Microscale Electrical Resistivity Measurements to Investigate Particle Distribution

The functional performance of a particulate thin film depends greatly on the particle distribution that forms during drying. In situ methods for monitoring the impact of different processing parameters on the distribution of particles currently require expensive and specialized equipment. This work addresses this gap by miniaturizing a geophysical prospecting method to thin-film applications. In this method, four-electrode resistivity measurements at variable probe spacing detect changes in the vertical particle concentration profile. A heuristic colloidal drying model describes the particle distribution during drying in terms of the relative effects of Brownian diffusion, sedimentation, and evaporation. For sedimentation- and evaporation-dominated drying, the film is modeled as two stratified layers of different concentrations. Solving this model simultaneously alongside Laplace's equation for electrostatic resistance identifies the parameters necessary to distinguish between diffusion-, sedimentation-, and evaporation-dominated drying. For resistive particles in a conductive solvent, simulations predict that the normalized thickness of the top layer, δ/H₀, must exceed a critical value to distinguish between different drying regimes. The heuristic model results are validated theoretically by comparison to a physics-based drying model. Model predictions are experimentally validated by fabricating a custom microlithography four-line probe device and measuring the transient resistance of systems for which the drying mechanism is known. This work offers a low-cost and in situ method to identify drying mechanisms and extract physical parameters that better characterize the processing-structure-function relationships for many coatings.