Jeffrey W. Bullard

Numerical methods for computing interfacial mean curvature

A procedure is described for computing the mean curvature along condensed phase interfaces in two or three dimensions, without knowledge of the spatial derivatives of the interface. For any point P on the interface, the method consists of computing the portion of volume enclosed by a small template sphere, centered on P, that lies on one side of the interface. That portion of the template volume is shown to be linear in the mean curvature of the surface, relative to the phase lying on the opposite side of the interface, to within terms that can usually be made negligible. An analogous procedure is described in two dimensions. Application of the procedure to compute the mean curvature along a digitized surface is demonstrated. A burning algorithm can be included to improve computational accuracy for interfaces having sharp curvature fluctuations. A minor extension of the method allows computation of the orientation of an interfacial element relative to a fixed reference frame.

A parallel reaction-transport model applied to cement hydration and microstructure development

A recently described stochastic reaction-transport model on three-dimensional lattices is parallelized and is used to simulate the time-dependent structural and chemical evolution in multicomponent reactive systems. The model, called HydratiCA, uses probabilistic rules to simulate the kinetics of diffusion, homogeneous reactions and heterogeneous phenomena such as solid nucleation, growth and dissolution in complex three-dimensional systems. The algorithms require information only from each lattice site and its immediate neighbors, and this localization enables the parallelized model to exhibit near-linear scaling up to several hundred processors. Although applicable to a wide range of material systems, including sedimentary rock beds, reacting colloids and biochemical systems, validation is performed here on two minerals that are commonly found in Portland cement paste, calcium hydroxide and ettringite, by comparing their simulated dissolution or precipitation rates far from equilibrium to standard rate equations, and also by comparing simulated equilibrium states to thermodynamic calculations, as a function of temperature and pH. Finally, we demonstrate how HydratiCA can be used to investigate microstructure characteristics, such as spatial correlations between different condensed phases, in more complex microstructures.

A three-dimensional microstructural model of reactions and transport in aqueous mineral systems

A stochastic three-dimensional microstructure model is introduced for simulating spatial and temporal variations in aqueous mineral systems. Dissolution, nucleation, precipitation and solute transport are governed by local probabilistic rules applied on a regular computational lattice. The model is shown to accurately simulate ion diffusion in a dilute electrolyte. The reaction algorithms faithfully reproduce kinetics expected from standard rate equations, and reversible reactions are shown to converge to the correct equilibrium state determined by detailed balance of forward and reverse reaction rates, or the law of mass action. Accounting for the exponential temperature dependence of the reaction rate constants is shown to provide accurate predictions of the influences of temperature on both the kinetics and equilibrium of reactions. A simulation of the hydration of a generic metal oxide in water demonstrates the important relationships between microstructure development and the mechanisms of nucleation, growth and solute diffusion.

Factors That Influence Electrical Resistivity Measurements in Cementitious Systems

The electrical resistivity of cement-based materials can be used in quality control or service life prediction as an indicator of the fluid transport properties of these materials. Although electrical tests have the advantage of being easy and rapid to perform, several key factors can influence the results: (a) specimen geometry, (b) specimen temperature, and (c) sample storage and conditioning. This paper addresses these issues and compares the measurements from several commercially available testing devices. First, the role of sample geometry is explained with the use of three common geometries: surface, uniaxial, and embedded electrodes. If the geometry is properly accounted for, measurements from different test geometries result in electrical resistivity values that are similar. Second, the role of sample temperature is discussed for both pore solution and uniaxial tests on cylinders. Third, the paper examines the importance of sample curing, storage, and conditioning. Sample storage and conditioning influence both the degree of hydration and the degree of saturation. The role of sample volume to solution volume is discussed, as this ratio may influence alkali leaching and pore solution conduction. This paper is intended to identify factors that influence the results of rapid electrical test measurements and to help identify areas of future research that are needed so that robust specifications and standard test methods can be developed. Standardization will enable electrical tests to provide rapid, accurate, repeatable measurements of concretes electrical properties.

A comparison of viscosity-concentration relationships for emulsions.

Differential effective medium theory (D-EMT) has been used by a number of investigators to derive expressions for the shear viscosity of a colloidal suspension or an emulsion as a function of the volume fraction of the dispersed phase. Pal and Rhodes [R. Pal, E. Rhodes, J. Rheol. 33 (7) (1989) 1021-1045] used D-EMT to derive a viscosity-concentration expression for non-Newtonian emulsions, in which variations among different oil-water emulsions were accommodated by fitting the value of an empirical solvation factor by matching the volume fraction at which the ratio of each emulsion was experimentally observed to have a viscosity 100 times greater than that of the pure solvent. When the particles in suspension have occluded volume due to solvation or flocculation, we show that the application of D-EMT to the problem becomes more ambiguous than these investigators have indicated. In addition, the resulting equations either do not account for the limiting behavior near the critical concentration, that is, the concentration at which the viscosity diverges, or they incorporate this critical behavior in an ad hoc way. We suggest an alternative viscosity-concentration equation for emulsions, based on work by Bicerano and coworkers [J. Bicerano, J.F. Douglas, D.A. Brune, J. Macromol. Sci., Rev. Macromol. Chem. Phys. C 39 (4) (1999) 561-642]. This alternative equation has the advantages that (1) its parameters are more closely related to physical properties of the suspension and (2) it recovers the correct limiting behavior both in the dilute limit and near the critical concentration for rigid particles. In addition, the equation can account for the deformability of flexible particles in the semidilute regime. The proposed equation is compared to the equation proposed by Pal and Rhodes.

Digital-image-based models of two-dimensional microstructural evolution by surface diffusion and vapor transport

A new and versatile model of capillary-driven microstructural evolution is described. The model operates on digital images of microstructures, and uses the local phase distribution to form an interpolated “equivalent sharp surface.’’ Local surface properties, like outward normal vectors and curvatures, are calculated and local driving forces for mass transport are determined using standard irreversible thermodynamic concepts. Mass transport kinetics are simulated using discretized rate laws for a specified path and rate-controlling step. Models of surface diffusion and of surface-attachment-limited kinetics are described and applied to several systems. Results for simple microstructures agree well with analytical predictions of transport rates and scaling laws, and useful quantitative information is extracted from simulations on more complex microstructures for which analytical predictions do not exist.

Constrained phase evolution in gel-derived thin films of magnesium oxide

We investigate possible influences of substrate constraints on the phase evolution of thin films synthesized from liquid precursors. MgO films are formed on Si (111) substrates by spin casting an acetate-substituted magnesium ethoxide liquid precursor. The phase evolution and crystallinity of the films are tracked as a function of temperature by differential scanning calorimetric/thermogravimetric analyses (DSC/TGA) and X-ray diffraction. There are two major differences between the phase evolution of thin films and that of bulk powders formed from the same solution: (1) in the films, highly [010]-textured triclinic magnesium acetate forms at room temperature, while in the powders an orthorhombic polymorph of magnesium acetate is selected that transforms to the triclinic structure at 150-250 °C. Both films and powders undergo complete pyrolysis by 360 °C to form magnesium oxide. However, (2) although powders decompose to phase-pure periclase, thin films form both periclase and a rarely observed pseudo-spinel polymorph, both with strong 〈001〉 preferred orientation. Both selection of the triclinic acetate polymorph in films at room temperature and formation of the spinel-like MgO structure are consequences of interaction with the underlying substrate.

Cements in the 21st Century: Challenges, Perspectives, and Opportunities

In a book published in 1906, Richard Meade outlined the history of portland cement up to that point1. Since then there has been great progress in portland cement-based construction materials technologies brought about by advances in the materials science of composites and the development of chemical additives (admixtures) for applications. The resulting functionalities, together with its economy and the sheer abundance of its raw materials, have elevated ordinary portland cement (OPC) concrete to the status of most used synthetic material on Earth. While the 20th century was characterized by the emergence of computer technology, computational science and engineering, and instrumental analysis, the fundamental composition of portland cement has remained surprisingly constant. And, although our understanding of ordinary portland cement (OPC) chemistry has grown tremendously, the intermediate steps in hydration and the nature of calcium silicate hydrate (C-S-H), the major product of OPC hydration, remain clouded in uncertainty. Nonetheless, the century also witnessed great advances in the materials technology of cement despite the uncertain understanding of its most fundamental components. Unfortunately, OPC also has a tremendous consumption-based environmental impact, and concrete made from OPC has a poor strength-to-weight ratio. If these challenges are not addressed, the dominance of OPC could wane over the next 100 years. With this in mind, this paper envisions what the 21st century holds in store for OPC in terms of the driving forces that will shape our continued use of this material. Will a new material replace OPC, and concrete as we know it today, as the preeminent infrastructure construction material?

Numerical simulations of transient-stage Ostwald ripening and coalescence in two dimensions

Abstract A new numerical method for tracking interface motion in microstructures is described and used to simulate two-dimensional, transient-stage Ostwald ripening at high volume fractions of coarsening phase. Two limiting kinetic regimes are explicitly simulated, namely diffusion-controlled mass transport and surface-attachment/detachment-limited kinetics (SALK). The simulations indicate important qualitative and quantitative differences between these two mechanisms at high volume fractions. These differences include: (1) The persistence of coalescence events under SALK that are completely absent under diffusion control; and (2) stable circular shapes for isolated domains under SALK; under diffusion control, the morphology of an isolated domain is dependent on its nearby surroundings, as reported by other investigators. Spatial correlations amongst the coarsening domains are also investigated using two-point correlation functions and medium polarization functions.

Direct measurements of 3d structure, chemistry and mass density during the induction period of C 3 s hydration

The reasons for the start and end of the induction period of cement hydration remain topic of controversy. One long-standing hypothesis is that a thin metastable hydrate forming on the surface of cement grains significantly reduces the particle dissolution rate; the eventual disappearance of this layer re-establishes higher dissolution rates at the beginning of the acceleration period. However, the importance, or even the existence, of this metastable layer has been questioned because it cannot be directly detected in most experiments. In this work, a combined analysis using nano-tomography and nano-X-ray fluorescence makes the direct imaging of early hydration products possible. These novel X-ray imaging techniques provide quantitative measurements of 3D structure, chemical composition, and mass density of the hydration products during the induction period. This work does not observe a low density product on the surface of the particle, but does provide insights into the formation of etch pits and the subsequent hydration products that fill them.