How wrong is the Debye–Hückel approximation for dilute primitive model electrolytes with moderate bjerrum parameter?

摘要: Monte Carlo (MC) simulations have been performed for primitive model electrolytes moderate Bjerrum parameters (B= 1, B= 1.546 and a few with 1.681) values of κa in the range ca. 0.015–0.45. Emphasis has laid on very dilute systems. Several millions configurations used, number ions each simulation (N) was varied between N= 32 1000 (N= 1728 single case). It is shown, by means ‘universal scaling’ comparing Debye length 1/κ periodic boundary conditions, that excess energies (Eex/NkT) should be extrapolated using polynomial commencing power 2/3 1/N rather than usual plots against 1/N. The same seems to case electrostatic, Helmholtz free energy heat capacity. However, logarithm activity coefficients (In y±, In y+ y–) as calculated test particle method Widom leading term, which cube root 1/N.The thermodynamic compare well high-precision HNC calculations DHX calculations. summary, conclusion drawn, Debye–Huckel laws (including correction) not limiting are true low-correlation limits (limit low plasma parameter Bκa) electrostatic contributions properties. even 1 : there small, but significant deviations from DH laws. These increase B. For capacity, quite large. They predicted accurately approximation. A consistency check made theory, calculating y± various ways. This consistent at κa, when we depart Eex, less Kirkwood–Buff formalism, dependent second moment respect radial distance distribution functions.The results functions statistically indistinguishable functions. Also, cannot distinguished up least κa= 0.45. unequal radii ions, straightforward generalisation (GDHX) found hold MC simulations. properties systems dominated contact cation anion. Fixing this 1.546), increasing ratio two 3 leads though systematic changes κa=ca. 0.10 0.14. particular, one observes y+= y–= good approximation, system.