Advanced Computer Simulation Approaches for Soft Matter by Marcus Müller, Friederike Schmid (auth.), Christian Holm,

By Marcus Müller, Friederike Schmid (auth.), Christian Holm, Kurt Kremer (eds.)

This sequence offers serious experiences of the current and destiny developments in polymer and biopolymer technological know-how together with chemistry, actual chemistry, physics and fabrics technological know-how. it's addressed to all scientists at universities and in who desire to maintain abreast of advances within the themes coated.

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126 without invoking the random phase approximation. The approximation (Eq. 127) is obviously exactly valid for a homogeneous system, because the pair-correlation function only depends on the distance |r – r | between two points. It is expected to be reasonably good for weakly perturbed chain conformations [95]. Generally, one can approximately relate the time evolution of the field W to the dynamic SCF theory [31]. The saddle point approximation in the external 42 M. Müller · F. Schmid fields leads to a bijective relation between the external fields iΩA∗ , iΩB∗ and φA , φB .

Different forms for the Onsager coefficient Λ will be discussed in Sect. 5. In each step of the Langevin simulation Fluctuations and Dynamics in Self-Consistent Field Theories 33 one updates all field variables simultaneously [29] and the the self-consistent equations for the saddle point U ∗ (W) have to be solved. The approach is commonly referred to as external potential dynamics (EPD). A related approach was originally introduced by Maurits and Fraaije [31]. However, these authors do not determine U ∗ (W) exactly, but only approximately by solving separate Langevin equations for real fields WA and WB .

In order to study this effect, Düchs et al. have performed field-theoretic Monte Carlo simulations of the system of Fig. 5 [80, 83, 104], in two dimensions. (For the reasons explained in Sect. 2, most of these simulations were carried out in the EP approximation). Some characteristic snapshots were already shown in Fig. 4. 5 for increasing homopolymer concentrations (Fig. 8). For all these points, the self-consistent field theory would predict an ordered lamellar phase. In the Fig. 7 Transmission electron micrographs from symmetric PE/PEP/PE-PEP blends: (a) fluctuating lamellae; (b) microemulsion phase.

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