Definition
- 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.
