Computer simulation material properties

The complexity of polymeric systems make tire development of an analytical model to predict tlieir stmctural and dynamical properties difficult. Therefore, numerical computer simulations of polymers are widely used to bridge tire gap between tire tlieoretical concepts and the experimental results. Computer simulations can also help tire prediction of material properties and provide detailed insights into tire behaviour of polymer systems. A simulation is based on two elements a more or less detailed model of tire polymer and a related force field which allows tire calculation of tire energy and tire motion of tire system using molecular mechanisms, molecular dynamics, or Monte Carlo teclmiques 1631. 

Cillan M J 1991. Calculating the Properties of Materials from Scratch, In Meyer M and V Pontikis (Editors). Computer Simulation, NATO ASI Series E 205 (Computer Simulations in Materials Science) pp. 257-281. 

An area of great interest in the polymer chemistry field is structure-activity relationships. In the simplest form, these can be qualitative descriptions, such as the observation that branched polymers are more biodegradable than straight-chain polymers. Computational simulations are more often directed toward the quantitative prediction of properties, such as the tensile strength of the bulk material. 

Material properties can be further classified into fundamental properties and derived properties. Fundamental properties are a direct consequence of the molecular structure, such as van der Waals volume, cohesive energy, and heat capacity. Derived properties are not readily identified with a certain aspect of molecular structure. Glass transition temperature, density, solubility, and bulk modulus would be considered derived properties. The way in which fundamental properties are obtained from a simulation is often readily apparent. The way in which derived properties are computed is often an empirically determined combination of fundamental properties. Such empirical methods can give more erratic results, reliable for one class of compounds but not for another. 

The response factors are characteristic for the layer buildup of the selected wall and are calculated before (by a preprocessor program) or at the beginning ol the simulation. Numerical reasons limit the time step to approximately 10 to 60 min, depending on the thickness and material properties of the wall layers. The method allows the calculation of surface temperatures and heat fluxes bur not the determination of the temperature distribution within the wall. Due to the precalculation of these response factors, the computer time for the simulation might be significantly reduced. 

Computer simulations therefore have several inter-related objectives. In the long term one would hope that molecular level simulations of structure and bonding in liquid crystal systems would become sufficiently predictive so as to remove the need for costly and time-consuming synthesis of many compounds in order to optimise certain properties. In this way, predictive simulations would become a routine tool in the design of new materials. Predictive, in this sense, refers to calculations without reference to experimental results. Such calculations are said to be from first principles or ab initio. As a step toward this goal, simulations of properties at the molecular level can be used to parametrise interaction potentials for use in the study of phase behaviour and condensed phase properties such as elastic constants, viscosities, molecular diffusion and reorientational motion with maximum specificity to real systems. Another role of ab initio computer simulation lies in its interaction... 

It is clear from the forgoing discussions that the important material properties of liquid crystals are closely related to the details of the structure and bonding of the individual molecules. However, emphasis in computer simulations has focused on refining and implementing intermolecular interactions for condensed phase simulations. It is clear that further work aimed at better understanding of molecular electronic structure of liquid crystal molecules will be a major step forward in the design and application of new materials. In the following section we outline a number of techniques for predictive calculation of molecular properties. 

As computer power continues to increase over the next few years, there can be real hope that atomistic simulations will have major uses in the prediction of phases, phase transition temperatures, and key material properties such as diffusion coefficients, elastic constants, viscosities and the details of surface adsorption. 

All the macroscopic properties of polymers depend on a number of different factors prominent among them are the chemical structures as well as the arrangement of the macromolecules in a dense packing [1-6]. The relationships between the microscopic details and the macroscopic properties are the topics of interest here. In principle, computer simulation is a universal tool for deriving the macroscopic properties of materials from the microscopic input [7-14]. Starting from the chemical structure, quantum mechanical methods and spectroscopic information yield effective potentials that are used in Monte Carlo (MC) and molecular dynamics (MD) simulations in order to study the structure and dynamics of these materials on the relevant length scales and time scales, and to characterize the resulting thermal and mechanical proper-... 

Monte Carlo computer simulations were also carried out on filled networks [50,61-63] in an attempt to obtain a better molecular interpretation of how such dispersed fillers reinforce elastomeric materials. The approach taken enabled estimation of the effect of the excluded volume of the filler particles on the network chains and on the elastic properties of the networks. In the first step, distribution functions for the end-to-end vectors of the chains were obtained by applying Monte Carlo methods to rotational isomeric state representations of the chains [64], Conformations of chains that overlapped with any filler particle during the simulation were rejected. The resulting perturbed distributions were then used in the three-chain elasticity model [16] to obtain the desired stress-strain isotherms in elongation. 

Advances in computational capability have raised our ability to model and simulate materials structure and properties to the level at which computer experiments can sometimes offer significant guidance to experimentation, or at least provide significant insights into experimental design and interpretation. For self-assembled macromolecular structures, these simulations can be approached from the atomic-molecular scale through the use of molecular dynamics or finite element analysis. Chapter 6 discusses opportunities in computational chemical science and computational materials science. 

From these early beginnings, computer studies have developed into sophisticated tools for the understanding of defects in solids. There are two principal methods used in routine investigations atomistic simulation and quantum mechanics. In simulation, the properties of a solid are calculated using theories such as classical electrostatics, which are applied to arrays of atoms. On the other hand, the calculation of the properties of a solid via quantum mechanics essentially involves solving the Schrodinger equation for the electrons in the material. 

Process simulators contain the model of the process and thus contain the bulk of the constraints in an optimization problem. The equality constraints ( hard constraints ) include all the mathematical relations that constitute the material and energy balances, the rate equations, the phase relations, the controls, connecting variables, and methods of computing the physical properties used in any of the relations in the model. The inequality constraints ( soft constraints ) include material flow limits maximum heat exchanger areas pressure, temperature, and concentration upper and lower bounds environmental stipulations vessel hold-ups safety constraints and so on. A module is a model of an individual element in a flowsheet (e.g., a reactor) that can be coded, analyzed, debugged, and interpreted by itself. Examine Figure 15.3a and b. 

In such cases it is reasonable to step down to the molecular level of these materials and to think of a conjecture that many of the condensed materials properties may actually be connected to the properties of the individual macromolecules. Pursuing this idea one may follow two approaches. The first consists of molecular modeling of structures on a computer and simulating the material properties of interest. Alternatively, attempts can be made to set up a rigorous basic molecular theory. 

Both routes have their limitations. The basic theory of complex structures, which are encountered with macromolecules, often does not allow analytic solutions. Incisive, though reasonable, approximations have to be introduced. On the other hand, rigorous simulations can be made by means of molecular dynamics, but this technique has the limitation that only rather small and fast moving objects can be treated within a reasonable time, even with the fastest computers presently available. This minute scale gives valuable information on the local structure and local dynamics, but no reliable predictions of the macro-molecular properties can be made by this technique. All other simulations have to start with some basic assumptions. These in turn are backed by results obtained from basic theories. Hence both approaches are complementary and are needed when constructing a reliable framework for macromolecules that reflects the desired relation to the materials properties. 

---