smart materials, including stimuli-responsive systems with a hierarchical structure,
have to be designed on the molecular level in the length scale of 0.1–10 nm and
need a deep understanding of synthesis–structure–property–processing–performance relations. A predictive description of synthesis processes leading to the
creation of sophisticated macromolecules requires consideration of complex
molecular models. This frequently includes such types of architecture as multi-arm
stars, hyperbranched polymers, dendrimers, comb-like or dendronized polymers,
rings, gels, etc. Furthermore, simulations of polymer blends, melts, solutions and
composites (and soft matter, in general) are somewhat challenging, because their
properties usually involve a variety of timescales and a broad range of sizes, as
Fig. 8.12 shows. The timescales cover the domain from 10
−13 to 10
−14 s (for bond
vibrations) up to, at least, a few seconds for phase separation processes. The size
scales range from single angstroms (for the bond length) up to centimetres (for
domains or crystals). Also, various intermolecular interactions should be taken into
consideration, often between amphiphilic polymers and solvents with complex
supramolecular structure like water. Therefore, a successful solution to a problem in
the material design usually requires hierarchical, multiscale simulation involving a
combination of atomistic (below *10
−7 m), mesoscopic (up to *10
−4 m) and
macroscopic methods. How to link them together remains a challenging problem
and there is still no single universal method covering the whole above-mentioned
range of size and time. We are still and probably we will always be doomed only to
‘… relatively good approximation to truth - which is much too complicated to allow
anything but approximations’, as John von Neumann said. This is the reason why
various methods are used to simulate different levels of molecular complexity. The
more complex and detailed atomistic model, the shorter times are available in the
simulation. This is mainly caused by hardware limitations; however, the limits shift
systematically towards a more precise description of complex systems in longer
timescales.
A detailed description of various simulation methods is available in books [172],
and thus in next paragraphs, only the most useful techniques in relation to polymer
science (excluding macroscopic methods) will be introduced shortly.
Quantum mechanical calculations use generally two approaches, ab initio and
empirical or semi-empirical methods, to solve a set of simplified Schrödinger
equations. At present, the most popular first principles calculation method is Kohn–
Sham density functional theory (DFT) [173] with B3LYP hybrid functional [174,
175]. In DFT, the energy of a system is expressed in terms of electron density rather
than the wave function as in ab initio. Empirical methods use some parameters
determined experimentally. Quantum mechanics (QM) is particularly useful for the
structure optimization, calculation of energy (including the energy of interactions),
IR, Raman and NMR spectra prediction. The structure optimization is performed
without the temperature; moreover, solvent, e.g. water, can be present explicit or
with a reaction field using the integral equation formalism model (IEFPCM [176]).
From a technical point of view, QM calculations are practically limited to only a
few hundreds of atoms, which mean a few monomer units in the field of polymer
science. This limitation arises from strong dependence of computing time on the
246
M. Kozanecki et al.
have to be designed on the molecular level in the length scale of 0.1–10 nm and
need a deep understanding of synthesis–structure–property–processing–performance relations. A predictive description of synthesis processes leading to the
creation of sophisticated macromolecules requires consideration of complex
molecular models. This frequently includes such types of architecture as multi-arm
stars, hyperbranched polymers, dendrimers, comb-like or dendronized polymers,
rings, gels, etc. Furthermore, simulations of polymer blends, melts, solutions and
composites (and soft matter, in general) are somewhat challenging, because their
properties usually involve a variety of timescales and a broad range of sizes, as
Fig. 8.12 shows. The timescales cover the domain from 10
−13 to 10
−14 s (for bond
vibrations) up to, at least, a few seconds for phase separation processes. The size
scales range from single angstroms (for the bond length) up to centimetres (for
domains or crystals). Also, various intermolecular interactions should be taken into
consideration, often between amphiphilic polymers and solvents with complex
supramolecular structure like water. Therefore, a successful solution to a problem in
the material design usually requires hierarchical, multiscale simulation involving a
combination of atomistic (below *10
−7 m), mesoscopic (up to *10
−4 m) and
macroscopic methods. How to link them together remains a challenging problem
and there is still no single universal method covering the whole above-mentioned
range of size and time. We are still and probably we will always be doomed only to
‘… relatively good approximation to truth - which is much too complicated to allow
anything but approximations’, as John von Neumann said. This is the reason why
various methods are used to simulate different levels of molecular complexity. The
more complex and detailed atomistic model, the shorter times are available in the
simulation. This is mainly caused by hardware limitations; however, the limits shift
systematically towards a more precise description of complex systems in longer
timescales.
A detailed description of various simulation methods is available in books [172],
and thus in next paragraphs, only the most useful techniques in relation to polymer
science (excluding macroscopic methods) will be introduced shortly.
Quantum mechanical calculations use generally two approaches, ab initio and
empirical or semi-empirical methods, to solve a set of simplified Schrödinger
equations. At present, the most popular first principles calculation method is Kohn–
Sham density functional theory (DFT) [173] with B3LYP hybrid functional [174,
175]. In DFT, the energy of a system is expressed in terms of electron density rather
than the wave function as in ab initio. Empirical methods use some parameters
determined experimentally. Quantum mechanics (QM) is particularly useful for the
structure optimization, calculation of energy (including the energy of interactions),
IR, Raman and NMR spectra prediction. The structure optimization is performed
without the temperature; moreover, solvent, e.g. water, can be present explicit or
with a reaction field using the integral equation formalism model (IEFPCM [176]).
From a technical point of view, QM calculations are practically limited to only a
few hundreds of atoms, which mean a few monomer units in the field of polymer
science. This limitation arises from strong dependence of computing time on the
246
M. Kozanecki et al.