# RepTate: Rheology of Entangled Polymers: Toolkit for the Analysis of Theory and Experiments
# --------------------------------------------------------------------------------------------------------
#
# Authors:
# Jorge Ramirez, jorge.ramirez@upm.es
# Victor Boudara, victor.boudara@gmail.com
#
# Useful links:
# http://blogs.upm.es/compsoftmatter/software/reptate/
# https://github.com/jorge-ramirez-upm/RepTate
# http://reptate.readthedocs.io
#
# --------------------------------------------------------------------------------------------------------
#
# Copyright (2017-2023): Jorge Ramirez, Victor Boudara, Universidad Politécnica de Madrid, University of Leeds
#
# This file is part of RepTate.
#
# RepTate is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RepTate is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with RepTate. If not, see <http://www.gnu.org/licenses/>.
#
# --------------------------------------------------------------------------------------------------------
"""Module TheoryDTDStars
Dynamics Tube Dilution for Stars
"""
import numpy as np
from RepTate.core.Parameter import Parameter, ParameterType, OptType
from RepTate.gui.QTheory import QTheory
import RepTate.theories.dtd_ctypes_helper as dtdh
[docs]
class TheoryDTDStarsFreq(QTheory):
"""Fit DTD Theory for stars.
Theory of stress relaxation in star polymer melts with no adjustable parameters beyond those measurable in linear melts
* **Function**
See `Milner-McLeish (1997) <http://www.che.psu.edu/faculty/milner/group/eprints/1997/Macromolecules1997Milner.pdf>`_
and
`Larson et al. (2003) <http://www.personal.reading.ac.uk/~sms06al2/papers/definit.pdf>`_ for details.
* **Parameters**
- ``G0`` :math:`\\equiv G_N^0`: Plateau modulus
- ``tau_e`` :math:`\\equiv \\tau_\\mathrm e = \\left(\\dfrac{M_\mathrm e^\\mathrm G}{M_0}\\right)^2 \\dfrac{\\zeta b^2}{3\\pi^2k_\\mathrm B T}`:
Entanglement equilibration time
- ``Me`` :math:`\\equiv M_\mathrm e^\mathrm G = \\dfrac 4 5 \\dfrac{\\rho R T} {G_N^0}`: Entanglement molecular weight
- ``alpha``: Dilution exponent
where:
- :math:`\\rho`: polymer density
- :math:`\\zeta`: monomeric friction coefficient
- :math:`b`: monomer-based segment length
- :math:`k_\\mathrm B T`: thermal energy
- :math:`M_0`: molar mass of an elementary segment
"""
thname = "DTD Stars"
description = "Dynamic Tube Dilution for stars, frequency domain"
citations = ["Milner S.T. and McLeish T.C.B., Macromolecules 1997, 30, 2159-2166"]
doi = ["http://dx.doi.org/10.1021/ma961559f"]
html_help_file = "http://reptate.readthedocs.io/manual/Applications/LVE/Theory/theory.html#dynamic-dilution-equation-for-stars"
single_file = (
False # False if the theory can be applied to multiple files simultaneously
)
def __init__(self, name="", parent_dataset=None, axarr=None):
"""**Constructor**"""
super().__init__(name, parent_dataset, axarr)
self.function = self.calculate
self.has_modes = False
self.parameters["G0"] = Parameter(
"G0",
1e1,
"Modulus c*kB*T/N",
ParameterType.real,
opt_type=OptType.opt,
min_value=0,
)
self.parameters["tau_e"] = Parameter(
"tau_e",
2e-6,
"Entanglement relaxation time",
ParameterType.real,
opt_type=OptType.opt,
min_value=0,
)
self.parameters["Me"] = Parameter(
"Me",
5.0,
"Entanglement Molecular Weight",
ParameterType.real,
opt_type=OptType.opt,
min_value=0,
)
self.parameters["alpha"] = Parameter(
"alpha",
1.0,
"Dilution parameter",
ParameterType.real,
opt_type=OptType.const,
min_value=0,
)
self.get_material_parameters()
self.G0 = self.parameters["G0"].value
self.tau_e = self.parameters["tau_e"].value
self.Me = self.parameters["Me"].value
self.alpha = self.parameters["alpha"].value
self.Z = 1
self.w = 0
[docs]
def calculate(self, f=None):
"""DTDStarsFreq function"""
ft = f.data_table
tt = self.tables[f.file_name_short]
tt.num_columns = ft.num_columns
tt.num_rows = ft.num_rows
tt.data = np.zeros((tt.num_rows, tt.num_columns))
self.G0 = self.parameters["G0"].value
self.tau_e = self.parameters["tau_e"].value
self.Me = self.parameters["Me"].value
self.alpha = self.parameters["alpha"].value
try:
Mw = float(f.file_parameters["Mw"])
except (ValueError, KeyError):
self.Qprint("Invalid Mw value")
return
# self.Z = int(np.rint(Mw / self.Me))
omega = ft.data[:, 0]
params = [self.G0, self.alpha, self.tau_e, Mw / self.Me, omega]
gp, gpp, success = dtdh.calculate_dtd_freq(params, self.eps)
if not success:
self.Qprint("Too many steps in routine qtrap")
return
tt.data[:, 0] = omega
tt.data[:, 1] = gp[:]
tt.data[:, 2] = gpp[:]
#############################################################################################
#############################################################################################
[docs]
class TheoryDTDStarsTime(QTheory):
"""Fit DTD Theory for stars
* **Function**
See `Milner-McLeish (1997) <http://www.che.psu.edu/faculty/milner/group/eprints/1997/Macromolecules1997Milner.pdf>`_
and
`Larson et al. (2003) <http://www.personal.reading.ac.uk/~sms06al2/papers/definit.pdf>`_ for details.
* **Parameters**
- ``G0`` :math:`\\equiv G_N^0`: Plateau modulus
- ``tau_e`` :math:`\\equiv \\tau_\\mathrm e = \\left(\\dfrac{M_\mathrm e^\\mathrm G}{M_0}\\right)^2 \\dfrac{\\zeta b^2}{3\\pi^2k_\\mathrm B T}`:
Entanglement equilibration time
- ``Me`` :math:`\\equiv M_\mathrm e^\mathrm G = \\dfrac 4 5 \\dfrac{\\rho R T} {G_N^0}`: Entanglement molecular weight
- ``alpha``: Dilution exponent
where:
- :math:`\\rho`: polymer density
- :math:`\\zeta`: monomeric friction coefficient
- :math:`b`: monomer-based segment length
- :math:`k_\\mathrm B T`: thermal energy
- :math:`M_0`: molar mass of an elementary segment
"""
thname = "DTD Stars"
description = "Dynamic Tube Dilution for stars, time domain"
citations = ["Milner S.T. and McLeish T.C.B., Macromolecules 1997, 30, 2159-2166"]
doi = ["http://dx.doi.org/10.1021/ma961559f"]
html_help_file = "http://reptate.readthedocs.io/manual/Applications/Gt/Theory/theory.html#dtd-stars-time"
single_file = (
False # False if the theory can be applied to multiple files simultaneously
)
def __init__(self, name="", parent_dataset=None, axarr=None):
"""**Constructor**"""
super().__init__(name, parent_dataset, axarr)
self.function = self.calculate
self.has_modes = False
self.parameters["G0"] = Parameter(
"G0",
1e1,
"Modulus c*kB*T/N",
ParameterType.real,
opt_type=OptType.opt,
min_value=0,
)
self.parameters["tau_e"] = Parameter(
"tau_e",
2e-6,
"Entanglement relaxation time",
ParameterType.real,
opt_type=OptType.opt,
min_value=0,
)
self.parameters["Me"] = Parameter(
"Me",
5.0,
"Entanglement Molecular Weight",
ParameterType.real,
opt_type=OptType.opt,
min_value=0,
)
self.parameters["alpha"] = Parameter(
"alpha",
1.0,
"Dilution parameter",
ParameterType.real,
opt_type=OptType.const,
min_value=0,
)
self.get_material_parameters()
self.G0 = self.parameters["G0"].value
self.tau_e = self.parameters["tau_e"].value
self.Me = self.parameters["Me"].value
self.alpha = self.parameters["alpha"].value
[docs]
def calculate(self, f=None):
"""DTDStarsTime function"""
ft = f.data_table
tt = self.tables[f.file_name_short]
tt.num_columns = ft.num_columns
tt.num_rows = ft.num_rows
tt.data = np.zeros((tt.num_rows, tt.num_columns))
self.G0 = self.parameters["G0"].value
self.tau_e = self.parameters["tau_e"].value
self.Me = self.parameters["Me"].value
self.alpha = self.parameters["alpha"].value
try:
Mw = float(f.file_parameters["Mw"])
except (ValueError, KeyError):
self.Qprint("Invalid Mw value")
return
try:
gamma = float(f.file_parameters["gamma"])
if gamma == 0:
gamma = 1
except:
gamma = 1
# self.Z = int(np.rint(Mw / self.Me))
times = ft.data[:, 0]
params = [self.G0, self.alpha, self.tau_e, Mw / self.Me, times]
gt, success = dtdh.calculate_dtd_time(params, self.eps)
if not success:
self.Qprint("Too many steps in routine qtrap")
return
tt.data[:, 0] = times
tt.data[:, 1] = gamma * gt[:]
