Two independent measurements of Debye lengths in doped nonpolar liquids

Electric current measurements were performed between 2.5 cm x 7.5 cm parallel-plate electrodes separated by 1.2 mm of heptane doped with 0-15% w/w poly(isobutylene succinimide) (PIBS) having a molecular weight of about 1700. The rapid (microsecond) initial charging of the capacitor can be used to infer the dielectric constant of the solution. The much slower decay of current arising from the polarization of electrodes depends on the differential capacitance of the diffuse clouds of charge carriers accumulating next to each electrode and on the ohmic resistance of the fluid. Using the Gouy-Chapman model for the differential capacitance, Debye lengths of 80-600 nm were deduced that decrease with increasing concentration of PIBS. Values of the Debye lengths were confirmed by performing independent measurements of double-layer repulsion between a 6 microm polystyrene (PS) latex sphere and a PS-coated glass plate using total internal reflection microscopy in the same solutions. The charge carriers appear to be inverted PIBS micelles having apparent Stokes diameters of 20-40 nm. Dynamic light scattering reveals a broad distribution of sizes having an intensity-averaged diameter of 15 nm. This smaller size might arise (1) from overestimating the electrophoretic mobility of micelles by treating them as point charges or (2) because charged micelles are larger on average than uncharged micelles. When Faradaic reactions and zeta potentials on the electrodes can be neglected, such current versus time experiments yield values for the Debye length and ionic strength with less effort than force measurements. To obtain the concentration of charge carriers from measurements of conductivity, the mobility of the charge carriers must be known.