From experiments with images to 3D models
For developing the next generation sustainable materials, it is often crucial to understand and control their properties and function. This work presents cross-disciplinary research starting with experimentally fabricated porous soft biomaterials and images of their micro-structure obtained by electron or laser microscopy. It is investigated how much information on the three-dimensional material structure can be extracted from two-dimensional images and how conclusions compare to three-dimensional image analysis. Based on the image data, spatial statistical models are constructed and fitted to two different materials: a colloidal nanoparticle gel and a porous polymer blended film. Colloidal systems are everywhere in our everyday life and of high interest for the development of new advanced materials. Polymer films are popular for pharmaceutical coatings which control the release of a drug to obtain important therapeutic benefits.
Besides presenting image analysis routines, three-dimensional finite Gibbs point processes with inhomogeneous and anisotropic pair-potential functions are introduced. Observed point patterns are formed by silica particle positions or pore branching points located at intersections of at least three pore channels. Due to physical chemical forces between particles and polymers, it is assumed that the points interact with each other. The pairwise interaction is described in the pair-potential function of a Gibbs process. In this way, there is a link between static Gibbs point process models and dynamic physical chemical processes like colloidal particle aggregation and polymer phase separation. Furthermore, a new spatial statistical summary function is suggested for the cluster size analysis on different length scales in aggregated structures. This function is a useful tool for comparing two regimes for particle aggregation resulting in different size and shape distributions of particle clusters. More precisely, it is used to study the diffusion limited and the reaction limited cluster aggregation.
The methods introduced in this work can be applied to point processes in general and are important contributions to the point process literature. The results are useful for setting up a virtual design framework for the study of properties of various materials, which may not yet have even been synthesized, in simulation studies instead of experiments involving valuable resources.
porous polymer blended films
colloidal particle aggregation
Gibbs point processes
Pascal, Matematiska vetenskaper, Chalmers tvärgata 3, Göteborg
Opponent: Associate Professor Ute Hahn, Department of Mathematics, Aarhus University, Denmark