Mayer f-function - Revision history

Carl McBride: Defined as

2015-02-20T17:50:59Z

Defined as

← Older revision		Revision as of 19:50, 20 February 2015
Line 1:		Line 1:
	The '''Mayer ''f''-function''', or ''f-bond'' is defined as (Ref. 1 Chapter 13 Eq. 13.2):		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		where

Dduque: link to Boltzmann factor

2008-02-22T11:42:32Z

link to Boltzmann factor

← Older revision		Revision as of 13:42, 22 February 2008
Line 7:		Line 7:
	* <math>T</math> is the [[temperature]].		* <math>T</math> is the [[temperature]].
	* <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]].		* <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		[[Cluster diagrams \| Diagrammatically]] the Mayer ''f''-function is written as

Carl McBride at 12:50, 31 July 2007

2007-07-31T12:50:04Z

← Older revision		Revision as of 14:50, 31 July 2007
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>

Carl McBride: /* References */

2007-07-31T12:49:30Z

References

← Older revision		Revision as of 14:49, 31 July 2007
Line 23:		Line 23:
	where <math>\sigma</math> is the hard sphere diameter.		where <math>\sigma</math> is the hard sphere diameter.
	==References==		==References==
			# Joseph Edward Mayer and Maria Goeppert Mayer "Statistical Mechanics" John Wiley and Sons (1940)
	#[http://dx.doi.org/10.1063/1.1723631 Joseph E. Mayer "Contribution to Statistical Mechanics", Journal of Chemical Physics '''10''' pp. 629-643 (1942)]		#[http://dx.doi.org/10.1063/1.1723631 Joseph E. Mayer "Contribution to Statistical Mechanics", Journal of Chemical Physics '''10''' pp. 629-643 (1942)]

	[[Category: Statistical mechanics]]		[[Category: Statistical mechanics]]
	[[Category: Integral equations]]		[[Category: Integral equations]]

Carl McBride at 10:45, 13 July 2007

2007-07-13T10:45:14Z

← Older revision		Revision as of 12:45, 13 July 2007
Line 8:		Line 8:
	* <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]].		* <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]].

	Diagrammatically the Mayer ''f''-function is written as		[[Cluster diagrams \| Diagrammatically]] the Mayer ''f''-function is written as

	:[[Image:Mayer_f_function.png]]		:[[Image:Mayer_f_function.png]]

Carl McBride at 10:29, 13 July 2007

2007-07-13T10:29:13Z

← Older revision		Revision as of 12:29, 13 July 2007
Line 1:		Line 1:
	The '''Mayer ''f''-function''', or ''f-bond'' is defined as:		The '''Mayer ''f''-function''', or ''f-bond'' is defined as:

	:<math>f_{12}=f(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		where
Line 11:		Line 11:

	:[[Image:Mayer_f_function.png]]		:[[Image:Mayer_f_function.png]]

			==Hard sphere model==
			For the [[hard sphere model]] the Mayer ''f''-function becomes:

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

			where <math>\sigma</math> is the hard sphere diameter.
	==References==		==References==
	#[http://dx.doi.org/10.1063/1.1723631 Joseph E. Mayer "Contribution to Statistical Mechanics", Journal of Chemical Physics '''10''' pp. 629-643 (1942)]		#[http://dx.doi.org/10.1063/1.1723631 Joseph E. Mayer "Contribution to Statistical Mechanics", Journal of Chemical Physics '''10''' pp. 629-643 (1942)]
	[[Category: Statistical mechanics]]		[[Category: Statistical mechanics]]
	[[Category: Integral equations]]		[[Category: Integral equations]]

Carl McBride at 13:29, 25 June 2007

2007-06-25T13:29:24Z

← Older revision		Revision as of 15:29, 25 June 2007
Line 10:		Line 10:
	Diagrammatically the Mayer ''f''-function is written as		Diagrammatically the Mayer ''f''-function is written as

	[[Image:Mayer_f_function.png]]		:[[Image:Mayer_f_function.png]]
	==References==		==References==
	#[http://dx.doi.org/10.1063/1.1723631 Joseph E. Mayer "Contribution to Statistical Mechanics", Journal of Chemical Physics '''10''' pp. 629-643 (1942)]		#[http://dx.doi.org/10.1063/1.1723631 Joseph E. Mayer "Contribution to Statistical Mechanics", Journal of Chemical Physics '''10''' pp. 629-643 (1942)]
	[[Category: Statistical mechanics]]		[[Category: Statistical mechanics]]
	[[Category: Integral equations]]		[[Category: Integral equations]]

Carl McBride at 13:27, 25 June 2007

2007-06-25T13:27:27Z

← Older revision		Revision as of 15:27, 25 June 2007
Line 1:		Line 1:
	~~Definition~~:		The '''Mayer ''f''-function''', or ''f-bond'' is defined as:

	:<math>f_{ij}=f(r_{ij})= \exp\left(-\frac{u(r)}{k_BT}\right) -1 </math>		:<math>f_{12}=f(r_{12})= \exp\left(-\frac{\Phi_{12}(r)}{k_BT}\right) -1 </math>

	where		where
	* <math>k_B</math> is the [[Boltzmann constant]]		* <math>k_B</math> is the [[Boltzmann constant]].
	* <math>T</math> is the temperature		* <math>T</math> is the [[temperature]].
	* <math>u(r)</math> is the potential		* <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]].

			Diagrammatically the Mayer ''f''-function is written as

			[[Image:Mayer_f_function.png]]
	==References==		==References==
			#[http://dx.doi.org/10.1063/1.1723631 Joseph E. Mayer "Contribution to Statistical Mechanics", Journal of Chemical Physics '''10''' pp. 629-643 (1942)]
	[[Category: Statistical mechanics]]		[[Category: Statistical mechanics]]
	[[Category: Integral equations]]		[[Category: Integral equations]]

Carl McBride at 14:02, 25 May 2007

2007-05-25T14:02:07Z

← Older revision		Revision as of 16:02, 25 May 2007
Line 1:		Line 1:
	Definition:		Definition:

	<math>f_{ij}=f(r_{ij})= \exp\left(-\frac{u(r)}{k_BT}\right) -1 </math>		:<math>f_{ij}=f(r_{ij})= \exp\left(-\frac{u(r)}{k_BT}\right) -1 </math>

	where		where

Carl McBride: New page: Definition: $f_{ij}=f(r_{ij})= \exp\left(-\frac{u(r)}{k_BT}\right) -1$ where * $k_B$ is the Boltzmann constant * $T$ is the temperature * $u(r...$

2007-02-27T13:50:46Z

New page: Definition: <math>f_{ij}=f(r_{ij})= \exp\left(-\frac{u(r)}{k_BT}\right) -1 </math> where * <math>k_B</math> is the Boltzmann constant * <math>T</math> is the temperature * <math>u(r...

New page

Definition:

<math>f_{ij}=f(r_{ij})= \exp\left(-\frac{u(r)}{k_BT}\right) -1 </math>

where
* <math>k_B</math> is the [[Boltzmann constant]]
* <math>T</math> is the temperature
* <math>u(r)</math> is the potential

==References==
[[Category: Statistical mechanics]]
[[Category: Integral equations]]