A recurrent problem in materials science is the prediction of the percolation threshold of suspensions and composites containing complex-shaped constituents. We consider an idealized material built up from freely overlapping objects randomly placed in a matrix, and numerically compute the geometrical percolation threshold p, where the objects first form a continuous phase. Ellipsoids of revolution, ranging from the extreme oblate limit of platelike particles to the extreme prolate limit of needlelike particles, are used to study the inhuence of object shape on the value of p, . The reciprocal threshold 1/p, (p, equals the critical volume fraction occupied by the overlapping ellipsoids) is found to scale linearly with the ratio of the larger ellipsoid dimension to the smaller dimension in both the needle and plate limits. Ratios of the estimates of p, are taken with other important functionals of object shape (surface area, mean radius of curvature, radius of gyration, electrostatic capacity, excluded volume, and intrinsic conductivity) in an attempt to obtain a universal description of p, . Unfortunately, none of the possibilities considered proves to be invariant over the entire shape range, so that p, appears to be a rather unique functional of object shape. It is conjectured, based on the numerical evidence, that 1/p, is minimal for a sphere of all objects having a finite volume.

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Equilibrium thermodynamic calculations, coupled to a kinetic model for the dissolution rates of clinker phases, have been used in recent years to predict time-dependent phase assemblages in hydrating cement pastes. We couple this approach to a 3D microstructure model to simulate microstructure development during the hydration of ordinary portland cement pastes. The combined simulation tool uses a collection of growth/dissolution rules to approximate a range of growth modes at material interfaces, including growth by weighted mean curvature and growth by random aggregation. The growth rules are formulated for each type of material interface to capture the kinds of cement paste microstructure changes that are typically observed. We make quantitative comparisons between simulated and observed microstructures for two ordinary portland cements, including bulk phase analyses and two-point correlation functions for various phases. The method is also shown to provide accurate predictions of the heats of hydration and 28 day mortar cube compressive strengths. The method is an attractive alternative to the cement hydration and microstructure model CEMHYD3D because it has a better thermodynamic and kinetic basis and because it is transferable to other cementitious material systems.

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