Download e-book for iPad: Advanced Computer Simulation: Approaches for Soft Matter by Christian Holm, Kurt Kremer, S. Auer, K. Binder, J.G. Curro,

By Christian Holm, Kurt Kremer, S. Auer, K. Binder, J.G. Curro, D. Frenkel, G.S. Grest, D.R. Heine, P.H. Hünenberger, L.G. MacDowell, M. Müller, P. Virnau

ISBN-10: 3540220585

ISBN-13: 9783540220589

Soft topic technological know-how is these days an acronym for an more and more vital classification of fabrics, which levels from polymers, liquid crystals, colloids as much as complicated macromolecular assemblies, overlaying sizes from the nanoscale up the microscale. computing device simulations have confirmed as an quintessential, if no longer the main robust, instrument to appreciate homes of those fabrics and hyperlink theoretical types to experiments. during this first quantity of a small sequence well-known leaders of the sphere assessment complex themes and supply serious perception into the state of the art tools and medical questions of this energetic area of soppy condensed topic research.

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Extra info for Advanced Computer Simulation: Approaches for Soft Matter Sciences I

Sample text

To investigate the properties of spatially inhomogeneous systems, we start from the grandcanonical partition function: ⎛ ⎞ ∞ E φˆ S , φˆ P eµ S n S / k B T eµ P Nn P / k B T ⎠ , (51) DP S DP P exp ⎝− Z= nS! nP! kB T n S ,n P =0 where we sum over all numbers of molecules n S and n P , and µ S and µ P denote the chemical potentials per segment. E denotes the interaction free energy functional for which we assume the following form E[φ S , φ P ] = kB T dr + v kB T 1 χ˜ ζ (φ S + φ P )2 − (φ S − φ P )2 + (φ S2 − φ 2P ) 2 4 2 wP P P 3 wS S S 3 φ S + w S S P φ S2 φ P + w S P P φ S φ 2P + φP .

In the same spirit of a rough but effective description, we represent a hexadecane molecule by a chain of N P = 5 segments. Again, segments interact via a truncated 23 Polymer + Solvent Systems Lennard-Jones potential that is characterized by an energy parameter P P and segment size σ P P . 5σ P P . No bond angle or torsional potentials are included in our model, and we do not attempt to match experimental data for the radius of gyration of hexadecane. 22σ P P [99]. In any case, these values would rather sensitively depend on the thermodynamic state [112, 150, 151].

The polymer and the solvent become more unlike. This behavior agrees qualitatively with TPT (cf. Sect. 5) and experiments [23]. The binodal and spinodals as a function of the solvent weight fraction are presented in panel (a) of Fig. 9, where we have used the ratio of the molar masses of hexadecane and carbon dioxide. This representation is more convenient for large molecular masses, because the molar faction x of the coexisting phases is very close to unity. For long polymers and pressures far below the triple pressure, the polymer– rich phase at saturation contains only a few weight-percent of the super-critical solvent, and this amount decreases upon increasing molecular mass.

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Advanced Computer Simulation: Approaches for Soft Matter Sciences I by Christian Holm, Kurt Kremer, S. Auer, K. Binder, J.G. Curro, D. Frenkel, G.S. Grest, D.R. Heine, P.H. Hünenberger, L.G. MacDowell, M. Müller, P. Virnau


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