7. Summary

In order to understand the dependence of diffusivity on the microstructure of a porous material like portland cement paste, there must first be quantitative understanding of microstructure, and then there must be methods to calculate the diffusivity for a given microstructure. Both these goals have been achieved, by using a random growth model for the generation of the microstructure of the cement paste, and by using exact algorithms applied to the underlying digital-image lattice of the model to calculate the diffusivity for a given microstructure. It should be emphasized that the quantitative representation of the microstructure was achieved by basing the model on a digital- image, and that the transport algorithms used were only applicable to a lattice structure, as was used here. The results obtained are summarized below.

a) The ionic diffusivity of cement paste can be calculated with algorithms applied to the digital-image-based microstructural model, with calculated values of steady-state chloride ion diffusivities in reasonable agreement with experimental data. The calculation techniques are equally applicable to actual as well as model microstructures.

b) The chloride diffusivity of plain portland cement paste can be expressed as a function of capillary porosity only, with the functional form being , where H(x) = 0 for x < 0, and 1 for x > 0. This relationship is dominated by the percolation properties of the capillary pore space above the critical capillary porosity _c = 0.18, where the capillary pore space becomes disconnected, and by simple Archie's law-type power law behavior below _c, where the pathways through C-S-H gel pores dominate the transport. The above functional form must break down at porosities somewhat higher than 0.6, as it does not give the correct = 0 limit.

c) The physical picture of diffusive transport in cement paste is as follows. Above = _c, transport is mainly through continuous capillary pores, with a smaller amount of flow through pathways of capillary pores linked by C-S-H gel pores. Below _c, the dominant pathways are now made up of isolated capillary pore clusters linked together by C-S-H gel pore connections, which determine the flow rate [3].

d) The minimum value of D/D_o for chloride ions diffusing through plain portland cement paste has been predicted to be about 0.001, obtained when the capillary porosity is zero. With silica fume present, the cutoff value becomes 0.0025.

e) For low w/s ratios, when sufficient silica fume is present to react with most of the CH produced, and when the capillary porosity is much less than _c = 0.18, so that the diffusivity is controlled by the C-S-H phase, the addition of silica fume can increase the relative diffusivity by consuming CH (D/D_o = 0), and replacing it with C-S-H (D/D_o = 0.0025).

8. Acknowledgements

The authors would like to thank: the National Science Foundation Science and Technology Center for Advanced Cement- Based Materials, for partial support of this work; P.M. Duxbury, for supplying a working copy of a 2-d conjugate gradient code; and C.J. Lobb, for several helpful conversations.