Stress tensor in model polymer systems with periodic boundaries (original) (raw)
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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]
Molecular Dynamics Simulations of Polymers
Simulation Methods for Polymers, 2004
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]
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]
Recent advances in polymer molecular dynamics simulation and data analysis
Macromolecular Theory and Simulations, 1997
ABSTRACT Significant advances in molecular simulation methodology over the past decade have greatly reduced the traditional size-timescale bottleneck in molecular dynamics calculations. The development of the geometric statement function method allows for systems up to several hundred thousand atoms to be simulated for up to several nanoseconds in reasonable times on standard workstations. For constant energy simulations, the use of symplectic integrators ensures accurate dynamics, even at long simulation times, without velocity or other artificial rescaling schemes. Finally, new methods of frequency estimation allow for accurate vibrational mode frequency calculations even in the presence of chaotic motion on time scales twenty times shorter than the standard fast Fourier transform, with an additional improvement in the sensitivity of the results when initial dynamics conditions are carefully chosen.
Virtual polymeric materials were created and used in computer simulations to study their behavior under uniaxial loads. Both single-phase materials of amorphous chains and two-phase polymer liquid crystals (PLCs) have been simulated using the molecular dynamics method. This analysis enables a better understanding of the molecular deformation mechanisms in these materials. It was confirmed that chain uncoiling and chain slippage occur concurrently in the materials studied following predominantly a mechanism dependent on the spatial arrangement of the chains (such as their orientation). The presence of entanglements between chains constrains the mechanical response of the material. The presence of a rigid second phase dispersed in the flexible amorphous matrix influences the mechanical behavior and properties. The role of this phase in reinforcement is dependent on its concentration and spatial distribution. However, this is achieved with the cost of increased material brittleness, as crack formation and propagation is favored. Results of our simulations are visualized in five animations.
Structure, molecular dynamics, and stress in a linear polymer
Mechanics of Materials, 2013
We present a study correlating uniaxial stress in a polymer with its underlying structure when it is strained. The uniaxial stress is significantly influenced by the mean-square bond length and mean bond angle. In contrast, the size and shape of the polymer, typically represented by the end-to-end length, mass ratio, and radius of gyration, contribu te negligibly. Among externally set control variables, density and polymer chain length play a critical role in influencing the anisotropic uniaxial stress. Short chain polymers more or less behave like rigid molecules. Temperature and rate of loadin g, in the range considered, have a very mild effect on the uniaxial stress.
Atomistic Molecular Dynamics Simulations of Polymer/Graphene Nanostructured Systems
Materials Today: Proceedings
A) Structural Properties B) Self-Diffusion C) Dynamic Structure Factor D) Friction Factor-Zero-Shear Rate Viscosity 5.4. Conclusions 6. DYNAMICS OF N-ALKANES-THE FREE VOLUME THEORY 6.1. Free Volume Theory 6.2. Molecular model, Methodology and Systems Studies 6.3. Density of Liquid n-alkanes 6.4. Geometrical Analysis of Free volume 6.5. Diffusion of Liquid n-alkanes 6.6. Conclusions 7. DIFFUSION OF BINARY LIQUID N-ALKANE MIXTURES iv 7.1. Molecular model, Methodology and Systems Studies 7.2. Free Volume Theory of Vrentas and Duda 7.3. Chain-End Free Volume Theory Proposed by Bueche and von Meerwall 7.4. Structure of Binary Blends 7.5. Terminal Relaxation-Diffusion of Binary Blends 7.6. Conclusions 8. ATOMISTIC MODELLING OF STRESS RELAXATION EXPERIMENT UPON CESSATION OF STEADY-STATE UNIAXIAL ELONGATIONAL FLOW 8.1. Introduction 8.2. A Hierarchical Methodology 8.2.1. Stage I: Generation of oriented configurations 8.2.2. Stage II: From field-on EBMC simulations to field-off MD simulations 8.2.3. Stage III: Mapping to a coarse-grained model of dynamics 8.3. Calculations by the Rouse model 8.3.1. Relaxation of the stress component σ xx 8.3.2. The relaxation of the conformation tensor component c xx 8.4. Calculation of the stress 8.5. Results A) Equilibrium conformational properties B) Relaxation of the chain end-to-end vector C) Relaxation of the conformation tensor components D) Relaxation of the stress tensor components E) Comparison to the Rouse model predictions F) The shear stress relaxation modulus G(t) 8.6. Conclusions 9. CONCLUSIONS AND RECOMMENDATIONS 9.1. Main results 9.2. Recommendations for future work v APPENDIX A. Time Correlation Functions B. The Fixman potential C. Finite Rouse Model D. Dynamic Structure factor S(q,t) according to Rouse model E. MD Simulations in the NTL x σ yy σ zz Statistical Ensemble BIBLIOGRAPHY CHAPTER 1 INTRODUCTION The ability to predict the key physical and chemical properties of polymers from their molecular structure is of great value in the design of polymers. Performance criteria, which must be satisfied for the technological applications of polymers, have become increasingly more stringent with the recent advances in many areas of technology. Consequently, the development of predictive computational schemes to evaluate candidates for specific applications has gained urgency. To this direction, with the huge development of computers nowadays, computer simulation techniques have become valuable tools of fundamental and basic research in polymer science. Brownian dynamics, molecular dynamics and non-equilibrium dynamics are the main methods that are employed for the study of dynamic and viscoelastic properties of polymer liquids [1]. Polymers, however, are macromolecular systems characterized by a complex internal microstructure that gives rise to an enormous spectrum of length scales in their structure and a very wide spectrum of time scales in their molecular motion. Consequently the dynamic behavior of polymers is substantially different than those of a simple Newtonian liquid, exhibiting both liquidlike and solidlike characteristics [2],[3]. Even a single chain exhibits a much more complicated structure, than the simple atomic liquids, as it is shown in Fig. 1.1 [1]; from the scale of a single chemical bond (~ 1 Å) to the persistence statistical length (~ 10 Å) to the coil radius of the chain (~ 100 Å). Intramolecular correlations and local packing of chains in the bulk exhibit features on the length scale of bond lengths and atomic radiii. The statistical, Kuhn, segment length of a typical synthetic randomly coiled polymer is on the order of 10 Å and can be considerable larger for very stiff polymers. The radius of gyration of entire chains in the amorphous bulk scales as N 1/2 with the chain length N and is on the order of 100 Å for common molecular weights. On the other hand the smallest dimension of microphases times for volume and enthalpy relaxation in a glassy polymer just a few degrees below the glass transition temperature are on the order of years. Molecular simulations, on the other hand, particularly those of atomistic nature typically tracks, the evolution of model systems of length scale of about 100 Å for times up to a few tens of ns. Thus a straightforward application of the molecular dynamics (MD) simulations, for example, in order to extract the dynamic properties of polymers is at least problematic since it would require enormous computer time and would also MD simulations and a thorough mapping of the MD simulation data onto proper theoretical coarse-grained models. Key in our hierarchical approach is the combination of both MC and MD atomistic simulations. First the simulated systems are equilibrated through a very powerful MC algorithm, the end-bridging Monte Carlo method. With this algorithm very long polymer melts have been fully equilibrated at all length scales. Then detailed atomistic MD simulations, incorporating the multiple time step algorithm, have been conducted to track the evolution of the simulated systems for very long times, up to a few hundreds of ns. simulations of short polyethylene (PE) melts in the unentangled regime are presented. In the next chapter, i.e. chapter 5, the hierarchical methodology introduced in chapter 4, is extended to longer polymer melts in the crossover regime from unentangled (Rouse behavior) to entangled regime. The short n-alkanes like regime, is studied in chapter 6 through atomistic MD simulations. In this regime extra free volume phenomena due to chain ends are very
Extracting continuum-like deformation and stress from molecular dynamics simulations
Computer Methods in Applied Mechanics and Engineering, 2015
We present methods that use results from molecular dynamics (MD) simulations to construct continuum parameters, such as deformation gradient and Cauchy stress, from all or any part of an MD system. These parameters are based on the idea of minimizing the difference between MD measures for deformation and traction and their continuum counterparts. The procedures should be applicable to non-equilibrium and inhomogeneous systems, and to any part of a system, such as a polymer chain. The resulting procedures provide methods to obtain first and higher order deformation gradients associated with any subset of the MD system, and associated expressions for the Cauchy and nominal stresses. As these procedures are independent of the type of interactions, they can be used to study any MD simulation in a manner consistent with continuum mechanics and to extract information exploitable at the continuum scale to help construct continuum-level constitutive models. c
Molecular-dynamics simulations of stress relaxation in metals and polymers
Physical Review B, 1994
Molecular-dynamics simulations of stress relaxation have been performed for models of metals and polymers. A method that employs coupling between the simulation cell and an applied stress as well as an external thermal bath has been used. Two-dimensional models of the materials are defined with interactions described by the Lennard-Jones (Mie 6-12) and harmonic potentials. A special method is employed to generate chains in dense polymeric systems. In agreement with experiments, simulated stressrelaxation curves are similar for metals and polymers. At the same time, there exists an essential difference in the stress-strain behavior of the two kinds of simulated materials. During the relaxation, trajectories of the particles in different materials display a common feature: There exist domains in which movement of the particles is highly correlated. Thus, the simulation results support the cooperative theory of stress relaxation.