Max Kolb

Percolation Theory and Compactibility of Binary Powder Systems

Defined size fractions of polyethyleneglycol powder (MW = 10,000) were mixed with defined size fractions of α-lactose monohydrate in order to study the effect of compaction as a function of the weight ratios of the two excipients. For a precise control of the compression cycle, tablets were compressed on a Universal Testing Machine (Zwick 1478). Tablet tensile strength σT was quantified as a function of compressional stress σc and relative density ρr using a two-parameter model with σTmax = maximal tensile strength at zero porosity and γ = compressibility. The results have been analyzed on the basis of the percolation theory. As soon as the component with the lower mechanical stability is percolating the powder system, tablet hardness is controlled entirely by this component. The percolation threshold is a function of the geometrical arrangement of the particles in the compressed powder system. The expected two percolation thresholds can be distinguished as a function of the composition weight ratios if the particle size distributions of the two components differ enough.

Molecule-based kinetic modeling by Monte Carlo methods for heavy petroleum conversion

A methodology for kinetic modeling of conversion processes is presented. The proposed approach allows to overcome the lack of molecular detail of the petroleum fractions and to simulate the reactions of the process by means of a two-step procedure. In the first step, a synthetic mixture of molecules representing the feedstock is generated via a molecular reconstruction method, termed SR-REM molecular reconstruction. In the second step, a kinetic Monte Carlo method, termed stochastic simulation algorithm (SSA), is used to simulate the effect of the conversion reactions on the mixture of molecules. The resulting methodology is applied to the Athabasca vacuum residue hydrocracking. An adequate molecular representation of the vacuum residue is obtained using the SR-REM algorithm. The reaction simulations present a good agreement with the laboratory data for Athabasca vacuum residue conversion. In addition, the proposed methodology provides the molecular detail of the vacuum residue conversion throughout the reactions simulations.

Multiblock Copolymer Solutions in Contact with a Surface: Self-Assembly, Adsorption, and Percolation

Amphiphilic copolymers are often used as compatibilizing or stabilizing agents, either in solution or at surfaces. In the special case of multiblock copolymers the connectivity of the blocks combines with the antagonistic behavior of the different types of blocks. Here we report on the behavior of solutions of amphiphilic multiblock copolymers with a large number of blocks and a low fraction of solvophobic monomers in contact with an attractive surface. Using lattice Monte Carlo simulations, the influence on the structures of the solvent quality and the type of surface from noninteracting to strongly attractive to the solvophobic monomers can be assessed. In the presence of a surface bulk micelles are formed that are not different in size and shape from the micelles observed in the absence of a surface. When increasing the surface attraction, solvophobic monomers tend to adsorb either as isolated blocks or forming surface micelles. Evidence is given of a surface concentration threshold above which surface micelles can form due to microphase separation. These surface micelles are in equilibrium with bulk micelles, some of which are connected to the surface through a path of either hydrophobic and/or hydrophilic blocks or hydrophobic cross-links, or both. The size distributions of bulk and connected micelles are similar. With increasing surface concentration surface micelles get organized due to the steric repulsion between core-shell surface micelles. Moreover, these organized surface micelles percolate. The connected micelles form a concentrated layer parallel to the attractive surface. In addition, these systems are governed by two very different time scales: The fast one leads to micellar self-assembly in the bulk and at the surface while the slow one prevents the system from reaching equilibrium in the course of the simulations and corresponds to the transfer of copolymers from the bulk to the attractive surface.

Monte-Carlo methods for simulating the catalytic oxidative dehydrogenation of propane over VMgO catalyst

Abstract The oxidative dehydrogenation of propane (ODHP) has been extensively studied by non-steady-state kinetic experiments and by various experimental characterization techniques under conditions as close as possible to reaction conditions. It can be described in terms of the Mars–Van Krevelen mechanism. This work reports on Monte-Carlo simulations of the ODHP over VMgO catalysts, aimed at relating the main experimental insights obtained previously on the catalytic reaction to a theoretical description of the working catalyst. The “theoretical field of catalysis” is explored by handling new Monte-Carlo models with a catalytic reaction graph, 2D pattern recognition of adsorbed molecules, 3D oxygen bulk diffusion and finally the description of the selective, non-selective routes of the ODHP process.

GELATION TRANSITION VERSUS PERCOLATION THEORY

Well over ten years ago, when percolation theory was developed, it was suggested that the behavior of the sol-gel transition near the gel point can be described by the percolation model.1,2 According to this identification, the static properties of a gel—its geometrical structure and the size distribution of the gel fragments—are independent of material details, provided the gel-forming process is local and uncorrelated. The same theory admits for several dynamical universality classes, dependent on the mechanism at work. One expects that the kinetics of the gelation process as well as hydrodynamics and entanglement effects influence the properties near a sol-gel transition.

Structure Formation by Aggregation: Models and Applications

Large, ramified structures can be observed in many different areas of science, and notably in colloidal and aerosol experiments. These structures have universal features and can be modelled by random aggregation processes. Their properties, notably their fractal characteristics, can be determined efficiently from numerical simulations. An account is given of several basic models describing the formation of disordered structures. Some of the numerous experimental realisations of such processes are reviewed. Recent developments consider the influence of such ramified structures on gel formation.