Discussions and Closures
Discussion of “Empirical Estimation of Pore Size Distribution in Cement, Mortar, and Concrete” by Fuyuan Gong, Dawei Zhang, Evdon Sicat, and Tamon Ueda DOI: 10.1061/(ASCE)MT.1943-5533.0000945
Qiang Zeng 1 Downloaded from ascelibrary.org by Zhejiang University on 09/02/15. Copyright ASCE. For personal use only; all rights reserved.
1
Assistant Professor, Collage of Civil Engineering and Architecture, Zhejiang Univ., Hangzhou 310058, P.R. China. E-mail: cengq08@ gmail.com;
[email protected]
Based on local equilibrium of chemical energy between vapor and liquid water confined in pores of mesosize, the original paper proposed a method to estimate pore size distribution (PSD) of hardened cement paste (HCP) from water vapor sorption isotherms (WVSIs). A previous study by Xi et al. (1994) provided functions of WVSIs to cement type, water-to-cement (W/C) ratio, curing age, and temperature. Those functions were developed from an extended Brunauer-Emmett-Teller (BET) model, the so-called BSB or GAB model (Timmermann 2003; Dutcher et al. 2011; Jiang et al. 2013), which bridges over two macromeasured quantities, i.e., the amount of the adsorbed water and the ambient relative humidity (RH), through three parameters [Eq. (11) in the original paper] The authors then discussed the PSD curves simulated from the models and compared them with the experimental data in the litereture, e.g., Baroghel-Bouny (2007), Fujikura and Oshita (2011), and Kaufmann et al. (2009). In the procedure of deducing the equations, the authors also considered an adsorbed liquidlike layer (ALLL) prior to capillary condensation when interpreting the relation between pore size and capillary pressure [Eq. (6) in the original paper]. It gives rp ¼ req þ t;
req ¼
−2γV l RT lnðRHÞ
0.02309 ðnmÞ 1.105 − RH
ð3Þ
Fig. 1. Thickness of adsorption liquidlike layer between solid surface and water vapor in terms of RH proposed by Hagymassy et al. (1969)
ð2Þ
Fig. 1 illustrates the thickness of ALLL t in terms of RH as shown in Eq. (2). Clearly, as RH increases, t rises first slowly © ASCE
δW ¼ δW cond þ δt · Aðr > req þ tÞ
ð1Þ
where rp = pore radius (m); req = radius of hemispheric meniscus under equilibrium (m); t = thickness of ALLL (m); γ = surface tension of liquid exposed to air (0.0725 N=m at 293 K); V l = molar volume of liquid water (18 × 10−6 m3 =mol); R = ideal gas constant (8.314 J=K=mol); and T = current temperature (K). The authors adopted a constant thickness of ALLL (t ¼ 0.9 nm) proposed by Brun et al. (1977). However, instead of the ALLL between pore wall and water vapor during adsorption and desorption, Brun et al. (1977) estimated the thickness of the unfrozen liquidlike layer between pore wall and ice confined in porous medium during freezing. Inappropriate use of the thickness of ALLL by the authors may lead to erroneous in estimation of the PSDs of the HCP samples. There have already had many equations correlating the thickness of ALLL with RH for porous media [e.g., Badmann et al. (1981), Hagymassy et al. (1969), and Halsey (1948), among others], among which the most widely used one may be the function proposed by Hagymassy et al. (1969). It shows t ¼ 0.834RH þ 0.0626 þ
and then quickly. The diameter of a water molecule approaches 3 × 10−10 m (0.3 nm); complete cover of a layer of water molecules on the surface of pores of the HCP sample thus requires RH ≈ 24%. When the thickness of ALLL approaches 0.9 nm (approximately three layers of water molecules), the corresponding RH ≈ 83% (Fig. 1). Owing to the inconstant thickness of ALLL between the solid surface and water vapor, the interpretation of WVSI data proposed by the authors may be debatable. Focus on the physical process of water-vapor adsorption on a graded-cylindrical pore as illustrated in Fig. 2. Water molecules cover the surface of all the open pores in the thickness of t after the previous absorption and may condense in the very thin pores that satisfy rp ≤ req ðRHÞ þ tðRHÞ. As RH is increased, more water molecules are adsorbed on the surface of the pores and the thickness of ALLL is increased. So the increased amount of water by adsorption is composed of two parts (Fig. 2): the capillary condensation in the matched pores in equilibrium and the ALLL on the larger pores. This gives
Fig. 2. Schematic illustration of multilayer adsorption and capillary condensation in graded-cylindrical pores
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where δW = increased mass fraction read on WVSI curve (g=g); δW cond = increased mass fraction of capillary condensation (g=g); δt = increased thickness of ALLL (m); and Aðr > rp Þ = surface area of pores obeying r > rp (g=g=m). In fact, δt · Aðr > rp Þ denotes the increased mass fraction of surface adsorption rather than capillary condensation (g=g). For the graded-cylindrical pores, the increases of the surface area δA depend on the increased mass fraction of capillary condensation δW p and the capillary radius req in equilibrium, i.e., δA ¼ 2δW cond =req . The specific surface area for the pores with r > rp can be thus expressed as Z r∞ X X 2δW cond eq dA ≈ δAðr > rp Þ ¼ ð4Þ Aðr > rp Þ ¼ req req where r∞ eq = pore radius in the infinity large size as RH ¼ 1. As an example, Fig. 3 shows the distribution of the increased adsorbed mass fraction read on WVSI data δW, surface adsorption δt · A, and capillary condensation δW cond for the HCP sample with W=C ¼ 0.5. As pore radius (or RH) decreases, δW and δW cond decrease rapidly and gradually, whereas δt · A increases progressively (Fig. 3). When pore radius is decreased to approximately 1.2 nm (RH ≈ 29%), the values of δW are equal to those of δt · A. This suggests that all the increased water is adsorbed on the surface of pores to thicken the liquidlike layer and there is no more extra water to condense in the capillary pores. For the porous material with the graded-cylindrical pores, the real pore space is composed of the stepwise condensed volume δW cond in the capillary size of req in equilibrium and the volume of ALLL in the thickness of t, which gives δW p ¼ δW cond
r2p ðrp − tÞ2
capillaries stepwise, a numerical discrete operation on W and RH is thus required. This also allows establishment of a function of the cumulative quantity of pore water W p to the pore radius rp , and the differential form. More details of the ALLL-corrected PSD calculation can be found in Zeng et al. (2014). The adsorbed quantity W in Xi et al. (1994) is in the unit of g=g (paste). To obtain the porevolume related quantity, a unit conversion operation is conducted, i.e., ϕ ¼ ðW=ρl Þ=ð1=ρs þ W=ρl Þ, where ϕ is the porosity (mL=mL), ρs is the density of cement-based solid (kg=m3 ), and ρl is the density of liquid water (ρl ≈ 1,000 kg=m3 ). Assuming ρs ≈ 2,000 kg=m3 roughly, one yields ϕ ≈ W=ð0.5 þ WÞ. Figs. 4 and 5 show the original PSD curves evaluated though the method proposed by the authors and the ones through the corrected method developed in this study, respectively, in the cumulative and differential forms. When plotting the differential PSD curves, a differential logarithmic scheme for the pore size is used, i.e., dϕ=d logðrÞ ¼ ð2.303rÞdϕ=dr. As shown in Figs. 4 and 5, the PSD curves by the two methods remain superimposed when the pores are in the range of rp ≥ 100 nm. As pore size decreases,
ð5Þ
where δW p = increased real pore volume fraction (g=g). A combination of Eqs. (3)–(5) yields X δW cond r2p ð6Þ δW p ¼ δW − δt rp − t ðrp − tÞ2 For the desorption process, Eq. (6) reduces to the BarrettJoyner-Halenda (BJH) model (Barrett et al. 1951). For the WVSI data shown in Xi et al. (1994), W and RH are known. To calculate the amount of the water adsorbed on pore wall and condensed in
Fig. 3. Distribution of the increased adsorbed mass fraction of δW, δt · A, and δW cond for the cement paste W=C ¼ 0.5 © ASCE
Fig. 4. Comparison of the original (cumulative) PSD curves evaluated though the method proposed by the authors and the ones through the corrected method in this study
Fig. 5. Comparison of the original (differential) PSD curves evaluated though the method proposed by the authors and the ones through the corrected method in this study
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the differences between the PSD curves by the two used methods rise and become significant. The corrected cumulative PSD curves are higher than the original ones due to the contribution of ALLL. The peaks of differential PSD curves appear in the pore range of 5–10 nm (Fig. 5), which are comparable with the mercury intrusion porosimetry (MIP) data for the blended cement pastes [e.g., Zeng et al. (2012)] and in the rank of the gel pores according to Jennings (2008), but systematically larger than those in the original paper. As the pores become thinner, e.g., rp < 2 nm, the contribution of capillary condensation becomes minor as shown in Fig. 3. However, this does not indicate that there are no pores distributed in the very small size. Instead, the surface adsorption is more likely to govern the changes of volume and mass as RH varies. Of course, more rigorous studies in the relative issues are required. Based on the physical principle of adsorption, this short discussion underlines the contribution of ALLL to the cumulative and differential PSD curves and the importance of using appropriate method to interpret the WVSI data.
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Dutcher, C. S., Ge, X., Wexler, A. S., and Clegg, S. L. (2011). “Statistical mechanics of multilayer sorption: Extension of the Brunauer–Emmett– Teller (BET) and Guggenheim–Anderson–de Boer (GAB) adsorption isotherms.” J. Phys. Chem. C, 115(33), 16474–16487. Fujikura, Y., and Oshita, H. (2011). “Pore structure model of hydrates comprising various cements and SCMs based on changes in particle size of constituent phases.” J. Adv. Concr. Technol., 9(2), 133–147. Gong, F. Y., Zhang, D. W., Sicat, E., and Ueda, T. (2014). “Empirical estimation of pore size distribution in cement, mortar, and concrete.” J. Mater. Civ. Eng., 10.1061/(ASCE)MT.1943-5533.0000945, 040140231–04014023-11. Hagymassy, J. J. R., Brunauer, S., and Mikhail, R. S. H. (1969). “Pore structure analysis by water vapour adsorption: I. t-Curves for water vapour.” J. Colloid Interface Sci., 29(3), 485–491. Halsey, G. (1948). “Physical adsorption on nonuniform surfaces.” J. Chem. Phys., 16(10), 931–937. Jennings, H. M. (2008). “Refinements to colloid model of C-S-H in cement: CM-II.” Cem. Concr. Res., 38(3), 275–289. Jiang, J., Yuan, Y., Zeng, Q., and Mo, T. (2013). “Discussion: Relationship of moisture content with temperature and relative humidity in concrete.” Mag. Concr. Res., 65(24), 1494–1496. Kaufmann, J., Loser, R., and Leemann, A. (2009). “Analysis of cementbonded materials by multi-cycle mercury intrusion and nitrogen sorption.” J. Colloid Interface Sci., 336(2), 730–737. Timmermann, E. O. (2003). “Multilayer sorption parameters: BET or GAB values?” Colloids Surf. A: Physicochem. Eng. Aspects, 220(1), 235–260. Xi, Y., Bazant, Z. P., and Jennings, H. M. (1994). “Moisture diffusion in cementitious materials Adsorption isotherms.” Adv. Cem. Based Mater., 1(6), 248–257. Zeng, Q., Li, K., Fen-Chong, T., and Dangla, P. (2012). “Pore structure characterization of cement pastes blended with high-volume fly-ash.” Cem. Concr. Res., 42(1), 194–204. Zeng, Q., Zhang, D., Sun, H., and Li, K. (2014). “Characterizing pore structure of cement blend pastes using water vapor sorption analysis.” Mater. Charact., 95, 72–84.
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