FJC model thermodynamics (modified canonical)
- class FJC(number_of_links, link_length, hinge_mass)
The freely-jointed chain (FJC) model thermodynamics in the modified canonical ensemble.
- number_of_links
The number of links in the chain.
- link_length
The length of each link in the chain in units of nm.
- hinge_mass
The mass of each hinge in the chain in units of kg/mol.
- asymptotic
The thermodynamic functions of the model in the isotensional ensemble approximated using an asymptotic approach.
- end_to_end_length(potential_distance, potential_stiffness, temperature)
The expected end-to-end length as a function of the applied potential distance, potential stiffness, and temperature.
- Parameters:
potential_distance (numpy.ndarray) – The potential distance.
potential_stiffness (float) – The potential stiffness.
temperature (float) – The temperature \(T\).
- Returns:
The end-to-end length \(\xi\).
- Return type:
numpy.ndarray
- end_to_end_length_per_link(potential_distance, potential_stiffness, temperature)
The expected end-to-end length per link as a function of the applied potential distance, potential stiffness, and temperature.
- Parameters:
potential_distance (numpy.ndarray) – The potential distance.
potential_stiffness (float) – The potential stiffness.
temperature (float) – The temperature \(T\).
- Returns:
The end-to-end length per link \(\xi/N_b=\ell_b\gamma\).
- Return type:
numpy.ndarray
- nondimensional_end_to_end_length(nondimensional_potential_distance, nondimensional_potential_stiffness)
The expected nondimensional end-to-end length as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
- Parameters:
nondimensional_potential_distance (numpy.ndarray) – The nondimensional potential distance.
nondimensional_potential_stiffness (float) – The nondimensional potential stiffness.
- Returns:
The nondimensional end-to-end length \(N_b\gamma=\xi/\ell_b\).
- Return type:
numpy.ndarray
- nondimensional_end_to_end_length_per_link(nondimensional_potential_distance, nondimensional_potential_stiffness)
The expected nondimensional end-to-end length per link as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
- Parameters:
nondimensional_potential_distance (numpy.ndarray) – The nondimensional potential distance.
nondimensional_potential_stiffness (float) – The nondimensional potential stiffness.
- Returns:
The nondimensional end-to-end length \(\gamma\equiv\xi/N_b\ell_b\).
- Return type:
numpy.ndarray
- force(potential_distance, potential_stiffness, temperature)
The expected force as a function of the applied potential distance, potential stiffness, and temperature.
- Parameters:
potential_distance (numpy.ndarray) – The potential distance.
potential_stiffness (float) – The potential stiffness.
temperature (float) – The temperature \(T\).
- Returns:
The force \(f\).
- Return type:
numpy.ndarray
- nondimensional_force(nondimensional_potential_distance, nondimensional_potential_stiffness)
The expected nondimensional force as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
- Parameters:
nondimensional_potential_distance (numpy.ndarray) – The nondimensional potential distance.
nondimensional_potential_stiffness (float) – The nondimensional potential stiffness.
- Returns:
The nondimensional force \(\eta\equiv\beta f\ell_b\).
- Return type:
numpy.ndarray
- helmholtz_free_energy(potential_distance, potential_stiffness, temperature)
The Helmholtz free energy as a function of the applied potential distance, potential stiffness, and temperature.
- Parameters:
potential_distance (numpy.ndarray) – The potential distance.
potential_stiffness (float) – The potential stiffness.
temperature (float) – The temperature \(T\).
- Returns:
The Helmholtz free energy \(\psi\).
- Return type:
numpy.ndarray
- helmholtz_free_energy_per_link(potential_distance, potential_stiffness, temperature)
The Helmholtz free energy per link as a function of the applied potential distance, potential stiffness, and temperature.
- Parameters:
potential_distance (numpy.ndarray) – The potential distance.
potential_stiffness (float) – The potential stiffness.
temperature (float) – The temperature \(T\).
- Returns:
The Helmholtz free energy per link \(\psi/N_b\).
- Return type:
numpy.ndarray
- relative_helmholtz_free_energy(potential_distance, potential_stiffness, temperature)
The relative Helmholtz free energy as a function of the applied potential distance, potential stiffness, and temperature.
- Parameters:
potential_distance (numpy.ndarray) – The potential distance.
potential_stiffness (float) – The potential stiffness.
temperature (float) – The temperature \(T\).
- Returns:
The relative Helmholtz free energy \(\Delta\psi\).
- Return type:
numpy.ndarray
- relative_helmholtz_free_energy_per_link(potential_distance, potential_stiffness, temperature)
The relative Helmholtz free energy per link as a function of the applied potential distance, potential stiffness, and temperature.
- Parameters:
potential_distance (numpy.ndarray) – The potential distance.
potential_stiffness (float) – The potential stiffness.
temperature (float) – The temperature \(T\).
- Returns:
The relative Helmholtz free energy per link \(\Delta\psi/N_b\).
- Return type:
numpy.ndarray
- nondimensional_helmholtz_free_energy(nondimensional_potential_distance, nondimensional_potential_stiffness, temperature)
The nondimensional Helmholtz free energy as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature.
- Parameters:
nondimensional_potential_distance (numpy.ndarray) – The nondimensional potential distance.
nondimensional_potential_stiffness (float) – The nondimensional potential stiffness.
temperature (float) – The temperature \(T\).
- Returns:
The nondimensional Helmholtz free energy \(\beta\psi=N_b\vartheta\).
- Return type:
numpy.ndarray
- nondimensional_helmholtz_free_energy_per_link(nondimensional_potential_distance, nondimensional_potential_stiffness, temperature)
The nondimensional Helmholtz free energy per link as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature.
- Parameters:
nondimensional_potential_distance (numpy.ndarray) – The nondimensional potential distance.
nondimensional_potential_stiffness (float) – The nondimensional potential stiffness.
temperature (float) – The temperature \(T\).
- Returns:
The nondimensional Helmholtz free energy per link \(\vartheta\equiv\beta\psi/N_b\).
- Return type:
numpy.ndarray
- nondimensional_relative_helmholtz_free_energy(nondimensional_potential_distance, nondimensional_potential_stiffness)
The nondimensional relative Helmholtz free energy as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
- Parameters:
nondimensional_potential_distance (numpy.ndarray) – The nondimensional potential distance.
nondimensional_potential_stiffness (float) – The nondimensional potential stiffness.
- Returns:
The nondimensional relative Helmholtz free energy \(\beta\Delta\psi=N_b\Delta\vartheta\).
- Return type:
numpy.ndarray
- nondimensional_relative_helmholtz_free_energy_per_link(nondimensional_potential_distance, nondimensional_potential_stiffness)
The nondimensional relative Helmholtz free energy per link as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
- Parameters:
nondimensional_potential_distance (numpy.ndarray) – The nondimensional potential distance.
nondimensional_potential_stiffness (float) – The nondimensional potential stiffness.
- Returns:
The nondimensional relative Helmholtz free energy per link \(\Delta\vartheta\equiv\beta\Delta\psi/N_b\).
- Return type:
numpy.ndarray
- gibbs_free_energy(potential_distance, potential_stiffness, temperature)
The Gibbs free energy as a function of the applied potential distance, potential stiffness, and temperature.
- Parameters:
potential_distance (numpy.ndarray) – The potential distance.
potential_stiffness (float) – The potential stiffness.
temperature (float) – The temperature \(T\).
- Returns:
The Gibbs free energy \(\varphi\).
- Return type:
numpy.ndarray
- gibbs_free_energy_per_link(potential_distance, potential_stiffness, temperature)
The Gibbs free energy epr link as a function of the applied potential distance, potential stiffness, and temperature.
- Parameters:
potential_distance (numpy.ndarray) – The potential distance.
potential_stiffness (float) – The potential stiffness.
temperature (float) – The temperature \(T\).
- Returns:
The Gibbs free energy per link \(\varphi/N_b\).
- Return type:
numpy.ndarray
- relative_gibbs_free_energy(potential_distance, potential_stiffness, temperature)
The relative Gibbs free energy as a function of the applied potential distance, potential stiffness, and temperature.
- Parameters:
potential_distance (numpy.ndarray) – The potential distance.
potential_stiffness (float) – The potential stiffness.
temperature (float) – The temperature \(T\).
- Returns:
The relative Gibbs free energy \(\Delta\varphi\).
- Return type:
numpy.ndarray
- relative_gibbs_free_energy_per_link(potential_distance, potential_stiffness, temperature)
The relative Gibbs free energy per link as a function of the applied potential distance, potential stiffness, and temperature.
- Parameters:
potential_distance (numpy.ndarray) – The potential distance.
potential_stiffness (float) – The potential stiffness.
temperature (float) – The temperature \(T\).
- Returns:
The relative Gibbs free energy per link \(\Delta\varphi/N_b\).
- Return type:
numpy.ndarray
- nondimensional_gibbs_free_energy(nondimensional_potential_distance, nondimensional_potential_stiffness, temperature)
The nondimensional Gibbs free energy as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature.
- Parameters:
nondimensional_potential_distance (numpy.ndarray) – The nondimensional potential distance.
nondimensional_potential_stiffness (float) – The nondimensional potential stiffness.
temperature (float) – The temperature \(T\).
- Returns:
The nondimensional Gibbs free energy \(\beta\varphi=N_b\varrho\).
- Return type:
numpy.ndarray
- nondimensional_gibbs_free_energy_per_link(nondimensional_potential_distance, nondimensional_potential_stiffness, temperature)
The nondimensional Gibbs free energy per link as a function of the applied nondimensional potential distance, nondimensional potential stiffness, and temperature.
- Parameters:
nondimensional_potential_distance (numpy.ndarray) – The nondimensional potential distance.
nondimensional_potential_stiffness (float) – The nondimensional potential stiffness.
temperature (float) – The temperature \(T\).
- Returns:
The nondimensional Gibbs free energy per link \(\varrho\equiv\beta\varphi/N_b\).
- Return type:
numpy.ndarray
- nondimensional_relative_gibbs_free_energy(nondimensional_potential_distance, nondimensional_potential_stiffness)
The nondimensional relative Gibbs free energy as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
- Parameters:
nondimensional_potential_distance (numpy.ndarray) – The nondimensional potential distance.
nondimensional_potential_stiffness (float) – The nondimensional potential stiffness.
- Returns:
The nondimensional relative Gibbs free energy \(\beta\Delta\varphi=N_b\Delta\varrho\).
- Return type:
numpy.ndarray
- nondimensional_relative_gibbs_free_energy_per_link(nondimensional_potential_distance, nondimensional_potential_stiffness)
The nondimensional relative Gibbs free energy per link as a function of the applied nondimensional potential distance and nondimensional potential stiffness.
- Parameters:
nondimensional_potential_distance (numpy.ndarray) – The nondimensional potential distance.
nondimensional_potential_stiffness (float) – The nondimensional potential stiffness.
- Returns:
The nondimensional relative Gibbs free energy per link \(\Delta\varrho\equiv\beta\Delta\varphi/N_b\).
- Return type:
numpy.ndarray