Model calculations are powerful mediators between experimental investigations and the development of theories providing a better understanding of systems on a molecular scale. Furthermore, in many cases the outcome of numerical calculations even exceeds the spectrum and resolution of experimental investigations thus allowing to check existing theories in detail and to give guidelines for new theories. Therefore, simulation methods developed into a further main pillar of science in addition to the two classical methods.
For quantum mechanical calculations from first principles approximations are minimal but enormously exhaustive for a larger number of atoms restricting these methods to rather small systems only. Larger systems of size (5-10 nm)3 over a time interval of several nanoseconds may be simulated by use of classical molecular dynamics based on proper force fields describing the interactions between atoms. Properties of oligomers (small polymers) in bulk and at surfaces, e.g., may be investigated in this way.
For these types of investigations we are using the commercial software package Materials Studio (MS Modeling) from Accelrys Inc. using the Visualizer module for generating the molecules and for visualization of results, the Amorphous Cell tool for preparing periodic systems and Discover with force field COMPASS (a class-II force field optimized for the simulation of condensed phases) as the molecular dynamics engine. Relevant data not directly supported by the client are extracted from the trajectories by use of proper BTCL-scripts. For the simulation of supercooled water the open source program GROMACS is used as well.
Among other projects our atomistic simulations (marked BLUE in the list of references) comprise the investigation of properties of (small) polymers in bulk, the interaction and orientation of molecules (e.g. silanes, dyes like eosin Y,...) adsorbed at surfaces (ZnO, TiO2) and the simulation of glass transition temperatures (polymer matrices with varying plasticizer content, amorphous carbohydrates, amorphous ice).
The picture shows a simulation box containing 456 hexane molecules (depicted as sticks) and one polyethylene chain (C120) with black (white) spheres representing carbon (hydrogen). Visualization by use of MS-Visualizer.
Especially for polymer systems length scales of structural properties as well as time scales of dynamic properties are spread over several orders of magnitude. Combining groups of monomers to single segments (coarse grained chains) and applying more simple potentials characterizing the principle behavior of interactions between chain segments only make these systems accessible to simulations which are still able to yield a lot of useful results. E.g., the chain length (i.e. the number of segments of the model chain) still serves as an independent parameter which allows the calculation of a wide range of universal features depending on this parameter.
Monte Carlo simulation techniques are preferred at least as long as static properties are of interest only. They explore the phase space in an extremely efficient stochastic way (generally using "unphysical" movements which are allowed in this context) thus yielding ensemble averages from a (large) number of randomly taken snapshots of the system. Dissipative particle dynamics (DPD) is a further most promising simulation technique for mesoscale simulations; interaction parameters are closely connected to Flory Huggins parameters: therefore, the transformation of experimentally obtained parameters characteristic for specific polymers into simulation parameters as well as the back-transformation of the simulation results into the atomistic picture should be possible. Furthermore, dynamic properties are accessible as well.
For these types of investigations (marked PURPLE in the list of references) all programs are developed and written by ourselves; among other projects our mesoscale simulations comprise the investigation of properties of linear, star-branched and ring shaped polymers in solution and bulk (size, shape, distribution of and correlation between them,…), the investigation of polymer surfaces and interfaces, polymer/polymer interactions within contact pairs as a function of separation (yielding the intermolecular excluded volume, pair distribution functions, and related quantities like concentrations dependences of characteristic data in the limit of high dilution and shielding factors for polymer/polymer reactions,…). Homopolymers as well as copolymers are examined.
The picture shows two snapshots of simulation boxes with polymers of equal length attached to the wall (periodic boundaries in other directions); concentration of chains in the right box is twice the concentration in the left one resulting in more expanded chains. Visualization by use of POVRAY.
The projects "P20124: Properties of star-branched (co)-polymers" and "P23142: Simulation of Polymer Nanocomposites" belonging to this type of investigations are funded from the Austian Science Fund (FWF) which is gratefully acknowledged.
Numerical and analytical modeling yielded a sound theoretical basis for the pulsed laser polymerization (PLP) method (invented 1987 by O.F. Olaj et al.) which in the meantime is used all over the world and is an IUPAC recommended benchmark method for the determination of kinetic constants; the propagation rate constant - strictly speaking coefficient, see below - is directly available from the position of "extra-peaks" appearing in the chain length distribution of polymers prepared by pulsed-laser initiated radical polymerization. Furthermore, the method could be extended to rotating sector initiation as well as (at least in principle) to arbitrary initiation profiles and the influence of side reactions has been studied in detail.
An important feature obtained in the course of the evaluation of pair-distribution functions mentioned above was the calculation of the thermodynamic shielding factor of polymer-polymer reactions which turned out to be chain-length dependent. As a consequence, the termination rate coefficient in free radical polymerization should be chain-length dependent, too. Based on the results of the simulation, the influence of a chain-length dependence of the termination rate coefficient on kinetic data was evaluated in detail for stationary as well as for pseudostationary polymerization processes.
On the basis of experimental results corroborated by simulations in 2000 we were the first to put forward the idea that chain-length dependence is not only to be expected for the termination rate coefficient but also for the propagation rate constant, a highly interesting task with enormous consequences for the whole field of polymerization kinetics.
In recent times a lot of effort has been put into further improving the quality of kinetic data obtained by the PLP method by developing correction functions in order to consider the effect of axial dispersion inherent in the size exclusion chromatography used to obtain the distribution curves.
Furthermore, the concept of shielding parameters was extended to Z-RAFT polymerization processes. Among other things our calculations reveal that shielding is smaller and chain-length dependence is less pronounced under bad solvent conditions as compared to the situation in a good solvent. Actually, experimental results are in full accordance with this theoretical predictions.
Investigations summarized in this paragraph (marked GREEN in the list of references) can be either treated by analytical methods or (especially in case of chain length dependent rate coefficients) by use of numeric methods. All programs needed are developed and written by ourselves; occasionally, the commercial software PREDICI © is used.
As an example, the figure shows the calculated influence of chain transfer on weight distributions obtained by PLP, the concentration of the transfer agent increasing from the brown curve over the red, the dark blue, and the blue to the green one. Visualization by use of PLOT © G. Zifferer.
A part of the calculations has been performed on the Vienna Scientific Cluster and in former times by making use of the facilities of the Vienna University Computer Center (Schrödinger Cluster and predecessors) which is gratefully acknowledged.