Isothermal-isobaric ensemble: Difference between revisions
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The '''isothermal-isobaric ensemble''' has the following variables: | |||
* N | * <math>N</math> is the number of particles | ||
* p | * <math>p</math> is the [[pressure]] | ||
* T | * <math>T</math> is the [[temperature]] | ||
The [[ | The classical [[partition function]], for a one-component atomic system in 3-dimensional space, is given by | ||
:<math> Q_{NpT} = \frac{\beta p}{\Lambda^ | :<math> Q_{NpT} = \frac{\beta p}{\Lambda^{3N} N!} \int_{0}^{\infty} d V V^{N} \exp \left[ - \beta p V \right] \int d ( R^*)^{3N} \exp \left[ - \beta U \left(V,(R^*)^{3N} \right) \right] | ||
</math> | </math> | ||
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* <math> \left. V \right. </math> is the Volume: | * <math> \left. V \right. </math> is the Volume: | ||
*<math> \beta = \frac{1}{k_B T} </math> | *<math> \beta := \frac{1}{k_B T} </math>, where <math>k_B</math> is the [[Boltzmann constant]] | ||
*<math> \left. \Lambda \right. </math> is the [[de Broglie wavelength]] | *<math> \left. \Lambda \right. </math> is the [[de Broglie thermal wavelength]] | ||
*<math> \left( R^* \right)^{3N} </math> represent the reduced position coordinates of the particles; i.e. <math> \int d ( R^*)^{3N} = 1 </math> | *<math> \left( R^* \right)^{3N} </math> represent the reduced position coordinates of the particles; i.e. <math> \int d ( R^*)^{3N} = 1 </math> | ||
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== | == Related reading == | ||
*[http://molsim.chem.uva.nl/frenkel_smit Daan Frenkel and Berend Smit "Understanding Molecular Simulation: From Algorithms to Applications", Second Edition (2002)] ISBN 0-12-267351-4 | |||
[[category: statistical mechanics]] | |||
Latest revision as of 16:41, 3 September 2009
The isothermal-isobaric ensemble has the following variables:
- is the number of particles
- is the pressure
- is the temperature
The classical partition function, for a one-component atomic system in 3-dimensional space, is given by
![{\displaystyle Q_{NpT}={\frac {\beta p}{\Lambda ^{3N}N!}}\int _{0}^{\infty }dVV^{N}\exp \left[-\beta pV\right]\int d(R^{*})^{3N}\exp \left[-\beta U\left(V,(R^{*})^{3N}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6ad8e394e6715d3cd9bca8ad8adaa5bd35af68b4)
where
- is the Volume:
- , where is the Boltzmann constant
- represent the reduced position coordinates of the particles; i.e.
- is the potential energy, which is a function of the coordinates (or of the volume and the reduced coordinates)
