Importance of Mass Transport and Spatially Heterogeneous Flux Processes for in Situ Atomic Force Microscopy Measurements of Crystal Growth and Dissolution Kinetics

Abstract

It is well-established that important information about the dissolution and growth of crystals can be obtained by the investigation of step movement on single crystal faces via in-situ AFM.However, a potential drawback of this approach for kinetic measurements is that the small region of investigation may not be representative of the overall surface. It is shown that the investigation of local processes without accounting for the processes outside the region of interest can lead to significant misinterpretation of the data collected. Taking the case of gypsum dissolution as an exemplar, we critically analyze literature data and develop 3 different finite element method models that treat in detail the coupled mass transport -surface kinetic problem pertaining to dissolution processes in typical AFM environment. It is shown that mass transport cannot be neglected when performing in-situ AFM on macroscopic surfaces even with highconvection fluid cells. Moreover, crystal dissolution kinetics determined by AFM are mainly influenced by processes occurring in areas of the surface outside the region of interest. When this is recognized, and appropriate models are applied, step velocities due to dissolution are consistent with expectations based on macroscopic measurements and the kinetic gap that is often apparent between nanoscale and macroscopic measurements is closed. This study provides a framework for the detailed analysis of AFM kinetic data that has wide utility and applicability.3

In situ nanoscale observations of gypsum dissolution by digital holographic microscopy

“…, ratio of the activity product to the gypsum solubility product) of about 0.5. However, the flow velocity of 0.47 mm s −1 measured in the current study is nearly five times greater than that simulated by Peruffo et al (2016). In addition, the absence in this study of a physical obstruction near the surface likely makes the flowing fluid more effective at removing dissolved nearsurface components.…”

“…The hydrodynamics within a fluid cell are complex (Gasperino et al, 2006; Peruffo et al, 2016), and in the case of in situ AFM the presence of the physical probe can cause local changes in flow velocity. In at least one in situ AFM study of gypsum, the flow perturbation was severe enough that actively dissolving sites in neighboring regions affected the topography changes and dissolution flux in the field of view (Peruffo et al, 2016).…”

“…In at least one in situ AFM study of gypsum, the flow perturbation was severe enough that actively dissolving sites in neighboring regions affected the topography changes and dissolution flux in the field of view (Peruffo et al, 2016). But in situ DHM uses an optical probe, and any localized velocity effects should not be as prominent at the surface as in in situ AFM because the DHM 20 × immersion objective is several millimeters away from the sample surface.…”

“…2 indicates a surface-controlled dissolution reaction at flow rates of 14.5 mL min −1 and greater, the average concentration of dissolved calcium and sulfate ions very near the surface is unlikely to be zero. Finite element simulations of fluid flow near an AFM tip at a dissolving gypsum surface (Peruffo et al, 2016) indicate that the calcium and sulfate concentrations at the surface decrease by about 50%, to about 6 mmol L −1 , when the fluid flow rate increases from zero to 0.1 mm s −1 . This corresponds to a gypsum saturation index ( i.e.…”

Calcite dissolution rate spectra measured by in situ digital holographic microscopy

“…If the rate of removal of ions by diffusion or advection from the surface is sufficiently low, then the concentration near the surface could increase to a significant fraction of the saturation point and the process could become kinetically controlled by mass transport. Reaction-transport simulations near an AFM tip at a dissolving gypsum surface by Peruffo et al (2016) indicated that calcium and sulfate concentrations decreased by about 50% when the liquid flow increased from zero to only 0.1 mm s −1 . In this paper, the flow velocity near the surface is nearly five times greater than that.…”