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Free energy landscapes and volumes of coexisting phases for a colloidal dispersion
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10.1063/1.3285267
/content/aip/journal/jcp/132/2/10.1063/1.3285267
http://aip.metastore.ingenta.com/content/aip/journal/jcp/132/2/10.1063/1.3285267

Figures

Image of FIG. 1.
FIG. 1.

Theoretical phase-diagram domains of a colloid-polymer system calculated at a fixed size ratio . The reservoir polymer volume fraction is plotted against the colloidal volume fraction . FEDM was carried out for several initial colloidal volume fractions shown in the figure at , 0.35, 0.45, and 0.54. All vertical line-domains lead to the same phase boundaries of coexisting phases, which are displayed as (black) crosses for L1S2 and L2S2 and (green) pluses for L1L2. The horizontal lines indicate several selected , two above and two below the triple point . The latter FEDLs are depicted in Figs. 2(a)–2(e). The triple-point line is given by the full curve. Other notations used are as follows: solid circles, fluid; open circles, gas-liquid; open triangle up, liquid-solid; solid square, gas-solid; (blue) triangle left, continuation of Ll of L1S2 to spinodal decomposition curve (solid triangle down) at ; and (red) triangle right, continuation of L2 of L2S2 to spinodal decomposition curve (solid triangle down) at .

Image of FIG. 2.
FIG. 2.

Free energy density vs colloidal volume fraction of colloid-polymer system calculated at a fixed size ratio . The dashed curve is the fluid free energy density , and the full curve is the solid free energy density . The reservoir polymer volume fractions are at (a) , (b) , (c) , (d) , and (e) . In all these figures, the (blue) dash-dotted line is L1L2, the (orange) dash-dot-dotted line is L1S2, and the (green) dash-dash-dotted line is L2S2. The triple points in (c) are denoted by solid circles.

Image of FIG. 3.
FIG. 3.

Schematic diagram depicting the geometric analysis of the spatial volumes of triple coexistence. The triangle shown as (orange) dashed lines shows the intersection of the equation of the plane on the axes , , and . The (red) solid line is the result of intersection of the (pink) plane with the (green) plane .

Image of FIG. 4.
FIG. 4.

Schematic diagram of the Helmholtz free energy densities, (dashed line for fluid) and (solid line for solid), vs colloidal volume fraction . Note that two and three phases in coexistence are shown.

Image of FIG. 5.
FIG. 5.

Spatial volumes of three coexisting phases for a colloid-polymer system at triple point (see Fig. 1). Straight lines on the triangular plane correspond to different initial volume fractions , and they are the results of the intersection of planes and . The (blue) thick solid line corresponds to , whereas the (red) solid circle and (red) open circle correspond to and , respectively. Other notations are as follows: open square, two coexisting phases L1S2; full square, liquid.

Image of FIG. 6.
FIG. 6.

Pressure vs for the colloid-polymer system calculated at a fixed size ratio . Along L1S2, L2S2, and L1L2, two equilibrium phases coexist, and their respective and , where , are uniquely determined. The point where the L1S2, L2S2, and L1L2 meet is the triple point whose , , and take on innumerable values, all of which yield a same free energy density value.

Tables

Generic image for table
Table I.

Spatial volume parameter and composite free energy density [in units of ] (see text) for a colloid-polymer system characterized by an attractive depletion potential. The size ratio is fixed at , and the initial volume fraction is given by (blue thick line in Fig. 5).

Generic image for table
Table II.

Spatial volume parameter and composite free energy density [in units of ] (see text) for a colloid-polymer system characterized by an attractive depletion potential. The size ratio is fixed at , and the initial volume fraction is given by (red thin line in Fig. 5).

Generic image for table
Table III.

Spatial volume parameter and composite free energy density [in units of ] (see text) for a colloid-polymer system characterized by an attractive depletion potential. The size ratio is fixed at , and the initial volume fraction is given by (orange thin line in Fig. 5).

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/content/aip/journal/jcp/132/2/10.1063/1.3285267
2010-01-13
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Free energy landscapes and volumes of coexisting phases for a colloidal dispersion
http://aip.metastore.ingenta.com/content/aip/journal/jcp/132/2/10.1063/1.3285267
10.1063/1.3285267
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