Bridging length scales in colloidal liquids and interfaces from near-critical divergence to single particles

Abstract

Boiling and condensation are among the best recognized phase transitions of condensed matter. Approaching the critical point, a liquid becomes indistinguishable from its vapour, the interfacial thickness diverges and the system is dominated by long-wavelength density fluctuations 1 . Long wavelength usually means hundreds of particle diameters, but here we consider the limits of this assumption, using a mesoscopic analogue of simple liquids, a colloid-polymer mixture 2,3 . We simultaneously visualize both the colloidal particles and near-critical density fluctuations, and reveal particle-level images of the critical clusters and liquid-gas interface. Surprisingly, we find that critical scaling does not break down until the correlation length approaches the size of the constituent particles, where there is a smooth transition to non-critical classical behaviour. Our results could provide a framework for unifying the disparate particle and correlation length scales, and bring new insight into the nature of the liquid-gas interface and the limit of the critical regime.Among the simplest pictures of two different phases is that of a magnet, whose sites can only point up or down, and do so depending solely on their neighbours. This Ising model in fact describes a general class of phase transitions 1 , from the original ferromagnetic transition in magnets to phase separation in alloys, binary liquids, emulsions and polymers, and the liquidgas transition in simple liquids and colloid-polymer mixtures. Although we shall consider the latter two cases, this work has implications for many systems that belong to the same universality class. Close to the critical point, many physical properties such as the bulk correlation length, ξ B , are described by simple scaling, such as ξ B = ξ 0 B ε −ν , where ξ 0 B is the bare correlation length (or critical amplitude) and ε = (T − T C )/T C is a reduced temperature where T is the temperature and T C is the critical temperature. The critical exponent ν = 0.5 according to mean-field theory, and very close to the critical point there is a crossover to ν = 0.63, 'three-dimensional (3D) Ising universality' 4 . We shall refer to the entire scaling regime, both mean field and 3D Ising as the critical region. Although criticality is well understood, the point at which it breaks down has so far received relatively little attention. Conventional theory of critical phenomena assumes a large separation in length scales, that is, that the correlation length is decoupled from other length scales. This length-scale separation lies at the heart of critical universality, implying that the microscopic details are irrelevant. Whereas length-scale coupling has been considered in complex fluids with much longer length scales, such as polymer 5 and ionic 6 solutions, we consider here a more general limit: the case that the correlation length approaches that of the constituent particles. Although it is difficult to approach this limit experimentally in molecular systems, a colloidpolymer mixture provides...

Enhanced wavelength-dependent surface tension of liquid-vapour interfaces

“…At elevated T , measurements of γ(q; T ) using GISAXS are challenging due to the significant vapour density. However, -v-like interfaces in suitable colloidal suspensions can be studied well [48] even close to criticality [49], which allows one to analyse γ(q; T ) along the lines presented here.…”

Identification of structure in condensed matter with the topological cluster classification

“…[29][30][31] This development means that the structure of experimental systems that display Brownian motion can now be analysed with higher-order structural detection algorithms, with interest in, for example, colloidal gels, 32 glasses, 29 and critical fluctuations. 33 Here we describe a recent addition to the collection of high-order structural detection algorithms, the topological cluster classification (TCC) algorithm. This algorithm has been used to investigate higher-order structure in colloidal 32,34 and molecular 35 gels, colloid-polymer mixtures, 36 colloidal clusters, [37][38][39] simple liquids, 60 liquidvapor interfaces, 40 supercooled liquids, [41][42][43] and crystallising fluids.…”

From Attraction to Repulsion to Attraction: Non-monotonic Temperature Dependence of Polymer-Mediated Interactions in Colloidal Dispersions

“…The length scale of forces generated by polymer addition can be varied by the degree of polymerization, the concentration, and the polymer structure. 18 In a recent publication, Feng et al 23 reported interesting reentrant flocculation behavior of colloidal particles in an aqueous dispersion containing polymers. Several different polymer and particle combinations were investigated, but the ones displaying the re-entrant behavior had one common property: a solvent (water) that becomes poorer (for the polymer) as the temperature was increased.…”

“…Colloidal dispersions have been the subject of many studies, with focus ranging from stability and drug delivery, to self-assembly, patch formation, and so on. − The stability of such dispersions can often be controlled by pH and temperature variation, or with additives, such as salt or polymers. − One advantage in a system where polymers are used is their ability to mediate attractive, as well as repulsive, interactions between the particles, depending on parameters such as polymer length, solvent quality, or the presence of grafting bonds to the particles. This may facilitate a controlled stability. − Crystallization of colloidal particles has also been investigated in many soft matter studies, and the coexistence between “gas” and ”liquid” phases can often be regulated by polymer properties. , Previous work , has established thermoresponsive aggregation, or cluster formation, in aqueous dispersions containing polystyrene (PS) particles, carrying a layer of grafted short polyethylene glycol (PEG) chains. A temperature increase from an ambient value, at which the dispersion remained sterically stabilized, caused a reduced solubility of the polymer grafts, which eventually resulted in gelation, aggregation, or cluster formation.…”

“…Adsorbing polymers can also mediate attractive interactions, but in these cases, the underlying mechanism is instead attractive polymer bridges connecting the particles. The length scale of forces generated by polymer addition can be varied by the degree of polymerization, the concentration, and the polymer structure …”