The Powers-Brownyard model

Structure of the material by a model based largely on evidence from total and non-evaporable water contents and water vapour sorption isotherms. Powers later modified the model in minor respects (P34). 

In this model, hep is assumed in the general case to comprise three components from the volumetric standpoint, viz. (a) unreacted cement, (b) hydration product and (c) capillary pores. Individual solid phases are not considered, whether in the cement or in its hydration products, which were collectively called cement gel . This term may be found confusing, because it includes the CH, which forms relatively large crystals and cannot reasonably be considered part of a gel we shall substitute the term hydration product . The water present in the paste was categorized as evaporable or non-cvaporable, the latter being defined in the later work (P34) as that retained on D-drying. Evaporable water, when present, was considered to reside partly in the capillary pores, and partly in so-called gel pores within the hydration product. This latter part was called gel water. 

The content of non-evaporable water, relative to that in a fully hydrated paste of the same cement, was used as a measure of the degree of hydration. Portland cement paste takes up additional water during wet curing, so that its total water content in a saturated, surface dry condition exceeds the initial w/c ratio. Evidence from water vapour sorption isotherms indicated that the properties of the hydration product that were treated by the model were substantially independent of w/c and degree of hydration, and only slightly dependent on the characteristics of the individual cement. The hydration product was thus considered to have a fixed content of non-evaporable water and a fixed volume fraction, around 0.28, of gel pores. 

The hydration product occupies more space than the cement from which it is formed, and the capillary pores were regarded as the remnants of the initially water-filled space. Their volume thus decreases, and that of the gel pores increases, as hydration proceeds. Evidence from water vapour sorption isotherms indicated that the hydration product was composed of solid units having a size of about 14 nm, with gel pores some 2 nm across (P34). The width of the capillary pores could not be determined from the available data, but they were considered to be generally much wider than the gel pores, though tending to become narrower as the water-filled space was used up, and thus in some regions indistinguishable from gel pores. 

2 Minimum water/cement ratio for complete hydration chemical shrinkage 

---

Brunauer and co-workers (B55,BI08) considered that the gel particles of the Powers-Brownyard model consisted of either two or three layers of C S-H, which could roll into fibres. D-drying caused irreversible loss of interlayer water, and the specific surface area could be calculated from water vapour sorption isotherms, which gave values in the region of 200m g for cement paste. Sorption isotherms using N2 give lower values of the specific surface area this was attributed to failure of this sorbate to enter all the pore spaces. 

The Feldman-Sereda model was based on the studies of sorption properties, porosities and relations between water content and physical properties. Alone among the proposed models, it is clearly compatible with the microstructural evidence and with the probable relationships between C-S-H gel and crystalline compounds. It is incompatible with that of Brunauer, but not with the essential features of that of Powers and Brownyard in its original form if the nature of the gel porosity is reinterpreted. Calculations of bound water (Section 7.3.3) indicate that about a third of the gel porosity of the Powers-Brownyard model is interlayer space, the remainder being micro or fine meso porosity of the kind shown in Fig. 8.4. However, as that figure illustrates, the boundary between interlayer space and micropores is ill defined. 

Table 8.1 Calculated porosities, based on the Powers-Brownyard model...

Parrott and co-workers (P30,P32,P35,P33) described a more sophisticated method for modelling the hydration process. The fraction of the total water porosity that was below 4nm was calculated by multiplying the volume fraction of C-S- H by an appropriate factor, which depended on whether the C-S-H was formed from alite or belite, the temperature and the amount of space available. The constants assumed were based on experimental data obtained using a procedure based on methanol sorption (Section 8.3.4). The effect of drying was allowed for (P35) by introducing a factor of 0.7 - -1.2(RH — 0.5) for 0.5 < RH < 1, or of 0.7 for RH 0.5. These refinements allow some deviation from the Powers-Brownyard postulate of a fixed volume ratio of gel porosity to product. Typical results for the volume fractions of pores larger than 4 nm in mature pastes of a cement with an alite content of 56% were approximately 0.26, 0.16 and 0.07 for w/c ratios of 0.65, 0.50 and 0.35, respectively (P32). For the two higher w/c ratios, these results are near the capillary porosities of Powers and Brownyard, but for w/c 0.35 the latter value is zero. 

Water sorption isotherms for hep show marked hysteresis. Powers and Brownyard (P20) found that, while it was difficult to obtain reproducible desorption curves, the low-pressure part of the water vapour resorption curve varied little with w/c ratio, between different Portland cements, or, if allowance was made for the contents of unreacted cement, with the degree of hydration. This was their main direct evidence for the conclusion (Section 8.2.1) that the properties of the hydration product considered in their model were essentially independent of these variables. However, the water sorption iostherms obtained by different investigators have varied considerably (e.g. Refs P20 and S79), and it is not clear to what extent the above conclusion would stand had different desorption conditions been used. 

---