1549380323-Statistical Mechanics Theory and Molecular Simulation

610 Critical phenomena

P

T

Solid

Gas

Liquid

Critical

point

Triple

point

L

L

L

1

2

3

Fig. 16.1Representative phase diagram of a simple, one-component system.L 1 ,L 2 , andL 3
are the sublimation, melting, and boiling curves, respectively.

to-solid phase transition occurs. Such a transition is accompanied by a discontinuous
change in the density, although the change is not as dramatic as in the gas-to-liquid
case. Other macroscopic observables known asorder parameters(see Section 16.4)
change as well. In order to map out the specific values of pressure and temperature
at which the different phases exist, aphase diagramis used. A typical phase diagram
for a simple, one-component system is shown in Fig. 16.1. In the phase diagram, the
lines that separate different phases are calledcoexistence curves. Among these, there
is themelting curve(L 2 ) between the liquid and solid phases, thesublimation curve
(L 1 ) between the solid and gas phases, and theboiling curve(L 3 ) between the liquid
and gas phases. The point at which all three curves meet is called thetriple point.
In the above discussion, where a constant temperature is assumed, the specific
value of the temperature determines whether or not a gas-to-liquid phase transition
can occur. If the temperature is too high, then the system cannot exist as a liquid
at any pressure. The temperature at which a gas–liquid phase transition just starts is
called thecritical temperature, denotedTc. The existence of a critical temperature is
the reason that the boiling curve in Fig. 16.1 terminates at a definite point, whereas the
melting curve, in principle, does not. The point at which the boiling curve terminates
is called thecritical point.
Consider next isotherms of the equation of state for a simple fluid, which are
illustrated in Fig. 16.2. For temperatures aboveTc, no phase transition occurs, and the
isotherms are continuous. In the phase diagram, the region to theright of the critical
point is known as thesupercritical fluidregion where the system exhibits both gas-like
and liquid-like properties. For temperatures belowTc, one sees a discontinuous change
in the volume, signifying the transition from gas to liquid. When a phasetransition is
characterized by a discontinuous change in an associated thermodynamic observable,
the transition is referred to as afirst-order phase transition. In Fig. 16.2, there is one
point labeledCat which the phase transition is characterized by a continuous volume
change. This point, which is an inflection point along the isotherm, corresponds to the