Effective Interparticle Potential Research Articles

Characterizing the Solvent‐Induced Inversion of Colloidal Aggregation During Electrophoretic Deposition

AbstractElectrophoretic deposition (EPD) of colloidal particles is a practical system for the study of crystallization and related physical phenomena. The aggregation is driven by the electroosmotic flow fields and induced dipole moments generated by the polarization of the electrode‐particle‐electrolyte interface. Here, the electrochemical control of aggregation and repulsion in the electrophoretic deposition of colloidal microspheres is reported. The nature of the observed transition depended on the composition of the solvent, switching from electrode‐driven aggregation in water to electrical field‐driven repulsion in ethanol for otherwise identical systems of colloidal microspheres. This work uses optical microscopy‐derived particles and a recently developed particle insertion method approach to extract model‐free, effective interparticle potentials to describe the ensemble behavior of the particles as a function of the solvent and electrode potential at the electrode interface. This approach can be used to understand the phase behavior of these systems based on the observable particle positions rather than a detailed understanding of the electrode‐electrolyte microphysics. This approach enables simple predictability of the static and dynamic behaviors of functional colloid‐electrode interfaces.

Remarks on a compact Abelian Higgs model

Aspects of screening and confinement are re-examined for a recently proposed compact Abelian Higgs model with a θ-term. Our discussion is accomplished using the gauge-invariant but path-dependent variables formalism, which is an alternative to the Wilson loop approach. We explicitly show that the static potential profile is the sum of an effective-Yukawa and a linear potential, leading to the confinement of static external charges. We point out the central role of the parameter measuring the stiffness of the vortex lines present in the model in both the Yukawa-like and the confining sectors of the effective inter-particle potential we have computed.

Rheological investigation of gels formed by competing interactions: A numerical study.

A transition from solid-like to liquid-like behavior occurs when colloidal gels are subjected to a prolonged exposure to a steady shear. This phenomenon, which is characterized by a yielding point, is found to be strongly dependent on the packing fraction. However, it is not yet known how the effective inter-particle potential affects this transition. To this aim, we present a numerical investigation of the rheology of equilibrium gels in which a short-range depletion is complemented by a long-range electrostatic interaction. We observe a single yielding event in the stress-strain curve, occurring at a fixed strain. The stress overshoot is found to follow a power-law dependence on the Péclet number, with an exponent larger than that found in depletion gels, suggesting that its value may depend systematically on the underlying colloid-colloid interactions. We also establish a mapping between equilibrium states and steady states under shear, which allows us to identify the structural modifications induced by the presence of the shear. Remarkably, we find that steady states corresponding to the same Péclet number, obtained by different combinations of shear rate and solvent viscosity, show identical structural and rheological properties. Our results highlight the importance of understanding the coupling between colloidal interactions, solvent effects, and flow to be able to describe the microscopic organization of colloidal particles under shear.

Activity mediated phase separation: Can we understand phase behavior of the nonequilibrium problem from an equilibrium approach?

We present results for structure and dynamics of mixtures of active and passive particles, from molecular dynamics (MD) simulations and integral equation theory (IET) calculations, for a physically motivated model. The perfectly passive limit of the model corresponds to the phase-separating Asakura-Oosawa model for colloid-polymer mixtures in which, for the present study, the colloids are made self-propelling by introducing activity in accordance with the well known Vicsek model. Such activity facilitates phase separation further, as confirmed by our MD simulations and IET calculations. Depending upon the composition of active and passive particles, the diffusive motion of the active species can only be realized at large time scales. Despite this, we have been able to construct an equilibrium approach to obtain the structural properties of such inherently out-of-equilibrium systems. In this method, effective inter-particle potentials were constructed via IET by taking structural inputs from the MD simulations of the active system. These potentials in turn were used in passive MD simulations, results from which are observed to be in fair agreement with the original ones.

Testing ion structure models with x-ray Thomson scattering

We investigate the influence of various ionic structure models on the interpretation of the X-ray Thomson scattering signal. For the calculation of the ion structure, classical hypernetted chain equations are used applying different effective inter-particle potentials. It is shown that the different models lead to significant discrepancies in the theoretically predicted weight of the Rayleigh peak, in particular for small k-values where correlation effects are important. Here, we propose conditions which might allow for an experimental verification of the theories under consideration of experimental constraints of k-vector blurring.

Origin of similarity of phase diagrams in amphiphilic and colloidal systems with competing interactions

We show that amphiphilic and colloidal systems with competing interactions can be described by the same Landau-Brazovskii functional. The functional is obtained by a systematic coarse-graining procedure applied tosystems with isotropic interaction potentials. Microscopic expressions for the coefficients in the functional are derived. We propose simple criteria to distinguish the effective interparticle potentials that can lead to macro- or microsegregation. Our considerations concern also charged globular proteins in aqueous solutions and other system with effective short-range attraction long-range repulsion interactions.

Direct comparison of the rheology of model hard and soft particle glasses

The effects of particle softness and the role of the outer shell mechanics on the linear viscoelasticity and yielding behaviour of colloidal glasses are critically assessed using three different model colloidal particles: (i) sterically stabilized PMMA particles with model hard sphere interactions, (ii) core–shell microgels with a deformable PNIPAM outer shell and (iii) ultra-soft star-like micelles with inter-penetrable multi-arms. The volume fraction dependence of the elastic modulus and the yield stress reflects the softness of the effective inter-particle potential. The yield strain exhibits distinct non-monotonic volume fraction dependence for hard spheres below close packing whereas for both soft particles it increases above close packing due to particle softness. Stress overshoots in start-up shear show a common increase with shear rate in all systems. However, the stress overshoots are significantly stronger in star-like micelles due to transient arm entanglements. In relation with that similar stress peaks are detected within the period of the large amplitude oscillatory shear only in star-like micelles. Finally, we discuss the scaling exponents for the G′ and G′′ decrease at large oscillatory strain amplitudes and their relation with steady shear stress.

Effective nonadditive pair potential for lock-and-key interacting particles: The role of the limited valence

Theoretical studies of self-assembly processes and condensed phases in colloidal systems are often based on effective interparticle potentials. Here we show that developing an effective potential for particles interacting with a limited number of "lock-and-key" selective bonds (due to the specificity of biomolecular interactions) requires-in addition to the nonsphericity of the potential-a (many body) constraint that prevents multiple bonding on the same site. We show the importance of retaining both valence and bond selectivity by developing, as a case study, a simple effective potential describing the interaction between colloidal particles coated by four single-strand DNA chains.

Calculation of pair correlations in a high-density electron gas: Constraints for effective interparticle potentials

The pair-correlation function $g(r)$ of an interacting, unpolarized electron gas is modelled by using the geminal representation and effective potentials for the two-electron relative motion. We put forward a generalization of the impurity-related Fumi theorem, in order to obtain the scattering-mediated part of the kinetic energy change. Considering the high-density limit, where a perturbatively exact expression for the ground-state energy is available, a rigorous constraint on the effective interactions in the even and odd channels is deduced. The constraint is implemented by using physically motivated one-parametric potentials in these channels.

Hard-Disk Behavior and Beyond in Langmuir Films of CdSe Nanoparticles

Harnessing the spontaneous behavior of a population of particles is an attractive approach to the fabrication of targeted nanostructures. Underlying this goal is the interparticle potential, as it dictates the spontaneous behavior of the system. To this end, we present methodology for using quantitative film balance studies of trioctylphosphine oxide (TOPO) stabilized CdSe nanoparticles to determine their effective interparticle potential on the air-water interface. A simple protocol for reducing the quantity of excess TOPO to negligible levels of surface activity is established. In studying clean populations of 2.08, 2.22, 2.36, 2.49, 2.63, and 2.91 nm nanoparticles, quantitative agreement between their pressure-area isotherms and the Carnahan-Starling hard-disk equation of state is achieved. This analysis indicates that CdSe nanoparticles of a given diameter behave how hard disks with significantly smaller diameters would behave. This finding suggests that an attractive contribution to the interparticle potential, such as the dipolar potential, plays a significant role in the spontaneous organization of these particles.

Microscopic origin of the non-Gaussian behavior of dynamic structure factors of glassy matter

We consider the Lamb-M\ossbauer factors corresponding to the structure factors of a material (ethyl alcohol) showing two glassy phases, one of those being an orientationally disordered crystal. The deviations from the idealized Gaussian behavior expected for an isotropic-harmonic vibrator within the amorphous phase and disordered crystal are found to be remarkably close. Such proximity enables us to take advantage of the crystal symmetry to gain access to specific details of the effective interparticle potential. Once this is done the treatment is extended to include the fully amorphous material. The results depict atomic motions within the glassy matrices as significantly anisotropic and highly anharmonic and thus provide a way to understand the microscopic origin of phenomena considered as fingerprints of glassy dynamics.

Long-range electrostatic attraction between like-charge spheres in a charged pore

The existence of long-range attractive electrostatic forces between particles of like charge is one of the great current controversies ofcolloid science. The established theory (Derjaguin–Landau–Vervey–Overbeek; DLVO) of colloidal interactions predicts that an isolated pair of like-charged colloidal spheres in an electrolyte should experience a purely repulsive screened electrostatic (coulombic) interaction1,2. Direct measurements of such interactions have shown quantitative agreement with DLVO theory3,4,5. Recent experiments, however, provide evidence that the effective interparticle potential can have a long-range attractive component in more concentrated suspensions6,7 and for particles confined by charged glass walls3,5,8,9,10. It is apparent that the long-range attraction in concentrated systems is due to multi-body interactions and may have a similar explanation to the attraction observed for otherwise confined colloids. Theoretical explanations have been proposed11,12,13 but remain the subject of controversy14,15. Here we present a quantitative theoretical explanation of these attractive forces between confined colloidal particles, based on direct solutions of the nonlinear Poisson–Boltzmann equation for two like-charged spheres confined in a cylindrical charged pore. The calculations show that the attraction may be explained by the redistribution of the electric double layers of ions and counterions in solution around the spheres, owing to the presence of the wall; there is thus no need to revise the established concepts underlying theories of colloidal interactions.

Correlations and Local Field Corrections for a Two-Dimensional Electronic System in an External Magnetic Field

It is shown that the correlation effects on a two-dimensional electron gas in a uniform perpendicular magnetic field are significantly affected by a strong magnetic field. A dielectric function approach is used to go beyond the RPA by improving the effective potential. This is done by including the local field correction Gq to the mean Hartree field. Following Singwi et al. we replace the two-particle distribution function ƒ2(r, p; r′, p′; t) by a product of two equilibrium one-particle distribution functions ƒ(r, p; t)ƒ(r′, p′; t) g(r − r′), where g(r) is the static equilibrium pair correlation function. We have shown that the form of the effective potential is not altered by a uniform magnetic field. Both Gq and the pair correlation function oscillate as functions of the magnetic field. The local field correction has maxima at half-odd integer fillings and minima at integer filling factors. As a result, the effective inter-particle potential has enhanced oscillations. The effect due to correlations on the plasma excitations is also discussed.

Reentrant phase transition in charged colloidal suspensions.

We report the observation of a novel phase transition in dilute aqueous suspensions of polystyrene particles as a function of ionic impurity concentration $C$. The suspension phase separates into dense and rare phases only for a restricted range of $C$ which depends on particle concentration $n$. The dense phase has liquidlike or crystalline order depending on $n$ and $C$. Free energies of the homogeneous and the phase-separated states are calculated with an effective interparticle potential. The calculated phase diagram is in qualitative agreement with the present experimental results.

On the Relation Between the Effective Pair-potential and the Static Structure Factor in Liquid Metals

Abstract Accurate neutron diffraction measurements of the static structure factor S(Q) for small wave-vector transfers Q have been used to obtain the ‘coarse’ structure of the long-range part of the effective inter-particle potential in liquid aluminium, lead and bismuth. An extended version of the random phase approximation developed by Gaskell has been used. It is found that for Al and Pb the potential is of simple oscillatory nature while for Bi it is of ledge type. Finer details of the shape of the potential could not be evaluated. Methods to determine a good pair-potential by combining experimental results and molecular dynamics calculations are suggested.

On the Ground State Energy of a Gas of Interacting Polarons

AbstractUsing a canonical transformation the Hamiltonian of a gas of interacting polarons is studied. After elimination of the phonons the reduced Hamiltonian describes a system of charged particles interacting through an effective interparticle potential. The Hartree‐Fock ground state of the reduced system is analysed.

Radial Distribution Functions for a Hydrogenous Plasma in Equilibrium

Radial distribution functions ${g}_{\mathrm{ab}}(r)$ for a dense hydrogenous plasma (${n}_{i}={n}_{e}={10}^{18}$ electrons/cc) are obtained near the ionization temperature by solving the Percus-Yevick equation and a modified Percus-Yevick equation. The effective interparticle potentials used were obtained previously by a direct evaluation of their corresponding two-particle Slater sums, and include the Heisenberg quantal effect, but not the statistical quantal effect. The iterative solution of the equations, even using a variety of numerical procedures, is found to break down when the ionization falls appreciably.

On the Coefficients of Irreversible Processes in a Highly Ionized Gas

An effective interparticle potential, which is a modified Debye-Huckel potential, is introduced and discussed in order to eliminate simultaneous interactions between three particles or more in an ionized gas. For this potential weak-interaction asymptotes of collision cross sections necessary for the theory of irreversible processes are calculated without making further approximations. These cross sections are applied to relaxation betwcen ion and electron temperatures and to the coefficient of viscosity. (auth)