The bipolar diffusion charging of nanoparticles: A review and development of approaches for non-spherical particles

Theoretical and experimental analyses of the steady state, bipolar diffusion charge distribution on nanoparticles are reviewed. This charge distribution plays a critical role in electrical mobility measurements of nanoparticle size distribution functions, where it is approximated via empirical regression equations. While the regression approach has been broadly successful, there remain several unresolved issues related to charge distribution calculations. Specifically, research to date has not revealed a method to reliably calculate nanoparticle-ion collision rates in the presence of strong attractive potentials, charge distribution predictions do not routinely consider the mass and (electrical) mobility distributions of the charging ions, and calculation approaches applicable to both spherical and nonspherical particles have not been compared to experimental data. In light of these issues, we examine the steady-state bipolar charge distribution on gold nanospheres and gold nanorods via tandem differential mobility analysis (TDMA). We compare measurements to regression equations as well as to Brownian Dynamics (BD) simulations, which take ion mobility and mass distributions as inputs. These distributions were measured using a DMA coupled to a mass spectrometer. Both regression equations and BD simulations are found to agree reasonably well with measurements in air, and we find that particle mobility diameter has a much greater influence on charging than particle morphology. Results support the use of BD calculations to predict bipolar charge distributions when ion properties are known. Nevertheless, our work supports continued use of regression equations when such information is not available.