A Molecular Dynamics Study of the Thermodynamic Properties of Calcium Apatites. 1. Hexagonal Phases

Abstract

Structural and thermodynamic properties of crystal hexagonal calcium apatites, Ca10(PO4)6(X)2 (X = OH, F, Cl, Br), were investigated using an all-atom Born-Huggins-Mayer potential by a molecular dynamics technique. The accuracy of the model at room temperature and atmospheric pressure was checked against crystal structural data, with maximum deviations of ca. 4% for the haloapatites and 8% for hydroxyapatite. The standard molar lattice enthalpy, delta(lat)H298(o), of the apatites was calculated and compared with previously published experimental results, the agreement being better than 2%. The molar heat capacity at constant pressure, C(p,m), in the range 298-1298 K, was estimated from the plot of the molar enthalpy of the crystal as a function of temperature, H(m) = (H(m,298) - 298C(p,m)) + C(p,m)T, yielding C(p,m) = 694 +/- 68 J x mol(-1) x K(-1), C(p,m) = 646 +/- 26 J x mol(-1) x K(-1), C(p,m) = 530 +/- 34 J x mol(-1) x K(-1), and C(p,m) = 811 +/- 42 J x mol(-1) x K(-1) for hydroxy-, fluor-, chlor-, and bromapatite, respectively. High-pressure simulation runs, in the range 0.5-75 kbar, were performed in order to estimate the isothermal compressibility coefficient, kappaT, of those compounds. The deformation of the compressed solids is always elastically anisotropic, with BrAp exhibiting a markedly different behavior from those displayed by HOAp and ClAp. High-pressure p-V data were fitted to the Parsafar-Mason equation of state with an accuracy better than 1%.

A comprehensive guide to experimental and predicted thermodynamic properties of phosphate apatite minerals in view of applicative purposes

“…It may be noted at this point that some authors have attempted to estimate apatites thermodynamic properties based on lattice energy computational estimations and molecular modeling calculations [30,61,86]. However, the outcomes of these computed methods sometimes deserve to be debated as they do not always agree well with experimental facts.…”

Molecular dynamics simulations of molten calcium hydroxyapatite

“…Although they considered the phosphate ion to be a rigid tetrahedron, they were able to reproduce the experimental crystal parameters with a maximum error of 1%. We have also found that such an assumption gives a good account of the physical properties of solid apatites under compression [12,13].…”

“…The experimental results were interpreted using a correlation with the enthalpy of formation of the species CaX 2 (X = OH − , F − , Cl − , and Br − ), allowing for the estimate of the standard molar enthalpy of formation of iodapatite (IAp), which had not been determined before. Later, the thermodynamic properties of the entire family of hexagonal [12] and monoclinic (P2 1 /b) [13] calcium apatites (hydroxy-, fluor-, chlor-, and bromapatite) were studied using the molecular dynamics technique (MD). The structural and energetic model employed reproduced well the experimental crystal data, and the standard molar lattice enthalpies calculated by the MD technique showed a good agreement with the experimental results.…”

Selective Laser Sintering of Poly(L-Lactide)/Carbonated Hydroxyapatite Nanocomposite Porous Scaffolds for Bone Tissue Engineering

“…Another possible reason for the lower degree of fusion of the PLLA/CHAp nanocomposite microspheres was the relatively high specific heat capacity of hydroxyapatite. According to Cruz et al (2005), the molar heat capacity (C p,m ) of HAp is 694 ± 68 J mol -1 K -1 in the temperature range 298-1298 K, which is much higher than that of PLLA, from 145.4 to 156.7 J mol -1 K -1 in the temperature range from 332.5K (T g ) to 480 K (T m ) (Pyda et al 2004;Malmgren et al 2006). Therefore, CHAp (a hydroxyapatite based ceramic) can be regarded as a huge energy reservoir to absorb laser energy.…”