EFJC model thermodynamics (isotensional/asymptotic/reduced)
- class EFJC(number_of_links, link_length, hinge_mass, link_stiffness)
The extensible freely-jointed chain (EFJC) model thermodynamics in the isotensional ensemble approximated using a reduced asymptotic approach.
- 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).
- legendre
The thermodynamic functions of the model in the isotensional ensemble approximated using a reduced asymptotic approach and a Legendre transformation.
- end_to_end_length(force, temperature)
The expected end-to-end length as a function of the applied force and temperature,
\[\xi(f, T) = -\frac{\partial\varphi}{\partial f}.\]- Parameters:
force (numpy.ndarray) – The force \(f\).
temperature (float) – The temperature \(T\).
- Returns:
The end-to-end length \(\xi\).
- Return type:
numpy.ndarray
- end_to_end_length_per_link(force, temperature)
The expected end-to-end length per link as a function of the applied force and temperature.
- Parameters:
force (numpy.ndarray) – The force \(f\).
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_force)
The expected nondimensional end-to-end length as a function of the applied nondimensional force.
- Parameters:
nondimensional_force (numpy.ndarray) – The nondimensional force \(\eta\equiv\beta f\ell_b\).
temperature (float) – The temperature \(T\).
- 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_force)
The expected nondimensional end-to-end length per link as a function of the applied nondimensional force, given by Buche et al.[1] as
\[\gamma(\eta) \sim \mathcal{L}(\eta) + \frac{\eta}{\kappa} \quad \text{for } \kappa\gg 1,\]where \(\mathcal{L}(x)=\coth(x)-1/x\) is the Langevin function.
- Parameters:
nondimensional_force (numpy.ndarray) – The nondimensional force \(\eta\equiv\beta f\ell_b\).
temperature (float) – The temperature \(T\).
- Returns:
The nondimensional end-to-end length per link \(\gamma\equiv \xi/N_b\ell_b\).
- Return type:
numpy.ndarray
- gibbs_free_energy(force, temperature)
The Gibbs free energy as a function of the applied force and temperature,
\[\varphi(f, T) = -kT\ln Z(f, T).\]- Parameters:
force (numpy.ndarray) – The force \(f\).
temperature (float) – The temperature \(T\).
- Returns:
The Gibbs free energy \(\varphi\).
- Return type:
numpy.ndarray
- gibbs_free_energy_per_link(force, temperature)
The Gibbs free energy per link as a function of the applied force and temperature.
- Parameters:
force (numpy.ndarray) – The force \(f\).
temperature (float) – The temperature \(T\).
- Returns:
The Gibbs free energy per link \(\varphi/N_b\).
- Return type:
numpy.ndarray
- relative_gibbs_free_energy(force, temperature)
The relative Gibbs free energy as a function of the applied force and temperature.
- Parameters:
force (numpy.ndarray) – The force \(f\).
temperature (float) – The temperature \(T\).
- Returns:
The relative Gibbs free energy \(\Delta\varphi\equiv\varphi(f,T)-\varphi(0,T)\).
- Return type:
numpy.ndarray
- relative_gibbs_free_energy_per_link(force, temperature)
The relative Gibbs free energy per link as a function of the applied force and temperature.
- Parameters:
force (numpy.ndarray) – The force \(f\).
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_force, temperature)
The nondimensional Gibbs free energy as a function of the applied nondimensional force and temperature.
- Parameters:
nondimensional_force (numpy.ndarray) – The nondimensional force \(\eta\equiv\beta f\ell_b\).
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_force, temperature)
The nondimensional Gibbs free energy per link as a function of the applied nondimensional force and temperature.
- Parameters:
nondimensional_force (numpy.ndarray) – The nondimensional force \(\eta\equiv\beta f\ell_b\).
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_force)
The nondimensional relative Gibbs free energy as a function of the applied nondimensional force.
- Parameters:
nondimensional_force (numpy.ndarray) – The nondimensional force \(\eta\equiv\beta f\ell_b\).
temperature (float) – The temperature \(T\).
- 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_force)
The nondimensional relative Gibbs free energy per link as a function of the applied nondimensional force, given by Buche et al.[1] as
\[\Delta\varrho(\eta) = \ln\left[\frac{\eta}{\sinh(\eta)}\right] - \frac{\eta^2}{2\kappa} \quad \text{for } \kappa\gg 1.\]- Parameters:
nondimensional_force (numpy.ndarray) – The nondimensional force \(\eta\equiv\beta f\ell_b\).
temperature (float) – The temperature \(T\).
- Returns:
The nondimensional relative Gibbs free energy per link \(\Delta\varrho\equiv\beta\Delta\varphi/N_b\).
- Return type:
numpy.ndarray
References