Molecular structures of ABCBA type model surfactant oligomer, with the nine different types of R groups in the -phobic segment.
Variation in the radial distribution functions, , of beads in the system with oligomer concentration. (a) Total distribution of beads in the system does not change. The pressure, however, monotonically decreases with increasing concentration (inset). Intermolecular number density distribution of beads decreases with concentration (b), whereas intramolecular distribution increases (c).
Change in the surface to volume ratio of surfactant 7 with oligomer concentration. Snapshots of the equilibrated structures from the and 0.80 concentrations are also shown.
Contributions to the free energy of spherical micelles in solution computed using Eqs. (9)–(12); all parameters of the calculations are deduced from the simulated systems. Data from these systems are shown as empty circles and the values beyond are extrapolated. Free energy of solvation of the micelles is shown with dashed lines [bottom curve, Eq. (10)], free energy of solvation of free oligomers is shown with dotted-dashed lines [Eq. (11)], and the free energy of micellization is shown with the dotted line [Eq. (12)]. The total free energy of the system is shown with the solid line. In the inset the free energy of spherical micelles (solid line) is compared to that of the homogeneous phase (dashed line). The free energy difference is shown at the bottom curve; the minimum occurs at approximately , shown by the filled circle. The break-even point occurs at , i.e., the spherical micelles are more stable than the miscible oligomers below this value. In reality, in the region , cylindrical micelles have lower free energy than spherical ones (shown by the gray dashed region in the inset). The main additional contribution in cylinders comes from the lower free energy of mixing of the corona region with the penetrating solvent [the third term in Eq. (12), modified for cylindrical geometry].
Morphologies of and 0.80 surfactant concentration under shear of 0.001 DPD units during the course of the DPD simulations with time also in DPD units. The initial structures are those shown in Fig. 3. Spherical micelles are more stable in that they are merely distorted and lose their fcc superstructure under shear. Cylindrical micelles are destroyed under the same forces; micelles are still observed as closed structures but cannot be ascribed a definite morphology. Similar results are obtained at shear rate of 0.01 units; at 0.2 units, spherical micelles are also destroyed.
Interaction parameters of compounds 1–9 (in units); also listed are the bead molar volumes. (The following parameters are the same in all compounds: , , ; , 125, 44 for beads A, B and D, respectively; molar mass of these units are 102, 56, and 44, respectively. Systems that tend to form micelles are shown in bold.)
Average root mean square end-to-end distances, of oligomers 1–9 at two different concentrations. (The standard error on the mean is less than 3% in all values. Systems that tend to form micelles are shown in bold.)
Average root mean square end-to-end distances, , and the surface to volume ratio, for different number of fluorinated beads ( in ) for oligomer 7 at 40% and 80% volume fractions.
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