Kinetic concepts for quantitative prediction of fluid-solid interactions

Abstract

In a unique “perspectives” format that examines both past and future, we appraise the field of crystal dissolution kinetics, showing how the last century's strong progress in experimental discovery has both driven, and been driven by, the tandem evolution of basic theory. To provide context for examining the current state-of-the-art in this critical field, we highlight the key milestones that have punctuated our progress in understanding the dynamics of crystalline surfaces. For crystal growth, these are the energy relations between kinks on stepped surfaces, and the phenomena of screw dislocations sustaining steady state growth at low thermodynamic overstep. For crystal dissolution, the corresponding recognition is the tie between defects, hollow cores, and macroscopic etch pits. These latter relationships have been more recently formalized in the stepwave model, incorporating etch pit nucleation, step generation, and global retreat of the crystal surface: the total dissolution rate. All these conceptual advances contain an assertion of a link, fundamental but often implicit, between mass action and kinetics, where chemical potential is the primary driver of rates of physical process. This link is inherent in many “classical” rate equations, whose parameterization is often the endgame of laboratory observations.Today, this extant framework serves as the conceptual basis for organizing the data available from a sophisticated suite of analytical and experimental instrumentation. These resources permit ever-increasing resolution of reacting surfaces in breathtaking detail, often under in situ conditions. These direct observations are now further enhanced by powerful computer-driven simulation and numerical modelling, allowing the virtual exploration of complex reaction systems, ranging from isolated single crystals to porous, multiphase networks. Despite the exhilarating breadth and detail of these accomplishments, it is also becoming increasingly apparent that we are moving further, not closer, from the goal of predictive understanding, a goal that is an increasingly vital social responsibility of our science. A major source of this divergence reflects the fact that at key intersecting points of study, our prowess in technical observation has effectively outpaced our theoretical understanding. In confronting the daunting complexity of these systems, we must be careful to first identify major vacancies in theory. Until we resolve these deficits, more observations may be of only limited utility.In assessing this problem, a major uncertainty is how to properly reconcile thermodynamics, by its very nature a macroscopic formalism, with our current focus on atomic scales of reaction. This may be a problem unique to crystalline materials and their interactions with phases whose components are otherwise mobile. Detailed balancing and related microscopic reversibility, the implicit link referred to above, is often used to form a mechanistic bridge between the macroscopic distribution of energy and microscopic heterogeneity of events in crystal surfaces, but its employment creates two problems: spatial and temporal. First, reaction mechanism is truly atomic in dimension, involving actual, nondegenerate collisions at crystal surface sites, whereas ∆Gr or ∆μ is macroscopic. Second, the rate at which a crystal surface dissolves reflects both the chemical composition of the ambient fluid and the distribution of surface energy. Reaction towards “equilibrium”, involving the typically slow redistribution of surface energy, may thus inherit topography inconsistent with the computed “driving force”. This reactivity mismatch yields surfaces that evolve over time, producing a heterogeneous distribution of rates. This distribution can be efficiently characterized by rate spectra: the span of non-steady-state rates reflecting diversity of reactive sites established under previous ∆Gr regimes. We use these spectra as a basic compact variable: a signal that encodes the complex link between site-specific surficial energy distributions, solution and surface chemistry, and the cumulative rate that results. Because this encoding is efficiently captured by numerous surface analytical microscopies (VSI, AFM), this approach permits the testing of hypotheses regarding the probabilistic nature of rate distributions, a process we hope the community will embrace, serving ultimately as a key step forward in establishing useful predictive approaches. We illustrate this potential with a series of case studies that target a range of composition, space, and time scales.