2.2.1 Critical Exponents and Order Parameters (continued)

Within this narrow range, various physical quantities exhibit the universal behavior described by critical exponents. A common observation is that a physical property χ(t), in the region of critical fluctuations, behaves as follows:

The critical exponent ε is defined as:

The system-specific order parameter o is particularly useful for describing critical systems. This variable plays an important role in the description of phase transitions: it measures the magnitude of the discontinuity at a critical phase transition, which is accompanied by the phenomenon of opalescence. In a liquid–liquid phase transition, the order parameter is the concentration difference between the coexisting phases, o = x_A − x_B.

In binary critical systems, the order parameter describes the difference between the two phases and vanishes at the apex of the binodal. The universality of the exponents offers a broad field for theoretical and experimental investigation: many different critical phenomena can be described by the same universal critical exponents. Sections 2.2.2 and 2.2.3 outline this idea.

2.2.2 Static Scaling Hypothesis

Thermodynamic functions near a critical point contain both a regular (classical) and a singular (critical) contribution. Classical thermodynamic functions can be described by molecular-field theories, such as the van der Waals equation of state. The critical contributions cannot be captured by classical equations of state and must therefore be treated separately.

Original footnote: Opalescence refers to the sudden clouding of an initially well-mixed substance at, or shortly before, the critical point.