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Calculation of chloride diffusion coefficients in concrete from ionic migration measurements
CEMENT and CONCRETE RESEARCH. Vol. 23, pp. 724-742, 1993. Printed in the USA. 0008-8846/93. $6.00+00. Copyright © 1993 Pergamon Press Ltd.
CALCULATION
OF CHLORIDE DIFFUSION COEFFICIENTS IN CONCRETE FROM IONIC MIGRATION MEASUREMENTS
Institute
C. A N D R A D E "Eduardo Torroja" of Construction CSIC - Madrid - Spain
Sciences
(Communicated by J.P. Skalny) (ReceivedJuly 21, 1992)
ABSTRACT
A critical review is offered on the Rapid Chloride P e r m e a b i l i t y Test standarized by AASHTO, p o i n t i n g out its limitations and errors but recognizing its c o n t r i b u t i o n to the developing of a simple and quick test for chloride migration. Then another review is made on the electrochemical fundaments of the p r o c e s s e s d e v e l o p p e d in concrete when an electrical field is a p p l i e d and on the basic equations of mass transport (Nernst-Plank and Nernst-Einstein) which can be applied to c a l c u l a t e ionic movements. The limitations and assumptions needed for a simplified resolution of these equations, are presented, as well as numerical examples of c a l c u l a t i o n of the Effective Diffusion Coefficient of chlorides, De~, in steady state condition. Finally, c o n s i d e r a t i o n s on the p o s s i b i l i t y of calculation of Dc~ from simple r e s i s t i v i t y m e a s u r e m e n t s are also offered.
INTRODUCTION
P e n e t r a t i o n of chlorides through concrete is one of the factors which aims to the depassivation of reinforcing bars and therefore, may shorten the life of the structure. The time needed by these ions to reach the rebar depends first, on the m e c h a n i s m of intrusion and secondly, on the external c o n c e n t r a t i o n of the chlorides and the microstructure of the concrete. W h e n concrete is completely water saturated, chlorides p e n e t r a t e by a pure diffusion mechanism, being the difference in concentration, the driving force. However in partial saturated concrete, chlorides may penetrate by absorption and capillary forces or d i s s o l v e d in the microdrops of marine fogs. These last ones m o r e complex penetration mechanisms, are not going to be c o n s i d e r e d in present paper. 724
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CHI.£)RIDE DIFFUSION,AASHTOTEST, RESISTIVH'Y
725
In t h e c a s e of p u r e d i f f u s i o n the c a l c u l a t i o n of t h e p e n e t r a t i o n r a t e of c h l o r i d e , has b e e n m a i n l y s t u d i e d by m e a n s of e x p e r i m e n t s a s s u m i n g e i t h e r s t e a d y - s t a t e or n o n - s t e a d y - s t a t e flow. In t h e case of s t e a d y - s t a t e c o n d i t i o n s (1-5), u s u a l l y a t h i n d i s c of c e m e n t paste is i n t r o d u c e d in b e t w e e n the two c h a m b e r s of a n a m e d " d i f f u s i o n cell", and first Fick's law is a p p l i e d (6) in o r d e r to calculate an Effective Diffusion Coeficient, D~, (diffusion c o e f f i c i e n t in a p o r o u s medium): dC -J(x)
dC(x)
=
= Dc~ dt
[i] dx
T h i s m e t h o d o l o g y p r e s e n t s some l i m i t a t i o n s w h i c h m a y be s u m a r i z e d as follows: a) c e m e n t p a s t e and not c o n c r e t e is u s e d w h i c h can lead to u n r e a l i s t i c results, b) it is t i m e - c o n s u m i n g and t a k e s w e e k s to o b t a i n one result, c) a c o n s t a n t c o n c e n t r a t i o n in the c h a m b e r c o n t a i n i n g c h l o r i d e s from the b e g i n n i n g s h o u l d be m a i n t a i n e d . In t h e c a s e of n o n - s t a t i o n a r y c o n d i t i o n s , c o n c r e t e b l o c k s or specimens can be u s e d w h i c h r e s u l t s in m u c h m o r e realistic c o n d i t i o n s . T h e s e c o n c r e t e b l o c k s are m a i n t a i n e d in c o n t a c t w i t h a s o l u t i o n of c o n s t a n t c h l o r i d e c o n c e n t r a t i o n and the c h l o r i d e p r o f i l e a l o n g the time is measured. In this case s e c o n d F i c k ' s law is a p p l i e d to c a l c u l a t e the, an A p p a r e n t D i f f u s i o n C o e f f i c i e n t D a (6):
ac(x) -J(x)
= at
This equation conditions: cx= c,, and the
is u s u a l l y
x = 0,
initial
Cx= 0,
a2c = D a - .... ax 2
solved
the
following
boundary
t > 0
[3]
condition: x > 0,
applying
[2]
t = 0
O b t a i n i n g the f o l l o w i n g s o l u t i o n w h i c h is the m o s t w i d e l y u s e d
(7-
11). Cx
x = 1 - erf
C,
[4] 2(Dat) I/2
T h i s t y p e of t e s t also r e s u l t s v e r y t i m e - c o n s u m i n g and m a i n t a i n s s e v e r a l u n c e r t a i n t i e s on the r i g o r o u s a p p l i c a t i o n of F i c k ' s law. S o m e a u t h o r s (12) r a t h e r p r e f e r to c o m p a r e c h l o r i d e p r o f i l e s t h a n c a l c u l a t e D,. In a d d i t i o n , in b o t h s t e a d y and n o n - s t e a d y t e s t c o n d i t i o n s , it is not u s u a l l y c a l c u l a t e d the r e a c t i o n or a d s o r p t i o n of c h l o r i d e s by c e m e n t phases. T h i s c i r c u n s t a n c e is c o n s i d e r e d of m i n o r i n f l u e n c e
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Vol. 23, No. 3
although few researchers (13-14) do take into account. Thus, A t k i n s o n (3) refers to it by defining: a) a Da: A p p a r e n t Diffusion Coefficient in a porous medium, which considers the average c o n c e n t r a t i o n gradients of the diffusing substance, t h e r e f o r e the a d s o r p t i o n phenomena, and b) a Di: Intrinsic D i f f u s i o n Coefficient w h i c h tries to take into account the average flux per unit of area, and therefore, the volume fraction of porosity. There are also a variety of improvement p r o p o s a l s basic approaches (15-18) which make much more c a l c u l a t i o n of the chloride D,.
Electrical
to these complex
two the
methods
B e c a u s e of testing "natural" chloride p e n e t r a t i o n results timeconsuming, attempts have been made to calculate the D a from resistivity measurementes (3)(19) or to accelerate the rate of penetration of chloride ions by applying a n - e l e c t r i c a l field (1)(20-29). B o t h k i n d of test types will be commented in present paper in order to a n a l y s e their possibilities and limitations. First a critical r e v i e w will be done on the test known as "AASHTO TEST" (30) explaining why its mode of operation leads to erroneous conclusions. Secondly a brief summary will be made on the basic k n o w l e d g e needed to understand migration phenomena in electrolytes. Finally, a proposal will be presented on how to c a l c u l a t e Diffusion C o e f f i c i e n t from electrical (migration) m e a s u r e m e n t s and which are the t h e o r e t i c a l limitations. Numerical examples will be given. E x t e n s i v e experimental trials will be needed to verify whether the a s s u m p t i o n s taken in the numerical examples are r e l i a b l e or not.
CRITICAL
REVIEW
OF THE
RAPID
CHLORIDE
PERMEABILITY
TEST
That chlorides move quicker troughout the concrete when an electrical field is applied arose from earlier experiments, (31)(32) on that known at present as chloride removal (33)(34). Actually, this fact on chloride migration was already experienced by m a n y r e s e a r c h e r s using electrochemical techniques (as cathodic p r o t e c t i o n (12) for instance). However, it was W h i t i n g who, (2021)(30) p r o p o s e d a "Rapid Chloride Permeability Test" in order to o b t a i n in few hours an appraisal on concrete permeability. This s t a n d a r d test has promoted a strong controversy (28)(29), w i t h more heat than light in clarifying the meaning of the test and its a b i l i t y to predict concrete resistance to p e r m e a t i o n of chlorides. The real fact is that the test is increasingly being used although e v e r y b o d y recognizes some still unknown uncertainties. S u m m i n g up, this test uses a thick (usually 5 b e t w e e n two electrodes (usually copper meshes) similar to that of the diffusion cell. Sodium weight) is added to one of the chambers and NaOH the other. Then, an electrical field of 60V is a p p l i e d between electrodes and the amount of
cm) c o n c r e t e disc in an arrangement chloride (3% per of about 0.i M to r e c o m m e n d e d to be coulombs recorded
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CHLORIDE DIFFUSION, AASHTO TEST, RESISTIVITY
727
a l o n g 6 h o u r s of testing, are m e a s u r e d . The t e s t d e f i n e s t h a t a h i g h e r a m o u n t of c o u l o m b s r e p r e s e n t s a h i g h e r p e r m e a b i l i t y of the c o n c r e t e to the c h l o r i d e s .
Movement
of
ions
in
concrete
under
an
electrical
field
L e t us a n a l y s e n o w step by step w h a t h a p p e n s from the b e g i n n i n g of t h e e x p e r i m e n t and try to e x p l a i n w h a t is w r o n g in the test. W h e n t h e c o n c r e t e d i s c is i n t r o d u c e d in the cell, b e f o r e any e l e c t r i c a l f i e l d is a p p l i e d a d i f f u s i o n (leaching) is p r o d u c e d m a i n l y of OH- ions due to t h e i r h i g h ionic m o b i l i t y as f i g u r e 1 a shows. T h i s d i f f u s i o n due the d i f f e r e n c e in c o n c e n t r a t i o n s of d i f f e r e n t ions m a y be m a i n t a i n e d a l o n g the e x p e r i m e n t . In a d d i t i o n , w h e n the e l e c t r i c a l field is applied, m i g r a t i o n of all ions o c c u r s t o w a r d s the o p p o s i t e sign e l e c t r o d e (figure ib). Not o n l y c h l o r i d e s move, but all the ions do and the t o t a l c u r r e n t is spent in the a d d i t i o n of all t h e s e m o v e m e n t s w h i c h w i l l be commented later. Therefore, diffusion plus m i g r a t i o n happens s i m u l t a n e o u s l y as f i g u r e 1 c depicts. The final r e s u l t w i l l d e p e n d on t h e r e l a t i v e i m p o r t a n c e of both m o v e m e n t s . T h e n the p r o c e s s e s d e v e l o p p i n g (36) in the cell w h e n an e l e c t r i c a l f i e l d is applied, are the f o l l o w i n g (figure 2):
a)
Electrode processes
-
a.l)
M e t a l d i s s o l u t i o n - w h i c h g e n e r a t e s o x y d e s at t h e a n o l y t e (possitive electrode chamber), if the anode is an o x i d a b l e metal, as for i n s t a n c e copper. In the c a s e of g r a p h i t e e l e c t r o d e s the p r o c e s s w i l l be: C --> CO + CO 2.
a.2)
E v o l u t i o n of gases - as e l e c t r o l y s i s of water, in b o t h anolyte and catholyte, generating 02 a n d H 2. This e v o l u t i o n w i l l stirr the s o l u t i o n in b o t h c h a m b e r s .
The r e a c t i o n s possitive negative
o c u r r i n g are the w e l l known:
electrode electrode
- 2H20 --> 202 - 2H20 + 2 e
+ 4H ÷ + 4e °
--> H 2
+
20H °
In the case of u s i n g not c o r r o d i b l e e l e c t r o d e s as Pt, the w a t e r e l e c t r o l y s i s will be the o n l y e l e c t r o d i c process.
Not o n l y w a t e r e l e c t r o l y s i s but o x i d a t i o n of Cl ° a l s o m a y h a p p e n if the v o l t a g e is h i g h e n o u g h to p r o d u c e Cl 2 evolution. possitive
electrode:
- 2Ci ° --> Cl 2 + 2 e
728
C. Andrade
As well reaction, negative
as
oxygen
electrode:
Vol. 23, No. 3
reduction
following
the
known
202 + H20 + 4e" -> 4OH °
All these reactions tends to maintain the total e l e c t r o n e u t r a l i t y of the e x p e r i m e n t w h i c h is one of the f u n d a m e n t a l s of e l e c t r o c h e m i c a l r e a c t i o n s . CQncrete
No + •, , , - - - C I -
OHNa ÷
a) DIFFUSION
®
Concrete
~--- CINo+-~,.
b)
MIGRATION
®
Concrete
(~
Y//.//I OHNQ ÷
~ - - 0H-
V/N/
"o'-
c) DIFFUSION + MIGRATION Figure
i. M a s s
transport processes
in concrete.
Vol. 23, No. 3
CHLORIDE DIFFUSION,AASHTOTEST, RESISTIVITY
(~) HEAT=IZ.Rohm
:"
729
(~
No+._...
0
00
2 H20 "-" 0 2 0 2 H +
No
CI "-" CI2~ Cu--Cu +I
2 H 2 0 - " H2t+ 2OH-
02+ 2H20 "" 4OH"
F
Figure 2. Processes occurring when an electrical field is applied in a diffusion cell: Joule effect, anode dissolution, electrolysis of the electrolite (gas e v o l u t i o n at electrodes and reduction reactions) and ionic m i g r a t i o n and diffusion. b)
Migration The third process happening in a cell is the m o v e m e n t of ions in the electrolyte in order to carry the e l e c t r i c i t y passing through the cell. Therefore, migration is developed and diffusion may appear if this m i g r a t i o n leads to concentration differences. As it was mentioned, not only chlorides move but all ions take part in migration in a proportion what is known as their "transport or transference number". T r a n s f e r e n c e number Let us try to explain something here about this parameter. The transference number of an ion m o v i n g under the action of an external electrical field is defined by the "proportion of the current carried by this ion in relation to the current carried by the rest of the ions" (36). It is formulated as:
i, t~.
.
. i
%%xj .
.
. . Z ZCX
[5] A
Hence, the transference number is a function of the ionic m o b i l i t y or the equivalent conductivity. This means that OH- ions will carry much more p r o p o r t i o n of current than Cl- ones due to the ionic conductivity of OH" is 198,5 o h ~ l'cm2"eq-] and that of C I is 76,34 ohm-*.cm2.eq-I (36). This fact is very important in the case of concrete because
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Vol. 23, No. 3
it m e a n s that the m a i n p r o p o r t i o n of the c u r r e n t w o u l d be t a k e n by O H ions and not by the Cl ° and t h e r e f o r e , h y d r o x y d e s m i g h t b e h a v e as a " s u p p o r t i n g e l e c t r o l y t e " . Therefore, only if c h l o r i d e t r a n s f e r e n c e n u m b e r s are c a l c u l a t e d is p o s s i b l e to s p e c i f i c a l l y d e d u c e c h l o r i d e t r a n s p o r t feasability, w h i c h is not t a k e n into a c c o u n t by the R a p i d C h l o r i d e P e r m e a b i l i t y t e s t w h i c h only r e c o r d s the total a m o u n t of c u r r e n t (that c o r r e s p o n d i n g to the m o v e m e n t of all ions). In a d d i t i o n w h e n f l o w i n g t h r o u g h the c o n c r e t e the c h l o r i d e s m a y r e a c t w i t h the C3A and t h e r e f o r e a s t a t i o n a r y flow c a n n o t be a c h i e v e d u n t i l all r e a c t i v e sites are saturated.
Movement
of c a t i o n s
-
An a d d i t i o n a l a s p e c t to be s t r e s s e d n o w is r e l a t e d to the " a n o m a l o u s " D i f f u s i o n C o e f f i c i e n t t h a t is m e a s u r e d in the c a s e of the c a t i o n s of small ionic radius, as Na ÷ and K ÷ (i). T h i s b e h a v i o u r is v e r y w e l l d e s c r i b e d by B o c k r i s (36) and G l a s s t o n e (37) c o n s i d e r i n g t h a t t h e s e ions m i g r a t e solvated, that is, due to its s m a l l ionic radius, Na ÷ and K ÷ d i f f u s e or m i g r a t e surrounded by w a t e r m o l e c u l e s , as they n o r m a l l y are in solution. T h a t m a k e s t h e i r m o v e m e n t m o r e d i f f i c u l t and t h e r e f o r e , D v a l u e s s m a l l e r t h a n t h o s e of c h l o r i d e ions are r e p o r t e d (i). T h i s fact also e x p l a i n s w h y w a t e r m a y c o n c e n t r a t e at the cathode, as was s o m e t i m e s n o t i c e d in the c a s e of c a t h o d i c p r o t e c t i o n . Na ÷ and K ÷ m i g r a t i o n m e a n s t h a t a net f l o w of water (electroosmosis) is also s i m u l t a n e o u s l y p r o d u c e d . T h i s fact can be also a p p l i e d to e x p l a i n the b a s i c process of electrochemical realkalization: there, h y d r o x y d e s are p r o d u c e d at the r e b a r a c t i n g as cathode, and s o l v a t e d Na ÷ ions m o v e from the e x t e r n a l c a r b o n a t e s o l u t i o n in order to b a l a n c e the e l e c t r i c a l c h a r g e s and, finally they support the r e c o n s t r u c t i o n of a N a O H solution around the rebars. Anyway, as water is simultaneously r e d u c e d at the c a t h o d e t o g e t h e r w i t h oxygen, the d i l u t i o n e f f e c t m a y be b a l a n c e d . In the case of the m i g r a t i o n test, h a v i n g t w o c h a m b e r s w i t h solutions, the e f f e c t of i n c r e a s i n g w a t e r a r o u n d the r e b a r is not noticeable, but in the c a s e of c o n c r e t e ( c a t h o d i c p r o t e c t i o n , r e a l k a l i z a t i o n or c h l o r i d e removal) the e f f e c t w i l l be d e p e n d e n t of the p o t e n t i a l a p p l i e d or the l a s t i n g of the t r e a t m e n t . A c o n s e q u e n c e of this e f f e c t in the case of c a t h o d i c p r o t e c t i o n , is t h a t the r e s i s t i v i t y will i n c r e a s e at the a n o l y t e (and t h e r e f o r e d e c r e a s i n g the e f f i c i e n c y of the a n o d e s ) a n d a dilution of the s o l u t i o n a r o u n d the cathode, and t h e r e f o r e a " b u f f e r i n g " of the i n c r e a s e in pH v a l u e on the c a t h o l y t e , m a y happen.
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CHLORIDE DIFFUSION, AASHTO TEST, RESISTIVITY
731
S u m m i n g up w h a t has been said up to now, when an electrical field (direct current) is applied between two electrodes p l a c e d both sides of a concrete block, several phenomena d e v e l o p as figure 2 depicts: a) The anodic material, if possible, dissolves and gases may evolve at b o t h electrodes, b) all ions of the electrolyte m o v e in order to carry the current passing through the cell and to m a i n t a i n e l e c t r o n e u t r a l i t y c) in addition heat is produced as a consequence of the current flow. At the sight of these comments, it can be deduced that, the R a p i d C h l o r i d e Permeability test contains the following errors:
i)
It accounts the total the chloride flow.
2)
W h e n integrating the total current from the b e g i n n i n g of the e x p e r i m e n t it does not distinguish between chloride flow plus r e a c t i o n and simple flow.
3)
The high voltage drop used (60v) in turn changes the flow speed.
current
and not that
induces heat
T h e r e f o r e a m i g r a t i o n test of this type cannot transport of chlorides (38) and much less "permeability" of the concrete specimen. CALCULATION
OF
DIFFUSION
COEFFICIENTS
corresponding
FROM
(23)(27)
which
at all inform on p o r o s i t y
MIGRATION
to
on or
MEASUREMENTS
A l t h o u g h it has been mentioned the errors involved in the "Rapid C h l o r i d e P e r m e a b i l i t y Test" which invalidates its d e d u c t i o n s , i t m u s t be r e c o g n i z e d the importance of its aim of shortening the time n e e d e d to test concrete resistance to ionic diffusion, and how much W h i t i n g ideas have estimulated the discussion on this area. Now an attempt is presented on how to calculate, not he "permeability", but the Diffusion Coefficient from an electrical m e a s u r e m e n t similar to that described in the AASHTO test. Diffusion c o e f f i c i e n t is the parameter which may characterize a concrete in order to p r e d i c t its long term performance, that is, its resistance to the p e n e t r a t i o n of ions. The calculation of D from electrical measurements has to be based in the fundamental of transport p r o c e s s e s in electrolytes, very well established in the traditional books of E l e c t r o c h e m i s t r y Science (36)(37)(39-43). There, it appears that the general equation for t r a n s p o r t processes in s o l u t i o n is that named Nernst-Planck (36) equation which can be w r i t t e n as:
0Cj (X)
-J~(x) = %
ZjF
+ 0x
0E (X)
%q RT
+ qv(x) 0 (x)
[6]
732
C. Andrade
J(x)
= = = = = = = = = = =
ax Zj F R
T
V
Vol. 23, No. 3
u n i d i r e c t i o n a l flux of species j (mol/cm2s) d i f f u s i o n c o e f f i c i e n t of species j (cm2/s) v a r i a t i o n of c o n c e n t r a t i o n (mol/c~) v a r i a t i o n of d i s t a n c e (cm) e l e c t r i c a l c h a r g e of species j F a r a d a y ' s n u m b e r (coul/eq) gas c o n s t a n t (cal.voltl.eq l) a b s o l u t e t e m p e r a t u r e (~) b u l k c o n c e n t r a t i o n of the species j ( m o l / c m 3) v a r i a t i o n of p o t e n t i a l (V) a r t i f i c i a l or forced v e l o c i t y of ion (cm/s)
w h i c h m e a n s that the u n i d i r e c t i o n a l (x) flux of a p a r t i c u l a r ion (5) is a f u n c t i o n of its d i f f u s i o n plus its m i g r a t i o n c o m p o n e n t s and p l u s the flux due to convection. That is: Flux = d i f f u s i o n T h e r e f o r e this e q u a t i o n ionic f l u x recorded.
+ migration
+ convection
allows the c a l c u l a t i o n
of D f r o m the total
However, some c o n s i d e r a t i o n s have to be m a d e b e f o r e a p p l i c a t i o n of e q u a t i o n [6] is tried. These
an a p p r o p r i a t e
are:
A)
The n e e d to p r o v i d e the c o n d i t i o n s for s t e a d y - s t a t e flow (equation [6] as it is, is f o r m u l a t e d for s t e a d y state conditions).
B)
The r e a c t i o n of c h l o r i d e s w i t h the C3A and t h e r e f o r e the d e f i n i t i o n of D as an " A p p a r e n t D", D a w h e n it t a k e s it into account, or an E f f e c t i v e one, D~, w h e n it m e a s u r e s the net c h l o r i d e flow w i t h o u t reaction.
c)
L i m i t s of a c c u r a c y due c o n c r e t e p o r e solution.
D)
The p o t e n t i a l d i f f e r e n c e to a v o i d Joule effect.
NaO
NaCI
STATIONARY FLOW
Figure
to
the
high
applied
ionic
should
strengths
be small
of
enough
NeOH~ _ N a C i
NON-STATIONARY
FLOW
3. S t a t i o n a r y and n o n - s t a t i o n a r y flow in f u n c t i o n s p e c i m e n t h i c k n e s s and time of testing.
of
the
Vol. 23, No. 3
B)
e)
CHLORIDE DIFFUSION, AASHTO TEST, RESISTIVITY
733
Stationary flow - in order to apply e q u a t i o n [6] in its p r e s e n t formulation, a s t e a d y - s t a t e flow has to be e s t a b l i s h e d as f i g u r e 3 depicts. If n o n - s t a t i o n a r y flow is p r o d u c e d , then the v a r i a t i o n w i t h the d i s t a n c e of the c h l o r i d e c o n c e n t r a t i o n , s h o u l d be also t a k e n into a c c o u n t a i m i n g to an e q u a t i o n in p a r t i a l d e r i v a t i v e s of second order s i m i l a r to s e c o n d Fick's law. R e a o t i o m - the first c h l o r i d e ions t r a v e r s i n g the c o n c r e t e d i s c w i l l react w i t h AC 3 and t h e r e f o r e an e r r o n e o u s D m a y be c a l c u l a t e d as has been d e t e c t e d in the case of p u r e d i f f u s i o n cells. In order to n e g l e c t this fact, the c a l c u l a t i o n of D has to be m a d e w h e n a linear increase of c h l o r i d e s is r e c o r d e d in the c h a m b e r not c o n t a i n i n g them at the beginning, t h a t is to r e c o r d the c h l o r i d e flow when the r e a c t i v e AC 3 was s a t u r a t e d w i t h the first m i g r a t i n g Cl ° (figure 4). I o n i c s t r e n g t h - In order to take into a c c o u n t the h i g h ionic s t r e n g t h of the c o n c r e t e pore solution, two m a i n a s p e c t s h a v e to be considered: a) that a c t i v i t i e s i n s t e a d of c o n c e n t r a t i o n m u s t be c o n s i d e r e d and therefore, either a selective ion electrode for chloride is used or activities must be c a l c u l a t e d , for instance as is s u g g e s s t e d in (44), and b) the i n f l u e n c e of the ionic s t r e n g t h in the t r a n s p o r t number, ~, and in the v a l u e itself of D ~ should be c o n s i d e r e d .
Let us a g a i n try to a n a l y z e this a s p e c t of the i n f l u e n c e of the ionic s t r e n g t h on D w i t h m o r e detail. It has been e s t a b l i s h e d that D is not a constant, but a f u n c t i o n of the c o n c e n t r a t i o n of the solution (36) and therefore, h i g h ionic s t r e n g t h i n f l u e n c e s D value. In a r e c e n t p a p e r (44) a s i m p l e w a y to c a l c u l a t e activity factors from conductivity m e a s u r e m e n t s has been offered, and t h e r e f o r e a t r i a l w i l l be p r e s e n t e d in the n u m e r i c a l examples, on h o w Dc~ v a r i a t i o n w i t h c o n c e n t r a t i o n is calculated. tool
cm =. sg
Cl- in the catholite
I
~
,
!
r
w
,
TIME Figure
4. Flux (J) of c h l o r i d e s time.
leaving the c a t h o d i c
chamber
along
734
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Vol. 23, No. 3
Anyway, it is important to stress that being the concrete pore solution a very concentrated one, the influence of ionic strength cannot be neglected in the calculation. D)
J o u l e e f f e c t - The potential difference applied to drive m i g r a t i o n should be as high to promote a quick enough m o v e m e n t of chlorides, and as small as to avoid a waste in heating. Ten to fifteen volts could be a sensible compromise.
Solving
Nernst
- Plank
equation
Really a rigourous solution for equation [6] cannot be a c h i e v e d in solutions as concentrated as concrete pore solution (36)(43). In polielectrolytes (more than binary solutions) a rigourous a p p l i c a t i o n of flux equation [6] fails, an even m o r e if the s o l u t i o n is concentrated, because D has to take into account interaction of all ionic species. Therefore at least two main d i f f i c u l t i e s arise when facing our particular problem: 1) first that of the high ionic strength previously commented and 2) how to apply the e q u a t i o n to a particular ion and not to the solution as a whole (19).
A semirigourous aproaches:
calculation might be undertaken using two p o s s i b l e
a) To consider phenomenological
Onsager's
equations
b) To use a M e a n D for the whole electrolyte
(36),
or
(43).
Both approaches lead to unsatisfactory solutions for the sake of practical purposes. The first because needs many and s o p h i s t i c a t e d m a t h e m a t i c a l equations and the second, because does not allow to d i f f e r e n t i a t e between the different ions. Thus, w i t h the aim of looking for a simple and p r a c t i c a l solution, a simplified approach should be tried. This will be based in several assumptions able to overcome previous difficulties.
Simplified
calculation
of De~
The several assumptions which have to be taken order to solve equation [6] are (36)(39-43):
into
account
in
i.
Only what happens inside the concrete disc is influencing the measurements. This assumption may be accepted from the fact that ionic mobilities in solution are 3 or 4 orders of m a g n i t u d e higher than in the concrete and therefore, for the sake of the measurement, the slowest process is the only c o n s i d e r e d relevant.
2.
The t e r m dealing with convection in e q u a t i o n [6] can be neglected. This seems not difficult to be accepted, if only w h a t happens inside the concrete disc is considered.
3.
The diffusion component of equation [6] is considered negligible in comparison to that due to migration. As well,
Vol. 23, No. 3
CHLORIDE DIFFUSION, AASHTO TEST, RESISTIVITY
735
e l e c t r o n e u t r a l i t y in this e x p e r i m e n t is m a i n t a i n e d by m e a n s of the electrodic processes (gas evolution or metal dissolution) and t h e r e f o r e counter diffusion or m e m b r a n e e f f e c t s are not considered.
4.
The c o n c r e t e disc is thin enough to a l l o w to r e a c h a s t e a d y s t a t e c o n d i t i o n is few hours, w h i c h in turns m e a n s that all r e a c t i v e AC 3 in the disc is s a t u r a t e d w i t h the first d i f f u s i n g c h l o r i d e s and therefore, after the t r a n s i e n t i n i t i a l period, a linear flux of c h l o r i d e s along time, is e s t a b l i s h e d (figure 4), This allows to make the term a E/a 1 = AE/I, b e i n g 1 the c o n c r e t e disc thickness, and ~E the p o t e n t i a l applied.
5.
The c o n c e n t r a t i o n of c h l o r i d e s in one c h a m b e r of the cell is m u c h h i g h e r than in the other. That is, c h l o r i d e c o n c e n t r a t i o n in the c a t h o l i t e should be high and that in the anolite, zero. T h i s a l l o w s to a c c e p t that the c o n c e n t r a t i o n (activity better) of c h l o r i d e s in one side of the cell r e m a i n s c o m p a r a t i v e l y constant.
O n c e all expressed
t h e s e a s s u m p t i o n s are in the f o l l o w i n g way:
Total
where ions. The
considered
the
mol ZF flux = -J( ...... ) . . . . . . . sg'cm 2 RT
~E De,CoL .... 1
i= disc
is the
equation
thickness
and
Ca
equation
can
be
[7]
activity
of
chloride
may be also writen: JRT
1
De,=
[8 ] z F Ccl ~E
in w h i c h all p a r a m e t e r s are known and J can be c a l c u l a t e d from an e x p e r i m e n t a l test in w h i c h the amount of c h l o r i d e s is m o n i t o r e d a l o n g the time. Thus, from a plot s i m i l a r to that of f i g u r e 4, the flux J can be c a l c u l a t e d from the slope of the linear part.
Calculation equation
of
D~
from
the value
of
intensity.
Nernst-Einstein
A n o t h e r w a y to c a l c u l a t e D ~ is from the r e c o r d i n g of the i n t e n s i t y d u r i n g the experiment, b e c a u s e it is also well e s t a b l i s h e d (36)(3943) t h a t the flux of a m i g r a t i n g species is also p r o p o r t i o n a l to the t o t a l intensity:
itj J=
[9] nF
b e i n g the t r a n s f e r e n c e number (of the c h l o r i d e in this p a r t i c u l a r case) the p r o p o r t i o n a l i t y factor. Therefore, on the c o n t r a r y from the v a l u e of J o b t a i n e d in an e x p e r i m e n t a l test, it is p o s s i b l e to
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C. Andrade
Vol. 23, No. 3
calculate the t r a n s f e r e n c e number ~, and by s u b s t i t u t i o n e q u a t i o n [9] in e q u a t i o n [7], the f o l l o w i n g is obtained: itcl
ZF =
nF
.
.
.
.
of
AE Def t Ccl
RT
.
.
.
[i0]
.
1
T h i s e x p r e s s i o n r e s u l t s s i m i l a r to N e r n s t - E i n s t e i n (32) e q u a t i o n but a p p l i e d for a single ionic species t h r o u g h the use of the t r a n s f e r e n c e number: RT Def~
RT
itcl
nF 2
AE
1
1
A cl = nF 2
[ii] A
C~Z
b e i n g A = cross s e c t i o n area of the c o n c r e t e disc. This e q u a t i o n o p e n s the d o o r to the p o s s i b i l i t y of c a l c u l a t i o n of D i f f u s i o n Coefficients from a simple measurement of resistivity or c o n d u c t i v i t y p r o v i d i n g that ~ of the p a r t i c u l a r ion c o u l d be accurately calculated (see n u m e r i c a l example later on). This approach would represent a very p r o m i s i n g s i m p l e way for the future, if the t h e o r e t i c a l d i f f i c u l t i e s of c a l c u l a t i n g a c c u r a t e t r a n s f e r e n c e n u m b e r s of c h l o r i d e ions in concrete, c o u l d be solved. Even, as it w i l l be p r e s e n t e d at the n u m e r i c a l example, this e q u a t i o n s e r v e s for an a p p r o x i m a t e c a l c u l a t i o n of the order of m a g n i t u d e of D from w a t e r s a t u r a t e d c o n c r e t e r e s i s t i v i t y values, o n c e p r o p e r a c c o u n t of the influence of the ionic s t r e n g t h of pore s o l u t i o n is c o n s i d e r e d (3)(44)(45)(46). F i n a l l y it has to be m e n t i o n e d that, if the c a l c u l a t i o n is m a d e f r o m r e s i s t i v i t y m e a s u r e m e n t s the r e a c t i o n w i t h the AC 3 is also m i s l e d and therefore, the v a l u e s o b t a i n e d are t h o s e of Den and not of D a.
0.1M NoOH
0.5 M NoCl
0.5¢m Figure
5. S i m p l e r e p r e s e n t a t i o n migration.
of the
cell
for
testing
chloride
Vol. 23, No. 3
CHLORIDE DIFFUSION,AASH'ID TEST, RESISTIVITY
737
NUMERICAL EXAMPLES Nernst-Plank
equation
Figure 5 depicts an e x a m p l e in w h i c h N a C l catholyte of a m i g r a t i o n c e l l a n d N a O H 0.1 following parameters are assumed: Cross-section
area:
0 . 5 M is M to the
added to anolyte.
the The
30 c m 2
D, = i0 -s cm2.sg -I R 1 . 9 8 7 2 c a l ' m o l l ' ~ ~I F = 2 3 0 6 3 cal'volt'1"eq "I Z = 1 Applied
potential
Concrete
thickness
between 1 = 0,5
electrodes
A E = 12 V
cm.
Considering the activity equal to produced for a concrete having a D~
the concentration, of 10 .8 cm2.s -I w o u l d
( i ) (23063) (10 .8) (0.5X10 3) (12) J =
the be:
flux
mol = 0,47
x 10 .8
(1.9872) (293) (0.5)
s.cm 2
T h i s is t h e o r d e r of m a g n i t u d e of t h e f l u x t h a t w i l l b e r e c o r d e d in t h i s k i n d of e x p e r i m e n t s , and a period of s e v e r a l h o u r s of t e s t i n g a r e n e e d e d in o r d e r t o m i n i m i z e e r r o r s in m o n i t o r i n g it. In figure 6 a graphic representation of t h e v a r i a t i o n of f l u x J w i t h t h o s e of D~, C a n d ~ E b e i n g t h e r e s t of p a r a m e t e r s constant, is g i v e n . It is a p p a r e n t t h a t an i n c r e a s e of A E f r o m 2 t o 20 v o l t s , c a n i n c r e a s e o n e o r d e r of m a g n i t u d e t h e flux. A s w a s r e f e r e d in (i) a potential of 2 volts almost does not influences the pure diffusional flux. As an example too, in (47) c h l o r i d e fluxes are reported of t h e o r d e r of a b o u t i0 m m o l / d a y f o r a c o n c r e t e c u r e d at 20°C a n d w i t h a w / c = 0,5. T h u s t a k e n i n t o a c c o u n t t h e e x p e r i m e n t a l conditions used b y t h e a u t h o r s a n d a s s u m i n g a n s t a t i o n a r y flow, t h e D ~ v a l u e s w o u l d r e s u l t t h e s e n s i b l e v a l u e of: Dc~ = 3.1 x i0 -s cm2/s
Calculation
from intensity values
The theoretical calculation of c h l o r i d e t r a n s f e r e n c e solution 0.2M NaOH + 0.5M NaCl from equation [5] w i l l of:
n u m b e r in a give a value
(0.5)(76.34) to =
,=
(o.5) (50.1)+(0.5) (76.34)+(o.2) (198)+(0.2) (50.1)
0. 338
738
C. Andrade
C = 0.5 mol/cm s AE=lEV t=0.5cm
Vol. 23, No. 3
D= 10-Scm?-/s AE=IZV L = 0.5cm
D =lO-ScmZ/s C=0,5mol/cm 3 L =0,Scm
rnol
cm2.sg
f
10-o
J
10-~ 10-1o !
,
,
,
I0 -7 I0 -s I0 -9
0.I
D (crag/s)
,
v
0.3
0.5
r
20
C(mol/cm 3)
40
r
60
AE (V)
NERNST- PLANK EQUATION Figure
6. R e p r e s e n t a t i o n of the c h l o r i d e flux after N e r n s t - P l a n k e q u a t i o n [6] (migration term) in f u n c t i o n of c h l o r i d e a c t i v i t y values.
A s s u m i n g t h e n this v a l u e as a r e f e r e n c e one, w h i c h has to be r e c o r d e d to o b t a i n a flux of w o u l d be, f o l l o w i n g e q u a t i o n [9]:
(0.47) (i0 s) (i) (96500)
JnF i =
= 1.338.10 .3 A / c m 2
= tcl
using shown
these next.
0.338
values
Nernst-Einstein
the i n t e n s i t y value 0.47 x i0 g mol/cm2"s
in e q u a t i o n
[i0]
De~ can
be
calculated,
as
is
equation
F i g u r e 7 shows a g r a p h i c r e p r e s e n t a t i o n of N e r n s t - E i n s t e i n e q u a t i o n [ii] a s s u m i n g a s o l u t i o n 0.2 M N a O H plus of NaCl w i t h a c t i v i t y v a l u e s of 0.i, 0.35 and 0.5 m o l / c m 3 and a c h l o r i d e t r a n s f e r e n c e n u m b e r of 0.338: This representation let us deduce that D concentration as is theoretically stated r e s i s t i v i t y the m o s t i n f l u e n c i n g parameter.
varies with (36), being
the the
In o r d e r to a p p l y this e q u a t i o n the c o n c r e t e has to be w a t e r s a t u r a t e d to a s s u r e p u r e d i f f u s i o n p e n e t r a t i o n m e c h a n i s m . C a p i l l a r y f o r c e s a p p e a r i n g in p a r t i a l l y dry c o n c r e t e w i l l i n t r o d u c e other m e c h a n i s m s of c h l o r i d e p e n e t r a t i o n w h i c h c o u l d v a r y the p r e d i c t i o n , which, as was a f o r e m e n t i o n e d , opens the door to the c a l c u l a t i o n of D coefficient from simple, but proper resistivity values (3) (45) (46).
Vol. 23, No. 3
CHLORIDE DIFFUSION,AASHTOTEST, RESISTIVITY
DCi4C~,g)
A o x
739
a = 0 . 1 mol/cm 3 a=0.3,5 ,, 0=0.5 ,,
10 - 4 10-5
10-e 10-7 lO-e
i
10 ,6' ,6' 16"
P (ohm .cm-1)
NERNST-EINSTEIN EQUATION Figure 7. Graphic representation of Nernst-Einstein equation in function of chloride activity values.
[i0]
Summing up, Nernst-Plank equation has to be used when values of chloride flux along time in a Migration Cell, are a c c u r a t e l y recorded, providing steady-state conditions are established. Alternatively, Nernst-Einstein equation may be used w h e n instead of chloride flux, intensity values are accurately recorded, steadystate conditions are operating and the chloride t r a n s f e r e n c e number is also accurately calculated.
CONCLUSIONS
More than conclusions, the following paragraphs are a summary of comments which can be drawn up from a thorough study of basic books on e l e c t r o c h e m i s t r y and a careful meditation on their a p p l i c a t i o n to the p a r t i c u l a r case of concrete. The Rapid Chloride Permeability Test (AASHTO) in its present formulation cannot inform on concrete permeability to chlorides. The recording of the total current p a s s i n g across the cell is a function of the amount and type of ions, but not of the chloride flux or chloride mobility. The calculation of ionic migration can be only r i g o r o u s l y r e s s o l v e d in homogeneous, binary and dilute solutions. Concrete and concrete pore solution is a p o l i e l e c t r o l y t e with high ionic strength and therefore, a rigourous c a l c u l a t i o n cannot be performed or results very difficult.
740
C. Andrade
Vol. 23, No. 3
However, as a p p r o x i m a t e values may be e n o u g h for p r a c t i c a l purposes, simplified ways of calculation of Diffusion Coefficient of c h l o r i d e s may be tried. This s u p p o s e s the a c c e p t a n c e of some a s s u m p t i o n s and u n c e r t a i n t i e s . Thus, a s s u m i n g some simplifications, N e r n s t - P l a n k and N e r n s t E i n s t e i n e q u a t i o n s can be used in a d i s p o s i t i o n s i m i l a r to a d i f f u s i o n cell (migration cell): the m a i n b e i n g to a c c e p t that c o n v e c t i o n does not o p e r a t e inside the c o n c r e t e and that d i f f u s i o n is n e g l i g i b l e c o m p a r e d to m i g r a t i o n w h e n e l e c t r i c a l f i e l d s h i g h e r than 10v are operating. F r o m equations, [8] and [ii], E f f e c t i v e D i f f u s i o n C o e f f i c i e n t , De, , can be c a l c u l a t e d in an e x p e r i m e n t of few days. N e r n s t P l a n k e q u a t i o n can be used w h e n only c h l o r i d e flux a l o n g time is r e c o r d e d and N e r n s t - E i n s t e i n e q u a t i o n w h e n i n t e n s i t y v a l u e s and c h l o r i d e t r a n s f e r e n c e numbers are a c c u r a t e l y a p p l i e d and measured respectively. An extensive experimental program, which at p r e s e n t is b e i n g c a r r i e d out by the author, is n e e d e d to c h e c k w h e t h e r the a s s u m p t i o n s c o n s i d e r e d are c o r r e c t or not.
F i n a l l y it has to be m e n t i o n e d that the same e q u a t i o n s can be a p p l i e d to c a l c u l a t e ionic m o v e m e n t s in the case of c a t h o d i c p r o t e c t i o n , c h l o r i d e removal or r e a l k a l i z a t i o n , a l t h o u g h in these cases a n o n - s t a t i o n a r y p r o c e s s is e s t a b l i s h e d w h i c h m a k e s m o r e s o p h i s t i c a t e d the s o l u t i o n of e q u a t i o n [6] and [ii]. S p e c i a l l y seems v e r y a t t r a c t i v e the r e s s o l u t i o n in the case of c h l o r i d e removal, because it may give the t h e o r e t i c a l t i m e n e e d e d to d e c r e a s e the a m o u n t of c h l o r i d e s below a c e r t a i n t h r e s h o l d .
ACKNOWLEDGEMENTS
The a u t h o r is g r a t e f u l to several r e s e a r c h e r s for t h e i r c o m m e n t s and e x p e r i m e n t a l trials. First she is g r a t e f u l to Dr. J. G a l v e l e of A r g e n t i n a for the d i s c u s s i o n on the p r e l i m i n a r y s t a t e s of the p a p e r and the c o m m e n t s i n t r o d u c e d in the final version. T h a n k s are also g i v e n for the d i s c u s s i o n s to her c o l l e a g u e s at the Institute: Dr. S. Gofii and Dr. C. Alonso, and finally to Mr. M.A. S a n j u ~ n for his e x p e r i m e n t a l trials.
BIBLIOGI~PHY
(i) (2) (3) (4)
S. GOTO, D.M. ROY - Cement and C o n c r e t e Research, ii pp 751757 (1981). M. COLLEPARDI, A. MARCIALIS, R. T U R R I Z I A N I - Ii Cemento, 67, pp 157-164 (1979). A. ATKINSON, A.K. N I C K E R S O N - J o u r n a l of M a t e r i a l s S c i e n c e 19, pp 3068 - 1078 (1984). C.L. PAGE, N.R. SHORT, A. EL TARRAS - C e m e n t and C o n c r e t e Res. Ii, pp 395-406 (1981).
Vol. 23, No. 3
CHLORIDE DIFFUSION, AASHTO TEST, RESISTIVITY
(5)
N.R.
(6)
(RILEM), J. C R A N K
741
J.B. NEWMAN Materials and Structures, 20, p p 3 - 1 0 (1987). - The Mathematics of D i f f u s i o n , Ed. O x f o r d U n i v e r s i t y
BUENFELD,
(1975). (7)
H. D I A B , A. B E N T U R , C. H E I T N E R - W I R G U I N , L. B E N - D O R - C e m e n t a n d Concrete Research, 18, p p 7 1 5 - 7 2 2 (1988). (8) R.D. B R O W N E - P e r f o r a n c e of C o n c r e t e in M a r i n e E n v i r o n m e n t A C I S P - 6 5 , p p 169, 204 (1980). (9) K. B Y F O R S - C h l o r i d e i n i t i a t e d r e i n f o r c e m e n t corrosion - CBI R e p o r t 1 / 9 0 - 121 p p (1990). (i0) R.K. DHIR, M.R. J O N E S , H . E . H . A H M E D - M a g a z i n e of C o n c r e t e Research, 4_/3, p p 3 7 - 4 4 (1991). (ii) K. T U U T T I - C o r r o s i o n of S t e e l in C o n c r e t e - D o c t o r a l T h e s i s , Swedish Cement and Concrete Institute, Stockholm, 469 pp. (1982). (12) O . E . G J O R V , O. V E N N E S L A N D - C e m e n t a n d C o n c r e t e R e s e a r c h , 9, pp 229-238 (1979). (13) J. T R I T T H A R T - Cement and Concrete Research 19, p p 683 - 691 (1989). (14) L. H A C H A N I , E. T H I K I , A. R A H A R I N A I V O , M.T. CHAIEB - Materials and Structures (RILEM), 2__44, PP 1 7 2 - 1 7 6 (1991). (15) P. S C H I E S S L - D i f f u s i o n s m o d e l l zur rechnerischen Erfassung der Chloridionendiffusion in B e t o n - IBS - Bo. 238 (1983). (16) R . K . D H I R , M . R . J O N E S , A.M. S E N E V I R A T N E - C e m e n t a n d C o n c r e t e R e s . , 2_!1, p p 1 0 9 2 - 1 1 0 2 (1991). (17) Y. M A S U D A - ist. I n t e r n a t i o n a l RILEM Congress: Durability of Construction Materials, v o l 3, P a r i s , p p 9 3 5 - 942 (1987). (18) A. R A H A R I N A I V O , J.M. G E N I N - B u l l L i a i s o n L C P C , nQ 144, p p 5964 (1986). (19) N . R . B U E N F E L D , J.B. N E W M A N - M a g a z i n e of C o n c r e t e R e s . , 36, p p 6 7 - 8 0 (1984). (20) D. W H I T I N G - P u b l i c R o a d s , 45, p p 1 0 1 - 1 1 2 (1981) (21) D. W H I T I N G - A m e r i c a n C o n c r e t e I n s t i t u t e S P - 8 2 - 2 5 , p p 5 0 1 - 5 2 4
(1981) (22)
S.
LI,
D.M.
ROY
- Cement
and
Concrete
Res.,
1-6, p p
749-759
(1986). (23) (24) (25) (26)
(27)
(28) (29) (30)
(31) (32)
J.G. CABRERA, P.A. C L A I S S E - C e m e n t a n d C o n c r e t e Composites i__22, p p . 1 5 7 - 1 6 1 (1990). Y. GAU, I. C O R N E T - C o r r o s i o n (NACE), 4_!1, p p 9 3 - 1 0 0 (1985). T . C . H A N S E N , H. J E N S E N , T. J O H A N N E S S O N - Cement and Concrete Research, 16, p p 7 8 2 - 7 8 4 (1986). C.M. HANSSON, B. S O R E N S E N - Corrosion Rates of S t e e l in C o n c r e t e . A S T M S T P / 1 0 6 5 , N.S. B e r k e , V. C h a k e r , D. W h i t i n g Ed, p p 3 - 1 6 (1990). M. GEIKER, N. THAULOW, J. ANDERSEN - 5th International C o n f e r e n c e o n D u r a b i l i t y of b u i l d i n g M a t e r i a l s a n d C o m p o n e n t s , Brighton, U . K . , pp. 4 9 3 - 5 0 2 , N o v (1990). R.J. DETWILER, K.O. KJELLSEN, O.E. GJOR - ACI Materials Journal, 8-8, p p 1 9 - 2 4 (1991). P. R E C H B E R G E R - Zement-Kalk-Gips, 3-8, p p 6 7 9 - 6 8 4 (1985). D. W H I T I N G - R a p i d D e t e r m i n a t i o n of t h e C h l o r i d e P e r m e a b i l i t y of Concrete. R e p o r t No. F H W A / R D - 8 1 / I I 9 , A u g u s t 1981, N T I S DB No. 8 2 1 4 0 7 2 4 . A . A . H A C H E M I , M. M U R A T , J.C. C U B A U D - R e v u e d e s M a t ~ r i a u x de Construction, n~ 700, p p 1 4 9 - 1 5 5 (1976) V . K . G O U D A , G.E. M O N F O R E - Journal PCA - Research a n d Dev. Lab. Z, P P 2 4 - 3 6 (1965).
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(33) (34) (35) (36) (37) (38)
(39) (40)
(41)
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Vol. 23, No. 3
G. GRIMALDI, J.C. LANGUEHARD - Bulletin de Liaison des Laboratoires d e s P o n t s et C h a u s s ~ e s , p p - 7 9 - 8 4 M a y - J u n (1986). J.E. B E N N E T T , T.J. S C H U E - C o r r o s i o n 90. N A C E . P a p e r No. 316, (1990). J.A. B A B O R , J. I B A R Z - Q u i m i c a G e n e r a l M o d e r n a - M a n u a l M a r i n Ed. B a r c e l o n a - S p a i n - p p 4 8 3 - 8 6 (1958). J.O'M. BOCKRIS, A.K.N. REDDY - Modern Electrochemistry P l e n u m P r e s s Ed. N e w Y o r k (1974). S. G L A S S T O N E - T e x t b o o k of P h y s i c a l C h e m i s t r y - Van Nostrand Ed. N e w York. (1947). H.K. HILSDORF, J. K R O P P - Permeability of C o n c r e t e as a criterion of its d u r a b i l i t y - Report of R I L E M Technical Committee T C 116 (1992). A.J. BARD, L.R. FAULKNER Electrochemical Methods. Fundamentals and Applications - J o n W i l e y & S o n s Ed., (1980). J.M. COSTA Fundamentos de Electrodica. Cin~tica Electroquimica y sus a p l i c a c i o n e s . Alhambra Universidad Ed. S p a i n (1981). W. F O R K E R - C i n ~ t i c a E l e c t r o q u i m i c a - E u d e b a Ed. B u e n o s A i r e s Argentina (1986). Southampton Electrochemistry Group - Instrumental M e t h o d s in Electrochemistry - E l l i s H o r w o o d S e r i e s in P h y s i c a l C h e m i s t r y Ed. (1990). J.S.NEWMAN - Electrochemical Systems - Prentice Hall Ed. Englewood C l i f f s , N e w J e r s e y (1991). A. M O R A G U E S , S. GONI, C. A N D R A D E - Ceramic Transactions. A d v a n c e s in C e m e n t i t i o u s M a t e r i a l s . S. M i n d e s s Ed., 16, p p 57-
(42)
(43) (44)
65 (1991). (45)
E.J.
GARBOCZI
- Cement
and Concrete
Research,
20,
pp
591-601,
(1990). (46) (47)
P. LAY, P.F. L A W R E N C E , N . J . M . W I L K I N S , D.E. W I L L I A M S - J o u r n a l of Applied Electrochemistry 15, p p 7 5 5 7 5 5 - 7 6 6 (1985). R.J. D E T W I L E R , K.O. K J E L L S E N , O . G J O R V - A C I M a t e r i a l s J o u r n a l , J a n - F e b , p p 1 9 - 2 4 (1991).
CALCULATION
OF CHLORIDE DIFFUSION COEFFICIENTS IN CONCRETE FROM IONIC MIGRATION MEASUREMENTS
Institute
C. A N D R A D E "Eduardo Torroja" of Construction CSIC - Madrid - Spain
Sciences
(Communicated by J.P. Skalny) (ReceivedJuly 21, 1992)
ABSTRACT
A critical review is offered on the Rapid Chloride P e r m e a b i l i t y Test standarized by AASHTO, p o i n t i n g out its limitations and errors but recognizing its c o n t r i b u t i o n to the developing of a simple and quick test for chloride migration. Then another review is made on the electrochemical fundaments of the p r o c e s s e s d e v e l o p p e d in concrete when an electrical field is a p p l i e d and on the basic equations of mass transport (Nernst-Plank and Nernst-Einstein) which can be applied to c a l c u l a t e ionic movements. The limitations and assumptions needed for a simplified resolution of these equations, are presented, as well as numerical examples of c a l c u l a t i o n of the Effective Diffusion Coefficient of chlorides, De~, in steady state condition. Finally, c o n s i d e r a t i o n s on the p o s s i b i l i t y of calculation of Dc~ from simple r e s i s t i v i t y m e a s u r e m e n t s are also offered.
INTRODUCTION
P e n e t r a t i o n of chlorides through concrete is one of the factors which aims to the depassivation of reinforcing bars and therefore, may shorten the life of the structure. The time needed by these ions to reach the rebar depends first, on the m e c h a n i s m of intrusion and secondly, on the external c o n c e n t r a t i o n of the chlorides and the microstructure of the concrete. W h e n concrete is completely water saturated, chlorides p e n e t r a t e by a pure diffusion mechanism, being the difference in concentration, the driving force. However in partial saturated concrete, chlorides may penetrate by absorption and capillary forces or d i s s o l v e d in the microdrops of marine fogs. These last ones m o r e complex penetration mechanisms, are not going to be c o n s i d e r e d in present paper. 724
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CHI.£)RIDE DIFFUSION,AASHTOTEST, RESISTIVH'Y
725
In t h e c a s e of p u r e d i f f u s i o n the c a l c u l a t i o n of t h e p e n e t r a t i o n r a t e of c h l o r i d e , has b e e n m a i n l y s t u d i e d by m e a n s of e x p e r i m e n t s a s s u m i n g e i t h e r s t e a d y - s t a t e or n o n - s t e a d y - s t a t e flow. In t h e case of s t e a d y - s t a t e c o n d i t i o n s (1-5), u s u a l l y a t h i n d i s c of c e m e n t paste is i n t r o d u c e d in b e t w e e n the two c h a m b e r s of a n a m e d " d i f f u s i o n cell", and first Fick's law is a p p l i e d (6) in o r d e r to calculate an Effective Diffusion Coeficient, D~, (diffusion c o e f f i c i e n t in a p o r o u s medium): dC -J(x)
dC(x)
=
= Dc~ dt
[i] dx
T h i s m e t h o d o l o g y p r e s e n t s some l i m i t a t i o n s w h i c h m a y be s u m a r i z e d as follows: a) c e m e n t p a s t e and not c o n c r e t e is u s e d w h i c h can lead to u n r e a l i s t i c results, b) it is t i m e - c o n s u m i n g and t a k e s w e e k s to o b t a i n one result, c) a c o n s t a n t c o n c e n t r a t i o n in the c h a m b e r c o n t a i n i n g c h l o r i d e s from the b e g i n n i n g s h o u l d be m a i n t a i n e d . In t h e c a s e of n o n - s t a t i o n a r y c o n d i t i o n s , c o n c r e t e b l o c k s or specimens can be u s e d w h i c h r e s u l t s in m u c h m o r e realistic c o n d i t i o n s . T h e s e c o n c r e t e b l o c k s are m a i n t a i n e d in c o n t a c t w i t h a s o l u t i o n of c o n s t a n t c h l o r i d e c o n c e n t r a t i o n and the c h l o r i d e p r o f i l e a l o n g the time is measured. In this case s e c o n d F i c k ' s law is a p p l i e d to c a l c u l a t e the, an A p p a r e n t D i f f u s i o n C o e f f i c i e n t D a (6):
ac(x) -J(x)
= at
This equation conditions: cx= c,, and the
is u s u a l l y
x = 0,
initial
Cx= 0,
a2c = D a - .... ax 2
solved
the
following
boundary
t > 0
[3]
condition: x > 0,
applying
[2]
t = 0
O b t a i n i n g the f o l l o w i n g s o l u t i o n w h i c h is the m o s t w i d e l y u s e d
(7-
11). Cx
x = 1 - erf
C,
[4] 2(Dat) I/2
T h i s t y p e of t e s t also r e s u l t s v e r y t i m e - c o n s u m i n g and m a i n t a i n s s e v e r a l u n c e r t a i n t i e s on the r i g o r o u s a p p l i c a t i o n of F i c k ' s law. S o m e a u t h o r s (12) r a t h e r p r e f e r to c o m p a r e c h l o r i d e p r o f i l e s t h a n c a l c u l a t e D,. In a d d i t i o n , in b o t h s t e a d y and n o n - s t e a d y t e s t c o n d i t i o n s , it is not u s u a l l y c a l c u l a t e d the r e a c t i o n or a d s o r p t i o n of c h l o r i d e s by c e m e n t phases. T h i s c i r c u n s t a n c e is c o n s i d e r e d of m i n o r i n f l u e n c e
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Vol. 23, No. 3
although few researchers (13-14) do take into account. Thus, A t k i n s o n (3) refers to it by defining: a) a Da: A p p a r e n t Diffusion Coefficient in a porous medium, which considers the average c o n c e n t r a t i o n gradients of the diffusing substance, t h e r e f o r e the a d s o r p t i o n phenomena, and b) a Di: Intrinsic D i f f u s i o n Coefficient w h i c h tries to take into account the average flux per unit of area, and therefore, the volume fraction of porosity. There are also a variety of improvement p r o p o s a l s basic approaches (15-18) which make much more c a l c u l a t i o n of the chloride D,.
Electrical
to these complex
two the
methods
B e c a u s e of testing "natural" chloride p e n e t r a t i o n results timeconsuming, attempts have been made to calculate the D a from resistivity measurementes (3)(19) or to accelerate the rate of penetration of chloride ions by applying a n - e l e c t r i c a l field (1)(20-29). B o t h k i n d of test types will be commented in present paper in order to a n a l y s e their possibilities and limitations. First a critical r e v i e w will be done on the test known as "AASHTO TEST" (30) explaining why its mode of operation leads to erroneous conclusions. Secondly a brief summary will be made on the basic k n o w l e d g e needed to understand migration phenomena in electrolytes. Finally, a proposal will be presented on how to c a l c u l a t e Diffusion C o e f f i c i e n t from electrical (migration) m e a s u r e m e n t s and which are the t h e o r e t i c a l limitations. Numerical examples will be given. E x t e n s i v e experimental trials will be needed to verify whether the a s s u m p t i o n s taken in the numerical examples are r e l i a b l e or not.
CRITICAL
REVIEW
OF THE
RAPID
CHLORIDE
PERMEABILITY
TEST
That chlorides move quicker troughout the concrete when an electrical field is applied arose from earlier experiments, (31)(32) on that known at present as chloride removal (33)(34). Actually, this fact on chloride migration was already experienced by m a n y r e s e a r c h e r s using electrochemical techniques (as cathodic p r o t e c t i o n (12) for instance). However, it was W h i t i n g who, (2021)(30) p r o p o s e d a "Rapid Chloride Permeability Test" in order to o b t a i n in few hours an appraisal on concrete permeability. This s t a n d a r d test has promoted a strong controversy (28)(29), w i t h more heat than light in clarifying the meaning of the test and its a b i l i t y to predict concrete resistance to p e r m e a t i o n of chlorides. The real fact is that the test is increasingly being used although e v e r y b o d y recognizes some still unknown uncertainties. S u m m i n g up, this test uses a thick (usually 5 b e t w e e n two electrodes (usually copper meshes) similar to that of the diffusion cell. Sodium weight) is added to one of the chambers and NaOH the other. Then, an electrical field of 60V is a p p l i e d between electrodes and the amount of
cm) c o n c r e t e disc in an arrangement chloride (3% per of about 0.i M to r e c o m m e n d e d to be coulombs recorded
Vol. 23, No. 3
CHLORIDE DIFFUSION, AASHTO TEST, RESISTIVITY
727
a l o n g 6 h o u r s of testing, are m e a s u r e d . The t e s t d e f i n e s t h a t a h i g h e r a m o u n t of c o u l o m b s r e p r e s e n t s a h i g h e r p e r m e a b i l i t y of the c o n c r e t e to the c h l o r i d e s .
Movement
of
ions
in
concrete
under
an
electrical
field
L e t us a n a l y s e n o w step by step w h a t h a p p e n s from the b e g i n n i n g of t h e e x p e r i m e n t and try to e x p l a i n w h a t is w r o n g in the test. W h e n t h e c o n c r e t e d i s c is i n t r o d u c e d in the cell, b e f o r e any e l e c t r i c a l f i e l d is a p p l i e d a d i f f u s i o n (leaching) is p r o d u c e d m a i n l y of OH- ions due to t h e i r h i g h ionic m o b i l i t y as f i g u r e 1 a shows. T h i s d i f f u s i o n due the d i f f e r e n c e in c o n c e n t r a t i o n s of d i f f e r e n t ions m a y be m a i n t a i n e d a l o n g the e x p e r i m e n t . In a d d i t i o n , w h e n the e l e c t r i c a l field is applied, m i g r a t i o n of all ions o c c u r s t o w a r d s the o p p o s i t e sign e l e c t r o d e (figure ib). Not o n l y c h l o r i d e s move, but all the ions do and the t o t a l c u r r e n t is spent in the a d d i t i o n of all t h e s e m o v e m e n t s w h i c h w i l l be commented later. Therefore, diffusion plus m i g r a t i o n happens s i m u l t a n e o u s l y as f i g u r e 1 c depicts. The final r e s u l t w i l l d e p e n d on t h e r e l a t i v e i m p o r t a n c e of both m o v e m e n t s . T h e n the p r o c e s s e s d e v e l o p p i n g (36) in the cell w h e n an e l e c t r i c a l f i e l d is applied, are the f o l l o w i n g (figure 2):
a)
Electrode processes
-
a.l)
M e t a l d i s s o l u t i o n - w h i c h g e n e r a t e s o x y d e s at t h e a n o l y t e (possitive electrode chamber), if the anode is an o x i d a b l e metal, as for i n s t a n c e copper. In the c a s e of g r a p h i t e e l e c t r o d e s the p r o c e s s w i l l be: C --> CO + CO 2.
a.2)
E v o l u t i o n of gases - as e l e c t r o l y s i s of water, in b o t h anolyte and catholyte, generating 02 a n d H 2. This e v o l u t i o n w i l l stirr the s o l u t i o n in b o t h c h a m b e r s .
The r e a c t i o n s possitive negative
o c u r r i n g are the w e l l known:
electrode electrode
- 2H20 --> 202 - 2H20 + 2 e
+ 4H ÷ + 4e °
--> H 2
+
20H °
In the case of u s i n g not c o r r o d i b l e e l e c t r o d e s as Pt, the w a t e r e l e c t r o l y s i s will be the o n l y e l e c t r o d i c process.
Not o n l y w a t e r e l e c t r o l y s i s but o x i d a t i o n of Cl ° a l s o m a y h a p p e n if the v o l t a g e is h i g h e n o u g h to p r o d u c e Cl 2 evolution. possitive
electrode:
- 2Ci ° --> Cl 2 + 2 e
728
C. Andrade
As well reaction, negative
as
oxygen
electrode:
Vol. 23, No. 3
reduction
following
the
known
202 + H20 + 4e" -> 4OH °
All these reactions tends to maintain the total e l e c t r o n e u t r a l i t y of the e x p e r i m e n t w h i c h is one of the f u n d a m e n t a l s of e l e c t r o c h e m i c a l r e a c t i o n s . CQncrete
No + •, , , - - - C I -
OHNa ÷
a) DIFFUSION
®
Concrete
~--- CINo+-~,.
b)
MIGRATION
®
Concrete
(~
Y//.//I OHNQ ÷
~ - - 0H-
V/N/
"o'-
c) DIFFUSION + MIGRATION Figure
i. M a s s
transport processes
in concrete.
Vol. 23, No. 3
CHLORIDE DIFFUSION,AASHTOTEST, RESISTIVITY
(~) HEAT=IZ.Rohm
:"
729
(~
No+._...
0
00
2 H20 "-" 0 2 0 2 H +
No
CI "-" CI2~ Cu--Cu +I
2 H 2 0 - " H2t+ 2OH-
02+ 2H20 "" 4OH"
F
Figure 2. Processes occurring when an electrical field is applied in a diffusion cell: Joule effect, anode dissolution, electrolysis of the electrolite (gas e v o l u t i o n at electrodes and reduction reactions) and ionic m i g r a t i o n and diffusion. b)
Migration The third process happening in a cell is the m o v e m e n t of ions in the electrolyte in order to carry the e l e c t r i c i t y passing through the cell. Therefore, migration is developed and diffusion may appear if this m i g r a t i o n leads to concentration differences. As it was mentioned, not only chlorides move but all ions take part in migration in a proportion what is known as their "transport or transference number". T r a n s f e r e n c e number Let us try to explain something here about this parameter. The transference number of an ion m o v i n g under the action of an external electrical field is defined by the "proportion of the current carried by this ion in relation to the current carried by the rest of the ions" (36). It is formulated as:
i, t~.
.
. i
%%xj .
.
. . Z ZCX
[5] A
Hence, the transference number is a function of the ionic m o b i l i t y or the equivalent conductivity. This means that OH- ions will carry much more p r o p o r t i o n of current than Cl- ones due to the ionic conductivity of OH" is 198,5 o h ~ l'cm2"eq-] and that of C I is 76,34 ohm-*.cm2.eq-I (36). This fact is very important in the case of concrete because
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Vol. 23, No. 3
it m e a n s that the m a i n p r o p o r t i o n of the c u r r e n t w o u l d be t a k e n by O H ions and not by the Cl ° and t h e r e f o r e , h y d r o x y d e s m i g h t b e h a v e as a " s u p p o r t i n g e l e c t r o l y t e " . Therefore, only if c h l o r i d e t r a n s f e r e n c e n u m b e r s are c a l c u l a t e d is p o s s i b l e to s p e c i f i c a l l y d e d u c e c h l o r i d e t r a n s p o r t feasability, w h i c h is not t a k e n into a c c o u n t by the R a p i d C h l o r i d e P e r m e a b i l i t y t e s t w h i c h only r e c o r d s the total a m o u n t of c u r r e n t (that c o r r e s p o n d i n g to the m o v e m e n t of all ions). In a d d i t i o n w h e n f l o w i n g t h r o u g h the c o n c r e t e the c h l o r i d e s m a y r e a c t w i t h the C3A and t h e r e f o r e a s t a t i o n a r y flow c a n n o t be a c h i e v e d u n t i l all r e a c t i v e sites are saturated.
Movement
of c a t i o n s
-
An a d d i t i o n a l a s p e c t to be s t r e s s e d n o w is r e l a t e d to the " a n o m a l o u s " D i f f u s i o n C o e f f i c i e n t t h a t is m e a s u r e d in the c a s e of the c a t i o n s of small ionic radius, as Na ÷ and K ÷ (i). T h i s b e h a v i o u r is v e r y w e l l d e s c r i b e d by B o c k r i s (36) and G l a s s t o n e (37) c o n s i d e r i n g t h a t t h e s e ions m i g r a t e solvated, that is, due to its s m a l l ionic radius, Na ÷ and K ÷ d i f f u s e or m i g r a t e surrounded by w a t e r m o l e c u l e s , as they n o r m a l l y are in solution. T h a t m a k e s t h e i r m o v e m e n t m o r e d i f f i c u l t and t h e r e f o r e , D v a l u e s s m a l l e r t h a n t h o s e of c h l o r i d e ions are r e p o r t e d (i). T h i s fact also e x p l a i n s w h y w a t e r m a y c o n c e n t r a t e at the cathode, as was s o m e t i m e s n o t i c e d in the c a s e of c a t h o d i c p r o t e c t i o n . Na ÷ and K ÷ m i g r a t i o n m e a n s t h a t a net f l o w of water (electroosmosis) is also s i m u l t a n e o u s l y p r o d u c e d . T h i s fact can be also a p p l i e d to e x p l a i n the b a s i c process of electrochemical realkalization: there, h y d r o x y d e s are p r o d u c e d at the r e b a r a c t i n g as cathode, and s o l v a t e d Na ÷ ions m o v e from the e x t e r n a l c a r b o n a t e s o l u t i o n in order to b a l a n c e the e l e c t r i c a l c h a r g e s and, finally they support the r e c o n s t r u c t i o n of a N a O H solution around the rebars. Anyway, as water is simultaneously r e d u c e d at the c a t h o d e t o g e t h e r w i t h oxygen, the d i l u t i o n e f f e c t m a y be b a l a n c e d . In the case of the m i g r a t i o n test, h a v i n g t w o c h a m b e r s w i t h solutions, the e f f e c t of i n c r e a s i n g w a t e r a r o u n d the r e b a r is not noticeable, but in the c a s e of c o n c r e t e ( c a t h o d i c p r o t e c t i o n , r e a l k a l i z a t i o n or c h l o r i d e removal) the e f f e c t w i l l be d e p e n d e n t of the p o t e n t i a l a p p l i e d or the l a s t i n g of the t r e a t m e n t . A c o n s e q u e n c e of this e f f e c t in the case of c a t h o d i c p r o t e c t i o n , is t h a t the r e s i s t i v i t y will i n c r e a s e at the a n o l y t e (and t h e r e f o r e d e c r e a s i n g the e f f i c i e n c y of the a n o d e s ) a n d a dilution of the s o l u t i o n a r o u n d the cathode, and t h e r e f o r e a " b u f f e r i n g " of the i n c r e a s e in pH v a l u e on the c a t h o l y t e , m a y happen.
Vol. 23, No. 3
CHLORIDE DIFFUSION, AASHTO TEST, RESISTIVITY
731
S u m m i n g up w h a t has been said up to now, when an electrical field (direct current) is applied between two electrodes p l a c e d both sides of a concrete block, several phenomena d e v e l o p as figure 2 depicts: a) The anodic material, if possible, dissolves and gases may evolve at b o t h electrodes, b) all ions of the electrolyte m o v e in order to carry the current passing through the cell and to m a i n t a i n e l e c t r o n e u t r a l i t y c) in addition heat is produced as a consequence of the current flow. At the sight of these comments, it can be deduced that, the R a p i d C h l o r i d e Permeability test contains the following errors:
i)
It accounts the total the chloride flow.
2)
W h e n integrating the total current from the b e g i n n i n g of the e x p e r i m e n t it does not distinguish between chloride flow plus r e a c t i o n and simple flow.
3)
The high voltage drop used (60v) in turn changes the flow speed.
current
and not that
induces heat
T h e r e f o r e a m i g r a t i o n test of this type cannot transport of chlorides (38) and much less "permeability" of the concrete specimen. CALCULATION
OF
DIFFUSION
COEFFICIENTS
corresponding
FROM
(23)(27)
which
at all inform on p o r o s i t y
MIGRATION
to
on or
MEASUREMENTS
A l t h o u g h it has been mentioned the errors involved in the "Rapid C h l o r i d e P e r m e a b i l i t y Test" which invalidates its d e d u c t i o n s , i t m u s t be r e c o g n i z e d the importance of its aim of shortening the time n e e d e d to test concrete resistance to ionic diffusion, and how much W h i t i n g ideas have estimulated the discussion on this area. Now an attempt is presented on how to calculate, not he "permeability", but the Diffusion Coefficient from an electrical m e a s u r e m e n t similar to that described in the AASHTO test. Diffusion c o e f f i c i e n t is the parameter which may characterize a concrete in order to p r e d i c t its long term performance, that is, its resistance to the p e n e t r a t i o n of ions. The calculation of D from electrical measurements has to be based in the fundamental of transport p r o c e s s e s in electrolytes, very well established in the traditional books of E l e c t r o c h e m i s t r y Science (36)(37)(39-43). There, it appears that the general equation for t r a n s p o r t processes in s o l u t i o n is that named Nernst-Planck (36) equation which can be w r i t t e n as:
0Cj (X)
-J~(x) = %
ZjF
+ 0x
0E (X)
%q RT
+ qv(x) 0 (x)
[6]
732
C. Andrade
J(x)
= = = = = = = = = = =
ax Zj F R
T
V
Vol. 23, No. 3
u n i d i r e c t i o n a l flux of species j (mol/cm2s) d i f f u s i o n c o e f f i c i e n t of species j (cm2/s) v a r i a t i o n of c o n c e n t r a t i o n (mol/c~) v a r i a t i o n of d i s t a n c e (cm) e l e c t r i c a l c h a r g e of species j F a r a d a y ' s n u m b e r (coul/eq) gas c o n s t a n t (cal.voltl.eq l) a b s o l u t e t e m p e r a t u r e (~) b u l k c o n c e n t r a t i o n of the species j ( m o l / c m 3) v a r i a t i o n of p o t e n t i a l (V) a r t i f i c i a l or forced v e l o c i t y of ion (cm/s)
w h i c h m e a n s that the u n i d i r e c t i o n a l (x) flux of a p a r t i c u l a r ion (5) is a f u n c t i o n of its d i f f u s i o n plus its m i g r a t i o n c o m p o n e n t s and p l u s the flux due to convection. That is: Flux = d i f f u s i o n T h e r e f o r e this e q u a t i o n ionic f l u x recorded.
+ migration
+ convection
allows the c a l c u l a t i o n
of D f r o m the total
However, some c o n s i d e r a t i o n s have to be m a d e b e f o r e a p p l i c a t i o n of e q u a t i o n [6] is tried. These
an a p p r o p r i a t e
are:
A)
The n e e d to p r o v i d e the c o n d i t i o n s for s t e a d y - s t a t e flow (equation [6] as it is, is f o r m u l a t e d for s t e a d y state conditions).
B)
The r e a c t i o n of c h l o r i d e s w i t h the C3A and t h e r e f o r e the d e f i n i t i o n of D as an " A p p a r e n t D", D a w h e n it t a k e s it into account, or an E f f e c t i v e one, D~, w h e n it m e a s u r e s the net c h l o r i d e flow w i t h o u t reaction.
c)
L i m i t s of a c c u r a c y due c o n c r e t e p o r e solution.
D)
The p o t e n t i a l d i f f e r e n c e to a v o i d Joule effect.
NaO
NaCI
STATIONARY FLOW
Figure
to
the
high
applied
ionic
should
strengths
be small
of
enough
NeOH~ _ N a C i
NON-STATIONARY
FLOW
3. S t a t i o n a r y and n o n - s t a t i o n a r y flow in f u n c t i o n s p e c i m e n t h i c k n e s s and time of testing.
of
the
Vol. 23, No. 3
B)
e)
CHLORIDE DIFFUSION, AASHTO TEST, RESISTIVITY
733
Stationary flow - in order to apply e q u a t i o n [6] in its p r e s e n t formulation, a s t e a d y - s t a t e flow has to be e s t a b l i s h e d as f i g u r e 3 depicts. If n o n - s t a t i o n a r y flow is p r o d u c e d , then the v a r i a t i o n w i t h the d i s t a n c e of the c h l o r i d e c o n c e n t r a t i o n , s h o u l d be also t a k e n into a c c o u n t a i m i n g to an e q u a t i o n in p a r t i a l d e r i v a t i v e s of second order s i m i l a r to s e c o n d Fick's law. R e a o t i o m - the first c h l o r i d e ions t r a v e r s i n g the c o n c r e t e d i s c w i l l react w i t h AC 3 and t h e r e f o r e an e r r o n e o u s D m a y be c a l c u l a t e d as has been d e t e c t e d in the case of p u r e d i f f u s i o n cells. In order to n e g l e c t this fact, the c a l c u l a t i o n of D has to be m a d e w h e n a linear increase of c h l o r i d e s is r e c o r d e d in the c h a m b e r not c o n t a i n i n g them at the beginning, t h a t is to r e c o r d the c h l o r i d e flow when the r e a c t i v e AC 3 was s a t u r a t e d w i t h the first m i g r a t i n g Cl ° (figure 4). I o n i c s t r e n g t h - In order to take into a c c o u n t the h i g h ionic s t r e n g t h of the c o n c r e t e pore solution, two m a i n a s p e c t s h a v e to be considered: a) that a c t i v i t i e s i n s t e a d of c o n c e n t r a t i o n m u s t be c o n s i d e r e d and therefore, either a selective ion electrode for chloride is used or activities must be c a l c u l a t e d , for instance as is s u g g e s s t e d in (44), and b) the i n f l u e n c e of the ionic s t r e n g t h in the t r a n s p o r t number, ~, and in the v a l u e itself of D ~ should be c o n s i d e r e d .
Let us a g a i n try to a n a l y z e this a s p e c t of the i n f l u e n c e of the ionic s t r e n g t h on D w i t h m o r e detail. It has been e s t a b l i s h e d that D is not a constant, but a f u n c t i o n of the c o n c e n t r a t i o n of the solution (36) and therefore, h i g h ionic s t r e n g t h i n f l u e n c e s D value. In a r e c e n t p a p e r (44) a s i m p l e w a y to c a l c u l a t e activity factors from conductivity m e a s u r e m e n t s has been offered, and t h e r e f o r e a t r i a l w i l l be p r e s e n t e d in the n u m e r i c a l examples, on h o w Dc~ v a r i a t i o n w i t h c o n c e n t r a t i o n is calculated. tool
cm =. sg
Cl- in the catholite
I
~
,
!
r
w
,
TIME Figure
4. Flux (J) of c h l o r i d e s time.
leaving the c a t h o d i c
chamber
along
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Vol. 23, No. 3
Anyway, it is important to stress that being the concrete pore solution a very concentrated one, the influence of ionic strength cannot be neglected in the calculation. D)
J o u l e e f f e c t - The potential difference applied to drive m i g r a t i o n should be as high to promote a quick enough m o v e m e n t of chlorides, and as small as to avoid a waste in heating. Ten to fifteen volts could be a sensible compromise.
Solving
Nernst
- Plank
equation
Really a rigourous solution for equation [6] cannot be a c h i e v e d in solutions as concentrated as concrete pore solution (36)(43). In polielectrolytes (more than binary solutions) a rigourous a p p l i c a t i o n of flux equation [6] fails, an even m o r e if the s o l u t i o n is concentrated, because D has to take into account interaction of all ionic species. Therefore at least two main d i f f i c u l t i e s arise when facing our particular problem: 1) first that of the high ionic strength previously commented and 2) how to apply the e q u a t i o n to a particular ion and not to the solution as a whole (19).
A semirigourous aproaches:
calculation might be undertaken using two p o s s i b l e
a) To consider phenomenological
Onsager's
equations
b) To use a M e a n D for the whole electrolyte
(36),
or
(43).
Both approaches lead to unsatisfactory solutions for the sake of practical purposes. The first because needs many and s o p h i s t i c a t e d m a t h e m a t i c a l equations and the second, because does not allow to d i f f e r e n t i a t e between the different ions. Thus, w i t h the aim of looking for a simple and p r a c t i c a l solution, a simplified approach should be tried. This will be based in several assumptions able to overcome previous difficulties.
Simplified
calculation
of De~
The several assumptions which have to be taken order to solve equation [6] are (36)(39-43):
into
account
in
i.
Only what happens inside the concrete disc is influencing the measurements. This assumption may be accepted from the fact that ionic mobilities in solution are 3 or 4 orders of m a g n i t u d e higher than in the concrete and therefore, for the sake of the measurement, the slowest process is the only c o n s i d e r e d relevant.
2.
The t e r m dealing with convection in e q u a t i o n [6] can be neglected. This seems not difficult to be accepted, if only w h a t happens inside the concrete disc is considered.
3.
The diffusion component of equation [6] is considered negligible in comparison to that due to migration. As well,
Vol. 23, No. 3
CHLORIDE DIFFUSION, AASHTO TEST, RESISTIVITY
735
e l e c t r o n e u t r a l i t y in this e x p e r i m e n t is m a i n t a i n e d by m e a n s of the electrodic processes (gas evolution or metal dissolution) and t h e r e f o r e counter diffusion or m e m b r a n e e f f e c t s are not considered.
4.
The c o n c r e t e disc is thin enough to a l l o w to r e a c h a s t e a d y s t a t e c o n d i t i o n is few hours, w h i c h in turns m e a n s that all r e a c t i v e AC 3 in the disc is s a t u r a t e d w i t h the first d i f f u s i n g c h l o r i d e s and therefore, after the t r a n s i e n t i n i t i a l period, a linear flux of c h l o r i d e s along time, is e s t a b l i s h e d (figure 4), This allows to make the term a E/a 1 = AE/I, b e i n g 1 the c o n c r e t e disc thickness, and ~E the p o t e n t i a l applied.
5.
The c o n c e n t r a t i o n of c h l o r i d e s in one c h a m b e r of the cell is m u c h h i g h e r than in the other. That is, c h l o r i d e c o n c e n t r a t i o n in the c a t h o l i t e should be high and that in the anolite, zero. T h i s a l l o w s to a c c e p t that the c o n c e n t r a t i o n (activity better) of c h l o r i d e s in one side of the cell r e m a i n s c o m p a r a t i v e l y constant.
O n c e all expressed
t h e s e a s s u m p t i o n s are in the f o l l o w i n g way:
Total
where ions. The
considered
the
mol ZF flux = -J( ...... ) . . . . . . . sg'cm 2 RT
~E De,CoL .... 1
i= disc
is the
equation
thickness
and
Ca
equation
can
be
[7]
activity
of
chloride
may be also writen: JRT
1
De,=
[8 ] z F Ccl ~E
in w h i c h all p a r a m e t e r s are known and J can be c a l c u l a t e d from an e x p e r i m e n t a l test in w h i c h the amount of c h l o r i d e s is m o n i t o r e d a l o n g the time. Thus, from a plot s i m i l a r to that of f i g u r e 4, the flux J can be c a l c u l a t e d from the slope of the linear part.
Calculation equation
of
D~
from
the value
of
intensity.
Nernst-Einstein
A n o t h e r w a y to c a l c u l a t e D ~ is from the r e c o r d i n g of the i n t e n s i t y d u r i n g the experiment, b e c a u s e it is also well e s t a b l i s h e d (36)(3943) t h a t the flux of a m i g r a t i n g species is also p r o p o r t i o n a l to the t o t a l intensity:
itj J=
[9] nF
b e i n g the t r a n s f e r e n c e number (of the c h l o r i d e in this p a r t i c u l a r case) the p r o p o r t i o n a l i t y factor. Therefore, on the c o n t r a r y from the v a l u e of J o b t a i n e d in an e x p e r i m e n t a l test, it is p o s s i b l e to
736
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Vol. 23, No. 3
calculate the t r a n s f e r e n c e number ~, and by s u b s t i t u t i o n e q u a t i o n [9] in e q u a t i o n [7], the f o l l o w i n g is obtained: itcl
ZF =
nF
.
.
.
.
of
AE Def t Ccl
RT
.
.
.
[i0]
.
1
T h i s e x p r e s s i o n r e s u l t s s i m i l a r to N e r n s t - E i n s t e i n (32) e q u a t i o n but a p p l i e d for a single ionic species t h r o u g h the use of the t r a n s f e r e n c e number: RT Def~
RT
itcl
nF 2
AE
1
1
A cl = nF 2
[ii] A
C~Z
b e i n g A = cross s e c t i o n area of the c o n c r e t e disc. This e q u a t i o n o p e n s the d o o r to the p o s s i b i l i t y of c a l c u l a t i o n of D i f f u s i o n Coefficients from a simple measurement of resistivity or c o n d u c t i v i t y p r o v i d i n g that ~ of the p a r t i c u l a r ion c o u l d be accurately calculated (see n u m e r i c a l example later on). This approach would represent a very p r o m i s i n g s i m p l e way for the future, if the t h e o r e t i c a l d i f f i c u l t i e s of c a l c u l a t i n g a c c u r a t e t r a n s f e r e n c e n u m b e r s of c h l o r i d e ions in concrete, c o u l d be solved. Even, as it w i l l be p r e s e n t e d at the n u m e r i c a l example, this e q u a t i o n s e r v e s for an a p p r o x i m a t e c a l c u l a t i o n of the order of m a g n i t u d e of D from w a t e r s a t u r a t e d c o n c r e t e r e s i s t i v i t y values, o n c e p r o p e r a c c o u n t of the influence of the ionic s t r e n g t h of pore s o l u t i o n is c o n s i d e r e d (3)(44)(45)(46). F i n a l l y it has to be m e n t i o n e d that, if the c a l c u l a t i o n is m a d e f r o m r e s i s t i v i t y m e a s u r e m e n t s the r e a c t i o n w i t h the AC 3 is also m i s l e d and therefore, the v a l u e s o b t a i n e d are t h o s e of Den and not of D a.
0.1M NoOH
0.5 M NoCl
0.5¢m Figure
5. S i m p l e r e p r e s e n t a t i o n migration.
of the
cell
for
testing
chloride
Vol. 23, No. 3
CHLORIDE DIFFUSION,AASH'ID TEST, RESISTIVITY
737
NUMERICAL EXAMPLES Nernst-Plank
equation
Figure 5 depicts an e x a m p l e in w h i c h N a C l catholyte of a m i g r a t i o n c e l l a n d N a O H 0.1 following parameters are assumed: Cross-section
area:
0 . 5 M is M to the
added to anolyte.
the The
30 c m 2
D, = i0 -s cm2.sg -I R 1 . 9 8 7 2 c a l ' m o l l ' ~ ~I F = 2 3 0 6 3 cal'volt'1"eq "I Z = 1 Applied
potential
Concrete
thickness
between 1 = 0,5
electrodes
A E = 12 V
cm.
Considering the activity equal to produced for a concrete having a D~
the concentration, of 10 .8 cm2.s -I w o u l d
( i ) (23063) (10 .8) (0.5X10 3) (12) J =
the be:
flux
mol = 0,47
x 10 .8
(1.9872) (293) (0.5)
s.cm 2
T h i s is t h e o r d e r of m a g n i t u d e of t h e f l u x t h a t w i l l b e r e c o r d e d in t h i s k i n d of e x p e r i m e n t s , and a period of s e v e r a l h o u r s of t e s t i n g a r e n e e d e d in o r d e r t o m i n i m i z e e r r o r s in m o n i t o r i n g it. In figure 6 a graphic representation of t h e v a r i a t i o n of f l u x J w i t h t h o s e of D~, C a n d ~ E b e i n g t h e r e s t of p a r a m e t e r s constant, is g i v e n . It is a p p a r e n t t h a t an i n c r e a s e of A E f r o m 2 t o 20 v o l t s , c a n i n c r e a s e o n e o r d e r of m a g n i t u d e t h e flux. A s w a s r e f e r e d in (i) a potential of 2 volts almost does not influences the pure diffusional flux. As an example too, in (47) c h l o r i d e fluxes are reported of t h e o r d e r of a b o u t i0 m m o l / d a y f o r a c o n c r e t e c u r e d at 20°C a n d w i t h a w / c = 0,5. T h u s t a k e n i n t o a c c o u n t t h e e x p e r i m e n t a l conditions used b y t h e a u t h o r s a n d a s s u m i n g a n s t a t i o n a r y flow, t h e D ~ v a l u e s w o u l d r e s u l t t h e s e n s i b l e v a l u e of: Dc~ = 3.1 x i0 -s cm2/s
Calculation
from intensity values
The theoretical calculation of c h l o r i d e t r a n s f e r e n c e solution 0.2M NaOH + 0.5M NaCl from equation [5] w i l l of:
n u m b e r in a give a value
(0.5)(76.34) to =
,=
(o.5) (50.1)+(0.5) (76.34)+(o.2) (198)+(0.2) (50.1)
0. 338
738
C. Andrade
C = 0.5 mol/cm s AE=lEV t=0.5cm
Vol. 23, No. 3
D= 10-Scm?-/s AE=IZV L = 0.5cm
D =lO-ScmZ/s C=0,5mol/cm 3 L =0,Scm
rnol
cm2.sg
f
10-o
J
10-~ 10-1o !
,
,
,
I0 -7 I0 -s I0 -9
0.I
D (crag/s)
,
v
0.3
0.5
r
20
C(mol/cm 3)
40
r
60
AE (V)
NERNST- PLANK EQUATION Figure
6. R e p r e s e n t a t i o n of the c h l o r i d e flux after N e r n s t - P l a n k e q u a t i o n [6] (migration term) in f u n c t i o n of c h l o r i d e a c t i v i t y values.
A s s u m i n g t h e n this v a l u e as a r e f e r e n c e one, w h i c h has to be r e c o r d e d to o b t a i n a flux of w o u l d be, f o l l o w i n g e q u a t i o n [9]:
(0.47) (i0 s) (i) (96500)
JnF i =
= 1.338.10 .3 A / c m 2
= tcl
using shown
these next.
0.338
values
Nernst-Einstein
the i n t e n s i t y value 0.47 x i0 g mol/cm2"s
in e q u a t i o n
[i0]
De~ can
be
calculated,
as
is
equation
F i g u r e 7 shows a g r a p h i c r e p r e s e n t a t i o n of N e r n s t - E i n s t e i n e q u a t i o n [ii] a s s u m i n g a s o l u t i o n 0.2 M N a O H plus of NaCl w i t h a c t i v i t y v a l u e s of 0.i, 0.35 and 0.5 m o l / c m 3 and a c h l o r i d e t r a n s f e r e n c e n u m b e r of 0.338: This representation let us deduce that D concentration as is theoretically stated r e s i s t i v i t y the m o s t i n f l u e n c i n g parameter.
varies with (36), being
the the
In o r d e r to a p p l y this e q u a t i o n the c o n c r e t e has to be w a t e r s a t u r a t e d to a s s u r e p u r e d i f f u s i o n p e n e t r a t i o n m e c h a n i s m . C a p i l l a r y f o r c e s a p p e a r i n g in p a r t i a l l y dry c o n c r e t e w i l l i n t r o d u c e other m e c h a n i s m s of c h l o r i d e p e n e t r a t i o n w h i c h c o u l d v a r y the p r e d i c t i o n , which, as was a f o r e m e n t i o n e d , opens the door to the c a l c u l a t i o n of D coefficient from simple, but proper resistivity values (3) (45) (46).
Vol. 23, No. 3
CHLORIDE DIFFUSION,AASHTOTEST, RESISTIVITY
DCi4C~,g)
A o x
739
a = 0 . 1 mol/cm 3 a=0.3,5 ,, 0=0.5 ,,
10 - 4 10-5
10-e 10-7 lO-e
i
10 ,6' ,6' 16"
P (ohm .cm-1)
NERNST-EINSTEIN EQUATION Figure 7. Graphic representation of Nernst-Einstein equation in function of chloride activity values.
[i0]
Summing up, Nernst-Plank equation has to be used when values of chloride flux along time in a Migration Cell, are a c c u r a t e l y recorded, providing steady-state conditions are established. Alternatively, Nernst-Einstein equation may be used w h e n instead of chloride flux, intensity values are accurately recorded, steadystate conditions are operating and the chloride t r a n s f e r e n c e number is also accurately calculated.
CONCLUSIONS
More than conclusions, the following paragraphs are a summary of comments which can be drawn up from a thorough study of basic books on e l e c t r o c h e m i s t r y and a careful meditation on their a p p l i c a t i o n to the p a r t i c u l a r case of concrete. The Rapid Chloride Permeability Test (AASHTO) in its present formulation cannot inform on concrete permeability to chlorides. The recording of the total current p a s s i n g across the cell is a function of the amount and type of ions, but not of the chloride flux or chloride mobility. The calculation of ionic migration can be only r i g o r o u s l y r e s s o l v e d in homogeneous, binary and dilute solutions. Concrete and concrete pore solution is a p o l i e l e c t r o l y t e with high ionic strength and therefore, a rigourous c a l c u l a t i o n cannot be performed or results very difficult.
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Vol. 23, No. 3
However, as a p p r o x i m a t e values may be e n o u g h for p r a c t i c a l purposes, simplified ways of calculation of Diffusion Coefficient of c h l o r i d e s may be tried. This s u p p o s e s the a c c e p t a n c e of some a s s u m p t i o n s and u n c e r t a i n t i e s . Thus, a s s u m i n g some simplifications, N e r n s t - P l a n k and N e r n s t E i n s t e i n e q u a t i o n s can be used in a d i s p o s i t i o n s i m i l a r to a d i f f u s i o n cell (migration cell): the m a i n b e i n g to a c c e p t that c o n v e c t i o n does not o p e r a t e inside the c o n c r e t e and that d i f f u s i o n is n e g l i g i b l e c o m p a r e d to m i g r a t i o n w h e n e l e c t r i c a l f i e l d s h i g h e r than 10v are operating. F r o m equations, [8] and [ii], E f f e c t i v e D i f f u s i o n C o e f f i c i e n t , De, , can be c a l c u l a t e d in an e x p e r i m e n t of few days. N e r n s t P l a n k e q u a t i o n can be used w h e n only c h l o r i d e flux a l o n g time is r e c o r d e d and N e r n s t - E i n s t e i n e q u a t i o n w h e n i n t e n s i t y v a l u e s and c h l o r i d e t r a n s f e r e n c e numbers are a c c u r a t e l y a p p l i e d and measured respectively. An extensive experimental program, which at p r e s e n t is b e i n g c a r r i e d out by the author, is n e e d e d to c h e c k w h e t h e r the a s s u m p t i o n s c o n s i d e r e d are c o r r e c t or not.
F i n a l l y it has to be m e n t i o n e d that the same e q u a t i o n s can be a p p l i e d to c a l c u l a t e ionic m o v e m e n t s in the case of c a t h o d i c p r o t e c t i o n , c h l o r i d e removal or r e a l k a l i z a t i o n , a l t h o u g h in these cases a n o n - s t a t i o n a r y p r o c e s s is e s t a b l i s h e d w h i c h m a k e s m o r e s o p h i s t i c a t e d the s o l u t i o n of e q u a t i o n [6] and [ii]. S p e c i a l l y seems v e r y a t t r a c t i v e the r e s s o l u t i o n in the case of c h l o r i d e removal, because it may give the t h e o r e t i c a l t i m e n e e d e d to d e c r e a s e the a m o u n t of c h l o r i d e s below a c e r t a i n t h r e s h o l d .
ACKNOWLEDGEMENTS
The a u t h o r is g r a t e f u l to several r e s e a r c h e r s for t h e i r c o m m e n t s and e x p e r i m e n t a l trials. First she is g r a t e f u l to Dr. J. G a l v e l e of A r g e n t i n a for the d i s c u s s i o n on the p r e l i m i n a r y s t a t e s of the p a p e r and the c o m m e n t s i n t r o d u c e d in the final version. T h a n k s are also g i v e n for the d i s c u s s i o n s to her c o l l e a g u e s at the Institute: Dr. S. Gofii and Dr. C. Alonso, and finally to Mr. M.A. S a n j u ~ n for his e x p e r i m e n t a l trials.
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CHLORIDE DIFFUSION, AASHTO TEST, RESISTIVITY
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