Packing fraction of particles with a Weibull size distribution

Advancements in reliability of mechanical performance of 3D PRINTED Ag-doped bioceramic antibacterial scaffolds for bone tissue engineering

The current gold-standard approach for addressing bone defects in load-bearing applications sees the use of either autographs or allographs. These solutions, however, have limitations as autographs and allographs carry the risk of additional trauma, the threat of disease transmission, and potential donor rejection. An attractive candidate for overcoming the challenges associated with the use of autographs and allographs is a 3D porous scaffold displaying the needed mechanical competency for use in load-bearing applications that can stimulate bone tissue regeneration and provide antibacterial capabilities. To date, no reports document a 3D porous scaffold that fully meets the criteria specified above. In this work, we show how the use of fused filament fabrication (FFF) 3D printing technology in combination with a bimodal distribution of Ag-doped bioactive glass-ceramic (Ag-BG) micro-sized particles can successfully deliver porous 3D scaffolds with attractive and reliable mechanical performance characteristics capable of stimulating bone tissue regeneration and the ability to provide inherent antibacterial properties. To characterize the reliability of the mechanical performance of the FFF-printed Ag-BG scaffolds, Weibull statistics were evaluated for both the compressive (N = 25; m = 13.6 ± 0.9) and flexural (N = 25; m = 7.3 ± 0.7) strengths. Methicillin-resistant Staphylococcus aureus (MRSA) was used both in planktonic and biofilm forms to highlight the advanced antibacterial characteristics of the FFF-printed Ag-BG scaffolds. Biological performance was evaluated in vitro through indirect exposure to human marrow stromal cells (hMSCs), where the FFF-printed Ag-BG scaffolds were found to provide an attractive environment for cell infiltration and mineralization. Our work demonstrates how fused filament fabrication technology can be used with bioactive and antibacterial materials such as Ag-BG to deliver mechanically competent porous 3D scaffolds capable of stimulating bone tissue regeneration while simultaneously providing antibacterial performance capabilities.

Weibull function to describe the cumulative size distribution of clumps formed by two-dimensional grains randomly arranged on a plane

Many manifestations of natural processes give rise to interesting morphologies; it is all too easy to cite the corrugation of the Earth's surface or of planets in general. However, limiting ourselves to 2D cases, the morphology to which crystal growth gives rise is also intriguing. In particular, it is interesting to study some characteristics of the cluster projection in 2D, namely the study of the shapes of the speckles (fractal dimension of their rims) or the distribution of their areas. Recently, for instance, it has been shown that the size cumulative distribution function (cdf) of "voids" in a corrole film on Au(111) is well described by the well known Weibull distribution. The present article focuses on the cdf of cluster areas generated by numerical simulations: the clumps (clusters) are generated by overlapping grains (disks) whose germs (disk centers) are chosen randomly in a 2000×2000 square lattice. The obtained cdf of their areas is excellently fitted to the Weibull function in a given range of surface coverage. The same type of analysis is also performed for a fixed-time clump distribution in the case of Kolmogorov-Johnson-Mehl-Avrami (KJMA) kinetics. Again, a very good agreement with the Weibull function is obtained.

Estimation and fingerprinting of the size distribution of non-interacting spherical particles from small-angle scattering data

A new method to estimate the size distribution of non-interacting colloidal particles from small-angle scattering data is presented. The method demonstrates that the distribution can be efficiently retrieved through features of the scattering data when plotted in the Porod representation, thus avoiding the standard fitting procedure of nonlinear least squares. The present approach is elaborated using log-normal and Weibull distributions. The method can differentiate whether the distribution actually follows the functionality of either of these two distributions, unlike the standard fitting procedure which requires a prior assumption of the functionality of the distribution. After validation with various simulated scattering profiles, the formalism is used to estimate the size distribution from experimental small-angle X-ray scattering data from two different dilute dispersions of silica. At present the method is limited to monomodal distributions of dilute spherical particles only.