High-efficient calculation of the interaction energies between dissimilar double layers for Na2SO4-type asymmetric electrolytes at y0>yd>0

Several rapidly convergent series for highly efficient calculation of the interaction energies between dissimilar double layers for Na2SO4-type electrolytes at y (0) > y (d) > 0 are derived, the accurate numerical results are given, and several approximate expressions are obtained for y (0) < 1. The number of the series terms required to obtain the interaction energies with six significant digits via the use of the series derived is no more than 2 when the dimensionless surface potential of double layers y (0) <= 20. The interaction energies between dissimilar double layers for NaCl-or Na2SO4-type electrolytes are remarkably affected by the value of y (d),, but the interaction energies for Na2SO4-type electrolytes are hardly affected by the value of y (0). The present results can also be applied to CaCl2-type electrolytes at y (0) < y (d) < 0.