Machine learning-accelerated small-angle X-ray scattering analysis of disordered two- and three-phase materials

Small-angle X-ray scattering (SAXS) is a useful technique for nanoscale structural characterization of materials. In SAXS, structural and spatial information is indirectly obtained from the scattering intensity in the spectral domain, known as the reciprocal space. Therefore, characterizing the structure requires solving the inverse problem of finding a plausible structure model that corresponds to the measured scattering intensity. Both the choice of structure model and the computational workload of parameter estimation are bottlenecks in this process. In this work, we develop a framework for analysis of SAXS data from disordered materials. The materials are modeled using Gaussian Random Fields (GRFs). We study the case of two phases, pore and solid, and three phases, where a third phase is added at the interface between the two other phases. Further, we develop very fast GPU-accelerated, Fourier transform-based numerical methods for both structure generation and SAXS simulation. We demonstrate that length scales and volume fractions can be predicted with good accuracy using our machine learning-based framework. The parameter prediction executes virtually instantaneously and hence the computational burden of conventional model fitting can be avoided

Large-Scale Statistical Learning for Mass Transport Prediction in Porous Materials Using 90,000 Artificially Generated Microstructures

Effective properties of functional materials crucially depend on their 3D microstructure. In this paper, we investigate quantitative relationships between descriptors of two-phase microstructures, consisting of solid and pores and their mass transport properties. To that end, we generate a vast database comprising 90,000 microstructures drawn from nine different stochastic models, and compute their effective diffusivity and permeability as well as various microstructural descriptors. To the best of our knowledge, this is the largest and most diverse dataset created for studying the influence of 3D microstructure on mass transport. In particular, we establish microstructure-property relationships using analytical prediction formulas, artificial (fully-connected) neural networks, and convolutional neural networks. Again, to the best of our knowledge, this is the first time that these three statistical learning approaches are quantitatively compared on the same dataset. The diversity of the dataset increases the generality of the determined relationships, and its size is vital for robust training of convolutional neural networks. We make the 3D microstructures, their structural descriptors and effective properties, as well as the code used to study the relationships between them available open access

Inverse design of anisotropic spinodoid materials with prescribed diffusivity

The three-dimensional microstructure of functional materials determines its effective properties, like the mass transport properties of a porous material. Hence, it is desirable to be able to tune the properties by tuning the microstructure accordingly. In this work, we study a class of spinodoid i.e. spinodal decomposition-like structures with tunable anisotropy, based on Gaussian random fields. These are realistic yet computationally efficient models for bicontinuous porous materials. We use a convolutional neural network for predicting effective diffusivity in all three directions. We demonstrate that by incorporating the predictions of the neural network in an approximate Bayesian computation framework for inverse problems, we can in a computationally efficient manner design microstructures with prescribed diffusivity in all three directions

DeepFRAP: Fast fluorescence recovery after photobleaching data analysis using deep neural networks

Conventional analysis of fluorescence recovery after photobleaching (FRAP) data for diffusion coefficient estimation typically involves fitting an analytical or numerical FRAP model to the recovery curve data using non-linear least squares. Depending on the model this can be time-consuming, especially for batch analysis of large numbers of data sets and if multiple initial guesses for the parameter vector are used to ensure convergence. In this work, we develop a completely new approach, DeepFRAP, utilizing machine learning for parameter estimation in FRAP. From a numerical FRAP model developed in previous work, we generate a very large set of simulated recovery curve data with realistic noise levels. The data is used for training different deep neural network regression models for prediction of several parameters, most importantly the diffusion coefficient. The neural networks are extremely fast and can estimate the parameters orders of magnitude faster than least squares. The performance of the neural network estimation framework is compared to conventional least squares estimation on simulated data, and found to be strikingly similar. Also, a simple experimental validation is performed, demonstrating excellent agreement between the two methods. We make the data and code used publicly available to facilitate further 34development of machine learning-based estimation in FRAP

Three-dimensional reconstruction of porous polymer films from FIB-SEM nanotomography data using random forests

Combined focused ion beam and scanning electron microscope (FIB-SEM) tomography is a well-established technique for high resolution imaging and reconstruction of the microstructure of a wide range of materials. Segmentation of FIB-SEM data is complicated due to a number of factors; the most prominent is that for porous materials, the scanning electron microscope image slices contain information not only from the planar cross-section of the material but also from underlying, exposed subsurface pores. In this work, we develop a segmentation method for FIB-SEM data from ethyl cellulose porous films made from ethyl cellulose and hydroxypropyl cellulose (EC/HPC) polymer blends. These materials are used for coating pharmaceutical oral dosage forms (tablets or pellets) to control drug release. We study three samples of ethyl cellulose and hydroxypropyl cellulose with different volume fractions where the hydroxypropyl cellulose phase has been leached out, resulting in a porous material. The data are segmented using scale-space features and a random forest classifier. We demonstrate good agreement with manual segmentations. The method enables quantitative characterization and subsequent optimization of material structure for controlled release applications. Although the methodology is demonstrated on porous polymer films, it is applicable to other soft porous materials imaged by FIB-SEM. We make the data and software used publicly available to facilitate further development of FIB-SEM segmentation methods. Lay Description For imaging of very fine structures in materials, the resolution limits of, e.g. X-ray computed tomography quickly become a bottleneck. Scanning electron microscopy (SEM) provides a way out, but it is essentially a two-dimensional imaging technique. One manner in which to extend it to three dimensions is to use a focused ion beam (FIB) combined with a scanning electron microscopy and acquire tomography data. In FIB-SEM tomography, ions are used to perform serial sectioning and the electron beam is used to image the cross section surface. This is a well-established method for a wide range of materials. However, image analysis of FIB-SEM data is complicated for a variety of reasons, in particular for porous media. In this work, we analyse FIB-SEM data from ethyl cellulose porous films made from ethyl cellulose and hydroxypropyl cellulose (EC/HPC) polymer blends. These films are used as coatings for controlled drug release. The aim is to perform image segmentation, i.e. to identify which parts of the image data constitute the pores and the solid, respectively. Manual segmentation, i.e. when a trained operator manually identifies areas constituting pores and solid, is too time-consuming to do in full for our very large data sets. However, by performing manual segmentation on a set of small, random regions of the data, we can train a machine learning algorithm to perform automatic segmentation on the entire data sets. The method yields good agreement with the manual segmentations and yields porosities of the entire data sets in very good agreement with expected values. The method facilitates understanding and quantitative characterization of the geometrical structure of the materials, and ultimately understanding of how to tailor the drug release

Structure formation and coarsening kinetics of phase-separated spin-coated ethylcellulose/hydroxypropylcellulose films

Porous phase-separated ethylcellulose/hydroxypropylcellulose (EC/HPC) films are used to control drug transport from pharmaceutical pellets. The drug transport rate is determined by the structure of the porous films that are formed as water-soluble HPC leaches out. However, a detailed understanding of the evolution of the phase-separated structure in the films is lacking. In this work, we have investigated EC/HPC films produced by spin-coating, mimicking the industrial fluidized bed spraying. The aim was to investigate film structure evolution and coarsening kinetics during solvent evaporation. The structure evolution was characterized using confocal laser scanning microscopy and image analysis. The effect of the EC:HPC ratio (15 to 85 wt% HPC) on the structure evolution was determined. Bicontinuous structures were found for 30 to 40 wt% HPC. The growth of the characteristic length scale followed a power law, L(t) ∼ t(n), with n ∼ 1 for bicontinuous structures, and n ∼ 0.45-0.75 for discontinuous structures. The characteristic length scale after kinetic trapping ranged between 3.0 and 6.0 μm for bicontinuous and between 0.6 and 1.6 μm for discontinuous structures. Two main coarsening mechanisms could be identified: interfacial tension-driven hydrodynamic growth for bicontinuous structures and diffusion-driven coalescence for discontinuous structures. The 2D in-plane interface curvature analysis showed that the mean curvature decreased as a function of time for bicontinuous structures, confirming that interfacial tension is driving the growth. The findings of this work provide a good understanding of the mechanisms responsible for morphology development and open for further tailoring of thin EC/HPC film structures for controlled drug release

Convolutional neural networks for segmentation of FIB-SEM nanotomography data from porous polymer films for controlled drug release

Phase-separated polymer films are commonly used as coatings around pharmaceutical oral dosage forms (tablets or pellets) to facilitate controlled drug release. A typical choice is to use ethyl cellulose and hydroxypropyl cellulose (EC/HPC) polymer blends. When an EC/HPC film is in contact with water, the leaching out of the water-soluble HPC phase produces an EC film with a porous network through which the drug is transported. The drug release can be tailored by controlling the structure of this porous network. Imaging and characterization of such EC porous films facilitates understanding of how to control and tailor film formation and ultimately drug release. Combined focused ion beam and scanning electron microscope (FIB-SEM) tomography is a well-established technique for high-resolution imaging, and suitable for this application. However, for segmenting image data, in this case to correctly identify the porous network, FIB-SEM is a challenging technique to work with. In this work, we implement convolutional neural networks for segmentation of FIB-SEM image data. The data are acquired from three EC porous films where the HPC phases have been leached out. The three data sets have varying porosities in a range of interest for controlled drug release applications. We demonstrate very good agreement with manual segmentations. In particular, we demonstrate an improvement in comparison to previous work on the same data sets that utilized a random forest classifier trained on Gaussian scale-space features. Finally, we facilitate further development of FIB-SEM segmentation methods by making the data and software used open\ua0access

Computational Screening of Diffusive Transport in Nanoplatelet-Filled Composites: Use of Graphene to Enhance Polymer Barrier Properties

Motivated by the substantial interest in various fillers to enhance the barrier properties of polymeric films, especially graphene derivatives, we perform a computational screening of obstructed diffusion to explore the design parameter space of nanoplatelet-filled composites synthesized in silico. As a model for the nanoplatelets, we use circular and elliptical nonoverlapping and impermeable flat disks, and diffusion is stochastically simulated using a random-walk model, from which the effective diffusivity is calculated. On the basis of 4000 generated structures and diffusion simulations, we systematically investigate the impact of different nanoplatelet characteristics such as orientation, layering, size, polydispersity, shape, and amount. We conclude that the orientation, size, and amount of nanoplatelets are the most important parameters and show that using nanoplatelets oriented perpendicular to the diffusion direction, under reasonable assumptions, with approximately 0.2% (w/w) graphene, we can reach 90% reduction and, with approximately 1% (w/w) graphene, we can reach 99% reduction in diffusivity, purely because of geometrical effects, in a defect-free matrix with perfect compatibility. Additionally, our results suggest that the existing analytical models have some difficulty with extremely large aspect ratio (extremely flat) nanoplatelets, which calls for further development

Tessellation-based stochastic modelling of 3D coating structures imaged with FIB-SEM tomography

To facilitate printing, coatings are typically applied to paperboard used for packaging to provide a good surface for application. To optimise the performance of the coating, it is important to understand the relationship between the microstructure of the material and its mass transport properties. In this work, three samples of paperboard coating are imaged using combined focused ion beam and scanning electron microscope (FIB-SEM) tomography data appropriately segmented to characterise the internal microstructure. These images are used to inform a parametric, tessellation-based stochastic three-dimensional model intended to mimic the irregular geometry of the particles that can be seen in the coating. Parameters for the model are estimated from the FIB-SEM image data, and we demonstrate good agreement between the real and virtual structures both in terms of geometrical measures and mass transport properties. The development of this model facilitates exploration of the relationship between the structure and its properties

New characterization measures of pore shape and connectivity applied to coatings used for controlled drug release

Pore geometry characterization-methods are important tools for understanding how pore structure influences properties such as transport through a porous material. Bottlenecks can have a large influence on transport and related properties. However, existing methods only catch certain types of bottleneck effects caused by variations in pore size. We here introduce a new measure, geodesic channel strength, which captures a different type of bottleneck effect caused by many paths coinciding in the same pore. We further develop new variants of pore size measures and propose a new way of visualizing 3-D characterization results using layered images. The new measures together with existing measures were used to characterize and visualize properties of 3-D FIB-SEM images of three leached ethyl-cellulose/hydroxypropyl-cellulose films. All films were shown to be anisotropic, and the strongest anisotropy was found in the film with lowest porosity. This film had very tortuous paths and strong geodesic channel-bottlenecks, while the paths through the other two films were relatively straight with well-connected pore networks. The geodesic channel strength was shown to give important new visual and quantitative insights about connectivity, and the new pore size measures provided useful information about anisotropies and inhomogeneities in the pore structures. The methods have been implemented in the freely available software MIST