Nucleation on surfaces and in confinement
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oduction Mineralized tissues support locomotion (e.g., bones), predation (teeth), and defense (shells), and are used for sensing acceleration (e.g., vertebrate otoliths and otoconia), gravity (statoliths), light (lenses), and magnetic fields (magnetosomes), often doubling as nutrient/waste storage.1 Many of their remarkable properties emerge from the hierarchical organization of organic and inorganic building blocks (Figure 1)2–7 (also see the June 2015 MRS Bulletin issue: Biomineralization). Despite new experimental techniques8–12 and continuous improvements in computational approaches,13,14 we are still far from understanding how the organisms direct mineral nucleation and subsequent processes that lead to assembly.15–17 This article focuses on our current understanding of two critical aspects of biomineralization—(1) how self-assembled surfaces direct location, orientation, and timing through heterogeneous nucleation; and (2) the effect of confinement within small volumes on the rate of phase transformations.
A brief review of nucleation in biomineralization Biomineralization typically starts with precipitation from a supersaturated aqueous solution.16,18 The driving force for the formation of a new phase with the chemical formula [(A1 ) k1 (A 2 ) k2 ! (A i ) ki ] can be expressed in terms of the supersaturation: [A ] σ = ln ¡¡ i i ¢¡ Ksp
ki
¯ °, ° ±°
where Ksp is the solubility product of the new phase, [Ai] refers to the activity of the aquo-complex of the ith species (Ai) in solution, and ki is the associated stoichiometric coefficient. Clusters of the new phase arise from concentration fluctuations. According to classical nucleation theory (CNT), a cluster that is exactly of critical size, the nucleus, is in unstable equilibrium, and either loss or gain of additional building blocks will reduce its free energy. Smaller clusters will on average shrink, and larger ones will grow. The reversible work of nucleation W* is the free-energy cost (barrier) associated with the formation of a spherical, incompressible nucleus: 2
W* =
16π Vm ¬ γ 3 , 3 RT ® σ 2
(2)
where γ is the (average) surface free energy of the newly formed interface, R is the universal gas constant, T is temperature, and VM is the molar volume of the new phase.19 As discussed in the article by Sear in this issue, the intrinsic nucleation rate JV, the number of nuclei formed per unit time and unit volume, then takes the form:20 JV ∝ e
(1)
−
W* k BT
,
(3)
where kB is the Boltzmann constant.
Michael L. Whittaker, Department of Materials Science and Engineering, Northwestern University, USA; [email protected] Patricia M. Dove, Department of Geosciences, Virginia Polytechnic Institute and State University, USA; [email protected] Derk Joester, Department of Materials Science and Engineering, Northwestern University, USA; [email protected] doi:10.1557/mrs.2016.90
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MRS BULLETIN • VOLUME 41 • MAY 2016 • www.mrs.org/bulletin
© 2016 Materials Research Society
NUCLEATION ON SURFACES AND IN CONFINEMENT
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