1st RILEM workshop on Chloride Penetration into Concrete october 1995, St Rémy lès Chevreuse, France

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1 12 FUNDAMENTALS OF MIGRATION EXPERIMENTS by C. ANDRADE, M. CASTELLOTE, D. CERVIGON and C. ALONSO Institute of Construction Sciences "Eduardo Torroja" of the CSIC, Madrid, Spain SUMMARY The application of high electrical fields to concrete specimens have opened a new field of research, when the phenomena are interpreted with an electrochemical background. Thus, the movement of the ions contained in the pore solution induced by the electrical field (migration), can be quantified and predicted. In present paper the electrochemical fundamentals of ionic migration or electrodiffusion are presented. Equations as Nemst-Plank or Nernst-Einstein are commented. Stationary and non-stationary movements are considered. In the case of non-stationary conditions, the concept of ionic mobility is explained in order to present a solution for this kind of situations. Finally, the application of this concept to chloride extraction is mentioned. INTRODUCTION Chloride ions penetrate into concrete usually by diffusion, that is, by means of a difference of concentration that acts as driving force (1). When the concrete is furthermore submitted to the action of an electrical field the chloride ions experiment: 1% directioning of their movement towards the positive electrode and 2") an acceleration which is proportional to their mobility (h= ZFD,/RT) and to the magnitude of the electrical field applied (2). The action of the electrical field is therefore to modify the "random walk" of the ions when they move only by diffusion and to direction it towards the electrode of opposite sign. In consequence, the movement comes to an acceleration which is counterbalanced by the frictional drag force. In general, all ions present in the aqueous phase of concrete experiment the same kind of directioning towards the electrode of opposite sign, and the acceleration. Figure 1 depicts the overall movements of most abundant ions for the case of a concrete disc, introduced in a diffusion cell arrangement (1). This relative movement (named migration or electrodiffusion) of ions in the electrolyte under the action of an electrical field, will depend on their transference number (2), which is the proportion of current carried by a particular ion in relation to the current canied by the rest of ions: 95

2 To balance the ionic movement, the electroneutrality of the whole arrangement is maintained by the electrodic reactions, which are shown as well in the figure 1 for the case of concrete: a) water electrolysis, b) corrosion of anode when it is not a noble metal, c)possible chloride oxidation to chlorine and d) reduction of oxygen at the cathode. QUANTIFICATION OF MIGRATION The quantification of ionic movement in electrolytes can be solved in steady-state conditions by using Nernst-Plank equation (2): where the terms have the usual meaning (2). Its application to solve the kind of test like that named "Rapid chloride permeability test" (3)(4) has been made recently (5), by assuming the following simplifications: 1. The ionic mobility is much higher in the solutions than in the concrete disc and therefore the "distance" of the experiment is the disc thickness. 2. The term dealing with Convection is not taken into account, as it is assumed that it does not apply to concrete pore solution. 3. The Diffusion term is also not considered, as its influence is negligeable when compared with the term of Migration. This is due the high value that the expression zf/rt has when multiplied by the applied voltage difference (usually beyond 10 V). 4. The electrical field along the concrete disc follows a linear decay. By means of these assumptions it is possible to calculate the diffusion coefficient D,,, in steady-state conditions: This expression enables the possibility to obtain D values from tests similar to the AASHTO T-277 (4) one, although with longer duration. Typically one week may be enough for ordinary concretes in specimens 1 cm thick. Comparison of D, values calculated from equation [2] have given good agreement with values obtained from conventional diffusion cell experiments (6). Nernst-Eiein equation is a particular case of N&P one and therefore, it can be used in a 96

3 similar manner (2): The application to a particular ion is made by using transference values (S) (equation on [S]). The most interesting practical aspect of this equation regarding the concrete, is the possibility of calculating D,, from a simple measurement of concrete resistivity. That is, if a particular external chloride concentrations is assumed (for instance 0.5 M) the transference number may be deduced (L-,- 0.35) and so, the activity factor (0.7). Introducing these values in equation [3], it results: 26,lxlO D, -' (cm 2/s) = P QUANTIFICATION IN NON-STEADY STATE CONDITIONS The solution of N&P equation in non-steady-state conditions is a more complex problem. In fact, if has remained unsolved during many years in spite that numerous attempts were made (7). Its analytical solution has been achieved only in very particular situations always with certain amount of empirism or simplifying assumptions (8). Its expression, when not account is taken of convection, results: Application of Ionic Mobility Concept to quantify migration in non-steady state conditions Due to the mentioned difficulties to accmtely soive N&P equation (7)(8), and having in mind the high electrical fields applied in the experiments in concrete, the non-stationary movement has been approached (9) by using an analogy with pure diffusion movements. First, it was taken into consideration the definition of the ionic mobility, ui, as "the limiting velocity reached by an ion submitted to an electrical field of unit strength (1VIcm) when the frictional drag counterbalances the electric force". In consequence, multiplying the applied voltage by the mobility, it may be defined a new parameter (D*): 97

4 in which: zfae/rt is the acceleration term introduced by the electrical field into the diffusional movement. The units of this m eter De are consistent with those of a diffusion coefficient. The approach undertaken is then, to substitute D, by D, in any of the expressions already developed to solve diffusional non-steady-state situations. Thus, second Fick's law may now be presented as: or what is the same: which reminds the following equation: in which equation [6] collapses when the diffusion term is neglected and 8~/ax~= 0. Equations [8] and [8'] in semi-&te which is: space, have the named solution of the "error function", X Cc= Cserjc - 2,m Equation [l01 shows a quite good agreement between experimental results and theoretical predictions (6)(9). As an example, using the arrangement shown in figure 2, figure 3 shows the real chloride profile (blocks in the figure) found in a concrete of w/c= 0.4, after 189 h of application of 12V and the theoretical fitting (continuous line) of equation [10]. The D, so obtained is 0.4x10-' cmz/s, which is in the range of the values obtained by means of natural diffusion test. The upper part of figure 4 shows a three-dimensional (concentration, distance and time) representation of the results of equation [l01 for a D= 10-8cm2/s and AE= 10V, while the bottom part of the figure shows the profiles generated for increasing times. The important advantage of the use of Ionic Mobility Concept is that it can be applied to any circumstance already solved for a diffusional problem, and that this equation [l01 is a familiar expression for concrete specialists. 98

5 OTHER SOLUTIONS IN NON-STEADY STATE CONDITIONS l Related to chloride migration through concrete, two other solutions to equation [6] have been published (10)(11). For the case of a column of finite length, Xu & Chandra (10) offer the same solution previously published by Tang & Nilsson in (11). Both arrive to the expression: where: This equation gives chloride profiles that are like a "moving boundary" and although, [l11 seems a correct analytical solution of [6] for the particular boundary conditions considered, the theoretical chloride profiles given in (10) are much sharper and slower than those obtained in experiments (9)(10) or that shown in figure 3. Thus, figure 5 shows the theoretical chloride profiles obtained through equation [l01 (named A) and through equation [l l] (named T&N), for the case of AE= 10V and D= 10-l2 m2/s. As well, figure 6 depicts the fitting of equation [l01 into T&N experimental chloride profiles. While equation [l l] of T&N gave a value of D- 6x10" m2/s, the fitting of equation [l01 ('A" in figure 6) gives a closer value (around 1~10''~ m2/s) to that obtained in a diffusion experiment (l. 1x10-Iz m2/s). This discrepancy of equation [l l] with the experimental profiles may be due to the particular boundary conditions selected to solve Nernst-Plank equation, which, for instance, do not take into account that the chemical composition of the catholyte changes during the test. CONCLUSIONS Present paper summarizes the formulation of a theoretical background for ionic migration or electro-diffusion in concrete, which represents an important advance as multiple future applications appear feasible from their understanding. Its quantification is presented as well, following a rigourous solution in the case of steady-state experiments, and a more conceptuayempirical approach working by analogy (Ionic Mobility Concept) for the case of non-stationary situations. This approach fits better into experimental results than those apparently more rigourous solutions to Nernst Plank equation in non stationary conditions. 99

6 REFERENCES 1. Page, C.L., Short, N.R., El Tarras, A. "Diffusion of chloride ions in hardened cement pastes" Cement and Concrete Res. U, pp (1981). 2. Boclais, J.OIM., Readdy, A.K.N. "Modem Electrochemistry", Plenum Press Ed. New York (1974). 3. Whiting, D. "Rapid Determination of the Chloride Permeability of Concrete". Report No. FHWAJRD , August 1981, NTIS DB No AASHTO "Standard Method of test for Rapid Determination of Chloride Permeability of Concrete" 5. Andrade, C. "Calculation of chloride diffusion coefficients in concrete from ionic migration measurements", Cement and Concrete Research, vo1.23, (1993), pp Andrade, C., Alonso, C., Acha, M. "Chloride diffusion coefficient of concrete containing fly ash calculated from migration tests". 7. Cole, K.S. "Electrodiffusion models for the membrane of squid grint axon", Phisiol. Rev. 45 (1965) Hill, B. "Ionic channels of excitable membranes", Washington University, Sirares Ass. Inc. Sundesland, Massachusets. 9. Andrade, C., Sanjh, M.A., Recuero, A. and Rio, 0. "Calculation of chloride diffusivity in concrete from migration experiments, in non steady-state conditions", Cement and Concrete Research, vol, 24, no. 7, (1994) pp Xu, A., Chandra, S. "A discussion of the paper "Calculation of chloride diffusion coefficients in concrete from ionic migration measurements" by C. Andrade - Cement and Concrete Research 24, no.2 (1994) Tang, L., Nilsson, L.O. "Rapid determination of the chloride diffusivity in concrete by applying an electrical field". ACI Materials Journal, Jan (1992)

7 Figure 2. Phenomena noticed in a concrete sample, the electrodes and the electrolytes after the application of high voltage differences between electrdes. Figure 2. Arrangements of 101 solution in order to perform a non experiment.

8 Voltage applied= 12 W onding,o:l -M,NaCI Dapp= 0.4E-8 crn2lseg I Figure 3. Experimental chloride profile (blocks) obtained after 189 hours of testing in the arrangement shown in figure 2, (continuous line) of equation [l l]. 102

9 Figure 4.Three-dimensional plotting of equation 1101 for a D = 10Jcm21s and 10 V. Distance (m) Figure 5. Theoretical chhide profiles equation 103 by equation [l01 (Andrade et al) and by and Nilsson)

10 c:s:w 1:2:0.4 E:= -600V/m ' ( pure diffusion ) EXPERIMENTAL RESULTS (mm) Figure 6. Fitting of T&N eq, Into their experimental results. Continuous lines TA") are the fitting of equation [l01 suggest by Andrade et al. 104

13 AN ELECTROCHEMICAL METHOD FOR ACCELERATED TESTING OF CHLORIDE DIFFUSIVITY IN CONCRETE

13 AN ELECTROCHEMICAL METHOD FOR ACCELERATED TESTING OF CHLORIDE DIFFUSIVITY IN CONCRETE TIEWEI. ZHANG and ODD E. GJ@RV Division of Building Materials, The Norwegian Institute of Technology - NTH N - 7034