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Moisture Sorption of Building Materials
Ser THl N21t2 n.. 2l+2 c . 2 BLDG
NATIONAIJ RESEARCH COUNCIL OF. CANADA DIVISION OF BUILDINC RESEARCH
MOTSTURE SORPTION OF BUILDING MATERIAI.S by
T. Z. Harmatby
A N A L Y Z E D
Technical Paper No. 242 of the
Division of Building Research
O T T A W A March 7967
MOISTURE SORPTION OF BUILDING MATERIALS by
T . Z . H a r r n a t h v
Moisture affects the perforrrrance of buirding elernente
both in norrnal service and under unusual circurnstances such
. as fire. The rnagnitude of this effect is closely related to the
arnount of rnoisture and, in turn, to the sorption characteristics
of the rnaterials. Although sorption characteristics can be
deterrnined frorn sirnple .xp.ti,,'ents (for example, References
(l) and (2))' it is often desirable to have at least an estirnate of
t h e s e c h a r a c t e r i s t i c s a t h a n d .
rn this paper solne experirnental data will be presented that may facilitate the estirnation of sorption characteristics
of building rnaterials. rt will also be shown how the basic laws
of adsorption can be trtilized to calculate the arnount of rnoisture
that these rnaterials can hold in equilibrium with a certain
environrnent. (Nornenclature is listed.at the end of the paper. )
ADSORPTION
N o n - r n e t a l l i c s o l i d s , a s a r u l e , c o n t a i n r n o r e o r l e s s
r a n d o r n l y d i s p e r e e d v o i d spaces called pores. Because of these void spaces the true volume of the solid is less than its exterior volurne, and its effective surface is larger than its exterior s u r f a c e .
All solids have the ability to capture rnorecures frorn the s u r r o u n d i n g g a s e o u s p h a s e . T h e p r o c e s s of capturing gaseous rnolecules is called adsorption (this word is sornetirnes used in a r n o r e r e s t r i c t e d s e n s e ) , and the participants in the process, the solid and the gas rnolecules (when attached to the solid), are
c a l l e d a d s o r b e n t a n d a d s o r b a t e , respectively. B e c a u s e i t i s a t
the surface of the solid that adsorption takes place, the arnount of a d s o r b e d g a s b e c o r n e s n o t i c e a b l e only if the solid possesses large effective surface areas; in other words, if the solid is a porous
rnaterial. Besides the specific surface (effective surface area
per unit mass of solid) and the affinity between solid and gas, the arnount of adsorbate taken up by unit rnass of solid was found to depend on the ternperature and the pressure of the adsorbate. Thus
2
-To deterrnine the explicit forrn of this equation for a certain adsorbent-adsorbate systern one can plan the experi-rnents in two different ways. one can keep the ternperature constant and vary the pressure, or keep the pressure constant and vary the ternperatureo with the first procedure, adsorption isotherrns,
a = f ( p ) T = c o n s t with the second, adsorption isobars
a = f ( T ) p = c o n s t ( 3 ) are obtained. It is often advisable to replot the experirnental
r e s u l t s a s a d s o r p t i o n i s o s t e r e s , eince these plots can be utilized for the calculation of the heat of adsorptionn The adsorption isosteres are generally werl approxirnated by the following equation!
p = g e x p a = const
(4)
which can be derived frorn the crausius-clapeyron equation with certain sirnplifying assurrrptions, and is valid within rnoderate ternperature intervals (say 100 c degl. According to Equation (4! a plot of log p against r/r rcr a = const is a straight line with a slope -0.4343 Q/n. As the heat of adsorption, e, is a
function of. zt the lines forming the farnily of the log p versus l / T i s o s t e r e s a r e n o t e x a c t l y p a r a l l e l ( s e e Fig. ld|.
rt can be shown (l) trrat adsorption is always an exotherrnic Process, in other words, that it is always accompanied by evo-lution of heat. Because of the exotherrnic nature of the process, the value of a (at equilibrium) must decrease as the ternperature increases, according to the Lechatelier-Braurr principle.
The usual way of evaluating the adsorption characteristice of an adsorbent-adsorbate systern is by an experirnental study of its isotherrns. Two very cornrnon types of adsorption isotherrns are, shown in tr'igure 2, curve r is typical of gases above their critical ternperature. The asyrnptote to the curve generally corresponds to the value of a at a unirnolecular coverage of the adsorbent surface. The fixJion of the gas rnolecules on the solid surface takes place by true adsorption, i. e. by adsorbent-adsorbate interaction. The surface free energy (rsurface tensionrr due to unbalanced surface forces) of the solid is reduced by the
(zl
3
-c a p t u r e o f g a s m o l e -c u l e s ; t h u s a d s o r p t i o n i s a s p o n t a n e o u s p r o c e s s .
F o r v a p o u r s ( g a s e s b e l o w their critical ternperature) s - s h a p e d i s o t h e r r n s , l i k e curve Ir in Figure ?, are probably the rnost corrlmono The sirnilarity of the low-pressure
portions of curves r and rr suggests that up to a certain p r e s s u r e t h e f i x a t i o n of adsorbate rnolecules on the solid s u r f a c e t a k e s p l a c e h e r e , toorbytrue adsorption. T h e c o n v e x p o r t i o n o f t h e c u r v e at higher pressures is the result of a p h e n o r n e n o n c a l l e d capillary condensation. Since this process i s n o t b r o u g h t a b o u t b y adsorbent-adsorbate interaction, it c a n b e r e g a r d e d a s adsorption only in the loose sense of the w o r d .
The peak of the adsorption isotherrns of vapours g e n e r a l l y r e p r e s e n t s the condition of cornplete fllling of the e f f e c t i v e p o r e s p a c e b y the condensed adsorbate, and is r e a c h e d w h e n t h e p r e s s u r e of the adsorbate is equal to its s a t u r a t i o n p r e s s u r e . B e c a u s e t h e s a t u r a t i o n p r e s s u r e is the h i g h e s t p r e s s u r e a t w h i c h the adsorbate can exist in gaseous s t a t e , i t i s c u s t o r r r a r y t o r e l a t e all lower pressures to the s a t u r a t i o n p r e s s u r e a n d . to think in terrns of relative pressure expressed as p/po. (For water the terrn relative hurnidity is u s e d f o r t h e s a r r r e expression. )
TRUE ADSORPTION
The concave portion of the adsorption isotherms of vapours, representing the capturing of adsorbate rnolecules by t r u e a d s o r p t i o n , c a n be satisfactoriry described by the Brunauer-E r n r n e t t - T e l l e r ( b r i e f l y B E T ) E q u a t i o n ( 1 , 3):
c(p/po)
F
(n/no) I tl - (n/eo) + c(p/pJ
This equation is valid up to about p/p = 0.4. With sorne r n o d i f i c a t i o n i t a l s o d e s c r i b e s satisfa8torily the low-pressure p o r t i o n o f a d s o r p t i o n isotherrns of gases. For gases, however, the use of the sirnpler Langrnuir equation is appropriate. Equation (5) contains two constants,"r' and c, which can be deterrnined
a a
lTr
frorn experirnental of Equation (5):
4
-using the following r r l i n e a r i z e d
f o r r n r l data by
Frorn the values of the slope and intercept of a
(t/^l (p/po) / U - (p/po)l versus p/po ir"r
"r.
and c can be
c a l c u l a t e d . a i s r e l a t e d t o t h e s p e c i f i c s u r f a c e as follows: rn ( 5 a )( 6 )
M S A = r n N A ITIc can be expressed by rneans of the heat of adsorption of the first l a y e r o f a d s o r b a t e
/ A , _ \
c = k e x p t - ,
i
( ? )
\ - - ' /rf the assurnption of Brunauer, Ernrnett and reller (l) trrat k - I w e r e c o r r e c t , t h e e x p e r i r n e n t a l l y d e t e r r n i n e d v a l u e s of c could b e u s e d f o r t h e c a l c u l a t i o n of Q1. powers and Brownyard (z) found, however, that k is often rnuch less than unityi thus it is advisable to regard c as just an ernpirical constant and use the a d s o r p t i o n i s o s t e r e s f o r the calculation of e1, if necessary.
In the low-pressure dornain a is, in principle, always a single-valued function of p. This irnplies that the arnount of adsorbate taken up by the solid is independent of whether the e q u i l i b r i u r n w a s a p p r o a c h e d with increasing or decreasing values o f p r e s s u r e ; i n o t h e r w o r d s , t h a t t h e t r u e a d s o r p t i o n is not
s u b j e c t t o h y s t e r e s i s . T h e r e a r e , h o w e v e r , n u r n b r o u s e x c e p t i o n s t o t h i s r u l e . r n r n o s t s u c h e x c e p t i o n a r c a s e s h y s t e r e s i s in the ] s v o p r e s s u r e d o r n a i n i s c a u s e d b y i r r e v e r s i b r e c h a n g e s i n t h e p o r e s t r u c t u r e o f t h e adsorbent or by the presence of a second a d s o r b a t e , g e n e r a l l y air.
CAPILLARY CONDENSATION
For p/po
mechanism of adsorption. rt is caused by the development of
c u r v e d l i q u i d s u r f a c e s i n the poreso The vapour pressure in equilibriurn with a curved liquid surface is given by the Kelvin equation which, in general forrn, can be written as
I r , 3
' % = - - R r -
= - o ( w r / P l L
+ t \
( E + " " )
( 8 )
\ ' " /I
a I C - l= J ? * - b / v o l
5
-When the developrnent of a curved liquid surface is due t o t h e n e a r n e s s o f solid surfaces, the curvature is determined by the geometry of solid and the angle of contact between the solid and liquid. For porous rnateriars the pore geornetry and the arnount of occupying liquid are the main geornetrical factors; thus
f ( a , 0 , p o r e g e o m e t r y )
The principal radii of curvature can be either positive or negative, but under conditions prevailing during adsorption of vapours, ( l/nf + I/F.ZI cannot be negative. Thus Equation (g) is an expression of the fact that adsorbates can stay permanenily i n l i q u i d s t a t e i n p o r o u s solids even if their relative pressure is less than unity. By cornbining Equations (g) an4 (9) or" can arso see that the arnount of adsorbate held by a solid by capillary
condensation at a definite relative pressure is a function of the p o r e g e o m e t r y .
The usefulness of Equation (g) is lirnited by the fact that, d i r e c t l y o r i n d i r e c t l y , o a n d p a r e a r s o f u n c t i o n s o f p , a n d the exact nature of these functions is not known. Fortunately, the t h e o r y o f c a p i l l a r y condensation is not concerned with the n a t u r e o f t h e c o r r e l a t i o n between p and (l/nf + I / F . Z I a t v e r y s r n a l l V a l u e s o f p . A s P o w e r s (4) pointed out, capilrary con-d e n s a t i o n c a n n o t t a k e prace at rerative pressures rower than a b o u t 0 . 4 .
The capillary condensation is that rnechanism responsible f o r t h e s o r p t i o n h y s t e r e s i s in the range 0.4 < p/po < l, i:e. for the dependence of the isotherrns on the previous history of the s y s t e r n . B e c a u s e o f h y s t e r e s i s the sorption isotherrn is generally r e p r e s e n t e d b y t w o r n a i n b r a n c h e s ; the adsorption branch (curve r in Figure lb) obtained by rnonotonicaily increasing the pressure of adsorbate from 0 to po through very srnall equilibriurn steps, and the desorption branch (curve rr) obtained by the reverse
p r o c e d u r e . T h e t w o b r a n c h e s j o i n at a pressure p6 (equal to about 0 . 4 p o ) b e l o w w h i c h the adsorbate rnolecules are held on the solid surface rnainly by true adsorption.
Points within the hysteresis roop can be obtained by scanning the loop (5)" rf, starting frorn a point on the adsorption b r a n c h , t h e p r e s s u r e is reduced, a desorption scanning curve is
6
-o b t a i n e d ( s e e c u r v e r r r ) that cr-osses the l-o-op and reaches the d e s o r p t i o n b r a n c h a t some pressure generaily higher than p5. rf, however, starting frorn sorne point on the desorption branch, t h e p r e s s u r e i s i n c r e a s e d , t h e l o o p w i l l n o t b e c r o s s e d . A new curve (adsorption scanning curve) wiil be obtained, passing b e t w e e n t h e m a i n b r a n c h e s of the isotherrn (curve IV).
Three explanations have so far been suggested to account f o r t h e h y s t e r e s i s . Z s i g r n o n d y ( 6 ) a n d s o m e o i h " " workers
thought that hysteresis was caused by changing values of Q due to t h e p r e s e n c e o f a d s o r b e d perrnanent gases. The second explanation, t h e s o c a l l e d r r i n k - b o t t l e t r theory, was advanced by Kraern"" (z) and McBain (8). The third, which in its rnost general forrn incorpo-r a t e s t h e i n k - b o t t l e t h e o incorpo-r y as well, is cailed the incorpo-rincorpo-ropen- poincorpo-reincorpo-rt
t h e o r y a n d w a s s u g g e s t e d b y Cohan (9, l0).
c o h a n a s s u r n e d t h a t , as the pressure is increased, the s u r f a c e o f c y l i n d r i c a l capillaries first becornes covered with a rnonornolecular layer of the adsorbate by true adsorption. Thus t h e c a p i l l a r y r a d i u s d e c r e a s e s frorn.to ( r - D ) , a s i s shown in F i g u r e 3 a . F o r t h e cylindrical surface so obtained R1 = r-D a n d R 2 - @ . W i t h t h e s e v a l u e s Equation (g) reduces to p ^ r d l n p - o
I n t h i s e q u a t i o n Pa is clearly the pressure at which capillary c o n d e n s a t i o n b e g i n s , Since, however, pa is larger than the pressure pertaining to any ring further away frorn the capillary walls, it is obvious that upon reaching pa the capillary fills c o r n p l e t e l y a n d r e r n a i n s so at any higher pressure.
w h e n t h e p o r e i s c o r n p l e t e l y filled, sphericar rnenisci forrn at the entrances of the capillary, as shown in Figure 3b. F o r s u c h r n e n i s c i R 1 = RZ = r (if e = $o)i thus no appreciable arnount of liquid can be rernoved frorn the capillary as long as the pressure of the adsorbate is higher than sorne p6 value given by the following equation
t r &
=
p o = _ o ( t v t / p ) I R T r - D ( l 0 )( t l )
7
-Figure 3b also shows that the radius of the spherical rneniscus rernains r, and the pressure constant p6, until the capillary is cornpletely ernptied. B y c o r n b i n i n g E q u a t i o n s ( I 0 ) a n d ( 1 1 ) ,
T-zD/ r
(tzl
F o r w i d e c a p i l l a r i e s r > > D ; t h u s E q u a t i o n ( 1 2 ) b e c o r n e s pd N P o( 1 3 )
If, on the other hand, r = 2D, frorn Equation (tZ) pa = pa and n o h y s t e r e s i s t a k e s p l a c e .
Figure 4b-2 shows the adsorption and desorption isotherrns due to capillary condensation of a hypothetical solid cornprising solely open pores of uniforrn diarneter" Cohan (10) showed that in a sirnilar rnanner the sorption isotherrns for other shapes can a l s o b e c a l c u l a t e d . T h e i n f l u e n c e o f p o r e g e o m e t r y o n t h e s o r p t i o n i s o t h e r r n s w a s f u r t h e r i n v e s t i g a t e d b y , a r n o n g o t h e r s , d e B o e r ( 1 1 ) , E v e r e t t ( I Z l , H i g u t i a n d U t s u g i ( 1 3 ) , a n d A r i s t o v a n d c o w o r k e r s ( 1 4 ) .
A s s e v e r a l d i f f e r e n t p o r e s h a p e s c a n r e s u l t i n i d e n t i c a l isotherrns, it is generally not irnportant to know exactly the predorninant shape of pores in the adsorbent. lf it is assurned that any pore size within a continuous range is represented in all
s o l i d s , a n y c a p i l l a r y s o r p t i o n i s o t h e r r n c a n b e r e g a r d e d a s r e s u l t i n g frorn the three basic pore shapes shown in Figure 4. In this figure t h e c a p i l l a r y c o n d e n s a t i o n i s o t h e r r n s y i e l d e d b y t h e s e s h a p e s a r e also shown. The rrink-bottlerr type pore shape is characterized by two dirnensions. Of these rZ controls the value of pa, and r1 that of pd.
B e c a u s e o f t h e c o n t i n u o u s d i s t r i b u t i o n o f p o r e s i z e s , r e a l s o l i d s r a r e l y e x h i b i t v e r y s t e e p i s o t h e r r n s , e x c e p t p o s s i b l y r - e a r t h e n o r m a l s a t u r a t i o n p r e s s u r e . I f a c o n s i d e r a b l e p r o p o r t i o n o f the pores is wider than 0. I rnicron, any pore type yields practically vertical isotherms as pJpo. Substitutions of different values of r
8
-i n t o E q u a t -i o n s ( 1 0 ) ana (ll) w-ill reveal that as r -increases frorn 0 . 0 5 r n i c r o n t o v i s i b l e sizes, p/po wiil increase only within the 0 . 9 8 t o I r a n g e .
cohan showed (r0) that if Equation (lz) is varid for the p r e s s u r e s at the two end points of a desorption scanning curve ( a s c u r v e T T T i n F i g u r e l u j t n e n the pores can be regarded as c o n s i s t i n g o f . a range of open and closed pores onlylsee Figures 4a'r and 4b-1). rf Equation (tz) is not .'ru.tid, the pore structure can be rnodelled as a rnixture of rrink-bottler type and closed p o r e s ( s e e F i g u r e s 4a-l and 4c-l). O n c e a m o d e l h a s b e e n s e l e c t e d , t h e size distribution or structure curve of the porous a d s o r b e n t c a n b e calculated [for exarnple References (l) and (13]'1.
MOISTURE SORPTION ISOTHERMS AND ISOSTERES
What has so far been said about adsorberlt-vapour adsorbate s y s t e r n s i n g e n e r a l holds true also for any adsorbent-water system. N e v e r t h e l e s s , t h e w a t e r r n o l e c u l e s h a v e certain properties that d i s t i n g u i s h t h e r n frorn rnost other adsorbates. Their srnall sizes ( a b o u t 3.5 d in diarneter) rnake possible their penetration into v e r y f i n e p o r e s , which may be irnpenetrable for other rnolecules. Another characteristic of water rnolecules is their high affinity f o r a l r n o s t a n y adsorbent. B e c a u s e o f t h i s p r o p e r t y , water can d i s p l a c e a n y cornponent of air from the surface of adsorbents. T h u s m o i s t u r e isotherrns obtained in the presence and absence o f a i r a r e p r a c t i c a l l y identical (2).
rt is clear by now that in the knowledge of certain data a fair estirnate of the rnoisture sorption propu"tius of building materials can be rnade. rt has been shown that in the range ! < v/vo < 0- 4 the shape of the isotherrn is uniquely deterrnined b y t w o c o n s t a n t s , S and C [see Equations (5) ana (6) ]. An estirnate of these constants can be obtained for a nurnber of comrnon rnaterials frorn Table I.
To estirnate the shape of adsorption and desorption isotherms in the range of capillary condensation to. + a p/po . iy orr. has to know the effective porosity of the solid, ahd an approxirnate rnodel o f t h e p o r e s t r u c t u r e . T h e e f f e c t i v e p o r o s i t y is c w h e r e e < t b e c a u s e ( 1 4 ) e of t h e p r e s e n c e o f p o r e s i r n p e r v i o u s to water,
ru tr {, l{ o) c) d t n o a / ) d ) d N d . I N t r t H r O r n . N F -N r o o o \o rf) \o a l o r r } ro d) A - * \ o r o * * I g r - r * f ' . . r o r o o o . n o - 3 f , T \ o V L n o { . o $ { , o . 6 c d + r v ) c 1 r . -: . r | -r | ! | | t r ' r 9 q N N N F - r n o r o o 6 V o o o . c o n r F F 6 d , n o H x (r) \ O N t l 1 . \ O O . H N . . @ H 9 \ \ O r J ) c ' o N O O L n N H c o \ O d ^ t 9 $ O ( i r o r - ( f } @ $ N ! I o I I . I r ! i ' i - : | | . I I r ) \ O O F - O o | . @ I O r O , O , O d @ t r ) ( f ) d - . d . . . r a . ( \ ( ' l r { \ O t i { ( v ) u 1 u 1 $ d \tt t{ t o E - t l d
x 5
t A d ro o . 6 ^ _ . c ! . o c | o N \ o o d " : , ? o N H o o t oi ? T i i f
t t t r r
: -
X { - * i
S B X s
g - + o . 1 c o 6 i + ^ 1 i I r I t o r i i r r v . d d o d * u " ( f ) o q l r . l r J , | ( f ) F _ O O , O N - d s : d d 3 i-fi
5
s3
C' k o (d 9 -ls +t € v O H d H . N N N N * t s J + r $ v v v e r f J $ r + t E -l - @ o c o ^ € r . o F . o F . o F , d H d H N H d H d v v v v g I v g v . O ^ . \ O * 9 F . t t d H l f x v v v Ita
q l +3 a
- \ o + d e ; i - * # t & t + l$ Jf t$ In \O \O \O -N^^l_ tT J$ H d d d l+ v v 9 V V V o € d a t a E C) o (u k d) c, tr Q) o , o b 0 d . E + : h q r { ! ' d P + x o v h3 3
r { . c l e€Hr
H - g f
o e t rf r . g
\ o ,p T x
d t ;g i T
g o .P r 5
6 o t ' { q rl H & f'l F{ (') Do
H d, h H Oe a
E9
i s
d f.l t{u
d 4 rr.u
z
o
H ti A to
at) t f # i E Jg tf JA_ 1 0 _
and the true porosity is given by p - p
s s
The arnount of water held by a s w a t e r u n d e r g r e a t p r e s s u r e ( l ) ; sation as water under tension (ZZl. adsorbed rnoisture are very sirnilar ?rnax can be taken roughly as
( l 5 )
t r u e a d s o r p t i o n ' c a n b e r e g a r d e d that held by capillary
conden-N e v e r t h e l e s s , t h e p r o p e r t i e s o f to those of liquid water. Thus p
' s
e is obviously that property which deterrnines the rnaxirnum amount o? rnoisture a solid can hold, i, e. the value of ,rrr"* at p = po. (rn certain rare cases (t/*t + l/Rzl rnay droi'To-r"ro ^" P-:t po, so that cornplete filling of the pores rnay be achieved only by irnrnersion. ) a rnax p w A r e = -e p ' s
( 1 6 )
b y c o r n b i n i n g E q u a t i o n s ( 1 4 ) , (15) and (16), as ( e P * "rrr"* = I; ; s( t 7 )
sorne data concerning the values of e and p" are also given in Table I.Figure lb shows the sorption isotherms of a certain kind of clay brick estirnated by data taken frorn Table r. (These curvea can be regarded as typical of building rnaterials in general. ) rn t h e r a n g e 0 . 4 < p / p o < 0.8 Equation (fZ) yields, as a rule, a fair correlation of the pressures at the two end points of a desorption scanning curve (_e.^g: ,curve TTI), but at higher pressures the pa/po < (erlnoP-ZD/ r condition definitely prevails. A possibte rnodel of the pore structure is shown in Figure la" According to this nnodel the coarse structure is rnade up prirnarily of rrink-bottolerr type pore,s, with characteristic r values ranging frorn about 5 0 A t o v i s i b l e s i z e s . These pores are responsible for the failure o f E q u a t i o n ( 1 2 ) . i n c o r r e l a t i n g pa and p6 when p/po > 0.g. The f i n e s t r u c t u r e c o n s i s t s of closed and open tuburar pores. The c l o s e d p o r e s f i l l a n d ernpty reversibly. T h e o p e n p o r e s y i e l d capillary condensation with hysteresis according to Equation (lz).
t l
-e f f -e c t o f p a r t i a l v a p o u r p r -e s s u r -e , th-e -eff-ect of t-ernp-eratur-e on rnoisture content rnay be of sorne interest, it is advisable to p r e s e n t t h e a d s o r b e n t - a d s o r b a t e s y s t e m b y i t s i s o s t e r e s i n s t e a d of by a farnily of isotherrns with r as a pararneter. To plot the i s o s t e r e s o n e h a s to know either (i) the isotherrns of the systern at any temperature within the ternperature range of interest, plus the average value of Q in this dornain, as a function of a or P/Ps, or (ii) the isotherrns of the systern at two ternperatrr"u-", preferably at the two end points of the range of interest. one r n a y a l s o a t t e r n p t to plot the sorption isosteres, based. on
knowledge of the isotherrns at a single temperature level and on estirnated values of e. At a =
(4) becornes
the equation
or ,rrpoSl';f"IJ"t";
:l]: ::;JI""
c o n s e q u e n t l y Q = 1. with the decrease of a or p/po e increases a n d r e a c h e s i t s h i g h e s t varue, which is genEraily belween l.l0 a n d 1 . 9 0 w h e n 2 s a,rn or (roughtql p/po< e.Z, i.e. when the p o r e s a r e c o v e r e d by not rnore than a single layer of water rnolecules. As Qrrr"*
i At, a rough estirnate of e*"* can be obtained frorn Equation (?) -itf, k o l.
, The graph in Figure P/ Po in an idealized forrn. known, rigorous evaluation
lc shows the variation of Q with I f t h e s t r u c t u r e c u r v e o f p o r e s is o f Q i s a l s o p o s s i b l e ( 2 3 ) .
T h e a d s o r p t i o n i s o s t e r e s shown in Figure rd have been plotted bv (i) locating a few points at z0"c with the aid of the adsorption branch of the isotherrns shown in Figure lb and (ii) d r a w i n g s t r a i g h t lines frorn these points with slopes deterrnined b y t h e v a l u e s of Q given in the Q versus p/po prot in Figure rc. A s s a i d b e f o r e , the a = zrnax (0. 0Bg g per ! ) i s o s t e r e h a s t o b e i d e n t i c a l w i t h t h e vapour pressure curve of free water.
SORPTION CHARACTERISTICS OF CONCRETE
Frorn the point of view of rnoisture content of a solid the d r y s t a t e , t h e s t a t e in which the solid is free of adsorbed water r n o l e c u l e s s h o u l d be regarded as the reference state. Unfortunately there are sorne materials, of which hydrated portland cernent is a noted one, that cannot be freed frorn adsorbed water without
p r o d u c i n g o t h e r changes bearing on their sorption characteristics. The rnain difficulty in drying hydrated portland cernent is that for some water rnolecures held by chernical bonds the binding e n e r g y i s l e s s t h a n the energy needed to dislodge the rnost firrnly h e l d a d s o r b e d w a t e r rnolecules. consequently, at sorne advanced stage of drying desorption and partial dehydration will take place
t 2
-sirnultaneously. Since the arnount of water held by adsorption thus cannot be determined exactly, it is rnore accurate to call that part of water dislodged by sorne standard drying procedure
evaporable water, instead of rnoisture. For similar reasons, the arnount of water retained by the hydrated cement throughout drying should be terrned non-evaporable water. A method of defining the two kinds of waters independently of the drying technique has r e c e n t l y b e e n s u g g e s t e d by Feldrnan and Sereda (?41.
rt is obvious now, that for hydrated portland cement and. concrete the reference state of the rnaterial is not their t,dr"rt
state but a state deterrnined by sorne standardized drying procedure. T h e r e a r e t h r e e d r y i n g techniques that are recognized as standards: (i) drying at roorn ternperature over a rnixture
"r furg (cro412.z]H2o a n d M g ( C I 0 4 ) 2 . 4 H 2 0 , o f t e n c a t l e d ( p ) - d r y i n g ; ( i i ) d r y i n g o v e r i c e at -78.5"C (sublirnation ternperature of Co2l, so-called (D)-drying;, and (iii) drying in an oven at 105oc. rn rigorous scientific work, generally, the first two drying techniques are used. Most d.ata on
sorption properties of hydrated portland cernent relate to (p)- or (D)-ariua specirnens. oven drying rnay result in some changes in t h e s o r p t i o n c h a r a c t e r i s t i c s o f t h e r n a t e r i a l , b u t i n r e s s r i g o r o u s work it is preferred because of the substantiar saving in time.
When interpreting data taken frorn the literature it should be kept in rnind that (P)-dried specirnens contain about l0 per cent more t1on-evaporable water than (D)-dried or ov€n-dried
s p e c i m e n s ( 2 5 l - .
The hydrated portland cernent owes its unique sorption c h a r a c t e r i s t i c s ( T a b l e I ) t o i t s p e c u l i a r rnicrostructure. I t s b a s i c constituent is a colloidal calcium-silicateo hydrate consisting of very thin sheets of up to a few hundred A in size, rolled into tubes. rn this colloidal mass, cod.rser but stitl very srnall crystals of Ca(OH)r, unreacted anhydrous cernent compounds, and various A l 2 O 3 , F e 2 O a a n d S O r - c o n t a i n i n g phases are ernbedded (4, 26l. The c*olloidal ?nass and the crystalline particles together constitute the cernent gel. Because it is cornposed prirnarily of thin sheets, the cernent gel has a very large specific surface and a very fine pore structure. 'These fine gel pores always arnount to about 28 per cent by volurne.
A c c o r d i n g t o P o w e r s ( 4 ) c e r n e n t g e l of such characteristics f o r m s i f t h e i n i t i a l w a t e r cernent ratio is relatively low; *J"< o " 3 7 g . I t w J c > 0 . 3 7 g , a coarse pore structure develops in the g.f in
addition to the essentially unaltered fine structure. These larger p o r e s a r e c a l l e d capillary spaces. The capitlary porosity depends
_ 1 3 _
on the initial water cernent ratio. The term cement paste covers t h e c e m e n t g e l a s w e l l as the capillary spaces, if any.
The sorption isotherrns of hydrated portland cement are somewhat different frorn those yielded by most other building r n a t e r i a l s . H e r e t o o , b o t h the adsoiption branch and the desorption branch up to about p/po = e. g are of the farniliar S - s h a p e , b u t t h e two branches do not join at about p/po = 0.4. rt seerns probable that this unusuar phenomenon is caused by partial or cornplete rehydration, during adsorption, of the water o f c o n s t i t u t i o n l o s t at very low pressures during desorption.
Powers and. Brownyard (z) and powers (4) tound that the s p e c i f i c s u r f a c e o f hydrated portland cernent for the adsorption following the first drying can be calculated frorn the following expre s sion:
S = 3 . 8 x l o 7 x
I
The values of K and *J. depend on the cornposition of the anhydrous cernent, and can be calculated with the empirical equations developed b y s c i e n t i s t s o f the Portland Cernent Association (2, ZZl. For types r a n d r l l p o r t l a n d c e r n e n t s 0 . z 7 < K < 0 . 3 5 and 0. 17 < idc < o.zili rn is a function of the age of. paste, the initial water cernent ratio, t h e f i n e n e s s o f t h e cernent particles, the ternperature, and the equilibriurn relative hurnidity. Figure 5 shows the variation of rn with the curing period and water cement ratio for a portland cernent paste made frorn finely ground clinker kept at zs"c in
water-saturated condition. The plot has been based rnainly on data presented by Taplin (28) for a particular kind of portland cernent; it is, however, probably applicable to a variety of portland
c e m e n t s , e s p e c i a l l y at advanced stages of hydration. For Y - J . , > 0 . 3 8 t h e a s y r n p t o t e to the *J" = c o n s t c u r v e s m = l. I t w J c < 0 . 3 8 ( 4 )
r n = 2 . 6 3 w o / c a s t - > c o
( l 8 )
( l e)
r n s u c h c a s e s r n < 1 ; i.e. cornplete hydration will never take place. u n d e r o r d i n a r y c i r c u m s t a n c e s it is rarely possible to
ensure the aging of paste in water-saturated. condition. Nevertheless, because of the slowness of rnoisture rnigration in a cornpletely
saturated paste and of the vapour pressure rowering effect of dissolved alkalies, a sufficientry large rrrass of paste can retain e n o u g h w a t e r i n i t s pores to secure the progress of hydration for a
1 4
-very long period after the rernoval of forrns and protecting covers. rf, however, the paste is subjected to forced drying, the hydration
slows down considerablywhen the relative hurnidity in the pores becornes lower than 95 per cent, and stops cornpletely at gb per c e n t ( 2 9 ) .
A s s h o w n p r e v i o u s l y ( E q u a t i o n ( 1 5 ) ) , porosity can be calculated frorn the true and bulk densities, O" "rd p,"; on the other hand, these can be expressed with the aid of tw5 alreadv introduced quantities, rn and (Wrr/c), as follows:
I + rn(mrr/c) p
,/r. + ,-(r/t;r-(m7a
f + r n ( w /c)n(zol
( 2 1 )
- t l s L l p c By combining Equations+
ttlp*Il*"El-( r 5 ) , ttlp*Il*"El-( 2 0 ) a n d ttlp*Il*"El-( Z l ) ,For a rnixture of n solids
a = ' l " r * t z ^ z r
Thus the sorption isotherrns of a
,/0" + 'n(r/pnl (w,r/c)
, / 0 " + ( V p t(*7c)
u r r a , * ' '
c o n c r e t e ,( z z l
. * o a ( ? 3 1 n nfor exarnple can be e = l
-' w i t h
t h e a i d o f E q u a t i o n s ( l z ) , ( r g ) and, (?zI and Figure 5 all inforrnation necessary for ptotting the adsorption branch of the sorption isotherrn of portland. cement paste is now available. (The constant c can be taken frorn Table r,) when plotting the desorption branch, an apparent value for s about 7o to g0 per cent higher than t h a t y i e l d e d b y E q u a t i o n (I8) can be selected.
with the aging of the paste rn increases; thus s is expected t o i n c r e a s e ( E q u a t i o n ( 1 8 ) ) and e to d.ecrease (Equation (zz)). Data reported by Powers and Brownyard (z) confirrn these expectations. The amount of evaporable water held by the paste in equilibriurn with relative hurnidites up to about 90 per cent increases with the t i r n e o f c u r i n g b u t decreases near the norrnal saturation pressure.
_ 1 5 _
calculated frorn those of its components by the mixture law. Table I shows that among all cornrnon constituents of concrete the portland cernent paste has by far the largest s p e c i f i c s u r f a c e . T h u s , e x p e c i a l r y f o r g r a v e l - c o n c r e t e s o r sand-rnortars, the water sorption can be taken as
"" & tn"n Q4l
at Ieast up to about 80 per cent relative humidity.
To calculate aO one has to know S- and e_, and therefore, first of atl, *o/.. FJr concretes this r#io i" Srrr"-h;;;;;iernatic owing to the uncertainty in the arnount of water adsorbed by the aggregates and to bleeding. Table rr rnay serve as a rough guide in estirnating the water adsorption of aggregates during the mixing of c o n c r e t e .
TABLE II
WATER SORPTION OF VARIOUS CONCRETE AGGREGATES DURING MIXING
A g g r e g a t e s a n d , g r a v e l , s t o n e expanded shale expanded slag ve rrniculite p e r l i t e W a t e r Sorption (wt of water per wt of dry
a g g r e g a t e ) 0 . 0 l - 0 . 0 3 0 . 1 5
0 . 2 5
2 . 3
3 . 5
- Although the bleeding of fresh portrand cernent paste has been under study for rnany years 1lo, ll, 3zl and, the variables g o v e r n i n g t h e p r o c e s s are well known, it is seldorn possible to estirnate with sufficient accuracy the total arnount of water lost by concrete under practical conditions. rf there is sorne uncertainty about the actual water cernent ratio for portland cernent paste in a c o n c r e t e , * J c ^ , 0 . 5 r n a y b e c h o s e n for the calculation of the s o r p t i o n p r o p e r t i e s .
t 6
-rn Figure 6 the application of the rnixture raw to the calculation of the sorption isotherrns of a lightweight concrete is shown. The concrete was rnixed from ZBZ lb per cu yd
cu yd expanded shale. Assurning = 0 . 3 2 s q c r n p e r g a n d
r t i o n s ( 1 8 ) a n d ( Z Z I , a n d ( 6 ) and E , e = 0 . 4 1 5 , a y y y - O . 0 5 2 5 g p"| g and arrr.* = 0. 283 g per g. Assuming, further, that C - 30, and that s for the desorption branch is z0 per cent higher than the above calculated value, the sorption isotherrns shown in broken l i n e s a r e o b t a i n e d . . ( F o r building materials the pore structure can almost always be rnodelled as shown in Figure la. )
F r o r n T a b l e I , S = 24.0 x 104 sq c1n per g and €e = 0.3g h a v e b e e n s e l e c t e d for expanded shale. with these values
? r n = 0 . 0 0 6 3 0 g p e r g a n d ? r n a x = O . Z L O g p e r g. Using c = l 2 ( s e e also Table r) the isotherrns shown in dotted lines r e s u l t . T h e f u l l - l i n e c u r v e s were calculated by using .Equation (23I. Experirnental data show that these curves are sufficiently accurate up to about Z0 per cent relative humidity"
Table I indicates that autoclaving causes rnarked reduction i n t h e s p e c i f i c surface of cernent pastes. consequentry, the s o r p t i o n p r o p e r t i e s of autoclaved concrete products are generally g o v e r n e d b y t h o s e of the aggregates.
ACKNOWLEDGEMENT
T h e a u t h o r w i s h e s to thank E. oracheski for his assistance i n c o n d u c t i n g t h e various laboratory tests.
- t 7 _
a a ln A rn r R R E l - - I r ' - z S t T w NOMENCLATUREamount of adsorbate per grarn of adsorbentl g per g amount of adsorbate held in a one rnolecule deep layer b y o n e g r a m o f adsorbent, g per g s u r f a c e o c c u p i e d - . b y " s i n g l e a d s o r b a t e m o l e c u l e l f o r w a t e r 1 1 . 4 x l 0 - r O s q c m p e r r n o l e c u l e c C D t g k K IN M N p p o
o
- lcement in anhydrous state, g constant, defined by Equation d e p t h o f f i r s t adsorbate layer function
constant in Equation (4), dyre per sq crn (or mmHg) c o n s t a n t i n E q u a t i o n ( Z ) , dirnensionless
c o n s t a n t i n E q u a t i o n ( 1 8 ) , sq cm per g
rnaturity factor; dirnensionless
m o l e c u l a r w e i g h t ; f o r water 18.016 g per rnole
A v o g a d r o l s n u r n b e r , 6.023 x 1023 rnole.culeB per mole p r e s s u r e , d y n e p e r s q c r n ( o r r n r n H g )
norrnal saturation pressure, dyne per sq cfir
i s o s t e r i c h e a t o f adsorption, J per mole
i s o s t e r i c h e a t o f adsorption of first adsorbate layer, J p e r m o l e
p o r e r a d i u s , crn
g a s c o n s t a n t , 8 . 315 J per rnole K principal radii of curvature, crrr
s p e c i f i c s u r f a c e , sq crn per g t i m e , h r
a b s o l u t e t e r n p e r a t u r e , K
w a t e r i n f r e s h c e m e n t paste, corrected for bleeding, g
non-evaporable water retained by the paste throughout
( D ) - d r y i n g , g *r, "" t--rc", g ( 7 ) , d i r n e n s i o n l e s s o n p o r e s u r f a c e , c m o w n w G r e e k l e t t e r s c t
e
I p p porosity, cu crn per cu ctn c o n s t a n t i n E q u a t i o n ( 1 4 ) , dirnensionless c o n t a c t a n g l e , dirnensionlesslatent heat of condensation, J per rnole
true density; without subscript! density of adsorbate, g
per cu cfir
b u l k d e n s i t y , as defined by ASTM Designation E L?, E per cu crTr
- 1 8 _
9 . t r u e d e n s i t y o f c e m e n t , - 3 . l5 g per cu crn
9 r , t r u e d e n s i t y o f n o n - e v ? p o r a b l e water in the paste, l . Z , z g per cu crn
o surface tension, dy.re per crn trt weight fraction, g per g
S u b s c r i p t s a at adsorption c w i t h c o n c r e t e as adsorbent d at desorption e effective h a t t h e p o i n t w h e r e hysteresis rnax rnaxirnurn
p with portland cernent paste as s o f t h e s o l i d ( a d s o r b e n t ) w of water b e g i n s a d s o r b e n t REFERENCES
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0 . 0 1 0 \
a\
Q o . o o , \s
0 0 . 5 1 . 0P/o
' / l o ( 0 / s o R P T t o N t s o T H E R M s A T 2 0 " c I A D S O R P T I O N B R A N C H I I D E S O R P T I O N B R A N C H I I I D E S O R P T I O N S C A N N I N G C U R V E I V A D S O R P T I O N S C A N N T N G C U R V E l0-th.Y ro2
\ \\ r o
120u)
(o)
M O D E L O F P O R E S T R U C T U R E . 52 x /o344
x /O3 {o \ \ q)a_
s
(c)
0 . 5 1 . 0 t1 tr/p
. l o H E A T O F A D S O R P T I O N . Q Temperat'rre, C A D S O R P T I O N I S O S T E R E S . F I G U R E I P R E D I C T I O N O F T H E M O I S T U R E I S O S T E R E S O F A C E R T A I N C L A Y c u c m , € = O . Z O c u c m p e r c u s q c m p e r g , C = 3 0 ) . S O R P T I O N I S O T H E R M S A N D B R f C K , 1 P < = 2 . 7 0 g p e r . c n , € = 0 . 9 5 , 5 = 5 . 0 x l 0 ' E 4 3 t 2 d - 2Q,
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F I G U R E
3
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HysrERESts
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PORES..
ACCORDING
TO COHAN
b
T
0
(o-z)
(b-2)
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(c-2)
F I G U R E
4
B A S I C
P O R E
S H A P E S
A N D T H E I R
C A P I L L A R Y
C O N D E N S A T I O N
I S O T H E R M S
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PoRE
, pd=po
(il oPEN
PoRE,
4 /po
= (po /po f
-20/r
(c) "rNK BorrLE" TYPE
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= boao f-20/r
'
1 . 0
0 . 9
0 . 8
0 . 7
0 . 6
0 . 5
0 . 4
0 . 3
0 . 2
0 . 1
0
100
T i m e o f
C u r i n g , h r
1m
100,000
F I G U R E 5
M A T U R I T Y
F A C T O R
O F C U R
I N G .
A T 2 5 " C A S A F U N C T I
O N O F
w o / c A N D T H E
T t M E
a4 3/2 a -3I , t I , , I I I t -I I I t I I I I I /' I f f / / ' / l / ' l / t t 1 / / l / l a l . / t / r ' / r . / , t a / / / / a X I - concr6te
--- Hyfrrted Portland Cemont ':'-.'- Eryanrhd Shde Ag$egatB €xgerimental Values: o Ad$orpthn Cycfe x D€rorptbn Cycl6 / , J , / , . /- ,' ./ /? f / l . ' l z '
