- Email: [email protected]
Importance of the liquid to solid weight ratio in the powdered solid-liquid reactions
SOLID STATE Solid State Ionics
ELSWIER
Importance
101-103
IONICS
(1997) 359-365
of the liquid to solid weight ratio in the powdered solid-liquid reactions
Example drawn from cement constituent hydration P. Barret’“, D. Bertrandie Laboratnire de Recherche SW la R&activite’ des Solides. UMR 5613, CNRS - UnivrrsitP de Bourpgne, France
B.P. 400, 21011 Dijon cedex,
Abstract It seems justified to wonder if the chemical processes which have been evidenced from diluted stirred suspensions are or are not in accordance with those involved in a stagnant paste. The present paper is aimed at clarifying this question which is in connection with the problem of the so called ‘dormant period’ or ‘induction period’ at the beginning of the hydration of Portland cement. Kepvrd.s: Tricalcium silicate hydration; Kinetic influence of the liquid to solid weigth ratio; Diluted stirred suspensions; Specific surface area: Maximum supersaturation; Slowing down factors Muteriulst Ca,SiO,;
Ca,(OH),H,Si20,;
pastes;
Ca(OH)?
1. Introduction In general, the liquid to solid weight ratio, labelled with l/s, is a significant factor of the reactivity in the powdered solid-liquid systems. In particular, the hydration of hydraulic binders gives many examples in which a finely divided solid reagent is mixed with less than half its weight of water. The mixing, which often requires the presence of chemical admixtures, called water reducers [ 11, results in a paste. The extraction of the liquid phase with the aim of analysing it at successive times of the hydration, constitutes a difficult experiment needing a powerful *Corresponding
Stagnant
author. Fax: +33 3 8039 6132.
0167.2738/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PII SOl67-2738(97)00129-X
press [2,3], and the setting that occurs at the end of a certain time increases the difficulty of liquid extraction. That is why many studies devoted to thermodynamic and kinetic aspects of cement hydration used stirred diluted aqueous suspensions rather than pastes enabling the solid and liquid constituents to be filtrated off more easily [4-71 in order to follow the changes of the liquid composition with time and the modifications of the solid products, notably by XRDA and other morphology, structure and composition determination techniques. In our works, our concern was the reactivity of solids and not the cement chemistry. That is why we used a synthesized cement constituent such as tricalcium silicate, Ca,SiO, and not cements which are complex mixtures. A few previous works using this constituent had been performed in order to study systematically the
360
P. Barret,
D. Bertrandie
I Solid State lonics
influence of the l/s ratio. In 1969, A. Zelver, in his thesis [8-lo], investigated the changes of the time needed by the Ca*+ ion concentration to reach the maximum supersaturation as a function of l/s, from Its = 0.3 to Ils = 3, thus essentially on pastes made of samples of various specific surface areas. Later (in 1984) Brown et al. [ 1I], using automated colorimetric method, measured the concentration of calcium and silica in solution during the first 4 h of hydration of Ca,SiO, (3525 cm’/g) at l/s ratios ranging from 0.7 to 20; stirring was used at 11s ratios above 0.7. A strong dependence of the rate of early hydration on the 11s ratio was observed, while the dependence on the surface area of the Ca,SiO, was minimal. Recently, Damidot in his thesis [ 121 and Nonat et al. [ 13,141 took advantage of the sensitivity of the TianCalvet heat flow isothermal calorimeter by adapting it to study very diluted Ca,SiO, suspensions at different l/s ratios. They designed a microelectrode allowing them to measure the electrical conductivity of the suspension simultaneously with the heat flow.
101-103
(1997)
3Ca2+ + 40H
359-365
+ 2H,SiO,
In order to test the influence of factor l/s, we chose also to perform kinetic experiments, but limiting them to a well-defined period of Ca,SiO, hydration (called period 3) and that, at room temperature and at different 11s ratios going from 11s = 0.35 to l/s = 100. Indeed, in a previous paper [15], we had shown that the tricalcium silicate hydration was a complex reaction resulting from 3 simultaneous reactions, the time-zero of the second and the third ones being delayed by the time required for the maximum supersaturation with respect to the hydrates being reached, these hydrates being: calcium silicate hydrate from the second reaction and calcium hydroxide from the third, the first reaction representing the passage into solution of the Ca’+, OH- and silicate ions released by Ca,SiO,,, on contact with water. These three rections can be written: 2Ca,SiO,,,
+ 8H,O,
-+ 6Ca*+ + 2H,SiO, suffix sh meaning:
+ lOOH-
‘superficially
hydroxylated’
(1) [ 171.
C-S-H + H,O,, (2)
3Ca’+ + 6(OH))
+
3Ca(OH),.
2.1. Delimitation
of the part ofreaction used
(3)
The reaction used to compare the effect of the liquid to solid weight ratio, denoted by l/s (generalizing the cement chemistry notation +V/C meaning water to cement ratio) may be considered as the sum of the first and the second above reactions in which the number of silicate ions passing into solution and that consumed by the formation of calcium silicate hydrate per unit of time are about the same. That is the translation of a quasi-steady state in the silicate ion concentration. Such a single reaction may be written: 2Ca,SiO,,,
+ 7H,O,
+ C-S-H + 3Ca2+ + 60H2. Experimental
+
(4)
C-S-H meaning: Caj(OH)4H4Si20,, formula in which the Ca/Si ratio was taken as an average value = 1.5 because this ratio was not constant, but [ 181; besides, from linked to the lime concentration trimethylsilylation and gas chromatography experiments [ 191 and, more recently, from *“Si MAS NMR spectroscopy with cross-polarization [20-231, the silicate ions in C-S-H should be considered, at least, as dimeric. This reaction offers the advantage to be bounded very well by a lower and a upper limits nearly independent of 11s: indeed, the experiments consisted of building two sets of graphs from the data collected at 21°C a set of kinetic graphs and a set of the corresponding ‘associated paths’. We used T, triclinic Ca,SiO, prepared by Lafarge Central Laboratory. This solid compound was ground and its specific surface area, determined by Blaine’s method, was 350 m*/kg. The free lime content was less than 0.1%. The main parameter, the l/s weight ratio, was fixed by mixing the suitable mass of Ca,SiO, with the required mass of deionized decarbonated water, in an appropriate vessel. The choice of this vessel depended upon whether it was a stirred aqueous suspension of Ca,SiO, or a paste:
P. Barret, D. Bertrandie 1 Solid State Ionics 101-103
2.2. Kinetics
experimental
techniques
With a stirred suspension, the tests were performed on 400 g of solvent (deionized decarbonated water) and a suited mass of Ca,SiO, for a given l/s ratio, for example, 80 g for Z/s =5 or 20 g for l/s =20, and so on. The mixture was magnetically stirred in the closed vessel. One of the ground joints was used for removing 5 or 6 ml portions of the mixture. The samples were filtrated immediately. For the Ca2+ titration, flame atomic absorption spectrometry (Perkin Elmer 3030) was used and for the total SiO,, photocolorimetry at 850 nm was implemented with a Hach spectrophotometer, model DR/300. At the start of the test, the frequency of sampling was increased in order to determine accurately the maximum in the silica concentration [ 15,161. The filtrates were mixed with 0.1 cm3 of 6 N HCl so that the reaction was stopped immediately and the times brought to abscissae corresponded justly to the sampling dates. The procedures described above were discontinuous. Such procedures have been complemented by continuous ones, at least for Ca2+ titration. In this way, one of the ground joints was used to set an electrical conductivity electrode. Then, the curves [Ca2’]=,f(t) plotted by calibration of the recorded electrical conductivity were confirmed by comparison with the measurements at successive times, performed by atomic absorption flame spectrometry. With a paste, the electrical conductivity measurement also enabled the end of the third period to be detected, thanks to the drop in the Ca’+ and OHion concentrations accompanying the break of the maximum supersaturation with respect to the portlandite (period 4). A similar cell as that described by Zelver [8-lo] was realized; such a conductivity cell was submitted to the possibility of maintaining the sample-carrier in a thermostated bath. The highest difficulty in the use of this conductivity cell consisted of the mixing at an I/s value as low as 0.35. Although the enclosure made of plexiglass allowed trials with mixing under vacuum, a prior mixing in another vessel maintained in the thermostated bath appeared to be more efficient, dispite the uncertainty caused in the definition of the initial time. An approximate value of the fractional conversion LY, drawn from the integration of the thermal flow, can
361
(1997) 359-365
also be obtained by microcalorimetry [24,25], which is more easily brought into play with a paste (I/s< 0.5) than with an aqueous suspension. 2.3. Example of the limit determination
for 11s =20
Taking as an example the kinetic graph of Ca,SiO, hydration with an l/s ratio of 20 (Fig. l), it can be seen that the lower limit corresponds to the end of the short plateau AB appearing at the beginning of the curve of lime concentraton plotted versus time t and whose ordinate OA is about 5 mmol/kg in lime, whatever l/s. The end B of the plateau occurs at time t,. On the other hand, the upper limit corresponds to the maximum M, of lime concentration plotted versus time and which is also the maximum supersaturation with respect to calcium hydroxide as portlandite whose value changes weakly with l/s ratio, passing from 0.038 mol/kg at lls=O.35 (in a paste) to 0.030 mol/kg at l/s= 100 in a very diluted stirred suspension and occurring at time tz (see Table 1, column 2). The limits in the ‘associated path’ graph (Fig. 2) are Q, corresponding to B, and R, corresponding to M,, in the kinetic graph (Fig. 1). The graph that we called ‘associated path’ is obtained from the same data as those (lime concentration, silica concentration, time) used to built the kinetic graphs. But instead of plotting lime concentration in Yl, silica concentration in Y2 and t in abscissa, we plotted
--++a0
(mmol/kg)
-+-S102
(micromol/kg)
time
t (h)
Fig. I. Ca,SiO, hydration kinetics with l/s ratio=20 at 21°C: M, maximum of silicate ion concentration, MC, maximum of Ca’+ ion concentration plotted vs. time. AB, short plateau in Ca*+ ion concentration curve. f, and I_, starting and ending times of period 3.
P. Barrer, D. Bertrandie I Solid Sme Ionics IOI- 103 (1997) 359-365
362 Table 1 Experimental 1 11s
0.35 0.5 5 10 15 20 30 40 50 75 100
tSiO2
results and calculation 2 [Ca”] (mol/kg)
3 A[Ca”] (mol/kg)
(exp.)
(exp.)
0.038 0.037 0.037 0.037 0.037 0.035 0.035 0.033 0.0305 0.030 0.030
0.033 0.033 0.033 0.032 0.032 0.030 0.030 0.028 0.025 0.025 0.025
(micromol/kg)
.__.
of an empirical
slowing down factor labelled with f
4 AMY(calcul)
5 At (hours)
[Eq. (911
(exp.)
2. 0 2.30 2.50 3.50 4.804 6.14 11.5 19.0 39.0 74.0 126.30
0.00175 0.0025 0.025 0.048 0.073 0.0912 0.1368 0.172 0.190 0.285 0.380
4
-time (h) -12
6 AculAr (%)/h
I k, x lor
f empir.
(exp.)
[Es. (16)l
[Eq. (16)l
0.0875 0.108 1.0 1.371 1.520 1.353 1.19 0.90 0.487 0.385 0.301
0.550 0.684 6.38 8.99 10.0 9.04 8.21 6.36 3.55 3.047 2.63
0.945 0.932 0.362 0.101 0.0 0.096 0.179 0.364 0.645 0.695 0.737
9 A&Al (%)(k,=
lOma)
1.589 1.588 1.566 1.524 1.520 1.498 1.448 1.407 1.372
1.264 1.145
calcium ion concentration. To sum up, the experiments consisted of establishing the kinetic graph and the related ‘associated path’ as a function of l/s weight ratio from the low l/s such as 0.35 and 0.5 in the field of the stagnant pastes to 5, 10, 15,. 50,. . 100 in the field of the aqueous stirred suspensions of Ca,SiO,.
3. Results and discussion (:a0 (mmol/kg) Fig. 2. ‘Associated path’ to the hydration kinetics graph (Fig. 1) for l/s ratio=20 at 21°C: OP, congruent dissolution of Ca,SiO,,, in pure water. PQ: silicate ion concentration fall during the plateau AB of Ca2+ Ion concentration. R, point corresponding to the maximum of Ca2+ ion concentration.
silica concentration in Yl, lime concentration in abscissa and t in Y2 so that t appears as the reciprocal function of the lime concentration such that t=f-‘[CaO]. The lower and upper limits in time are given by times t, and t,. P indicates the maximum silicate ion concentration reached after congruent dissolution OP of Ca,SiO,,,. That is also the maximum supersaturation with respect to C-S-H. The vertical segment PQ corresponding to the plateau AB in the kinetic graph expresses an abrupt fall of the supersaturation due to the sudden precipitation of C-S-H leading to a steady state in the
The experimental results are collected in Table 1. The values of the upper limits in calcium ion concentrations [Ca2+], are given in column 2 and the difference A between the upper and the lower limits can be found in column 3 for calcium ion concentrations and in column 5 for the time, for Instead of A[Ca2’], it would be which At = t, -t, better to express Aa representing the change of the fractional conversion (Y from the lower to the upper limits (third period). (Y is also the molar percentage of Ca,SiO, (which is the limitative reagent), consumed at time t. As we saw above, Eq. (4) may be considered as a single reaction in a closed system; the relations drawn from the law of definite proportions enable us to write: dn(Ca,SiO,)
= - 2dt
(5)
where 5 is the extent of the reaction and n the number of moles in the stoichiometric equation.
P. Barret, D. Bertrandie I Solid State Ionics 101-103
dn(Ca2’)
= 3&.
(6)
The fractional conversion cy and the extent reaction [ satisfy the relation:
(1997) 359-365
specific surface follows that:
of d[Ca*‘]ldt Account
area in kg/m*.
363
From
Eq. (6), it
d5
= 3Fldt.
being taken of Eq. (7), dt can be written:
(11)
where V, and rry are the stoichiometric coefficent and the initial number of moles of the limitative reagent, here, Ca,SiO,. Combining Eq. (6) and Eq. (7), we obtain:
Bringing Eq. (8) and Eq. (10) close together, following equation appears:
da = 2/3M
dcu=2M (Cs,Slos,kr(m,‘mo,adt.
(8)
(calsio,)(l/s)d[Ca2+l
is the molar mass of Ca,SiO, where MCCa3Si05) (0.228 kg/mol) and (l/s) the liquid to solid weight ratio, 1 indicating the initial mass (in kg) of the amount of water and s, the initial mass (in kg) of mixed solid Ca,SiO,. By integration between lower and upper limits 1 and 2, Eq. (8) gives:
m,lm,=l-ff
(13)
so that dcz becomes: (14) And after integration limit, Eq. (14) gives:
or Aa = O.l52(Z/s)A[Ca*‘].
(9)
Thus, Aa is proportional both to (I/s) and to the value of A[Ca2’] corresponding to this (l/s). The results may be expressed as the quotient AalAt (Table 1, columns 4, 5 and 6) which appears to be the ‘experimental average rate of tricalcium silicate hydration in mol% of Ca,SiO, consumed per hour between the above defined limits’. It appears from Fig. 1 that this average rate of hydration, denoted by AcYlAt%(exp.)lh, varies strongly as a function of l/s, passes through a maximum for l/s = 15 and decreases again when lls increases beyond 15. of a theoretical
interpretation
of At
An extra hypothesis has been introduced by assuming that the reaction rate was proportional to the surface area of the solid sample, which leads to: dcldt
= k,m,u
(12)
Indeed, s =mO is the initial mass of the solid sample. From Eq. (5) and Eq. (7), m,lm, can be expressed as a function of (Y:
Aa = 2/3M,,,~,,,,(Zls)A[Ca*‘l
3.1. Attempt
the
(10)
where k, is a constant depending on temperature T, m,, the mass of the sample at time t and u, its
from the lower to the upper
ln(1+ $) =2Mo,s,o,+At.
(15)
This equation has been computed with a program bringing the following variables into play: l/s, [Ca*+]*, A[Ca*‘], At, u and k,, and enabling one of them to be calculated when the others are given. Let it be assumed that we want to calculate k, from the data of Table 1: the computed values have been plotted in Fig. 3 versus l/s in the form of k,(exp.)= 105. This curve lies close to the curve of AU/ At(exp.)%lh and showed that k,(exp.)= lo5 is not constant, but passes also through a maximum for l/s= 15 where its value is 10.0 (Table 1, column 7), i.e. that, at this maximum, k,= 10P4. Now, if we introduce k,= 10e4 in the program as datum in order to compute At denoted by ‘theoretical At’, the results plotted in Fig. 4 versus l/s give an arc of hyperbola with a great radius of curvature. The values of At(exp.) in hours have been plotted in the same graph. It can be seen that the theoretical curve is the tangent to the experimental curve at a point of coodinates: l/s = 15, At(exp.) = At(theor.) =
P. Barrel, D. Berrrandie I Solid Stare lonics 101-103
364
Aa/At(exp.)% * _. . . . .- . . .
: ._
AdAt (theor.) % wth k, = IO '
tYl=f
k&exp.)lO’ . . .
(1997) 359-365
-12
I
0.8
-6
; j ! . I . . ..
-4
2
0
0
"/""'/"""j"l'I" 20
40
60
80
100
I*"0
0
- 20
40
60
*O
I/s
loo
x = I/s
Fig. 3. AalAt%(exp.)lh and k,(exp.)X from columns 3 and 7 (Table 1).
10’ plotted
vs. l/s ratio
Fig. 5. Slowing down factor f and average theoretical rate ACY/ At%(th)lh with k,=cte= IO-” vs. l/s ratio, from columns 8 and 9 (Table 1).
Hours
ln( 1 + +)
0
10
20
30
40
50
x = I/s
60
Fig. 4. Ar(theor.) computed from Eq. (15) with k,= lo-’ and Ar(exp.) drawn from column 5 Table 1, plotted vs. l/s ratio (limited to l/s =50).
= 2Q+s,ogjk#
-f)gAt.
(16)
The values of f are collected in column (8) of Table 1 and have been plotted versus l/s in Fig. 5: f increases and tends to one on both sides of l/s = 15 for which f = 0, quickly when 11s decreases towards the most concentrated stirred suspensions and stagnant pastes, slower when Its increases towards the most diluted stirred suspensions. The theoretical average rate, AculAt(theor.)% computed with k,= 10m4 and f=O has been plotted versus l/s in the same figure, giving a straight line practically (Table 1, column 9).
4. Conclusion 4.8 h. The two curves are very close between 11s = 5 and lls=20. .25. But at the contact point, At(exp.) is always much higher than At(theor.). 3.2. Other formulation
of the results
These considerations led us to introduce an additionnal term (1 -f) into Eq. (15), f playing the role of an empirical slowing factor enabling k, to be maintained constant at 10-4. That consists of replacing k,(exp.) by k,(theor.)( 1 -f), that is to say: (1 f)lO-” = k,(exp.) drawn from column 7 of Table 1 so that Eq. (15) becomes:
At 21”C, in pure water and with a sample of Ca,SiO, having a fineness of 350 m’/kg, the ideal situation for its average hydration rate between the limits of period 3 roughly independent of the l/s weight ratio appears to be that of a fairly diluted stirred suspension for 11s = 15 and on both sides close to l/s= 15, because it is for these values of l/s that the slowing down factor is smallest or nought, the rate of hydration being effectively proportional to the surface area of tricalcium silicate following our assumption. No discontinuity appears when passing from this domain to that of the stagnant pastes and
P. Barret, D. Bertrandie / Solid State Ionics 101-103
most concentrated stirred suspensions or to that of the more diluted ones. But, k, being kept constant, the slowing down factor is increasing towards one, on both sides. The determination of the nature of the slowing down factor was not within the scope of this paper, see [26,27].
References [II M. Collepardi,
Proceedings of an Engineering Foundation Conference, American Society of Civil Engineers, 345 East 47th Street, New York 10017.2398, 1994, p. 257. VI P. Longuet, L. Burglen, A. Zelver, Rev. Mat. Cons@. 676 (1973) 35. Jr., S. Diamond, Cement Concrete Res. [31 R.S. Barneyback ll(2) (1981) 279. 141 E.M. Gartner, H.M. Jennings, J. Am. Ceram. Sot. 70( 10) (1987) 743. 151 V.P. Kasperchick, VS. Soldatov, Vestn. Skad. Nauk., SSSR, Ser. Khim. Nauk. (1983) 120. 161 CD. Lawrence, Spec. Rep. Highway Res. Board 90 (1966) 378. M.W. Grutzeck, Proc. 8th. Int. Symp. L71 R.R. Ramachandran, Chem. Cem., Rio de Janeiro III, 1986, p. 225. 181 A. Zelver, Thesis C.N.A.M., Conservatoire National des Arts et Metiers, Paris, 1969. I91 A. Zelver, Rev. Mat. Constr. 681 (1973) 227. [lOI A. Zelver, Ciments, B&tons, PlCtres et Chaux 749 (1984). H.F.W. Taylor, [Ill P.W. Brown, E. Franz, G. Frohnsdorff, Cement Concrete Res. 14 (1984) 257.
(1997) 359-365
365
[121 D. Damidot, Thesis, University of Burgundy, Dijon, France, 1990. [I31 D. Damidot, A. Nonat, P. Barret, J. Am. Ceram. Sot. 73( 11) (1990) 3319. [I41 D. Damidot, A. Nonat, Adv. Cement Res. 6(21) (1994) 27. Biol. [I51 P. Barret, D. Bertrandie, J. Chim. Phys. Phys-Chim. (1986) 795. 1161 P. Barret, D. Bertrandie, J. Am. Ceram. Sot. 73( 11) (1990) 3486. [171 P. Barret, CR. Acad. Sci. Paris 288 (1979) 461. [I81 S.A. Greenberg, T.N. Chang, J. Phys. Chem. 69 (1965) 182. Cl91 F.D. Tamas, A.K. Sarkar, D.M. Roy, Hung. J. Indust. Chem. Veszprtm 5 (1977) 115. 1201 N.J. Clayden, C.M. Dobson, G.W. Groves, C.J. Hayes, S.A. Rodger, Proc. Brit. Ceram. Sot. 35 (1984) 55. [211 S.A. Rodger, G.W. Groves, N.J. Clayden, CM. Dobson, J. Am. Ceram. Sot. 71(2) (1988) 91. C. Vemet, D. Heidemmann, w-1 R. Rassem, H. Zanni-Theveneau, A.R. Grimmer, P. Barret, A. Nonat, D. Bertrandie, D. Damidot, Proc. of the International RILEM Workshop, Dijon, France, 1991, p. 77. ~231 D. Damidot, A. Nonat, P. Barret, D. Bertrandie, H. Zanni, R.R. Rassem, Adv. Cement Res. 25 (1995) 1. ~241 B. Courtault, P. Longuet, 36eme Congres de Chimie Industrielle, G.R. 7, S. 17, Bruxelles, 1966, p. 752. B. Couttault, Rev. Mat. Constr. Trav. Publics 687 (1974) PI 117. WI H.F.W. Taylor et al., RILEM Committee 68 MMH, Task Group 3, Materials and Structures, Research and Testing, I IO (1986) 137. ~271 H.F.W. Taylor, Cement Chemistry, Academic Press, New York, 1990, p. 162.
ELSWIER
Importance
101-103
IONICS
(1997) 359-365
of the liquid to solid weight ratio in the powdered solid-liquid reactions
Example drawn from cement constituent hydration P. Barret’“, D. Bertrandie Laboratnire de Recherche SW la R&activite’ des Solides. UMR 5613, CNRS - UnivrrsitP de Bourpgne, France
B.P. 400, 21011 Dijon cedex,
Abstract It seems justified to wonder if the chemical processes which have been evidenced from diluted stirred suspensions are or are not in accordance with those involved in a stagnant paste. The present paper is aimed at clarifying this question which is in connection with the problem of the so called ‘dormant period’ or ‘induction period’ at the beginning of the hydration of Portland cement. Kepvrd.s: Tricalcium silicate hydration; Kinetic influence of the liquid to solid weigth ratio; Diluted stirred suspensions; Specific surface area: Maximum supersaturation; Slowing down factors Muteriulst Ca,SiO,;
Ca,(OH),H,Si20,;
pastes;
Ca(OH)?
1. Introduction In general, the liquid to solid weight ratio, labelled with l/s, is a significant factor of the reactivity in the powdered solid-liquid systems. In particular, the hydration of hydraulic binders gives many examples in which a finely divided solid reagent is mixed with less than half its weight of water. The mixing, which often requires the presence of chemical admixtures, called water reducers [ 11, results in a paste. The extraction of the liquid phase with the aim of analysing it at successive times of the hydration, constitutes a difficult experiment needing a powerful *Corresponding
Stagnant
author. Fax: +33 3 8039 6132.
0167.2738/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PII SOl67-2738(97)00129-X
press [2,3], and the setting that occurs at the end of a certain time increases the difficulty of liquid extraction. That is why many studies devoted to thermodynamic and kinetic aspects of cement hydration used stirred diluted aqueous suspensions rather than pastes enabling the solid and liquid constituents to be filtrated off more easily [4-71 in order to follow the changes of the liquid composition with time and the modifications of the solid products, notably by XRDA and other morphology, structure and composition determination techniques. In our works, our concern was the reactivity of solids and not the cement chemistry. That is why we used a synthesized cement constituent such as tricalcium silicate, Ca,SiO, and not cements which are complex mixtures. A few previous works using this constituent had been performed in order to study systematically the
360
P. Barret,
D. Bertrandie
I Solid State lonics
influence of the l/s ratio. In 1969, A. Zelver, in his thesis [8-lo], investigated the changes of the time needed by the Ca*+ ion concentration to reach the maximum supersaturation as a function of l/s, from Its = 0.3 to Ils = 3, thus essentially on pastes made of samples of various specific surface areas. Later (in 1984) Brown et al. [ 1I], using automated colorimetric method, measured the concentration of calcium and silica in solution during the first 4 h of hydration of Ca,SiO, (3525 cm’/g) at l/s ratios ranging from 0.7 to 20; stirring was used at 11s ratios above 0.7. A strong dependence of the rate of early hydration on the 11s ratio was observed, while the dependence on the surface area of the Ca,SiO, was minimal. Recently, Damidot in his thesis [ 121 and Nonat et al. [ 13,141 took advantage of the sensitivity of the TianCalvet heat flow isothermal calorimeter by adapting it to study very diluted Ca,SiO, suspensions at different l/s ratios. They designed a microelectrode allowing them to measure the electrical conductivity of the suspension simultaneously with the heat flow.
101-103
(1997)
3Ca2+ + 40H
359-365
+ 2H,SiO,
In order to test the influence of factor l/s, we chose also to perform kinetic experiments, but limiting them to a well-defined period of Ca,SiO, hydration (called period 3) and that, at room temperature and at different 11s ratios going from 11s = 0.35 to l/s = 100. Indeed, in a previous paper [15], we had shown that the tricalcium silicate hydration was a complex reaction resulting from 3 simultaneous reactions, the time-zero of the second and the third ones being delayed by the time required for the maximum supersaturation with respect to the hydrates being reached, these hydrates being: calcium silicate hydrate from the second reaction and calcium hydroxide from the third, the first reaction representing the passage into solution of the Ca’+, OH- and silicate ions released by Ca,SiO,,, on contact with water. These three rections can be written: 2Ca,SiO,,,
+ 8H,O,
-+ 6Ca*+ + 2H,SiO, suffix sh meaning:
+ lOOH-
‘superficially
hydroxylated’
(1) [ 171.
C-S-H + H,O,, (2)
3Ca’+ + 6(OH))
+
3Ca(OH),.
2.1. Delimitation
of the part ofreaction used
(3)
The reaction used to compare the effect of the liquid to solid weight ratio, denoted by l/s (generalizing the cement chemistry notation +V/C meaning water to cement ratio) may be considered as the sum of the first and the second above reactions in which the number of silicate ions passing into solution and that consumed by the formation of calcium silicate hydrate per unit of time are about the same. That is the translation of a quasi-steady state in the silicate ion concentration. Such a single reaction may be written: 2Ca,SiO,,,
+ 7H,O,
+ C-S-H + 3Ca2+ + 60H2. Experimental
+
(4)
C-S-H meaning: Caj(OH)4H4Si20,, formula in which the Ca/Si ratio was taken as an average value = 1.5 because this ratio was not constant, but [ 181; besides, from linked to the lime concentration trimethylsilylation and gas chromatography experiments [ 191 and, more recently, from *“Si MAS NMR spectroscopy with cross-polarization [20-231, the silicate ions in C-S-H should be considered, at least, as dimeric. This reaction offers the advantage to be bounded very well by a lower and a upper limits nearly independent of 11s: indeed, the experiments consisted of building two sets of graphs from the data collected at 21°C a set of kinetic graphs and a set of the corresponding ‘associated paths’. We used T, triclinic Ca,SiO, prepared by Lafarge Central Laboratory. This solid compound was ground and its specific surface area, determined by Blaine’s method, was 350 m*/kg. The free lime content was less than 0.1%. The main parameter, the l/s weight ratio, was fixed by mixing the suitable mass of Ca,SiO, with the required mass of deionized decarbonated water, in an appropriate vessel. The choice of this vessel depended upon whether it was a stirred aqueous suspension of Ca,SiO, or a paste:
P. Barret, D. Bertrandie 1 Solid State Ionics 101-103
2.2. Kinetics
experimental
techniques
With a stirred suspension, the tests were performed on 400 g of solvent (deionized decarbonated water) and a suited mass of Ca,SiO, for a given l/s ratio, for example, 80 g for Z/s =5 or 20 g for l/s =20, and so on. The mixture was magnetically stirred in the closed vessel. One of the ground joints was used for removing 5 or 6 ml portions of the mixture. The samples were filtrated immediately. For the Ca2+ titration, flame atomic absorption spectrometry (Perkin Elmer 3030) was used and for the total SiO,, photocolorimetry at 850 nm was implemented with a Hach spectrophotometer, model DR/300. At the start of the test, the frequency of sampling was increased in order to determine accurately the maximum in the silica concentration [ 15,161. The filtrates were mixed with 0.1 cm3 of 6 N HCl so that the reaction was stopped immediately and the times brought to abscissae corresponded justly to the sampling dates. The procedures described above were discontinuous. Such procedures have been complemented by continuous ones, at least for Ca2+ titration. In this way, one of the ground joints was used to set an electrical conductivity electrode. Then, the curves [Ca2’]=,f(t) plotted by calibration of the recorded electrical conductivity were confirmed by comparison with the measurements at successive times, performed by atomic absorption flame spectrometry. With a paste, the electrical conductivity measurement also enabled the end of the third period to be detected, thanks to the drop in the Ca’+ and OHion concentrations accompanying the break of the maximum supersaturation with respect to the portlandite (period 4). A similar cell as that described by Zelver [8-lo] was realized; such a conductivity cell was submitted to the possibility of maintaining the sample-carrier in a thermostated bath. The highest difficulty in the use of this conductivity cell consisted of the mixing at an I/s value as low as 0.35. Although the enclosure made of plexiglass allowed trials with mixing under vacuum, a prior mixing in another vessel maintained in the thermostated bath appeared to be more efficient, dispite the uncertainty caused in the definition of the initial time. An approximate value of the fractional conversion LY, drawn from the integration of the thermal flow, can
361
(1997) 359-365
also be obtained by microcalorimetry [24,25], which is more easily brought into play with a paste (I/s< 0.5) than with an aqueous suspension. 2.3. Example of the limit determination
for 11s =20
Taking as an example the kinetic graph of Ca,SiO, hydration with an l/s ratio of 20 (Fig. l), it can be seen that the lower limit corresponds to the end of the short plateau AB appearing at the beginning of the curve of lime concentraton plotted versus time t and whose ordinate OA is about 5 mmol/kg in lime, whatever l/s. The end B of the plateau occurs at time t,. On the other hand, the upper limit corresponds to the maximum M, of lime concentration plotted versus time and which is also the maximum supersaturation with respect to calcium hydroxide as portlandite whose value changes weakly with l/s ratio, passing from 0.038 mol/kg at lls=O.35 (in a paste) to 0.030 mol/kg at l/s= 100 in a very diluted stirred suspension and occurring at time tz (see Table 1, column 2). The limits in the ‘associated path’ graph (Fig. 2) are Q, corresponding to B, and R, corresponding to M,, in the kinetic graph (Fig. 1). The graph that we called ‘associated path’ is obtained from the same data as those (lime concentration, silica concentration, time) used to built the kinetic graphs. But instead of plotting lime concentration in Yl, silica concentration in Y2 and t in abscissa, we plotted
--++a0
(mmol/kg)
-+-S102
(micromol/kg)
time
t (h)
Fig. I. Ca,SiO, hydration kinetics with l/s ratio=20 at 21°C: M, maximum of silicate ion concentration, MC, maximum of Ca’+ ion concentration plotted vs. time. AB, short plateau in Ca*+ ion concentration curve. f, and I_, starting and ending times of period 3.
P. Barrer, D. Bertrandie I Solid Sme Ionics IOI- 103 (1997) 359-365
362 Table 1 Experimental 1 11s
0.35 0.5 5 10 15 20 30 40 50 75 100
tSiO2
results and calculation 2 [Ca”] (mol/kg)
3 A[Ca”] (mol/kg)
(exp.)
(exp.)
0.038 0.037 0.037 0.037 0.037 0.035 0.035 0.033 0.0305 0.030 0.030
0.033 0.033 0.033 0.032 0.032 0.030 0.030 0.028 0.025 0.025 0.025
(micromol/kg)
.__.
of an empirical
slowing down factor labelled with f
4 AMY(calcul)
5 At (hours)
[Eq. (911
(exp.)
2. 0 2.30 2.50 3.50 4.804 6.14 11.5 19.0 39.0 74.0 126.30
0.00175 0.0025 0.025 0.048 0.073 0.0912 0.1368 0.172 0.190 0.285 0.380
4
-time (h) -12
6 AculAr (%)/h
I k, x lor
f empir.
(exp.)
[Es. (16)l
[Eq. (16)l
0.0875 0.108 1.0 1.371 1.520 1.353 1.19 0.90 0.487 0.385 0.301
0.550 0.684 6.38 8.99 10.0 9.04 8.21 6.36 3.55 3.047 2.63
0.945 0.932 0.362 0.101 0.0 0.096 0.179 0.364 0.645 0.695 0.737
9 A&Al (%)(k,=
lOma)
1.589 1.588 1.566 1.524 1.520 1.498 1.448 1.407 1.372
1.264 1.145
calcium ion concentration. To sum up, the experiments consisted of establishing the kinetic graph and the related ‘associated path’ as a function of l/s weight ratio from the low l/s such as 0.35 and 0.5 in the field of the stagnant pastes to 5, 10, 15,. 50,. . 100 in the field of the aqueous stirred suspensions of Ca,SiO,.
3. Results and discussion (:a0 (mmol/kg) Fig. 2. ‘Associated path’ to the hydration kinetics graph (Fig. 1) for l/s ratio=20 at 21°C: OP, congruent dissolution of Ca,SiO,,, in pure water. PQ: silicate ion concentration fall during the plateau AB of Ca2+ Ion concentration. R, point corresponding to the maximum of Ca2+ ion concentration.
silica concentration in Yl, lime concentration in abscissa and t in Y2 so that t appears as the reciprocal function of the lime concentration such that t=f-‘[CaO]. The lower and upper limits in time are given by times t, and t,. P indicates the maximum silicate ion concentration reached after congruent dissolution OP of Ca,SiO,,,. That is also the maximum supersaturation with respect to C-S-H. The vertical segment PQ corresponding to the plateau AB in the kinetic graph expresses an abrupt fall of the supersaturation due to the sudden precipitation of C-S-H leading to a steady state in the
The experimental results are collected in Table 1. The values of the upper limits in calcium ion concentrations [Ca2+], are given in column 2 and the difference A between the upper and the lower limits can be found in column 3 for calcium ion concentrations and in column 5 for the time, for Instead of A[Ca2’], it would be which At = t, -t, better to express Aa representing the change of the fractional conversion (Y from the lower to the upper limits (third period). (Y is also the molar percentage of Ca,SiO, (which is the limitative reagent), consumed at time t. As we saw above, Eq. (4) may be considered as a single reaction in a closed system; the relations drawn from the law of definite proportions enable us to write: dn(Ca,SiO,)
= - 2dt
(5)
where 5 is the extent of the reaction and n the number of moles in the stoichiometric equation.
P. Barret, D. Bertrandie I Solid State Ionics 101-103
dn(Ca2’)
= 3&.
(6)
The fractional conversion cy and the extent reaction [ satisfy the relation:
(1997) 359-365
specific surface follows that:
of d[Ca*‘]ldt Account
area in kg/m*.
363
From
Eq. (6), it
d5
= 3Fldt.
being taken of Eq. (7), dt can be written:
(11)
where V, and rry are the stoichiometric coefficent and the initial number of moles of the limitative reagent, here, Ca,SiO,. Combining Eq. (6) and Eq. (7), we obtain:
Bringing Eq. (8) and Eq. (10) close together, following equation appears:
da = 2/3M
dcu=2M (Cs,Slos,kr(m,‘mo,adt.
(8)
(calsio,)(l/s)d[Ca2+l
is the molar mass of Ca,SiO, where MCCa3Si05) (0.228 kg/mol) and (l/s) the liquid to solid weight ratio, 1 indicating the initial mass (in kg) of the amount of water and s, the initial mass (in kg) of mixed solid Ca,SiO,. By integration between lower and upper limits 1 and 2, Eq. (8) gives:
m,lm,=l-ff
(13)
so that dcz becomes: (14) And after integration limit, Eq. (14) gives:
or Aa = O.l52(Z/s)A[Ca*‘].
(9)
Thus, Aa is proportional both to (I/s) and to the value of A[Ca2’] corresponding to this (l/s). The results may be expressed as the quotient AalAt (Table 1, columns 4, 5 and 6) which appears to be the ‘experimental average rate of tricalcium silicate hydration in mol% of Ca,SiO, consumed per hour between the above defined limits’. It appears from Fig. 1 that this average rate of hydration, denoted by AcYlAt%(exp.)lh, varies strongly as a function of l/s, passes through a maximum for l/s = 15 and decreases again when lls increases beyond 15. of a theoretical
interpretation
of At
An extra hypothesis has been introduced by assuming that the reaction rate was proportional to the surface area of the solid sample, which leads to: dcldt
= k,m,u
(12)
Indeed, s =mO is the initial mass of the solid sample. From Eq. (5) and Eq. (7), m,lm, can be expressed as a function of (Y:
Aa = 2/3M,,,~,,,,(Zls)A[Ca*‘l
3.1. Attempt
the
(10)
where k, is a constant depending on temperature T, m,, the mass of the sample at time t and u, its
from the lower to the upper
ln(1+ $) =2Mo,s,o,+At.
(15)
This equation has been computed with a program bringing the following variables into play: l/s, [Ca*+]*, A[Ca*‘], At, u and k,, and enabling one of them to be calculated when the others are given. Let it be assumed that we want to calculate k, from the data of Table 1: the computed values have been plotted in Fig. 3 versus l/s in the form of k,(exp.)= 105. This curve lies close to the curve of AU/ At(exp.)%lh and showed that k,(exp.)= lo5 is not constant, but passes also through a maximum for l/s= 15 where its value is 10.0 (Table 1, column 7), i.e. that, at this maximum, k,= 10P4. Now, if we introduce k,= 10e4 in the program as datum in order to compute At denoted by ‘theoretical At’, the results plotted in Fig. 4 versus l/s give an arc of hyperbola with a great radius of curvature. The values of At(exp.) in hours have been plotted in the same graph. It can be seen that the theoretical curve is the tangent to the experimental curve at a point of coodinates: l/s = 15, At(exp.) = At(theor.) =
P. Barrel, D. Berrrandie I Solid Stare lonics 101-103
364
Aa/At(exp.)% * _. . . . .- . . .
: ._
AdAt (theor.) % wth k, = IO '
tYl=f
k&exp.)lO’ . . .
(1997) 359-365
-12
I
0.8
-6
; j ! . I . . ..
-4
2
0
0
"/""'/"""j"l'I" 20
40
60
80
100
I*"0
0
- 20
40
60
*O
I/s
loo
x = I/s
Fig. 3. AalAt%(exp.)lh and k,(exp.)X from columns 3 and 7 (Table 1).
10’ plotted
vs. l/s ratio
Fig. 5. Slowing down factor f and average theoretical rate ACY/ At%(th)lh with k,=cte= IO-” vs. l/s ratio, from columns 8 and 9 (Table 1).
Hours
ln( 1 + +)
0
10
20
30
40
50
x = I/s
60
Fig. 4. Ar(theor.) computed from Eq. (15) with k,= lo-’ and Ar(exp.) drawn from column 5 Table 1, plotted vs. l/s ratio (limited to l/s =50).
= 2Q+s,ogjk#
-f)gAt.
(16)
The values of f are collected in column (8) of Table 1 and have been plotted versus l/s in Fig. 5: f increases and tends to one on both sides of l/s = 15 for which f = 0, quickly when 11s decreases towards the most concentrated stirred suspensions and stagnant pastes, slower when Its increases towards the most diluted stirred suspensions. The theoretical average rate, AculAt(theor.)% computed with k,= 10m4 and f=O has been plotted versus l/s in the same figure, giving a straight line practically (Table 1, column 9).
4. Conclusion 4.8 h. The two curves are very close between 11s = 5 and lls=20. .25. But at the contact point, At(exp.) is always much higher than At(theor.). 3.2. Other formulation
of the results
These considerations led us to introduce an additionnal term (1 -f) into Eq. (15), f playing the role of an empirical slowing factor enabling k, to be maintained constant at 10-4. That consists of replacing k,(exp.) by k,(theor.)( 1 -f), that is to say: (1 f)lO-” = k,(exp.) drawn from column 7 of Table 1 so that Eq. (15) becomes:
At 21”C, in pure water and with a sample of Ca,SiO, having a fineness of 350 m’/kg, the ideal situation for its average hydration rate between the limits of period 3 roughly independent of the l/s weight ratio appears to be that of a fairly diluted stirred suspension for 11s = 15 and on both sides close to l/s= 15, because it is for these values of l/s that the slowing down factor is smallest or nought, the rate of hydration being effectively proportional to the surface area of tricalcium silicate following our assumption. No discontinuity appears when passing from this domain to that of the stagnant pastes and
P. Barret, D. Bertrandie / Solid State Ionics 101-103
most concentrated stirred suspensions or to that of the more diluted ones. But, k, being kept constant, the slowing down factor is increasing towards one, on both sides. The determination of the nature of the slowing down factor was not within the scope of this paper, see [26,27].
References [II M. Collepardi,
Proceedings of an Engineering Foundation Conference, American Society of Civil Engineers, 345 East 47th Street, New York 10017.2398, 1994, p. 257. VI P. Longuet, L. Burglen, A. Zelver, Rev. Mat. Cons@. 676 (1973) 35. Jr., S. Diamond, Cement Concrete Res. [31 R.S. Barneyback ll(2) (1981) 279. 141 E.M. Gartner, H.M. Jennings, J. Am. Ceram. Sot. 70( 10) (1987) 743. 151 V.P. Kasperchick, VS. Soldatov, Vestn. Skad. Nauk., SSSR, Ser. Khim. Nauk. (1983) 120. 161 CD. Lawrence, Spec. Rep. Highway Res. Board 90 (1966) 378. M.W. Grutzeck, Proc. 8th. Int. Symp. L71 R.R. Ramachandran, Chem. Cem., Rio de Janeiro III, 1986, p. 225. 181 A. Zelver, Thesis C.N.A.M., Conservatoire National des Arts et Metiers, Paris, 1969. I91 A. Zelver, Rev. Mat. Constr. 681 (1973) 227. [lOI A. Zelver, Ciments, B&tons, PlCtres et Chaux 749 (1984). H.F.W. Taylor, [Ill P.W. Brown, E. Franz, G. Frohnsdorff, Cement Concrete Res. 14 (1984) 257.
(1997) 359-365
365
[121 D. Damidot, Thesis, University of Burgundy, Dijon, France, 1990. [I31 D. Damidot, A. Nonat, P. Barret, J. Am. Ceram. Sot. 73( 11) (1990) 3319. [I41 D. Damidot, A. Nonat, Adv. Cement Res. 6(21) (1994) 27. Biol. [I51 P. Barret, D. Bertrandie, J. Chim. Phys. Phys-Chim. (1986) 795. 1161 P. Barret, D. Bertrandie, J. Am. Ceram. Sot. 73( 11) (1990) 3486. [171 P. Barret, CR. Acad. Sci. Paris 288 (1979) 461. [I81 S.A. Greenberg, T.N. Chang, J. Phys. Chem. 69 (1965) 182. Cl91 F.D. Tamas, A.K. Sarkar, D.M. Roy, Hung. J. Indust. Chem. Veszprtm 5 (1977) 115. 1201 N.J. Clayden, C.M. Dobson, G.W. Groves, C.J. Hayes, S.A. Rodger, Proc. Brit. Ceram. Sot. 35 (1984) 55. [211 S.A. Rodger, G.W. Groves, N.J. Clayden, CM. Dobson, J. Am. Ceram. Sot. 71(2) (1988) 91. C. Vemet, D. Heidemmann, w-1 R. Rassem, H. Zanni-Theveneau, A.R. Grimmer, P. Barret, A. Nonat, D. Bertrandie, D. Damidot, Proc. of the International RILEM Workshop, Dijon, France, 1991, p. 77. ~231 D. Damidot, A. Nonat, P. Barret, D. Bertrandie, H. Zanni, R.R. Rassem, Adv. Cement Res. 25 (1995) 1. ~241 B. Courtault, P. Longuet, 36eme Congres de Chimie Industrielle, G.R. 7, S. 17, Bruxelles, 1966, p. 752. B. Couttault, Rev. Mat. Constr. Trav. Publics 687 (1974) PI 117. WI H.F.W. Taylor et al., RILEM Committee 68 MMH, Task Group 3, Materials and Structures, Research and Testing, I IO (1986) 137. ~271 H.F.W. Taylor, Cement Chemistry, Academic Press, New York, 1990, p. 162.