Mayer f-function: Difference between revisions

Latest revision as of 18:50, 20 February 2015

The Mayer f-function, or f-bond is defined as (Ref. 1 Chapter 13 Eq. 13.2):

f_{12}=f({\mathbf {r} }_{12}):=\exp \left(-{\frac {\Phi _{12}(r)}{k_{B}T}}\right)-1

where

In other words, the Mayer function is the Boltzmann factor of the interaction potential, minus one.

Diagrammatically the Mayer f-function is written as

For the hard sphere model the Mayer f-function becomes:

f_{12}=\left\{{\begin{array}{lll}-1&;&r_{12}\leq \sigma ~~({\rm {overlap}})\\0&;&r_{12}>\sigma ~~({\rm {no~overlap}})\end{array}}\right.

where $\sigma$ is the hard sphere diameter.

@@ Line 1: / Line 1: @@
-The '''Mayer ''f''-function''', or ''f-bond'' is defined as:
+The '''Mayer ''f''-function''', or ''f-bond'' is defined as (Ref. 1 Chapter 13 Eq. 13.2):
-:<math>f_{12}=f({\mathbf r}_{12})= \exp\left(-\frac{\Phi_{12}(r)}{k_BT}\right) -1 </math>
+:<math>f_{12}=f({\mathbf r}_{12}) := \exp\left(-\frac{\Phi_{12}(r)}{k_BT}\right) -1 </math>
 where
@@ Line 7: / Line 7: @@
 * <math>T</math> is the [[temperature]].
 * <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]].
+In other words, the Mayer function is the [[Boltzmann factor]] of the interaction potential,
+minus one.
 [[Cluster diagrams | Diagrammatically]] the Mayer ''f''-function is written as