Bending Potential Research Articles

In-plane force fields and elastic properties of graphene

Bond stretching and angle bending force fields, appropriate to describe in-plane properties of graphene sheets, are derived using first principles' methods. The obtained force fields are fitted by analytical anharmonic potential energy functions, providing efficient means of calculations in molecular mechanics simulations. Using both molecular dynamics simulations and first principles' methods, numerical results regarding the mechanical behavior of graphene monolayers under various loads, like uniaxial tension in different directions or hydrostatic tension, are presented and compared. Graphene's response in shear stress is also investigated using molecular dynamics, where a noticeable asymmetric mechanical behavior is found. Stress-strain curves and elastic constants, such as, Young modulus, Poisson's ratio, bulk modulus, and shear modulus, are calculated. Our results are compared with available experimental estimates, as well as, with corresponding theoretical calculations. Finally, the effects of the anharmonicity of the extracted bond stretching and angle bending potentials on the mechanical properties of graphene are discussed.

Mechanical modeling of a single-walled carbon nanotube using the finite element approach

Summary — An analytical procedure to determine the elastic modulus of a single-walled carbon nanotube of armchair type is presented. The interacting forces between atoms are determined based on potentials derived from quantum mechanics. For the axial stretching, the Morse potential parameters were used, along with the bending potential. The model associates a hexagonal lattice where the nodes correspond to atoms and bars to the links (bonds) between them. The finite element model considers fixed position of one end while the tension forces are applied at the other end. The result of the simulation is the shape of the deformed nanotube and its elastic modulus. The influence of the overall dimensions of the nanotube on the modulus of elasticity was also examined.

Analytical Solution of Sidewise Buckling of Two-Hinged Circular Arch under Concentrated Force

By the setting torsional and lateral displacement function of sidewise buckling of two-hinged circular arch under concentrated force, the single-arch structure's bending, torsional deformation and external force potential can be constructed. An analytical solution for the lateral critical buckling load of two-hinged arch is first deduced by using the energy method; the results are also compared and analyzed by the finite element method. The results show that the analytical solution of single arch’s lateral critical buckling load is in good agreement with the finite element numerical solution, and the validity of the formula is proven.

Molecular Level Study of Negative Thick-Film Resist in MEMS by Employing a Coarse-Grained Molecular Dynamics Simulation

This paper reports on a newly developed coarse-grained molecular dynamics simulation for epoxy-based chemically-amplified photoresist dedicated to MEMS. To analyze photoresists material properties, Kremer-Grest model (bead-spring model) with an extended angle bending potential was newly employed. A uniaxial elongation simulation and the molecular diffusion simulation were performed to analyze the dependence of an elastic modulus and a molecular permeability on the cross-linked ratio of a photoresists, since these characteristics are important for a permeable membrane made of photoresist to control biological molecules diffusion in biomedical applications. The simulated dependencies of the elastic modulus and the molecular permeability on the cross-linked ratio of photoresists showed good correspondences with the experimental results. This suggests a photoresists membrane can be used as a molecular permeable membrane with controllable permeability by varying photolithography process parameters.

Coarse-Grained Potentials for Local Interactions in Unfolded Proteins.

Recent studies have revealed the key role of natively unfolded proteins in many important biological processes. In order to study the conformational changes of these proteins, a one-bead-per-amino-acid coarse grained (CG) model is developed, and a method is proposed to extract the potential functions for the local interactions between CG beads. Experimentally obtained Ramachandran data for the coil regions of proteins are converted into distributions of pseudo-bond and pseudo-dihedral angles between neighboring alpha-carbons in the polypeptide chain. These are then used to derive bending and torsion potentials, which are residue and sequence specific. The validity of the developed model is testified by studying the radius of gyration as well as the hydrodynamic properties of chemically denatured proteins.

Simulation of mechanical properties of epoxy-based chemically amplified resist by coarse-grained molecular dynamics

The mechanical properties of an epoxy-based chemically amplified resists with various cross-linking ratios were simulated using a newly developed coarse-grained molecular dynamics simulation that employs a bead–spring model. Models with the different cross-linking ratios were created in the molecular dynamics calculation step and uniaxial elongation simulations were performed. The results reveal that the simulated elastic modulus of the resist modeled by the Kremer–Grest model with an extended angle bending potential depends on the cross-linking ratio, its dependency exhibits good agreement with that determined by nanoindentation tests.

Time correlations and persistence probability of a Brownian particle in a shear flow

In this article, results have been presented for the two-time correlation functions for a free and a harmonically confined Brownian particle in a simple shear flow. For a free Brownian particle, the motion along the direction of shear exhibit two distinct dynamics, with the mean-square-displacement being diffusive at short times while at late times scales as $t^3$. In contrast the cross-correlation $\la x(t) y(t) \ra $ scales quadratically for all times. In the case of a harmonically trapped Brownian particle, the mean-square-displacement exhibits a plateau determined by the strength of the confinement and the shear. Further, the analysis is extended to a chain of Brownian particles interacting via a harmonic and a bending potential. Finally, the persistence probability is constructed from the two-time correlation functions.

An analytical molecular mechanics model for the elastic properties of crystalline polyethylene

We present an analytical model to relate the elastic properties of crystalline polyethylene based on a molecular mechanics approach. Along the polymer chains direction, the united-atom (UA) CH2-CH2 bond stretching, angle bending potentials are replaced with equivalent Euler-Bernoulli beams. Between any two polymer chains, the explicit formulae are derived for the van der Waals interaction represented by the linear springs of different stiffness. Then, the nine independent elastic constants are evaluated systematically using the formulae. The analytical model is finally validated by present united-atom molecular dynamics (MD) simulations and against available all-atom molecular dynamics results in the literature. The established analytical model provides an efficient route for mechanical characterization of crystalline polymers and related materials.

Molecular Structure of Methyldifluoroisocyanato Silane: A Combined Microwave Spectral and Theoretical Study

The structure of methyldifluoroisocyanato silane, MeF2SiNCO (2), has been studied by molecular rotational spectroscopy. The rotational spectrum has a complicated structure from (14)N nuclear quadrupole coupling and internal rotation of the methyl group. Cavity Fourier-transform microwave spectroscopy measurements were important for providing high spectral resolution to analyze the quadrupole and internal rotation fine structure. Broadband chirped-pulse Fourier-transform microwave spectroscopy was used to achieve high measurement sensitivity making it possible to observe the lower abundance C, N, O, and Si isotopologues in natural abundance for structure determination. Analysis of the microwave spectrum of the most abundant isotopomer of MeF2SiNCO (2) yields the rotational constants: A = 3827.347(7), B = 1264.5067(14), and C = 1240.6182(11) MHz. The spectrum has been analyzed in the I(r) representation for Cs symmetry, with inclusion of the 3-fold rotor (V3 = 446(50) cm(-1)). A partial substitution structure was obtained for the C, Si, N, and O atoms. The analysis was assisted by calculations of the equilibrium structure, using a 6-311++G (3df, 3pd) basis set, with calculations at each of the B3LYP, MP2, and CCSD(T) levels. The calculated and experimental rotational constants are only consistent with a trans-orientation at each of the HCSiN, CSiNC, and SiNCO centers; there is relatively close agreement between the experimental and the theoretical structures, especially at the CCSD(T) level. In addition, the observed low value for the (14)N quadrupole coupling term (χbb - χcc) implies a wide SiNC angle, which is consistent with the calculated values: 165.3° (B3LYP), 157.6° (MP2), and 157.4° (CCSD(T)). The skeletal bending potential is discussed.

Probing the Elasticity of DNA on Short Length Scales by Modeling Supercoiling under Tension

The wormlike-chain (WLC) model is widely used to describe the energetics of DNA bending. Motivated by recent experiments, alternative, so-called subelastic chain models were proposed that predict a lower elastic energy of highly bent DNA conformations. Until now, no unambiguous verification of these models has been obtained because probing the elasticity of DNA on short length scales remains challenging. Here we investigate the limits of the WLC model using coarse-grained Monte Carlo simulations to model the supercoiling of linear DNA molecules under tension. At a critical supercoiling density, the DNA extension decreases abruptly due to the sudden formation of a plectonemic structure. This buckling transition is caused by the large energy required to form the tightly bent end-loop of the plectoneme and should therefore provide a sensitive benchmark for model evaluation. Although simulations based on the WLC energetics could quantitatively reproduce the buckling measured in magnetic tweezers experiments, the buckling almost disappears for the tested linear subelastic chain model. Thus, our data support the validity of a harmonic bending potential even for small bending radii down to 3.5 nm.

Effect of substituents at the heteroatom on the structure and ligating properties of carbodicarbenes and its silicon analogs: a theoretical study

Density functional calculations have been carried out to investigate the effect of substituents attached to the heteroatoms of N-heterocyclic carbenes (NHCs) on the structure and ligating properties of carbon(0) [C(NHC)2] and silicon(0) [Si(NHC)2] compounds. The substituents were found to have a profound role on the structure and ligating properties of these classes of compounds. Fluoro- and chloro-substituted carbon(0) compounds were found to have quasi-linear geometries in which their C(0) characteristics are “masked.” However, their C(0) characteristics become prominent in their protonated species. Large negative charges and shallow bending potential of the central Cc–C0–Cc angle provide evidence for the “hidden C(0) characteristics” of these two compounds. Electron withdrawing substituents at N-atoms of the two NHCs dramatically decreases the basicity of these compounds. Both natural bonding and atoms in molecules analysis suggest that the most favorable Lewis structure of C(NHC)2 and Si(NHC)2 in their equilibrium geometries should be described (portrayed) as L=C=L and L → Si ← L, respectively, where L = NHCs.

Methyl branch effects on rheological behaviours of short-chain polypropylene under steady shear studied via nonequilibrium molecular dynamics simulations

The rheological behaviours of the steady sheared short-chain polypropylene (PP) fluid are studied using isobaric isothermal nonequilibrium molecular dynamics simulations. By comparing the behaviours of PP fluid with that of the linear alkane fluid of n-hexadecane (C16) having equal backbone length, we investigated the effects of the branch structure on shear thinning, rotational relaxation time, critical shear rate and potential energies. The results showed that the degree of shear thinning of the PP fluid is lower than that of the C16 fluid. With respect to different temperatures, the degree of shear thinning of the former is less sensitive than that of the latter. At the molecular level, potential energies including van der Waals nonbonding interaction and bond stretching, bond bending, and bond torsion interactions are discussed. Significantly, the varying tendency of the bending potential of the PP fluid at very high shear rates is contrary to that of the C16 fluid. We propose, therefore, that the branch structure affects the bending angle distribution such that it causes differences in the rheological behaviours of these two fluids. Furthermore, in all the molecular potentials of the PP fluid, the torsion potential of the dihedral angle is observed to be the strongest dependent upon temperature.

Synchronization and bundling of anchored bacterial flagella

The synchronization and bundling process of bacterial flagella is investigated by mesoscale hydrodynamic simulations. Systems with two to six flagella are considered, which are anchored at one end, and are driven by a constant torque. A flagellum is modelled as a linear helical structure composed of mass points with their elastic shape maintained by bonds, bending, and torsional potentials. The characteristic times for synchronization and bundling are analyzed in terms of motor torque, separation, and number of flagella. We find that hydrodynamic interactions determine the bundling behavior. The synchronization time is smaller than the bundling time, but their ratio depends strongly on the initial separation. The bundling time decreases with increasing number of flagella at a fixed radius in a circular arrangement due to multi-helix hydrodynamics.

Directional interactions in semiflexible single-chain polymer folding

Precise control over folded conformations of synthetic polymers is highly desirable in the development of functional nanomaterials for diverse applications. Introducing monomers capable of strong intramolecular hydrogen bonding is a promising route to achieve this control. In the present work we report the use of Wang–Landau Monte Carlo simulations of coarse-grained copolymers to explore the design parameters of these systems on their pathway to collapse. The highly directional nature of hydrogen-bonded supramolecular interactions is modelled by a directional non-bonded potential while a harmonic bending potential is used to take into account the flexibility of the polymer chain, thus making it possible to look at the interplay of both factors. The introduction of directional interactions in the copolymer chain leads to a sharper coil-globule collapse when compared to homopolymers composed of isotropic interacting beads only. Simultaneously, some of the stiffness-dependent structural properties become exacerbated when directional beads are present. Finally, from the heat capacity profiles for the different chain stiffness values we are able to distinguish the prevalence of the collapse of the backbone for highly flexible chains, while as chain stiffness increases folding of the co-polymer due to the directional interactions becomes the dominant feature.

Investigation of Molecular Diffusivity of Photoresist Membrane using Coarse-Grained Molecular Dynamics Simulation

Biocompatible permeable membranes integrated with a microfluidic system, which allow the diffusion of biological molecules with certain molecular weight, are desirable in biomedical applications. This paper reports on a molecular level study of the molecules permeability of epoxy-based chemically-amplified photoresists in MEMS by employing a coarse-grained molecular dynamics simulation. For analyzing diffusion coefficient of molecular in photoresists, Kremer-Grest model (bead-spring model) with an extended angle bending potential was employed. The simulation results show that, with increasing the cross-linked ratio of photoresists, the diffusion coefficient of small molecules in photoresist have larger diffusion coefficient, and which suggests photoresist membrane can be used as permeable membranes with controllable permeability by varying photolithography parameters.

Coarse-Grained Molecular Dynamics Simulation of Epoxy-Based Chemically-Amplified Resist for MEMS Application

ABSTRACTA unique simulation method of epoxy-based chemically-amplified resist by coarse-grained molecular dynamics was proposed. The mechanical properties of an epoxy-based chemically-amplified resists with various cross-linking ratios were simulated using a newly developed coarse-grained molecular dynamics simulation that employs a bead-spring model. Models with the different cross-linking ratios were created in the molecular dynamics calculation step and uniaxial elongation simulations were performed. The results reveal that the simulated elastic modulus of the resist modeled by the bead-spring model with an extended angle bending potential depends on the cross-linking ratio; its dependency exhibits good agreement with that determined by nanoindentation tests.

Testing Models For DNA Elasticity on Short Length Scales by Simulating DNA Supercoiling under Tension

The worm-like-chain (WLC) model is widely used to describe the energetics of DNA bending. However, for length scales much shorter than the persistence length the validity of a purely harmonic bending potential has been questioned by recent experiments. So-called sub-elastic chain (SEC) models were proposed that predict a lower elastic energy of highly bent DNA conformations. Until now, no unambiguous verification of these models has been obtained since probing the elasticity of DNA on short length scales remains challenging.

Mayer-sampling Monte Carlo calculations of uniquely flexible contributions to virial coefficients

We present methods for computing contributions to the virial coefficients uniquely associated with molecular flexibility, and we demonstrate their use with application to the third, fourth, and fifth virial coefficients of united-atom models of linear alkanes and methanol belonging to the suite of transferrable potentials for phase equilibria (TraPPE-UA). We find that these uniquely flexible contributions are more difficult to compute than the remainder of the coefficient, especially for the conditions at which they appear to be most important. The significance of these contributions relative to the full virial coefficient grows with the number of sites (the size of the molecule), the number of molecules, and, to a certain extent, the temperature. The nature of the site-site interactions is of great importance: the significance of the uniquely flexible contribution at third and fourth order is orders of magnitude larger for TraPPE-UA methanol, which has Coulombic interactions, than for TraPPE-UA propane, which does not, even though both models have three sites per molecule and comparable bending potentials. While the uniquely flexible contribution of TraPPE-UA propane has a negligible impact on its third-order virial-equation-of-state estimate of the critical point, the uniquely flexible contribution of TraPPE-UA methanol increases this estimate of its critical pressure by about 5%.

Branched Semiflexible Polymers: Theoretical and Simulation Aspects

AbstractRecent approaches for taking stiffness effects into account when modeling multifunctional polymer structures are reported. The theoretical part is focused on arbitrary tree‐like polymers, modeled through extensions of the GGS scheme that allows the inclusion of local constraints. The theoretical findings are compared to the results of numerical simulations in which stiffness is included into the bond fluctuation model with the help of additional bending potentials. The procedure is illustrated by evaluating the static properties of semiflexible linear chains, stars, cospectral polymers and rings. The dynamical properties are exemplified by the mechanical relaxation of semiflexible polymers, including situations in which the local conditions at different sites are the same or different.magnified image

Acceleration of trapped particles and beams

The dynamics of a quantum particle bound by an accelerating delta-functional potential is investigated. Three cases are considered, using the reference frame moving along with the δ-function, in which the acceleration is converted into the additional linear potential. (i) A stationary regime, which corresponds to a resonance state, with a minimum degree of delocalization, supported by the accelerating potential trap. (ii) A pulling scenario: an initially bound particle follows the accelerating delta-functional trap, within a finite time. (iii) The pushing scenario: the particle, which was initially localized to the right of the repulsive delta-function, is shoved to the right by the accelerating potential. For the two latter scenarios, the lifetime of the trapped particle and the largest velocity to which it can be accelerated while staying trapped are found. Analytical approximations are developed for the cases of small and large accelerations in the pulling regime and also for a small acceleration in the stationary situation, and in the regime of pushing. The same regimes may be realized by Airy-like planar optical beams guided by a narrow bending potential channel or crest. Physical estimates are given for an atom steered by a stylus of a scanning tunnelling microscope, and for the optical beam guided by a bending stripe.