The Mayer f-function is an auxiliary function that often appears in the series expansion of
thermodynamic
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of ther ...
quantities related to classical
many-particle system
The many-body problem is a general name for a vast category of physical problems pertaining to the properties of microscopic systems made of many interacting particles. ''Microscopic'' here implies that quantum mechanics has to be used to provid ...
s.
[Donald Allan McQuarrie, ''Statistical Mechanics'' (]HarperCollins
HarperCollins Publishers LLC is one of the Big Five English-language publishing companies, alongside Penguin Random House, Simon & Schuster, Hachette, and Macmillan. The company is headquartered in New York City and is a subsidiary of News Cor ...
, 1976), page 228
It is named after chemist and physicist
Joseph Edward Mayer Joseph Edward Mayer (February 5, 1904, New York City – October 15, 1983) was a chemist who formulated the Mayer expansion in statistical field theory.
He was professor of chemistry at the University of California San Diego from 1960 to 1972, and ...
.
Definition
Consider a system of classical particles interacting through a pair-wise potential
:
where the bold labels
and
denote the continuous degrees of freedom associated with the particles, e.g.,
:
for spherically symmetric particles and
:
for rigid non-spherical particles where
denotes position and
the orientation parametrized e.g. by
Euler angles
The Euler angles are three angles introduced by Leonhard Euler to describe the Orientation (geometry), orientation of a rigid body with respect to a fixed coordinate system.Novi Commentarii academiae scientiarum Petropolitanae 20, 1776, pp. 189†...
. The Mayer f-function is then defined as
:
where
the inverse absolute
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
in units of (Temperature times the
Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
)
−1 .
See also
*
Virial coefficient
Virial coefficients B_i appear as coefficients in the virial expansion of the pressure of a many-particle system in powers of the density, providing systematic corrections to the ideal gas law. They are characteristic of the interaction potential ...
*
Cluster expansion
In statistical mechanics, the cluster expansion (also called the high temperature expansion or hopping expansion) is a power series expansion of the partition function of a statistical field theory around a model that is a union of non-interac ...
*
Excluded volume The concept of excluded volume was introduced by Werner Kuhn in 1934 and applied to polymer molecules shortly thereafter by Paul Flory. Excluded volume gives rise to depletion forces.
In liquid state theory
In liquid state theory, the 'excluded ...
Notes
{{reflist
Special functions