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Polymer Thermodynamics pp 329–387Cite as

Computer Simulations and Coarse-Grained Molecular Models Predicting the Equation of State of Polymer Solutions

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Part of the book series: Advances in Polymer Science ((POLYMER,volume 238))

Abstract

Monte Carlo and molecular dynamics simulations are, in principle, powerful tools for carrying out the basic task of statistical thermodynamics, namely the prediction of macroscopic properties of matter from suitable models of effective interactions between atoms and molecules. The state of the art of this approach is reviewed, with an emphasis on solutions of rather short polymer chains (such as alkanes) in various solvents. Several methods of constructing coarse-grained models of the simple bead–spring type will be mentioned, using input either from atomistic models (considering polybutadiene as an example) or from experiment. Also, the need to have corresponding coarse-grained models of the solvent molecules is emphasized, and examples for various dipolar and quadrupolar fluids and their mixtures with short alkanes are given. Finally, we mention even more simplified models, such as the bond fluctuation model on the simple cubic lattice, treating applications like micelle formation in block copolymer solutions or isotropic–nematic phase transitions in solutions of stiff polymers as case studies. Comparisons with pertinent predictions from approximate analytical theories will be briefly mentioned, as well as applications, to understand experimental results.

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Abbreviations

AO:

Asakura–Oosawa model

CMC:

Critical micelle concentration

DPD:

Dissipative particle dynamics

EPM:

Elementary physical model

EPM2:

Second elementary physical model

FENE:

Finitely extensible nonlinear elastic

GEMC:

Gibbs ensemble Monte Carlo

LJ:

Lennard–Jones

MC:

Monte Carlo

MD:

Molecular dynamics

NIST:

National Institute of Standards and Technology

\(\mathcal{N}pT\) :

Constant particle number, constant pressure, and constant temperature ensemble

\(\mathcal{N}VE\) :

Constant particle number, constant volume, and constant energy ensemble (= microcanonical ensemble)

\(\mathcal{N}VT\) :

Constant particle number, constant volume, and constant temperature ensemble (= canonical ensemble)

PC-SAFT:

Perturbed-chain statistical associating fluid theory

rRESPA:

Reversible reference systems propagator algorithm

SAFT:

Statistical associating fluid theory

SAW:

Self-avoiding walk

SCFT:

Self-consistent field theory

SM:

Stockmayer model

SW:

Square well

TI\(\mu VT\) :

Thermodynamic integration in the constant chemical potential, constant volume, and constant temperature ensemble

TPT:

Thermodynamic perturbation theory

TPT1-MSA:

First-order thermodynamic perturbation theory combined with the mean spherical approximation

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Acknowledgement

Part of the work reviewed here has been carried out in a fruitful and productive collaboration with A. Cavallo, V. Ivanov, L. G. MacDowell, M. Müller, M. Oettel, and T. Strauch; it is a pleasure to thank them. Stimulating discussions with H. Weiss and F. Heilmann are acknowledged as well. Financial support has been provided by the BASF SE and by the Deutsche Forschungsgemeinschaft (DFG) in the framework of projects DFG 436 RUS 113/791, PA473/7-1 and PA473/8-1, and Sonderforschungsbereich 625. Computer time grants were provided by John von Neumann Institute for Computing (NIC) and the Network of Excellence SOFTCOMP.

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  1. Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, 55099, Mainz, Germany

    Kurt Binder, Wolfgang Paul, Peter Virnau & Leonid Yelash

  2. The Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, UK

    Bortolo Mognetti

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  1. Kurt Binder
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Correspondence to Kurt Binder .

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  1. Inst. Physikalische Chemie, Universität Mainz, Jakob-Welder-Weg 13, Mainz, 55099, Germany

    Bernhard A. Wolf

  2. Sekr. TK7, TU Berlin, Straße des 17. Juni 135, Berlin, 10623, Germany

    Sabine Enders

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Binder, K., Mognetti, B., Paul, W., Virnau, P., Yelash, L. (2010). Computer Simulations and Coarse-Grained Molecular Models Predicting the Equation of State of Polymer Solutions. In: Wolf, B., Enders, S. (eds) Polymer Thermodynamics. Advances in Polymer Science, vol 238. Springer, Berlin, Heidelberg. https://doi.org/10.1007/12_2010_82

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