Attractive interaction and bridging transition between neutral colloidal particles due to preferential adsorption in a near-critical binary mixture

Mechanism of polymer molecular weight-dependent suppression and promotion of liquid-liquid phase separation of a protein solution by the addition of polymer

Polyethylene glycol (PEG) is a widely used precipitant to concentrate proteins. The effect of PEG is generally understood to be an entropic attraction between proteins due to the depletion effect of PEG around proteins. However, measurements by Bloustine et al. [Phys. Rev. Lett. 96, 087803 (2006)] of the liquid-liquid phase separation (LLPS) temperature have shown that a lysozyme solution is stabilized and destabilized by the addition of low and high molecular-weight PEG, respectively. They also presented a theoretical model of the LLPS temperature as a virial expansion of the free energy and concluded that, in addition to the depletion effect, the attractive interaction between protein and PEG is necessary to explain the experiments. In the present study, theoretical calculations based on liquid-state density functional theory utilizing coarse-grained models are conducted to demonstrate that the protein-PEG effective attraction is responsible for the suppression and promotion of LLPS upon the addition of low- and high-weight PEG, respectively. In contrast, if the interactions between the protein and the PEG are solely due to the excluded volume effect, PEG of any molecular weight destabilizes the solution. These results suggest the necessity to reconsider the conventional understanding of the effects of polymer addition, which have been historically attributed to solely the depletion force.

Wetting behavior of a colloidal particle trapped at a composite liquid-vapor interface of a binary liquid mixture

A partially miscible binary liquid mixture, composed of A and B particles, is considered theoretically under conditions for which a stable A-rich liquid phase is in thermal equilibrium with the vapor phase. The B-rich liquid is metastable. The liquids and the thermodynamic conditions are chosen such that the interface between the A-rich liquid and the vapor contains an intervening wetting film of the B-rich phase. In order to obtain information about the large-scale fluid structure around a colloidal particle, which is trapped at such a composite liquid-vapor interface, three related and linked wetting phenomena at planar liquid-vapor, wall-liquid, and wall-vapor interfaces are studied analytically, using classical density functional theory in conjunction with the sharp-kink approximation for the number density profiles of the A and B particles. If in accordance with the so-called mixing rule the strength of the A-B interaction is given by the geometric mean of the strengths of the A-A and the B-B interactions, and similarly the ratio between the wall-A and the wall-B interaction, the scenario, in which the colloid is enclosed by a film of the B-rich liquid, can be excluded. Up to six distinct wetting scenarios are possible, if the above mixing rules for the fluid-wall and for the fluid-fluid interactions are relaxed. The way the space of system parameters is divided into domains corresponding to the six scenarios, and which of the domains actually appear, depends on the signs of the deviations from the mixing rule prescriptions. Relevant domains, corresponding, e.g., to the scenario in which the colloid is enclosed by a film of the B-rich liquid, emerge, if the ratio between the strengths of the wall-A and the wall-B interactions is reduced as compared to the mixing rule prescription, or if the strength of the A-B interaction is increased to values above the one from the mixing rule prescription. The range, within which the contact angle may vary inside the various domains, is also studied.

Concentration and size effects on the size-selective particle purification method using the critical Casimir force

Critical Casimir force (CCF) is a solvent fluctuation introduced interaction between particles dispersed in a binary solvent. Recently, it has been demonstrated that the CCF induced attraction between particles can trigger particle size-sensitive aggregation, and has thus been used as an efficient way to purify nanoparticles by size. Here, combining small angle neutron scattering and dynamic light scattering, we investigate the effects of size and concentration on this particle size separation method. Increasing the particle concentration does not significantly affect the purification method, but the solvent composition needs to be adjusted for an optimized efficiency. This purification method is further demonstrated to work also very efficiently for systems with particle size ranging from 15 nm to about 50 nm with a very large size polydispersity. These results indicate that for both short-ranged and long-ranged attraction relative to the particle diameter, the CCF introduced particle aggregation is always size sensitive. This implies that particle aggregation is strongly affected by size polydispersity for many colloidal systems. We further propose a method to use light scattering to help identify the temperature range within which this particle purification method can work efficiently instead of using neutron scattering.

Bridging transitions and capillary forces for colloids in a slit

Capillary bridges can form between colloids immersed in a two-phase fluid, e.g., in a binary liquid mixture, if the surface of the colloids prefers the species other than the one favored in the bulk liquid. Here, we study the formation of liquid bridges induced by confining colloids to a slit, with the slit walls having a preference opposite to the one of the colloid surface. Using mean field theory, we show that there is a line of first-order phase transitions between the bridge and the no-bridge states, which ends at a critical point. By decreasing the slit width, this critical point is shifted toward smaller separations between the colloids. However, at very small separations and far from criticality, we observe only a minor influence of the slit width on the location of the transition. Monte Carlo simulations of the Ising model, which mimics incompressible binary liquid mixtures, confirm the occurrence of the bridging transitions, as manifested by the appearance of "spinodal" regions where both bridge and no-bridge configurations are stable or metastable. Interestingly, we find that there is no such spinodal region in the case of small colloids, but we observe a sharpening of the transition when the colloid size increases. In addition, we demonstrate that the capillary force acting between the colloids can depend sensitively on the slit width and varies drastically with temperature, thus achieving strengths orders of magnitude higher than at criticality of the fluid.

Nanoparticle separation based on size-dependent aggregation of nanoparticles due to the critical Casimir effect

Nanoparticles typically have an inherent wide size distribution that may affect the performance and reliability of many nanomaterials. Because the synthesis and purification of nanoparticles with desirable sizes are crucial to the applications of nanoparticles in various fields including medicine, biology, health care, and energy, there is a great need to search for more efficient and generic methods for size-selective nanoparticle purification/separation. Here we propose and conclusively demonstrate the effectiveness of a size-selective particle purification/separation method based on the critical Casimir force. The critical Casimir force is a generic interaction between colloidal particles near the solvent critical point and has been extensively studied in the past several decades due to its importance in reversibly controlling the aggregation and stability of colloidal particles. Combining multiple experimental techniques, we found that the critical Casimir force-induced aggregation depends on relative particle sizes in a system with larger ones aggregating first and the smaller ones remaining in solution. Based on this observation, a new size-dependent nanoparticle purification/separation method is proposed and demonstrated to be very efficient in purifying commercial silica nanoparticles in the lutidine/water binary solvent. Due to the ubiquity of the critical Casimir force for many colloidal particles in binary solvents, this method might be applicable to many types of colloidal particles.

Nonadditive interactions and phase transitions in strongly confined colloidal systems

The behaviour of colloids can be controlled effectively by tuning the solvent-mediated interactions among them. An extensively studied example is the temperature-induced aggregation of suspended colloids close to the consolute point of their binary solvent. Here, using mean field theory and Monte Carlo simulations, we study the behaviour of colloids confined to a narrow slit containing a nearly-critical binary liquid mixture. We found that the effective interactions in this system are highly non-additive. In particular, the effective interactions among the colloids can be a few times stronger than the corresponding sum of the effective pair potentials. Inter alia, this non-additivity manifests itself in the phase behaviour of confined colloids, which depends sensitively on the slit width and temperature. In addition, we demonstrate the possibility of a first-order bridging transition between colloids confined to a slit and suspended in a phase-separated fluid well below the critical point of the solvent and at its critical composition in the bulk. This transition is accompanied by a remarkably large hysteresis loop, in which the force between the colloids varies by two orders of magnitude.

Colloidal suspensions in one-phase mixed solvents under shear flow

We numerically studied the behaviour of colloidal suspensions in one-phase binary liquid mixtures under shear flows. Far from the phase-separation point, the colloidal particles are well dispersed and the suspension exhibits a Newtonian viscosity. When the mixture is close to the coexistence curve, the colloidal particles aggregate by attractive interactions due to the concentration heterogeneity caused by surface wetting, and the viscosity of the suspension increases. Near the phase-separation point, the viscosity increases when the fraction of species favoured by the surface of a colloid particle is small. The mixture also exhibits shear thinning behaviour, since the aggregated structure is rearranged into small clusters due to the shear flow. Our simulations indicate that the concentration profile around each particle is not significantly disturbed by the shear flow at the onset of the structural rearrangements. The effective interaction is independent of the shear flow and remains isotropic.

Critical adsorption profiles around a sphere and a cylinder in a fluid at criticality: Local functional theory

We study universal critical adsorption on a solid sphere and a solid cylinder in a fluid at bulk criticality, where preferential adsorption occurs. We use a local functional theory proposed by Fisher et al. [M. E. Fisher and P. G. de Gennes, C. R. Acad. Sci. Paris Ser. B 287, 207 (1978); M. E. Fisher and H. Au-Yang, Physica A 101, 255 (1980)PHYADX0378-437110.1016/0378-4371(80)90112-0]. We calculate the mean order parameter profile ψ(r), where r is the distance from the sphere center and the cylinder axis, respectively. The resultant differential equation for ψ(r) is solved exactly around a sphere and numerically around a cylinder. A strong adsorption regime is realized except for very small surface field h_{1}, where the surface order parameter ψ(a) is determined by h_{1} and is independent of the radius a. If r considerably exceeds a, ψ(r) decays as r^{-(1+η)} for a sphere and r^{-(1+η)/2} for a cylinder in three dimensions, where η is the critical exponent in the order parameter correlation at bulk criticality.

Phoretic motion of colloids in a phase separating medium

The enhanced motion of dispersed particles driven by a concentration gradient is the basis for diffusiophoresis. Here we present the dynamics of colloids in a phase separating medium probed by X-Ray Photon Correlation Spectroscopy (XPCS) in the ultra-small angle scattering range. Charge stabilized silica colloids suspended in a binary mixture of 3-methylpyridine and water/heavy water are preferentially wetted by 3-methylpyridine and consequently display a phoretic motion towards that phase upon demixing. This activity lasts for hundreds of seconds before the phase separation is complete and the enhanced motion is arrested as the colloids return to normal diffusive dynamics.

Ionization at a solid-water interface in an applied electric field: Charge regulation

We investigate ionization at a solid-water interface in an applied electric field. We attach an electrode to a dielectric film bearing silanol or carboxyl groups with an areal density Γ₀, where the degree of dissociation α is determined by the proton density in water close to the film. We show how α depends on the density n₀ of NaOH in water and the surface charge density σ_m on the electrode. For σ_m > 0, the protons are expelled away from the film, leading to an increase in α. In particular, in the range 0 < σ_m < eΓ₀, self-regulation occurs to realize α ≅ σ_m/eΓ₀ for n₀ ≪ n_c, where n_c is 0.01 mol/L for silica surfaces and is 2 × 10^-5 mol/L for carboxyl-bearing surfaces. We also examine the charge regulation with decreasing the cell thickness H below the Debye length κ^-1, where a crossover occurs at the Gouy-Chapman length. In particular, when σ_m ∼ eΓ₀ and H ≪ κ^-1, the surface charges remain only partially screened by ions, leading to a nonvanishing electric field in the interior.

Critical adsorption and critical Casimir forces in the canonical ensemble

Critical properties of a liquid film between two planar walls are investigated in the canonical ensemble, within which the total number of fluid particles, rather than their chemical potential, is kept constant. The effect of this constraint is analyzed within mean-field theory (MFT) based on a Ginzburg-Landau free-energy functional as well as via Monte Carlo simulations of the three-dimensional Ising model with fixed total magnetization. Within MFT and for finite adsorption strengths at the walls, the thermodynamic properties of the film in the canonical ensemble can be mapped exactly onto a grand canonical ensemble in which the corresponding chemical potential plays the role of the Lagrange multiplier associated with the constraint. However, due to a nonintegrable divergence of the mean-field order parameter profile near a wall, the limit of infinitely strong adsorption turns out to be not well-defined within MFT, because it would necessarily violate the constraint. The critical Casimir force (CCF) acting on the two planar walls of the film is generally found to behave differently in the canonical and grand canonical ensembles. For instance, the canonical CCF in the presence of equal preferential adsorption at the two walls is found to have the opposite sign and a slower decay behavior as a function of the film thickness compared to its grand canonical counterpart. We derive the stress tensor in the canonical ensemble and find that it has the same expression as in the grand canonical case, but with the chemical potential playing the role of the Lagrange multiplier associated with the constraint. The different behavior of the CCF in the two ensembles is rationalized within MFT by showing that, for a prescribed value of the thermodynamic control parameter of the film, i.e., density or chemical potential, the film pressures are identical in the two ensembles, while the corresponding bulk pressures are not.

Density functional theory of gas-liquid phase separation in dilute binary mixtures

We examine statics and dynamics of phase-separated states of dilute binary mixtures using density functional theory. In our systems, the difference of the solvation chemical potential between liquid and gas [Formula: see text] (the Gibbs energy of transfer) is considerably larger than the thermal energy [Formula: see text] for each solute particle and the attractive interaction among the solute particles is weaker than that among the solvent particles. In these conditions, the saturated vapor pressure increases by [Formula: see text], where [Formula: see text] is the solute density added in liquid. For [Formula: see text], phase separation is induced at low solute densities in liquid and the new phase remains in gaseous states, even when the liquid pressure is outside the coexistence curve of the solvent. This explains the widely observed formation of stable nanobubbles in ambient water with a dissolved gas. We calculate the density and stress profiles across planar and spherical interfaces, where the surface tension decreases with increasing interfacial solute adsorption. We realize stable solute-rich bubbles with radius about 30 nm, which minimize the free energy functional. We then study dynamics around such a bubble after a decompression of the surrounding liquid, where the bubble undergoes a damped oscillation. In addition, we present some exact and approximate expressions for the surface tension and the interfacial stress tensor.

Critical Casimir forces for colloidal assembly

Critical Casimir forces attract increasing interest due to their opportunities for reversible particle assembly in soft matter and nano science. These forces provide a thermodynamic analogue of the celebrated quantum mechanical Casimir force that arises from the confinement of vacuum fluctuations of the electromagnetic field. In its thermodynamic analogue, solvent fluctuations, confined between suspended particles, give rise to an attractive or repulsive force between the particles. Due to its unique temperature dependence, this effect allows in situ control of reversible assembly. Both the force magnitude and range vary with the solvent correlation length in a universal manner, adjusting with temperature from fractions of the thermal energy, k B T, and nanometre range to several ten kT and micrometer length scale. Combined with recent breakthroughs in the synthesis of complex particles, critical Casimir forces promise the design and assembly of complex colloidal structures, for fundamental studies of equilibrium and out-of-equilibrium phase behaviour. This review highlights recent developments in this evolving field, with special emphasis on the dynamic interaction control to assemble colloidal structures, in and out of equilibrium.

Hydrodynamics in bridging and aggregation of two colloidal particles in a near-critical binary mixture

We investigate bridging and aggregation of two colloidal particles in a near-critical binary mixture when the fluid far from the particles is outside the coexistence (CX) curve and is rich in the component disfavored by the colloid surfaces. In such situations, the adsorption-induced interaction is enhanced, leading to bridging and aggregation of the particles. We realize bridging firstly by changing the temperature with a fixed interparticle separation and secondly by letting the two particles aggregate. The interparticle attractive force dramatically increases upon bridging. The dynamics is governed by hydrodynamic flow around the colloid surfaces. In aggregation, the adsorption layers move with the particles and squeezing occurs at narrow separation. These results suggest relevance of bridging in the reversible colloid aggregation observed so far. We use the local functional theory [J. Chem. Phys., 2012, 136, 114704] to take into account the renormalization effect and the simulation method [Phys. Rev. Lett., 2000, 85, 1338] to calculate the hydrodynamic flow around the colloidal particles.

Orientational order of one-patch colloidal particles in two dimensions

We studied the orientational order of one-patch colloidal particles (Janus particles) in a close-packed monolayer. In an experiment on hemispherically patched particles, we realized a highly ordered zigzag stripe pattern by inducing directional growth of the pattern via a phase transition of the solvent. Upon spontaneous ordering by strengthening the inter-patch attraction, however, the particles are trapped in a poorly ordered zigzag pattern, illustrating the importance of controlling kinetics to attain a highly ordered state. The patch-size dependence of an equilibrium orientational order is experimentally observed under moderate inter-patch attraction. We also calculated the equilibrium order against the patch size and attraction in a Monte Carlo simulation. In the simulation, the rather discrete transition between a zigzag stripe, tiling of triangular trimers and tiling of dimers under strong attraction becomes continuous with weakening attraction. The experimental result not only coincides with the simulation qualitatively but also suggests that a particular cluster is selectively formed by nonuniform inter-patch attraction in the experiment. The effect of patch-substrate attraction and commonalities of the order with liquid crystals are also discussed.

Critical Casimir interactions around the consolute point of a binary solvent

Spatial confinement of a near-critical medium changes its fluctuation spectrum and modifies the corresponding order parameter distribution, resulting in effective, so-called critical Casimir forces (CCFs) acting on the confining surfaces. These forces are attractive for like boundary conditions of the order parameter at the opposing surfaces of the confinement. For colloidal particles dissolved in a binary liquid mixture acting as a solvent close to its critical point of demixing, one thus expects the emergence of phase segregation into equilibrium colloidal liquid and gas phases. We analyze how such phenomena occur asymmetrically in the whole thermodynamic neighborhood of the consolute point of the binary solvent. By applying field-theoretical methods within mean-field approximation and the semi-empirical de Gennes-Fisher functional, we study the CCFs acting between planar parallel walls as well as between two spherical colloids and their dependence on temperature and on the composition of the near-critical binary mixture. We find that for compositions slightly poor in the molecules preferentially adsorbed at the surfaces, the CCFs are significantly stronger than at the critical composition, thus leading to pronounced colloidal segregation. The segregation phase diagram of the colloid solution following from the calculated effective pair potential between the colloids agrees surprisingly well with experiments and simulations.