Asymptotic analysis of the potential energy difference because of a crack at a V-notch edge in a 3D domain

2014 ◽  
Vol 131 ◽  
pp. 232-256 ◽  
Author(s):  
Brigit Mittelman ◽  
Zohar Yosibash
Keyword(s):  
Potential Energy ◽  
Asymptotic Analysis ◽  
Energy Difference ◽  
Notch Edge

Validity of the Finite Fracture Mechanics Based Asymptotic Analysis for Predictions of Crack Deflection in Thin Layers of Ceramic Laminates

2014 ◽  
Vol 627 ◽  
pp. 237-240 ◽  
Author(s):  
Oldřich Ševeček ◽  
Dominique Leguillon ◽  
Tomáš Profant ◽  
Michal Kotoul
Keyword(s):  
Potential Energy ◽  
Asymptotic Solution ◽  
Asymptotic Analysis ◽  
Crack Extension ◽  
Crack Deflection ◽  
Thin Layers ◽  
Reference Solution ◽  
Finite Fracture Mechanics ◽  
Higher Order Terms ◽  
Good Agreement

The work studies and compares different approaches suitable for predictions of the crack deflection (bifurcation) in ceramic laminates containing thin layers under high residual stresses and discuss a suitability and limits of using of the asymptotic analysis for such problems. The thickness of the thin compressive layers where the crack deflection occurs is only one order higher than the crack extension lengths considered within the solution. A purely FEM based calculation of the energy and stress conditions, necessary for the crack propagation, serves as the reference solution to the problem. The asymptotic analysis is used after for calculations of the same quantities (especially of energy release rate – ERR). This concept enables semi-analytical calculations of ERR or changes in potential energy induced by the crack extensions of different lengths and directions. Such approach can save a large amount of simulations and time compared with the pure FEM based calculations. It was found that the asymptotic analysis provides a good agreement for investigations of the crack increments enough far from the adjacent interfaces but for longer extensions (of length above 1/5-1/10 of the distance from the interface) starts more significantly to deviate from the correct solution. Involvement of the higher order terms in the asymptotic solution or other improvement of the model is thus advisable.

Study of Flexoelectricity in Graphene Composite Structures

MRS Advances ◽  
2016 ◽  
Vol 1 (39) ◽  
pp. 2723-2729 ◽  
Author(s):  
Mohamed Serry ◽  
Mahmoud A. Sakr
Keyword(s):  
Potential Energy ◽  
Residual Stresses ◽  
Composite Structure ◽  
Platinum Catalyst ◽  
Catalyst Layer ◽  
Energy Difference ◽  
Radius Of Curvature ◽  
Thermally Induced ◽  
Graphene Layers ◽  
Graphene Composite

ABSTRACTThis paper introduces the theoretical and experimental investigation of flexoelectric behavior in a graphene composite structure consisting of multilayer CVD-graphene deposited on an ALD-platinum catalyst layer deposited on top of n-silicon substrate. The polarization induced by varying the radius of curvature from 200–1500 mm by applying bending stresses was investigated experimentally. Meanwhile, due to the cluster-growth nature of the ALD-platinum catalyst layer, a strong correlation was observed between the resulting number of graphene layers and the Pt catalyst layer thickness, which subsequently had a strong impact on the induced polarization. A polarization current of up to 7.4 mA was detected when the composite structure was bent through a 600-mm radius of curvature. Residual stresses at the interface of the different layers were estimated experimentally in the order of 85–217 MPa. The effect of thermally-induced stresses, residual stresses at the interface layers, thickness of graphene layers, and radius of curvature were investigated theoretically using the finite element method (FEM) and first-principle analyses. Theoretically, it was confirmed that non-uniform strain results in an appreciable non-uniform graphene band gap opening, in addition to non-uniform change of the band structure across the surface and thickness which results in increasing the potential energy difference between the graphene layers. FEM confirmed that thermally induced strains could further enhance the power output of the device by inducing a flexoelectric current combined with the thermionic response. This is verified by estimating a lattice displacement up to 0.31 Å in response to 2-mW heat flux, which corresponds to an appreciable graphene band opening and a potential energy difference across the graphene layers in the order of 1.23 eV, as estimated by the tight binding model.

Computational studies, NMR, Raman and infrared spectral analysis of centrosymmetric (2Z,4Z)-Hexa-2,4-dienedinitrile

2019 ◽  
Vol 18 (02) ◽  
pp. 1950011 ◽  
Author(s):  
Tarek A. Mohamed ◽  
Ibrahim A. Shaaban ◽  
Usama A. Soliman ◽  
Wajdi M. Zoghaib
Keyword(s):  
Spectral Analysis ◽  
Potential Energy ◽  
Energy Difference ◽  
Basis Sets ◽  
Vibrational Assignments ◽  
Infrared Spectral ◽  
Point Groups ◽  
Surface Scan ◽  
Energy Surface Scan ◽  
Good Agreement

The Raman (50–3500[Formula: see text]cm[Formula: see text]) and infrared (200–3500[Formula: see text]cm[Formula: see text]) spectra of (2Z,4Z)-Hexa-2,4-dienedinitrile (C6H4N2; cis,cis-HDDN) have been recorded. Initially, three conformers were proposed based on following point groups: C2h, C2v and [Formula: see text] (gauche). For comparison purposes, M05-2X, M06-2X method were used in addition to B3LYP, MP2[Formula: see text]full and MP4[Formula: see text]full quantum mechanical calculations employing 6-31G(d) and 6-311+G(d,p) basis sets using Gaussian 09 program. Aided by potential energy surface scan, the C2h conformer is verified as a global minimum and the gauche ([Formula: see text]) being a local minimum with an energy barrier of 2.82[Formula: see text]kcal/mol. The energy difference ranged from 4.87 to 13.70[Formula: see text]kcal/mol favors the C2h conformer in good agreement with Raman and infrared spectral analysis. These results were also supported by the observed [Formula: see text] value (H9-H[Formula: see text]) at 10.8[Formula: see text]Hz which is consistent to 10.19[Formula: see text]Hz estimated for centrosymmetric conformer (C2h) rather than 4.81[Formula: see text]Hz predicted for gauche ([Formula: see text]). Complete vibrational assignments are proposed herein based on normal coordinate analysis (NCA) and potential energy distributions (PEDs) combined with theoretical vibrational frequencies and force constants in internal coordinates. It is crucial that NCA using VEDA 4 program with mixing shows large deviations from ours due to neglecting symmetry elements while mixing molecular vibrational motions. The results of these spectroscopic and theoretical studies are reported herein and compared with similar molecules whenever appropriate.

scholarly journals Stereomutation in Tetracoordinate Centers via Stabilization of Planar Tetracoordinated Systems

Atoms ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 79
Author(s):  
Komal Yadav ◽  
Upakarasamy Lourderaj ◽  
U. Deva Priyakumar
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Central Atom ◽  
Lone Pair ◽  
Energy Difference ◽  
Covalent Bonds ◽  
Energy Profiles ◽  
Planar Structures ◽  
Planar Form

The quest for stabilizing planar forms of tetracoordinate carbon started five decades ago and intends to achieve interconversion between [R]- and [S]-stereoisomers without breaking covalent bonds. Several strategies are successful in making the planar tetracoordinate form a minimum on its potential energy surface. However, the first examples of systems where stereomutation is possible were reported only recently. In this study, the possibility of neutral and dications of simple hydrocarbons (cyclopentane, cyclopentene, spiropentane, and spiropentadiene) and their counterparts with the central carbon atom replaced by elements from groups 13, 14, and 15 are explored using ab initio MP2 calculations. The energy difference between the tetrahedral and planar forms decreases from row II to row III or IV substituents. Additionally, aromaticity involving the delocalization of the lone pair on the central atom appears to help in further stabilizing the planar form compared to the tetrahedral form, especially for the row II substituents. We identified 11 systems where the tetrahedral state is a minimum on the potential energy surface, and the planar form is a transition state corresponding to stereomutation. Interestingly, the planar structures of three systems were found to be minimum, and the corresponding tetrahedral states were transition states. The energy profiles corresponding to such transitions involving both planar and tetrahedral states without the breaking of covalent bonds were examined. The systems showcased in this study and research in this direction are expected to realize molecules that experimentally exhibit stereomutation.

An ab initio approach to creating a simple stable enol

1978 ◽  
Vol 31 (8) ◽  
pp. 1649 ◽  
Author(s):  
WJ Bouma ◽  
L Radom
Keyword(s):  
Potential Energy ◽  
Ab Initio ◽  
Energy Difference ◽  
Electron Acceptors ◽  
Molecular Orbital Theory ◽  
Orbital Theory ◽  
Keto Form ◽  
Conformational Preferences ◽  
Alcohol System ◽  
Ab Initio Approach

Ab initio molecular orbital theory is used to examine the effect of four substituents (CN, NO2, NO and CHO) which are π-electron acceptors and σ-electron acceptors on the keto-enol equilibrium in the acetaldehyde/vinyl alcohol system. Each substituent destabilizes the keto isomer and stabilizes the enol isomer as desired and hence decreases the enol-keto energy difference. For the NO and CHO substituents, the effect is sufficiently large that the enol isomer is predicted to be slightly lower in energy than the keto form. The conformational preferences of the keto isomers are discussed in detail and a conformational potential energy map is presented for malondialdehyde.

scholarly journals The application of quantum mechanics to chemical kinetics

1933 ◽  
Vol 139 (838) ◽  
pp. 466-474 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Potential Energy ◽  
Classical Mechanics ◽  
Energy Difference ◽  
Chemical Processes ◽  
Quantum Mechanical ◽  
Simple Type ◽  
Heat Of Reaction ◽  
Initial State ◽  
Approximate Methods

Much work has recently been done on the application of quantum mechanics to chemical reactions. In the majority of cases, however, the actual reaction processes have been considered as taking place according to the laws of classical mechanics, quantum-mechanical theory being only employed in calculating the interatomic forces. It has, however, been suggested by various authors that the actual transition processes involved must be treated as non-classical. Some of these authors have claimed that this method of treatment is essential for the true explanation of chemical processes, just as in the case of radioactive disintegration, where it is well established that classical considerations are unable to explain the phenomena observed. It appears, however, to be the general consensus of opinion that for chemical processes the results obtained by a strict quantum-mechanical treatment would differ negligibly from the results of classical mechanics. This opinion appears to be based only on approximate methods of treatment, and no actual figures have been published. The present paper is a contribution to a more exact knowledge of the problem. According to modern views on reaction mechanism, the reacting system passes through a maximum of potential energy in passing adiabatically from the initial to the final state. The energy difference between the initial state and the maximum is the heat of activation for the reaction (E). As a simple type of chemical reaction we may take the system shown in fig. 1. A particle of mass m passes from a to b through a region of varying potential energy V ( x ). Between a and b the potential energy reaches a maximum value E. The energy difference between a and b is Q, the heat of reaction.

scholarly journals Thermodynamics of adaptive molecular resolution

2016 ◽  
Vol 374 (2080) ◽  
pp. 20160152 ◽  
Author(s):  
R. Delgado-Buscalioni
Keyword(s):  
Free Energy ◽  
Potential Energy ◽  
Local Thermodynamic Equilibrium ◽  
Thermodynamic Formalism ◽  
Energy Difference ◽  
Chem Phys ◽  
Coarse Grained ◽  
Coarse Grained Model ◽  
Thermodynamic Potentials ◽  
Energy Compensation

A relatively general thermodynamic formalism for adaptive molecular resolution (AMR) is presented. The description is based on the approximation of local thermodynamic equilibrium and considers the alchemic parameter λ as the conjugate variable of the potential energy difference between the atomistic and coarse-grained model Φ = U (1) − U (0) . The thermodynamic formalism recovers the relations obtained from statistical mechanics of H-AdResS (Español et al ., J. Chem. Phys. 142 , 064115, 2015 ( doi:10.1063/1.4907006 )) and provides relations between the free energy compensation and thermodynamic potentials. Inspired by this thermodynamic analogy, several generalizations of AMR are proposed, such as the exploration of new Maxwell relations and how to treat λ and Φ as ‘real’ thermodynamic variables . This article is part of the themed issue ‘Multiscale modelling at the physics–chemistry–biology interface’.

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