4.6.1. Polymer analysis — MDAnalysis.analysis.polymer¶
- Author
Richard J. Gowers
- Year
2015, 2018
- Copyright
GNU Public License v3
This module contains various commonly used tools in analysing polymers.
4.6.1.1. Persistence length worked example¶
This example shows how to find the persistence length of a polymer using MDAnalysis.
from MDAnalysis.tests.datafiles import TRZ_psf, TRZ
import MDAnalysis as mda
from MDAnalysis.analysis import polymer
u = mda.Universe(TRZ_psf, TRZ)
# this system is a pure polymer melt of polyamide,
# so we can select the chains by using the .fragments attribute
chains = u.atoms.fragments
# select only the backbone atoms for each chain
backbones = [chain.select_atoms('not name O* H') for chain in chains]
# sort the chains, removing any non-backbone atoms
sorted_backbones = [polymer.sort_backbone(bb) for bb in backbones]
lp = polymer.PersistenceLength(sorted_backbones)
# Run the analysis, this will average over all polymer chains
# and all timesteps in trajectory
lp = lp.run()
print('The persistence length is: {}'.format(lp.pl))
# always check the visualisation of this:
lp.plot()
-
class
MDAnalysis.analysis.polymer.PersistenceLength(atomgroups, **kwargs)[source]¶ Calculate the persistence length for polymer chains
The persistence length is the length at which two points on the polymer chain become decorrelated. This is determined by first measuring the autocorrelation (\(C(n)\)) of two bond vectors (\(\mathbf{a}_i, \mathbf{a}_{i + n}\)) separated by \(n\) bonds
\[C(n) = \langle \cos\theta_{i, i+n} \rangle = \langle \mathbf{a_i} \cdot \mathbf{a_{i+n}} \rangle\]An exponential decay is then fitted to this, which yields the persistence length
\[C(n) \approx \exp\left( - \frac{n \bar{l_B}}{l_P} \right)\]where \(\bar{l_B}\) is the average bond length, and \(l_P\) is the persistence length which is fitted
- Parameters
atomgroups (iterable) – List of AtomGroups. Each should represent a single polymer chain, ordered in the correct order.
verbose (bool (optional)) – Show detailed progress of the calculation if set to
True; the default isFalse.
-
results¶ the measured bond autocorrelation
- Type
-
fit¶ the modelled backbone decorrelation predicted by lp
- Type
See also
sort_backbone()for producing the sorted AtomGroup required for input.
The run method now automatically performs the exponential fit
- Parameters
trajectory (mda.Reader) – A trajectory Reader
verbose (bool, optional) – Turn on more logging and debugging, default
False
-
MDAnalysis.analysis.polymer.fit_exponential_decay(x, y)[source]¶ Fit a function to an exponential decay
\[y = \exp\left(- \frac{x}{a}\right)\]- Parameters
y (x,) – The two arrays of data
- Returns
a – The coefficient a for this decay
- Return type
Notes
This function assumes that data starts at 1.0 and decays to 0.0
-
MDAnalysis.analysis.polymer.sort_backbone(backbone)[source]¶ Rearrange a linear AtomGroup into backbone order
Requires that the backbone has bond information, and that only backbone atoms are provided (ie no side chains or hydrogens).
- Parameters
backbone (AtomGroup) – the backbone atoms, not necessarily in order
- Returns
sorted_backbone – backbone in order, so sorted_backbone[i] is bonded to sorted_backbone[i - 1] and sorted_backbone[i + 1]
- Return type
New in version 0.20.0.
