WLC model thermodynamics (isometric/legendre)

class WLC(number_of_links, link_length, hinge_mass, persistance_length)

The worm-like chain (WLC) model thermodynamics in the isometric ensemble approximated using a Legendre transformation.

The number of links in the chain.

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.

persistance_length

The persistance length of the chain in units of nm.

gibbs_free_energy(end_to_end_length, temperature)

The Gibbs free energy as a function of the applied end-to-end length and temperature,

\[\varphi(\xi, T) \sim \psi(\xi, T) - \xi f(\xi, T) \quad \text{for } N_b\gg 1,\]

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 Gibbs free energy \(\varphi\).

Return type:

numpy.ndarray

The Gibbs 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 Gibbs free energy per link \(\varphi/N_b\).

Return type:

numpy.ndarray

relative_gibbs_free_energy(end_to_end_length, temperature)

The relative Gibbs 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 Gibbs free energy \(\Delta\varphi\equiv\varphi(\xi,T)-\varphi(0,T)\).

Return type:

numpy.ndarray

The relative Gibbs 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 Gibbs free energy per link \(\Delta\varphi/N_b\).

Return type:

numpy.ndarray

nondimensional_gibbs_free_energy(nondimensional_end_to_end_length_per_link, temperature)

The nondimensional Gibbs 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 Gibbs free energy \(N_b\varrho=\beta\varphi\).

Return type:

numpy.ndarray

The nondimensional Gibbs 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 Gibbs free energy per link \(\varrho\equiv\beta\varphi/N_b\).

Return type:

numpy.ndarray

nondimensional_relative_gibbs_free_energy(nondimensional_end_to_end_length_per_link)

The nondimensional relative Gibbs 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 Gibbs free energy \(\beta\Delta\varphi=N_b\Delta\varrho\).

Return type:

numpy.ndarray

The nondimensional relative Gibbs 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 Gibbs free energy per link \(\Delta\varrho\equiv\beta\Delta\varphi/N_b\).

Return type:

numpy.ndarray