Simulation and Comparison with Experiment

Experimentally, as in aPP, the methylene and methyl region show the largest effect. Therefore, we have chosen the tetramer depicted in the insert of Fig. 40 as model molecule for the extended polymer chain. The y-neighbors 

In [26], the conformational statistics is encoded by a pair of a priori matrices, p ij and plj (In PIB, two matrices are necessary as there are two different types of main chain atoms, methylene and quaternary). As for PE, the probability for a larger sequence of dihedral angles can be calculated by a modified version of Eq. (2.14). 

In this formula, p denotes the vector of a priori probabilities for a single dihedral angle, and q p qj - the respective matrices of conditional probabilities. In the numerical implementation, Eq. (5.3) was taken as a basis for the generation of a large number of chains by a random sampling technique, and p(0fj. fj was obtained as a numerical average. 

Unfortunately, the a priori matrices were available only for T = 400 K which differs markedly from the experimental glass transition temperature 

The insert displays the model molecule for PIB with the labels of the atoms in the center of the molecule. They are considered representative of an extended chain. The relevant dihedral angles are depicted 

---

Lokhman, V. N., Makarov, A. A., Petrova, I. Yu., Ryabov, E. A., and Letokhov, V. S. (1999). Transition spectra in the vibrational quasicontinuum of polyatomic molecules. IR multiple-photon absorption in SFe. II. Theoretical simulations and comparison with experiment. Journal of Physical Chemistry, 103, 11299-11309. 

Schneider, C., Schwetz, M., Miinstedt, H., Kaschta, JK. The axial velocity distribution of a polyethylene strand during extrusion Simulation and comparison with experiments. Mech. Time-Depend. Math. (2004) 8, pp. 215-224... 

Yang X, Wang L, He X (2010) Kinetics of nonideal hyperbranched A2-1-B3 polycondensation Simulation and comparison with experiments. J Polym Sci A Polym Chem 48 5072-... 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

The remainder of this contribution is organized as follows In the next section, the connection between the experimentally observed dynamic Stokes shift in the fluorescence spectrum and its representation in terms of intermolecular interactions will be given. The use of MD simulation to obtain the SD response will be described and a few results presented. In Section 3.4.3 continuum dielectric theories for the SD response, focusing on the recent developments and comparison with experiments, will be discussed. Section 3.4.4 will be devoted to MD simulation results for e(k, w) of polar liquids. In Section 3.4.5 the relevance of wavevector-dependent dielectric relaxation to SD will be further explored and the factors influencing the range of validity of continuum approaches to SD discussed. 

Fig. 3. Resolution of subsurface atomic positions in STM scans on Al(lll) and comparison with experiments. The difference in apparent height between the fee hollow site and the hep hollow site of about 5 pm in experiments (a) and (b) is fully accounted for in the simulations (c).

Figure 4.7. Simulation Results by Mujtaba (1989) and Comparison with Experiment and Simulation of Nad and Spiegel (1987)...

Fig. 1.31 Simulated stress-strain curve for unidirectional SiC/SiC and comparison with experiment.

Talu, O. and Myers, A.L. (2001). Molecular simulation of adsorption Gibbs dividing surface and comparison with experiment. AIChEJ., 47, 1160-8. 

Kairn, T., Daivis, P. J., Ivanov, I., and Bhattacharya, S. N., Molecular-dynamics simulation of model polymer nanocomposite rheology and comparison with experiment, J. Chem. Phys., 123, 194905-1 (2005). 

COMPUTER-SIMULATED SPECTRA AND COMPARISON WITH EXPERIMENT... 

Ungureanu, C., Rayavarapu, R. G., Manohar, S., and van Leeuwen, T. G. (2009) Discrete dipole approximation simulations of gold nanorod optical properties Choice of input parameters and comparison with experiment,/ Appl. Phys., 105,102032/1-7. 

Computer simulation can be used to provide a stepping stone between experiment and the simplified analytical descriptions of the physical behavior of biological systems. But before gaining the right to do this, we must first validate a simulation by direct comparison with experiment. To do this we must compare physical quantities that are measurable or derivable from measurements with the same quantities derived from simulation. If the quantities agree, we then have some justification for using the detailed information present in the simulation to interpret the experiments. 

Ideally, experiments and simulations should be performed simultaneously, and the results obtained should complement each other. The computer model for a basic configuration can be verified by comparison with experiment and then applied to more complex configurations. 

There have also been a number of simulations of more realistic models of polymers at surfaces [65-77], The behavior of these more realistic models of polymers is similar to that of the model systems discussed above with no real surprises. Of course, the use of realistic models allows a direct comparison with experiment. For example, surface forces apparatus measurements [78] show that in some branched alkanes the force is a monotonic rather than oscillatory function of the separation. This is a surprising result because these branched alkanes pack quite efficiently (in fact they crystallize under some conditions), and this would imply that the surface forces should be oscillatory. Several... 

The numerical jet model [9-11] is based on the numerical solution of the time-dependent, compressible flow conservation equations for total mass, energy, momentum, and chemical species number densities, with appropriate in-flow/outfiow open-boundary conditions and an ideal gas equation of state. In the reactive simulations, multispecies temperature-dependent diffusion and thermal conduction processes [11, 12] are calculated explicitly using central difference approximations and coupled to chemical kinetics and convection using timestep-splitting techniques [13]. Global models for hydrogen [14] and propane chemistry [15] have been used in the 3D, time-dependent reactive jet simulations. Extensive comparisons with laboratory experiments have been reported for non-reactive jets [9, 16] validation of the reactive/diffusive models is discussed in [14]. 

A proposal for the comprehensive study of chemical processes in a variety of important condensed-phase systems using modern theoretical methodology has been presented. The primary goals of the research are to provide microscopic information on the mechanisms and structural and dynamical properties of the chemical systems proposed for investigation, to test the applicability of modern ab initio molecular dynamics (MD) by comparison with experiment, and to develop and apply novel ab initio MD techniques in simulating complex chemical systems. The proposed research will contribute to the forefront of modern theoretical chemistry and address a number of important technological issues. The PI has carefully attempted to demonstrate his knowledge, ability, and resources to carry out the proposed research projects. 

Fig. 16 Plots of interfacial position as a function of time for AOT/water thin-layer experiment and comparison with simulation for La/Vi interface (upper panel), V1/H2 interface (lower panel)...

Two general approaches have been used in low-temperature studies. In the first, the uncompensated resistance, electrode capacitance, diffusion coefficient, and kinetic and thermodynamic parameters describing the electrode reaction are incorporated in a master model, which is treated (usually by some form of digital simulation) to calculate the expected voltammetric response for comparison with experiment [7,49]. 

In the applications of the PCM approach to SD, the focus so far has been mainly on the comparison with experiment [45,46] and very good agreement with experimental results has been obtained for C153 in several polar liquids [45], In the case of SD in water, the theory was implemented using two different approaches to obtain e(w), either a fit to experimental data [45] or a calculation of the dipole density time correlation from molecular dynamics simulation [46], While the results for S(t) that use experimental dielectric permittivity as input look quite similar to those shown in Figure 3.16, the results based on the simulation data exhibit more pronounced oscillatory features at the characteristic frequency of the hydrogen bond librations. 

---