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Much indirect information on the nanopore structure of C-S-H has been generated from sorption- type experiments. Simulation of two types of experiments will be described here: generation of an adsorption/desorption isotherm and the measurement of pore volume using molecules of different sizes. Both algorithms are based on purely geometrical analyses of the 3-D digitized representation of the solid/pore structure.
The algorithm for adsorption/desorption in two dimensions has been described previously [23]. Here, two modifications are employed to extend the model to three dimensions and consider surface adsorption. The conversion between the physical process of capillary condensation and a geometrical algorithm is achieved based on the Kelvin-Laplace equation which relates the vapor pressure to a characteristic pore size via:
is the liquid surface tension,
Vm its molar volume, T is absolute temperature,
R is the universal gas constant, and
Po is
the vapor pressure for a planar (r = 
) surface at standard conditions. For water at a
temperature of 25C, upon substitution, one obtains
During adsorption, the condition for capillary condensation at a given relative humidity (RH) is that the radius of a pore has to be lower than the radius computed from the Kelvin-Laplace equation. Thus, for a given radius, rc, one can remove from consideration all the locations in the pore system where a digitized sphere of radius rc can be located without overlapping any solid pixels. Any pore space remaining would indicate the volumes occupied by adsorbed water at this RH. For desorption, this geometrical constraint is augmented by a connectivity analysis. A capillary pore can only empty when its size equals or exceeds the Kelvin-Laplace radius and it is connected to the exterior of the sample by a pathway consisting exclusively of the same size or larger "empty" pores. This is similar to the connectivity analysis by a critical sphere recently introduced by Thovert et al [24] and is also the basis of the Katz-Thompson theory for relating permeability to pore structure [25].
It must be noted that assuming a spherical structure for condensed water is only an approximation, as two radii of curvature are present in 3-D so that a variety of ellipsoidal shapes are possible, a problem not encountered in the 2-D model [23]. Also, for the C-S-H model, we are applying this equation at very low RH (<40%), where its validity is known to be questionable. Recognizing these limitations, it is nevertheless useful to compare computed to measured isotherms.
Because the C-S-H structure has a large surface area (about 400 meters squared per gram D-dried C-S-H [26]), surface adsorption is also an important consideration. For hardened cement paste, the statistical thickness (defined as the adsorbed volume divided by the BET surface area), t, of an adsorbed layer of water as a function of RH has been measured and fitted to an equation of the form [27]:
Also of interest for C-S-H gel is the accessibility of the pore structure to molecules of different sizes. In the literature, for example, different porosities have been measured by water, nitrogen, methanol, isopropanol, and cyclohexane [29]. The determination of the porosity available to a given size molecule is computed in two steps. First, an algorithm similar to the desorption described earlier is used to determine all locations in the structure which are accessible to a sphere of a given radius. Second, digitized spheres of this radius are packed into the volume determined in step 1 with the condition that the spheres cannot overlap one another. The porosity is measured as the number of spheres placed multiplied by the volume of a single sphere. Using digitized spheres to represent molecular shapes is once again an approximation. Furthermore, the molecular shapes could be altered significantly in very small pores due to intermolecular forces, etc.
This algorithm is applied directly to the micro-level model of the C-S-H. For the macro-level model, as the smallest pores are larger than the diameter of the largest molecule of interest, it is assumed that all of the porosity will be measured. The same assumption is made for the capillary pores existing in a hardened cement paste.