Abstract
Order classification is particularly important in photonics, optoelectronics, nanotechnology, biology, and biomedicine, as self-assembled and living systems tend to be ordered well but not perfectly. Engineering sets of experimental protocols that can accurately reproduce specific desired patterns can be a challenge when (dis)ordered outcomes look visually similar. Robust comparisons between similar samples, especially with limited data sets, need a finely tuned ensemble of accurate analysis tools. Here we introduce our numerical Mathematica package disLocate, a suite of tools to rapidly quantify the spatial structure of a two-dimensional dispersion of objects. The full range of tools available in disLocate give different insights into the quality and type of order present in a given dispersion, accessing the translational, orientational and entropic order. The utility of this package allows for researchers to extract the variation and confidence range within finite sets of data (single images) using different structure metrics to quantify local variation in disorder. Containing all metrics within one package allows for researchers to easily and rapidly extract many different parameters simultaneously, allowing robust conclusions to be drawn on the order of a given system. Quantifying the experimental trends which produce desired morphologies enables engineering of novel methods to direct self-assembly.
Highlights
Order is important in a wide variety of fields ranging from optics and nanotechnology to biology and biomedicine
Angular order can be calculated by using the bond order parameter[35], which compares the angle between the central particle and its closest neighbours against a specified symmetry basis vectors (Fig. 2(c) and (f))
Using the full range of tools available in disLocate, we examined as a representative example of atomic force microscopy (AFM) images of polystyrene-block-poly-2-vinylpyridine (PS-b-P2VP) diblock copolymer micelles distributed on a Si wafer surface with three different deposition approaches
Summary
Order is important in a wide variety of fields ranging from optics and nanotechnology to biology and biomedicine. The quantitative classification of naturally occurring limits thereby provides a road-map to reproducibly produce a desired result In this contribution, we outline a series of tools and metrics that can be used for a fine grained understanding of both global and local spatial order patterns, within the package disLocate (Detecting Intermolecular Structure Located at particle positions). We outline a series of tools and metrics that can be used for a fine grained understanding of both global and local spatial order patterns, within the package disLocate (Detecting Intermolecular Structure Located at particle positions) This provides a convenient tool, using a variety of numerical techniques, for researchers to quantify the relative disorder of a point pattern of objects and engineer desired outcomes to a higher degree of specificity. If any one of these types of order are not met, the system can be considered in a mesophase[28], such as that observed for plastic crystals (limited orientational or rotational order, but long range translational order)[30] or liquid crystals (limited translational order but long range angular order)[31]
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