"""
The freely-jointed chain (FJC) model thermodynamics in the isotensional ensemble.
"""
module Isotensional
using DocStringExtensions
using ......Polymers: PROJECT_ROOT
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the FJC model in the isotensional ensemble.
$(FIELDS)
"""
struct FJC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The thermodynamic functions of the model in the isotensional ensemble approximated using a Legendre transformation.
"""
legendre::Any
"""
The expected end-to-end length ``\\xi`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length::Function
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length_per_link::Function
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length::Function
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length_per_link::Function
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy::Function
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy_per_link::Function
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy::Function
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy_per_link::Function
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy::Function
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy_per_link::Function
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy::Function
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy_per_link::Function
end
"""
The expected end-to-end length ``\\xi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``,
given by [Rubinstein and Colby](https://global.oup.com/academic/product/polymer-physics-9780198520597) as
```math
\\xi(f, T) = -\\frac{\\partial\\varphi}{\\partial f} = N_b \\ell_b \\mathcal{L}(\\beta f\\ell_b),
```
where ``\\mathcal{L}(x)=\\coth(x)-1/x`` is the Langevin function.
$(TYPEDSIGNATURES)
"""
function end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
force,
temperature,
)
end
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
link_length_i,
force_i,
temperature_i,
),
link_length,
force,
temperature,
)
end
"""
The expected nondimensional end-to-end length ``N_b\\gamma\\equiv\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_force,
)
end
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
nondimensional_force_i -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64,),
nondimensional_force_i,
),
nondimensional_force,
)
end
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``,
```math
\\varphi(f, T) = -kT\\ln Z(f, T).
```
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, hinge_mass_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
force,
temperature,
)
end
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
force_i,
temperature_i,
),
link_length,
hinge_mass,
force,
temperature,
)
end
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b`` and link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
force,
temperature,
)
end
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the link length ``\\ell_b``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64),
link_length_i,
force_i,
temperature_i,
),
link_length,
force,
temperature,
)
end
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_force_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_force_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_force,
temperature,
)
end
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the link length ``\\ell_b`` and hinge mass ``m``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy_per_link(
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(link_length_i, hinge_mass_i, nondimensional_force_i, temperature_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64, Float64, Float64, Float64),
link_length_i,
hinge_mass_i,
nondimensional_force_i,
temperature_i,
),
link_length,
hinge_mass,
nondimensional_force,
temperature,
)
end
"""
The nondimensional relative Gibbs free energy ``\\beta\\Delta\\varphi=N_b\\Delta\\varrho`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_force_i) -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64),
number_of_links_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_force,
)
end
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
nondimensional_force_i -> ccall(
(
:physics_single_chain_fjc_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(Float64,),
nondimensional_force_i,
),
nondimensional_force,
)
end
"""
Initializes and returns an instance of the thermodynamics of the FJC model in the isotensional ensemble.
$(TYPEDSIGNATURES)
"""
function FJC(number_of_links::UInt8, link_length::Float64, hinge_mass::Float64)
return FJC(
number_of_links,
link_length,
hinge_mass,
Legendre.FJC(number_of_links, link_length, hinge_mass),
(force, temperature) ->
end_to_end_length(number_of_links, link_length, force, temperature),
(force, temperature) -> end_to_end_length_per_link(link_length, force, temperature),
nondimensional_force ->
nondimensional_end_to_end_length(number_of_links, nondimensional_force),
nondimensional_force ->
nondimensional_end_to_end_length_per_link(nondimensional_force),
(force, temperature) ->
gibbs_free_energy(number_of_links, link_length, hinge_mass, force, temperature),
(force, temperature) ->
gibbs_free_energy_per_link(link_length, hinge_mass, force, temperature),
(force, temperature) ->
relative_gibbs_free_energy(number_of_links, link_length, force, temperature),
(force, temperature) ->
relative_gibbs_free_energy_per_link(link_length, force, temperature),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy_per_link(
link_length,
hinge_mass,
nondimensional_force,
temperature,
),
nondimensional_force -> nondimensional_relative_gibbs_free_energy(
number_of_links,
nondimensional_force,
),
nondimensional_force ->
nondimensional_relative_gibbs_free_energy_per_link(nondimensional_force),
)
end
end