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Scattering intensity of bicontinuous microemulsions and sponge phases
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10.1063/1.3701265
/content/aip/journal/jcp/136/13/10.1063/1.3701265
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/13/10.1063/1.3701265

Figures

Image of FIG. 1.
FIG. 1.

Monte Carlo step for changing the topology of a triangulated surface. (a) Two surface triangles are removed. (b) The two holes are connected by a prism of six triangles.

Image of FIG. 2.
FIG. 2.

Typical configurations from simulations for N = 2207 beads for κ = 3.5, , and p = 0.01 (upper panel) as well as for κ = 5.0, , and p = 0.03 (lower panel). The two sides of the membrane are colored differently to make the bicontinuous structure more easily visible. A view of the structure for κ = 3.5, , and p = 0.01 from different angles to reveal the shape and topology more clearly, and an animation of the temporal evolution of the microemulsion structure are shown (enhanced online) (a), (b). [URL: http://dx.doi.org/10.1063/1.3701265.1] [URL: http://dx.doi.org/10.1063/1.3701265.2]10.1063/1.3701265.110.1063/1.3701265.2

Image of FIG. 3.
FIG. 3.

The equation of state [p(ϕ)δ3/T−3 vs. ln (ϕ) of sponge phases for several values of κ and as indicated by the legend. All data are for system size N = 2207. The symbols show the simulation results, and the thick dotted lines are the fits as discussed in the text.

Image of FIG. 4.
FIG. 4.

Bulk scattering intensity S b (q) (symbols) as a function of the wave vector q for p = 0.1, , N = 2207, and several values of the bending rigidity κ (upper panel), and for , N = 2207, and several values of the bending rigidity κ and the osmotic pressure p (lower panel). In the upper panel, the solid lines are fits corresponding to the Teubner-Strey formula, Eq. (5), with the line colors matching the symbol colors in the corresponding simulation data.

Image of FIG. 5.
FIG. 5.

The amplitude of the large-q tail of the bulk scattering intensity S b (q) as a function of S/V for several values of κ and , together with a linear fit forced to go through the origin.

Image of FIG. 6.
FIG. 6.

The scaled domain size, dS/V, as a function of S/V for several values of κ and for system size N = 2207. The inset shows the same for N = 607.

Image of FIG. 7.
FIG. 7.

The correlation length ξS/V as a function of S/V for several values of κ and for system size N = 2207. The inset shows the same for N = 607.

Image of FIG. 8.
FIG. 8.

The length scale ratio k 0ξ as a function of S/V for several values of κ and for system sizes (a) N = 2207 and (b) N = 607. The symbols show the simulation results and the dashed-dotted lines are the fits discussed in the text. The color coding indicates which values of κ and the dashed-dotted lines correspond to.

Image of FIG. 9.
FIG. 9.

Film scattering intensity S f (q) as a function of the wave vector q for p = 0.01, , N p = 2207, and several values of the bending rigidity κ together with a power law fit to the tail (line shifted upwards for clarity).

Image of FIG. 10.
FIG. 10.

The amplitude a f of the large-q tail of the film scattering intensity S f (q) as a function of S/V for several values of κ an , together with a linear fit forced to go through the origin.

Image of FIG. 11.
FIG. 11.

The small-q behavior of the film scattering intensity for various cases. (a) , p = 0.1, N = 2207, and κ varies as indicated by the legend. (b) κ = 3.0, p = 0.01, N = 2207, and varies as indicated by the legend. The main panels show the small-q part of S f (q) on linear scale, where the full lines are fits to Eq. (19). The insets display the full scattering functions on double-logarithmic scales. The colors of the data sets in the insets match those in the main figures.

Image of FIG. 12.
FIG. 12.

The scaled Euler characteristic γ = 〈χ E V 2 S −3〉, as a function of the surfactant density δS/V. The symbols denote the simulation data for various values of κ and , as indicated. The dashed-dotted lines are a least-squares fit to Eq. (38). The inset shows the constant term γ0 in Eq. (38) as a function of κ for different values of . The solid lines are guides to the eye.

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/content/aip/journal/jcp/136/13/10.1063/1.3701265
2012-04-06
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Scattering intensity of bicontinuous microemulsions and sponge phases
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/13/10.1063/1.3701265
10.1063/1.3701265
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