The apparent activation energy and pre-exponential kinetic factor for heterogeneous calcium carbonate nucleation on quartz

Abstract

Nucleation occurs widely in materials synthesis and natural environments. However, in the nucleation rate equation, values for the apparent activation energy (E a ) and the preexponential kinetic factor (A) are thus far unknown because real-time nanoscale observations are difficult to perform. Here we experimentally determine E a and A using heterogeneous calcium carbonate nucleation on quartz as a model system. Nucleation rates are measured with in situ grazing incidence small-angle X-ray scattering and ex situ atomic force microscopy, and the experiments are conducted with a fixed supersaturation of IAP/K sp (calc) = 10 1.65 at 12, 25, and 31°C. E a is calculated as 45 ± 7 kJ mol −1 , and A is 10 12.0 ± 1.1 nuclei μm −2 min −1 , or 10 2.9 ± 1.3 mol m −2 min −1 . Increasing the temperature shortens the induction time, but does not change nucleus sizes. These parameter values are critical for predicting and controlling the nucleation of materials.

Thermodynamics and ordering kinetics in asymmetric PS-b-PMMA block copolymer thin films

“…In particular, in the latter case, enzymes instead of stochastic forces (as thermal fluctuations) are used to activate the crossing of the barrier. [69][70][71][72][73][74][75][76] Perspectives A direct extrapolation of these results to other PS-b-PMMA morphologies is not straightforward because of the different connectivity in spheres, cylinders and lamellae forming BCP thin films. In particular, hexagonally packed cylinders perpendicularly oriented with respect to the surface are characterized by a zero-dimensional connectivity, so that hopping diffusion drives the grain-coarsening process.…”

Studies of aqueous U(iv) equilibrium and nanoparticle formation kinetics using spectrophotometric reaction modeling analysis

“…where A is the pre-exponential kinetic factor related to ion diffusion, and nuclei surface properties, and DG * and E a are the thermodynamic and kinetic energy barriers (J mol À1 ), respectively. 34,35 DG * is related to interfacial energies, and E a is the apparent activation energy. Eqn (7) is based on the theoretical pathway where nuclei are formed by the addition of one monomer at a time until the nucleus grows large enough to stabilize the nucleus as a new phase.…”

Effect of Metal Ions on Hybrid Graphite-Diamond Nanowire Growth: Conductivity Measurements from a Single Nanowire Device

“…The temperature-dependent electrical resistance and static resistivity decrease as the temperature is increased from 80 K to 300 K, as shown in Figure S26a,b in supporting information. By fitting the plots of “lnR vs. 1/T” (Figure S27a–c in supporting information), the activation energies (E a ) with values of 29.41 meV and 12.43 meV for L2 are determined for temperature ranges of 300~200 K and 200~80 K, respectively, which clearly indicates that two kinds of transport mechanisms are involved [54]. In addition, the plot of “lnσ Vs 1/T” (Figure S27d in supporting information) also support the manifestation of different transport mechanisms in the temperature-dependent conductivity studies.…”