Abstract
While biological crystallization processes have been studied on the microscale extensively, there is a general lack of models addressing the mesoscale aspects of such phenomena. In this work, we investigate whether the phase-field theory developed in materials’ science for describing complex polycrystalline structures on the mesoscale can be meaningfully adapted to model crystallization in biological systems. We demonstrate the abilities of the phase-field technique by modeling a range of microstructures observed in mollusk shells and coral skeletons, including granular, prismatic, sheet/columnar nacre, and sprinkled spherulitic structures. We also compare two possible micromechanisms of calcification: the classical route, via ion-by-ion addition from a fluid state, and a nonclassical route, crystallization of an amorphous precursor deposited at the solidification front. We show that with an appropriate choice of the model parameters, microstructures similar to those found in biomineralized systems can be obtained along both routes, though the time-scale of the nonclassical route appears to be more realistic. The resemblance of the simulated and natural biominerals suggests that, underneath the immense biological complexity observed in living organisms, the underlying design principles for biological structures may be understood with simple math and simulated by phase-field theory.
Highlights
Crystalline materials formed by solidification from the liquid state play an essential role in our civilization.[1,2] This class of matter incorporates most of the technical alloys, polymers, minerals, drugs, food products, and so on
In the case of Phase-Field Model 1 (PF1), reduction of the driving force leads to a transition of a chemically homogeneous solid to alternating solid−liquid layers, whereas in the case of Phase-Field Model 2 (PF2) partitioning appears via alternating α−β bands
In a recent orientation field based phase-field (OF-PF) study,[26] we made the following assumptions that define the conditions under which eqs 1−6 were solved, when modeling the formation of mollusk shells within model PF1:
Summary
Crystalline materials formed by solidification from the liquid state play an essential role in our civilization.[1,2] This class of matter incorporates most of the technical alloys, polymers, minerals, drugs, food products, and so on. They include ab initio computations; particle-based methods like molecular dynamics (MD), Monte Carlo, or population dynamics simulations and different types of continuum models ranging from the density functional theory of classical particles, via coarse-grained models (such as the time-dependent Ginzburg−Landau, Cahn−Hilliard, and phase-field type order parameter theories that belong to the family of classical field theoretical models widely used in modeling phase transitions of various complexity), to the macroscopic continuum models applicable on engineering timeand length-scales While this inventory allows the modeling of a substantial range of crystallization phenomena, there are complex cases, for which its use is not straightforward.
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