weak 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 weak 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.

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, given by Buche and Rimsza[1] as

\[\gamma(\eta) = \gamma_0(\eta)\left[1 - N_b\varpi\gamma_0'(\eta)\right],\]

where \(\gamma_0(\eta)=\mathcal{L}(\eta)=\coth(\eta)-1/\eta\) is the Langevin function.

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)

The expected force as a function of the applied potential distance and potential stiffness.

Parameters:

potential_distance (numpy.ndarray) – The potential distance.
potential_stiffness (float) – The potential stiffness.

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

gibbs_free_energy(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

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

References