Triple Junction at the Triple Point Resolved on the Individual Particle Level

Abstract

At the triple point of a repulsive screened Coulomb system, a face-centered-cubic (fcc) crystal, a bodycentered-cubic (bcc) crystal and a fluid phase coexist. At their intersection, these three phases form a liquid groove, the triple junction. Using confocal microscopy, we resolve the triple junction on a single particle level in a model system of charged PMMA colloids in a nonpolar solvent. The groove is found to be extremely deep and the incommensurate solid-solid interface to be very broad. Thermal fluctuations hence appear to dominate the solid-solid interface. This indicates a very low interfacial energy. The fcc-bcc interfacial energy is quantitatively determined based on Young's equation and, indeed, it is only about 1.3 times higher than the fcc-fluid interfacial energy close to the triple point. PACS numbers:According to the traditional Gibbs phase rule of thermodynamics [1], in a one-component system up to three phases can coexist. Their coexistence is represented by a triple point in the temperature-pressure phase diagram and a triple line in the temperature-density phase diagram. At triple conditions, the three phases are in mutual mechanical, thermal and chemical equilibrium. The three possible interfaces only occur at the same time if the interfacial energies are similar; if an interfacial energy is larger than the sum of the other two, this interface is unstable and the third phase intervenes. When the three interfaces intersect, they form an interfacial line, the triple junction line (which is a point in the slice shown in Fig. 1). Triple junctions have been studied on the macroscopic level, for example in metals where liquid lenses form on top of a crystallite surrounded by coexisting vapor [2,3]. Another classical example is the triple point of water where vapor, liquid water and ice coexist. Such a gas-liquid-solid triple point involves two disordered and one ordered phase and can exist in systems governed by sufficiently long-ranged attractive interparticle interactions [4][5][6]. In contrast, the coexistence of a fluid and two different solids involves two ordered structures and hence an interface between two crystallites that are not commensurate. The corresponding phase behavior has been studied in suspensions of charged colloids [7][8][9][10][11][12][13][14][15][16] Using charged colloids [24,25], we investigate the triple junction at the triple point on an individual-particle level, i.e. including the smallest relevant length scale. At the triple point, we find a deep and tight fluid groove between the two solid phases and a very broad solid-solid interface. This indicates a small solid-solid interfacial energy and hence a considerable effect of thermal fluctuations. Indeed, a quantitative determination of the interfacial energy using Young's equation confirms this suggestion. The interactions of highly charged colloids in the presence of small ions can be described by a purely repulsive screened Coulomb (or Yukawa) effective pair interaction U(r) = (Q 2 4π 0 r) exp(−r λ) with the partic...

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