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The dataset generation failed
Error code: DatasetGenerationError
Exception: TypeError
Message: Couldn't cast array of type struct<page: int64, text: string, rect: list<item: double>> to null
Traceback: Traceback (most recent call last):
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 2011, in _prepare_split_single
writer.write_table(table)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/arrow_writer.py", line 585, in write_table
pa_table = table_cast(pa_table, self._schema)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 2302, in table_cast
return cast_table_to_schema(table, schema)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 2261, in cast_table_to_schema
arrays = [cast_array_to_feature(table[name], feature) for name, feature in features.items()]
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 2261, in <listcomp>
arrays = [cast_array_to_feature(table[name], feature) for name, feature in features.items()]
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 1802, in wrapper
return pa.chunked_array([func(chunk, *args, **kwargs) for chunk in array.chunks])
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 1802, in <listcomp>
return pa.chunked_array([func(chunk, *args, **kwargs) for chunk in array.chunks])
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 2075, in cast_array_to_feature
casted_array_values = _c(array.values, feature.feature)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 1804, in wrapper
return func(array, *args, **kwargs)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 2116, in cast_array_to_feature
return array_cast(
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 1804, in wrapper
return func(array, *args, **kwargs)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 1964, in array_cast
raise TypeError(f"Couldn't cast array of type {_short_str(array.type)} to {_short_str(pa_type)}")
TypeError: Couldn't cast array of type struct<page: int64, text: string, rect: list<item: double>> to null
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1529, in compute_config_parquet_and_info_response
parquet_operations = convert_to_parquet(builder)
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1154, in convert_to_parquet
builder.download_and_prepare(
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1027, in download_and_prepare
self._download_and_prepare(
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1122, in _download_and_prepare
self._prepare_split(split_generator, **prepare_split_kwargs)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1882, in _prepare_split
for job_id, done, content in self._prepare_split_single(
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 2038, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
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[] |
[
{
"page": 1,
"text": "Russian Chemical Reviews",
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"page": 1,
"text": "CHEMICAL CHARACTERISTICS, STRUCTURE,",
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"text": "AND PROPERTIES OF LIQUID CRYSTAL",
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"text": "To cite this article: V A Usol'tseva and I G Chistyakov 1963 Russ. Chem. Rev. 32 495",
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"text": "View the article online for updates and enhancements.",
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"page": 1,
"text": "You may also like",
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},
{
"page": 1,
"text": "- THE EXTRACTION OF HETEROPOLY-",
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"page": 1,
"text": "COMPOUNDS AND ITS APPLICATION IN",
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"page": 1,
"text": "INORGANIC ANALYSIS",
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"page": 1,
"text": "I P Alimarin, F P Sudakov and V I Klitina",
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"page": 1,
"text": "- THE FORMATION OF BIOCHEMICALLY",
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"page": 1,
"text": "IMPORTANT COMPOUNDS IN THE PRE-",
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"page": 1,
"text": "BIOLOGICAL STAGE OF THE EARTH'S",
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"page": 1,
"text": "DEVELOPMENT",
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"page": 1,
"text": "A G Pasynskii and T E Pavlovskaya",
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"text": "-",
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"text": "This content was downloaded from IP address 128.151.150.113 on 17/07/2024 at 19:50",
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[
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"page": 1,
"text": "research papers",
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"text": "ISSN 2053-2733",
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{
"page": 1,
"text": "Crystallographic phase retrieval method for liquid",
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"page": 1,
"text": "crystal bicontinuous phases: indicator-based",
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"page": 1,
"text": "method",
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"page": 1,
"text": "Toshihiko Oka*",
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"text": "Received 27 January 2022",
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"text": "Accepted 7 July 2022",
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"text": "Department of Physics, Faculty of Science, Shizuoka University, Shizuoka, 422-8529, Japan, and Nanomaterials Research",
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"page": 1,
"text": "Division, Research Institute of Electronics, Shizuoka University, Shizuoka, 422-8529, Japan. *Correspondence e-mail:",
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"text": "oka.toshihiko@shizuoka.ac.jp",
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"page": 1,
"text": "Edited by I. Margiolaki, University of Patras,",
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"page": 1,
"text": "Greece",
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"text": "Keywords: lyotropic liquid crystals; triply",
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"text": "periodic minimal surfaces; crystallographic",
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"page": 1,
"text": "phase retrieval.",
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"page": 1,
"text": "Supporting information: this article has",
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"page": 1,
"text": "supporting information at journals.iucr.org/a",
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"text": "An indicator-based crystallographic phase retrieval method has been developed",
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"text": "for diffraction data of bicontinuous cubic phases of lyotropic liquid crystals.",
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"text": "Such liquid crystals have large structural disorder; the number of independent",
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"page": 1,
"text": "Bragg reflections that can be observed is limited. This paper proposes two",
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"page": 1,
"text": "indicators to identify plausible combination(s) of crystallographic phases, i.e.",
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"text": "electron-density distribution. The indicators are based on the characteristics of",
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"text": "the liquid crystals: amphiphilic molecules diffuse mainly in the direction parallel",
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"text": "to polar–nonpolar interfaces and the electron density in the direction parallel to",
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"text": "the interfaces is averaged. One indicator is the difference between the maximum",
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"text": "and minimum electron density, and the other is calculated from the Hessian",
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"text": "matrix of the electron density. Using test data, the electron densities were",
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"text": "calculated for all possible phase combinations and indicators were obtained. The",
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"text": "results indicated that the electron densities with the minimum indicators were",
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"text": "close to the true electron density. Therefore, this method is effective for phase",
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"text": "retrieval. The accuracy of the phase retrieval decreased when the volume",
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"text": "fraction of the region including the triply periodic minimal surface increased.",
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"text": "Published",
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"text": "430",
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"text": "under a CC BY 4.0 licence",
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"text": "1. Introduction",
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"text": "Restoring the phases of the structure factors is a crucial",
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"text": "problem",
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"text": "crystal",
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"text": "determination",
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"text": "X-ray",
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"text": "diffraction",
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"text": "(XRD)",
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"text": "Direct",
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"text": "methods",
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"text": "solve",
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"text": "problem",
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"text": "(atomicity, positivity and zero density regions) (Sayre, 1952;",
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"text": "measurements.",
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"text": "triply periodic minimal surfaces (TPMSs) (Hyde et al., 1996),",
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"text": "and diffraction data can be obtained as if they were 3D crystals",
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"text": "[Fig. 1(a)]. However, the spatial resolution of the observed",
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"text": "constraints, except the positivity, are not satisfied. There is",
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"text": "https://doi.org/10.1107/S2053273322006970",
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"text": "Cryst.",
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"text": "430–436",
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"text": "thus a problem in restoring the electron density from XRD",
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"text": "data, although the centrosymmetry of the LLC bicontinuous",
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"text": "phase restricts the phase to 0 or \u0002. Luzzatti and colleagues first",
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"text": "clarified the electron-density distribution of an LLC bicon-",
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"text": "tinuous phase (Luzzati et al., 1988; Mariani et al., 1988). They",
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"text": "electron density as an indicator for phase retrieval. They",
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"text": "value was the most reliable. However, as they admitted, the",
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"text": "samples (Oka, 2017; Oka et al., 2018, 2020). In these studies,",
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"text": "the structures of the bicontinuous cubic phases were deter-",
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"text": "mined using models based on available information. However,",
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"text": "phase could be revealed without a structural model. Here, a",
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"text": "simple indicator-based phase retrieval method is reported.",
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"text": "like structure. Although this method was designed to clarify",
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"text": "(a) A gyroid (G) surface (orange), one of the triply periodic minimal",
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"text": "of the two interwoven spaces where the surface divides. A single unit cell",
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"text": "(blue). The volume fraction of the TPMS side is 0.4. (c) Structural model",
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"text": "with fluctuations. In the structure shown in (b), the TPMS side region is",
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"text": "set to an electron density of 1 and thenetwork side region is set to 0, and a",
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"text": "Acta Cryst. (2022). A78, 430–436",
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"text": "be applicable to thermotropic liquid crystals, polymers, and",
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"text": "other materials with TPMS-like structures.",
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"text": "2. Indicators for bicontinuous structure (TPMS-like",
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"text": "structure)",
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"text": "2.1. Bicontinuous structure (TPMS-like structure)",
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"text": "An LLC consists of two or more components, amphiphilic",
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"text": "molecules and water (or oil). There are two types of LLC, oil-",
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"text": "(Israelachvili,",
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"text": "2011).",
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"text": "type",
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"text": "bicontinuous cubic phases of LLCs, three different TPMS-like",
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"text": "structures, P surface, D surface and gyroid (G) surface, have",
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"text": "been observed, while only the G surface has been observed in",
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"text": "type I (Hyde et al., 1996). The space groups of the three",
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"text": "TPMS as the center surface, and the polar region is located on",
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"text": "the two networks separated by the TPMS [Fig. 1(a)]. In the",
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"text": "type I bicontinuous cubic phase, the positions of the polar and",
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"text": "nonpolar regions are swapped with those of type II (Israe-",
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"text": "lachvili, 2011). In both cases, the polar–nonpolar interface is",
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"text": "on the amphiphilic molecule, and the amphiphilic molecule",
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"text": "can move like a liquid molecule in the direction parallel to the",
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"text": "polar–nonpolar interface. Therefore, the electron density in",
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"text": "the direction parallel to the interface is averaged, but not that",
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"text": "in the perpendicular direction. This averaging leads to the",
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"text": "separation of the polar and nonpolar regions. In the case of an",
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"text": "the polar parts of the amphiphilic molecules and waters are",
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"text": "almost the same, then the electron density can be described in",
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"text": "two levels, polar and nonpolar, without considering fluctua-",
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"text": "Figure 2",
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"text": "Sliced contour plots of idealized electron densities of (a) sphere-like, (b)",
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"text": "cylinder-like and (c) minimal surface like structures. Only in (a) is there a",
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"text": "strictly convex upward density region where all eigenvalues of the",
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"text": "Hessian matrix are negative. The strictly convex upward density region",
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"text": "forms a closed isoelectron density surface. On the other hand, there is no",
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"text": "closed isoelectron density surface in (b) and (c).",
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"text": "Toshihiko Oka \u0002 Liquid crystal bicontinuous phases 431",
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"text": "research papers",
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"text": "structures with branches (Fig. 2). If the electron densities of",
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"text": "electron-density regions if fluctuations are not considered [Fig.",
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"text": "between the minimum electron density in a unit cell, \u0003min, and",
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"text": "This indicator corresponds to the range in statistics. A smaller",
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"text": "cubic",
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"text": "phase",
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"text": "because",
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"text": "it",
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"text": "seemingly",
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"text": "contradicts",
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"text": "molecular",
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"text": "diffusion",
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"text": "over",
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"text": "a",
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"text": "long",
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"text": "distance.",
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"text": "Therefore,",
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"text": "few",
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"page": 3,
"text": "density",
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"text": "regions",
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"page": 3,
"text": "that",
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"page": 3,
"text": "are",
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"text": "convex",
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"text": "upward or downward are expected. Convex regions can be",
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"text": "determined by the eigenvalues of the Hessian matrix of the",
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"page": 3,
"text": "electron density, \u0003ðrÞ:",
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"text": "HðrÞ ¼ 0@\u0003\u0003\u0003zyxxxx \u0003\u0003\u0003xyzyyy \u0003\u0003\u0003yzxzzz A1;",
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"text": "where subscripts indicate partial derivatives. If all eigenvalues",
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"text": "of the Hessian matrix are positive, then the region is strictly",
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"text": "convex downward, and if all are negative, then the region is",
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"text": "strictly convex upward (Rockafellar & Wets, 2010). Let C be",
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"page": 3,
"text": "the",
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"page": 3,
"text": "electron-density",
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"text": "regions",
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"page": 3,
"text": "that",
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"page": 3,
"text": "are",
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"text": "convex",
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"text": "upward",
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"text": "or",
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"text": "downward and let K(r) be the determinant of H(r): K(r) =",
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"page": 3,
"text": "432 Toshihiko Oka \u0002 Liquid crystal bicontinuous phases",
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"text": "det[H(r)]. Therefore, K(r) is the product of three eigenvalues.",
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"text": "The following indicator was considered:",
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"text": "IK ¼ R\u0002\u0002KðrÞ\u0002\u0002dr;",
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"text": "C",
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"text": "which is the integral of the absolute value of KðrÞ in the region",
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"text": "C of the electron density in which the three eigenvalues are of",
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"text": "the same sign in a unit cell, where r is the position in a unit cell.",
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"text": "Thus, IK is an indicator that expresses the total (integrated)",
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"text": "convexity.",
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"text": "With",
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"text": "regard",
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"text": "to",
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"text": "geometrical",
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"page": 3,
"text": "meaning,",
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"text": "the",
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"text": "eigenvalues of the Hessian matrix are the principal curvatures,",
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"text": "and K(r) is the Gaussian curvature if the 3D electron density is",
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"text": "regarded as a hypersurface in a 4D hyperspace (Monga &",
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"page": 3,
"text": "Benayoun, 1995; Goldman, 2005).",
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"page": 3,
"text": "3. Phase retrieval method based on the Iq and IK",
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"page": 3,
"text": "indicators",
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"text": "The structure factor FðhÞ can be divided into the amplitude",
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"text": "jFðhÞj and the phase part exp½i\u0004ðhÞ\u0004, where \u0004ðhÞ is the phase.",
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"page": 3,
"text": "In a diffraction experiment, intensities are measured as the",
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"text": "squares of the amplitudes and the phases are not observable.",
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"text": "The electron density \u0003ðrÞ can be obtained by Fourier trans-",
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"text": "formation of the structure factors as follows:",
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"text": "1",
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"text": "\u0003ðrÞ ¼ V X \u0002\u0002FðhÞ\u0002\u0002exp½i\u0004ðhÞ\u0004expð\u0003i2\u0002h \u0005 rÞ;",
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"page": 3,
"text": "h2Hobs",
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"text": "where ris the position in the unit cell, h is the reciprocal-lattice",
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"text": "vector and V is the volume of the unit cell. Hobs is the set of h",
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"text": "for which the structure factor could be observed. F(000) was",
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"text": "not used in this paper; therefore, the integrated value of the",
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"page": 3,
"text": "electron density \u0003ðrÞ in the unit cell is zero. High-electron-",
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"page": 3,
"text": "density regions are thus positive, whereas low-electron-density",
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"page": 3,
"text": "regions are expressed as negative in \u0003ðrÞ.",
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"text": "In the phase retrieval, the electron densities were calculated",
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"text": "for all possible phase combinations by placing them into the",
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"text": "phase part exp½i\u0004ðhÞ\u0004 of the structure factor. The structures of",
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"text": "the bicontinuous cubic phasesare centrosymmetric,so that the",
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"text": "phase values are 0 or \u0002 (if the unit-cell origin is placed on a",
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"page": 3,
"text": "symmetry center), i.e. the structure factors are real (positive",
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"text": "or negative, respectively). When n is the number of the",
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"text": "independent",
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"page": 3,
"text": "structure-factor",
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"page": 3,
"text": "amplitude,",
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"text": "the",
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"page": 3,
"text": "corresponding",
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"page": 3,
"text": "number of phase combinations is 2n. The electron density was",
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"text": "calculated in 32 \u0006 32 \u0006 32 voxels as a unit cell. I",
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"text": "\u0003",
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"text": "the",
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"text": "difference",
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"text": "maximum",
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"text": "minimum",
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"text": "electron",
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"text": "densities.",
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"text": "To",
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"page": 3,
"text": "obtain",
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"page": 3,
"text": "IK,",
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"page": 3,
"text": "the",
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"text": "Hessian",
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"page": 3,
"text": "matrices were obtained from the electron densities for all",
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"page": 3,
"text": "voxel points in the unit cell, which yielded three eigenvalues at",
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633.1048583984375
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"text": "all points. The region where the signs of the three eigenvalues",
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"text": "1988). F(000) was not used in this paper; therefore, h½\u0003ðrÞ\u00044i",
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"text": "Acta Cryst. (2022). A78, 430–436",
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"page": 4,
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"text": "(Brakke, 1992; Shearman et al., 2007). The PSs were generated",
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"text": "as surfaces at fixed distances from the TPMSs [Fig. 1(b)].",
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"text": "electron density was calculated in 128 \u0006 128 \u0006 128 voxels as a",
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"text": "unit cell. The density from the interface to the TPMS side was",
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"text": "0.4, 0.6, 0.7 and 0.8. PS models with different Vfrac were",
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"text": "generated by varying the constant distance from the TPMS to",
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"text": "the P surface; therefore, only P-CMCS models with Vfrac ¼ 0.2",
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"text": "and 0.4 were used. Using values from previous papers as a",
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"text": "reference (Oka, 2017; Oka et al., 2018, 2020), the lattice",
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"text": "constant was set to 1 and the width of the Gaussian function",
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"text": "was set to 0.05 for the G surface based models and 0.07 for the",
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"text": "other models.",
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"text": "The structure factors FðhÞ were obtained by Fourier trans-",
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"text": "formation of the model densities \u0003ðrÞ:",
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"text": "FðhÞ ¼ \u0002\u0002FðhÞ\u0002\u0002exp½i\u0004ðhÞ\u0004 ¼ R \u0003ðrÞexpði2\u0002h \u0005 rÞdr: ð5Þ",
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"text": "uc",
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"text": "Acta Cryst. (2022). A78, 430–436",
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{
"page": 4,
"text": "research papers",
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"text": "Integration is performed in a unit cell. The numbers of inde-",
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"text": "pendent structure-factor amplitudes used were 22, 19 and 13",
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"text": "for the G, D and P surface based models, respectively. The",
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"text": "model density construction, except for the formation of the",
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"text": "TPMS and CMCS, and other calculations were conducted",
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"text": "using Mathematica 12.1 (Wolfram Research, Inc., USA).",
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"text": "4.2. Rp value to evaluate the quality of phase retrieval",
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"text": "The Rp value is defined as a quantity that evaluates how well",
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"text": "the phase combination used in the calculation agrees with the",
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"text": "true phase combination:",
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"text": "Rp ¼ Ph\u0002\u0002FðP hÞ\u0002\u0002h\u0002\u0002\u0002\u0002\u0004FtrðuheðÞh\u0002\u0002ðÞ\u0002\u0003=2\u0004ÞcalcðhÞ\u0002\u0002:",
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"text": "Rp close to 0 indicates a good agreement with the true phase",
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"text": "combination. From the Babinet principle, the inverted elec-",
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"text": "tron density was also treated in the same way, and the \u0002-",
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"text": "shifted phase combination from \u0004true was also treated as the",
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"text": "true phase. Of the Rp calculated from the original and \u0002-",
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"text": "shifted phase combinations, that with the smaller value was",
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"text": "adopted.",
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"text": "Figure 3",
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"text": "Distributions of the I\u0003 and IK indicators of G-PS models at (a) Vfrac ¼ 0:4",
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"text": "and (b) Vfrac ¼ 0:8. The indicators were calculated from the electron",
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"text": "densities using all phase combinations. The colors of the points indicate",
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"text": "Rp that compare the phase combinations with the true phase combina-",
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"text": "tion. The black circles show the true phase combination indicators of the",
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"page": 4,
"text": "model.",
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"page": 4,
"text": "Toshihiko Oka \u0002 Liquid crystal bicontinuous phases 433",
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"text": "research papers",
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"text": "5. Results",
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"text": "5.1. Phase retrieval for constructed models",
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"text": "Phase retrieval was performed for model densities with",
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"text": "known true phase combinations. The electron density was",
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"text": "calculated for all phase combinations, and the corresponding",
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"text": "IK and I\u0003 indicators were calculated.",
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"text": "Fig. 3(a) shows the distribution of IK and I\u0003 for all phase",
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"text": "combinations at Vfrac ¼ 0:4 of the G-PS model. The points are",
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"text": "distributed from the lower left to upper right. Therefore, there",
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"text": "is an approximate positive correlation between IK and I\u0003. The",
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"text": "Rp values of the points tend to be smaller in the lower left",
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"text": "region; points with Rp of approximately 0.1 or less are",
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"text": "concentrated in the lower left region. IK and I\u0003 for the true",
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"text": "phase combination are in the lower left corner,which indicates",
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"text": "that both indicators of the true phase are almost the smallest,",
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"text": "as expected; the same is true when Vfrac is 0.2 and 0.6 in the",
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"text": "other",
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"text": "models",
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{
"page": 5,
"text": "(Fig.",
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{
"page": 5,
"text": "S1",
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"text": "in",
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"text": "the",
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"text": "supporting",
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"text": "information).",
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"text": "However, when Vfrac is 0.8, IK for the true phase combination",
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"text": "is roughly minimized, whereas I\u0003 is clearly not minimized [Fig.",
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"text": "3(b)]. The tendency that the indicator for the true phase",
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"text": "combination is not minimized when Vfrac is large is also true",
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"text": "for the G-CMCS model and the other surface-based models",
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"text": "(Fig. S1). For example, in the G-CMCS model, both IK and I\u0003",
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"text": "are not minimized when Vfrac is 0.7 or 0.8.",
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"text": "The Rp values of the phase combinations with the minimum",
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"text": "indicators in the G-PS and G-CMCS models are shown in Fig.",
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"text": "4. When the volume fraction is smaller than 0.6, R of the",
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"text": "p",
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"text": "phase combinations at the minimum indicators is approxi-",
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"text": "mately 0.1 or less. Therefore, in this range of volume fractions,",
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"text": "both IK and I\u0003 indicators are useful for phase retrieval. When",
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"text": "Vfrac is 0.7 or 0.8, some of the phase combinations at the",
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"text": "minimum indicator are Rp > 0.2, which indicates that the phase",
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"text": "retrieval by the indicator is not realized. In particular, the",
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"text": "phase combination with the minimum I\u0003 differs significantly",
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"text": "from the true combination for Vfrac ¼ 0:8 with all the models.",
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"text": "This indicates that when Vfrac is large, the constraint that the",
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"text": "difference",
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"text": "between",
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"text": "minimum",
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"text": "and",
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"text": "electron",
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"text": "density is minimal does not hold. On the other hand, the Rp",
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"text": "value for minimum IK is relatively small, even when the",
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"text": "volume fraction is 0.7 or 0.8. Including other models, Rp > 0.2",
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"text": "with minimum IK is limited to three conditions: the G-CMCS",
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"text": "model with Vfrac ¼ 0:8 and the P-PS model with Vfrac = 0.7 and",
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"page": 5,
"text": "434 Toshihiko Oka \u0002 Liquid crystal bicontinuous phases",
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"text": "Rp of",
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"text": "minimum",
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"text": "IK",
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"text": "0",
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"text": "retrieval to some extent, even if",
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"text": "based on the eigenvalues.",
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"text": "electron density h½\u0003ðrÞ\u00044i (Luzzati et al., 1988), was compared",
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"text": "with I\u0003. In all models, when Vfrac = 0.2, the Rp value of the",
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"text": "(Figs. 3 and S2). When Vfrac = 0.7 for D-PS and D-CMCS and",
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"text": "larger than that based on I\u0003. Although there are conditions in",
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"text": "which the Rp values are similar for both indicators, I\u0003 gives",
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"text": "better results than h½\u0003ðrÞ\u00044i under several conditions. Both I\u0003",
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"text": "electron",
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"text": "densities.",
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"text": "h½\u0003ðrÞ\u00044i",
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"text": "uses",
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"text": "information",
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"text": "from",
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"text": "the",
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"text": "intermediate-electron-density region, which is not used in I\u0003.",
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"text": "Figure 4",
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"text": "Rp of the phase combinations with the minimum indicators in models",
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"text": "b(oarsaendgoensq(uaa)rGes-)P,Sanadndh½\u0003(bðr)Þ\u0004G4i-C(sMkyC-bSluseurtfraicaensg:leI\u0003s)(.black circles) and IK",
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"text": "Acta Cryst. (2022). A78, 430–436",
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"text": "This may cause the phase retrieval results of I\u0003 to be better",
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"text": "under several conditions.",
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"text": "5.2. Phase retrieval for experimental data",
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"text": "The experimental data of LLC bicontinuous cubic phases",
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"text": "acquired in previous X-ray single-crystal structure analyses",
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"text": "(Oka, 2017; Oka et al., 2018, 2020) were used as test data. In",
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"text": "the",
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"text": "previously derived from the model analysis were taken as the",
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"text": "true combinations.",
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"text": "Monoolein, a type of lipid, and water form three type II",
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"text": "bicontinuous cubic phases with TPMSs of G, D and P (Oka,",
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"text": "2017). The number of independent structure factors is from 8",
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"text": "to 14. Vfrac can be estimated to be around 0.43 to 0.54 (Table",
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"text": "S2). The scatter plot shows that IK and I\u0003 are roughly posi-",
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"text": "tively correlated, and that the Rp value is smaller toward the",
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"text": "lower left [Fig. S3(a)]. This is the same as when Vfrac \b 0:6 in",
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"text": "the model densities. The phase combinations obtained from",
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"text": "the structural models in the previous paper are also located at",
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"text": "the lower left of the scatter plot. In the phase combinations",
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"text": "with the minimum indicators, the calculated R values were",
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"text": "p",
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"text": "almost zero (Table 1). This shows a good agreement between",
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"text": "the structure shown by the indicator-based phase retrieval",
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"text": "method and the structural model in the previous paper (Oka,",
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"text": "2017). For the two type II bicontinuous cubic phases of",
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"text": "phytantriol with TPMSs of G and D, the number of inde-",
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"text": "pendent reflections is 21, and the Vfrac values are 0.57 and 0.66",
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"text": "(Oka et al., 2018). These data are also similar to those of",
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"text": "monoolein, and the structure shown by the phase retrieval",
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"text": "method and the structure model in the previous paper (Oka et",
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"text": "al., 2018) are in good agreement (Table 1).",
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"text": "Hexaethylene",
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"text": "glycol",
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"text": "monododecyl",
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"text": "ether",
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"page": 6,
"text": "(C12EO6)",
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"text": "and",
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"text": "water form a type I bicontinuous cubic phase of G TPMS, with",
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"text": "Vfrac 0:72 (Oka et al., 2020). In the scatter plot of IK and I\u0003,",
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"text": "the distribution of points is split in two on the lower left side",
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"text": "[Fig. S3(c)]. IK is a minimum near the point of the phase",
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"text": "combination that was considered true in the previous paper",
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"text": "(Oka et al., 2020) (I\u0003 20), whereas I\u0003 is not a minimum near",
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"text": "the point. On the other hand, close to the point where I\u0003 is",
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"text": "corresponding electron densities are shown in Fig. 5. The",
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"text": "electron density of the minimum IK is in very good agreement",
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"text": "with the electron density in the previous paper (Oka et al.,",
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"text": "2020). A comparison of the electron density of the minimum",
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"text": "IK [Fig. 5(b)] with Figs. 1(b) and 1(c) indicates that the width",
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"text": "Figure 5",
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"text": "Electron densities of C12EO6 calculated with phase combinations of (a)",
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"text": "minimum I\u0003 and (b) minimum IK.",
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"text": "Acta Cryst. (2022). A78, 430–436",
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"text": "research papers",
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"text": "of the high-electron-density region on the TPMS side is wider,",
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"text": "which is consistent with the large volume fraction on the",
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"text": "TPMS side of C12EO6. With the minimum I\u0003, the high-",
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"text": "electron-density region on the TPMS side is narrower and the",
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"text": "electron-density",
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"text": "regions",
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"text": "network",
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"text": "sides",
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"text": "compared with the minimum IK. If the volume fraction is",
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"text": "known in advance, then the electron density indicates that the",
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"text": "are",
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"text": "summarized in Table 1. The Rp values for the phase combi-",
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"text": "nation with the minimum indicator h½\u0003ðrÞ\u00044i are comparable",
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"text": "with those of I\u0003 for four of the six experimental data sets. On",
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"text": "is approximately 0.1 for monoolein P and 0.2 for D, which are",
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"text": "electron densities show similar structures, but there are non-",
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"text": "negligible differences in the details (Fig. S6). Considering the",
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"text": "the widest range of applicable conditions, followed by I\u0003 and",
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"text": "the Fourier synthesis of electron density, \u0003ðrÞ. The truncation",
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"text": "errors may make the indicatorsinaccurate. However,given the",
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"text": "observed amplitudes, the amplitudes of unobservable struc-",
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"text": "ture factors are probably less than 1% of the maximum",
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"text": "amplitude. The amplitude decreases rapidly at high scattering",
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"text": "angles due to the structural disorder of the liquid crystal (this",
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"text": "structure model, i.e. indicators, seems insignificant. On the",
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"text": "6. Conclusion",
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"text": "The indicators I\u0003 and IK were determined to be useful for the",
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"text": "crystallographic phase retrieval in LLC bicontinuous phases.",
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"text": "The phase combination with the minimum indicator was very",
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"text": "was less than 0.6. Even for volume fractions of approximately",
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"text": "In the scatter plots of IK and I\u0003, when Vfrac is small, the points",
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"text": "extending to the lower left do not spread much [Fig. 3(a)]. On",
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"text": "corner branch and spread out [Fig. 3(b)], which seems to be",
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"text": "The model used for the phase retrieval was a simple",
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"text": "and the network side. On the other hand, the sample of",
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"text": "complicated structure. In the case of a type I bicontinuous",
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"page": 6,
"text": "Toshihiko Oka \u0002 Liquid crystal bicontinuous phases 435",
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"text": "research papers",
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"text": "cubic phase such as C12EO6, the polar region is located on the",
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"text": "TPMS side and the nonpolar region is located on the network",
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"text": "side. The hydrophobic chain of the amphiphilic molecule is",
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"text": "located in the nonpolarregion, water is located in the TPMS in",
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"text": "polar region. Therefore, the electron density differs among the",
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"text": "three regions, with the hydrophilic part of the amphiphilic",
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"text": "molecule having the highest electron density [Fig. 5(b)]. Phase",
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"text": "retrieval was possible even in such a system.",
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"text": "It takes a long time to calculate the indicators of electron",
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"text": "densities for all phase combinations; especially for IK, it was",
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"text": "necessary to calculate the eigenvalues of the Hessian matrix at",
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"text": "each voxel, which takes a long time. On the other hand, the",
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"text": "structures of the LLC bicontinuous cubic phase have highly",
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"text": "symmetric space groups of Ia3d, Im3m and Pn3m. Therefore,",
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"text": "the computational time can be reduced by calculating only in",
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"text": "the asymmetric units. In addition, the Babinet principle does",
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"text": "C12EO6–8 (Oka et al., 2018, 2020). When the number of voxels",
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"text": "was 323, the computation times of the Python script were 16 to",
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"text": "conditions would thus take 10 to 14 days. It may be possible to",
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"text": "increase the calculation speed by revising the algorithm. If the",
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"text": "436 Toshihiko Oka \u0002 Liquid crystal bicontinuous phases",
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"text": "Funding information",
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"text": "The following funding is acknowledged:",
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"text": "(grant Nos. JP20H04634, JP18K03557).",
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[] |
[] |
[
{
"page": 1,
"text": "Molecular Crystals and Liquid Crystals Science and",
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"page": 1,
"text": "Technology. Section A. Molecular Crystals and Liquid",
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},
{
"page": 1,
"text": "ISSN: 1058-725X (Print) (Online) Journal homepage: www.tandfonline.com/journals/gmcl19",
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},
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"page": 1,
"text": "Density-Functional Theory of Liquid Crystal",
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},
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"page": 1,
"text": "Surfaces",
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},
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"page": 1,
"text": "Yashwant Singh & Jokhan Ram",
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"page": 1,
"text": "To cite this article: Yashwant Singh & Jokhan Ram (1996) Density-Functional Theory of Liquid",
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},
{
"page": 1,
"text": "Crystal Surfaces, Molecular Crystals and Liquid Crystals Science and Technology. Section A.",
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"page": 1,
"text": "Molecular Crystals and Liquid Crystals, 288:1, 143-152, DOI: 10.1080/10587259608034591",
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"text": "Published online: 24 Sep 2006.",
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"text": "Submit your article to this journal",
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"text": "Article views: 27",
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"page": 1,
"text": "View related articles",
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"page": 1,
"text": "Full Terms & Conditions of access and use can be found at",
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},
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"page": 1,
"text": "https://www.tandfonline.com/action/journalInformation?journalCode=gmcl20",
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[{"page":1,"text":"Current Applied Physics 12 (2012) 1387e1412","rect":[235.05307006835938,54.185859(...TRUNCATED) |
[{"page":1,"text":"molecules","rect":[74.43930053710938,71.11058044433594,174.35299861995279,53.7426(...TRUNCATED) |
[{"page":1,"text":"Cite This: Acc. Chem. Res. 2019, 52, 1653−1664","rect":[251.25770568847656,84.0(...TRUNCATED) |
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