Michel Keddam
email: michel.keddam@upmc.fr

Pierre Ponthiaux

Vincent Vivier

Tribo-electrochemical impedance

ouverte pluridisciplinaire HAL, est destinée au dépôt

Introduction

Tribo-corrosion is defined as the degradation of a material under the effect of both mechanical and reactive damages. It is established that these two modes of attack are not simply additive and that in most cases intricate cross-effects are at work. Therefore the main goal of investigations carried out in this domain is to understand the mechanisms involved in this so-called synergism and to establish techniques for forecasting the behavior of a material exposed to a risk of tribocorrosion.

Incorporating a mechanical disturbance of the interface within an electrochemical environment of the interface has led to the concept of tribo-electrochemistry. However, the extension of traditional electrochemical techniques developed for corrosion free of mechanical contribution is facing both experimental and conceptual problems. Their theoretical background, experimental applicability and limitations have been reviewed in a recent publication [START_REF] Keddam | Electrochemical methods in tribocorrosion. From principles to applications[END_REF]. Open-circuit potential, current-voltage curves and electrochemical impedance [START_REF] Ponthiaux | Electrochemical techniques for studying tribocorrosion processes[END_REF] have been used under tribological conditions compatible with a permanent regime, e.g. a constant current at a given potential. Valuable results were reported but no quantitative treatments are available. Electrochemical responses to transient abrasion regimes have been also investigated and tentatively interpreted on the basis of repassivation models depicting the growth of the passive film after being removed by the rubbing body [START_REF] Jemmely | Electrochemical modeling of passivation phenomena in Tribocorrosion[END_REF]. This paper presents a new approach exploring the kinetics of the film healing by a sine-wave modulation of the velocity of rotation of a Pin-On-Disc tribometer. A complex transfer function is hence defined depicting, in the frequency domain, the repassivation transient behind the sliding body on the disc.

The background of the technique, its experimental aspects and first results obtained in the passive range of a stainless steel are presented.

Background

In contrast with traditional physicochemical parameters, the interaction between a metal and an antagonistic abrading body cannot be directly incorporated in the framework of electrode kinetics. The effect is definitely invasive and for an electrochemist the result is a nightmare: the total destruction of the interface. Referring to classical interfacial electrochemistry, the only available examples of abrading the interface and focussing on what happens immediately afterwards are relative to studies of the double layer capacitance. [START_REF] Lazarova | Dependence of zero-charge potential for iron, cobalt and nickel on the pH of a solution[END_REF], [START_REF] Clark | A comparison of the immersion and open-circuit scrape methods for determining the potential of zero-charge of metal electrodes[END_REF], [START_REF] Andersen | The nature of fresh metal surfaces in aqueous solutions[END_REF]. The same concept of fresh surface created by mechanical surface removal was thoroughly exploited in works aimed at understanding the mechanism of various type of corrosion such as abrasion corrosion, SCC, laser and ultrasonic impacts…. All are supposed to be in some way controlled by the competition between the local mechanical breakdown of a protective film and the reconstitution of the later by a healing process. The first explicit expression of the current generated by a rubbing body has been given in the form of an integral in [START_REF] Mischler | Wear-accelerated corrosion of passive metals in tribocorrosion systems[END_REF]. It remains the background of the quantitative applications of electrochemical techniques to tribocorrosion. In Fig. 1 a formally general case is considered in which rubbing removes all the surface layer and further ploughs deeper into the underlying metal.

Insert Fig 1 here.

It is noteworthy that the quantity |v|. t f  is the mechanical power W m injected in the system.

It is consumed in irreversible processes of heat generation, plastic deformation, breakdown of the metallic bonds… and reversible ones like elastic deformation. The double layer charging current j dl is generally not mentioned in tribocorrosion and can be actually neglected, [START_REF] Jemmely | Electrochemical modeling of passivation phenomena in Tribocorrosion[END_REF]. The surface charge, around 1mC.cm -2 being orders of magnitude smaller than that consumed in the electrochemical reactions associated to passivation, typically a fraction of C.cm -2 and a fortiori to anodic dissolution during the transient regime. A more detailed discussion of this model can be found in [START_REF] Keddam | Electrochemical methods in tribocorrosion. From principles to applications[END_REF].

General mathematical developments

If the sample is supposed to be at a constant potential, the current measured at any distance x from the starting point is given by integrating the local current density j(x) over the width w of the track and its length, with the origin of the successive positions being attached to the abrasive pin and the x axis oriented positively to the left:

x 0 I(x) w j(x)dx   (1)
In the case of a constant velocity, v, changing the variable from x to t gives:

t 0 I(t) w.v j(t)dt   ( 2
)
where v is the modulus of v  defined in Fig. 1. If the integral is convergent, I(t) reaches a limiting value I  given by Eq.2 for t>characteristic-time of the surface recovery.

Iw . v . Q   (3)
where Q is the total surface density of charge, in C by unit area, consumed in the whole transient.

From a kinetics viewpoint, in Eq.(3) v plays a role identical to a rate constant in the expression of an electrochemical current. However it must be emphasized that I(t) does not give access directly to j(t); Eq (2) has been exploited in various ways for interpreting many tribocorrosion measurements in transient regimes of sliding velocity and current. The present work is based on a generalized form of Eq (2) valid for any case where v is no longer independent of time t. At any time t, the contribution to the total current I(t) of a small section of the track created at the time (t-) when the velocity was v(t-) is given by j().v(t-).

Insert Fig 2 here.

Hence the current I(t) is expressed as the convolution product of the functions j and v:

t 0 I(t) w j( ).v(t )d      (4)

The Tribo-Electrochemical Impedance

Now if we consider the case of a small amplitude sine wave modulation of v(t) about a

constant mean value v o , jt o v(t) v v e   
, Eq (4) can be rewritten as:

tt j( t ) o 00 I(t) wv j( )dt w j( ) v e d         (5)
In Eq(5) the first term is the response to the velocity v o given by Eq(2) while the second one is the ac response I of the current induced by the modulated component of the velocity jt ve   . Therefore a complex transfer function, TEI E (Tribo-Electrochemical Impedance at constant potential) can be defined relating the frequency response of the current to the velocity modulation:

T j E 0 I TEI w j( ).e d v        (6)
Only this derivation has a physical meaning only if a constant mean current can be reached given by Eq [START_REF] Ponthiaux | Electrochemical techniques for studying tribocorrosion processes[END_REF]. A linear abrasion trajectory should in practice have an "infinite" length for Eq(3) to be valid. This problem has been overcome by the design of rotating tribometers of the Pin-On-Disc or Ball-On-Disc type where the abrading body moves on a circular trajectory. According to the foregoing model, after one period of rotation, T, the current reaches a constant value:

T 0 I(T) w.v j(t)dt   (7)
The linear velocity v can be converted into an angular one, e.g. RPM :

RPM v2 πrΩ /60  .
It must be emphasized that this constant value of the current must not be mistaken with a steady-state as in traditional electrochemistry. In fact any point of the abraded surface is in a dynamic regime given by j(t), the constant current results only from the travelling transient current attached to the abrading body. This is why modeling the traditional EIS response of this "pseudo-steady-state system" could be a delicate but worthy task.

The final form of Eq(7) becomes:

T j E 0 I TEI w j( ).e d v         (8)
The TEI E expressed by Eq(8) is a one-sided ( t>0) Fourier transform of j(t) in a time-window of length T. As shown below, even though j(t) is not readily extracted from the TEI E , pertinent information on j(t) can be gained by a simulation approach. It must be emphasized that Eq(8) offers a totally original way of investigating the electrochemical response of a surface about a mean steady-state tribo-corrosion regime whilst available techniques are confined to large transients between no abrasion and full abrasion conditions.

3.Experimental

The equipment shown in

Results

Validation and data processing

In a first step, experimental data were validated in several ways. TEI implying an additional quantity  with respect to the usual pair I-E must be tested against the general relationship holding between the 3 pairs of command inputs:

I IE E TEI EE I () Z ( ) / ( ) IT E I            ( 9
)
Where Z is the traditional electrochemical impedance at the mean value of: = o, , TEI I and TEI E are the Tribo-Electrochemical-Impedances at constant current and constant potential respectively. Eq (9) initially introduced with the Electro-Hydrodynamic-Impedance was recently generalized in [START_REF] Orazem | Electrochemical Impedance Spectroscopy[END_REF]. In order to apply Eq (9) the Open-Circuit condition was selected where the interface can be maintained either at constant current or at constant potential, a requirement not fulfilled in the passive range where the rest of the study was performed.

Insert

Analysis of the repassivation transient in the passive range

The I and  data have been collected between 0.01Hz and 10 Hz at a potential in the full passive domain of the AISI 316 L S.S. in the same conditions as for Fig. 6 and for three mean rotation speeds: 8, 20 and 50RPM of the abrading pin. After processing frequency by frequency, the complex TEI E was plotted in the Nyquist plane.

Insert Fig 8 here

Fig 8 displays the plot corresponding to 20 RPM, its lies in the third quadrant of the complex plane (like for a capacitive impedance plot the imaginary axis is reversed). The low frequency limit, positive, is in satisfactory agreement with the slope of the steady-state I() curve and the loop is consistent with a time-delayed increase of the current following an increment of abrasion velocity. The shape, clearly depressed, is not compatible with an exponential j(t) which would generate a semi-circle for the integral in Eq(8) extending to infinity as shown by Eq [START_REF] Mischler | Triboelectrochemical techniques and interpretation methods in tribocorrosion: A comparative evaluation[END_REF].

               (10)
The same features were obtained at the rotation speeds 8 and 50 RPM with a frequency dispersion that can be displayed clearly only in the Bode plot (log, modulus, log, frequency). These Bode plots suggested rather than a quite formal exploitation in terms of a CPE, to propose an interpretation by the sum of two exponentials 8) by using the values of parameters given in the Table 1. A quite satisfactory match is observed considering the rather large scattering of the TEI points.

The main source of error is the parasitic modulation of the current at the rotation frequency due to the lack of levelness of the electrode surface in spite of a careful machining.

 o ; RPM w 1 ; A.m -1 w  2 ; A.m -1  1; s  2 , s  1 ; A.m -2  2 ; A.m -2  1  1 ; C.m -2  2  2 ; C.m -

Discussion

It is clear that j(t)= 1. The charge associated to the shorter timeconstant  2 can be regarded as constant whilst the charge passed during the larger timeconstant  1 increases with the rotation period. One can infer that the time-constants correspond to two different surface processes. The shorter would reflect a fast process independent of the overall electrochemical activity, linked to  o , of the surface, the longer one to a slower relaxation strongly coupled to the average degree of recovery of the surface. This is clearly not included in the model initially considered in this work and must be the starting point of an original effort of modeling in the field.

Another problematic aspect is raised by the order of magnitude of the surface charges. If compared to the reference density of faradaic charge involved in the growth of a conventional passive film, they are far too small. The same remark would be easily formulated by comparing the steady-state current at any  o value to its value calculated by Eq(1). One possible explanation is a strong overestimation of the true active area. An effective contact area restricted by the surface roughness has been already pointed out on the same material [START_REF] García | Corrosion-wear of passivating materials in sliding contacts based on a concept of active wear track area[END_REF].

The total damage width is also probably much larger than that really affected by the mechanical interaction with the pin at a given stage of the experiment. The final aspect would be due to both the superposition of a large number of rotations and of an active dissolution of the nearby metal sustained by ohmic drop [START_REF] Mischler | Triboelectrochemical techniques and interpretation methods in tribocorrosion: A comparative evaluation[END_REF][START_REF] Benea | Tribocorrosion of stellite 6 in sulphuric acid medium : electrochemical behaviour and wear[END_REF]. Repassivation by galvanic coupling to the surrounding passive area, not detected in the measured current, well-known in the case of local depassivation experiments [START_REF] Oltra | Depassivation and repassivation phenomena:synergism in tribocorrosion, Chapter 2 in 'Testing Tribocorrosion of passivating materials supporting research and industrial innovation[END_REF] must be also considered.

This mathematical form of j(t) provided by TEI E being not explicitly reported in the literature has prompted to perform independent characterization of the transient response. Current decays were recorded at the end of each TEI E sequence on steping to zero the rotation of the pin led, they led to the same conclusions. The current returned to its undisturbed passive value, an example is given in Fig10 with the best fit to a sum of two exponentials, Unlike for the TEI E data of Table 1, both time-constants T 1 and T 2 decrease as the rotation speed goes up, the larger  o and the associated steady current, the faster the surface recovery from abrasion. This can be explained by the huge non-linear character of the perturbation forced in the interface by switching off the pin rotation in contrast to TEI E . Again the smallest surface charge is associated to the short time-constant whilst the slowest relaxation implies a surface charge of roughly one order of magnitude larger. It can be reasonably supposed that these two time-constants correspond to the formation of a 2-D layer (short times and small charge) followed by the growth of a 3-D layer (longer times and larger charge). Even though the charges, given in Table 2, are more compatible with a film, a few monolayers thick, than those of Table 1, galvanic coupling are also likely to contribute to the anodic charge balance of the surface healing.

Insert

Conclusion

A new contribution to the understanding of the electrochemistry driven on a passive material under tribological conditions is proposed. An original impedance function, ratio of a mechanical and an electrochemical quantity, is defined and measured. It provides the form of the repassivation kinetics attached to a given steady-state of friction, information generally considered as not accessible to the direct experiment. A two-time-constant response was evidenced, corroborated by additional analysis of the current decay on switching-off the abrasion. These results are discussed in the framework of surface recovery and associated charge balance.

  figure 1) and pin velocity are controlled by a P-O-D tribometer Falex and the associated RSAI

Fig 4 and 5 Fig 6

 56 Fig 6 shows a sample of a current response after a low-pass filtering (f<0.1Hz) with the

Fig 9

 9 Fig 9 shows the experimental data for three values of  o in the Bode modulus plane and the results of simulation with Eq(8) by using the values of parameters given in the Table1. A

  on  o , in contrast with the literature model at the origin of this work which is based on a same kernel transient. The time-constants  1 and 2 remained of the same order of magnitude and their ratio  1/  2 close to 10. The amplitude  1 decreased as the rotation speed goes up whilst  2 is little dependent with no clear trend. The consideration of the density of charge  i  i involved under the two components of j(t) brings about a more relevant insight since likely less sensitive to experimental dispersion. The results are given in the right hand side of the

Fig 1 :

 1 Fig 1: Time-space representation of the surface rubbing by an abrasive body and of

Fig 2 :

 2 Fig 2 : time profile of the current density j(t) weighted by the velocity of the pin at

Fig 3 :

 3 Fig 3: experimental setup for simultaneous measurement and data acquisition of the tribological and electrochemical quantities in a Pin-On-Disc configuration.

Fig 4 :

 4 Fig 4: Electrochemical Impedance of AISI 316 in H 3 BO 3 (1000 ppm in B) + LiOH (130 ppm in Li) under abrasion at OCP (-0,348 Volt/Ag-AgCl/KCl saturated), rotation speed   =50RPM, relative modulation amplitude /  =0.1, f n =10N.

Fig 5 :

 5 Fig 5: Electrochemical Impedance calculated with Eq(8) from TEI I and TEI E measured in the conditions of Fig 4.

Fig 6 :

 6 Fig 6 : sample of the current response to the ac modulation of  AISI 316 L S.S.in boric acid (1000 ppm of boron) and lithia (12 ppm of lithium). Passive range. +0.1V/ Ag/AgCl/KCl saturated). o=50 RPM. Modulation frequency: f=/2π=0.025 Hz, relative

Fig 7 :

 7 Fig 7: linear-log scale frequency spectrum of the current sample shown in Fig 5.

Fig 8 :

 8 Fig 8: Nyquist plot of the TEI E . same conditions as for Fig 6.

 o = 20 RPMFig 9 :

 209 Fig 9: Bode modulus plots of TEI E at three rotation speeds  o : "a", 8RPM, "b", 20RPM, and "c", 50RPM. Same conditions as for Fig 6. "d" : Bode phase plot associated to "b". Solid lines: simulation from Eq(8).

Fig 10 :

 10 Fig 10: current transient at the end of the rubbing sequence of TEI E measurement. Same conditions as for Fig 9 b. Crosses: experiments, solid line: Least Square fit to a two-exponentials decay, correlation coefficient R=0.991.

Table 1 :

 1

	2 

values of the parameters, pre-exponential factors, time-constants and surface charges determined by a simulation procedure of the TEI E data for three rotation speeds of the abrading pin shown in Figs 8 and 9.

Table 1 ,

 1 in surface density of charge. A value of w close to 0.0005m was estimated by surface examination giving respectively for 8, 20 and 50 RPM the values of  1 and  2 reported in the Table

Fig 10 here

	tt --TT 12 I=L .e +L .e by a Least Square Regression, performed in Kaleidagraph 4.03 (Synergy
	Software). A similar behaviour was obtained for the three values of  o . The data are reported
	in Table 2.
	 o	  s	  s	L 1 ; A.m -2	L 2 ; A.m -2	T 1 .L 1 ; Cm -2	T 2 .L 2 ; Cm -2
	8 RPM	50	5	0.1	0.115	5	0.575
	20 RPM	25	1.2	0.17	0.36	4.25	0.43
	50 RPM	13.9	0.66	0.57	2.5	7.9	1.65

Table 2 :

 2 values of the parameters, pre-exponential factors, time-constants and surface charges determined by a Least Square Fitting of the current transients after stopping the pin rotation for the three rotation speeds. The transient at 20 RPM is shown in Fig 10.


B Díaz

X R Nóvoa
email: rnovoa@uvigo.es

V Vivier

Macro and micro aspects of the transport of chlorides in cementitious membranes

A study of the transport of chlorides through hardened Portland cement paste membranes is reported. The flux of chlorides was induced by migration (AC and DC fields) and diffusion.

Two parallel studies were developed. A macroscopic one where the migration of chlorides was followed by Electrochemical Impedance Spectroscopy (EIS) and a microscopic one in which the natural diffusion was investigated using the scanning electrochemical microscopy (SECM). Both studies have revealed to be complementary. The local investigations performed with the SECM were successfully employed for the interpretation of the EIS data.

The results have shown that the transport of chlorides occurs mainly through pores of submicrometre equivalent diameter. The study of the transition time has allowed to conclude that the diffusion coefficient approaches the usual value obtained in bulk solution. The macroscopic study has allowed presenting an explanation for the beneficial effect of the AC current in the transport of chlorides. A possible method for estimating the flux of chlorides from the percolation resistance is also discussed.

Introduction

The presence of chlorides at the steel/concrete interface level is the main factor responsible for the corrosion of rebars in concrete. In new structures, the penetration rate of chloride ions through the concrete cover is a key aspect in the service life prediction. In damaged structures, the rate of chloride transport is also of major importance for the application of chloride extraction techniques. In that context, the forced migration test is employed as an accelerated and useful method to determine the chloride transport coefficients [START_REF] Stanish | Testing the chloride penetration resistance of concrete: A literature review[END_REF] and several standard methods have been established and used [START_REF] Aashto T | Standard Method of Test for Electrical Indication of Concrete's Ability to Resist Chloride Ion Penetration[END_REF][START_REF] Astm C | Standard Test Method for Electrical Indication of Concrete's Ability to Resist Chloride Ion Penetration[END_REF]. However, significant microstructural changes are caused by the application of electrics fields [START_REF] Sáchez | Microstructural modifications in Portland cement concrete due to forced ionic migration tests[END_REF] that, among other already known aspects dealing with surface treatments [START_REF] Andrade | A comparison of chloride ion diffusion coefficients derived from concentration gradients and non-steady state accelerated ionic migration[END_REF][START_REF] Yang | A comparison of transport properties for concrete using the ponding test and the accelerated chloride migration test[END_REF][START_REF] Yoon | The effects of surface treatments on rapid chloride permeability tests[END_REF], makes those tests controversial.

Investigations based on electrochemical impedance spectroscopy, EIS, [START_REF] Díaz | Study of the chloride diffusion in mortar: A new method of determining diffusion coefficients based on impedance measurements[END_REF][START_REF] Cabeza | Impedance spectroscopy study of hardened portland cement paste[END_REF] have already evidenced the presence of several concurrent ionic-conduction phenomena in cementitious materials, which involve percolating conduction and ionic exchange between the pore's solution and pore's walls. As each phenomenon occurs at a specific frequency, it is possible to tune the frequency of the electrical signal to act on the conduction paths, thus increasing the current efficiency on the ionic transport and diminishing the structural damage [START_REF] Díaz | Chloride transport through cementitious membranes using pulsed current[END_REF]. The use of pulsed current has been reported to be beneficial for preserving the integrity of the concrete microstructure [START_REF] Koleva | Electrical resistivity and microstructural properties of concrete materials in conditions of current flow[END_REF].

The chloride diffusion coefficients obtained for concrete either through diffusion or migration experiments are always controversial and strongly dependent on the testing conditions and concrete type [START_REF] Gergely | Concrete Diffusion Coefficients and Existing Chloride Exposure in North Carolina[END_REF][START_REF] Song | Factors influencing chloride transport in concrete structures exposed to marine environments[END_REF]. However, all procedures have in common that the amount of transported chlorides is referred to the geometrical surface normal to the transport direction. In neither case the pore structure of the material is taken into account although in some studies a "formation factor" was introduced [START_REF] Snyder | The relationship between the formation factor and the diffusion coefficient of porous materials saturated with concentrated electrolytes: theoretical and experimental considerations[END_REF][START_REF] Mercado | Chloride diffusion coefficient: A comparison between impedance spectroscopy and electrokinetic tests[END_REF]. The present contribution is aimed at rationalising the macroscopic approaches on the transport of chlorides in the light of microstructural information obtained from impedance spectroscopy measurements and scanning electrochemical microscopy, SECM. A new insight in the field is provided, highlighting the need of microstructural information for reliable results.

Experimental

Cement paste samples were prepared using Portland cement type CEM I 52.5R according to the composition, specifications and conformity criteria of EN 197-1:2000, with a water to cement ratio of 0.5. The water-cement mix were cast in cylindrical moulds of 9 cm in diameter and 20 cm in height, and cured in 100% RH chamber for 24 hours. Afterwards, the samples were demoulded and maintained in the same chamber for a minimum of 28 days before starting the measurements. The cement paste samples were cut into 2.5 cm thick slices to be used in the permeation experiments.

Unless otherwise stated, the samples were pre-conditioned prior testing following a standardized water saturation procedure [START_REF] Astm C | Standard Test Method for Electrical Indication of Concrete's Ability to Resist Chloride Ion Penetration[END_REF]. It should be mentioned that the probability for large pores to percolate the sample is almost null. Indeed, the thickness of the samples was chosen to cancel the presence of large percolating pores (inherent in small thicknesses) or cracks (formed during cutting and polishing, due to mechanical stress in thin samples). In this way the samples are representative of the real rebar's cover thickness (larger than 2-3 cm), but are thin enough to develop the microscale experiments within a reasonable and reproducible time scale. The samples microstructure was evaluated using mercury intrusion porosimetry (MIP) performed with an Autopore IV 9500 from Micromeritics. The covered pores diameter range is from 18 m down to 5 nm.

Setup for macroscopic permeation experiments

The experimental setup for macro-migration experiments consisted of a classical permeation cell with two-solution compartments at both sides of the cementitious sample under test. The upstream (or cathodic) compartment was filled with 1 M sodium chloride solution, containing also sodium hydroxide and potassium hydroxide to [OH -] = 0.5 M. The downstream (or anodic) compartment was filled with only sodium hydroxide and potassium hydroxide solutions to [OH -] = 0.5 M. The concentrations for NaOH and KOH were chosen to be similar to the pH of the pore solutions of the cement. Each electrolyte compartment was 200 cm 3 in volume. A schematic view of the experimental cell is given in Fig. 1.

Figure 1

As depicted in Fig. 1, the AC or DC electric fields were applied to the cementitious membrane using two graphite sheets located at both ends of the cell. The specimens were subjected to two regimes, direct current and pulsed current. In both regimes the nominal current density applied was 0.3 mA•cm -2 . As the pulsed current was applied as a square wave of 50% duty cycle, the imposed current during the "on" time was 0.60 mA•cm -2 to reach the average effective value of 0.3 mA.cm -2 .

The investigated frequency was 1 kHz. In all cases the potential drop across the cell was about 12 V.

The impedance of the cell was measured periodically between 40 MHz and 10 Hz to assess the evolution of the resistivity of the membrane, through which the diffusion coefficient can be derived [START_REF] Díaz | Study of the chloride diffusion in mortar: A new method of determining diffusion coefficients based on impedance measurements[END_REF]. The impedance measurements were performed using an Agilent 4294A impedance/gain-phase analyser, which allows impedance frequency range investigation from 100 MHz down to 10 Hz in pure AC mode. This instrument allows capacitance measurements down to 10 -14 F with a maximum resolution of 10 -16 F.

The cross-section of the sample in contact with the electrolyte was 20 cm 2 and the measurements were corrected for the ratio sample's geometrical cross section to cross section in contact with the electrolyte as described in [START_REF] Díaz | Resistivity of cementitious materials measured in diaphragm migration cells: the effect of the experimental set-up[END_REF].

Setup for microscopic permeation experiments

For micro-diffusion experiments, a specific experimental setup was designed (Fig. 2) in which a 2.5 mm thick cement paste slice acts as membrane between a concentred (0.5 M) KCl solution (upstream compartment) and a diluted (0.01M) KCl solution (downstream compartment). Small amounts (5 mM and 50 mM) of K The downstream compartment allows the scanning electrochemical microscopy (SECM) experiments to be performed and contains the tip, the counter electrode (a Pt mesh), and the reference electrode (a saturated calomel -SCE).

The flux of chlorides through the cement paste membrane stream compartments was detected using the SECM tip polarised at the appropriate potential. The whole SECM setup used in this work has already been described elsewhere [START_REF] Gabrielli | Scanning electrochemical microscopy for investigating gas bubble/liquid interfaces[END_REF][START_REF] Gabrielli | Development of a coupled SECM-EQCM technique for the study of pitting corrosion on iron[END_REF].

Results

Microstructural characterisations of the samples were performed by mercury intrusion porosimetry. The results depicted in Fig. 3 are in good agreement with those reported for a similar system [START_REF] Cabeza | Electrical effects generated by mechanical loading of hardened Portland cement paste[END_REF], with two main pore families centred at about 20 and 90 nm in diameter, the overall porosity being about 14%.

Macroscopic experiments

The flux of chlorides through cementitious membranes is usually split in two regimes: the steady state and the non-steady state regimes [START_REF] Shi | Durability of steel reinforced concrete in chloride environments: An overview[END_REF]. The latter corresponds to the time required for chlorides to reach the downstream compartment, while the former corresponds to the period starting at the end of the non-steady state. Those two periods are clearly identified in Fig. 4 where differential behaviour is observed for the DC and AC regimes. At steady state, the larger slope of the 1 kHz curve indicates that the transport of chlorides is more efficient under AC regime. The fluxes of chlorides obtained directly from the both slopes are 15 µmol.h -1 and 6 µmol.h -1 , for the AC regime and DC regime, respectively. Figure 4 During the migration experiments periodic impedance measurements were performed on the cells, after being disconnected from the corresponding power sources and a 15 minute waiting-time as a relaxation period, i.e., the average the time necessary for stabilisation of the potential difference across the samples. A typical impedance diagram is presented in Fig. 5. It was obtained after 30 days under AC regime at 1 kHz. The impedance data were modelled using the equivalent circuit depicted in the inset of Fig. 5. The equivalent impedance is given by Equation 1.

 12 12 e ZZ ZR ZZ     (1)
where

  1 1 1 11 Z= 1 R jR C   (2)
and

    2 22 2 2 Z= R 1 jR C   . (3)
Figure 5 The physical meaning of the parameters in Equation 1 has been reported in Refs [START_REF] Díaz | Study of the chloride diffusion in mortar: A new method of determining diffusion coefficients based on impedance measurements[END_REF][START_REF] Cabeza | Impedance spectroscopy study of hardened portland cement paste[END_REF]. R e accounts for the electrolyte resistance at both sides of the membrane, R 1 is the resistance associated to the percolating porosity, and C 1 is the geometric capacitance of the sample, corresponding to the solid phase. The time constant R 2 C 2 is associated to the ionic exchange between the liquid phase and the pore walls, C 2 being the corresponding double layer capacitance [START_REF] Cabeza | Impedance spectroscopy study of hardened portland cement paste[END_REF][START_REF] Cabeza | Electrical effects generated by mechanical loading of hardened Portland cement paste[END_REF]. The dispersion parameters  1 and  2 are introduced to account for the Cole-Cole dispersion of the RC time constants. The high dispersion obtained for the R 1 C 1 time constant can be attributed to the heterogeneous distribution of the current in the cement paste membrane [START_REF] Díaz | Resistivity of cementitious materials measured in diaphragm migration cells: the effect of the experimental set-up[END_REF].

The data presented in Fig. 5 show that the electrical model reproduces well the experimental data. The relative error between the experimental impedance data and the fitted values remains below 0.2% in the whole frequency range investigated.. Above 10 MHz the measured impedance is dominated by the series inductance introduced by the graphite electrodes and wires, about 0.4 H (data not shown). Below 10 kHz, the main contribution to the impedance comes from the interfacial processes at the electrodes. Thus, about three frequency decades are available to study the transport through the cement paste membrane.

The parameter of interest here is R 1 , associated to the percolating porosity [START_REF] Díaz | Study of the chloride diffusion in mortar: A new method of determining diffusion coefficients based on impedance measurements[END_REF]. The results obtained from the fitting of the impedance spectra with time as parameter are reported in Fig. 6. A continuous increase of the resistance is observed for both regimes from the beginning of the measurement. However, after about 15 days, an inflexion point can be observed on the curve for the DC regime that corresponds to a higher slope and a higher resistance values.

The evolution of the R 1 values in Fig. 6 seems contradictory with a process corresponding to chloride incorporation into the cement because a higher ionic concentration should be associated with a lower resistance, i.e. a negative slope as a function of time should have been expected. This apparent contradiction will be discussed later in the section 4.

Microscopic experiments

The CV curve at 100 mVs -1 of the solution with a Pt microelectrode is presented in Fig. 7A, which shows that chloride ions are oxidised at about 1.25 V/SCE. Thus, this potential can be used for the detection of the chlorides arriving from the upstream compartment of the cell. Moreover, at about 0.3V/SCE the reversible response of the ferri/ferrocyanide is evidenced (inset in Fig. 7A).

Thus biasing the SECM tip at -0.3 V/SCE (i.e. on the diffusion limited regime for the reduction reaction) allows approach curves (Fig. 7B) and topographic profiles of the cement paste membrane to be performed [START_REF] Bard | Scanning Electrochemical Microscopy[END_REF].

Diffusion of chlorides

Starting form a high concentration (0.5M KCl) in the upstream compartment, chlorides could diffuse towards the downstream compartment in which a diluted solution (0.01M KCl) was used. The detection of chlorides flux was performed by cyclic voltammetry between 0.5 and 1.55 V/SCE on the SECM tip as a function of time as shown in Fig. 8A. A continuous increase of the peak current at 1.3V/SCE after 30 minutes was observed, which corresponds to the arrival of chlorides from the upstream compartment.

After verification of the reproducibility of the measurement using different experimental conditions, including using distilled water in the downstream compartment or unsaturated cement paste samples, it was decided to investigate the transport process by performing additional potentiostatic experiments.

Topography examinations

Topographic profiles of the cement paste surface have been obtained by two different methods: the high frequency conductivity measurement, which is obtained from the electrolyte resistance measurement of the probe and for which no redox mediator is required [START_REF] Gabrielli | Scanning Electrochemical Microscopy Imaging by Means of High-Frequency Impedance. Measurements in Feedback Mode[END_REF], and the classical negative feedback mode using a mediator (e.g. the ferro/ferricyanide redox couple). Both methods provided similar results and only the last one is presented here.

A typical topographic map of the cement paste surface is presented in Fig. 9. The main feature to highlight here is its dynamic nature that can be better noticed through the iso-current surfaces plotted in the X-Y plane. The main pores present have been labelled A to D so that it is possible to qualitatively follow at a glance their evolution with as a function of time from Fig. 9-I to Fig. 9-III.

Figure 9 A quantitative approach to the dynamic behaviour of the interface can be obtained by the integration of the "active surface" at each time on the basis of the identified pores. This integration was performed in Fig. 9 and Fig. 10 using the current contour plots of the XY plane. The results, in percentage of active surface, %S, are 2.6, 5.6 and 2.9, for the initial condition, at 80 minutes and at 410 minutes, respectively. Obviously, these values are only apparent because they depend on the minimum area that can be sense by the SECM tip (lateral resolution), which in turn depends on the tip radius and the tip-to-substrate distance.

The dynamic behaviour of the interface can be understood in terms of dissolution/precipitation processes occurring at the ionic channels. Possible processes are portlandite lixiviation, and precipitation of chloride-containing compounds as Friedel's salt.

Some experiments have been performed using a smaller diameter tip ( = 1 m) to improve the lateral resolution of the mapping. The results are presented in Fig. 10. Besides the dynamic feature evident when Figs 10I and 10II are compared, more interesting is the percentage of active surface, which is decreased of about one order of magnitude with respect to the values shown in Fig. 9.

Such a decrease corresponds to the ratio of the two microelectrodes used for performing experiments presented in Figs. 9 and 10.

This result represents, to our knowledge, the first evidence that the ionic flux through cementitious membranes occurs through pores equal or smaller than 1 m, which approaches the pore family at 100 nm present in Fig. 3. Several attempts were performed to improve the lateral resolution; however, due to the roughness of the interface, these attempts to use smaller probes failed.

Discussion

This last finding allows us to give a reasonable interpretation to the results presented in Fig. 8, and advance an image of the actual meaning of the diffusion coefficient concept in cementitious materials, beyond the "forming factor" usually used in the literature [START_REF] Snyder | The relationship between the formation factor and the diffusion coefficient of porous materials saturated with concentrated electrolytes: theoretical and experimental considerations[END_REF][START_REF] Mercado | Chloride diffusion coefficient: A comparison between impedance spectroscopy and electrokinetic tests[END_REF].

From Fig. 8 data, the transition time, , for chlorides through the 2.5 mm thick membrane, d m , in Equation 4, lies between 30 and 40 minutes which, for linear diffusion, gives a diffusion coefficient, D, in the range 6.6 -8.7x10 -6 cm 2 .s -1 . Those values are larger than those found for chalk rock using a radiometric method (0.52-3.23 × 10 -6 cm 2 s -1 ) [START_REF] Hill | Diffusion coefficients of nitrate, chloride, sulphate and water in cracked and uncracked Chalk[END_REF] and smaller than those for chloride ions in diluted solution (2x10 -5 cm 2 .s -1 ). The difference with diluted solution, a factor 2.3 to 3, can be ascribed to pore tortuosity. For the macroscopic case, the slopes of the curves shown in Fig. 4 at the steady state period correspond to fluxes, J, of 2.1x10 -10 mol.s -1 .cm -2 and 8.2x10 -10 mol.s -1 .cm -2 for the AC and DC regimes, respectively. From these values the corresponding diffusion coefficients, D, can be obtained from the Equation 5, and values of 2.2x10 -8 cm 2 .s -1 and 0.9x10 -8 cm 2 .s -1 are obtained for the AC and DC regimes, respectively. These values lie in the usual experimental range [START_REF] Stanish | Testing the chloride penetration resistance of concrete: A literature review[END_REF], but are three orders of magnitude smaller than those previously discussed for the micro experiments.

   J D zF C RT x  (5)
The discrepancy between the micro and macro experiments can however be rationalised if the "active surface" is considered as critical parameter. The active surface, defined as the apparent cross section of the chloride emitting pores, has been considered to build up Fig. 11. When the pore cross section equals the surface of the macro experiment, both diffusion coefficients are equal.

However, when the surface is explored with the tip of = 10 µm, the active surface represents only 3% of the total surface, as shown in Fig 9 . When the surface is explored at higher resolution, with the tip of = 1 µm, the actual active surface falls to 0.2% (see Fig. 10), which makes the macrodiffusion coefficient values lie in the range of those obtained from the micro experiments. Higher spatial resolution of the SECM tip will be necessary to sense the actual active surface limit, which is as mentioned previously not possible.

Figure 11 The immediate conclusion from these results is that the transport of chlorides through the cement paste membrane involves the porosity below 1 m pore size, which matches with the pore structure presented in Fig. 3.

In addition, the results presented in Figures 9 and 10 give a clear evidence of the dynamic behaviour of the chloride transport, involving pore blockage, opening and structure changing, as already reported [START_REF] Sáchez | Microstructural modifications in Portland cement concrete due to forced ionic migration tests[END_REF][START_REF] Díaz | Study of the chloride diffusion in mortar: A new method of determining diffusion coefficients based on impedance measurements[END_REF]. The dynamic behaviour can be at the origin of the positive slope for the R 1 values in Fig. 6, because the pore blocking can compensate the increase in conductivity due to the ingress of chlorides. More subtle is the difference between AC and DC regimes, also evident in Fig 4.

The dissimilar effect in concrete's microstructure during AC and DC chloride extraction and cathodic protection experiments has already been reported in literature [START_REF] Koleva | Conventional and Pulse Cathodic Protection of Reinforced Concrete: Electrochemical Approach and Microstructural Investigations[END_REF][START_REF] Koleva | Investigation of Corrosion and Cathodic Protection in Reinforced Concrete II. Properties of Steel Surface Layers[END_REF]. However, no interpretation to this fact has been given so far. In our opinion, the data reported in the present study allow to advance some causes for the faster ionic transport under AC conditions. As the diffusion coefficient values for ionic motion in the pores approach that of the bulk solution, a characteristic frequency, f c , for the process of ionic exchange between pore walls and pore solution can be defined by the Equation 6 [START_REF] Alonso | Study of the dielectric characteristics of cement paste[END_REF]:

  2 2 c D f ( 6
)
where  represents the pore length along the electric field. As from mercury intrusion porosimetry it is only possible to access the connecting pore necks [START_REF] Cook | Mercury porosimetry of hardened cement pastes[END_REF], it is probable that the pore lengths involved in the motion associated to the electric field are higher than the 0.1 m threshold pore diameter in Fig. 3. Thus, if D = 10 -5 cm 2 .s -1 we get, from Equation 6, a range of f c between 0.6 kHz and 60 kHz for the limiting lengths ranging from 1 m and 0.1 m, respectively.

The application of an AC field, provided it is in the range of f c , will induce local stirring effects that will make difficult the adsorption process involved in the formation of chloride rich phases (Friedel's salt) [START_REF] Suryavanshi | Mechanism of Friedel's salt formation in cements rich in tri-calcium aluminate[END_REF], hence the local free chloride concentration will be higher and the transport more efficient, which explains the differences observed in Figs. 4 and6.

Another interesting relationship between the percolation resistance R 1 (Fig. 6) and the flux of chlorides (Fig. 4) under different regimes can be derived from the application of the Nernst-Einstein relation for the ionic transport through membranes [START_REF] Gottlieb | Failure of the Nernst-Einstein equation to correlate electrical resistances and rates of ionic self-exchange across certain fixed charge membranes[END_REF]. The ionic flux, , is given by Equation 7, which is independent of the geometry of the membrane :

 2 1 RT FR (7)
At T= 298 K, and taking R= 8.31 J•K -1 .mol -1 , and F= 96500 C•mol -1 , Equation 7gives:

   1 958 . () eq Rh ( 8
)
Data presented in Fig. 6 have been re-written in terms of flux through Equation 8 and compared with the flux data from chemical analysis (Fig. 4), all in Table 1. The conclusion from these data is that the flux under AC regime is higher than under DC conditions. As at the steady-state period most of the porosity is filled with the electrolyte, the discrepancies between the electrochemical data and the actual flux (the slope obtained analytically) can be viewed as the reaction of chlorides with the pore walls, which is more important for the DC regime. Indeed, after 34 days a good agreement was obtained between the electrochemical and chemical data (40.9 mol•h -1 and 39.0 mol•h -1 , respectively) for the AC regime.

Table 1 The study of R 1 opens the possibility of knowing the flux of chlorides from the environment to the rebar in reinforced concrete structures. This knowledge could be of importance in the definition of the critical chloride concentration for pit initiation. The data available so far, on the basis of chlorides to cement ratio, are highly dispersed [START_REF] Angst | Critical chloride content in reinforced concretea review[END_REF] without any apparent rationale. Thus, a new deal could be introduced by combining information on the empty space at the rebar's level and the ionic flux to that space to reach the critical concentration.

Conclusions

The SECM technique has been applied for the first time to the study of the transport of chlorides through cementitious membranes. The results presented show that the transport of chlorides occurs mainly through pores of sub-micrometre diameter. The study of the transition time has allowed concluding that the diffusion coefficient approaches the value usually obtained in bulk solution.

Moreover, the SECM study has evidenced the dynamic character of the chloride transport that involves pore blockage and pore opening. This dynamics allowed interpreting the macroscopic results on the variation of the percolation resistance with time. The resistance increases due to blockage of the porosity.

The macroscopic study, mainly based on EIS, has also allowed to present here an interpretation that explains the beneficial effect of the AC current in the transport of chlorides. A possible method for estimating the flux of chlorides was too presented.

Data from R 1 (Fig. 6) Data from the slopes (Fig. 4 logarithm of the differential intruded volume (ml.g -1 ) vs. pore diameter (nm), for a hardened cement paste with 0.5 water to cement ratio, after 30 days of curing time.

3 Fe

 3 to the chlorinated solutions when a redox mediator was required for surface imaging purposes.

Figure 2

 2 Figure 2

Figure 7

 7 Figure 7

Fig. 8B corresponds

  Fig. 8B corresponds to an example of the potentiostatic approach. After a fast line scan to locate a pore domain the tip is located in that position and polarised at 1.3V, recording the current as a function of time. The current rise starting at 38 minutes can be associated to the arrival of chlorides which increases the local concentration till about 60 minutes when the diffusion of species into the bulk solution makes the current decrease.

Figure 1 .

 1 Figure 1. Schematic view of the experimental permeation cell employed for the macroscopic experiments. Each compartment is 10 cm in length and 5 cm in diameter, thus containing 200 cm 3 solution in each compartment with a cross section area of 20 cm 2 .

Figure 2 .Figure 3 .

 23 Figure 2. Schematic view of the experimental permeation cell employed for the microscopic experiments of natural diffusion.

Figure 4 .Figure 5 .Figure 6 .Figure 7 .Figure 8 .Figure 9 .Figure 10 .

 45678910 Figure 4. Concentration of chlorides in the anode side (200 cm 3 downstream compartment) as a function of the treatment time under DC and AC (1 kHz) regimes.

Figure 11 .

 11 Figure 11. Dependence of the measured diffusion coefficient on the apparent size of the emitting pores.

Table 1 .

 1 Flux of chlorides, in mol.h -1 , through the cement paste membrane obtained from R 1 data (Fig.6) using equation 8, and from the slopes inFig 4.

	)

Acknowledgement

The Spanish authors would like to thank the Spanish Government for partially funding this work under project #BIA2010-16950. The European Regional Development Fund is also acknowledged for financing the DURATINET project nr. 2008-1/049.