Torsional Energy Research Articles

Geometric mechanics of kiri-origami-based bifurcated mechanical metamaterials.

We explore a new design strategy of leveraging kinematic bifurcation in creating origami/kirigami-based three-dimensional (3D) hierarchical, reconfigurable, mechanical metamaterials with tunable mechanical responses. We start from constructing three basic, thick, panel-based structural units composed of 4, 6 and 8 rigidly rotatable cubes in close-looped connections. They are modelled, respectively, as 4R, 6R and 8R (R stands for revolute joint) spatial looped kinematic mechanisms, and are used to create a library of reconfigurable hierarchical building blocks that exhibit kinematic bifurcations. We analytically investigate their reconfiguration kinematics and predict the occurrence and locations of kinematic bifurcations through a trial-correction modelling method. These building blocks are tessellated in 3D to create various 3D bifurcated hierarchical mechanical metamaterials that preserve the kinematic bifurcations in their building blocks to reconfigure into different 3D architectures. By combining the kinematics and considering the elastic torsional energy stored in the folds, we develop the geometric mechanics to predict their tunable anisotropic Poisson's ratios and stiffnesses. We find that kinematic bifurcation can significantly effect mechanical responses, including changing the sign of Poisson's ratios from negative to positive beyond bifurcation, tuning the anisotropy, and overcoming the polarity of structural stiffness and enhancing the number of deformation paths with more reconfigured shapes.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

On the Torsional Energy of Deformed Curves and Knots

On the Torsional Energy of Deformed Curves and Knots

Three Diterpene Lactones from Andrographis paniculata (Burm. f) Nees In vitro, In silico Assessment of the Anticancer and Novel Liposomal Encapsulation Efficiency

: Three compounds from Andrographis paniculata (Burm. f) Nees leaf were isolated and identified using 1H, 13C, 2D-NMR, and HR-MS techniques for the first time. Compound 3,19-Di-O-acetylandrographolide (3,19-DAA) or (4) is produced by acetylating compound (2). Compounds (2) and (4) have been investigated for their cytotoxic effects on three human cancer cell lines (SK-LU-1, Hela, and HepG2) using the MTT method. Compound (4) demonstrated significant cytotoxicity against all three cancer cell lines, with IC50 values ranging from 8.38 to 10.15 μM. This represents an increase in cytotoxicity of 2.67 to 3.12-fold compared to compound (2). One way to deal with the problem of low water solubility is by encapsulating (4) into liposomes using a thin-film hydration technique. The optimal conditions for maximizing encapsulation efficiency involve molar ratios of phosphatidylcholine, 3,19-DAA, and cholesterol at 4:1:1. Encapsulating compound (4) within nanoscale liposomes increases its water solubility compared to the free form of compound (4). Pose 324 of compound (4) demonstrated the best conformation among 500 docking conformations when docked to enzyme 1T8I in a in silico docking study. The free Gibbs energy and inhibition constant were determined to be -7.09 Kcal/mol and 6.32 μM, respectively. These values help elucidate the strong interaction between compound (4) and the enzyme in the ligand interaction model. The molecular dynamics simulation using Desmond software in the Linux environment was conducted for a duration of 0 to 100 nanoseconds on the complex formed by pose 324 and 1T8I. The results showed effective interactions within the complex, with stability observed from 0 to 60 nanoseconds. Throughout the simulation, specific amino acids such as Ala 499 (involved in 90% of the simulation time with hydrogen bonding via a water bridge) and Thr 501 (involved in 50% of the simulation time with one hydrogen bond via a water bridge) were found to play significant roles. The majority of torsion bondings are C-O bondings in the acetyl group of compound (4), with torsion energy values of 13.47 Kcal/mol. Carbon atom C-29 at position 324 exhibits the highest fluctuation.

Description of Short-Range Interactions of Carbon-Based Materials with a Combined AIREBO and ZBL Potential.

An accurate description of short-range interactions among atoms is crucial for simulating irradiation effects in applications related to ion modification techniques. A smooth integration of the Ziegler-Biersack-Littmark (ZBL) potential with the adaptive intermolecular reactive empirical bond-order (AIREBO) potential was achieved to accurately describe the short-range interactions for carbon-based materials. The influence of the ZBL connection on potential energy, force, and various AIREBO components, including reactive empirical bond-order (REBO), Lennard-Jones (LJ), and the torsional component, was examined with configurations of the dimer structure, tetrahedron structure, and monolayer graphene. The REBO component is primarily responsible for the repulsive force, while the LJ component is mainly active in long-range interactions. It is shown that under certain conditions, the torsional energy can lead to a strong repulsive force at short range. Molecular dynamics simulations were performed to study the collision process in configurations of the C-C dimer and bulk graphite. Cascade collisions in graphite with kinetic energies of 1 keV and 10 keV for primary knock-on atoms showed that the short-range description can greatly impact the number of generated defects and their morphology.

Multi-Objectives Optimization of Plastic Injection Molding Process Parameters Based on Numerical DNN-GA-MCS Strategy.

An intelligent optimization technique has been presented to enhance the multiple structural performance of PA6-20CF carbon fiber-reinforced polymer (CFRP) plastic injection molding (PIM) products. This approach integrates a deep neural network (DNN), Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Monte Carlo simulation (MCS), collectively referred to as the DNN-GA-MCS strategy. The main objective is to ascertain complex process parameters while elucidating the intrinsic relationships between processing methods and material properties. To realize this, a numerical study on the PIM structural performance of an automotive front engine hood panel was conducted, considering fiber orientation tensor (FOT), warpage, and equivalent plastic strain (PEEQ). The mold temperature, melt temperature, packing pressure, packing time, injection time, cooling temperature, and cooling time were employed as design variables. Subsequently, multiple objective optimizations of the molding process parameters were employed by GA. The utilization of Z-score normalization metrics provided a robust framework for evaluating the comprehensive objective function. The numerical target response in PIM is extremely intricate, but the stability offered by the DNN-GA-MCS strategy ensures precision for accurate results. The enhancement effect of global and local multi-objectives on the molded polymer-metal hybrid (PMH) front hood panel was verified, and the numerical results showed that this strategy can quickly and accurately select the optimal process parameter settings. Compared with the training set mean value, the objectives were increased by 8.63%, 6.61%, and 9.75%, respectively. Compared to the full AA 5083 hood panel scenario, our design reduces weight by 16.67%, and achievements of 92.54%, 93.75%, and 106.85% were obtained in lateral, longitudinal, and torsional strain energy, respectively. In summary, our proposed methodology demonstrates considerable potential in improving the, highlighting its significant impact on the optimization of structural performance.

A single-particle mechanofluorescent sensor

Monitoring mechanical stresses in microchannels is challenging. Herein, we report the development of a mechanofluorescence sensor system featuring a fluorogenic single polydiacetylene (PDA) particle, fabricated using a co-flow microfluidic method. We construct a stenotic vessel-mimicking capillary channel, in which the hydrodynamically captured PDA particle is subjected to controlled fluid flows. Fluorescence responses of the PDA particle are directly monitored in real time using fluorescent microscopy. The PDA particle displays significant nonlinear fluorescence emissions influenced by fluid viscosity and the presence of nanoparticles and biomolecules in the fluid. This nonlinear response is likely attributed to the torsion energy along the PDA’s main chain backbone. Computational fluid dynamic simulations indicate that the complete blue-to-red transition necessitates ~307 μJ, aligning with prior research. We believe this study offers a unique advantage for simulating specific problematic regions of the human body in an in vitro environment, potentially paving the way for future exploration of difficult-to-access areas within the body.

Direct Determination of Torsion in Twisted Graphite and MoS2 Interfaces.

The design space of two-dimensional materials is undergoing significant expansion through the stacking of layers in non-equilibrium configurations. However, the lack of quantitative insights into twist dynamics impedes the development of such heterostructures. Herein, we utilize the lateral force sensitivity of an atomic force microscope cantilever and specially designed rotational bearing structures to measure the torque in graphite and MoS2 interfaces. While the extracted torsional energies are virtually zero across all angular misfit configurations, commensurate interfaces of graphite and MoS2 are characterized by values of 0.1533 and 0.6384 N-m/m2, respectively. Furthermore, we measured the adhesion energies of graphite and MoS2 to elucidate the interplay between twist and slide. The adhesion energy dominates over the torsional energy for the graphitic interface, suggesting a tendency to twist prior to superlubric sliding. Conversely, MoS2 displays an increased torsional energy exceeding its adhesion energy. Consequently, our findings demonstrate a fundamental disparity between the sliding-to-twisting dynamics at MoS2 and graphite interfaces.

Photophysical mechanism study of photophysical properties of new red BODIPY chromophores with or without methyl substitution

The relationship between the photophysical properties and structure of BODIPY derivatives always has attracted much attention. Two new BODIPY derivative chromophores with phenyl group substitutions at meso-/6- positions, with or without methyl substitutions at 1/3/5/7 positions were investigated by ways of combination of multiple experimental techniques and theoretical methods. The chromophore without methyl substitutions has a larger Stokes shift and better viscosity sensitivity compared to the other one. The intrinsic reason is that considerable charge transfer between the BODIPY core and the 6- position group is achieved in chromophore. However, this charge transfer process is severely weakened, if 1-/3-/5-/7- methyl substitutions existing, via restricting rotation between the core and side groups. At the same time, the non-radiative process is amplified significantly in chromophore without methyl substitution and the fluorescence efficiency decrease from 51.7% (with methyl substitutions) to 1.84% (without methyl substitutions) in DMSO. Quantum calculations indicate the presence or absence of methyl substitution can change both the shape and height of the torsional potential energy curve of the side groups, thereby affecting the fluorescence quantum yield and viscosity response performance of chromophores. Our work can provide foundation and ideas for designing and optimizing BODIPY derivatives with objective photophysical properties.

High-resolution spectroscopic study of asymmetric [formula omitted] stretch [formula omitted] Torsion [formula omitted] combination band and other higher-lying vibrational fundamental, overtone, combination, and hot bands of astrophysically significant methanol [formula omitted] molecule

In this paper, the spectrum of high energy vibrational bands has been recorded in the range 1900-6000cm-1with the highest possible resolution. New assignments have been obtained for a large number of transitions belonging to several fundamental and combination bands. Varios bands of importance in the range 1950 − 3420 cm-1 are shown in Fig. 1. Notable are those belonging to a new combination band comprising the asymmetric CH3- Stretch band and OH internal rotation (or torsion) band lying in a very crowded region of the three coupled fundamental CH3- stretching bands. A large number of ΔK=±1 transitions have been observed from the ground and the first excited torsional states of the ground vibrational state. In addition, new transitions have been obtained for the torsionally excited OH- stretch band. The majority of the transitions have been confirmed using closed combination loops. In addition, detailed assignment work has been performed with improved accuracy on the overtone CO stretch band 2ν8, CO- Stretch:CH3-rock (ν8+ν7) combination band, and the overtone asymmetric CH3-bending band 2ν4. Due to an accidental state mixing in the first excited torsional state of the ground vibrational state, many forbidden transitions have been detected in the torsional band of the OH–stretch state (ν1). Lastly, a new and elegant method has been employed to obtain the pure torsional energies of many vibrational states. The most exciting finding from these studies has been the inversion of A/E energy structure. Some explanations from the literature have been reviewed, and more work is needed to understand the coupling between torsion and vibration in methanol. The work should be helpful in the astronomical search for methanol in interstellar space.

Long-chain alkyl groups enhance the water-repellent properties of short-chain perfluoroalkyl compounds: An experimental and computer simulation study

The polymers composed of long-chain stearyl acrylate (SA) and short-chain (perfluorohexyl) ethyl methacrylate (FA) were synthesized using the emulsion polymerization technique. Cotton fabric was then coated with these polymers to act as a water-repellent agent. Surface wetting properties of the coated cotton fabric were tested. In a peculiar manner, the water repellency of the coatings did not improve with the increase of the perfluorohexyl group. Therefore, the polymer's crystallization behaviors and melting temperature were assessed through differential scanning calorimetry (DSC) and computer simulation. A computer simulation was employed to analyze the density, surface energy, element distribution, chain arrangement, bond order parameter, and surface images of the polymer film. The results suggest that water repellency is not directly related to the film's surface energy but rather depends on the element proportion, bond angle distribution, and dihedral angle torsion energy. The key points will serve as invaluable indicators for the development of a highly efficient water-repellent coating with a low proportion of fluorine and provide a more sustainable solution for water-repellent applications.

Comparing ANI-2x, ANI-1ccx neural networks, force field, and DFT methods for predicting conformational potential energy of organic molecules

In this study, the conformational potential energy surfaces of Amylmetacresol, Benzocaine, Dopamine, Betazole, and Betahistine molecules were scanned and analyzed using the neural network architecture ANI-2 × and ANI-1ccx, the force field method OPLS, and density functional theory with the exchange-correlation functional B3LYP and the basis set 6-31G(d). The ANI-1ccx and ANI-2 × methods demonstrated the highest accuracy in predicting torsional energy profiles, effectively capturing the minimum and maximum values of these profiles. Conformational potential energy values calculated by B3LYP and the OPLS force field method differ from those calculated by ANI-1ccx and ANI-2x, which account for non-bonded intramolecular interactions, since the B3LYP functional and OPLS force field weakly consider van der Waals and other intramolecular forces in torsional energy profiles. For a more comprehensive analysis, electronic parameters such as dipole moment, HOMO, and LUMO energies for different torsional angles were calculated at two levels of theory, B3LYP/6-31G(d) and ωB97X/6-31G(d). These calculations confirmed that ANI predictions are more accurate than density functional theory calculations with B3LYP functional and OPLS force field for determining potential energy surfaces. This research successfully addressed the challenges in determining conformational potential energy levels and shows how machine learning and deep neural networks offer a more accurate, cost-effective, and rapid alternative for predicting torsional energy profiles.

A new model of thermo-mechanical actuation for twisted and coiled polymer muscles with initial curvature

The twisted and coiled polymer (TCP) artificial muscle is one type of novel soft actuator for mimicking natural skeletal muscle that can provide large linear and torsional actuation and energy density. Twisting and coiling are the pivotal steps in fabricating TCP muscles. The influence of twisting on the actuation response of TCP muscles has been extensively investigated recently. However, the influence of coiling remains unclear. Based on the finite strain theory, we establish a new thermo-mechanical actuation model for TCP muscles with initial curvature. The theoretical predictions based on the model align well with the finite element simulations, accurately capturing the actuation response of thermally-activated TCP muscles. It is revealed that twisting contributes positively to the actuation, while coiling has a passive effect. Geometrical parameters, such as the helix radius and helix angle, can effectively regulate the actuation performance of TCP muscles. Furthermore, an optimal bias angle is identified that maximizes both the recovery torque and the linear actuation. This study sheds light on the structural optimization design of TCP muscles.

Γ-convergence of a discrete Kirchhoff rod energy

This work is motivated by the classical discrete elastic rod model by Audoly et al. We derive a discrete version of the Kirchhoff elastic energy for rods undergoing bending and torsion and prove Γ-convergence to the continuous model. This discrete energy is given by the bending and torsion energy of an interpolating conforming polynomial curve and provides a simple formula for the bending energy depending in each discrete segment only on angle and adjacent edge lengths. For the liminf-inequality, we need to introduce penalty terms to ensure arc-length parametrization in the limit. For the recovery sequence a discretization with equal Euclidean distance between consecutive points is constructed. Particular care is taken to treat the interaction between bending and torsion by employing a discrete version of the Bishop frame.

Efficient Generation of Conformer Ensembles Using Internal Coordinates and a Generative Directional Graph Convolution Neural Network.

We present a neural-network-based high-throughput molecular conformer-generation algorithm. A chemical graph-convolutional network is trained to predict low-energy conformers in internal coordinate representation (bond lengths, bond, and torsion angles), starting from two-dimensional (2D) chemical topology. Generative neural network (NN) architecture performs denoising from torsion space, producing conformer ensembles with populations that are well correlated with torsion energy profiles. Short force-field-based energy minimization is applied to refine final conformers. All computation-intensive stages of the algorithm are GPU-optimized. The procedure (termed GINGER) is benchmarked on a commonly used test set of bioactive three-dimensional (3D) conformers from the PDB. We demonstrate highly competitive results in conformer recovery and throughput rates suitable for giga-scale compound library processing. A web server that allows interactive conformer ensemble generation by GINGER and their viewing is made freely available at https://www.molsoft.com/gingerdemo.html.

A biogenic organic molecule involved in the formation of secondary organic aerosols: Microwave and millimeter-wave spectroscopy of 3-methylcatechol backed by quantum chemistry

3-methylcatechol (3MC) is a molecule of environmental interest due to its presence in the atmosphere during biomass burning events, leading to the formation of secondary organic aerosols. This paper goes one step further than the paper from A.S. Hazrah et al. (2022) [10]. A three-dimensional torsional potential energy surface was determined, confirming the existence of three rotamers for 3MC. One dimensional potential energy curves along the rotation of the methyl group were computed and fitted to estimate the barrier height in each conformer. Experiments were performed at low temperature in the microwave domain (2−20GHz range) and, for the first time, in the millimeter-wave domain (70−110GHz range) at T=323K with a specially designed heated absorption cell. The rotational linelist was fitted to provide updated spectroscopic parameters for the two 3MC conformers of lowest energies. In particular, the A−E splitting is observed in the microwave region for both conformers while in the millimeter-wave region, it is only seen for the conformer of the lowest energy.

Mesoscopic irreversible thermodynamics of aging kinetics of alpha polypeptides [DNA] under various constraints: Special reference to the simple spring mechanics

The mesoscopic irreversible thermodynamic treatment of α-polypeptides and the helical polynucleotides (DNA) furnishes two sets of analytical expressions, which allow us not only to analyze the reversible force–extension experiments performed by atomic force microscopy (AFM) but also to predict the irreversible “aging” kinetics of the single-stranded and double-stranded polynucleotides (ssDNA and dsDNA) helical conformations exposed to aqueous solutions and applied static stress systems under the various constraints. The present physicochemical cage model emphasizes the fact that the global Helmholtz free energy of the helical conformation acts not only under the stored “intrinsic” unusual torsional and bending elastic energies inherited by the unfolded helical structure of the amino-acid (peptides) or the nucleic-acid (nucleotide) backbone but also reveals the importance of the interfacial Helmholtz free energy density associated with the interaction of the side-wall branches within the surrounding aqueous solutions. The analytical expression obtained for the unfolding force vs extension (FE) shows a strong non-linear elasticity behavior under the twist angle constraint when the interfacial Helmholtz energy term is incorporating into the scenario. This behavior is in excellent quantitative agreement with the AFM test results obtained by Idiris et al. (2000) on the poly-L-glutamic acid [Glu(n)-Cys] exposed to aqueous solutions, which show that acidity increases the degrees of helicity.

Reducing shimmy oscillation of a dual-wheel nose landing gear based on torsional nonlinear energy sink

Reducing shimmy oscillation of a dual-wheel nose landing gear based on torsional nonlinear energy sink

Coupling and biological free-energy transduction processes as a bridge between physics and life: Molecular-level instantiation of Ervin Bauer’s pioneering concepts in biological thermodynamics

The nonequilibrium coupled processes of oxidation and ATP synthesis in the biological process of oxidative phosphorylation (OXPHOS) are fundamental to all life on our planet. These steady-state energy transduction processes ‒ coupled by proton and anion/counter-cation concentration gradients in the OXPHOS pathway ‒ generate ∼95 % of the ATP requirement of aerobic systems for cellular function. The rapid energy cycling and homeostasis of metabolites involved in this coupling are shown to be responsible for maintenance and regulation of stable nonequilibrium states, the latter first postulated in pioneering biothermodynamics work by Ervin Bauer between 1920 and 1935. How exactly does this occur? This is shown to be answered by molecular considerations arising from Nath’s torsional mechanism of ATP synthesis and two-ion theory of energy coupling developed in 25 years of research work on the subject. A fresh analysis of the biological thermodynamics of coupling that goes beyond the previous work of Stucki and others and shows how the system functions at the molecular level has been carried out. Thermodynamic parameters, such as the overall degree of coupling, q of the coupled system are evaluated for the state 4 to state 3 transition in animal mitochondria with succinate as substrate. The actual or operative P to O ratio, the efficiency of the coupled reactions, η, and the Gibbs energy dissipation, Φ have been calculated and shown to be in good agreement with experimental data. Novel mechanistic insights arising from the above have been discussed. A fourth law/principle of thermodynamics is formulated for a sub-class of physical and biological systems. The critical importance of constraints and time-varying boundary conditions for function and regulation is discussed in detail. Dynamic internal structural changes essential for torsional energy storage within the γ-subunit in a single molecule of the FOF1-ATP synthase and its transduction have been highlighted. These results provide a molecular-level instantiation of Ervin Bauer’s pioneering concepts in biological thermodynamics.

On CCGG, the De Donder‐Weyl Hamiltonian formulation of canonical gauge gravity

AbstractThis short paper gives a brief overview of the manifestly covariant canonical gauge gravity (CCGG) that is rooted in the De Donder‐Weyl Hamiltonian formulation of relativistic field theories, and the proven methodology of the canonical transformation theory. That framework derives, from a few basic physical and mathematical assumptions, equations describing generic matter and gravity dynamics with the spin connection emerging as a Yang Mills‐type gauge field. While the interaction of any matter field with spacetime is fixed just by the transformation property of that field, a concrete gravity ansatz is introduced by the choice of the free (kinetic) gravity Hamiltonian. The key elements of this approach are discussed and its implications for particle dynamics and cosmology are presented. New insights: Anomalous Pauli coupling of spinors to curvature and torsion of spacetime, spacetime with (A)dS ground state, inertia, torsion and geometrical vacuum energy, Zero‐energy balance of the Universe leading to a vanishing cosmological constant and torsional dark energy.

Understanding the torsional mechanical behavior of twisting carbon nanotube ribbon with different boundary conditions

Twisting can generate internal stress and store torsional energy, which is widely used as actuators and energy harvesters in electronic and biomedical fields. However, uncovering the effect of internal stress remains unclear. Herein, the experimental and theoretical mechanical model of the twisted ribbon with different boundary conditions was derived and analyzed. The dynamic experimental results indicate that the polymer inclines to constrain the unraveling process of carbon nanotube fiber. Then the elastic/plastic theoretical equations reveal that the internal stress gradually increases as the twisted angle, and the simulated internal stress agrees well with the theoretical results. The simulation results also indicate that the twisting-induced deformation and failure behavior of twisted ribbons are affected by the strain-rate sensitivity of the matrix and the loading velocity. Then, the releasing of the stored energy for twisted ribbons with different boundary conditions demonstrates the contraction and repulsion behaviors. This work investigating the mechanical behavior of twisted ribbons could provide a better guideline for designing twisted actuators with high reliability.