Reply to comment of Dr Meier on “Reactivity of Stressed molecules…” J. Mol. Struct. (Theochem) 677 (2004) 77–83 (original) (raw)
Related papers
Stress tensor in model polymer systems with periodic boundaries
Die Makromolekulare Chemie, Theory and Simulations, 1993
The calculation of the stress tensor from molecular simulations of atomistic model polymer systems employing periodic boundary conditions is discussed. Starting from the dynamical equations governing the motion of sites, correct double summation forms of the atomic and the molecular virial equations are derived, which are valid for flexible, infinitely stiff and rigid chain models even in the presence of interactions between different images of the same parent macromolecule. A new expression for the true instantaneous stress (flux of momentum through the faces of the simulation box) is derived and shown to exhibit large fluctuations when applied in molecular dynamics simulations. A new equation for the thermodynamic stress, cast exclusively in terms of intermolecular forces on interaction sites, is also derived. Application to Monte Carlo simulations shows that the molecular virial expression exhibits the smallest fluctuations among all stress expressions discussed, and thus allows computation of the thermodynamic stress with least uncertainty. A scheme is developed for the calculation of surface tension from intermolecular forces only.
Polymer fracture—A simple model for chain scission
Journal of Polymer Science: Polymer Physics Edition, 1984
A simple model for calculating the fracture process for a single extended-chain molecule such as polyethylene is considered. The model consists of a chain of N coupled Morse oscillators. There exists a critical overall extension AL, below which the fracture is energetically unfavorable but above which fracture is favored both energetically and kinetically. This elongation AL, scales as N''2.
Shock Hugoniot calculations of polymers using quantum mechanics and molecular dynamics
The Journal of Chemical Physics, 2012
Using quantum mechanics (QM) and classical force-field based molecular dynamics (FF), we have calculated the principle shock Hugoniot curves for numerous amorphous polymers including poly[methyl methacrylate] (PMMA), poly[styrene], polycarbonate, as well as both the amorphous and crystalline forms of poly[ethylene]. In the FF calculations, we considered a non-reactive force field (i.e., polymer consistent FF). The QM calculations were performed with density functional theory (DFT) using dispersion corrected atom centered pseudopotentials. Overall, results obtained by DFT show much better agreement with available experimental data than classical force fields. In particular, DFT calculated Hugoniot curves for PMMA up to 74 GPa are in very good agreement with experimental data, where a preliminary study of chain fracture and association was also performed. Structure analysis calculations of the radius of gyration and carbon-carbon radial distribution function were also carried out to elucidate contraction of the polymer chains with increasing pressure.
Breaking of a polymer – multidimensional classical transition state theory and beyond
Chemical Physics Letters, 1999
When a mechanical force stretches a polymer molecule, each bond in the chain becomes metastable. The polymer breaks by the escape of any bond from this state. Multidimensional classical transition state theory is used to calculate the frequency Ž. Ž. factor for the rate of breaking n. Using a continuum approach, we also calculate the frequency factor n associated cross sep with the rate of separation of the two broken ends from one another. The net frequency factor is taken to be the harmonic mean of n and n. While our results are lower than those of simple transition state theory, it is orders of magnitude cross sep larger than the results of the available simulations. This difference is ascribed to the friction that has been included in the simulations.
Physical Review E
The main issue of our original paper ͓Phys. Rev. E 58, 6766 ͑1998͔͒ is to demonstrate that the so-called atomic scaling, in which all available degrees of freedom are coupled to the pressure bath, is more efficient for stress relaxation in large molecules than the conventional molecular scaling in which the molecular centers of mass are coupled to the pressure bath, and internal degrees of freedom are left unchanged. Marchi and Procacci ͑MP͒ claim that this is not the case and try to demonstrate this by a simulation of the alkane system II ͑dotriacontanes, 32 monomers͒ treated in our paper, comparing atomic and molecular scaling with their R-RESPA integrator. They state that the stress-relaxation process should happen within a few picoseconds. As a possible explanation for their findings, they state an incorrect computation of the molecular pressure in our paper. Furthermore, MP claim there are further inconsistencies in our paper. In this Reply, it will be shown that contrary to the statements of MP, the virial has been computed correctly. Moreover, the inconsistency statement by MP results from the fact that MP have confused features in the figures of our paper. Finally, we do not agree that the stress relaxation of dotriacontanes seen in our simulations on the time scale of hundreds of picoseconds should happen within a few picoseconds. At room temperature, these systems form waxes and a slowing down of stress relaxation with respect to the liquid phase is to be expected. ͓S1063-651X͑00͒11412-6͔
Molecular dynamics (MD) is a powerful technique for computing the equilibrium and dynamical properties of classical many-body systems. Over the last fifteen years, due to the rapid development of computers, polymeric systems have been the subject of intense study with MD simulations [1]. At the heart of this technique is the solution of the classical equations of motion, which are integrated numerically to give information for the positions and velocities of atoms in the system [2], [3], [4]
The molecular dynamics of polymer chains with rigid bonds. Local relaxation times
1980
Local movements of small elements (one or a pair of chain units) of the chain composed of parts joined by rigid bonds have been examined by molecular dynamics. "]7he chain was immersed in a solvent of low molecular weight. The interactions between the particles or between them and similar solvent particles are described by the Lennard-Jones potential. Chains possessing various numbers of units were examined at various temperatures and concentrations. The results of numerous experiments have been compared with the analytical results for the elastic Hearst-Harris model. The relaxation of the average eonsine of angles of rotation of the rigid chain elements is ldentmal in practme with that of the equivalent pseudo-elastic elements of the Hearst~-Harris model. Each elastic element in the model is equivalent to one rigid chain unit and the average angle between the elements in the elastxc model is similar to that between rigid chain units. The relaxation of the mean square cosine of angles of rotation is more rapid than in the elastic model. The ratio of t, the average and the mean square cosine of angles of rotation is similar to that for a separate, lagid, anisotropie particle in a viscous solvent. Pronounced anisotropy of the local relaxation properties is shown to exist; the values of the various times which can elapse in dielectrm relaxation and the depolalazation of luminescence have been established.
CHAPTER XX MOLECULAR DYNAMICS SIMULATIONS OF POLYMERS
2000
Molecular dynamics (MD) is a powerful technique for computing the equilibrium and dynamical properties of classical many-body systems. Over the last fifteen years, due to the rapid development of computers, polymeric systems have been the subject of intense study with MD simulations [1]. At the heart of this technique is the solution of the classical equations of motion, which are integrated numerically to give information for the positions and velocities of atoms in the system [2], [3], [4]
Physical Review E, 2001
Contrary to the findings of Mülders, Toxvaerd, and Kneller ͓Phys. Rev. E 58, 6766 ͑1998͔͒ ͑MTK͒, we are unable to discern any difference in the behavior of long chain alkanes simulated by molecular dynamics at constant pressure using either atomic or molecular scaling schemes. This result confirms our previous study ͓M. Marchi and P. Procacci, J. Chem. Phys. 109, 5194 ͑1998͔͒ on hydrated proteins published at the same time as the MTK's paper. This Comment indicates that errors in the calculation of the pressure tensor might be responsible for at least a part of the MTKs results.