A Simple Method for Determining Charge Distributions, Potentials, and Electric Fields Associated with an Electrospray Capillary

The electric field emanating from an electrospray ionization (ESI) capillary triggers the formation of a Taylor cone and the release of charged droplets. Uncovering the properties of this electric field is essential for developing a comprehensive understanding of the ESI process. The field is the negative gradient of the electric potential. The potential can be obtained by numerically solving the Poisson or Laplace equations, e.g., by using commercial software packages. However, such software tools do not necessarily provide mass spectrometry practitioners (many of whom were trained as biological or analytical chemists) with an intuitive grasp of the underlying concepts. The current work proposes an equivalent but much simpler method for uncovering the electrostatic properties of an ESI source. We focus on a charged capillary with an adjacent counter electrode (the latter represents the mass spectrometer). Instead of solving differential equations, the algorithm developed here adjusts the charge distribution on the ESI capillary until the potential anywhere on the capillary surface is constant. By definition, this scenario defines electrostatic equilibrium. The counter electrode can be included via simple image charge arguments. Our algorithm correctly predicts charge accumulation at the narrow capillary outlet, giving rise to a strong and highly divergent electric field in this area. Application of the method to various capillary geometries provides insights into the effects of experimental parameters. The code developed here is not intended to replace existing software packages, but it may provide practitioners with a more intuitive understanding of basic electrostatic principles. In addition, the method should be helpful for designing improved molecular dynamics simulations of ESI emitters.