Modeling of self-organization processes in crystal-forming systems: Symmetry and topology code for the cluster self-assembly of crystal structures of intermetallic compounds

We performed the combinatorial and topological modeling of 1D, 2D, and 3D packs of symmetrically connected metal clusters in the form of tetrahedra А₄. Three types of 1D chains with tetrahedral connectivity of 4, 6, and 8 were used to model 2D layers L-1, L-2, and L-3 and 3D frameworks FR-1, FR-2, FR-3, and FR-4. The model structures of the identified suprapolyhedral precursor clusters were used in topological analysis of crystal structures of intermetallic compounds (program package TOPOS and data bases ICSD and CRYSTMET). A match was found between the topological models of tetrahedral 3D frameworks and all types of crystal structures formed in binary systems; in Au–Cu: FR-1 for Cu₃Au-cP4 (Auricupride), Cu₂Au₂-tP2 (Tetraauricupride), CuAu₃-cP4 (Bogdanovite), and Cu_2–x Au_{2 + x} -cF4; in Mg–Cd: FR-3 for Mg₃Cd-hP8, Mg₂Cd₂-oP4, MgCd₃-hP8, and Mg_2–x Cd_{2 + x} -hP2; in Li–Hg: FR-2 for Li₃Hg-cF16 and Li₂Hg₂-cP2 and FR-3 for LiHg₃-hP8; in ternary system Li–Ag–Al: FR-2 for LiAg₂Al-cF16 and Li₂AgAl-cF16; and in quaternary system: framework FR-2 for LiMgPdSn-cF16. Framework FR-4 was identified in ternary intermetallic compounds A(Li₂Sn₂)-tI20, where A = Cu, Ag, Au. The structures of precursor nanoclusters were identified for other most abundant types of crystal structures of intermetallic compounds. For this purpose, we used the algorithms for partitioning the structural graph into nonintersecting cluster substructures and constructed the basal 3D network of the crystal structure in the form of a graph whose nodes correspond to the positions of the centers of precursor clusters. The cluster self-assembly was modeled for the following intermetallic compounds: Mg₂Cu₄-cF24, MgSnCu₄-cF24, (ZrCu)Cu₄-cF24,Mg₂Zn₄-hP12, (CaCu)Cu₄-hP6, Cr₃Si-cP8, Lu₃Co(Fe₃C)-cP16, Ca₂Ge₂(Cr₂B₂)-oC8, Y₂Ni₂(Fe₂B₂)-oP8, AlB₂-hP3, Ca₂Ge-oP12, CaHg₂-hP3, Co₂Ge(Ni₂In)-hP6, Cs₂Hg₄-oI12, Ba₄Po₄-cF8, Mn₅Ge₃-hP16, and NaZn₁₃-cF112. The symmetry and topological code of self-assembly from precursor nanoclusters was reconstituted for all crystal structure types of intermetallic compounds as: primary chain → microlayer → microframework. An abundance frequency analysis of topological and symmetry routes for the generation and evolution of precursor clusters enabled us to elucidate the crystal-formation laws in intermetallic systems on the microscopic level.     

Symmetry and topology code of cluster self-assembly of icosahedral framework structures of boron and borides

The topological types of suprapolyhedral clusters composed of i-B₁₂ icosahedra have been modeled. The models of icosahedral supraclusters have been used in analysis of the crystal structures of boron and borides (the TOPOS program package). To identify nanocluster precursors in crystal structures, there have been used special algorithms for partitioning structural graphs into disjoint substructures and constructing a basis 3D network of the structure as a graph with the nodes corresponding to the positions of the centroids of the cluster precursors. The cluster self-assembly have been modeled for 25 types of icosahedral framework structures of boron—B₁₂-hR ₁₂, (B₁₂)2(B₂)₂-oP ₂₈, (B₁₂)₄B₂-P50, B₁₉₆-tP ₁₉₆, and B₃₃₃-hR ₃₃₃; binary borides—(B₁₂)O₂-hR ₁₄, (B₁₂)P₂-hR ₁₄, and (B₁₂)(CBC)-hR ₁₅; templated metal borides—Na₂(B₁₂)₂B₆-oI ₆₄, Mg₂(B₁₂)B₂-oI ₆₈, Tb(B₁₂)(B₄)-mI ₆₀, Al₄(B₁₂)₄B₈-oC ₈₈, (B₁₂)₄(Si4)₄-oI ₆₄, (B₁₂)₄B₂Be₄-tP ₅₈, Ti₂(B₁₂)₄B₂-tP ₅₂, Sc₁₂B₁₈₀-tP ₁₉₂, Cu₄Sc₁₂B₁₈₀-tP ₁₉₂, Si_1.5Sc₉B₁₇₈-tP ₂₁₆, Mg₂₈B₃₆₀-oP ₃₈₈, Al₂₈B₃₅₂-oP ₃₈₄, Si₂₈B₃₅₂-oP ₃₀₆, Y₂₄(B₁₅₆)₈(B₃₉)₈-cF1944, Sc₁₀B₃₁₅-hR339, and Li₂₄B₃₁₅-hR336. The symmetry and topology code of the crystal structure self-assembly from nanocluster precursors in the form of primary chain → microlayer → microframework has been completely restored. Frequency analysis of various topological and symmetry pathways for the formation and evolution of cluster precursors makes it possible to elucidate crystal-formation trends in inorganic systems at the microscopic level.     

Modeling of self-organization processes in crystal-forming systems. Structural mechanism of self-assembly of zirconosilicate Na2ZrSi2O7 from suprapolyhedral clusters

Topological analysis of the crystal structure of Na₂ZrSi₂O₇ (parakeldyshite, space group P1^–) with an MT framework, where M are ZrO₆ octahedra and T are SiO₄ tetrahedra, was carried out by the method of coordination sequences (TOPOS.3.2 program package), and the self-organization of this structure was modeled. The cyclic-type suprapolyhedral cluster precursor Na₂M₂T₄ with the local symmetry 1^– was identified by bicolor decomposition of the 4646+664 net. The cluster is composed of six polyhedra with two Na atoms located in the center. The precursors control the evolution of high-level crystal-forming clusters. The cluster coordination number is six. The centers of eight cluster precursors in the superprecursor of the Na₂ZrSi₂O₇ structure are related by translation vectors.     

Theory of cluster self-organization for crystal-forming systems: A model of transition from disodered to ordered systems

The current state of ideas concerning the self-organization of crystal-forming systems where long-range order spontaneously appears in the arrangement of nanolevel structural units of any nature (micro- and macromolecules or atomic clusters) that initially existed in a dynamic state as a chaotic mixture is considered. Three partially overlapping stages of self-organization of a system accepted in physical models of “order-disorder” kinetic transitions are matched to those used in supramolecular chemistry. An algorithmically constructed model of transition from disordered to hierarchically ordered systems is considered. The geometrical and topological modeling of density fluctuations of n-atomic species (clusters) An in a crystal-forming medium is carried out. A specific set of An clusters with block-diagonal connectivity matrices is recognized. These types of clusters (S ₃⁰), having “sectional” or “hierarchic” partition, are defined as precursors of crystal structures that are capable of evolving most rapidly to give rise to a long-range order in structures. For an S ₃⁰ ring cluster shaped as a triangle, geometrical and topological modeling is carried out for all of the eight topologically and symmetrically possible types of S ₃¹ primary chains built of S ₃⁰ using theory of one-dimensional symmetry groups. Thirty three structural variants of morphologically and topologically different types of S ₃² micronets described by two-dimensional groups of symmetry are considered. Algorithms are presented for combinatorial and topological analysis to search for precursor clusters and restore a three-dimensional net of covalent and noncovalent bonds in a crystal structure by the matrix (cluster) self-assembly mechanism. The model advanced is universal. Examples of self-assembly of a series of cluster-assembled structures of AB₂ alloys of the unique Friauf-Laves family (which counts in 1400 of binary and ternary compounds) are given: for MgCu₂ (cF24) (with its superstructures of ZrCu ₅ and MgSnCu₄ types), MgZn₂ (hP12), and MgNi₂ (hP24) (from AB₂ or A₂B + B₃ three-atom clusters); for ZrZn₂₂ icosahedral structures (from a suprapolyhedral cluster built of a ZrZn₁₆ Friauf polyhedron and two ZnZn₁₂ icosahedra); NaCd₂ (from one A cluster with 61 atoms and two B clusters with 63 atoms); and for a bimolecular compound C₇₈H₃₀ (which is formed of fullerene C₆₀ and a C₂₈H₃₀ molecule). The scenario of formation of self-curving nets with icosahedral symmetry is considered: to form a B₁₂ icosahedron from two isomers with n = 3, a C₂₀ dodecahedron from two isomers with n = 5, and C₆₀ fullerene from pentagonal clusters with n = 5.     

Cluster self-organization theory for crystal-forming systems: The geometrical and topological model of formation, selection, and evolution of precursor nanoclusters of molecular and framework compounds

This review concerns the contemporary state of the problem of self-organization in crystal-forming systems, where a long-range order appears spontaneously in the arrangement of nanoscale structural units of any nature (atomic clusters and molecules), which initially existed as a chaotic mixture. Examples are provided where combinatorial topological analysis algorithms are used to restore, from structure data, the convergent matrix self-assembly code of crystal structures in the form of the sequence of significant elementary events e _i . For a cyclic six-node cluster S ₃ ⁰ , the geometrical and topological modeling of various self-organization levels of hierarchic structures was carried out for six types of primary chains S ₃ ¹ , fifteen types of networks S ₃ ² , and thirty types of frameworks S ₃ ³ . The model is universal and has been used to model the self-assembly of the following crystal structures: monomolecular compound S₆ and bimolecular compound S₆ + S₁₀, ozone O₃, benzene C₆H₆, cubane C₈H₈, Zn₄O₄ (NaCl structure type), carbon oxides C₆-GRA (graphite), C₆-DIA (diamond), and C₆-LON (lonsdaleite), boron nitrides B₃N₃-GRB, B₃N₃-DIA, and B₃N₃-LON, Ni₃As₃-NIC, B₆(OH)₁₆, zeolite K₃(Al₂Si₄O₁₂(OH)-LIT, Na₂ZrSi₂O₇-PKL (parakeldyshite), La₃Ga₅GeO₁₄ (LGG), and La₃GaGe₅O₁₆ (LAN). It is for the first time that structural invariants are recognized in topologically different crystal structures of chemical systems. Bifurcations in the evolution pathways of precursor clusters (structural branching points) have been determined for the formation of three-dimensional periodic structures. Frequency analysis carried out for the topological and symmetry pathways in the formation and evolution of clusters (primary chain S ₃ ¹ -microlayer S ₃ ² -microframework S ₃ ³ ) elucidated new crystal-formation trends in diverse chemical systems at the microscopic level.     

Combinatorial-topological modeling of the cluster self-assembly of zeolite crystal structures: computer search for molecular templates for new zeolite ISC-2

The combinatorial-topological modeling of 3D periodic packings of layers composed of T₁₂ polyhedral clusters (t-hpr tiles in the form of hexagonal prisms) was carried out. The T12 clusters are among the most abundant units in the crystal structures of zeolites. The layers were produced by decoration of the vertices of the square and hexagonal (graphite-like) nets with T₁₂ clusters. All combinatorially possible patterns of 3D frameworks, which were constructed based on packings of decorated square nets, correspond to known zeolite structures: CHA (mineral chabazite, Ca₆(H₂O)₄₀Al₁₂Si₂₄O₇₂), AEI (AlPO-18, Al₂₄P₂₄O₉₆), SAV ((C₁₈H₄₂N₆)₂(H₂O)₇Mg₅Al₁₉P₂₄O₉₆), and KFI (Na₃₀(H₂O)₉₈Al₃₀Si₆₆O₁₉₂). The modeling using the same scheme and a decorated hexagonal net gave rise to the frameworks of three known zeolites, GME (gmelinite, (Ca,Na)₄(H₂O)₂₄A_l8Si₁₆O₄₈), AFX (SAPO-56, H₃Al₂₃Si₅P₂₀O₉₆), and AFT (AlPO-52, Al₃₆P₃₆O₁₄₄), as well as of one previously unknown hypothetical zeolite ISC-2 with the unit cell parameters a = 13.90 Å, c = 30.00 Å, V = 5019.7 ų, sp. gr. \(P\bar 6m2\). Zeolite ISC-2 contains a cavity with a new t-isc-2 topology [4²¹.6².8¹⁵], which is responsible for its unique framework. An analysis of the specially created database of topological types of molecules (TTM collection) containing geometric and topological characteristics of more than 300000 different molecules suggested an organic structure-directing agent, which stabilizes the t-isc-2 cavity and which can be used for the synthesis of ISC-2.     

Cluster self-organization of Li-and TR-containing germanate systems: Suprapolyhedral precursors and self-assembly of LiScGeO4 and LiHo3(GeO4)2F2 crystal structures

The combinatorial and topologic analysis (the TOPOS 4.0 program package, the coordination sequences method) is carried out for the crystal structures of the orthogermanates Li^[6]Sc^[6]Ge^[4]O₄ (the olivine type, space group Pnuma) and Li^[6]Ho^[8]Ho ₂ ^[7] (GeO₄)₂F₂ (space group I2/c). The same type of 2D TR,Ge-net with the Schläfli index of 3⁴4² + 3²4² and the site ratio of TR: Ge = 1: 1 is discovered for both structures. Four-polyhedral ring precursor clusters (TR)₂T₂ are identified using the two-color decomposition of structural graphs. All the clusters have a symmetry center; they differ in the types of TR polyhedra (ScO₆ and HoO₆F), which are linked through GeO₄ orthotetrahedra into a ring. The Li atoms reside above and under the centers of the clusters. The Li₂(TR)₂T₂ clusters determine the formation of crystal-forming clusters of a higher level by means of matrix self-assembly. The coordination number of the precursor clusters in the 2D net is six, which is the highest possible value.     

Syntheses and molecular structures of new ferrocenylacetylide-bridged binuclear cobalt carbonyl cluster compounds

The reaction of ferrocenylacetylide compounds with Co₂(CO)₈ at room temperature affords four complexes bearing ferrocenyl units with approximately tetrahedral (μ-alkyne)dicobalt moieties [R–(C≡C) _n –R′] [Co₂(CO)₆] _{n ′} [R?=?C₅H₅FeC₅H₄-C(CH₃)₂-C₅H₄FeC₅H₄, R′?=?H, n?=?1, n′?=?1 (1); R?=?C₅H₅FeC₅H₄ [ferrocenyl (Fc)], R′?=?–CH=CHCl, n?=?1, n′?=?1 (2); R?=?Fc, R′?=?Fc, n?=?2, n′?=?1 (3), n′?=?2 (4)]. The compounds were characterized by elemental analysis, IR, ¹H(¹³C) NMR, MS and single-crystal X-ray diffraction analysis. The X-ray analyses show that coordination of the carbon–carbon triple bond and the dicobalt unit result in the formation of a Co₂C₂ tetrahedral core, and the substituents on the acetylenic units show a distortion from linearity that reflects this coordination mode.     

Cluster self-organization of silicate and germanate systems: Suprapolyhedral precursor clusters and self-assembly of orthotetrahedral structures in Na,TR-germanates (silicates)

The geometrical and topological analysis of all known types of the orthotetrahedral structures of Na,TR-germanates and their silicon analogues has been carried out using computer methods (TOPOS 4.0 program package). The full 3D reconstruction of the self-assembly mechanism of crystal structures has been performed as follows: precursor cluster-primary chain-microlayer-microframework (supraprecursor). For Na₂HLaSiO₅, NaHo₄(GeO₄)₂O₂OH, NaScGeO₄, and NaSm₃Ge₂O₈(OH)₂, the same type of 2D TR, T-network has been recognized: 433334 + T 4433. For Na₂HScGeO₅, network TR 44444 + T 444 has been recognized. The coordination number (CN) of a precursor cluster in 2D networks is six. In all structures, the invariant type of cyclic four-polyhedral precursor clusters built of tetrahedron-linked TR-polyhedra has been identified with CNs being eight, seven, or six. In the Na₅Y₄Si₄O₁₆F structure, a tubular-type primary chain in which precursor clusters are tetrahedron-linked TR polyhedra with CN = 8 has been recognized. Their stacking in a layer is characterized by the network TR 8 8 4 + T 8 4 8, where 8 corresponds to the cross section of the primary chain. In a 3D network, the total number of neighboring tubular primary chains linked to the main chain is four. In the structures with TR: T = 1: 1 or 1.5: 1, the positions above and below the center of the precursor cluster are occupied by Na atoms; in NaHo₄(GeO₄)₂O₂(OH), where TR: T = 2: 1, these positions are occupied by an Na atom and a TR atom.     

Modeling of ammonothermal growth processes of GaN crystal in large-size pressure systems

Gallium nitride (GaN) is a wide-bandgap semiconductor material with a wide array of applications in optoelectronics and electronics. Modeling of the fluid flow and thermal fields is discussed, and simulations of velocity and volumetric-flow-rate profiles in different pressure systems are shown. The nutrient is considered as a porous media bed, and the flow is simulated using the Darcy?CBrinkman?CForchheimer model. The resulting governing equations are solved using the finite-volume method. We analyzed the heat and mass transfer behaviors in autoclaves with diameters of 2.22, 4.44, and 10 cm. The effects of baffle design on flow pattern, and heat and mass transfer in different autoclaves are analyzed. For the research-grade autoclave with diameter of 2.22 cm, the constraint for the GaN growth is found to be the growth kinetics and the total area of seed surfaces in the case of baffle opening of 10%. For large-size pressure systems, the concentration profiles change dramatically due to stronger convection at higher Grashof numbers. The volumetric flow rates of the solvent across the baffles are calculated. Since ammonothermal growth experiments are expensive and time consuming, modeling becomes an effective tool for research and optimization of ammonothermal growth processes.     

Electron-density topology in molecular systems: paired and unpaired densities

This work studies the partitioning of the electron density into two contributions which are interpreted as the paired and the effectively unpaired electron densities. The topological features of each density field as well as of the total density are described localizing the corresponding critical points in simple selected molecules (local formalism). The results show that unpaired electron-density concentrations occur out of the topological bonding regions whereas the paired electron densities present accumulations inside those regions. A comparison of these results with those arising from population analysis techniques (nonlocal or integrated formalisms) is reported.     

Cluster self-organization of Na,Ti-silicate systems: Suprapolyhedral precursors and self-assembly of crystal structures of Na2Ti2Si2O9 (Ramzaite) and Na2TiSiO5 (paranatisite)

The initial stages of formation of precursor clusters are considered in an evolving system containing various types of polyhedra: T tetrahedra and M polyhedra (pyramids, octahedra, and others). A graph topological representation of the precursor clusters of different self-organization levels of a chemical system is given. The model has been applied to find precursor clusters for Na,Ti-silicates that crystallize in the Na-Ti-Si-O(H) systems. For ramzaite Na₂Ti₂Si₂O₉ (RAM) and a dimorph of natisite (NAT), namely, paranatisite Na₂TiSiO₅ (PNAT), computer techniques (the TOPOS 4.0 program package) have been used to perform the full 3D reconstruction of structure self-assembly: precursor cluster-primary chain-microlayer-microframework (supraprecursor). New types of eight-polyhedral ring precursor clusters have been identified. The packing specifics of precursor clusters in crystal-forming microlayers determine the platy habit of Na,Ti-silicate single crystals.     

Modeling of self-organization in crystal-forming MT systems: The structural mechanism of self-assembly from suprapolyhedral clusters for framework titanophosphates NaTiPO<Subscript>5</Subscript> (SYN), NaTiPO<Subscript>5</Subscript> (TIT), and KTiPO<Subscript>5</Subscript> (KTP)

Ring precursor clusters are derived for the MT-system containing two different polyhedra T and M, where T stands for a TO₄ tetrahedron and M is in the general case an MO_n polyhedron with the number of vertices n ≥ 5, i.e., a pyramid, octahedron, or others. The topological representation of the precursor cluster is given in the form of two-colored graphs. The model developed for describing the formation and evolution of clusters that form periodic structures is used to search for the precursor clusters of framework phosphate structures: NaTiPO₅ (SYN), NaTiPO₅ (TIT), and KTiPO₅ (KTP). Computer methods are used to perform the full 3D reconstruction of the self-assembly of phosphate crystal structures: precursor cluster—primary chain—micro-layer—microframework (supraprecursor). New eight-polyhedral ring precursor clusters are identified. The crystal-forming polynodal 2D nets with a hierarchic superstructure are recognized: M8833+T883 for SYN (NaTiPO₅), M84634+T843+M836+T864 for TIT (NaTiPO₅), M8939+2M8339+M839+3T893+T89 for KTP (KTiPO₅), and M8484+M88+2T848 for PNAT (Na₂TiSiO₅). The coordination numbers of the clusters in all 2D nets are four.     

Crystal and molecular structures of four model compounds for liquid crystal dimers with a methylene spacer of various lengths

The crystal and molecular structures of four model compounds for liquid crystal dimers namely, 4,4-[octyl]bis-acetophenone (B(AcP)8), 4,4-[heptyl]bis-acetophenone (B(AcP)7), 4,4-[hexyl]bis-acetophenone (B(AcP)6), and 1,1-(1,6-hexyldion)bis-benzene (DP6D), have been determined in order to gain an insight into observed differences in the textures of liquid crystalline phases of compounds with odd and even methylene spacers. All four compounds exhibit extended conformations with an all-trans conformation of the methylene chain but a twist between phenyl rings of about 125°, except DP6D for which the benzene groups lie in plane with the methylene chain. Half a molecule is necessary to represent the asymmetric unit of compounds with even numbers n of methylene groups in the spacer and belong to centrosymmetric space groups. The model compound with an odd value of n is non-centrosymmetric and shows another type of packing arrangement which may cause different textures and behaviour for dimesogenic compounds in the liquid crystalline state.     

Infrared spectroscopy of niobium oxide cluster cations in a molecular beam: identifying the cluster structures

Infrared spectra of niobium oxide cluster cations are measured via IR multiple photon dissociation spectroscopy in the 400-1650 cm(-1) region. The cluster cations are obtained directly from a laser vaporization source and irradiated with the infrared light emitted by a free electron laser. For those oxide clusters that fragment after excitation, the IR spectra are recorded by measuring the cluster intensity changes as a function of the IR wavelength. The spectra of all examined oxide clusters exhibit two main absorption features that can be assigned to vibrations of terminal (Nb=O) or bridging (Nb-O-Nb) oxide groups. For selected clusters DFT calculations at the B3LYP/LACVP* level have been performed and the calculated vibrational spectra are compared to the experimental data to identify the gas phase structures of the clusters.     

Synthesis and crystal structures of new sodium phenolate compounds: coordination chemistry

Four new sodium complexes of phenolate and bisphenolate ligands have been synthesized and characterized by NMR spectroscopy and X-ray crystallography to study their coordination chemistry. The monoanionic tridentate [ONN] phenolate ligand gave a dimeric compound [Na₂L₂] (2), which crystallized in the orthorhombic crystal system, where the sodium ions have four coordination environments. The dianionic tridentate [ONO] phenolate ligand gave a dimeric [Na₂(L^IH)₂] (4) compound in the tetragonal crystal system. The sodium ions Na(1) and Na(1?) are four-coordinate both having a tetrahedral geometry with the O–Na–O angle being ca. 93°, the O^N^O ligand string comprising a tridentate ligand. Interestingly, despite the steric bulk of N(SiMe₃)₂, a mixture of compounds [NaL] (2) and NaN(SiMe₃)₂ was isolated as a dimeric structure [Na₂L(N(SiMe₃)₂)]₂ (5) crystallized in the monoclinic crystal system. Na(1) is four-coordinate bonding to the phenolic oxygen atom and two N atoms of the ligand L and the N of the N(SiMe₃)₂ ligand. The coordination around Na(1) is tetrahedrally distorted square planar with the ‘cis’ angles ranging from 75.11(4) to 117.40(5)° and the ‘trans’ angles being 140.87(4) and 154.82(5)°. Na(2) is three-coordinate, bonding to the two phenolate oxygen atoms and the N atom of the N(SiMe₃)₂ ligand. Na(2), however, is not coplanar with these atoms being displaced 0.42 Å from it. The coordination chemistry for 5 is very intriguing as the sodium ions have mixed four- and three-coordination numbers, probably due to the steric hindrance of the silylamide groups.     

Cyano terminated tolane compounds for polymer dispersed liquid crystal application: relationship between cyano terminated tolane based molecular structures and electro-optical properties

ABSTRACT

The structures of the liquid crystal (LC) molecules have a key role in impacting the electro-optical performance of a polymer dispersed liquid crystal (PDLC) film. In this paper, the relationship between the LC molecular structures and the electro-optical properties of PDLC films is investigated based on an unexplored cyano-terminated tolane compounds (CTTCs) doped E8 LCs/UV polymers system. Due to the high polarity of CTTCs, LCs doped with the cyano-terminated tolane (CTT) molecules exhibit high birefringence and large positive dielectric anisotropy. On the whole, PDLC films doped with the CTT molecules exhibit a lower driving voltage than that doped with the pure E8. More excitingly, PDLC films based on CTT molecules with larger length-to-width ratio and longer conjugated system show higher contrast ratio (CR) and faster response time. Eventually, the mechanism of the effects of CTT-based molecular structures and the relationship between the electro-optical performance of PDLC films and CTT molecules are illustrated. This work paves a new way for optimising the electro-optical properties of PDLC films.     

Interfacial self-organization of bolaamphiphiles bearing mesogenic groups: relationships between the molecular structures and their self-organized morphologies

This article discusses the relationship between the molecular structure of bolaamphiphiles bearing mesogenic groups and their interfacial self-organized morphology. On the basis of the molecular structures of bolaamphiphiles, we designed and synthesized a series of molecules with different hydrophobic alkyl chain lengths, hydrophilic headgroups, mesogenic groups, and connectors between the alkyl chains and the mesogenic group. Through investigating their interfacial self-organization behavior, some experiential rules are summarized: (1) An appropriate alkyl chain length is necessary to form stable surface micelles; (2) different categories of headgroups have a great effect on the interfacial self-organized morphology; (3) different types of mesogenic groups have little effect on the structure of the interfacial assembly when it is changed from biphenyl to azobenzene or stilbene; (4) the orientation of the ester linker between the mesogenic group and alkyl chain can greatly influence the interfacial self-organization behavior. It is anticipated that this line of research may be helpful for the molecular engineering of bolaamphiphiles to form tailor-made morphologies.     

Cluster self-organization of TR-containing silicate and germanate systems: Suprapolyhedral precursors and self-assembly of A2HMTO5 (A = Li, Na; M = Sc, Lu, Yb) crystal structures with MTO5 frameworks

The combinatorial topological analysis is carried out using the coordination sequences method (the TOPOS 4.0 program package) and the matrix self-assembly is modeled for silicates Li₂HTRSiO₅ (TR = Lu, Yb; space group $P\bar 1$ ) and germanate Na₂HScGeO₅ (space group P2₁ ab). These compounds, having identical formulas, have different MT frameworks built of M octahedra (TRO₆) and T tetrahedra (SiO₄, GeO₄). New types of crystal-forming binodal nets are discovered: 4 4 6 6 + 4 4 6 for lutetium silicate and 44444(4⁵) + Ge 444(4³) for scandium germanate; the atom-site ratio in the nets is M: T = 1: 1. A ring invariant suprapolyhedral precursor cluster composed of four polyhedra is identified, with two (A = Li, Na) atoms lying one above and one below the center of the cluster. A₂M₂T₂ precursor clusters control the evolution of high-level crystal-forming clusters by means of the matrix assembly mechanism. The evolution routes of the suprapolyhedral precursor clusters bifurcate at the stage where topologically dissimilar layers are formed of equivalent chains. The cluster coordination numbers (CCNs) in a layer for the precursor clusters are four for lutetium silicate and six for scandium germanate.