Critical point (thermodynamics)

In the study of thermodynamics, a critical point is a specific state where the distinction between two phases of matter disappears.

Most substances exist in clearly defined phases, such as solids, liquids, or vapors. These phases are usually separated by phase boundaries, which are specific combinations of pressure and temperature where two phases can coexist. The critical point marks the end of such a boundary. It is the exact endpoint of a phase equilibrium curve. When a substance reaches this point, the physical properties of the liquid and the vapor become so similar that the boundary between them vanishes. This phenomenon is essential for understanding how matter behaves under extreme conditions.

To understand the mechanism, one must examine the relationship between temperature and pressure. A substance reaches its liquid–vapor critical point at a specific critical temperature, denoted as Tc, and a critical pressure, denoted as pc.

As a substance approaches these values, its physical properties change dramatically. For example, liquid water is normally nearly incompressible and has a low thermal expansion coefficient. However, near the critical point, water becomes highly compressible and expands easily. It also becomes a poor dielectric and a bad solvent for electrolytes. At the exact critical point, the heat of vaporization—the energy required to turn a liquid into a gas—becomes zero. Beyond this point, the substance enters a state called a supercritical fluid. This fluid is continuously connected to both the liquid and gaseous states.

There are different types of critical points depending on the system being studied. The liquid–vapor critical point is the most famous and well-studied version. However, critical points also occur in mixtures of liquids, known as liquid–liquid critical points.

These occur at a critical solution temperature, which is the limit of a two-phase region. There are two distinct types of these liquid-liquid transitions. The first is the upper critical solution temperature, or UCST. This is the hottest temperature at which cooling a mixture will cause it to separate into two distinct liquid phases. The second is the lower critical solution temperature, or LCST. This is the coldest temperature at which heating a mixture will induce phase separation.

Other systems exhibit different kinds of critical transitions as well. One example is the ferromagnet–paramagnet transition, which occurs at the Curie temperature. This happens in the absence of an external magnetic field. In some cases, the critical point might not be obvious through mechanical properties. Instead, it may be "hidden" and only reveal itself through changes in the local properties of droplets or a sudden increase in defect pair concentration. Scientists also study the Fisher–Widom line, which identifies a boundary separating states with different statistical properties even above the critical temperature.

History shows that discovering these points required careful experimentation. Charles Cagniard de la Tour first discovered the critical point in 1822 while working with carbon dioxide.

He observed that he could liquefy CO2 at 31 °C if the pressure was 73 atm. However, if the temperature was slightly higher, he could not liquefy it, even by increasing the pressure to 3000 atm. In 1860, Dmitri Mendeleev named the phenomenon. He referred to it as the "absolute temperature of boiling." Mendeleev defined this as the point where the cohesion of the liquid reaches zero and the latent heat of vaporization also reaches zero. In 1869, Thomas Andrews also contributed significantly to the study of these phase boundaries.

Every substance has its own unique set of critical values.

For water, the critical temperature is 374 °C and the critical pressure is 218 atm. Other elements and compounds have vastly different requirements. For instance, carbon dioxide has a much lower critical temperature than water. Scientists use the van der Waals equation to attempt to calculate these points mathematically. However, this equation is based on mean-field theory and often fails to predict the correct scaling laws near the critical point. To help with accuracy, researchers sometimes use the principle of corresponding states. This principle suggests that substances at equal reduced pressures and temperatures will have equal reduced volumes.

Understanding critical points connects thermodynamics to many broader scientific fields. The study of these points is a central part of understanding critical phenomena and phase transitions. It also relates to complex topics like conformal field theory and renormalization group theory. By studying how substances behave near these limits, scientists gain deeper insights into the fundamental nature of matter. Whether looking at the behavior of simple gases or complex polymer solutions, the critical point reveals how the very structure of matter can change.