strong potential)

class FJC(number_of_links, link_length, hinge_mass)

The freely-jointed chain (FJC) model thermodynamics in the modified canonical ensemble approximated using an asymptotic approach valid for strong potentials.

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.

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, given by Buche and Rimsza[1] as

\[\eta(\gamma) = \eta_0(\gamma) - \frac{1}{N_b\varpi}\left[\eta_0(\gamma)\eta_0'(\gamma) - \frac{\eta_0''(\gamma)}{2N_b}\right],\]

where \(\eta_0(\gamma)\) is the isometric mechanical response.

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

References