Log-squared-FJC model thermodynamics (isometric/asymptotic/reduced/legendre)
- class LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
The log-squared link potential freely-jointed chain (log-squared-FJC) model thermodynamics in the isometric ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
- 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.
- link_stiffness
The stiffness of each link in the chain in units of J/(mol⋅nm^2).
- force(end_to_end_length, temperature)
The expected force as a function of the applied end-to-end length and temperature.
- Parameters:
end_to_end_length (numpy.ndarray) – The end-to-end length \(\xi\).
temperature (float) – The temperature \(T\).
- Returns:
The force \(f\).
- Return type:
numpy.ndarray
- nondimensional_force(nondimensional_end_to_end_length_per_link)
The expected nondimensional force as a function of the applied nondimensional end-to-end length per link.
- Parameters:
nondimensional_end_to_end_length_per_link (numpy.ndarray) – The nondimensional end-to-end length per link \(\gamma\equiv \xi/N_b\ell_b\).
- Returns:
The nondimensional force \(\eta\equiv\beta f\ell_b\).
- Return type:
numpy.ndarray
- helmholtz_free_energy(end_to_end_length, temperature)
The Helmholtz free energy as a function of the applied end-to-end length and temperature,
\[\psi(\xi, T) \sim \varphi\left[f(\xi, T)\right] + \xi f(\xi, T) \quad \text{for } N_b\gg 1,\]where \(f(\xi, T)\) is given by the Legendre transformation approximation above.
- Parameters:
end_to_end_length (numpy.ndarray) – The end-to-end length \(\xi\).
temperature (float) – The temperature \(T\).
- Returns:
The Helmholtz free energy \(\psi\).
- Return type:
numpy.ndarray
- helmholtz_free_energy_per_link(end_to_end_length, temperature)
The Helmholtz free energy per link as a function of the applied end-to-end length and temperature.
- Parameters:
end_to_end_length (numpy.ndarray) – The end-to-end length \(\xi\).
temperature (float) – The temperature \(T\).
- Returns:
The Helmholtz free energy per link \(\psi/N_b\).
- Return type:
numpy.ndarray
- relative_helmholtz_free_energy(end_to_end_length, temperature)
The relative Helmholtz free energy as a function of the applied end-to-end length and temperature.
- Parameters:
end_to_end_length (numpy.ndarray) – The end-to-end length \(\xi\).
temperature (float) – The temperature \(T\).
- Returns:
The relative Helmholtz free energy \(\Delta\psi\equiv\psi(\xi,T)-\psi(0,T)\).
- Return type:
numpy.ndarray
- relative_helmholtz_free_energy_per_link(end_to_end_length, temperature)
The relative Helmholtz free energy per link as a function of the applied end-to-end length and temperature.
- Parameters:
end_to_end_length (numpy.ndarray) – The end-to-end length \(\xi\).
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_end_to_end_length_per_link, temperature)
The nondimensional Helmholtz free energy as a function of the applied nondimensional end-to-end length per link and temperature.
- Parameters:
nondimensional_end_to_end_length_per_link (numpy.ndarray) – The nondimensional end-to-end length per link \(\gamma\equiv \xi/N_b\ell_b\).
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_end_to_end_length_per_link, temperature)
The nondimensional Helmholtz free energy per link as a function of the applied nondimensional end-to-end length per link and temperature.
- Parameters:
nondimensional_end_to_end_length_per_link (numpy.ndarray) – The nondimensional end-to-end length per link \(\gamma\equiv \xi/N_b\ell_b\).
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_end_to_end_length_per_link)
The nondimensional relative Helmholtz free energy as a function of the applied nondimensional end-to-end length per link.
- Parameters:
nondimensional_end_to_end_length_per_link (numpy.ndarray) – The nondimensional end-to-end length per link \(\gamma\equiv \xi/N_b\ell_b\).
- 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_end_to_end_length_per_link)
The nondimensional relative Helmholtz free energy per link as a function of the applied nondimensional end-to-end length per link.
- Parameters:
nondimensional_end_to_end_length_per_link (numpy.ndarray) – The nondimensional end-to-end length per link \(\gamma\equiv \xi/N_b\ell_b\).
- Returns:
The nondimensional relative Helmholtz free energy per link \(\Delta\vartheta\equiv\beta\Delta\psi/N_b\).
- Return type:
numpy.ndarray