Chemically realistic modeling

Fig. 5.7. Simplified schematic flow chart for the optimization of the parameters of the bond length and bond angle potentials. The input parameters from the chemically realistic model are the moments (L), (L2), ( ), (02), (LG) taken from the bond length and bond angle distributions, and the reduced effective barrier (W) from the torsion potentials. From Tries [184]... 

At this point we return to the polymer which is simplest with respect to its chemical structure, namely polyethylene (PE). In addition, for this polymer, the experimental database is much more complete, and also simulations of chemically realistic models, such as those described by Eqs. (5.7)—(5.11), are possible at high temperatures (Fig. 5.2a). Thus the prospects are very good that more can be learnt about the merits, as well as the limitations, of this modeling approach. 

The Coulomb interaction is long-range, which necessitates use of special numerical methods for efficient simulation.30 When one tries to understand the glass transition in a chemically realistic model, these long-range Coulomb interactions add further numerical overhead so that the most extensive glass transition simulations of realistic models were done for apolar molecules. 

These models retain the form of the nonbonded interaction used in the chemically realistic modeling, i.e., they use either an interaction of the Lennard-Jones or of the exponential-6 type. The repulsive parts of these potentials generate the necessary local excluded volume, whereas the attractive long-range parts can be used to model varying solvent quality for dilute or semi-dilute solutions and to generate a reasonable equation-of-state behavior for polymeric melts. 

As we discussed in the section on the structural properties of amorphous polymers, the relative size of the bond length and the Lennard-Jones scale is very different when comparing coarse-grained models with real polymers or chemically realistic models, which leads to observable differences in the packing. Furthermore, the dynamics in real polymer melts is, to a large extent, determined by the presence of dihedral angle barriers that inhibit free rotation. We will examine the consequences of these differences for the glass transition in the next section. 

We can therefore conclude that differences in the structural relaxation between bead-spring and chemically realistic models can be attributed to either the differences in packing that we discussed above or the presence of barriers in the dihedral potential in atomistic models. To quantify the role of dihedral barriers in polymer melt dynamics, we now examine high-temperature relaxation in polymer melts. 

Poly butadiene Mode-Coupling Theory Analysis of Molecular Dynamics Simulations Using a Chemically Realistic Model. 

The next step should lead to the meeting point with the other line of research and should provide chemically realistic models of an actual reaction that shows irregular behaviour. Chaos in the model should be proved and understood theoretically, not just shown numerically. 

Abstract We present in this contribution results from Molecular Dynamics (MD) simulations of a chemically realistic model of 1,4-polybutadiene (PB). The work we will discuss exemplifies the physical questions one can address with these types of simulations. We will specifically compare the results of the computer simulations with nuclear magnetic resonance (NMR) experiments, neutron scattering experiments and dielectric data. These comparisons will show how important it is to understand the torsional dynamics of polymers in the melt to be able to explain the experimental findings. We will then introduce a freely rotating chadn (FRC) model where all torsion potentials have been switched off and show the influence of this procedure on the qualitative properties of local dynamics through comparison with the chemically realistic (CRC) model. 

Another strong point of the simulation approach is its ability to selectively change parts of the model Hamiltonian. In this way one can compare a chemically realistic model of PB with a freely rotating chain version of the same polymer and does not have to switch to a completely different polymer with some of the same properties like is unavoidable in experiments [33]. With this approach we could establish that identical structure on the two-body correlation function level (single chain and liquid structure factors) does not imply identical dynamics which raises questions on the applicability of the mode-coupling theory of the glass transition to polymer melts. 

An attractive virtue of PRISM theory is the ability to derive analytic solutions for many problems if the most idealized Gaussian thread chain model of polymer structure is adopted. The relation between the analytic results and numerical PRISM predictions for more chemically realistic models provides considerable insight into the question of what aspects of molecular structure are important for particular bulk properties and phenomena. Moreover, it is at the Gaussian thread level that connections between liquid-state theory and scaling and field-theoretic approaches are most naturally established. Thus, throughout the chapter analytic thread PRISM results are presented and discussed in conjunction with the corresponding numerical studies of more realistic polymer models. 

The second contribution to g(r) in Eq. (3.2) is called the correlation hole effect by deGennes and is associated with the longer wavelength universal aspects of chain connectivity and interchain repulsive forces. On intermediate length scales it has a critical power law form due to chain conformation self-similarity, and this simple analytic form remains an excellent representation even for chemically realistic models when intersite separations exceed an intrinsic (/V-independent) distance of the order of 3-5 site diameters... 

Fig. 9 (a) Zero pressure isobar in the 1,4-polybutadiene melt. The line shows MD results from the chemically realistic model. The symbols show average densities in the MpT MC simulation for the optimal choices of parameters for different versions of the LJ-type interaction. From Strauch et al. [117]. (b) Comparison between experimental data for polybutadiene melts in the temperature range from 299 to 461 K symbols) and calculations using PC-SAFT dashed curves) or TPTl-MSA solid curves) models. Parameters of the fits are quoted in the figure, where m is the effective degree of polymerization, which is also treated as a fit parameter and a and refer to a nonbonded LJ (12,6) potential). The bond length potential is the FENE -h LJ potential of Sect. 2.2, and no bond angle potential is used. Adapted from Binder et al. [120]... 

For fully atomistic aU-atom models, it is often difficult to find efficient MC moves to relax their configurations, and then MD is normally the method of choice. We note, however, that for chemically realistic models of polymer blends equilibration by MD methods is extremely difficult, if at all possible. Dealing with such systems is still an unsolved challenge. 

While the bond lengths between atomistic monomeric units in a chemically realistic model are fixed, the harmonic potential between the coarse-grained segments stems from the Gaussian distribution of distances between sufficiently distant monomeric units along the backbone of a chemically realistic representation. 

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