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Assessment of experimental evidence for models of hydrated portland
cement
Feldman, R. F.
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Ser
TKL
N21r2
no.
518
c.2
BLDG
Assessment
of
Experimental Evidence for
Models
of
Hydrated Portland Cement
by
R.
F.
Feldman
R e s e a r c h P a p e r No. 518 of the Division of Building R e s e a r c h National R e s e a r c h Council of Canada
Conseil National de Recherches du Canada
Reprinted from: National R e s e a r c h Council, Highway R e s e a r c h Board, Washington, D. C., Highway R e s e a r c h R e c o r d 370, 1971, pp.8-24, 25 cents
EVALUATION D E L'EVIDENCE E X P E R I M E N T A L E DES MODELES D E CIMENT P O R T LAND HYDRATE
SO MMAIRE
Ce mBmoire m o n t r e c o m m e n t l e nouveau mod'ele diff'ere d e s prCcCdents p a r l e s c o n c l u s i o n s s u i v a n t e s : ( 1 ) Quand l e c i m e n t p o r t l a n d hydrati: e s t assCchC 'a l a glace s'eche, l ' e a u d e s couches interrnCdiaires e s t enlevCe d e s s i l i c a t e s . E n l l e x p o s a n t de nouveau 'a l a vapeur d l e a u , l l e a u pCn'etre d e nouveau d a n s l e s couches i n t e r m k d i a i r e s , mGme 'a faible h u m i d i t & . ( 2 ) L e s a i r e s d e s u r h c e d l e a u e t l e s densitCs sont i n c o r r e c t e s . L e s m e s u r e s 2 l l a z o t e e t a u mCthano1, r e s p e c t i v e m e n t , donnent 'a peu pr'es l e s v a l e u r s c o r r e c t e s . ( 3 ) L e s propriCtCs f o n d a m e n t a l e s d e s c i m e n t s p o r t l a n d hydratCs ou d e s s i l i c a t e s hydratCs v a r i e n t s e l o n l e mode d e p r g p a r a t i o n . L e m g r n o i r e m o n t r e c o m m e n t l a c h a l e u r d e s o l u t i o n ne peut Gtre Bvaluke e n fonction d e l a s u r f a c e e t n o m b r e d e donnCes, dont l e s i s o t h e r m e s , l e s m e s u r e s de d e n s i t 6 e t l e c a l c u l d e s r a y o n s h y d r a u l i q u e s , s o n t interprBtBes p o u r a p p u y e r l e nouveau mod'ele. De nouveaux c a l c u l s s o n t f a i t s d e l a d e n s i t & , d e l l e s p a c e m e n t moyen s u r l l a x e c e t d e l a s t o e c h i o m B t r i e d e l l e a u . On p r e s e n t e d e nouveaux f a i t s p o r t a n t s u r une Btude d e s v i d e s l a i s s C s quand l e c i m e n t hydrati: e s t sBchi: e t d e s m e s u r e s d e s v a r i a t i o n s d i m e n s i o n n e l l e s du s o l i d e au c o u r s du sCchage; c e s f a i t s , s e m b l e - t - i l , appuient l e nouveau mod'ele d l u n e f a c o n p r o b a n t e .
Assessment
of
E x p e r i m e n t a l Evidence for
Models
of
Hydrated P o r i l a n d Cement
by
ASSESSMENT OF EXPERIMENTAL EVIDENCE
FOR MODELS OF HYDRATED PORTLAND CEMENT
R. F. Feldman, Division of Building R e s e a r c h , National R e s e a r c h Council of Canada, Ottawa
T h e relative m e r i t s of t h e "new" and "old" models of hydrated portland cement a r e p r e s e n t e d together with a n a s s e s s m e n t of published and s o m e unpublished evidence relating t o the models. T h e chief a r e a s of evidence discussed a r e those pertaining t o s u r f a c e e n e r g y of calcium-silicate- hydrate m a t e r i a l (C-S-H) by heat of solution, stoichiometry of C-S-H, and t h e effect of i n t e r l a y e r rehydration of D-dried C-S-H on density mea- s u r e m e n t s , c - a x i s and hydrated r a d i i calculations, length and weight change i s o t h e r m s , and porosity and mechanical p r o p e r t y correlations. Anew tech- nique of measuring the flow r a t e of helium into interlayer s p a c e s is dis- c u s s e d in t e r m s of evidence it produces. It is concluded that the "new" model of hydratedportland cement m o r e a c c u r a t e l y accounts f o r i t s nature a s indicated by a wide v a r i e t y of properties.
.THERE ARE many t e r m s used throughout t h i s discussion t o d e s c r i b e elements and conditions of hydrated portland cement. T h e s e a r e defined in the following:
1. C-S-H is the poorly crystallized, l a y e r e d calcium-silicate-hydrate m a t e r i a l found in well-hydrated portland cement, C3S and C2S.
2. A l a y e r is the b a s i c unit of the C-S-H s t r u c t u r e ; it is about 9
a
thick in t h e c - direction. T h i s t e r m is used synonymously with sheet.3. Interlayer s p a c e is the s p a c e between l a y e r s , when essentially parallel, s e p a r a t e d by no m o r e than about 5
.i.
Disorientation of l a y e r s may lead t o g r e a t e r distances in local a r e a s .4. Interlayer w a t e r occupies s p a c e between adjacent l a y e r s of C-S-H and is l e s s mobile than f r e e o r physically adsorbed water.
5. Physically adsorbed w a t e r is water that is held t o an open surface and that has e n e r g i e s not much m o r e than the latent heat of evaporation. It does not have a r o l e in the s t r u c t u r e , nor does it contribute t o the mechanical p r o p e r t i e s of the m a t e r i a l . As defined h e r e , it does not include i n t e r l a y e r water.
6. Nitrogen a r e a is the surface a r e a calculated f r o m nitrogen adsorption results. It does not include the a r e a between adjacent C-S-H l a y e r s .
7. Water a r e a is the s u r f a c e a r e a calculated f r o m w a t e r sorption r e s u l t s . T h e physi- c a l significance is difficult t o specify because interlayer water appears t o r e e n t e r in- t e r l a y e r s p a c e in a n unpredictable way throughout the BET region normally used f o r s u r f a c e a r e a calculations.
8. Solid volume is the volume of the C-S-H l a y e r s , the volume of the interlayer w a t e r , and t h e unoccupied interlayer space.
Sponsored by Committee on Basic Research Pertaining t o Portland Cement and Concrete and presented at the 50th Annual Meeting.
9. The D-dried condition is the condition in which a sample has been dried to equi- librium at the water-vapor p r e s s u r e of 5 x mm of mercury.
10. The P - d r i e d condition also involves drying but at a p r e s s u r e of 8.15 x mm of mercury.
11. Density is of 3 types: (a) density of undried material a t 11 percent relative humidity (RH) that includes the interlayer water and interlayer space a s solid volume in the calculation (physically adsorbed water is not counted a s solid volume); (b) den- s i t y of D-dried m a t e r i a l that does not include the partially collapsed interlayer spaces a s solid volume in the calculation (an approximation of t h i s value is obtained by using water a s the medium in the determination); and (c) density of D-dried material that includes the partially collapsed interlayer s p a c e s a s solid volume in the calculation.
Scientific interest in the experiments that provide evidence for a model f o r hy- drated portland cement paste is currently at a high level. A new model subsequently called the F-S model (Feldman-Sereda model) has recently been proposed (1) - that has given r i s e to extensive discussions (2, 3) comparing it with e a r l i e r ones.
The F-S model of hydrated portlandcement is based ultimately on 3 fundamental assumptions (considered h e r e a s established facts) concerning the nature of the hy- drated calcium s i l i c a t e s (assumed to be layered) normally found in hydrated portland cement. T h e s e assumptions a r e a s follows:
1. The fundamental physical properties, such a s density, equivalent c-spacing, Ca-Si ratio, H20-Si ratio, of hydrated portland cement o r of the hydrated silicates and s u r - face a r e a vary with conditions of preparation. T h e s e conditions include water-solid ratio, temperature, and perhaps the content of alkali, sulfate, and admixtures.
2. When the hydrated m a t e r i a l i s D-dried, interlayer water is removed from the silicates. When it is reexposed to water vapor, water r e e n t e r s the interlayer spaces even at low humidities.
3. In light of this conclusion, water s u r f a c e a r e a s and densities a r e therefore not c o r r e c t , but the respective measurements by nitrogen and methanol a r e approximately c o r r e c t .
T h e s e assumptions w e r e considered wholly o r partly incorrect in 1958 (4), even though s u r f a c e a r e a s determined by nitrogen before that date w e r e given some credence by Kalousek (5) and Brunauer, Copeland, and Bragg (6). The b a s i s of the old model, subsequently called the B - P model ( ~ r u n a u e r - p o w e r s model), was that t h e s e assump- tions w e r e essentially incorrect, and a g r e a t deal of effort was spent in attempting to c o r r e l a t e and understand new data. As m o r e and m o r e data w e r e accumulated, the assumptions had to b e reevaluated. In 1964, Feldman and Sereda (7) suggested that assumptions 2 and 3 w e r e true. In 1968 they described the F-S model (I), which is based on data f r o m a variety of measurements on both compact and paste samples. T h e s e data included sorption, length change (8), strength, and other mechanical
measurements (9), a s well a s surface a r e a , chemical, and mineralogical considerations. Other a u t h o r s h a v e a l s o r a i s e d questions about a s p e c t s of the B - P model. Taylor (10) has expressed doubt about the supposed s i m i l a r i t y of the hydrated silicates to the t o b e F m o r i t e s and thus about the relevancy of the t e r m "tobermorite gel"; hence, his p r e f e r - ence f o r the nomenclature C-S-H. He considered the silicates to b e very variable in composition and v e r y heterogeneous. He has a l s o questioned the v e r y high density values used by Brunauer, Kantro, and Copeland (4) for a c - a x i s calculation. Locher (11)
-
and Kurczyk and Schwiete (12) have questioned a ~ s u m p t i o n s and methods used in the Ca-Si r a t i o determinationsand r e s u l t s that show that the Ca-Si r a t i o v a r i e s inversely with the water-cement r a t i o (13). - Seligmann (14) has analyzed nuclear magnetic r e s o --
nance m e a s u r e m e n t s that he and o t h e r s obtained and concluded that a l a r g e portion of what was considered a s physically adsorbed water is interlayer water. Verbeck and Helmuth (15) have gone f u r t h e r and have concluded that the water f o r m e r l y considered as gel water is interlayer water and that gel pores a r e , in fact, interlayer spaces. These conclusions all fit in with the descriptions and predictions of the F-S model.
T h e r e s t i l l remain, however, s e v e r a l a r e a s of experimental evidence that a r e con- s i d e r e d t o c a s t doubt on the F-S model (2). T h e s e will be discussed in the following sections, and a considerable amount of new experimental evidence will b e introduced. It is believed that the analysis of all the r e s u l t s makes the c a s e f o r the F-S model convincing and provides the b a s i s f o r a revision of the stiochiometry and "average i n t e r l a y e r spacing" of C-S-H gel.
SURFACE ENERGY O F C-S-H BY HEAT OF SOLUTION
The g r e a t e s t difference between the F-S and B - P models of hydrated portland cement a r i s e s f r o m assumptions 2 and 3 given e a r l i e r . T h e measurement of the s u r f a c e energy of C-S-H gel by the heat-of-solution technique (16) h a s been considered by s o m e (2) t o b e the strongest supporting evidence f o r t h e B - P mydel. It has been claimed that t h i s m e a - s u r e m e n t indicates that the s u r f a c e a r e a is c o r r e c t when determined by water adsorption and is incorrect when determined by nitrogen adsorption. The following points indicate that this claim is doubtful:
1. Consideration of the s u r f a c e energy of a m a t e r i a l must include an a s s e s s m e n t of the nature of the m a t e r i a l and the type of s u r f a c e involved. C-S-H is considered t o be a l a y e r e d c r y s t a l , the thickness of each l a y e r being about 9
A.
Surface energy is the excess energy between the surface and the bulk. One is, therefore, immediately confronted with the difficult t a s k of establishing whether the t e r m "surface energyt' has any meaning in l a y e r e d m a t e r i a l s ; i.e., t h e r e is no r e a l "bulk state."2. As in t h e c a s e with many clays of a l a y e r e d nature, such as montmorillonite, C-S-H hydrates have both a n internal and external surface. Nitrogen s u r f a c e a r e a s yield the external surface. If the unit c e l l s t r u c t u r e o r s u r f a c e a r e a p e r l a y e r as pro- posed by Brunauer, Kantro, and Copeland (4) is c o r r e c t , the internal plus t h e external s u r f a c e s a r e approximately 755 m2/g; thus, without even considering the dubiousness of the concept of s u r f a c e energy a s considered in point 1, one evidently cannot u s e water a r e a s o r nitrogen a r e a s f o r computing c o r r e c t overall s u r f a c e energies.
3. The discussion in point 2 shows that it was erroneous t o reason (2) that s u r f a c e energies, b a s e d on nitrogen a r e a s , give values that a r e too high o r t o o i o w (negative). In fact, if 755 m2/g w e r e used a s a total a r e a , a value c l o s e r t o that of amorphous s i l i c a (16) would b e expected. T h i s emphasizes the i r r e l e v a n c e of the geometric mean of the s a a c e energies of C a ( 0 ~ , ) and amorphous s i l i c a that h a s been quoted by s o m e w o r k e r s (16). It c a n b e questioned why these w o r k e r s selected the values of c r y s t a l - line c ~ ( o % and amorphous s i l i c a (2) f o r this calculation of s u r f a c e energy because the C ~ ( O H ) , in C-S-H i s not crystalline.
4. The determination of specific s u r f a c e energy by the heat of solution method is based on a v e r y important assumption: The m a t e r i a l s being studied a r e alike in every way except f o r their s u r f a c e a r e a s . Unfortunately, because the C-S-H m a t e r i a l s were p r e p a r e d by different methods, the m a t e r i a l s would not be alike, as was pointed out e a r l i e r in assumption 1. T o s t a r t with, the Ca-Si r a t i o of the C-S-H is now known (13) to v a r y inversely with the water-cement r a t i o f o r normal paste hydrated samples.
his
leaves s e v e r a l possibilities: (a) If the change in Ca-Si r a t i o is due only to addi- tional Ca++ deposited between the l a y e r s (in an unknown state), then the internal s u r f a c e energy can be changed because the s u r f a c e s a r e different with different amounts ofCa++ and because the separation of the l a y e r s will vary. Evidence f o r the l a s t s t a t e - ment has been obtained and will b e discussed l a t e r ( s e e section on density measurements and C-spacing). (b) T h e change in Ca-Si r a t i o might a l s o be due e i t h e r to silicone being substituted by calcium within the l a y e r o r to a different degree of s i l i c a condensation that, a s h a s been shown by Lentz (17), o c c u r s continuously. Owing t o the d i v e r s e meth- ods of preparing and s t a r t i n g m a t e r i a l s , t h e r e is a c l e a r possibility that the degree of polymerization of s i l i c a v a r i e s f r o m preparation t o preparation. In other words, varia- tion in body s t r u c t u r e and, therefore, body energy is a distinct possibility.
5. An evaluation of a paper by Brunauer, Kantro, and Wiese (16) on s u r f a c e energy m e a s u r e m e n t s on C-S-H gel led t o the following abservations: T h e heat of solution f o r a l l t h e i r s a m p l e s v a r i e d between 473 and 487 ~ a l / ~ , a difference of 14 cal/g; f o r 2 identical sampies, the difference was about 3.75 ~ a l / ~ . It m u s t b e concluded that the precision of the data is not enough t o make far-reaching conclusions. (b) The data fell into 3 c l u s t e r s . Each c l u s t e r w a s almost completely composed of s a m p l e s p r e p a r e d by the s a m e method: either the ball-mill, the paste, o r the bottle-hydrated method. Within each c l u s t e r the r e s u l t s w e r e s c a t t e r e d and, in s o m e instances, negative s u r - f a c e e n e r g i e s could be calculated f r o m the data when plotted against the w a t e r s u r f a c e a r e a . (c) Brunauer, Kantro, and Wiese (16) cited 2 s a m p l e s , D-28 and D-35, when they discussed computation of s u r f a c e e n e r g y T ~ h e y suggested that if the s u r f a c e a r e a s of the s a m p l e s as determined by nitrogen adsorption w e r e used a negative s u r f a c e energy would result. T h e s e samples, however, w e r e made not only f r o m different groups with r e g a r d t o preparation but a l s o f r o m different m a t e r i a l s . Sample D-28 was p r e p a r e d by ball-millingp-CaS f o r 46 days; D-35 was p r e p a r e d by bottle-hydrating C S f o r 47 days. If one plots t h e nitrogen a r e a f o r a group and makes comparisons f o r the s a m e s t a r t i n g m a t e r i a l , negative e n e r g i e s a r e not obtained. T h e data f o r nitrogen a r e a , however, a r e v e r y s p a r s e .
6. A subsequent paper by Kantro, Wiese, and Brunauer ( l a ) , which contained heat of solution data, attempted to c o r r e c t empirically f o r variationof Ca-Si r a t i o and water content. T h e application of r e g r e s s i o n analysis h e r e r a i s e s the question, Did the varia- tion in Ca-Si r a t i o c a u s e the observed change in heat of solution, o r did it change some- thing e l s e that in t u r n caused the change? The change in Ca-Si r a t i o m o s t probably changed the nature of t h e s u r f a c e a s well as t h e s u r f a c e a r e a , body energy, and total heat of solution.
Kantro, Wiese, and Brunauer (18) attempted a difficult t a s k with many inherent com- plications. It appears, however, t r a t the ideas behind t h i s work w e r e b a s e d on the e a r l y concept of the nature of C-S-H ( s e e 3 assumptions in f i r s t p a r t of paper). With the present knowledge (assumption I ) , which Kantro, Wiese, and Brunauer helped in a l a r g e m e a s u r e t o accumulate, it is c l e a r that the heat of solution m e a s u r e m e n t s should be reevaluated.
INTERLAYER WATER AND RELATED PROBLEMS Density Measurements
Assumption 2 p r e s e n t s a n important concept concerning interlayer water reentering D-dried material. The significance of t h i s concept h a s been emphasized in the l i t e r a - t u r e (2), and important questions concerning s u r f a c e - a r e a determinations by water and density determinations by l i m e - s a t u r a t e d solutions have been raised. If inter- l a y e r water r e e n t e r s the structure-and s e v e r a l r e s e a r c h e r s (14, 15, 19) now believe
- - -
that t h i s is what happens-measured densities obtained by pycnometric techniques would approach that of the individual l a y e r s , if the value of the density of interlayer water is known and included in the calculation. It h a s been assumed, however, thatthe l a y e r s completely collapse on D-drying, but this does not occur (20, - - 21). T h i s in- c o r r e c t assumption will l e a d to e r r o r s in e s t i m a t e s of a c-spacing o r density and of a c-spacing of higher hydrates (e.g., P - d r i e d specimens). The interlayer s p a c e is normally occupied by the maximum amount of hydrate water under normal conditions of concrete use, and s o porosity o r density calculations with the s p a c e included a s solid m a t t e r a r e most relevant. T h i s point will b e discussed in detail in a l a t e r section.
In an experiment by Brunauer, Kantro, and Copeland (4), the weighed D-dried s a m - ple was soaked in a bottle o r s i m i l a r a r r a n g e m e n t until the liquid was eventually brought to a c e r t a i n level, a f t e r which the container w a s weighed. By t h i s t i m e the interlayer water would a l r e a d y have r e e n t e r e d the sample, with the r e s u l t that the solid volume would appear low and the density too high; this is precisely what r e s u l t e d (4). If the interlayer water had r e e n t e r e d very slowly subsequent to the m e a s u r e m e n t s , a grad- ual i n c r e a s e in apparent density f o r both completely o r partially d r i e d s a m p l e s would have resulted. Some authors, however, r e p o r t e d a gradual d e c r e a s e in density when m e a s u r e m e n t s w e r e made in t h i s way on partially d r i e d samples, and they explained it by assuming gradual interlayer penetration (4). Some other explanation will have to b e found; p r o g r e s s i v e changing in the s t a t e a i d position of Ca++ ions between the l a y e r s is perhaps a solution.
T h i s author is not a w a r e of any evidence
I I 1 I I 1 I I I
I
work (8) h a s shown that this phenomenon is0
l o 20 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 r e l a t e d t o the r e e n t r a n c e of interlayer water.
that shows that water cannot r e e n t e r the s p a c e s
R. H . ( % I T h e numbered points a r e given in Table 1 and
show the length of t i m e the s a m p l e s w e r e r e - ~i~~~~ 1. lsotherrns for hydrated portland ce- tained a t each condition. T h e r e s u l t s c l e a r l y rnent pastes. show that not only had a l l the interlayer water
20 1 8 1 6 1 4 - 1 2 8 4 2
o
0 0 2 4 - X 3 2 2 - , 1 1 1 1 1 - A . W-C Ratlo 0 . 6 -,eqO
- -L H ' d
1'
L
/
- y e < - -0 1 - 4- / l o L = - - ) - p - 4 - / 0,' 3.?>7' --+,"go
P o ~ n t s e s t ~ m a t e d from - prevlous work -/
Measured - - B . W-C Ratlo 0 . 46i
//
between the C-S-H layers. In fact, much evi- dence e x i s t s t o the contrary. F i g u r e 1 shows recent work by this author on 0.6 and 0.4 water- cement r a t i o p a s t e s hydrated f o r 2.5 years. T h e s e s a m p l e s w e r e s t o r e d f o r m o r e than 2 and 4 months respectively a t 11 percent RH, w e r e then d r i e d in s t a g e s well beyond the D-dried position during a period of 40 days, and w e r e finally heated under vacuum t o 190 C. They w e r e then exposed to various humidities but always taken back t o 11 percent RH before being advanced t o a higher humidity.
T h e dashed lines shown in F i g u r e 1 illus- t r a t e the significance of returning t o 11 p e r -
-
cent RH and how t h e s e paths a r e r e v e r s i b l e (8).2 0 -
a
/
'
I
In an ideal adsorpiion system, a l l the numbered1 8 - points a t 11 percent RH should be identical, but
1 6 - in t h i s c a s e the position changes with each fur-
1 4 - t h e r advance of humidity. (An ideal adsorption
/
- uniquely defined by t e m p e r a t u r e and relative s y s t e m is one in which the s y s t e m can b e1 0 8 6 4 7 -
y
4.-3-e - d - k 70' - - 3*-/ d --4'
--
p r e s s u r e f o r constant surf a c e a r e a and other adsorbent p r o p e r t i e s in a l l but the p r i m a r y h y s t e r e s i s region. T h i s region r a r e l y e x i s t s below 35 percent RH and 11 percent RH should uniquely define such a system.) Previous
T A B L E 1
RESULTS O F T E S T S ON PORTLAND CEMENT PASTES HYDRATED FOR 2'/2 YEARS
W a t e r - C e m e n t Ratio 0.6 W a t e r - C e m e n t Ratio 0.4 Relative
Conditioii Humidity Final P e r c e n t Final P e r c e n t ( p e r c e n t ) T i m e Change Point on T i m e Weig,lt Change Point on
( d a y s ) F r o m F i g u r e 1 ( d a y s ) F r o m F i g u r e 1 D r y Dry S t o r e d 11 117 16.2645 12.33 1 56 18.6848 12.14 1 D r i e d i n c r e m e n t a l l y bevond D-dried condition l m m e r s e d in s a t u r a t e d Ca(OH )Z solution 11 aEstimated. b ~ a m p dry.
r e e n t e r e d the sample after exposure t o 85 percent RH but a l s o it had done s o progres- sively f r o m low relative humidities. It should b e mentioned that this r e s u l t i s exactly the s a m e as that obtained by Feldrnan (8) when vacuum balance techniques w e r e used and when the desiccator technique on the s a m e sample was used. The s a m e r e s u l t has been subsequently obtained on other s a m p l e s when even longer t i m e s of equilibra- tion w e r e used. In this c a s e a c l e a r differentiation of interlayer and adsorbed water was made by t h e r m a l analysis (DTA and TGA) (22).
-
Densitv Measurements and c - S ~ a c i n e
In the l a s t section it was suggested that both water surface a r e a and a c e r t a i n density measurement a r e in e r r o r f o r the s a m e reason; i.e., water reentering the interlayer s p a c e s was not taken into account. T h i s density value was used by Brunauer, Kantro, and Copeland (4) in 1958, however, with c e r t a i n assumptions t o calculate a c-spacing, and a value of
9.3
W
resulted. T h i s density value (2.86 g/cc) is much higher than any listed by Taylor (23, 24) on the relationship between calcium s i l i c a t e s and clay minerals.-
- In addition, Taylor l i s t s a much lower value (2.44 g/cc) f o r the density of C-S-H than that published in 1956 by Brunauer, Copeland, and Bragg (6). It should b e pointed out that a calculation of c-spacing f r o m density a s s u m e s that the m a t e r i a l is homogeneous in composition, is layered, and has a regular arrangement. As already discussed, this m a t e r i a l does not strictly conform in a t l e a s t two of t h e s e requirements-homogeneity of composition and regularity of arrangement. Thus, the calculation of the c-spacing must b e considered as yielding, a t best, only the average value of l a y e r separation. AS such it must s t i l l b e considered as useful; revised calculations will be made.A m e a s u r e d c-axis spacing of 9.3
i
i s obtained by dehydrating (heating t o 300 C) 11.3-8 natural tobermorite (25). Megaw and Kelsey (25) suggested that the packing of adjacent l a y e r s in the dehydr%ted products differed f r o m that in 11.3-i tobermorite; i n 9 . 3 4 tobermorite the r i b s of 1 l a y e r w e r e likely t o pack into the grooves of the next. Brunauer, Odler, and Yudenfreund (2) a s s u m e d that the s a m e thing o c c u r s when C-S-His D-dried; they s t a t e that "the l a y e r s stick t o each other with such f o r c e that even soak- ing in water does not s e p a r a t e the layers. Obviously, therefore, a t the relative humidi-
t i e s of 0.07 t o 0.33, used in the BET s u r f a c e a r e a determinations, water cannot e n t e r between the layers."
It a p p e a r s that the 9.3
i
value f o r C-S-H obtained by Brunauer, Kantro, and Cope- land (4) was approximately the thickness of the l a y e r s themselves, if the l a y e r s w e r e like tobermorite. T h i s led to the belief that the l a y e r s had completely collapsed. Re- s u l t s f r o m helium comparison pycnometry by this author (details t o b e published l a t e r ) have shown that the m e a s u r e d density v a r i e s directly with water-cement ratio. T h e density f o r the D-dried C-S-H, calculated f r o m hydrated C3S paste p r e p a r e d a t a water- cement r a t i o of 0.5, is approximately 2.25 g/cc. The r e s u l t s a l s o show that collapse on D-drying is not very great because the undried C-S-H at 11 percent RH has a den- s i t y of approximately 2.34 g/cc (this value being c o r r e c t e d f o r adsorbed water). The value of the D-dried s a m p l e would b e the higher if drying w e r e accompanied by com- plete collapse (20,- -
21). The d e g r e e of collapse did not compensate f o r the l o s s in weight due to hydration; thus, t h i s resulted in the lower density f o r the D-dried sample. T h e s e values c o r r e l a t e well with those published f o r various calcium s i l i c a t e s of the tobermorite group, where none exceeds 2.35 g/cc (23,- -
24).Several comments can be made concerning the following calculations:
1. It was a s s u m e d by Brunauer, Kantro, and Copeland (4) that the density of C-S-H did not v a r y with preparation o r Ca-Si ratio. T h i s is c o n t r a r y t o assumption 1, given e a r l i e r . The observed variation in density l e a d s t o the conclusion (assuming one can calculate c-spacing f r o m density) that c-spacing a l s o v a r i e s with preparation and with the water-cement ratio. The m e a s u r e d densities would give a n average c-spacing of 11.8
i
f o r D-dried C-S-H p r e p a r e d f r o m C3S paste a t a water-cement r a t i o of 0.5 T h i s is within the range of values found by Taylor (23) f o r artificial tobermorites. However, the reservations s t a t e d in the preceding concerning this calculation a r e s t i l l maintained.2. The collapse of a badly oriented and organized m a t e r i a l with varying amounts of Ca++ ions between the l a y e r s h a s been a s s u m e d (4) to b e s i m i l a r t o the collapse of natural tobermorite. It a p p e a r s that the l a r g e amount of Ca++ ions between the l a y e r s o r t h e i r poor orientation a r e responsible f o r preventing a g r e a t e r collapse. It is in- t e r e s t i n g to note that nonswelling clays like vermiculite, although not the s a m e s t r u c - t u r e a s tobermorite, do allow w a t e r to r e e n t e r between the l a y e r s a f t e r they have been strongly d r i e d (24). As h a s been shown by density and X - r a y measurements, such m a t e r i a l s s u f f e r g r e a t e r collapse than does C-S-H.
3. T h e high-density value of 2.73 g/cc obtained by Brunauer, Kantro, and Copeland (4) -
f o r the P - d r i e d sample was high f o r much the s a m e r e a s o n tkat the value obtained f o r the D-dried s a m p l e was high. A c-spacing of 10.2 was calculated on the b a s i s of this density. On i m m e r s i o n of a P - d r i e d s a m p l e in w a t e r during the c o u r s e of a density determination, one could expect that the r e m a i n d e r of the interlayer water rapidly enters. Thus, the m e a s u r e d density will be only somewhat l e s s than that of the l a y e r s themselves.
4. The reasoning by s o m e authors with r e g a r d t o the stoichiometry of C-S-H is
considered incorrect. In 1958 Brunauer, Kantro, and Copeland (4) stated,
". . .
that one molecule of Ca3Si05 r e a c t s with exactly t h r e e molecules of w a t e r and one molecule of fi-
Ca,Si04 with two molecules of water could not b e demonstrated in t h e present investigation. The r e a s o n f o r this is that a reliable method is lacking to distinguish quantitatively between adsorbed water and chemically bound water in tobermorite."No new method has been applied by Brunauer, Odler, and Yudenfreund (2) in t h e i r recent discussion of the F-S model t o s e p a r a t e the types of water. T h e original con- clusion that the chemical formula of P - d r i e d C-S-H was Ca3Si,07
.
254H20 is basedon the assumption that on reexposure to 33 percent RH neither the P-dried nor the D-dried s a m p l e s experience r e e n t r y of interlayer water. T h i s assumption h a s now been proved incorrect. Brunauer, Kantro, and Copeland (4) continued in their paper in 1958 that "
. . .
the molecular formula of the t o b e r m o r i t e s i n C-18 and D-43, c o r r e c t e d f o r adsorbed water, is Ca3Sia07. 2.54H20. It
is c l e a r that drying at a vapour p r e s s u r e g r e a t e r than 8 x 1 0 - ~ m m would have led to a higher water content. On the b a s i s of arguments advanced in an e a r l i e r paper, a s well a s on the b a s i s of the present r e s u l t s , it s e e m s reasonable t o suppose that in a saturated ca(OH)2 solution tobermorite con- tains 3 molecules of combined water." It is this author's opinion that the formula Ca3Si207 * 3Ha0 should b e considered a s not having been established; a sounder basedestimation can, however, be made.
It will f i r s t be shown that the a r e a of the internal plus external s u r f a c e s of D-dried C-S-H, usually taken a s 755 m2/g, is of the right o r d e r . This is the value generally assumed f o r one layer of C-S-H.
In a recent paper, Feldman (8) showed that the total interlayer water f o r a sample of hydrated portland cement was7.54 percent by weight of D-dried material, with the sample having a nitrogen a r e a of 30 m2/g. I£ it is assumed that the interlayer water
molecule c o v e r s 10.8 i 2 / m o l e c u l e on 1 surface, the internal a r e a is 274 x 2m2/g (i.e., 548 m2/g) and, if nitrogen m e a s u r e s the external a r e a correctly, the total a r e a
is thus 578 m2/g. If corrections a r e made f o r incomplete hydration, the equivalent total a r e a is thus 670 m2/g. If one a s s u m e s that completely hydrated Type LI portland cement is composed of 80 percent C-S-H (27) and a s s i g n s the a r e a of internal plus external surface of 755 m2/g to the
C-S- portion,
the expected value of surface a r e a would be 80 percent of 755 m2/g (i.e., 604 ma/g). T h i s a g r e e s f a i r l y well with the 670 ma/g figure when one considers that in hydrated portland cement some of the water generally t e r m e d "interlayer" may have come f r o m the aluminates and sulfo- aluminates.A f u r t h e r s e r i e s of calculations may b e used t o establish the stoichiometry and the calculated c-axis spacing of C-S-H derived f r o m C3S. Hydrated C3S pastes, when f i r s t D-dried f r o m about 12 percent RH by Helmuth (19), yielded a water content of approximately 28.4 percent of the ignited weight. ~ c z r d i n ~ to Brunauer, Kantro, and Copeland (4) and t o Feldman (8), a t 12 percent RH the sample contains approximately all the i n t e r l a y e r and 1 monolayer of adsorbed water. Hydrated C3S paste, containing C-S-H dehydrated to Ca3Si207
.
2H20 (approximately D-dried), contains 19.7 percent water based on the ignited weight. The difference between 28.4 and 19.7 percent (8.7 percent) is made up of the interlayer and the adsorbed water. F o r a surface a r e a of 73 m2/g determined by this author on 0.5 water-cement r a t i o paste with nitrogen ad- sorption, the equivalent value of a monolayer of water is 2.0 percent by weight, leaving 6.7 percent a s interlayer water. This corresponds t o 1.7 molecules p e r formula unit a t about 12 percent RH. T h i s gives a formula of Cas+,Si2O, ' 3.7H20 for t h i s C-S-Ha t 12 percent RH. F o r a molecule coverage of 10.8 i/molecule, the 6.7 percent inter- layer water is equivalent t o 244 x 2 = 488 ma/& of internal a r e a . Adding internal t o ex- t e r n a l a r e a previously calculated made a total a r e a of 561 m2/g. One g r a m of hydrated Ca3SiOs p a s t e on the ignited weight b a s i s contains 0.71 g of D-dried C-S-H, giving the expected value of 755
x
535 mZ. This c o m p a r e s well with the 561 ma in the preceding. When only 1 molecule of interlayer water p e r formula unit i s used f o r the calculation instead of 1.7 molecules, a value of only 357 ma/g is obtained a s the total surface area. (In the formula, x r e p r e s e n t s the variation that is normally found f r o m Ca-Si r a t i o of 3 to 2.)Assuming the composition a t 12 percent RH t o b e Ca3+,SiaO7
-
3.7Ha0, assuming, a s Brunauer, Kantro, and Copeland (4) did, that a unit cell contains a formula unit and that it is orthorhombic with a - = 5.59i
and b-
= 3.64i,
and using a value of 2.34 g/ccf o r density, one obtains the value of the a v e r a g e c-spacing of 12.4
a,
as opposed to 11.8 f o r the D-dried C-S-H p r e p a r e d f r o m C3S paste a t a water-cement r a t i o of 0.5. T h i s value of 12.4a
must b e r e g a r d e d as tentative f o r some assumptions that w e r e in the calculation. T h e preceding calculation of average c-spacing is s t i l l subject to the previously mentioned r e s e r v a t i o n s with r e g a r d t o homogeneity in spacing and composition.Another interesting point about hydrated C B paste was observed by Helmuth (19). After the paste was D-dried and reexposed to w a t e r vapor, the total water contencat
12 percent RH was approximately 25.5 percent o r 2.9 percent l e s s (on the ignited weight b a s i s ) than that found f r o m the desorption branch. When the paste was exposed to increasing humidities a s high a s approximately 100 percent RH and then returned to 12 percent RH, a l l the water initially p r e s e n t was regained. T h i s evidence, which
is s i m i l a r t o that f o r portland cement as shown in F i g u r e 1, shows clearly that the interlayer water had completely r e e n t e r e d the sample.
Phenomena Related t o Hydraulic Radius of Hydrated Portland Cement
Brunauer, Odler, and Yudenfreund (2) presented the calculations, based on the con- cept of hydraulic radius, as evidence against the F-S model. Table 1 in the paper by Brunauer, Odler, and Yudenfreund gives the hydraulic radius of the p o r e s not pene- t r a b l e by nitrogen a s being much l a r g e r than the diameter of t h e nitrogen molecule. F a c e d with the question of why nitrogen cannot e n t e r t h e s e pores, Mikhail, Copeland, and Brunauer (28) suggested that t h e s e p o r e s have necks s m a l l e r than the diameter of the nitrogenmolecule. T h i s conclusion was based on the assumption that the i n t e r - l a y e r water did not r e e n t e r t h e D-dried sample. Brunauer, Odler and Yudenfreund concluded that the values they derived in column 10 of Table 1 in t h e i r paper (2) f o r
the "internal" hydraulic r a d i u s a r e too l a r g e t o b e attributed t o w a t e r o c c ~inter- ~ ~ i ~ ~ layer spaces. T h i s author suggests that in r e f e r e n c e s t o interlayer spaces, however,
other calculations would have been m o r e appropriate. Because the a r e a of a sheet of C-S-H, according t o Brunauer, Kantro, and Copeland (4), is 755 m2/g, the interlayer a r e a would be 755 &Z and not
&,o
-
SNZ a s used by Brunauer, Odler, and Yudenfreund(2). If the figure is corrected f o r Ca(0H)a in the hydrated portland cement, the interlayer a r e a p e r g r a m would be approximately 600
-
SN2 and the hydraulic radius should b e cal- culated b y the expression VHZo-
VN2/600-
SN2.In this calculation the correction t o r c ~ ( O H ) ~ giving the amount of C-S-H gel in hydrated portland cement was due t o P o w e r s (27); this was approximately 80 percent of the hydrated cement. No c o r r e c t i o n was made t o 755 m2/g f o r the other components because they a r e considered to b e incorporated with t h e C-S-H gel. However, it is
c l e a r that c o r r e c t i o n s f o r other components would be minor and would not a l t e r t h e r e s u l t s significantly. Table 2 gives calculations made according t o this mode f o r hydraulic radius of the p a s t e s cited by Brunauer, Odler, and Yudenfreund (2). -
T A B L E 2
SURFACES, POROSITIES, AND HYDRAULIC RADII O F PORTLAND CEMENT PASTES r l r I'xz W a t e r - C e m e n t S ~ 2 V 9 3 Vv, VMZ3 - Va, B r u n a u e r C o r r e c t e d R a t i o (rn2/g) 600 - S,,, (rnl/g) (rnl/g) ( m l / g ) (4) (9 (1) (2 ( 3 ) (4) (5) (6) (7 (8) -- - 0.35 56.7 543.3 0.1264 0.0748 0.0516 3.4 0.95 0.40 79.4 520.6 0.1776 0.1059 0.0717 5 . 8 1.38 0.50 97.3 502.7 0.2615 0.1792 0.0823 8.5 1.64 0.57 132.2 467.8 0.3110 0.2493 0.0617 10.0 1.32 0.10 139.5 460.5 0.4008 0.2758 0.1250 20.8 2.78 Montrnorillonite 1 5 735a - - 0.0964 - 1.26
Column 7 gives the calculations f r o m Table 1 in Bruno, Odler, and Yudenfreund's paper (2) and column 8 gives t h e suggested c o r r e c t e d values. Also included is a cal- c u l a t i o n f o r montomorillonite, a well-known l a y e r - s t r u c t u r e d clay. T h e s i m i l a r i t y between the average of the f i r s t 4 pastes, 1.32
.i,
and montmorillonite, 1.26i,
is v e r y significant. T h e 0.7 water-cement r a t i o paste gives a value of 2.78 (col. 8) which is much lower than that given in column 7. T h i s author believes, however, that the value in Table 1 (2) VHao-
VNa f o r t h i s paste is much too high. The values of &20 and SN2 f o r water-cement r a t i o s of 0.57 and 0.70 in the s a m e table a r e almost the s a m e , and t h e r e is no t r e n d of VHz0-
VN2 increasing with water-cement ratio. F u r t h e r m o r e , t h i s author h a s made determinations on 14 different preparations at a water-cement r a t i o of 0.8 and h a s found that f o r t h e s e the value f o r V,,-
VN2 varied between 0.06 and 0.08. Thus, it is thought that the hydraulic radius of the water-cement ratio 0.7 paste would a l s o be s i m i l a r t o that of montmorillonite. T h e hydraulic radius, then, gives f u r t h e r supporting evidence of the interlayer nature of the so-called g e l water.LENGTH- AND WEIGBT-CHANGE ISOTHERMS T h e Question of D-Drying
The w r i t e r h a s now cited considerable evidence t o indicate that the D-dried s a m p l e s do allow water t o r e e n t e r between the l a y e r s . It h a s been argued (2), however, that the s a m p l e s discussed in Feldman's r e c e n t work (8) w e r e not p r o p e r l y ~ - d r i e d and that t h i s fact explains his results. T h e following points should c l e a r l y establish that the s a m p l e s w e r e D-dried.
1. The amount of water removable f r o m a s t a t e in equilibrium with a relative humid- ity of 11 percent was determined by conventional D-drying. It was then found that heat- ing replicate s a m p l e s a t 85 C f o r 3 hours in a t h e r m a l balance under high-vacuum conditions gave a n equivalent weight loss. One sample was heated a t 95 C f o r 3 hours and a t 97 C f o r 2 hours m o r e without any m a j o r change in the weight loss.
2. The vapor p r e s s u r e a t the "dry" condition w a s m e a s u r e d with a sensitive Bour- don gage of 1p repeatability. It indicated a p r e s s u r e of l e s s than 1p.
3. Helmuth (19) on measuring i s o t h e r m s of hydrated C3S paste d r i e d the s a m p l e s (in the f o r m of 1-m% thick specimens) f o r 3 months by conventional means. His r e s u l t s f o r both sorption and length-change i s o t h e r m s w e r e qualitatively and quantitatively s i m i l a r t o those of Feldman (8); they showed s i m i l a r h y s t e r e s i s , complete regain of i n t e r l a y e r water, and i r r e v e r s i b i l i t i e s of length and weight change.
4. Brunauer, Odler, and Yudenfreund (2) a l s o argued that the nitrogen a r e a s pub- lished by the p r e s e n t w r i t e r (8) s u g g e s t e d t h a t h i s s a m p l e s were not D-dried. In point of fact, the paste s a m p l e hydrated a t a water-cement r a t i o of 0.5 was D-dried by the conventional method f o r determining s u r f a c e a r e a by nitrogen adsorption. Then the s a m p l e w a s heated t o progressively higher t e m p e r a t u r e s (up t o 400 C) and the a r e a m e a s u r e d a t each t e m p e r a t u r e d e c r e a s e d f r o m 47 t o 42 m2/g. Tomes, Hunt, and Blaine (29)) working with p a s t e s that w e r e 50 percent hydrated a t a water-cement r a t i o of 0.5, obtained s u r f a c e a r e a s by nitrogen adsorption of 10 t o 25 m2/g, a maximum s u r f a c e a r e a of 50 m2/g f o r complete hydration; a value of 97 m2/g w a s obtained by Mikhail, Copeland, and Brunauer (28)
-
and republished by Brunauer, Odler, and Yudenfreund (2).It is not being suggested h e r e that the value of 97 m2/g is incorrect but r a t h e r that nitrogen a r e a can be affected by s e v e r a l factors. T h e s e may include water-cement ratio, admixture dosage, and perhaps alkali and sul£ate content. T h i s suggests the importance of nitrogen a r e a and of i t s p r o p e r interpretation. With t h i s valuable tool one can detect the sensitivity of hydrated portland cement t o various agents and
understand i t s variability in relation t o the mechanical and physical p r o p e r t i e s of the hydrated cement. Certain t r e n d s in p r o p e r t i e s of hydrated portland cement a r e func- tions of water-cement r a t i o and admixture addition. It is interesting t o observe that a s water-cement r a t i o i n c r e a s e s the nitrogen a r e a i n c r e a s e s , the Ca-Si r a t i o d e c r e a s e s , and the f i r s t drying shrinkage and density increase. L a r g e dosages of s o m e admix- t u r e s (e.g., calcium lignosulfonates) enhance the effect of high water-cement ratio. T h e nitrogen a r e a r e f l e c t s t h e change in Ca-Si r a t i o and predicts differences in f i r s t drying-shrinkage properties.
Scanning Loops
Data used in developing the F-S model (1) indicate that interlayer w a t e r r e e n t e r s D-dried s a m p l e s in increments as t h e relative humidity they a r e exposed t o increases. When s o m e water r e e n t e r s t h e interlayer s p a c e s at, f o r example, 30 percent RH, it goes on s i t e s that will retain i t t o a v e r y low RH. Thus, one obtains a n i r r e v e r s i b i l i t y in the isotherm, a scanning loop (8). T h i s is probably caused by the collapsed l a y e r s mechanically blocking the water f r o m entry t o high-energy s i t e s ; the l a y e r s , however, subsequently reopen. One may r e f e r t o this a s a changing nature of the adsorbent. One of t h e assumptions made in adsorption equations is that the adsorbent s u r f a c e r e m a i n s constant qualitatively and quantitatively. In contrast, the water-scanning i s o t h e r m s of weight and length change showed that the interlayer water r e e n t e r s a t very low humidities and right through the BET range. Naturally then, any calculation of the monolayer capacity using this isotherm will b e incorrect. A s i m i l a r difficulty o c c u r s in a n attempt to calculate t h e s u r f a c e a r e a of s o m e montmorillonites f r o m water vapor adsorption.
In addition, above 7 percent RH a quantitative separation of the interlayer and physi- cally adsorbed water was made through interpretation of the scanning isotherms. It was a l s o made c l e a r that, even below 7 percent RH, a considerable portion of the water put on by t h e s a m p l e was interlayer. T h e u s e of a t r i a l - a n d - e r r o r procedure o r , alternatively, the assumption that the nitrogen a r e a was approximately c o r r e c t h a s shown that (a) the Gibbs and Bangharn equations (30) properly described the length change and sorption data f o r physical adsorption; andTb) calculation of Young's modu- l u s of t h e solid m a t e r i a l f r o m the length-change adsorption data yielded a value of 4.35 x
lo6 lb/in.2, which
is v e r y s i m i l a r to that obtained by d i r e c t measurement of E as a function of porosity and extrapolation t o z e r o porosity, 4.5 xlo6 lb/in.'
The l a t t e r work was done by Helmuth and T u r k (31) and they concluded that the interlayer s p a c e s a r e "gel pores." In t h e i r extrapolation they considered the porosity t o b e that obtained by w a t e r saturation methods, not recognizing that the water r e e n t e r e d be- tween the l a y e r s causing a higher porosity. Soroka and S e r e d a (32) confirmed the work of Helmuth and T u r k and made a s i m i l a r extrapolation. ~ e r b e c k and Helmuth (15) r e a s s e s s e d this work. They then c a m e to the conclusion that gel p o r e s w e r e i n t e r l a y e r spaces, and s o t h e i r new extrapolation excluded t h e s e spaces. Brunauer, Odler, and Yudenfreund (2) r e f e r to the work of Soroka and S e r e d a (32), s t a t e that "Feldman r e - jects the values of h i s colleagues," and find a n inconsistency in this. Subsequent t o t h e submission of the Soroka and S e r e d a paper (32), this author (8) found that the total volume of i n t e r l a y e r w a t e r derived by c a l c u l a t i o ~ f r o m scanningTsotherms was ap- proximately equal t o t h e difference between the total volume of w a t e r sorbed and the total volume of nitrogen o r methanol, a s given by the following:v
- (interlayer water)(,,
,)
-
(,,2 or methanol) -Subsequently, this author obtained helium comparison pycnometry data (21) - indicating that helium occupied essentially the s a m e volume a s methanol.
When the physically adsorbed w a t e r is deducted f r o m the observed adsorption iso- t h e r m , one obtains a n i s o t h e r m showing how the i n t e r l a y e r w a t e r r e e n t e r s a s a function of RH. T h i s enabled Feldman and S e r e d a t o propose the model that e m p h a s i z e s the inter- relationship of E, ~ w / w , A L / L , and RH (1). -
Reversibilitv and Eauilibration T i m e
T h e question of r e v e r s i b i l i t y is always r e l a t e d t o that of equilibration time. If weeks w e r e allowed f o r equilibration, months o r y e a r s could b e suggested if one did not wish t o accept t h e data. In the following p a r a g r a p h s , data cited by t h i s author (8) a r e u s e d to counteract t h i s type of argument. In t h e s e p a r a g r a p h s a l s o is a substantiation of the conclusion that t h e r e a r e 2 p r o c e s s e s o c c u r r i n g simultaneously. One is essentially in thermodynamic equilibrium with the water-vapor p r e s s u r e and involves adsorption on the s a m e s u r f a c e s on which nitrogen adsorbs. T h i s o c c u r s f a i r l y rapidly and is r e p r e - sented by the scanning loops. T h e o t h e r p r o c e s s involves intercalation of t h e l a y e r s and s t r o n g attachment to internal surfaces. T h e l a t t e r p r o c e s s is slow and does not r e p r e s e n t a path of thermodynamic equilibrium and is not r e v e r s i b l e . At lower hu- midities (below 50 p e r c e n t RH), the p r o c e s s , t o a l l p r a c t i c a l p u r p o s e s , c e a s e s a t the various RH steps. T h e s y s t e m is not in "thermodynamic" equilibrium with the r e l a - t i v e vapor p r e s s u r e a t those points.
1. T h e experimental points w e r e v e r y closely spaced. When the p r e s s u r e was changed by a s m a l l increment, a v e r y rapid i n c r e a s e of weight took place and was followed by a v e r y slow r a t e . Equilibrium w a s judged not only by weight change but by p r e s s u r e change, p r e s s u r e being m e a s u r e d with a sensitive Bourdon gage with r e - peatability of 1 p. A p r e s s u r e change of l e s s than 10 p a day w a s used a s t h e p r e s s u r e c r i t e r i o n f o r equilibrium. Below 50 p e r c e n t RH on the adsorption loop, 2 t o 3 d a y s p e r closely spaced point w e r e adequate t o m e e t t h i s c r i t e r i o n
2 . F i g u r e 1 in F e l d m a n ' s paper (8) shows i s o t h e r m s and numbered scanning loops. Loops 2, 5, 6, 7, and 8 show c l e a r l y h o w , a f t e r desorption on the loop, the readsorption m e e t s the exact point on the main c u r v e w h e r e the loop commenced; in the c a s e of loop 7 the complete cycle took 3% weeks.
3. On the main desorption curve, loops 9 and 10 a l s o r e t u r n exactly through the point they s t a r t e d f r o m 1 week e a r l i e r . If they w e r e s o f a r removed f r o m an equilib- r i u m position, it s e e m s unlikely that they would have rejoined; instead the point would have been well below a t the s a m e p r e s s u r e on the r e t u r n of the loop.
4. It was found that, in a p r e l i m i n a r y experiment on the desorption c u r v e using 7 days p e r point, t h e r e w a s no change a f t e r 1 day of using high-vacuum conditions. T h e data shown i n F i g u r e 1 and given in Table 1 of t h i s p a p e r support t h i s indication; f r o m 100 percent RH t o 11 percent RH, no f u r t h e r change w a s observed beyond t h e f i r s t m e a s u r e m e n t taken a f t e r 2 weeks. F u r t h e r conditioning of 1% months a t this point produced no f u r t h e r change.
5. It is c l e a r f r o m the length-change data that the 2 types of water separated by scanning loops a r e completely different and that t h e ( A ~ / ~ ) / ( A W / W ) relationship f o r the i n t e r l a y e r w a t e r is 4 t i m e s that f o r the physically adsorbed water. T h e length change due t o physically a d s o r b e d w a t e r is governed by the Gibbs and Bangham equa- tions. When the i n t e r l a y e r w a t e r r e e n t e r s , a considerably l a r g e r expansion p e r unit weight of adsorbed w a t e r than that predicted by t h e s e equations m u s t be expected. Work
in t h e s a m e p a p e r by Feldrnan (8), using methanol a s adsorbate, shows that t h e r e is also i n t e r l a y e r penetration by methanol, although not n e a r l y t o the s a m e extent a s by water. C o n t r a r y t o what is generally felt about methanol and length change c a u s e d by i t s s o r p - tion on hydrated portland cement, however, the (aa/a)/(Aw/w) is l a r g e r f o r the inter-
l a y e r penetration of methanol than of water. This, of c o u r s e , is not surprising on the b a s i s of molecular s i z e s .
6. T h e i s o t h e r m s of both length and weight change f o r water sorption on hydrated portland cement have been m e a s u r e d with g r e a t precision and detail (8) in a high- vacuum apparatus using exceedingly sensitive measuring devices. w a t e r i s o t h e r m s have been previously published by many authors (33,
- - -
34, 35) including P o w e r s and Brownyard (36), and recently Helmuth (19), Mikhail, Kamel, and Abo-el-enein (37) with none o f t h e m exhibiting closing secondary h y s t e r e s i s loops (neither does t h e isotherm shown in F i g u r e 1 of this paper).The e a r l y work of P o w e r s and Brownyard (36) is almost completely devoid of de- sorption i s o t h e r m s although this is not realized. T h e r e a r e , however, 2 such c u r v e s and the following s t a t e m e n t s a r e made:
As shown in F i g u r e 2-6, the adsorption and desorption c u r v e s coincided only a t p r e s s u r e s below 0.10 ps. (As a m a t t e r of fact, i t is not c e r t a i n that the c u r v e s coincided over this range, but i t s e e m s probable that they did so. P o w e r s and Brownyard then show (in essence) s o m e scanning iso- t h e r m s and continue.) Although the phenomenon has not been investigated extensively h e r e , t h e r e is little r e a s o n t o doubt that portland cerr~ent p a s t e s a l l show essentially t h e behaviour described above. T h i s m a t t e r of hystere- sis is significant.
. . .
At any r a t e the whole phenomenon cannot b e under- stood until t h e s e loops can b e adequately interpreted. However, practically all the m e a s u r e m e n t s r e p o r t e d in t h i s paper w e r e of adsorption only. T h e r e f o r e , the interpretation of t h e adsorption c u r v e i s the only p a r t of the problem that can b e considered here.It is now c l e a r that without complete understanding of t h e s e loops the adsorption curve could not be interpreted either.
Inaddition, in the workby P o w e r s andBrownyard, t h e point a t approximately 10 p e r - cent RH on f i r s t drying was reattained a f t e r f u r t h e r drying and a subsequent cycle of wetting and redrying t o the above humidity. T h i s m e a n s that a l l t h e water, including the interlayer water that had been removed, r e e n t e r e d during rewetting.
Helmuth (19) D-dried f r o m low humidities continually f o r 3 months and, in his work a s stated a l l t h e interlayer water a l s o returned. This, i t must b e reempha- sized, is a c r u c i a l point a s h a s been pointed out by others (2).
Helmuth's r e s u l t s (19) on CsS p a s t e contain a f u r t h e r interesting point. T h e desorp- tion isotherm a p p e a r e d o rejoin in t h e p r i m a r y h y s t e r e s i s region a t high humidities, but a s desorption continued t h e r e r e a p p e a r e d a v e r y l a r g e secondary h y s t e r e s i s equal in magnitude t o that of t h i s author's at t h e lower humidities. T h e preceding behavior is probably related t o the p r i m a r y hysteresis and may involve recrystallization of C a ( 0 ~ ) ~ and a changing of the p o r e s i z e , shape, and distribution. T h i s might explain the unpublished work of J. Hagymassy r e f e r r e d to by Brunauer, Odler, and Yuden- freund (2).
~ i k h a i l , Kamel, and Abo-el-enein (37) have recently published water i s o t h e r m s on various cement hydration products. ln<very c a s e l a r g e h y s t e r e s i s loops w e r e ob- tained without any closure. Mikhail, Kamel, and Abo-el-enein found that only 48 hours w e r e n e c e s s a r y between s u c c e s s i v e measurements. On s a m p l e s p r e p a r e d in paste f o r m , Mikhail s t a t e s that 12 days should b e allowed between measurements. T h e ex- perimental points, however, a r e spaced quite f a r a p a r t , e.g., f r o m 15 to 35 percent RH. He a l s o s t a t e s , "Desorption was then c a r r i e d down to extremely low relative p r e s s u r e s . The sample was then exposed t o out-gassing a t 30°C f o r a period of 30 hours, t o remove a l l the adsorbate and the sample weight was brought back to i t s original value."
7. Numerous data have been compiled by t h i s author s i n c e the International Sympo- s i u m work (8). T h e data w e r e obtained a f t e r allowing much longer t i m e s f o r equilib- r i u m (in t h e o r d e r of months) in both high-vacuum a p p a r a t u s and in d e s i c c a t o r s and by using the s a m e s a m p l e s . Some of the data a r e shown in F i g u r e 1 and given in T a b l e 1. They have confirmed t h e existence of scanning loops, t h e equilibrium of sorption points, and t h e complete r e e n t r y of i n t e r l a y e r w a t e r a f t e r v e r y s e v e r e drying and a f t e r a cycle of rewetting and drying t o 11 p e r c e n t RH.
8. T h e accepted method f o r D-drying h a s been worked out a ~ d published by Copeland and Hayes (38) who s t a t e that it t a k e s 4 t o 7 days f o r equilibrium. T h i s involves drying f r o m fairly<et conditions t o r e m o v a l of both the tightly held first l a y e r and t h e even m o r e tightly held i n t e r l a y e r w a t e r f r o m the v e r y n a r r o w s p a c e s . T h e s l o w e r - t h a n - n o r m a l t i m e s r e q u i r e d f o r equilibrium of w a t e r during t h e adsorption s t a g e is prob- ably due t o t h e lengthy p r o c e s s of reopening t h e l a y e r s .
NEW EXPERLMENTAL EVIDENCE
Recently t h i s author h a s done a n e n t i r e l y new type of work (20, 21, 22) that not only
- - -
provides f u r t h e r evidence f o r t h e F-S model but a l s o provides powerful new techniques t o study hydrated cement. A few of t h e r e s u l t s will b e briefly discussed.1. When w a t e r is removed f r o m C-S-H m a t e r i a l s , t h e p r i m e concern is what hap- pens t o the s p a c e s vacated by t h e w a t e r and what happens t o t h e solid. A method of studying t h e spacing i s t o m e a s u r e r a t e s of diffusion of helium g a s ( a s m a l l atom) into them (20). When hydrated portland c e m e n t equilibrated f o r s e v e r a l months at 11 p e r c e n t R ~ w a s exposed t o helium, helium v e r y quickly e n t e r e d t h e p o r e s of even 20 radius. When t h e g a s w a s c o m p r e s s e d t o 2 a t m o s p h e r e s , r a t e c u r v e s could b e m e a s u r e d f o r helium diffusing into t h e vacated s p a c e s . As w a t e r w a s r e m o v e d in- c r e m e n t a l l y f r o m t h e s a m p l e , t h e diffusion r a t e and absolute quantity a t e a c h w a t e r content i n c r e a s e d a t f i r s t ; but a s m o r e w a t e r w a s removed, the r a t e d e c r e a s e d al- though the quantity continued t o i n c r e a s e . Finally, t h e quantity a l s o d e c r e a s e d , and a t D-dry conditions the diffusion r a t e was v e r y low. T h e s e r e s u l t s c a n b e s t be ex- plained by t h e collapse of l a y e r s in the s a m e m a n n e r a s t h e F - S model h a s sug- g e s t e d (1). On readsorption of w a t e r , t h e helium diffusion r a t e again increased. After t h e s a m p l e w a s exposed t o high humidities, a l l t h e i n t e r l a y e r w a t e r had r e e n t e r e d
(diffusion e x p e r i m e n t s w e r e p e r f o r m e d at 11 p e r c e n t RH), and t h e r a t e c u r v e s w e r e s i m i l a r t o the c u r v e s obtained f o r t h e s a m p l e a t t h e beginning of the experiment. T h e s e r e s u l t s indicate t h a t t h e l a y e r s had reopened and that i n t e r l a y e r w a t e r had r e e n t e r e d ; if it had not, the v e r y low diffusion r a t e observed at t h e D - d r y condition would have r e m a i n e d the s a m e .
2. Density m e a s u r e m e n t s (21) obtained b y a helium penetration technique f r o m hydrated portland c e m e n t p r e p a r e d a t w a t e r - c e m e n t r a t i o s of 0.4 t o 1.0 showed that t h e computed densities of C-S-H g e l v a r y with water-cement r a t i o f r o m approximately 2.30 t o 2.18 g/cm3. F o r w a t e r - c e m e n t r a t i o s of l e s s than 0.6, the density d e c r e a s e d with d e c r e a s i n g w a t e r - c e m e n t ratio. B e c a u s e Ca-Si r a t i o and nitrogen s u r f a c e a r e a v a r y with w a t e r - c e m e n t r a t i o , one might reasonably expect changes in density and d e g r e e of collapse.
3. M e a s u r e m e n t of solid volume and length simultaneously a s a function of w a t e r content on drying t o the D-dried position and on rewetting h a s enabled a n independent calculation of t h e monolayer capacity f o r w a t e r t o b e made. On the assumption that
w h e r e
av/v
= r e l a t i v e change in v o l u n ~ e of solid p h a s e plus a d s o r b e d phase,~ a / a
= e x t e r n a l length change,a w = change in volume of a d s o r b e d w a t e r , and V = volume of solid,
it w a s found that t h e r e s u l t s f o r D-dried s a m p l e s yield a s u r f a c e a r e a varying only by about 15 p e r c e n t f r o m the r e s u l t obtained by nitrogen adsorption. R e s u l t s a l s o sug- g e s t e d that f i r s t D-drying r e d u c e s the s u r f a c e a r e a of t h e hydrated portland cement.
T h i s l a s t group of e x p e r i m e n t s (20, - - 2 1) p r e s e n t s evidence different, a n d p e r h a p s in a s u p e r i o r f o r m , f r o m that obtained f r o m conventional i s o t h e r m s . T h e l a t t e r ex- p e r i m e n t s indicate how much w a t e r e n t e r e d o r left t h e s p e c i m e n ; but in t h e s e new experiments, a s in length change studies, information is gained a l s o about the effect of the r e m o v a l of t h e w a t e r on the s o l i d body. Thus, i t is possible t o draw conclu- s i o n s a s t o w h e r e t h e w a t e r was likely t o have c o m e f r o m , the n a t u r e of the s p a c e s
it occupied, a n d its r o l e in t h e s t r u c t u r e of the solid.
4. T h e r m a l a n a l y s i s both DTA and TGA (22) w e r e p e r f o r m e d on s a m p l e s equili- b r a t e d a t a r e l a t i v e humidity f o r lengths of t i m e , in the o r d e r of months in d e s i c c a t o r s , and a t r e l a t i v e humidities s i m i l a r t o those r e p o r t e d h e r e f o r the i s o t h e r m s . It w a s found t h a t i n t e r l a y e r w a t e r and its r e e n t r y could be c o r r e l a t e d t o a n endothermic ef- f e c t a t 90 t o 105 C, and the physically a d s o r b e d w a t e r t o a n effect a t 65 t o 80 C. T h e r e s u l t s c o n f i r m e d the f a c t that 1 1 p e r c e n t i-2H w a s a nonunique s t a t e and a l s o confirmed the conclusions in t h e previous section concerning scanning loops, equilibration, and h y s t e r e s i s .
ACKNOWLEDGMENT
T h e author w i s h e s t o acknowledge the valuable d i s c u s s i o n s had with V. S. Ramachand- r a n and P. J. S e r e d a , and t h e e x p e r i m e n t a l work done by S. Dods. T h i s p a p e r is a contribution of the Division of Building R e s e a r c h , National R e s e a r c h Council of Canada, and i s published with the approval of the D i r e c t o r of t h e Division.
REFERENCES
1. Feldman, R. F., and S e r e d a , P. J. A Model f o r Hydrated P o r t l a n d Cement a s De- duced F r o m Sorption-Length Change and Mechanical P r o p e r t i e s . M a t k r i a w e t Constructions, Vol. 1, No. 6, 1968, pp. 509-520.
2. B r u n a u e r , S., O d l e r , I., and Yudenfreund, M. The New Model of Hardened P o r t l a n d Cement P a s t e . Highway R e s e a r c h R e c o r d 328, 1970, pp. 89-107.
3. Feldman, R. F., and S e r e d a , P. J . Discussion of T h e New Model of Hardened P o r t - l a n d Cement P a s t e . Highway R e s e a r c h R e c o r d 328, 1970, pp. 101-103.
4. B r u n a u e r , S., Kantro, D. L., and Copeland, L. E. T h e Stoichiometry of t h e Hydra- tion of p-Dicalcium Silicate and T r i c a l c i u m Silicate a t Room T e m p e r a t u r e . J o u r . of Amer. Chem. Soc., Vol. 80, No. 4, 1958, pp. 761-767.
5. Kalousek, G. L. Fundamental F a c t o r s in the Drying Shrinkage of Cement Block. ACI J o u r . P r o c . , Vol. 26, 1954, pp. 233-248.
6. B r u n a u e r , S., Copeland, L. E., and Bragg, R. H. T h e Stoichiometry of t h e Hydra- tion of T r i c a l c i u m Silicate a t Room T e m p e r a t u r e : P a r t 2, Hydration in P a s t e F o r m . J o u r . of Phys. Chem., Vol. 60, 1956, pp. 116-120.
7. Feldman, R. F., and S e r e d a , P. J. Sorption of W a t e r on Bottle-Hydrated Cement. J o u r . Appl. Chem., Vol. 14, 1964, pp. 87-93.
