In the present work, biomimetic hydroxyapatite (BHAP) doped with silicate and carbonate anions in the presence of citrate ions are synthesized by chemical precipitation from aqueous solutions. According to the results of X-ray phase analysis (XRD), all the obtained materials are single-phase. Scanning electron microscopy (SEM) demonstrates that BHAP powders are a collection of agglomerated particles with similar morphology. Dynamic light scattering confirms that the synthesized BHAPs consist of agglomerates 1–4μm in size. For all samples, with an increase in the number of introduced citrate ions, decreases in the average crystallite size and degree of crystallinity are observed. With an increase in the concentration of citrate ions, the content of agglomerate fractions of 1–2μm in size increases from 70.16 to 75.43%. The solubility of hydroxyapatite samples in physiological saline (ω(NaCl) = 0.9%) at temperatures of 22°C and 37°C is studied. It is revealed that for all synthesized BHAPs, the amount of released Ca2+ ions into the liquid phase increases. The maximum yield of Ca2+ ions in physiological saline is recorded in BHAP with the highest content of citrate ions. The obtained results allow to consider the synthesized BHAP as a promising medical biomaterial for the regeneration of bone tissue.
The present study investigated the phase composition, the structural, morphological, and bioactivity properties of silicon- and carbonate-doped biomimetic hydroxyapatite synthesized by precipitation from aqueous solutions in the presence of different amounts of citrate ions. The X-ray diffraction and Fourier transform infrared spectroscopy analyses confirmed that all the samples exhibited single-phase. Base on the results of the morphological study, all the obtained samples consisted of porous agglomerated particles made up of tiny crystallites in the nanometer range. The change in structural order, as well as the decrease in particle size and degree of crystallinity result from the presence of citrate ions were revealed by X-ray diffraction, dynamic light scattering, and scanning electron microscopy analyses. Bioactivity properties of samples were studied by analyzing their bioresorbability in physiological saline (ω (NaCl) = 0.9%) and evaluating their solubility in SBF solution after a certain period of soaking time. The amount of the released Ca2+ ions was found to increase with the increasing concentration of citrate ions introduced in the synthesis process. The better solubility of material with the presence of citrate ions was beneficial in the growth of apatite on its surface that made produced material more biocompatible.
We construct harmonic functions in the quarter plane for discrete Laplace operators. In particular, the functions are conditioned to vanish on the boundary and the Laplacians admit coefficients associated with transition probabilities of non-symmetric random walks. By solving a boundary value problem for generating functions of harmonic functions, we deduce explicit expressions for the generating functions in terms of conformal mappings. These mappings are yielded from a conformal welding problem with quasisymmetric shift and contain information about the growth of harmonic functions. Further, we describe the set of harmonic functions as a vector space isomorphic to the space of formal power series. Contents 1. Introduction 1 2. Study of the kernel 8 3. Conformal welding 18 4. Proof of the main theorems 26 5. Small jump random walks 29 References 33
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