Figure 7: Results of in situ AFM investigation of ACP and AP nucleation kinetics.
(a–c) Nucleation of HAP on collagen at (a) t=270, (b) 1,020 and (c) 5,280 s, respectively, where σAP=3.08, σOCP=1.51 and σACP=−0.23. (d) Nucleation of ACP on collagen followed by transformation to (e) OCP and then (f) AP at (d) t=552, (e) 3,660 and (f) 6,000 s, respectively, where σAP=3.36, σOCP=1.76 and σACP=0.04. Inserts are TEM images of mineral phase (a) AP, (d) ACP (e) OCP and (f) AP. Scale bars in AFM images are 100 nm. (g) Dependence of the steady-state nucleation rate Jn on time t at six different supersaturations. The supersaturations corresponding to the numeric labels are, 1: σAP=3.08, σOCP=1.51, σACP=−0.23; 2: σAP=3.24, σOCP=1.65, σACP=−0.08; 3: σAP=3.31, σOCP=1.71, σACP=−0.02; 4: σAP=3.45, σOCP=1.83, σACP=0.128; 5: σAP=3.46, σOCP=1.84, σACP=0.129 and 6: σAP=3.47, σOCP=1.85, σACP=0.1295. Analysis of the data using classical nucleation theory, which predicts that Jn=A·exp(−ΔGc/kT)=A·exp(−8πω2α3/3(kTσ)2) where A is the kinetic constant related to diffusional, steric and any other kinetic barriers, ΔGc is the free-energy barrier to nucleation, ω is the molecular volume of the solid, α is the interfacial energy, k is Boltzmann’s constant and T is the absolute temperature, gives αACP=40 mJ m−2 and αAP=90 mJ m−2 (see Supplementary Information Analysis of nucleation data: fitting of classical nucleation rate equation for details.) We note that nucleation on a substrate is completely equivalent to nucleation in the bulk solution in terms of this equation, which does not distinguish between heterogeneous and homogeneous nucleation except through the differences in α and the numerical factor 8/3.
