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Mean-field theory of the phase diagram of ultrasoft, oppositely charged polyions in solution
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10.1063/1.4748378
/content/aip/journal/jcp/137/9/10.1063/1.4748378
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/9/10.1063/1.4748378

Figures

Image of FIG. 1.
FIG. 1.

vs. x for T = 0.02, 0.04, 0.06, and 0.08 (from top to bottom), and n 1 = 0.0035 (panel a) and n 2 = 0.01 (panel b). The arrows along the x-axis indicate the position of the cut-off distance X(T, n) for T = 0.02.

Image of FIG. 2.
FIG. 2.

Fraction α of free ions vs. temperature T along the isochore n = 0.0035 (panel a) and n = 0.01 (panel b) calculated within approximation levels B, C, and D.

Image of FIG. 3.
FIG. 3.

Fraction α of free ions vs. total ion density n along the isotherms T = 0.02 (panel a) and T = 0.04 (panel b).

Image of FIG. 4.
FIG. 4.

Phase diagrams of the URPM in the (n, T) plane from approximation levels B, C, and D, and from MD simulations.15,16

Image of FIG. 5.
FIG. 5.

Positions of purely imaginary poles (open symbols), and of complex poles (filled symbols) in the (q 1, q 2) plane (upper right quadrant) for a low value of and a large value of .

Image of FIG. 6.
FIG. 6.

Full h +−(x) (panel a), and its asymptotic limit (45) (panel b) as a function of x for two cases: one state in the monotonic regime (low ), and one state in the damped oscillatory regime (high ). Note that for low the logarithmic plot ln[xh +−(x)] is a straight line for large x, indicating pure exponential decay at longest range, whereas for high exponentially damped oscillations persist for all distances x.

Image of FIG. 7.
FIG. 7.

Kirkwood line in the (n, T) plane, relative to the approximate phase diagram of the URPM.

Image of FIG. 8.
FIG. 8.

Integrand χ(x) of the integral ξ3 vs. x. Solid lines show the integrand for the exact potential v +−, while the dashed lines show the results for χ(x) based on the quadratic expansion (11) of v +−(x). Curves are for T = 0.02, 0.04, and 0.08 from top to bottom.

Image of FIG. 9.
FIG. 9.

Positions of the maximum X 1(T) and the minimum X 2(T) of the integrand χ(x) vs. temperature T, and the cut-off distances X(T), X(T, n 1 = 0.0035), and X(T, n 1 = 0.01) vs. T (see text).

Image of FIG. 10.
FIG. 10.

Ratio vs. T for cut-off distances X(T), X(T, n 1 = 0.0035), and X(T, n 1 = 0.01).

Image of FIG. 11.
FIG. 11.

Ratio ζ0/ζ of the reduced electric polarizabilities vs. T for cut-off distances X(T), X(T, n 1 = 0.0035), and X(T, n 1 = 0.01).

Image of FIG. 12.
FIG. 12.

Cut-off distances X(T = 0.02, n 1) and X(T = 0.06, n 1) vs. n 1.

Tables

Generic image for table
Table I.

Critical temperature T c , density n c , pressure P c , and osmotic coefficient Z c , estimated from approximations B, C, and D, and from MD simulations.15,16

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/content/aip/journal/jcp/137/9/10.1063/1.4748378
2012-09-07
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Mean-field theory of the phase diagram of ultrasoft, oppositely charged polyions in solution
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/9/10.1063/1.4748378
10.1063/1.4748378
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