Real-Space Mapping of the Two-Dimensional Phase Diagrams in Attractive Colloidal Systems

Abstract

Phase diagrams reflect the possible kinetic routes and guide various applications such as the designed assembly and synthesis of functional materials. Two-dimensional (2D) materials have been a focus of ongoing research due to their wide applications; therefore, researchers are highly motivated to discover the general principles that control the assembly of such materials. In this study, we map the 2D phase diagrams of short-and long-range attractive colloids at single-particle resolution by video microscopy. Phase boundaries, including (meta)critical or triple points and corresponding real-space configurations, are precisely specified. Profiles of 2D phase diagrams with attractive interactions resemble their 3D counterparts. For short-range systems, by measuring the deepest achievable supercooled states on the phase diagram, a "crater" structure surrounding the metastable fluid-fluid critical point indicates an enhanced nucleation rate within the crater and further suggests a local minimum of the free-energy barrier for crystallization in this area. During a dense fluid-mediated two-step crystallization process, we observe that multiple crystallites could form within a single dense fluid cluster, partly due to its highly amorphous shape. This highly amorphous shape is found for all observed well-developed dense fluid clusters. It is a supplement to the multistep nucleation process. For long-range systems, equilibrium vapor-liquid coexistence is observed, which paves the way for the exploration of critical behaviors. Rigidity percolation of crystallites, and bulk fluid-solid coexistence which provide clear evidence of a possible first-order transition for 2D melting, are observed for both systems. Our experiments reveal the general features of phase behaviors shared by 2D attractive systems including graphene, protein membranes, and adsorbed nanocrystals.

The role of attraction in the phase diagrams and melting scenarios of generalized 2D Lennard-Jones systems

“…Analysis of the case m = 9 (LJ12-9), very close to that studied in Ref. 65 , demonstrated that for short-range attraction in complex solvents we should witness the third melting scenario.…”

“…The role of attraction can be tested experimentally in colloidal systems, known for a long time as model systems demonstrating a wide range of "molecularlike" phenomena 1,[47][48][49][50] , in particular, crystallization and melting [51][52][53][54][55][56][57][58][59] , solid-solid phase transitions [60][61][62] , condensation and critical phenomena [63][64][65] caused by relatively short-range attractive depletion forces 66 . These collective phenomena can be visualized in real-time with spatial resolution of individual particles.…”

Crystallisation in a two-dimensional granular system at constant temperature

“…Several authors have used this parameter to quantify the two-dimensional crystallisation process 45 – 47 . It also allows us to identify phase transitions—for instance, from a liquid to a crystalline lattice 48 , 49 .…”

A Bidimensional Gay-Berne Calamitic Fluid: Structure and Phase Behavior in Bulk and Strongly Confined Systems

“…Much research has been devoted to three-dimensional (3D) self-assembly [25], though a two-dimensional (2D) variant continues to be of interest from an exploratory perspective [47][48][49][50][51][52][53][54][55] as well as in applied technologies [1,56]. Optimal function is achieved via slab geometry in many devices, including optoelectronic/photonic materials [57][58][59][60][61], sensors [60,[62][63][64][65][66][67][68], display technologies [69][70][71], smart glass [72,73], spatial light modulators [74][75][76][77], and tunable filters [78][79][80][81].…”