Scaling behavior molecular mechanics

Molecular dynamics is a deterministic process based on the simulation of molecular motion ly solving Newton s equations of motion for each atom and incrementing the position and velocity of each atom by use of a small time increment. If a molecular mechanics force field of adequate parameterization is available for the molecular system of interest and the phenomenon under study occurs within the time scale of simulation, this technique offers an extremely powerful tool for dissecting the molecular nature of the phenomenon and the details of the forces contributing to the behavior of the system. 

The molecular mechanism determining the chemical response induced by mechanical loading is crucial to identifying the mechanochemical properties of materials. Although it is challenging to address directly the behavior of the chemical bonds experimentally, the behavior of chemical bonds is reflected in mechanical properties in deformation. Thus, it is crucial to make an effort to measure the mechanical properties of materials and compare them with the computatimial results. From the computational methods, we could find reliable mechanisms that explain the behavior of chemical bonds on the atomic scale. 

As illustrated above, nonadiabatic dynamics exhibits vividly how electrons move in and between molecules. Complex natural orbitals, in particular SONO in the present case, clearly illustrate how the electronic wavefunction evolves in time. In addition to the time scale, the driving mechanism for the electron migration has also been illustrated. By clarifying such complex electron behavior, not available using stationary-state quantum chemistry, our understanding of realistic chemical reactions is greatly enhanced. As a result, it has clearly been shown that nonadiabatic electron wavepacket theory is invaluable in the analysis of non-rigid and mobile electronic states of molecular systems. 

The behavior given in the above examples for polymer response variation with time and temperature under steady-state dynamic loading is directly related to the deformation mechanisms associated with the long chain nature of polymer molecules. As illustrated in Fig. 5.23, low frequency response is similar to high temperature (rubbery) response, and high frequency response is similar to low temperature (glassy) response. The basic mechanical responses therefore relate across the time and temperature scales, as do the underlying molecular mechanisms. A brief description of these mechanisms follows. (For more detailed information the reader is referred to (Lazan, (1968)) and (Menard, (1999)). 

In polymers at very low temperatirres, the classical Bernoulli-Euler continuum elasticity becomes not valid below approximately 5 nm. The size of this characteristic volume increases with increasing temperature and higher order strain elasticity along with molecular dynamics approach has to be used as the bridging law to connect behavior of the discrete matter at nano-scale with the mechanical response of continuous matter at larger length scales. 

Numerical methods with different time- and length scales are employed and developed to investigate material properties and behaviors. Among them, molecular modeling can predict the molecular behaviors and correlate macroscopic properties of a material with various variables. The most popular techniques include molecular mechanics (MM), MD, and Monte Carlo (MC) simulation. These techniques are now routinely used to investigate the structure, dynamics, and thermodynamics of inorganic, biological, and polymer systems. They have recently been used to predict the thermodynamic and kinetic properties of nanoparticle-matrix mixtures, interfacial molecular structure and interactions, molecular dynamic properties, and mechanical properties. 

In literature, some researchers regarded that the continuum mechanic ceases to be valid to describe the lubrication behavior when clearance decreases down to such a limit. Reasons cited for the inadequacy of continuum methods applied to the lubrication confined between two solid walls in relative motion are that the problem is so complex that any theoretical approach is doomed to failure, and that the film is so thin, being inherently of molecular scale, that modeling the material as a continuum ceases to be valid. Due to the molecular orientation, the lubricant has an underlying microstructure. They turned to molecular dynamic simulation for help, from which macroscopic flow equations are drawn. This is also validated through molecular dynamic simulation by Hu et al. [6,7] and Mark et al. [8]. To date, experimental research had "got a little too far forward on its skis however, theoretical approaches have not had such rosy prospects as the experimental ones have. Theoretical modeling of the lubrication features associated with TFL is then urgently necessary. 

From experimental results, the variation of film thickness with rolling velocity is continuous, which validates a continuum mechanism, to some extent in TFL. Because TFL is described as a state in which the film thickness is at the molecular scale of the lubricants, i.e., of nanometre size, common lubricants may exhibit microstructure in thin films. A possible way to use continuum theory is to consider the effect of a spinning molecular confined by the solid-liquid interface. The micropolar theory will account for this behavior. 

The linkage of microscopic and macroscopic properties is not without challenges, both theoretical and experimental. Statistical mechanics and thermodynamics provide the connection between molecular properties and the behavior of macroscopic matter. Coupled with statistical mechanics, computer simulation of the structure, properties, and dynamics of mesoscale models is now feasible and can handle the increase in length and time scales. 

If the ordered, crystalline regions are cross sections of bundles of chains and the chains go from one bundle to the next (although not necessarily in the same plane), this is the older fringe-micelle model. If the emerging chains repeatedly fold buck and reenter the same bundle in this or a different plane, this is the folded-chain model. In either case the mechanical deformation behavior of such complex structures is varied and difficult to unravel unambiguously on a molecular or microscopic scale. In many respects the behavior of crystalline polymers is like that of two-ph ise systems as predicted by the fringed-micelle- model illustrated in Figure 7, in which there is a distinct crystalline phase embedded in an amorphous phase (134). 

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