doi:10.1016/j.cpc.2005.03.033
Copyright © 2005 Elsevier B.V. All rights reserved.
Phase diagram for self-assembly of amphiphilic molecule C12E6 by dissipative particle dynamics simulation
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Hiroaki Nakamuraa, b, 
, 
and Yuichi Tamuraa
aTheory and Computer Simulation Center, National Institute for Fusion Science, 322-6 Oroshi-cho, Toki, Gifu 509-5292, Japan
bDepartment of Fusion Science, School of Physical Sciences, The Graduate University for Advanced Studies, 322-6 Oroshi-cho, Toki, Gifu 509-5292, Japan
Available online 27 April 2005.
Abstract
In a previous study, dissipative particle dynamics simulation was used to qualitatively clarify the phase diagram of the amphiphilic molecule hexaethylene glycol dodecyl ether (C12E6). In the present study, the hydrophilicity dependence of the phase structure was clarified qualitatively by varying the interaction potential between hydrophilic molecules and water molecules in a dissipative particle dynamics (DPD) simulation using the Jury model. By varying the coefficient of the interaction potential x between hydrophilic beads and water molecules as x=−20,0,10, and 20, at a dimensionless temperature of T=0.5 and a concentration of amphiphilic molecules in water of 
=50%, the phase structures grew to lamellar (x=−20), hexagonal (x=0), and micellar (x=10) phases. For x=20, phase separation occurs between hydrophilic beads and water molecules.
Keywords: Dissipative particle dynamics; Amphiphilic molecule; Surfactant; Phase diagram; Packing parameter; Micelle; Lamellar; Hexagonal structure
PACS: 61.43.Bn; 36.40.-c; 36.20.Fz
Fig. 1. Schematic diagram of packing parameter [3] and [4]. A gray ball and a twisting black line are used to denote the hydrophilic and hydrophobic parts, respectively, of an amphiphilic molecule. The packing parameter p≡V/Sl controls the shape of the aggregates. Here, the parameter V is the volume occupied by the hydrophobic tail, S denotes the sectional area of a hydrophilic group, and l is the “maximum effective length” of the hydrophobic tail.
Fig. 2. Formed structures for each potential coefficient, x=−20 (a), 0 (b), 10 (c), and 20 (d). Each structure is shown in Table 2. Red and white beads denote hydrophilic (A) and hydrophobic molecules (B), respectively. Blue beads represent groups of water molecules (W). We set T=0.5 and =50% during simulation.
Fig. 3. Solute particle radial distribution function g(r) vs. distance between two particles r for x=−20,0,10, and 20. The function g(r) is the sum of the A–A radial distribution function, the B–B radial distribution function, and the A–B radial distribution function. The first peak l(x) of each curve corresponds to the length of AB dimer.
Table 1.
Table of coefficients aij depending on particle type for particles i and j, where W is a water particle, A is a hydrophilic particle, and B is a hydrophobic particle. By varying the coefficient x between A and W particles as x=−20,0,10, and 20, the dependence of the phase structure on the hydrophilicity is clarified
Table 2.
Table of formed structures for each x. Lamellar, hexagonal, and micelles phases are indicated as Lα, H1, and L1, respectively. For x=20, AB molecules and W molecules are separated, as shown in Fig. 2
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