SingleChainStructureFactor

class mdhelper.analysis.polymer.SingleChainStructureFactor(group: AtomGroup, grouping: str = 'atoms', n_points: int = 32, *, n_chains: int = None, n_monomers: int = None, dimensions: ndarray[float] | Quantity | Quantity = None, unwrap: bool = False, parallel: bool = False, verbose: bool = True, **kwargs)

Bases: DynamicAnalysisBase

Serial and parallel implementations to calculate the single-chain structure factor \(S_\mathrm{sc}(q)\) of a homopolymer.

It is defined as

\[S_{\mathrm{sc}}(\mathbf{q})=\frac{1}{MN_\mathrm{p}} \sum_{m=1}^M\sum_{i,j=1}^{N_\mathrm{p}}\left\langle \exp{[i\mathbf{q}\cdot(\mathbf{r}_i-\mathbf{r}_j)]}\right\rangle\]

where \(M\) is the number of chains, \(N_\mathrm{p}\) is the chain length, \(\mathbf{q}\) is the scattering wavevector, and \(\mathbf{r}_i\) is the position of the \(i\)-th monomer.

The single-chain structure factor reveals information about the characteristic length scales of the polymer:

• In the Guinier regime (\(qR_g\ll1\)), \(S_{\mathrm{sc}}(q)^{-1}\approx N_\mathrm{p}(1-(qR_g)^2/3)\) can be used to determine the radius of gyration \(R_g\).

• In the Porod regime (\(qR_g\gg1\)), \(S_{\mathrm{sc}}(q)=1\) since the only contribution is the self-scattering of the monomers.

• In the intermediate regime, the slope \(s\) of the log-log plot of \(S_{\mathrm{sc}}(q)\) is related to the scaling exponent \(\nu\) via \(\nu=-1/s\).

Parameters:

groupMDAnalysis.AtomGroup

Group of polymers to be analyzed. All polymers in the group must have the same chain length.

groupingstr, default: "atoms"

Determines whether the centers of mass are used in lieu of individual atom positions.

Note

In a standard trajectory file, segments (or chains) contain residues (or molecules), and residues contain atoms. This heirarchy must be adhered to for this analysis module to function correctly. If your trajectory file does not contain the correct segment or residue information, provide the number of chains and chain lengths in n_chains and n_monomers, respectively.

Valid values:

• "atoms": Atom positions (for coarse-grained polymer simulations).

• "residues": Residues’ centers of mass (for atomistic polymer simulations).

n_pointsint, default: 32

Number of points to sample the wavevector space.

n_chainsint, optional

Number of chains in group. Must be provided if the topology does not contain segment information.

n_monomersint, optional

Number of monomers per chain. Must be provided if the topology does not contain segment information.

dimensionsnumpy.ndarray or openmm.unit.Quantity, optional

System dimensions. If the MDAnalysis.core.universe.Universe object that group belongs to does not contain dimensionality information, provide it here.

Shape: \((3,)\).

Reference unit: \(\textrm{Å}\).

unwrapbool, keyword-only, default: False

Determines whether atom positions are unwrapped.

parallelbool, keyword-only, default: False

Determines whether the analysis is performed in parallel.

verbosebool, keyword-only, default: True

Determines whether detailed progress is shown.

**kwargs

Additional keyword arguments to pass to MDAnalysis.analysis.base.AnalysisBase.

Notes

In a standard trajectory file, segments (or chains) contain residues, and residues contain atoms. This heirarchy must be adhered to for this analysis module to function correctly. If your trajectory file does not contain the correct segment or residue information, provide the number of chains and chain lengths in n_chains and n_monomers, respectively.

Attributes:

universeMDAnalysis.Universe

MDAnalysis.core.universe.Universe object containing all information describing the system.

results.unitsdict

Reference units for the results. For example, to get the reference units for results.wavenumbers, call results.units["results.wavenumbers"].

results.wavenumbersnumpy.ndarray

Unique wavenumbers.

Shape: \((N_q,)\).

Reference unit: \(\textrm{Å}^{-1}\).

results.scsfnumpy.ndarray

Single-chain structure factors for the unique wavenumbers.

Shape: \((N_q,)\).

Methods

run	Performs the calculation.
save	Saves results to a binary or archive file in NumPy format.

run(start: int = None, stop: int = None, step: int = None, frames: slice | ndarray[int] = None, verbose: bool = None, **kwargs) → SerialAnalysisBase | ParallelAnalysisBase

Performs the calculation.

See also

For parallel-specific keyword arguments, see ParallelAnalysisBase.run().

Parameters:

startint, optional

Starting frame for analysis.

stopint, optional

Ending frame for analysis.

stepint, optional

Number of frames to skip between each analyzed frame.

framesslice or array-like, optional

Index or logical array of the desired trajectory frames.

verbosebool, optional

Determines whether detailed progress is shown.

**kwargs

Additional keyword arguments to pass to MDAnalysis.lib.log.ProgressBar.

Returns:

selfSerialAnalysisBase or ParallelAnalysisBase

Analysis object with results.

save(file: str | TextIO, archive: bool = True, compress: bool = True, **kwargs) → None

Saves results to a binary or archive file in NumPy format.

Parameters:

filestr or file

Filename or file-like object where the data will be saved. If file is a str, the .npy or .npz extension will be appended automatically if not already present.

archivebool, default: True

Determines whether the results are saved to a single archive file. If True, the data is stored in a .npz file. Otherwise, the data is saved to multiple .npy files.

compressbool, default: True

Determines whether the .npz file is compressed. Has no effect when archive=False.

**kwargs

Additional keyword arguments to pass to numpy.save(), numpy.savez(), or numpy.savez_compressed(), depending on the values of archive and compress.