# 4.6.1. Polymer analysis — MDAnalysis.analysis.polymer¶

Author

Richard J. Gowers

Year

2015, 2018

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 is False.

results

the measured bond autocorrelation

Type

numpy.ndarray

lb

the average bond length

Type

float

lp

calculated persistence length

Type

float

fit

the modelled backbone decorrelation predicted by lp

Type

numpy.ndarray

sort_backbone()

for producing the sorted AtomGroup required for input.

The run method now automatically performs the exponential fit

plot(ax=None)[source]

Visualise the results and fit

Parameters

ax (matplotlib.Axes, optional) – if provided, the graph is plotted on this axis

Returns

ax

Return type

the axis that the graph was plotted on

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

float

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

AtomGroup

New in version 0.20.0.