For binary solvent mixtures composed of ions and two kinds of polar solvents, electric double layer near a charged object is strongly affected by not only the binary solvent composition but also nature of solvents such as volume and dipole moment of a solvent molecule. Accounting for difference in sizes of solvents and orientational ordering of solvent dipoles, we theoretically obtain general expressions for the spatial distribution functions of solvents and ions, in planar geometry and within the mean-field approach. Although focusing on long-range electrostatic interaction, we neglect short-range interactions such as preferential solvation, our approach predicts an asymmetric depletion of the two solvents from the charged surface and a behavior of decreased permittivity of the binary solvent mixture. Furthermore, we suggest that the key factor for the depletion is the ratio of the solvent dipole moment to the solvent volume. The influence of binary solvent composition, volume of solvent and dipole moment of solvent on the number density of solvents, permittivity and differential capacitance are presented and discussed, respectively. We conclude that accounting for difference in the volume and dipole moment between polar solvents is necessary for new approach to represent more realistic situations such as preferential solvation.
We consider depletion effects of a pear-shaped colloidal particle in a hard-sphere solvent, for two different model realisations of the pear-shaped colloidal particle. The two models are the pear hard Gaussian overlap (PHGO) particles and the hard pears of revolution (HPR). The motivation for this study is to provide a microscopic understanding for the substantially different mesoscopic self-assembly properties of these pear-shaped colloids, in dense suspensions, that have been reported in the first part of this series. This is done by determining the differing depletion attraction via MC simu…
Macromolecular solubility in solvent mixtures often exhibit striking and paradoxical nature. For example, when two well miscible poor solvents for a given polymer are mixed together, the same polymer may swell within intermediate mixing ratios. We combine computer simulations and theoretical arguments to unveil the first microscopic, generic origin of this collapse-swelling-collapse scenario. We show that this phenomenon naturally emerges at constant pressure in mixtures of purely repulsive components, especially when a delicate balance of the entropically driven depletion interactions is achi…
As first explained by the classic Asakura-Oosawa (AO) model, effective attractive forces between colloidal particles induced by depletion of nonadsorbing polymers can drive demixing of colloid-polymer mixtures into colloid-rich and colloid-poor phases, with practical relevance for purification of water, stability of foods and pharmaceuticals, and macromolecular crowding in biological cells. By idealizing polymer coils as effective penetrable spheres, the AO model qualitatively captures the influence of polymer depletion on thermodynamic phase behavior of colloidal suspensions. In previous work…
Depletion force in the infinite-dilution limit in a solvent of nonadditive hard spheres
通过正则蒙特卡罗模拟和最近提出的有理函数近似[Phys. Rev. E \textbf{84}，041201（2011）]，计算了浸入非加性“小”硬球二元混合溶剂中的两个溶质“大”硬球感受到的相互熵耗尽力，该力是表面到表面距离的函数。四个有代表性的方案进行了研究：对称的溶质颗粒和限制，其中两个溶质球之一成为一个平面的硬壁，在这两种情况下与对称和不对称的溶剂。在所有情况下，由于溶剂中的非加和性对耗尽力的影响在混合状态下确定。从理论近似和模拟结果之间的比较表明，表面到表面的距离大于最小溶剂直径的良好协议。
A general class of nonadditive sticky-hard-sphere binary mixtures, where small and large spheres represent the solvent and the solute, respectively, is introduced. The solute-solute and solvent-solvent interactions are of hard-sphere type, while the solute-solvent interactions are of sticky-hard-sphere type with tunable degrees of size nonadditivity and stickiness. Two particular and complementary limits are studied using analytical and semi-analytical tools. The first case is characterized by zero nonadditivity, lending itself to a Percus-Yevick approximate solution from which the impact of s…
In this paper within a field-theoretical approach taking into account explicitly a co-solvent with a nonzero dipole and a polarizability tensor, we derive a modified Poisson-Boltzmann equation. Applying the modified Poisson-Boltzmann equation, we formulate a generalized Gouy-Chapman theory for the case when an electrolyte solution is mixed with a polar co-solvent having a large polarizability. We show that an increase of the co-solvent concentration as well as the co-solvent polarizability lead to a significant increase of differential capacitance at sufficiently high surface potentials of the…
In this paper, we study the electroosmotic transport in a nanofluidic channel by using a mean-field theory accounting for non-uniform size effect and solvent polarization effect. We witness that in the presence of the given zeta potential, an enhancement of ion size invariably lowers the electroosmotic velocity, thereby increasing the magnitude of electrostatic potential, irrespective of considering solvent polarization. It is also proved that solvent polarization allows both the magnitude of electrostatic potential and the electroosmotic velocities to decrease. In addition, we find that incre…
We study the electric double layer near a charged soft surface by using a mean-field approach including non-uniform size effect and solvent polarization. Based on a free energy model, electrostatic potential and number densities of water and ions are obtained numerically by solving coupled differential equations including the Poisson's equation. We find that the solvent polarization significantly affects electrostatic potential, ion number densities and permittivity in an electrolyte solution near a charged soft surface. We prove that the consideration of the solvent polarization increases the…
Using thermodynamics integration, we study the solvation free energy of 18 amino acid side chain equivalents in solvents with different polarity, ranging from the most polar water to the most non-polar cyclohexane. The amino acid side chain equivalents are obtained from the 20 natural amino acids by replacing the backbone part with a hydrogen atom, and discarding proline and glycine that have special properties. A detailed analysis of the relative solvation free energies suggests how it is possible to achieve a robust and unambiguous hydrophobic scale for the amino acids. By discriminating the…
We present a continuation of our theoretical research into the influence of co-solvent polarizability on a differential capacitance of the electric double layer [EPL 111, 28002 (2015)]. We formulate a modified Poisson-Boltzmann theory, using the formalism of density functional approach on the level of local density approximation taking into account the electrostatic interactions of ions and co-solvent molecules as well as their excluded volume. We derive the modified Poisson-Boltzmann equation, considering the three-component symmetric lattice gas model as a reference system and minimizing the…
Nanoscopic pores are used in various systems to attract nanoparticles. In general the behaviour is a result of two types of interactions: the material specific affinity and the solvent-mediated influence also called the depletion force. The latter is more universal but also much more complex to understand since it requires modeling both the nanoparticle and the solvent. Here, we employed classical density functional theory to determine the forces acting on a nanoparticle near a nanoscopic pore as a function of its hydrophobicity and its size. A simple capillary model is constructed to predict …
Entropic forces in colloidal suspensions and in polymer-colloid systems are of long-standing and continuing interest. Experiments show how entropic forces can be used to control the self-assembly of colloidal particles. Significant advances in colloidal synthesis made in the past two decades have enabled the preparation of high quality nano-particles with well-controlled sizes, shapes, and compositions, indicating that such particles can be utilized as "artificial atoms" to build new materials. To elucidate the effects of the shape of particles upon the magnitude of entropic interaction, we an…
We investigate dielectric saturation and increment in polar liquids under external fields. We couple a previously introduced dipolar solvent model to a uniform electric field and derive the electrostatic kernel of interacting dipoles. This procedure allows an unambiguous definition of the liquid dielectric permittivity embodying non-linear dielectric response and correlation effects.We find that the presence of the external field results in a dielectric anisotropy characterized by a two-component dielectric permittivity tensor. The increase of the electric field amplifies the permittivity comp…
Approximate additivity in the solvent-mediated potential of mean force for ultrasoft particle systems
The Hartree Centre, STFC Daresbury Laboratory（STFC达尔斯伯里实验室哈特里中心）；H. H. Wills Physics Laboratory, University of Bristol（布里斯托大学H.H.威尔斯物理实验室）；SUPA and School of Physics and Astronomy, The University of Edinburgh（爱丁堡大学SUPA及物理与天文学学院）
We calculate the effective force between two oppositely charged and similarly charged ions fixed in water as a function of separation distance R. At short separations, R less than 1 nm, the effective force is vastly different from the $1/ε_{s}R^2$ dependence advocated by the screened Coulomb force law (SCFL); $ε_{s}$ being the static dielectric constant of the medium. We also find an interesting asymmetry in the force between +ve and -ve ions. This breakdown of SCFL is shown to be due to the persistent interference between the polarizations created by the two charges, in a manner similar to th…
In this paper, we study electrostatic properties between two similar or oppositely charged surfaces immersed in an electrolyte solution by using mean-field approach accounting for solvent polarization and non-uniform size effect. Applying a free energy formalism accounting for unequal ion sizes and orientational ordering of water dipoles, we derive coupled and self-consistent equations to calculate electrostatic properties between charged surfaces. Electrostatic properties for similarly charged surfaces depend on counterion size but not coion size. Moreover, electrostatic potential and osmotic…
The possibility to induce demixing in a colloidal mixture by adding small polymers, or other equivalent depletant agents, is theoretically investigated. By use of Mean Field Theory, suitably generalized to deal with short range effective interactions, the phase diagram of a binary mixture ofcolloidal particles (modelled as hard spheres) in a solvent is determined as a function of the polymer concentration on the basis of the Asakura-Oosawa model.The topology of the phase diagram changes when the relative size of the colloidal particles is reduced: the critical line connecting the liquid-vapour…
Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of electrolyte can then be treated as a composite non-uniform dielectric body. Writing the electrostatic interactions as an integral over electric field energy density we show that the Poisson-Boltzmann functional in this formulation is convex and can be used to derive the equilibrium equations for electric potential and ion concentration by a variational procedure developed by Ericksen for dielectric continua (Arch. Ratio…
Interparticle Interactions in Nonlocal Media: Attraction and Repulsion from Charge-Polarization Coupling
University of Oxford（牛津大学）；Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford（牛津大学化学系物理与理论化学实验室）；The Kavli Institute for Nanoscience Discovery（卡弗里纳米科学发现研究所）
Understanding the atomic level interactions and the resulting structural characteristics is required for developing beta-cyclodextrin ($β$CD) derivatives for pharmaceutical and other applications. The effect of four different solvents on the structures of the native $β$CD and its hydrophilic (methylated $β$CD; ME$β$CD and hydroxypropyl $β$CD; HP$β$CD) and hydrophobic derivatives (ethylated $β$CD; ET$β$CD) were explored using molecular dynamics (MD) simulations and solvation free energy calculations. The native $β$CD, 2-ME$β$CD, 6-ME$β$CD, 2,6-DM$β$CD, 2,3,6-TM$β$CD, 6-HP$β$CD, 2,6-HP$β$CD and …
Many key industrial processes, from electricity production, conversion and storage to electrocatalysis or electrochemistry in general, rely on physical mechanisms occurring at the interface between a metallic electrode and an electrolyte solution, summarized by the concept of electric double layer, with the accumulation/depletion of electrons on the metal side and of ions on the liquid side. While electrostatic interactions play an essential role on the structure, thermodynamics, dynamics and reactivity of electrode-electrolyte interfaces, these properties also crucially depend on the nature o…
Light scattering and viscometric measurements on weak polyelectrolytes show two important aspects of counterion condensation, namely, non-monotonic variation in the polyelectrolyte size with the increase in the electrostatic strength, and, monovalent counterion selectivity in determining the nature of collapse transition at high electrostatic strengths. Here, we present a self-consistent variational theory for weak polyelectrolytes which includes the effects of the polarizability of monovalent counterions. Our theory reproduces several experimental findings including non-monotonic conformation…
We investigate the effective interactions between two nanoparticles (or colloids) immersed in a solvent exhibiting two-phase separation. Using a non-local density functional theory, we determine the dependence of the effective potential on the separation of the nanoparticles when the solvent is near bulk two-phase coexistence. If identical nanoparticles preferentially adsorbing phase $α$ are inserted into phase $β$, thick wetting layers of the preferable phase $α$ develop at their surfaces. At some particular separation $h_b$ of the nanoparticles, the wetting layers connect to form a single br…
