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Cortical bone is a tough biological material composed of tube-like osteons embedded in the organic matrix surrounded by weak interfaces known as cement lines. The cement lines provide a microstructurally preferable crack path, hence triggering in-plane crack deflection around osteons due to cement line-crack interaction. Inspired by this toughening mechanism and facilitated by a hybrid (3D-printing/casting) process, the study engineers architected tubular cement-based materials with the stepwise cracking toughening mechanism, that enables a non-brittle fracture. Using experimental and theoretical approaches, the study demonstrates the competition between tube size and shape on stress intensity factor from which engineering stepwise cracking can emerge. Two competing mechanisms, both positively and negatively affected by the growing tube size, arise to significantly enhance the overall fracture toughness by up to 5.6-fold compared to the monolithic brittle counterpart without sacrificing the specific strength. This is enabled by crack-tube interaction and engineering the tube size, shape, and orientation, which promotes rising resistance-curves (R-curve). "Disorder" curves and statistical mechanics parameters are proposed for the first time to quantitatively characterize the degree of disorder for describing the representation of the architected arrangement of materials in lieu of otherwise inadequate "periodicity" classification and misperceived disorder parameters (perturbation and Voronoi tessellation methods).

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Proteins from Crenarchaeal organisms exhibit remarkable thermal stability. The aromatic amino acids in Cren7, a Crenarchaeal protein, regulate protein stability and further modulate DNA binding and its compaction. Specific aromatic amino acids were mutated, and using spectroscopic and theoretical approaches, we have examined the structure, DNA binding affinity, and DNA bending ability of mutants. and compared with wild-type (WT) Cren7. The reverse titration profiles were analysed by a noncooperativeMcGhee-von Hippel model to estimate affinity constant (Ka) and site size (n) associated with binding to the DNA. Biolayer interferometry (BLI) measurements showed that the binding affinity decreased at higher salt concentrations. For theoretical analysis of extent of DNA bending, radius of gyration and bending angle were compared for WT and mutants. Time evolution of order parameters based on translational and rotational motion of tryptophan residue (W26) was used for qualitative detection of stacking interactions between W26 of Cren7 and DNA nucleobases. It was observed that orientation of W26 in F41A favored formation of a new lone pair-lone pair interaction between DNA and Cren7. Consequently, in thermostable proteins, the aromatic residues at the terminus maintain structural stability, whereas the residues at the core optimize the degree of DNA bending and compaction.

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Liquid crystal elastomers (LCEs) exhibit unique mechanical properties of soft elasticity and reversible shape-changing behaviors, and so serve as potentially transformative materials for various protective and actuation applications. This study contributes to filling a critical knowledge gap in the field by investigating the microscale mesogen organization of nematic LCEs with diverse macroscopic deformation. A polarized Fourier transform infrared light spectroscopy (FTIR) tester is utilized to examine the mesogen organizations, including both the nematic director and mesogen order parameter. Three types of material deformation are analyzed: uniaxial tension, simple shear, and bi-axial tension, which are all commonly encountered in practical designs of LCEs. By integrating customized loading fixtures into the FTIR tester, mesogen organizations are examined across varying magnitudes of strain levels for each deformation mode. Their relationships with macroscopic stress responses are revealed and compared with predictions from existing theories. Furthermore, this study reveals unique features of mesogen organizations that have not been previously reported, such as simultaneous evolutions of the mesogen order parameter and nematic director in simple shear and bi-axial loading conditions. Overall, the findings presented in this study offer significant new insights for future rational designs, modeling, and applications of LCE materials.

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Optically-controlled phase change materials, which are prepared by introducing molecular photoswitches into traditional phase change materials (PCMs), can convert and store solar energy into photochemical enthalpy and phase change enthalpy. However, the thermophysical properties of optically controlled PCMs, which are crucial in the practical, are rarely paid attention to. 4-(phenyldiazenyl)phenyl decanoate (Azo-A-10) is experimentally prepared as an optically-controlled PCMs, whose energy storage density is 210.0 kJ·kg-1, and the trans single crystal structure is obtained. The density, phase transition temperature, thermal conductivity, and other parameters in trans state are measured experimentally. Furthermore, a microscopic model of Azo-A-10 is established, and the thermophysical properties are analyzed based on molecular dynamics. The results show that the microstructure parameter (order parameters) and thermophysical properties (density, radial distribution function, self-diffusion coefficient, phase change temperature, and thermal conductivity) of partially or completely isomerized Azo-A-10, which are challenging to observe in experiments, can be predicted by molecular dynamics simulation. The optically-controlled phase change mechanism can be clarified according to the differences in microstructure. The optically-controlled switchability of thermophysical properties of an optically-controlled PCM is analyzed. This study provides ideas for the improvement, development, and application of optically-controlled PCMs in the future.

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A Model mesogen and its symmetrical Dimer made up of phenyl benzoate core unit are investigated by 13C NMR spectroscopy. The existence of layer order in smectic A and smectic C phases of Dimer mesogen is established by powder X-ray diffraction. The chemical shift anisotropy (CSA) tensors of Model mesogen are determined by 2D separation of undistorted powder patterns by effortless recoupling (SUPER) experiment and are utilized for calculating the order parameters employing the alignment-induced chemical shifts (AIS). Additionally, 2D separated local field (SLF) NMR is availed for extracting 13C-1H dipolar couplings for both mesogens and used for computing the order parameters. A good agreement in the order parameters calculated from 13C-1H dipolar couplings and AIS is observed. Accordingly, the main order parameter (Szz) for the phenyl rings of the Model mesogen is found to be in the range 0.54 - 0.82, and for the Dimer mesogen, the values span 0.64 - 0.82 across mesophases. Since the phenyl benzoate core unit is frequently employed structural moiety for constructing the main chain as well as side chain liquid crystalline polymers and liquid crystalline elastomers, the CSA tensors reported here will be of immense utility for the structural characterization of these materials.

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Phase transitions are typically quantified using order parameters, such as crystal lattice distances and radial distribution functions, which can identify subtle changes in crystalline materials or high-contrast phases with large structural differences. However, the identification of phases with high complexity, multiscale organization and of complex patterns during the structural fluctuations preceding phase transitions, which are essential for understanding the system pathways between phases, is challenging for those traditional analyses. Here, it is shown that for two model systems- thermotropic liquid crystals and a lyotropic water/surfactant mixtures-graph theoretical (GT) descriptors can successfully identify complex phases combining molecular and nanoscale levels of organization that are hard to characterize with traditional methodologies. Furthermore, the GT descriptors also reveal the pathways between the different phases. Specifically, centrality parameters and node-based fractal dimension quantify the system behavior preceding the transitions, capturing fluctuation-induced breakup of aggregates and their long-range cooperative interactions. GT parameterization can be generalized for a wide range of chemical systems and be instrumental for the growth mechanisms of complex nanostructures.

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An external electric field is an effective tool to induce the polymorphic transformation of molecular crystals, which is important practically in the chemical, material, and energy storage industries. However, the understanding of this mechanism is poor at the molecular level. In this work, two types of order parameters (OPs) were constructed for the molecular crystal based on the intermolecular distance, bond orientation, and molecular orientation. Using the K-means clustering algorithm for the sampling of OPs based on the Euclidean distance and density weight, the polymorphic transformation of TNT was investigated using a finite temperature string (FTS) under external electric fields. The potential of mean force (PMF) was obtained, and the essence of the polymorphic transformation between o-TNT and m-TNT was revealed, which verified the effectiveness of the FTS method based on K-means clustering to OPs. The differences in PMFs between the o-TNT and transition state were decreased under external electric fields in comparison with those in no field. The fields parallel to the c-axis obviously affected the difference in PMF, and the relationship between the changes in PMFs and field strengths was found. Although the external electric field did not promote the convergence, the time of the polymorphic transformation was reduced under the external electric field in comparison to its absence. Moreover, under the external electric field, the polymorphic transformation from o-TNT to m-TNT occurred while that from m-TNT to o-TNT was prevented, which was explained by the dipole moment of molecule, relative permittivity, chemical potential difference, nucleation work and nucleation rate. This confirmed that the polymorphic transformation orientation of the molecular crystal could be controlled by the external electric field. This work provides an effective way to explore the polymorphic transformation of the molecular crystals at a molecular level, and it is useful to control the production process and improve the performance of energetic materials by using the external electric fields.

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Complex crystal structures are composed of multiple local environments, and how this type of order emerges spontaneously during crystal growth has yet to be fully understood. We study crystal growth across various structures and along different crystallization pathways, using self-assembly simulations of identical particles that interact via multiwell isotropic pair potentials. We apply an unsupervised machine learning method to features from bond-orientational order metrics to identify different local motifs present during a given structure's crystallization process. In this manner, we distinguish different crystallographic sites in highly complex structures. Tailoring this order parameter to structures of varying complexity and coordination number, we study the emergence of local order along a multistep crystal growth pathway─from a low-density fluid to a high-density, supercooled amorphous liquid droplet and to a bulk crystal. We find a consistent under-coordination of the liquid relative to the average coordination number in the bulk crystal. We use our order parameter to analyze the geometrically frustrated growth of a Frank-Kasper phase and discover how structural defects compete with the formation of crystallographic sites that are more high-coordinated than the liquid environments. The method presented here for classifying order on a particle-by-particle level has broad applicability to future studies of structural self-assembly and crystal growth, and they can aid in the design of building blocks and for targeting pathways of formation of soft-matter structures.

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As a solid energy source, CH4 hydrate will inevitably break down physically as the result of geological movement or exploitation. Here, the molecular dynamics method was employed to simulate the uniaxial-deformation behavior of structure I (sI type) CH4 hydrate under stress. The stress increases regardless of whether the hydrate is stretched or squeezed, and other physical parameters also changed, such as hydrate cage numbers, order parameters, and the number of water molecules. A noticeable difference is observed between the two systems. Upon stretching, the stress immediately recovers to 0 GPa once the hydrate is completely stretched apart. During the squeeze process, the stress is ultimately not zero since solid and liquid are always in contact. When the hydrate is stretched apart, about 5% of water molecules change from solid to liquid, about 7.8% of CH4 molecules lose their shelter and become free due to the disintegration of water cages. While in the squeezing process, large cages (51262) are crushed more easily than small cages (512); in the end, about 93.5% of large cages and 73% of small cages are crushed, and approximately 87.5% CH4 is released from the cages. In mining CH4 hydrates, caution must be exercised, as if the hydrates break as a result of stress, a large release of CH4 may pose a security risk.

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External electric fields are an effective tool to induce phase transformations. The crystallization of ionic crystals from solution is a common phase transformation. However, understanding of mechanisms is poor at the molecular level. In this work, we carried out an experimental and theoretical investigation of the external electric-field-induced crystallization of TKX-50 from saturated formic acid solution by finite-temperature string (FTS) with order parameters (OPs) as collective variables for ionic crystals. The minimum-free-energy path was sketched by the string method in collective variables. The results show that the K-means clustering algorithm based on Euclidean distance and density weights can be used for enhanced sampling of the OPs in external electric-field-induced crystallization of ionic crystal from solution, which improves the conventional FTS. The crystallization from solution is a process of surface-mediated nucleation. The external electric field can accelerate the evolution of the string and decrease the difference in the potential of mean forces between the crystal and the transition state. Due to the significant change in OPs induced by the external electric field in nucleation, the crystalline quality was enhanced, which explains the experimental results that the external electric field enhanced the density, detonation velocity, and detonation pressure of TKX-50. This work provides an effective way to explore the crystallization of ionic crystals from solution at the molecular level, and it is useful for improving the properties of ionic crystal explosives by using external electric fields.

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Solid state NMR is widely used to study the orientation and other structural features of proteins and peptides in lipid bilayers. Using data obtained by PISEMA (Polarization Inversion Spin Exchange at Magic Angle) experiments, periodic spectral patterns arise from well-aligned α-helical molecules. Significant problems in the interpretation of PISEMA spectra may arise for systems that do not form perfectly defined secondary structures, like α-helices, or the signal pattern is disturbed by molecular motion. Here, we present a new method that combines molecular dynamics simulation with tensorial orientational constraints (MDOC) and chemical shift tensor calculations for the simulation and interpretation of PISEMA-like spectra. The calculations include the spectra arising from non α-helical molecules and molecules with non-uniform intrinsic mobility. In a first step, dipolar or quadrupolar interaction tensors drive molecular rotations and reorientations to obtain the proper mean values as observed in corresponding NMR experiments. In a second step, the coordinate snapshots of the MDOC simulations are geometry optimized with the isotropic 15 N chemical shifts as constraints using Bond Polarization Theory (BPT) to provide reliable 15 N CS tensor data. The averaged dipolar 1 H-15 N couplings and the δzz tensor components can then be combined to simulate PISEMA patterns. We apply this method to the ß-helical peptide gramicidin A (gA) and demonstrate that this method enables the assignment of most PISEMA resonances. In addition, MDOC simulations provide local order parameters for the calculated sites. These local order parameters reveal large differences in backbone mobility between L- and D-amino acids of gA.

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In order to investigate the viability of carbon dioxide (CO2) storage in seawater, molecular dynamics techniques were employed to study the dynamic evolution of CO2 hydrate in saline water. The simulation was conducted under specific conditions: a temperature of 275 K, a pressure of 10 MPa and a simulated marine environment achieved using a 3.4 wt% sodium chloride (NaCl) solution. The total simulation time was 1000 ns. The results of the simulation indicate that the pre-existence of CO2 hydrate crystals as seeds leads to rapid growth of CO2 hydrate. However, analysis of the F3 and F4 order parameters reveals that the hydrate does not meet the standard values of the perfect structure I (sI) type, confirming the existence of an imperfect structure during the simulation. Additionally, the changes in the number of different phase states of water molecules during the hydrate growth process shows that there are always some liquid water molecules, which means some water molecules fail to form solid water cages. Further investigation suggests that the presence of Na+ and Cl- hampers the hydrogen bonds between water molecules, resulting in incomplete cage structures. By analyzing the density variations in the system, it is observed that CO2 hydrate, with a density of around 1.133 g cm-3, forms rapidly, surpassing the average density of seawater. This density increase facilitates the efficient and swift containment of CO2 on the seabed, thereby supporting the feasibility of the CO2 storage theory.

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The two-dimensional Mercedes-Benz model of water has been studied by molecular simulations over a wide range of thermodynamic conditions as an attempt to locate the supercooled region where a liquid-liquid separation and, potentially, also other structures may occur. Both the correlation functions and a number of local structure factors have been used to identify different structural arrangements. These include, in addition to the hexatic phase, also the hexagon, pentagon, and quadruplet arrangements. All these structures result from the competition between the hydrogen bonding and Lennard-Jones interactions and their effect at different temperatures and pressures. Based on the obtained results, an attempt is made to sketch a (rather complex) phase diagram of the model.

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Structurally simple rod-like π-conjugated mesogens with thiophene directly connected to phenyl, biphenyl, and fluorenone rings with terminal chains are synthesized respectively. The occurrence of smectic A/smectic C phases is concurred by a hot-stage optical polarising microscope (HOPM), differential scanning calorimetry (DSC), and X-ray diffraction (XRD). The static 1D and 2D 13 C nuclear magnetic resonance (NMR) studies in the liquid crystalline phase are carried out to find the alignment-induced chemical shifts (AIS) and 13 C-1 H dipolar couplings. The orientational order parameters of the mesogens determined from 13 C-1 H dipolar couplings disclose that the long axis is not only collinear to the C3-C4 bond of the thiophene ring but also for the local axes of phenyl and biphenyl rings. For fluorenone-based mesogen, the molecular biaxiality is found to be high owing to the increased breadth of the molecule. The study unveils that the orientation of thiophene and the phenyl rings is similar in the current mesogens in stark contrast to mesogens, where thiophene is connected to phenyl rings through linking groups.

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AlphaFold2 has revolutionized protein structure prediction from amino-acid sequence. In addition to protein structures, high-resolution dynamics information about various protein regions is important for understanding protein function. Although AlphaFold2 has neither been designed nor trained to predict protein dynamics, it is shown here how the information returned by AlphaFold2 can be used to predict dynamic protein regions at the individual residue level. The approach, which is termed cdsAF2, uses the 3D protein structure returned by AlphaFold2 to predict backbone NMR NH S2 order parameters using a local contact model that takes into account the contacts made by each peptide plane along the backbone with its environment. By combining for each residue AlphaFold2's pLDDT confidence score for the structure prediction accuracy with the predicted S2 value using the local contact model, an estimator is obtained that semi-quantitatively captures many of the dynamics features observed in experimental backbone NMR NH S2 order parameter profiles. The method is demonstrated for a set nine proteins of different sizes and variable amounts of dynamics and disorder.

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The natural occurrence of precious opals, consisting of highly organized silica particles, has prompted interest in the synthesis and formation of these structures. Previous research has shown that a highly organized photonic crystal (PhC) array is only possible when it is based on a low polydispersity index (PDI) sample of particles. In this study, a solvent-only variation method is used to synthesize different sizes of silica particles (SiPs) by following the traditional sol-gel Stöber approach. The controlled rate of the addition of the reagents promoted the homogeneity of the nucleation and growth of the spherical silica particles, which in turn yielded a low PDI. The opalescent PhC were obtained via self-assembly of these particles using a solvent evaporation method. Analysis of the spatial statistics, using Voronoi tessellations, pair correlation functions, and bond order analysis showed that the successfully formed arrays showed a high degree of quasi-hexagonal (hexatic) organization, with both global and local order. Highly organized PhC show potential for developing future materials with tunable structural reflective properties, such as solar cells, sensing materials, and coatings, among others.

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2H NMR order parameters of the acyl chain of phospholipid membranes are an important indicator of the effects of molecules on membrane order, mobility, and permeability. So far, the evaluation procedures are case-by-case studies for every type of small molecule with certain types of membranes. Rapid screening of the effects of a variety of drugs would be invaluable if it were possible. Unfortunately, to date there is no practical or theoretical approach to this as there is with other experimental parameters, e.g., chemical shifts from 1H and 13C NMR. We aim to remedy this situation by introducing a model based on graph neural networks (GNN) capable of predicting 2H NMR order parameters of lipid membranes in the presence of different molecules based on learned molecular features. Rapid prediction of these parameters would allow fast assessment of potential effects of drugs on lipid membranes, which is important for further drug development and provides insight into potential side effects. We conclude that the graph network-based model presented in this work can predict order parameters with sufficient accuracy, and we are confident that the concepts presented are a suitable basis for future research. We also make our model available to the public as a web application at https://proteinformatics.uni-leipzig.de/g2r/.

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The influence of static compressional stress on the anisotropy of piezoelectric ceramics of BaTiO3 and PZT types is considered theoretically and experimentally. Static compression changes the domain structure of piezoceramics. These changes occur due to the reorientation of mostly 90° domain axes. As a result, all the parameters of the material change-elastic, piezoelectric, and dielectric. Some of them increase, and some, on the contrary, decrease. Changes occur in a nonlinear way, and higher-order parameters appear. The relationship between the total volume of the reoriented domains and the change in elastic moduli and piezomoduli is theoretically considered. The corresponding theoretical dependences are obtained. To confirm these theoretical dependences, experimental measurements were performed using the ultrasonic pulse-interference method at a frequency of 8 MHz. There is practically no oscillation movement of domain boundaries at this frequency, therefore, the change in the system of elastic and piezoelectric moduli is structural, not dynamic. The possibility of predicting changes in the structure of modules as a result of static compression is shown.

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A four-variable virus dynamics TIIV model was considered that involves infected cells in an eclipse phase. The state space description of the model was transferred into an amplitude space description which is the appropriate general, nonlinear physics framework to describe instabilities. In this context, the unstable eigenvector or order parameter of the model was determined. Subsequently, a model-based analysis of viral load data from eight symptomatic COVID-19 patients was conducted. For all patients, it was found that the initial SARS-CoV-2 infection evolved along the respective patient-specific order parameter, as expected by theoretical considerations. The order parameter amplitude that described the initial virus multiplication showed doubling times between 30 min and 3 h. Peak viral loads of patients were linearly related to the amplitudes of the patient order parameters. Finally, it was found that the patient order parameters determined qualitatively and quantitatively the relationships between the increases in virus-producing infected cells and infected cells in the eclipse phase. Overall, the study echoes the 40 years old suggestion by Mackey and Glass to consider diseases as instabilities.

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The COVID-19 pandemic has revealed new features in terms of substantial changes in rates of infection, cure, and death as a result of social interventions, which significantly challenges traditional SEIR-type models. In this paper we developed a symmetry-based model for quantifying social interventions for combating COVID-19. We found that three key order parameters, separating degree (S) for susceptible populations, healing degree (H) for mild cases, and rescuing degree (R) for severe cases, all display logistic dynamics, establishing a novel dynamic model named SHR. Furthermore, we discovered two evolutionary patterns of healing degree with a universal power law in 23 areas in the first wave. Remarkably, the model yielded a quantitative evaluation of the dynamic back-to-zero policy in the third wave in Beijing using 12 datasets of different sizes. In conclusion, the SHR model constitutes a rational basis by which we can understand this complex epidemic and policymakers can carry out sustainable anti-epidemic measures to minimize its impact.

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