Binary mixtures exhibiting coexistence between two phases: solid-liquid, solid-gas, liquid-gas, or liquid-liquid.
Examples include suspensions or solutions of macromolecules (polymers), granular forms (solid-gas), foams (liquid-gas), and emulsions (liquid-liquid).
Mechanical Responses
Geometrical constraints due to phase coexistence result in distinctive mechanical responses to stress or strain.
Transitions between solid-like and fluid-like behavior occur, accompanied by fluctuations.
Mechanical properties attributed to high disorder, caging, and clustering on multiple-length scales.
Competing Processes in Complex Systems
Competing self-organization (ordering) and self-disorganization (disordering) processes.
Establishment of a hierarchical adaptive structure.
Complexity extends to amorphous materials with slow and non-exponential relaxation, observed in glass-forming liquids and glasses.
Quantification of Complexity
Complexity in liquid complexes is presently a qualitative characteristic, not quantifiable.
Experimental, theoretical studies, and computer simulations reveal macro- and mesoscopic details.
Details include a dramatic slowing-down of structure changes upon cooling, a wide spectrum of relaxation times, stretched-exponential relaxation kinetics, and dynamic heterogeneity on microscopic length scales.
Criteria for Complexity
Practical but qualitative criteria for complexity often rely on features like slowing down of structure changes, relaxation times, and power law correlations.
Causes of Materials Complexity
Presumed physical cause is the dynamic competition between particle aggregation into preferred structures and factors preventing crystallization.
Understanding the origins of complexity and structure dynamics is a crucial and challenging problem in condensed matter physics.
Variability in Liquids’ Complexity Upon Cooling
Not all liquids undergo complexity upon cooling.
Three-dimensional (3D) liquids with simple two-particle interactions crystallize aggressively upon cooling (e.g., molten metals, salts, liquefied noble gases).
Complexity in Classical 3D Liquids
Classical 3D complex liquids exhibit intricate and competing interactions.
Special supercooling regimes are required to avoid crystallization during supercooling.
Behavior of Two-Dimensional (2D) Liquids
2D liquids with simple interactions undergo a continuous or nearly continuous transition from a simple liquid state to a crystal.
At crossover temperatures, particles aggregate to form a dynamic mosaic of crystalline-ordered regions (crystallites) and less-ordered clusters.
Mosaic States in 2D Liquids
Crystallites at higher temperatures are small and separated islands of order within a disordered matrix.
Fraction occupied by crystallites increases at lower temperatures, leading to percolation of crystallinity.
Crystallites amalgamate into a multiconnected crystalline matrix with an anticipated algebraic decay of orientation order at even lower temperatures (hexatic liquid or long-range order).
Characteristic of Mosaic
Mosaic is observed at temperatures where the correlation length for orientations is finite, and the 2D liquid is in a normal (not hexatic) state.
