LJPcalc calculates the liquid junction potential according to the stationary Nernst-Planck equation which is typically regarded as superior to the simpler Henderson equation used by most commercial LJP calculators (Marino et al., 2014). Both equations produce similar values, but the Henderson equation under-estimates the junction potential as ion concentrations increase (especially when solutions contain polyvalent ions). For these reasons the LJP reported by LJPcalc may be slightly greater in magnitude than that reported by other LJP calculators.
LJPcalc slightly adjusts ion concentrations as it calculates LJP. LJPcalc works to identify a solution that minimizes the difference between the adjusted concentrations and the user-provided concentrations. Except for the penultimate ion, only concentrations on side B are adjusted while calculating LJP. A solution is considered found when all adjusted side B concentrations are so close to the user-provided concentrations that the difference no longer has a significant influence on LJP. Note that the side A or side B concentration for the final and penultimate ions (respectively) may be adjusted to achieve electroneutrality.
LJPcalc automatically sorts the ions into an ideal order before calculating LJP. This is why the ions listed in the results table may appear in a different order than originally provided. The ion with the largest concentration difference is moved to the final position, and its side A concentration may be adjusted as needed to achieve electroneutrality. The remaining ion with the largest side B concentration is moved to the penultimate position, and its side B concentration is be adjusted as needed to achieve electroneutrality. Taken together, the ion-order-specific adjustments made to side B concentrations during the solving process is why the calculated LJP often differs by a few microvolts when the original list of ions is arranged in a different order.
Some ion sets are more difficult to analyze than others and may take longer to arrive at a solution. Users experiencing long calculation times are encouraged to re-sort the ion list randomly and try again. If the calculation runs for a very long time without producing a solution, consider omitting ions with the smallest concentrations since they do not contribute greatly to LJP anyway. Although I am not aware of any ion sets that LJPcalc cannot solve, if you think you have found one you are invited to share via email firstname.lastname@example.org or by creating a GitHub issue and include a copy of the ion table you are trying to solve including the temperature.
If you enjoy LJPcalc, consider citing it by name: Liquid junction potential was calculated according to the stationary Nernst–Planck equation (Marino et al., 2014) using LJPcalc software (https://swharden.com/LJPcalc).