Refinements to colloid model of C-S-H in cement: CM-II

Packing problems, such as how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible packing fraction phi=pi/18 approximately 0.74. It is also well known that certain random (amorphous) jammed packings have phi approximately 0.64. Here, we show experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely-up to phi= 0.68 to 0.71 for spheroids with an aspect ratio close to that of M&M's Candies-and even approach phi approximately 0.74 for ellipsoids with other aspect ratios. We suggest that the higher density is directly related to the higher number of degrees of freedom per particle and thus the larger number of particle contacts required to mechanically stabilize the packing. We measured the number of contacts per particle Z approximately 10 for our spheroids, as compared to Z approximately 6 for spheres. Our results have implications for a broad range of scientific disciplines, including the properties of granular media and ceramics, glass formation, and discrete geometry.

Although Portland cement concrete is the world's most widely used manufactured material, basic questions persist regarding its internal structure and water content, and their effect on concrete behaviour. Here, for the first time without recourse to drying methods, we measure the composition and solid density of the principal binding reaction product of cement hydration, calcium-silicate-hydrate (C-S-H) gel, one of the most complex of all gels. We also quantify a nanoscale calcium hydroxide phase that coexists with C-S-H gel. By combining small-angle neutron and X-ray scattering data, and by exploiting the hydrogen/deuterium neutron isotope effect both in water and methanol, we determine the mean formula and mass density of the nanoscale C-S-H gel particles in hydrating cement. We show that the formula, (CaO)1.7(SiO2)(H2O)1.80, and density, 2.604 Mg m(-3), differ from previous values for C-S-H gel, associated with specific drying conditions. Whereas previous studies have classified water within C-S-H gel by how tightly it is bound, in this study we classify water by its location-with implications for defining the chemically active (C-S-H) surface area within cement, and for predicting concrete properties.