and 2D/3D active rods of aspect ratio l/σ = 2. A stability analysis of the homogeneous isotropic phase allows us to predict the onset of MIPS based on the effective swimming speed and rotational diffusion of the particles. Both methods find suppression of MIPS as the particle shape is elongated. We propose a suppression mechanism based on the duration of collisions and argue that this mechanism can explain both the suppression of MIPS found here for rodlike particles and the enhancement of MIPS found for particles with Vicsek interactions.
We revisit the classical problem of flow of electrolyte solutions through charged capillary nanop... more We revisit the classical problem of flow of electrolyte solutions through charged capillary nanopores or nanotubes as described by the capillary pore model (also called "space charge" theory). This theory assumes very long and thin pores and uses a one-dimensional flux-force formalism which relates fluxes (electrical current, salt flux, fluid velocity) and driving forces (difference in electric potential, salt concentration, pressure). We analyze the general case with overlapping electric double layers in the pore and a nonzero axial salt concentration gradient. The 3 × 3 matrix relating these quantities exhibits Onsager symmetry and we report a significant new simplification for the diagonal element relating axial salt flux to the gradient in chemical potential. We prove that Onsager symmetry is preserved under changes of variables, which we illustrate by transformation to a different flux-force matrix given by Gross and Osterle (1968). The capillary pore model is well-suited to describe the nonlinear response of charged membranes or nanofluidic devices for electrokinetic energy conversion and water desalination, as long as the transverse ion profiles remain in local quasi-equilibrium. As an example, we evaluate electrical power production from a salt concentration difference by reverse electrodialysis, using an efficiency vs. power diagram. We show that since the capillary pore model allows for axial gradients in salt concentration, partial loops in current, salt flux or fluid flow can develop in the pore. Predictions for macroscopic transport properties using a reduced model where the potential and concentration are assumed to be invariant with radial coordinate ("uniform potential" or "fine capillary pore" model), are close to results of the full model.
We combine a general formulation of microswimmer equations of motion with a numerical bead-shell ... more We combine a general formulation of microswimmer equations of motion with a numerical bead-shell model to calculate the hydrodynamic interactions with the fluid, from which the swimming speed, power, and efficiency are extracted. From this framework, a generalized Scallop theorem emerges. The applicability to arbitrary shapes allows for the optimization of the efficiency with respect to the swimmer geometry. We apply this scheme to “three-body swimmers” of various shapes and find that the efficiency is characterized by the single-body friction coefficient in the long-arm regime, while in the short-arm regime the minimal approachable distance becomes the determining factor. Next, we apply this scheme to a biologically inspired set of swimmers that propel using a rotating helical flagellum. Interestingly, we find two distinct optimal shapes, one of which is fundamentally different from the shapes observed in nature (e.g., bacteria).
Manipulation of the charge of the dielectric interface between two bulk liquids not only enables ... more Manipulation of the charge of the dielectric interface between two bulk liquids not only enables the adjustment of the interfacial tension, but also controls the storage capacity of ions in the ionic double layers adjacent to each side of the interface.
We explore the crystallization of charged colloidal particles in a nonpolar solvent mixture. We s... more We explore the crystallization of charged colloidal particles in a nonpolar solvent mixture. We simultaneously charge the particles and add counterions to the solution with aerosol-OT (AOT) reverse-micelles. At low AOT concentrations, the charged particles crystallize into body-centered cubic (BCC) or face-centered cubic (FCC) Wigner crystals; at high AOT concentrations, the increased screening drives a thus far unobserved re-entrant melting transition. We observe an unexpected scaling of the data with particle size, and account for all behavior with a model that quantitatively predicts both the re-entrant melting and the data collapse.
We study numerically the effect of attractive triplet interactions on the phase behavior of suspe... more We study numerically the effect of attractive triplet interactions on the phase behavior of suspensions of highly charged colloidal particles at low salinity. In our computer simulations, we employ the pair and triplet potentials that were obtained from a numerical Poisson-Boltzmann study [C. Russ et al., Phys. Rev. E 66, 011402 (2002)]. On the basis of free energy calculations, we determine the phase diagram of an aqueous suspension of identical spheres of diameter = 32 nm and charge Z = 80 as a function of colloid concentration and salinity, both for the purely pairwise additive system and for the system with pair and triplet interactions. The main effect of including the triplet interactions is a destabilization of the body-centered-cubic (bcc) crystal phase in favor of the face-centered-cubic (fcc) crystal phase. As a consequence the phase diagram features the coexistence of a rather dilute fluid with an almost-close-packed fcc phase at low salinity and bcc-fcc coexistence with a big density jump at intermediate salinity. The triplet attractions do not affect the phase behavior at sufficiently high salinity; under these conditions the system is well described by the pairwise potential.
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Papers by René van Roij