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.
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.
Fraction α of free ions vs. total ion density n along the isotherms T = 0.02 (panel a) and T = 0.04 (panel b).
Phase diagrams of the URPM in the (n, T) plane from approximation levels B, C, and D, and from MD simulations.15,16
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 .
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.
Kirkwood line in the (n, T) plane, relative to the approximate phase diagram of the URPM.
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.
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).
Ratio vs. T for cut-off distances X(T), X(T, n 1 = 0.0035), and X(T, n 1 = 0.01).
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).
Cut-off distances X(T = 0.02, n 1) and X(T = 0.06, n 1) vs. n 1.
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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