Vicky Meiwen Huang

Shao-Ling Wu

Mark E Orazem

Nadine Pébère

Bernard Tribollet

Vincent Vivier
email: vincent.vivier@upmc.fr

Local electrochemical impedance spectroscopy: A review and some recent developments

Keywords:

Local electrochemical impedance spectroscopy (LEIS), which provides a powerful tool for exploration of electrode heterogeneity, has its roots in the development of electrochemical techniques employing scanning of microelectrodes. The historical development of local impedance spectroscopy measurements is reviewed, and guidelines are presented for implementation of LEIS. The factors which control the limiting spatial resolution of the technique are identified. The mathematical foundation for the technique is reviewed, including definitions of interfacial and local Ohmic impedances on both local and global scales. Experimental results for the reduction of ferricyanide show the correspondence between local and global impedances. Simulations for a single Faradaic reaction on a disk electrode embedded in an insulator are used to show that the Ohmic contribution, traditionally considered to be a real value, can have complex character in certain frequency ranges.

Introduction

Electrochemical techniques such as cyclic voltammetry or electrochemical impedance spectroscopy (EIS) are widely used to improve the understanding of multi-step reactions [START_REF] Bard | Electrochemical Methods: Fundamentals and Applications[END_REF][START_REF] Gabrielli | Physical Electrochemistry. Principles, Methods, and Applications[END_REF], allowing the kinetics of heterogeneous electron-transfer reactions, cou-pled chemical reactions, or adsorption processes to be studied. In such conventional electrochemical experiments, the electrode response to a perturbation signal corresponds to a surface-averaged measurement ascribable to the behaviour of the whole electrode surface. However, electrochemical systems rarely show an ideal behaviour, and this can lead to difficulties with data interpretation. For instance, in the case of localized corrosion, surface-averaged techniques cannot identify the time of initiation or the location of a single attack among many.

To overcome these difficulties, several scanning techniques using electrodes of small dimension such as metal microelectrodes [START_REF] Wightman | [END_REF][START_REF] Amatore | Physical Electrochemistry. Principles, Methods, and Applications[END_REF] have been developed to probe in situ the electrochemical doi:10.1016/j.electacta.2011.03.018 interface [START_REF] Lillard | Analytical Methods in Corrosion Science and Engineering[END_REF]. The scanning reference electrode technique (SRET) is a rather old technique which was first introduced by Evans and Thornhill [START_REF] Evans | [END_REF][7][8] in 1938. It consisted of measuring the potential distribution in solution with a Luggin capillary at different positions along the electrode surface, and it was successfully applied over the passing years for mapping heterogeneities during corrosion processes [9][10][11]. The scanning-vibrating-electrode technique (SVET), first developed for in situ monitoring of the steady-state current density near individual living cells by Jaffe and Nuccitelli [12], was also well-suited for studying corroding interfaces [13][14][15][16][17]. It is based on the use of a single microelectrode which is vibrated in one or two directions across the sample surface, allowing the potential gradient to be measured accurately with a lock-in amplifier referenced to the probe-vibration frequency [START_REF] Lillard | Analytical Methods in Corrosion Science and Engineering[END_REF]12]. Furthermore, the intense development of both microelectrodes and scanning electrochemical microscopy [18][19][20][21][22] allowed various kinds of interface to be imaged with a resolution in the micron range or lower, depending on both the electrochemical probe dimensions and the probe-to-substrate distance. In addition, various kinds of probes, such as amperometric or potentiometric sensors, can be used to selectively detect a large variety of species [START_REF] Denuault | Scanning Electrochemical Microscopy[END_REF][START_REF] Etienne | [END_REF].

The use of local dc-current-density measurements such as SVET allows surface heterogeneities to be identified but cannot explain the local reactivity. In an attempt to evaluate the local impedance of restricted active areas, Isaacs and Kendig [25] pioneered the development of the scanning-probe impedance technique. In this technique, a small probe containing both the counter and the reference electrodes was rastered at a height of about 30 m over the working electrode surface forming a thin-layer cell configuration. These measurements allowed qualitative results to be acquired on stainless steel welds and on coated galvanized steel plates. However, the current measured cannot be uniquely ascribable to the area under study, and, thus, no quantitative results could be obtained. Moreover, such an electrochemical-cell configuration with a small counterelectrode facing a large working electrode is not suited for impedance measurements.

A few years later, the Isaacs group introduced a novel method for generating quantitative local electrochemical impedance spectroscopy [26,27]. This technique is based on the hypothesis that the local impedance can be generated by measuring the ac-localcurrent density in the vicinity of the working electrode in a usual three-electrode cell configuration [26]. This was achieved with the use of a dual microelectrode for sensing the local ac-potential gradient, the local current being obtained from the direct application of the Ohm's law. It was also shown that 10 m diameter platinum microelectrodes spaced 170 m apart allowed a resolution of 30-40 m, which compared favorably with the calculated results described previously for SVET experiments [15,27]. However, these authors mentioned a significant discrepancy between theory and experiments when the probe was close to the electrode under conditions when the best resolution was expected. Using this experimental setup, impedance diagrams over an active pit were obtained allowing the direct comparison of local and global impedances [28]. A variant of the technique is the mapping mode at a single frequency, which permits identification of electrochemical active areas [26][27][28] or time-resolved imaging for the investigation of the dynamics of the interface modifications. For instance, Wittmann et al. [29] showed that defects in organic coating can be identified by this technique prior to detection by visual observation.

Bayet et al. [30][31][32] developed LEIS measurements based on the use of a SVET setup. By this way, the authors took advantage of the small vibrating probe size, allowing reduction of the screening effect of the probe. They also proposed to measure the local potential in combination with the local current to define local impedance [30]. Such an approach takes advantage of using a unique probe for sensing the potential at two locations. However, one of the main drawbacks is the forced convection induced by the vibration of the probe in the close vicinity of the analyzed surface area. Some LEIS investigations were also reported using larger probes. For instance, Baril et al. [33] investigated the electrochemical behaviour of the AZ91 magnesium alloy in Na 2 SO 4 solution. Some local impedance diagrams were obtained over an active pit after 4 days immersion in Na 2 SO 4 electrolyte. However, the resolution of the LEIS setup was not sufficient to describe the surface reactivity ascribable to the alloy structure of the sample. Using a home-made setup with probes of few tens of micrometers, Galicia et al. [34] were able to observe the influence of the microstructure on the corrosion rate of the AZ91 alloy. The same experimental set-up with large probes was used by Jorcin et al. [35] to investigate the initiation and propagation of delamination at the steel/organic coating interface and also by Lima-Neto [36] to determine the extension of sensitized zones in welded AISI304 stainless steel. It was shown that the length of the sensitized zone in the heat-affected zone was detected by the LEIS technique. For these two examples, industrial samples were investigated. This point is important because it emphasizes that, depending on the probe size, information can be obtained at different scales. Using a similar technique, Philippe et al. [37] investigated polymer-coated galvanized steel. They showed that the global electrochemical impedance measurements provided surface-averaged responses corresponding to both the polymer properties and its defects, whereas LEIS allowed coating defects to be isolated.

Pilaski et al. [38] developed a LEIS system based on the microcapillary cell technique [39]. The main advantage of this technique is the possibility to investigate a small surface area independently of the surrounding material. However, this can be seen as a drawback since the effect of the surrounding material (for instance galvanic coupling) is hindered.

It should also be mentioned that the development of a specific apparatus can also be required for special applications such as fuel cell investigations [40] or for studying metal hydride battery electrodes [41]. For instance, an experimental setup allowing the simultaneous measurement of 10-local electrochemical impedance responses to be recorded in parallel has been developed for the study of a polymer electrolyte fuel cell [42,43]. A unique feature of this setup is the use of a zero resistance ammeter based on the utilization of Hall effect current sensors for the local current measurements [42]. The local impact of water and drying effects could be observed by use of the local measurements.

In a recent series of papers [44][45][46], our group revisited the basis of the LEIS technique. A key contribution was the definition of three local impedances. The local interfacial impedance (z 0 ) was defined to involve both a local current density and the local potential drop across the diffuse double layer. The local Ohmic impedance (z e ) was defined to involve a local current density and potential drop from the outer region of the diffuse double layer to the distant reference electrode. The local impedance (z) was thus the sum of the local interfacial impedance and the local Ohmic impedance. The influence of the cell geometry and of probe height over a disk electrode was explored theoretically [47,48]. The calculated and experimentally observed frequency dispersion and imaginary contributions to Ohmic impedance were attributed to the current and potential distributions associated with the geometry of a disk electrode embedded in an insulating plane. This work suggested that the frequency dispersion effects should not be apparent for geometries, such as a recessed electrode, for which the primary current distribution is uniform. It was also shown that low-frequency dispersion can be seen when adsorbed species are involved [49,50].

The objective of the present work is to provide guidelines for implementation of LEIS and review experimental and simulation results which are characteristic of the technique.

The LEIS setup

A fundamental requirement for the LEIS device is the measurement of the local current density in the close vicinity of the interface under investigation. Among the different possibilities presented in the introduction part, the dual probe system appears to be well suited since the fabrication of sturdy metallic microelectrodes (UME) is now well established. Furthermore, the resolution of the probe should depend, in first approximation, on both UME dimension and the inter-microelectrode distance. These two parameters can be controlled during the fabrication process.

Probes used with commercial devices are generally large and will have a limited spatial resolution (some mm 2 ). All the experimental results presented here were obtained with a home-made system. However, as stated before, the size of the probes has to be chosen in accordance with the sample dimension.

Electrochemical device

The experimental setup (Fig. 1) for performing LEIS measurements consisted of a home-made potentiostat coupled with a Solartron 1254 four-channel frequency response analyzer (FRA), allowing both global and local impedances to be recorded simultaneously. Two home-made analog differential amplifiers with both variable gain and high input impedance were used to record simultaneously the local potential and current variations. The local current was obtained by measuring the local potential difference sensed by the two micro probes; whereas, the local potential was measured as the potential difference between the potential of the electrode and the closest micro reference electrode. The bielectrode was moved with a 3-axis positioning system (UTM25, Newport) driven by a motion encoder (MM4005, Newport) allowing a spatial resolution of 0.2 m in the three directions. All measurements were generally performed under potentiostatic regulation, with the amplitude of the applied sinusoidal voltage set to be as large as possible to improve the ratio signal/noise but sufficiently low that the linear approximation of the potential/current curve can be used. For instance, some experiments have been performed using a 100 mV peak-to-peak signal, 50 acquisition cycles, and 7 points per decade of frequency [45]. Home-made software developed for scanning electrochemical microscopy was used for data acquisition. One of the great advantages of using a home-made apparatus is that it provides the capability for measuring simultaneously local and global impedances, which is not, to our best of knowledge, possible with commercial LEIS devices.

Probe preparation

The bi-electrode consisted of two metallic wires, the dimension of which can usually vary from few micrometers to tens of micrometers in diameter. In the case of a Pt bi-electrode, wires were sealed into the bi-capillary by melting the glass using a resistance heater with a controllable current through a coiled nichrome wire. The tip was then polished with SiC paper and a deposit of Pt black from hydrogen hexachloroplatinate (IV) was performed daily on each microdisk to reduce the interfacial impedance of these electrodes [12]. Ag/AgCl bi-microelectrodes can be constructed from silver wires sealed into a dual capillary using an epoxy resin. The AgCl layer was formed by anodizing the Ag microelectrode in a KCl solution according to the following electrochemical reaction:

Ag + Cl -⇄ AgCl + e - (1)
The silver microelectrode was first cycled between -0.3 and 0.2 V/SCE at a rate of 100 mV s -1 in a 2 M KCl solution for cleaning, and then a potentiostatic oxidation of Ag was performed in the same electrolyte at 0.4 V/SCE during 5-10 min. It should be mentioned that the spatial resolution can be adapted to the size of the area to be investigated by changing the size of the Ag wires used for measuring the local current and potential.

The electrochemical measurements were generally carried out with a classical three-electrode cell at room temperature. The counterelectrode was a large platinum grid, and the potentials were measured with respect to a reference electrode located far from the sample in the solution bulk as shown in the schematic representation of the experimental cell given in Fig. 1a.

Definitions of local impedances

Using a bi-electrode for probing the solution potential and a 4-channel frequency response analyzer, global, local, and local interfacial impedances can be measured simultaneously [44]. In the following, the use of an upper-case letter signifies that Z is a global value; whereas, the use of a lower-case letter means that z is a local value, following the notation proposed by Huang et al. [44] and summarized in the Notation section. For local electrochemical measurements, the local AC-current density i loc (ω) can be obtained through the Ohm's law using

i loc (ω) = V probe (ω) d (2)
where is the electrolyte conductivity, V probe (ω) is the AC potential difference between the two probes, and d is the distance between the two probes (see Fig. 1b).

The local impedance (z) involves the electrode potential measured with respect to a reference electrode located far from the electrode surface (Fig. 2).

z(ω) = Ṽ (ω) -˚ref i loc (ω) = Ṽ (ω) V probe (ω) d (3)
where Ṽ (ω) -˚ref represents the AC potential difference between the electrode surface and the reference electrode in the bulk solution.

The local interfacial impedance (z 0 ) involves the potential of the electrode referenced to the potential of the electrolyte measured at the inner limit of the diffusion layer.

z 0 (ω) = Ṽ (ω) -˜0(ω) i loc (ω) = Ṽ (ω) -˜0(ω) V probe (ω) d (4)
Thus the local Ohmic impedance (z e ) can be deduced by calculating the difference between the local impedance and local interfacial impedance.

z e (ω) = z(ω) -z 0 (ω) (5)
From a practical point of view, it is not possible to perform a potential measurement just outside the double layer (Fig. 2). Thus the distance between the probe and the substrate, h, must be taken into account. Using the definitions presented above, the local interfacial impedance, z h (ω), estimated at y = h, can be obtained using

z h (ω) = Ṽ (ω) - ˜h i loc (ω) = Ṽ (ω) -˜h V probe (ω) d (6)
where Ṽ (ω) -˜h represents the AC potential difference between the electrode surface and the closest of the two probes of the bielectrode, located at a distance y = h from the electrode surface (Figs. 1 and2). However Eq. ( 6) is valid under the assumption that the spreading of the current in solution can be neglected, as previously shown by Zou and co-workers [27]. The local Ohmic impedance z e,h can thus be deduced by calculating the difference between the local impedance and local interfacial impedance, i.e. Experimental measurements can therefore be employed to verify the appearance of a local Ohmic impedance predicted by simulations. One can stress again that the use of home-made device for performing LEIS allowed simultaneous measurement of the global impedance and all the local impedances.

z e,h (ω) = z(ω) -z h (ω) (7)

Mathematical foundation

The mathematical treatment presented by Huang et al. [44] follows that presented by Newman for a simple Faradaic reaction on a planar disk electrode embedded in a coplanar insulator [51], but it can be extended to other cell geometries [47,48] in order to investigate the edge effect of the electrode on the electrochemical impedance response, and to different mechanisms involving intermediates [49,50]. The geometry of the system was defined by the radius of the electrode r 0 . The potential ˚ in solution surrounding this electrode is governed by Laplace's equation.

∇ 2 ˚ = 0 (8)
In cylindrical coordinates (r,,y), Eq. ( 8) can be expressed as

1 r ∂ ∂r r ∂∂ r + 1 r 2 ∂ 2 ∂ 2 + ∂ 2 ∂y 2 = 0 ( 9
)
where y is the normal distance to the electrode surface, r is the radial coordinate, and is the azimuth. The cylindrical symmetry condition requires that the geometry is invariant under rotation about the y axis (i.e. the symmetry axis), thus

∂∂ = 0 (10)
On the surrounding insulator and far from the electrode surface, the boundary conditions were given by ∂∂ y y=0 = 0 at r > r 0 (11) and

˚ → 0 as r 2 + y 2 → ∞ (12)
For a pure capacitive behaviour, the flux boundary condition at the electrode surface was written as

C 0 ∂(V -˚0) ∂t = - ∂∂ y y=0 (13)
where C 0 is the interfacial capacitance, is the electrolyte conductivity, V is the electrode potential, and ˚0 is the potential just outside the double layer. In the case of a CPE behaviour, the governing equations were similar; the only change to be done was the substitution of the capacitance C 0 on the flux boundary condition of the electrode surface by Q(jω) ˛. For more complex situations, applicable boundary conditions are detailed in Refs. [46,49,50]. The current density was thus calculated by integrating the local admittance of the system over the electrode disk surface. As previously observed for a planar embedded disk electrode [44][45][46], the results could be expressed in terms of a dimensionless frequency, K, which is defined by

K = Qω ˛r0 (14)
in which ˛ is taken to unity and Q = C 0 in the case of a pure capacitor. For data analysis, the origin of the normal axis y = 0 is always defined by the disk electrode surface, that is all the distance were measured from this origin. All calculations were performed using finite element method software (COMSOL ® ) with the conductive media DC module in a 2D axial symmetry. The geometry and the position of the reference electrode were shown to play a significant role on the numerical result of the calculated impedance. Thus, a spherical geometry, and a distance 2000 times larger than the disk electrode dimension were used to perform numerical calculation within an error range smaller than 0.2%.

Potential difference measurement and spatial resolution

Independent of the mechanism under investigation, LEIS is based on the measurement of a local potential difference in the close vicinity of the electrochemical interface. The size of the probe and the distance between the probe and the substrate are the relevant parameters. Fig. 3 shows the local potential difference measured over a planar-disk electrode (r 0 = 0.25 cm) for a probe located h = 100 m of the interface with a bi-electrode (distance between the two probes, d = 50 m). The calculations were performed for = 0.01 S cm -1 and a double layer capacitance C 0 = 10 F. Two cases were considered: a blocking electrode (R = infinity-circles) and R = 1 k, which represents a kineticallycontrolled electron-transfer reaction (squares on Fig. 3). In the case of a blocking electrode, the potential difference decreases linearly with the frequency and reaches 1 nV for 0.5 Hz. As 1 nV is a lower limit for a commercial apparatus, this is a strong limitation of the technique. However, when the system involves a single electron exchange, the curve is S-shaped and tends towards 500 nV. It should be noted that this latter value depends on both electrolyte conductivity as shown by Eq. ( 14) and charge-transfer resistance. As a guideline, a decrease of the electrolyte conductivity allows measurement at lower frequencies. However, if the system involves a smaller time constant, associated, for example, with diffusion or relaxation of adsorbed species, preliminary experiments are required for the determination of the lowest measurable frequency.

One approach for increasing the spatial resolution would be to decrease the probe size, but this makes sense only if the distance between the two probes also diminishes since the spatial resolution should depend on the total size of the probe. Fig. 4 shows the influence of the distance between the two microreference electrodes when the probe is located at a position 50 m from the interface. The potential difference between the two electrodes decreases with the inter-electrode distance and reaches a value smaller than 1 nV when the probe separation is smaller than 1 m. Fig. 5 shows that when a probe with the inter-electrode distance of 1 m is used, the distance between the probe and the substrate does not play a significant role if h > d. From this series of simulations, it is shown that to increase the spatial resolution, the probe size must decrease. However, a dimension in the micrometer range or lower seems to be the actual limit. The commercial probe sizes (electrode dimension and interelectrode distance) are significantly larger, which has the effect of decreasing the spatial resolution. However, use of larger probes allows measurement over a larger frequency domain (especially the lower frequency range).

6.

A simple example: the ferri/ferrocyanide system Fig. 6 shows experimental results for global and local impedance measurements performed in a ferri/ferrocyanide solution at the equilibrium potential. The bi-microelectrode which consisted of two silver/silver chloride microelectrodes of 40 m in diameter each, was positioned at 100 m above the carbon electrode (0.5 cm in diameter). Fig. 6a shows the global impedance. From the high-frequency loop, the electrolyte resistance, the charge transfer resistance and the double layer capacitance can be obtained. The low-frequency behaviour corresponds to the Warburg impedance (diffusion) as expected for a simple redox system at steady-state. Fig. 6b shows the local impedance diagram performed over the center of the carbon electrode, simultaneously with the global one. It is noteworthy to see that the two diagrams are identical, thus validating the local impedance measurement. In addition, the characteristic frequencies of the time constants are similar for each process. This simple experiment allows calibration of the experiment. It also shows that the same processes can be characterized with both global and local impedance spectroscopy, taking advantage of the spatial resolution of the LEIS technique. From an experimental point of view, all the requirements for performing a global impedance measurement (i.e. linearity, stability, and causality) remain the same for LEIS, and the validity of the measurements can be checked using the Kramers-Kronig relationship directly or through use of the measurement model [52][53][54].

Influence of the cell geometry on local impedance response

Huang et al. [44][45][46] have shown that the Ohmic contribution to the impedance response of a disk electrode embedded in an insu- lating plane takes the form of an impedance. The appearance of the complex Ohmic impedance was attributed to the nonuniform current and potential distributions induced by electrode geometry. For the disk embedded in an insulating plane, the radial current density is a function of radial position and has an associated decrease in cur- rent density with axial position. In this case, the Ohmic impedance must be represented by a complex number. For the recessed disk electrode geometry, there is no radial current and the current density is independent of axial position. In this case, the Ohmic impedance can be represented by a real number. The complex character of the Ohmic impedance is therefore not only a property of electrolyte conductivity, but also a property of electrode geometry and interfacial impedance.

The simulations presented by Huang et al. [46] are extended here for a single Faradaic reaction under Tafel kinetics. The electrochemical reaction is characterized by the parameter

J(r) = ˛F ¯i(r) r 0 RT = 4 R e R t . (15)
The global impedance response is presented in Fig. 7 with J as a parameter. When J is large, the kinetics are fast and R t is small as compared to the Ohmic resistance R e . For all cases, the slope of the lines given in Fig. 7b for low frequencies is equal to unity, but the slope is greater than -1 at large frequencies. The results presented in Fig. 7 are characterized by two frequencies: K = 1, above which the geometry influences the impedance response and induces pseudo-CPE behaviour, and K/J = 1, which corresponds to the frequency ω = 1/R t C 0 .

The scaled global impedance results presented in Fig. 8 shows that the influence of a large value of J is to increase the appearance of a depressed semicircle usually associated with CPE behaviour. This effect is made dramatic because the characteristic frequency at which K/J = 1 is greater than the frequency K = 1.

The influence of geometry on the impedance response can be understood by examining the local impedance response shown in Fig. 9a for J = 1. The local impedance is largest at the center of the electrode, consistent with the smaller current density seen at the electrode center. The local impedance is smallest at the periphery of the electrode. The size of the loops is decreased in Fig. 9b for J = 10, consistent with the smaller value of R t relative to R e . The highfrequency limit for the local impedance, however, is unchanged. The high-frequency inductive and/or capacitive loops seen in Fig. 9 are a consequence of the electrode geometry and have, in fact, been experimentally confirmed. These loops can be expressed in terms of the local Ohmic impedance discussed above.

The local Ohmic impedance for J = 1 and J = 10 is presented in Fig. 10a andb, respectively. The loops are inductive at the center of the electrode and capacitive at the electrode periphery. Again, these results have been confirmed by use of local impedance measurements. The loops associated with the local Ohmic impedance are smaller for the case where J = 10, which may seem to be in conflict with the result shown in Fig. 8 showing that the semicircle depres- sion increases with increasing J. The reason is that, while the Ohmic impedance loops are small, they represent a larger contribution as compared to the contribution associated with the kinetics.

The frequency dependence of the local Ohmic impedance is shown in Figs. 11 and 12 for J = 1 and J = 10, respectively. At frequencies below K = 1, the imaginary contribution, as shown in Figs. 11b and12b, tends toward zero. At frequencies well above K = 1, the imaginary contribution, again, tends toward zero. In a range of frequencies near K = 1, the local Ohmic contribution has a complex character. While not shown here, a similar complex character is seen for the global Ohmic contribution.

The time-constant dispersion of the global impedance response disk electrodes exhibiting geometry-induced current and potential distributions is seen for dimensionless frequency K = ωC 0 r 0 / > 1, which can be within the experimentally accessible range [START_REF] Gabrielli | Physical Electrochemistry. Principles, Methods, and Applications[END_REF]. The origin of the time-constant dispersion is considered in the present work to be a complex Ohmic impedance. Blanc et al. [55] demonstrated that the concept of an Ohmic impedance is fully consistent with the pioneering calculation of frequency dispersion presented by Newman in 1970. To show that this approach is in agreement with Newman's results, they considered a blocking interface with a frequency-independent capacitance C 0 and an interfacial impedance Z 0 = 1/jωC 0 . This interfacial impedance is independent of the electrode geometry. The overall impedance, which includes the Ohmic contribution, is Z = Z e + 1/jωC 0 , where the capacitance C 0 is independent of frequency and Z e is termed the Ohmic impedance. Newman, in contrast, represented the overall impedance as the sum of a frequency-dependent resistance R eff in series with a = R eff + 1 jωC eff (16) which yields

Z e = R eff - j ω C 0 -C eff C 0 C eff ( 17
)
The fact that Z e is frequency dependent is in perfect agreement with Newman's result. When the frequency tends towards infinity, the current distribution corresponds to the primary current distribution and lim ω→∞ Z e = 1/4r 0 , in agreement with Newman's formula.

Simulations and experiments were used to show that complex Ohmic impedances could be observed at frequencies substantially lower than K = 1 in cases where the Faradaic reactions involved adsorbed intermediates [49,50].

Conclusions

The origin of local electrochemical impedance spectroscopy measurements can be traced back to the original development of scanning reference electrodes in 1938. The development of LEIS was motivated by the need to probe the local reactivity of heterogeneous surfaces. The power of the technique can be demonstrated by the agreement reported between experimental results and simulations. Local impedance measurements were used, for example, to confirm the appearance of a local Ohmic impedance that was predicted by simulations.

LEIS can be performed easily by measuring the local potential difference in solution, allowing the local current to be calculated. Use of a multichannel frequency response analyzer allows simultaneous measurement of global and local behaviours. The resolution of the technique depends on the size of the electrodes used in the bi-electrode probe to sense the local potential and the spacing between the electrodes. The ultimate resolution achievable is constrained by the sensitivity of the potential measuring circuitry. Measurement sensitivity on the order of 1 nV limits the resolution to the micrometer range.

Calculated and measured local and Ohmic impedances have been shown to provide insight into the frequency dispersion associated with the geometry of disk electrodes. The global impedance associated with a simple Faradaic reaction on a disk electrode is purely capacitive, but the local impedance has high-frequency inductive loops. The local impedance is influenced by the local Ohmic impedance, which has complex behaviour near dimensionless frequency K = 1. The imaginary part of both the local and global Ohmic impedances is equal to zero at both high and low frequencies where the Ohmic impedance has purely resistive character.

Fig. 1 .

 1 Fig. 1. (a) Block diagram of the LEIS setup; (b) zoom on the microprobe close to the substrate. The probe-to-sample distance is h and the distance between the two microreference electrodes is d.

Fig. 2 .

 2 Fig. 2. Electrical equivalent representation of the electrochemical cell.

Fig. 3 .

 3 Fig. 3. Local potential difference measured at h = 100 m with a bi-electrode (d = 50 m) over a planar-disk electrode. Calculations were performed for = 0.01 S cm -1 ; r0 = 0.25 cm; C0 = 10 F; R = infinity (pure capacitance-circles) and R = 1 k (squares); V = 30 mVpp.

Fig. 4 .

 4 Fig. 4. Local potential difference measured at h = 50 m over a planar-disk electrode with the distance between the two sensing electrode (d) as a parameter. Calculations were performed for = 0.01 S cm -1 ; r0 = 0.25 cm; C0 = 10 F; R = 1 k; V = 30 mVpp.

Fig. 5 .

 5 Fig. 5. (a) Local potential difference measured with a bi-electrode (d = 1 m) over a planar-disk electrode with the probe-to-substrate distance (h) as a parameter. Calculations were performed for = 0.01 S cm -1 ; r0 = 0.25 cm; C0 = 10 F; R = 1 k; V = 30 mVpp. (b) Zoom on the potential difference in the low frequency range.

Fig. 6 .

 6 Fig. 6. Global (a) and local (b) impedance measurements performed simultaneously on a 0.5 cm in diameter carbon electrode in ferri-ferrocyanide solution (10 mM) + KCl (0.5 M) solution at the equilibrium potential. The local probe consisted of two 40 m in diameter Ag/AgCl wires at 100 m over the center of the carbon electrode.

Fig. 7 .

 7 Fig. 7. Dimensionless impedance response for a disk electrode with a single Faradaic reaction under Tafel kinetics with J as a parameter: (a) real part; and (b) imaginary part.

Fig. 8 .Fig. 9 .

 89 Fig. 8. Scaled impedance response in Nyquist format for the impedance results presented in Fig. 7.

Fig. 10 .

 10 Fig. 10. Local Ohmic impedance response for the impedance results presented in Fig. 7. (a) J = 1; and (b) J = 10.

Fig. 11 .

 11 Fig. 11. Local Ohmic impedance response for the impedance results presented in Fig. 10a for J = 1: (a) real part; and (b) imaginary part.

Fig. 12 .

 12 Fig. 12. Local Ohmic impedance response for the impedance results presented in Fig. 10b for J = 10: (a) real part; and (b) imaginary part.

Appendix A. Notation

Symbol Meaning units

C 0 interfacial capacitance (F cm -2 ) d distance between the two probes (cm) h distance between the probe and the sample (cm) i loc local ac current density (A cm 2 ) K dimensionless frequency (K = ωC 0 r 0 /) r radial coordinate (cm) r 0 electrode radius (cm) V electrode potential (V) V probe ac potential difference between the two probes (V) y axial coordinate (cm) Z global impedance ( or cm 2 )

Z ′ real part of the global impedance ( or cm 2 ) Z ′ imaginary part of the global impedance ( or cm 2 ) z local impedance ( cm 2 ) z ′ real part of the local impedance ( cm 2 ) z ′′ imaginary part of the local impedance ( cm 2 ) z e local Ohmic impedance ( cm 2 ) z ′ e real part of the local Ohmic impedance ( cm 2 ) z ′′ e imaginary part of the local Ohmic impedance ( cm 2 ) z 0 local interfacial impedance ( cm 2 ) z ′ 0 real part of the local interfacial impedance ( cm 2 ) z ′′ 0 imaginary part of the local interfacial impedance ( cm 2 ) z h local interfacial impedance estimated at y = h ( cm 2 ) z ′ h real part of the local interfacial impedance estimated at y = h ( cm 2 ) z ′′ h imaginary part of the local interfacial impedance estimated at y = h ( cm 2 ) z e,h local Ohmic impedance estimated at y = h ( cm 2 ) electrolyte conductivity ( -1 cm -1 ) ˚ref potential of the reference electrode (V) ˚0 potential at the inner limit of the diffusion layer (V) ω angular frequency, ω = 2f s -1


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Keywords: Laparoscopy, Robotics, prostatectomy, urology

Introduction

The advantages of minimally invasive surgery are now well documented and laparoscopy is challenging for both surgeon and assistant. Manual control during prolonged cases can be exhausting either for the assistant or the surgeon who need a stable image.

Among surgeons, urologists have early understood that robotic assistance could provide better comfort and surgical skills improvement. Despite the great advantages offered by the DaVinci® system (intuitive Surgical, Sunnyvale, US), this method remains expensive and cumbersome [START_REF] Ficarra | Retropubic, laparoscopic, and robotassisted radical prostatectomy: a systematic review and cumulative analysis of comparative studies[END_REF] Our group developed a robotic lightweight endoscope holder that is now marketed by the company Endocontrol™ under the name ViKY® . [START_REF] Berkelman | Development and testing of a compact endoscope manipulator for minimally invasive surgery[END_REF] . Previous cadaveric studies have shown the feasibility of the robot's use [START_REF] Long | Development of miniaturized light endoscope-holder robot for laparoscopic surgery[END_REF] . ViKY obtained CE marking in 2007 and FDA approval in 2008 [START_REF] Berkelman | Development and testing of a compact endoscope manipulator for minimally invasive surgery[END_REF] The aim of this pilot study is now to assess the feasibility and the safety of this innovative medical device in different urological surgical indications. We present the results of the first clinical trial carried out with this VIKY robot prior to a bicenter randomized clinical study.

. The first use of the robot occurred in our institution on July 5, 2007. The first procedure was a bilateral pelvic lymph node dissection in the context of high grade prostate cancer previously to external beam radiotherapy.

Materials and methods:

Study design

From March 2010 to September 2010, all the patients scheduled for a laparoscopic procedure in 2 institutions (Grenoble University Hospital and St Etienne University Hospital) were proposed to enrol the study. The clinical trial was approved by the French Ethical Committee CPP Sud-Est V. Exclusion criteria were: age < 18 years, pregnancy and inability to sign in the informed consent. Informed consent was obtained from 20 patients. All data were recorded in a case record form that was specifically designed for this study.

Surgery description

Two laparoscopic surgeons (one in Grenoble and one in St Etienne) performed robotic surgeries for different clinical indications: adrenalectomy, acrocolpopexy, pyeloplasty, radical prostatectomy and radical nephrectomy. Nevertheless, prior to the start of this study, the surgeon had to perform three surgeries using the robot which gave him some experience in manipulating the robot. All the procedures used a transperitoneal approach.

Robot description

The robot used in this trial consists of a compact motorized scope holder placed directly on the patients' abdomen (figure 1, 2 and3). Its architecture is based on a rotating circle. It is attached to the rail of the operating table using an articulated arm to improve the steadiness and the stability of the image. The endoscope manipulator is sufficiently small (110 mm in diameter) to be placed directly on the patient without interfering with other handheld instruments during minimally invasive surgery. It is 75 mm high and its weight is 625 g. The robot motors provide 3 degrees of freedom: 2 rotations allowing exploring the entire abdominal cavity, and translation allowing the endoscope to get closer to or further from the organs. It can be attached to any types of endoscopes and trocars. The robot is submersible and autoclavable. A console, which contains motor controllers and software, analyzes the surgeon's orders and translates them to commands for motors. It contains a touch panel screen for user interface. The system is controlled either by voice (Bluetooth microphone supervised by a single footswitch for security) or foot (6-function footswitch). The motors are backdrivable to allow a manual repositioning. Although the robot had been created for use in the dorsal supine position, it had the ability to extend the potential positions to include the lateral position.

Data assessment

Demographic data were recorded. Setup time including port placement and all the procedures until robot docking was reviewed as well as operative time, dismantling time and length of hospitalisation. Any robot technical problems or breakdown, manual completion or open conversion were recorded. After completion of each procedure, the surgeon's satisfaction was evaluated using a self 10 point scale to assess easiness of use, overall comfort, quality of vision and steadiness of image. Complications were separated as intraoperative or postoperative. The latter were classified according to the Clavien-Dindo classification [START_REF] Dindo | Classification of surgical complications: a new proposal with evaluation in a cohort of 6336 patients and results of a survey[END_REF] . Postoperative pain was evaluated using a 10 point scale the day after surgery and 1 moth after. We also used the painkiller records to evaluate the pain. Data were expressed as median and interquartile range or mean ± standard deviation in case of normal distribution. The descriptive statistical analysis was performed with GNU R software, version 2.13.

Results

Study population

Although 20 patients were enrolled in this clinical study, only 17 were involved in a robotic-assisted surgery : one patient has changed his mind before the surgery with a withdrawal of his consent (Grenoble) ; for another patient, a material malfunction of the robot was pre-operatively identified during the automatic functional check (hands-free headset problem) so that the robot could not be used during the surgery with a combination of the voice and foot, as wanted by the surgeon (Grenoble) ; lastly, the robot was not used in one case because of a difficult adhesiolysis requiring an human help (St Etienne). Per-protocol analysis is then performed on 17 patients for whom the surgery was effectively performed with ViKY.

Patient's description

Demographic data are summarized in table 1. Median age was 63 years (IQR: 58-70).

Ten patients were female (59 %). The median pre-operative BMI was 26.8 kg/m 2 (IQR: 25-28).

Surgery description

Two laparoscopic surgeons performed 17 robotic surgeries: 2 sacrocolpopexies, 1 pyeloplasty, 2 radical prostatectomies and 1 radical nephrectomy were made in Grenoble. Six adrenalectomies, 1 sacrocolpopexy and 4 pyeloplasties were performed in St Etienne.

Operative data

As summarized in table 2, the median operative time was 130 minutes (IQR: 110; 204) with a median overall setup time (including the robot set-up) at 19 minutes (IQR: 16; 25), i.e. 14.6% of the whole operative time. As illustrated figure 4, this setup time seems to be different according to the surgical indication. Especially for the radical prostatectomy which required a manual step for peritoneal incision and bladder detachment. Furthermore, as the same surgery is performed two times in a consecutive way, we observed a median time gain of 4.5 min, i.e. a relative gain time of 23%.The median assistant number was 0 per intervention (IQR: 0-1). Although the robot has fulfilled its role in 17 surgeries, 5 (29%) were not completed in their totality with the robot: a malfunction of the voice control occurred requiring to interrupt the robotic assisted surgery and four were interrupted because the surgical conditions required the help of a human assistant. After a robotic assisted pyeloplasty, one conversion to open surgery was performed to redo a pyeloureteral anastomosis. In 13 procedures (77%) the robot was voice controlled whereas it was pedal and voice controlled in 4 surgeries. Robots dismantle took a median time of 2 minutes (IQR: 1-4). The dismantle time seems to be linked to the surgical staff that uses the medical device (Figure 5a and 5b that illustrates different trends between Grenoble and St Etienne). One intraoperative complication occurred that was not due to the robot (pyeloureteral anastomosis leakage).

Post operative outcomes

Four grade II complications 1

Surgeon's satisfaction occurred in 2 patients (12%): a patient had acute prostatitis associated to a haematoma after an adrenalectomy and another one had a bacteraemia after a urinary leakage. Patients were discharged from the hospital after a mean of 6.94 days ± 2.3. No skin damage was observed.

The scores of easiness of use was 7 (IQR: 4-9), global comfort was 7 (IQR: 5-8), quality of the vision was 9 (IQR: 7-9) and steadiness was evaluated to 10 (IQR: 8-10).

Discussion

Among robots available for laparoscopic surgery, endoscope holders are designed to provide a steady, tremor-free image and a better visualization during the entire surgical procedure [START_REF] Jaspers | Camera and instrument holders and their clinical value in minimally invasive surgery[END_REF] ViKY robot had been designed by our group. This robot had been successfully validated through preclinical trials that showed the feasibility of the system in terms of workspace as well as compatibility of the system with an operating room environment on cadaver experiments . Surgeons themselves can direct their optical field, while the robot allows precise voice-activated, hand or foot control of the robotic camera holder.

3,6

This present study was designed to evaluate feasibility and safety of the use of this novel robotic endoscope holder for different urological surgical indications on human prior to a randomized control study whose inclusions began in September 2010.

. The robot was then improved and upgraded on animal models. 7 In this pilot study, we show that the robot is safe and user-friendly in human patients. Furthermore, the robot was easy and quick to set up and to dismantle in case of emergency. In this study, the learning curve was assessed by the dismantling time as the procedure is similar regardless to the intervention. The data show that in a team involved in the first steps of the robot, there was no improvement with the time suggesting a reproducible procedure whereas, this time quickly improved in a team not experienced with this robot. Consequently, we can assume that the main advantage of this system is its ease of use.

. The advantage of the robot was the surgeon's complete autonomy over camera control. He didn't have to rely to the skill of an assistant. Although most of the procedures described require an active assistant during all steps, a couple of procedures such as nephrectomy and pyeloplasty could be performed by the surgeon all by himself. This is shown in our study where the assistant's median number was 0.

The only intraoperative complication reported was a urinary leak during a pyeloplasty requiring an open conversion. It was absolutely independent of the use of the device.

Postoperative complications were rare. None of them could be connected to the use of the robot. We reported a bacteraemia after a urinary leakage, an acute prostatitis and a haematoma after an adrenalectomy that were all managed medically. The reliability of the robot is a crucial issue. During this clinical trial, one robotic surgery was interrupted because of a material issue. Voice recognition was useful to control the endoscope's position. However, one robotic surgery had to be cancelled because of a failure of the system detected prior to the surgery, requiring a setting. This case was excluded in the per-protocol analysis. In a second case, the microphone broke down during surgery.

Consequently, the robot was dismantled although the procedure could have been continued with the footswitch available. These shortcomings were corrected with the current version of the robot and a different positioning mechanism and actuators were installed to improve the reliability.

In 4 cases, the robotic procedure had to be interrupted indeed some limitations of motions in extreme positions exist with this robot

The robot can hamper the surgeon when wide motions are needed and when moving to an extreme upper position is required. Best surgeries for the endoscope holder are the one requiring few endoscope motions. However, this is the case with almost all the robots available including the DaVinci® system. It appears to us that in the urological field, the best indications seem to be pelvic surgery and adrenalectomy as the field of view is highly restricted. During a procedure, depending on the anatomical conditions, the range of motion can exceed the possibilities of the robot. As a result the robot needs to be replaced by a human assistant who is able to anticipate the surgeon's desired view without instruction especially when unexpected haemorrhage occurs. In our series, the robot had to be replaced in 4 cases.This high rate of robot's retrieval in our series can also partially be explained by the lack of experience with the robot given the novelty of the device. Since this robot was designed by our group, one of the 2 surgeons was involved in the preclinical development of the device leading to an inherent bias concerning ergonomics evaluation. However one surgeon, located in an outside hospital, was totally novice in the use of the robot before inclusion in the study. This difference explains why no dismantle time learning curve was observed in the Grenoble group although a time improvement was shown in the Saint-Etienne group. A potential drawback of the robot is the circular disk located at its base. This disk measures 10 cm. We showed that port placement had to be modified in 25% of the cases to avoid interferences between laparoscopic instruments and the robot. No consequence was reported due to the difference of port placement.

In comparison with existing robotic camera holders, the LER presents two advantages. First, its compactness compared to the other robots available (LapMan® (MedSys, Gembloux, Belgium) and Endoassist® (Armstrong Healthcare Ltd., High Wycombe, Buck, UK)) has a major influence on the acceptance in the operating room [START_REF] Polet | Gynecologic laparoscopic surgery with a palm-controlled laparoscope holder[END_REF][START_REF] Polet | Using a laparoscope manipulator (LAPMAN) in laparoscopic gynecological surgery[END_REF][START_REF] Wagner | Comparison of surgical performance during laparoscopic radical prostatectomy of two robotic camera holders, EndoAssist and AESOP: a pilot study[END_REF] . The robot AESOP that was the first endoscope holder created is no longer available. This robot has been the proof of the concept that using an endoscope holder was feasible. Its diffusion has been restricted by Intuitive Surgical™ that purchased the company that sold this robot (computer Motion) [START_REF] Mettler | One year of experience working with the aid of a robotic assistant (the voice-controlled optic holder AESOP) in gynaecological endoscopic surgery[END_REF] . This cumbersome robot had some limitations. Nevertheless its acceptation by many teams was excellent. These robotic endoscope holders cannot be compared to full robotic systems such as DaVinci®. Due to high definition, three dimensional optics and wristed instruments, DaVinci assistance may be particularly well suited for tackling difficult surgeries in a minimally invasive manner. However their prohibitive cost is a limitation to their extensive use. The design of robotic endoscope holders aims to provide a low-cost, compact and lightweight system to help the surgeon during a standard laparoscopic procedure.

Consequently, their objective is not to improve the dexterity of the surgeon but to provide to the surgeon a stable image and the capability to perform a solo-surgery in selected cases.

Robotic endoscope holders are alternatives to static endoscope positionners such as Endofreeze® (Aesculap, Tuttlingen Germany) or Endoboy® (Geyser-Endobloc, Coudes, France) [START_REF] Jaspers | Camera and instrument holders and their clinical value in minimally invasive surgery[END_REF][START_REF] Arezzo | Experimental assessment of a new mechanical endoscopic solosurgery system: Endofreeze[END_REF] As for robotic endoscope holders in general, the question is whether use of such a device is really necessary and if it is useful to provide to the surgeon the possibility to perform solo surgery without any human assistant . These static positionners provide a stable image, but are inherently slower in use compared to robotic systems since the operator must release instruments and interrupt the procedure to make operating field adjustments. [START_REF] Jaspers | Camera and instrument holders and their clinical value in minimally invasive surgery[END_REF] . Several studies comparing the differences between human and robotic control of the laparoscope have shown that the robotic system could be superior in terms of image steadiness [START_REF] Aiono | Controlled trial of the introduction of a robotic camera assistant (EndoAssist) for laparoscopic cholecystectomy[END_REF] . However very few of these studies were prospective and randomized [START_REF] Aiono | Controlled trial of the introduction of a robotic camera assistant (EndoAssist) for laparoscopic cholecystectomy[END_REF][START_REF] Tchartchian | Decreasing strain on the surgeon in gynecologic minimally invasive surgery by using semi-active robotics[END_REF] There were several limitations to the present study. This is a pilot study that can only assess the feasibility and the safety of the procedures using the robot. Further studies should investigate the clinical impact. Comparisons between standard laparoscopy and robotic . We believe that each robot has its own indications. Concerning radical prostatectomy, that is the most common laparoscopic procedure in urology, a laparoscope holder can not compete with a full robotic mostly due to the technical advantages offered by the articulated robotic instruments of a DaVinci system. Such a laparoscope holder represents an available alternative to a human help or to allow the assistant to use his two hands to grab instruments and provide a real 4 hands surgery. feasibility evaluation before a larger ongoing multi-institutional randomized and controlled study comparing different procedures performed with or without robotic camera assistance. Furthermore, the surgeon's assessment of image stability and comfort is subjective even using a visual analog scale. The good results obtained in terms of image quality (8.5/10), image 5 stadiness (10/10) contrast with a limited global comfort (6.5/10) and the high rate of manual completions (29%). These discrepancies could be explained by a bias induced by one surgeon's involvement in the development of this device.

Conclusion

In this pilot study, this novel robotic endoscope holder was evaluated for the first time in urologic surgery on human. VIKY use is feasible and safe. However, the high rate of manual completion and robot's dismantling needs to be evaluated on a further randomized controlled study to assess its real usefulness.

5

 5

Figure 1 :

 1 Figure 1: The robotic system including the console, the robot and the pedal.

Figure 2 :

 2 Figure 2: The robotic system in use. Pay attention to the headset device allowing voice recognition.

Figure 4 :

 4 Figure 4: Set up time (including port insertion and prior dissection to docking)


John Tolan

Of Milk and Blood: Innocent III and the Jews, revisited 1

Of Milk and Blood: Innocent III and the Jews, revisited

legal restrictions, host desecration and ritual murder accusations, massacres and expulsions.

Various key turning points have been suggested: the first crusade, for Bernhard Blumenkranz; the missionary preaching of the Franciscan and Dominican friars, for Jeremy Cohen; the anti-Talmudic polemics of Latin authors in the twelfth century, for myself and others. But key among the culprits blamed for the rise of anti-Judaism has been one of the most powerful and charismatic popes of the Middle Ages: Innocent III. Nineteenth-century historian Heinrich Hirsch Graetz, in his monumental Geschichte der Juden, makes Innocent into the principal culprit for the ills of European Jews. 2 Innocent represents -Das Papsttum in Kampfe gegen das Judentum‖ (p.1). "Dieser papst Innocenz III. war ein erbitterter Feind der Juden und des Judentums und hat ihnen tiefere Wunden geschlagen, als sämtliche vorangegangenen Widersacher.‖ If more recent historians have been more sanguine in their assessment, many have agreed on the central importance of Innocent's anti-Jewish policies: Edward Synan devotes a full chapter of his The Popes and the Jews in the Middle Ages to Innocent: -For many reasons, the pontificate of Pope Innocent III has been taken as the central instance of the medieval confrontation of popes and Jews. With his reign, all the major principles have been formulated and reduced to practice; . . . the main lines had been drawn by the time this most powerful of popes died‖. 3 For Robert Chazan, -the pontificate of Innocent III represents both a hardening of Church policy towards the Jews and a sharpening of anti-Jewish rhetoric‖4 .

Innocent indeed manages to confirm traditional papal policy towards Jews while simultaneously affirming a harder anti-Jewish line and stepping up anti-Jewish rhetoric. His issuance of the Constitutio pro Judeis is highly instructive. The Constitutio is the traditional text guaranteeing papal protection for Jews, specifically assuring that they may practice their religious rites, be free from undue pressure to convert, and have synagogues and cemeteries; violence against their persons and property is punished by excommunication. Innocent reissues the same privilege that several of his predecessors had issued, citing five of them by name. Yet he adds two brief paragraphs that change the tone considerably: first, an introduction in which he provides a theological justification for the limited and conditional 2 See Heinrich Hirsch Graetz, Geschichte der Juden von den ältesten Zeiten bis auf die Gegenwart aus den Quellen neu bearbeitet, vol.7, Von Maimunis Tod (1205) bis zur Verbannung der Juden aus Spanien und Portugal (Leipzig, 1890; reprint Darmstad, 1998), p. 1-10.

3 Edward Synan, The Popes and the Jews in the Middle Ages: An Intense Exploration of Judaeo-Christian relationships in the Medieval World (New York, 1965), p. 15. tolerance offered to Jews: -Although in many ways the disbelief of the Jews must be reproved, since nevertheless through them our own faith is truly proved, they must not be oppressed grievously by the faithful‖. 5 And at the end of his Constitution he adds a sentence which makes these traditional guarantees precariously conditional: -We desire, however, that only those be fortified by the guard of this protection who shall have presumed no plotting for the subversion of the Christian faith‖. 6 The implication is that some Jews plot against Christianity and for them there is no papal protection against violence.

In this article, I look at one aspect of Innocent's Jewish policy that has evoked little comment: I argue that, compared with earlier popes and legislators (lay or ecclesiastical) he shows a marked concern for questions of purity and of the dangers of pollution from contact with Jews (and for that matter, with heretics and Muslims, though that will not be our concern today). I will base my case on three letters the Pope sent to France (hence my justification for broaching this topic in a volume devoted to continuity and change in thirteenth-century France): a letter to King Philip II Augustus (16 January 1205), a mandate to the Archbishop of Sens and the bishop of Paris (15 July 1205), and a letter to the Count of Nevers (17 January 1208). In these missives Innocent expresses not only a mistrust of Jews who mock Christianity and bear violent designs against Christians, he worries about the polluting effects of contact transmitted physically through wet nurses and through consumption of Jewish meat and wine, particularly as the latter could be used for the Eucharist.

Up until the twelfth century, bodily purity seems to have little preoccupied canon law regarding Jews. When popes, church councils and other church authorities ruled on relations between Christians and Jews, concerns of bodily purity, of -pollution‖ from contact with infidels, is rarely if ever a concern. Early Christian legislation sought to keep Christians out of synagogues and to prevent Jews from mocking Christian rites or symbols (for example, from burning a crucified image of Haman on Purim), but the dangers were not expressed in terms of corruption or pollution coming from physical contact with Jews. Interreligious marriage was of course prohibited, but the danger is not seen as physical contact but contumelia creatoris (insult to the creator): they are worried about blasphemy, not pollution. This is all the more striking given that in other areas physical pollution was a real issue: a number of authors address the question, for example, of whether a man who has had a wet 5 Translated by Synan, The Popes and the Jews in the Middle Ages, 230. 6 Translated by Synan, The Popes and the Jews in the Middle Ages, 232. dream can participate in the Eucharist. 7 Jews might be seen as a theological threat to Christians, but not as a physical one.

By the end of the Middle Ages, of course, Jews were often portrayed as a real physical threat to Christians: this is seen most dramatically in the host desecration accusations and above all in the ritual murder accusations (or blood libel). Moreover, by the end of the middle ages and the early modern period, numerous texts present the physical contact with Jews (and increasingly, in the Iberian Peninsula, conversos) as dangerous and impure, a -pollution‖ that often involved contact with fluids: water poisoned by Jews that Christians unwittingly introduced into their bodies, or the blood, milk and semen of Jews. To cite one example among many, Vincente de Costa Mattos, in his Breva discurso contra a heretica perfidia da judaismo (Tolosa, 1696): affirms that children of Old Christians should not be suckled by -Jewish vileness because that milk, being of infected persons can only engender perverse implications.‖8

It is in the early thirteenth century that one sees the first signs of the emergence of this preoccupation with the -polluting‖ contact of Jews, and one sees it clearly in these three texts of Innocent III. Innocent is not the first to express such fears and concerns, but he is the first pope to give them wide credence and authority. We shall see that it is probably not mere coincidence that these concerns emerge concurrently with the establishment of the doctrine of the Transubstantiation, which affirmed the real, physical presence of God in the Eucharistic species. Let us first look at each of the three bulls in context.

On January 16 th 1205, Innocent sent a letter to King Philip II Augustus of France. In this bull, Etsi non displiceat Domino, the pope complains of the privileged status that the king accords to Jews, which unconscionably places them above Christians. 9 The Jews of the kingdom of the French have become « insolent », claims the pope. He attacks in particular the practice of money-lending, which inverses the normal power relationships between Christians and Jews: Jews abscond with the property of Christians and of the Church.

Particularly unacceptable, for the pope, is the trampling of traditional jurisprudence based on oral testimony (in which Christian witnesses were accorded more authority than Jews). Here, on the contrary, more credence is given to signed documents (contracts in the Jews' possession), inverting traditional hierarchies. The letter is a bitter (if implicit) criticism of the aid and abetment that the king and his officers grant to Jewish lenders, to the detriment of Christian debtors. Beyond the question of usury, the pope lambasts what for him are other examples of Jewish -insolence‖: they construct new synagogues (one of which is taller than the neighboring church); they have Christian servants, in clear violation of church law; they openly mock Christians and make jest of veneration of the cross during Holy Week. The pope accuses the Jews of being accomplices to thieves and even of killing Christians: he cites the example of a student found dead in a latrine (while some historians have seen this as an accusation of ritual murder, in fact the pope does not claim that there was any ritual or liturgical dimension to this murder, which is simply seen as a product of the Jews' implacable hatred of Christians). The final lines of this bull are a barely-veiled warning to the king and an exhortation to restrain the Jews and to punish their -blasphemies‖. Christians who have commerce with Jews who continue to employ Christian domestic servants. The pope is clearly attempting to go further than a principled condemnation, seeking to find efficacious remedies against a practice which had been frequently outlawed and remained widely practiced.

10 See John Tolan, -Etsi Iudeos‖, Notice n° 30352 , RELMIN project, «The legal status of religious minorities in the Euro-Mediterranean world (5 th -15 th centuries)» , Telma Web edition, IRHT, Institut de Recherche et d'Histoire des Textes -Orléans http://www.cn-telma.fr/relmin/extrait30352/. 11 While in the previous bull he had spoken of Christian serui working for Jews, here he uses the term seruientes. Indeed, serui generally refers to slaves, emphasizing their non-free legal status, while seruientes refers to their functions rather than their legal status. Innocent here distinguishes between the two terms, repeatedly using the word serui to designate the servile status imposed on Jews as punishment for the killing of Christ.

Innocent sent the third bull, Ut esset Cain, to Count Hervé IV de Donzy of Nevers on January 17, 1208 13 . He here takes up the same themes he had already addressed in his Etsi non displiceat Domino. His main goal is to put an end to -the exaction of usury‖ by Jews who benefit from the complicity and help of the count and his officers. These practices have dire consequences, according to the pope: widows and orphans are stripped of their possessions; Christians are imprisoned, while the Jewish lenders who extort exorbitant usurious interest occupy castles and palaces and refuse to respond to ecclesiastical courts (concerning cases, presumably, which involve clerics and ecclesiastical goods). This situation is made possible by the complicity and support of the count, whom Innocent enjoins to cease giving his aid to these Jewish lenders. As in Etsi non displiceat Domino, Innocent here evokes, in a second section of the letter, a whole series of Jewish practices which create -scandal‖. First of all, Jewish butchers kill animals -according to the Jewish rite‖ and sell the remaining meat (all that is inedible according to kosher restrictions) to the Christians. The pope is clearly bothered by the impression that the Jews consider themselves superior to Christians to whom they sell things that they themselves judge unfit for consumption; like the undue power of the money-lenders, this inverses the hierarchy that God established between Christians and Jews. The same principle applies to Jewish women who sell milk -publicly for the nourishment of children‖. Is he referring to wet-nurses? Elishiva Baumgartner thinks that this is improbable, since the Hebrew documentation frequently mentions Christian wet-nurses in Jewish employ, but never the reverse. Were these women selling the milk of their domestic animals? In any case, the pope's impression, once again, is that they are selling to Christians what they judge not good enough for their families. As for wine, it is even worse, because they keep the best for themselves and sell the inferior-quality wine to the Christians; this -Jewish‖ wine at times is even consecrated in the Eucharist.

What do these three bulls tell us about Innocent's vision of Jews' proper place in

Christian society and about how and why he thought they should be restricted to that place? I would like to focus on three elements apparent in these documents: Innocent's theology of Jewish slavery, his fear of the consequence of the -insolence‖ of Jews who do not accept their subservient place in Christian society, and the fears of pollution and sacrilege-notably stemming from contact between Jews and the Eucharistic species.

Theology of Jewish "slavery"

13 See John Tolan, -Ut esset Cain‖, Notice n° 30493 , RELMIN project, «The legal status of religious minorities in the Euro-Mediterranean world (5 th -15 th centuries)» , Telma Web edition, IRHT, Institut de Recherche et d'Histoire des Textes -Orléans http://www.cn-telma.fr/relmin/extrait30493/.

In the three bulls, Innocent justifies his exhortations to lay and ecclesiastical authorities to restrict Jewish -insolence‖ through the claim that Jews have submitted to slavery by rejecting and killing Christ. While Innocent is of course presenting well-worn themes, commonly found in anti-Jewish polemics and in other theological treatises, the bulls present an uncommonly clear and uncompromising legal argument founding Jewish social inferiority on theological principles.

In the three bulls, Innocent presents his action as a defense of divinely-ordained hierarchies merited by Jewish sins. In the opening words of Ut esset Cain, he compares the Jews to Cain.

Just as Cain was a murderer and an untouchable, despised and rejected by humanity because he killed his brother Abel, the Jews, guilty of murdering their Lord, are vagabonds on the face of the earth; their perpetual exile punishes and recalls their crime. But just as the sign of God prevented Cain from being killed, so we must let Jews live among us. The Jews are the enemies of Christ and utter blasphemies against his name. They should be tolerated but must be kept in a position of social inferiority; they must be prevented from exercising power over Christians. Innocent affirms that they have been reduced to slavery as punishment for the crime of having killed their Lord who had come to free them. In Etsi non displiceat Domino, he develops another Old Testament prefiguration: the story in Genesis of the two sons of Abraham: Isaac, -the son of the free woman‖ (Sarah), who prefigures the Christians, and Ishmael, the -son of a servant‖ (Hagar), who represents the Jews, whose destiny is eternal servitude. Moreover, the Jews themselves implicitly accepted their status as slaves: when Pontius Pilate washed his hands of his responsibility for the death of Jesus, Jerusalem's Jews cried out, according to Matthew: -His blood is on us and on our children!‖ [Mt. 27:25; cited in two of the three bulls]. The Son's blood still cries out to the ears of the father, says Innocent in Etsi non displiceat Domino: thus any prince who fears divine wrath must make sure that the Jews remain subservient to Christians. This continuity of punishment is natural because of a continuity of guilt: Jews are and remain agitated by their rabid hatred of their Christian benefactors, they delight when their affairs cause divisions and conflicts among Christians, the pope affirms in Ut esset Cain.

The consequence of the "insolence" of Jews who do not accept their subservient place in

Christian society

Having laid out the theological principles of Jewish servitude to Christians, Innocent is on a moral and theological high ground from which he can denounce those Jews and Christians who attempt to upset this divinely-ordained hierarchy. The fact that Jews have Christian servants and that they exercise undue power over Christians and over cult objects because of usurious loans inverses this divinely-decreed order and constitutes so many proofs, for the pope, of the -insolence‖ of the Jews. Christians who accept or even encourage such insolence are accused of aiding the Lord's enemies.

In Etsi Iudeos, Innocent affirms that even our enemies, the Saracens, cannot stand the insolent Jews and expel them from their territory. He is probably referring to the emigrations provoked by the Almohads' anti-Jewish (and anti-Christian) policies in North Africa and the Iberian Peninsula. The Jews are intolerable because of their -insolence‖, while they should humbly recognize their status as slaves in Christian society. Yet instead they seek to harm their Christian hosts. To illustrate this Jewish hostility, he cites a proverb which we find in other sources as early as the twelfth century, for example in the sermons of Peter of Blois 14 : the Jews are "like the mouse in a pocket, like the Snake around one's loin, like the fire in one's bosom." He returns to this proverb at the end of the bull, emphasizing the animal imagery attributed to the Jews, whom he accuses of already having begun -to gnaw in the manner of a mouse, and to bite in the manner of a serpent‖.

Philip Augustus had all the Jews of his royal domain arrested, confiscated their property, then expelled them in 1182. His biographer, Rigord, praises the king for this expulsion, affirming that the Jews, through their usurious money-lending, had obtained half of Paris, had locked up countless Christian debtors as prisoners in Jewish homes, and had converted their Christian servants to Judaism. These things clearly justified heir expulsion, claims Rigord, for whom this is a singular proof of the king's piety. But in 1198 the king allowed the Jews to return to the royal domain and those Jews who settled there (no doubt far fewer than the number that had been expelled in 1182) seem to have specialized in moneylending. Thus, when Pope Innocent III writes this letter to the king in 1205, he catalogues (just as Rigord had) the abuses caused by Jewish usury, emphasizing that goods belonging to the Church were now in Jewish hands. This bull has been studied by historians in particular as a testimony of the practice of money lending by Jews of the Ile de France and of the tensions caused both by the subsequent debt and by the fact that royal agents participated in the coercive enforcement of the loans: particular in the arrest and imprisonment of debtors. This was one of the causes of the 1182 expulsion and it continued to create problems for Philip and his successors, some of whom took measures to reduce the risks run by debtors and to limit the role played by royal agents in collection and enforcement. These tensions 14 See S. Singer, Thesaurus proverbiorum medii aevi (Berlin, 2000), p. 129-30. nevertheless continued until Philip IV the Fair, in 1306, expelled the Jews from the French kingdom (a territory much larger than the royal domain of 1182).

The situation in 1205-1208 is one of renewed tensions for the now quite small Jewish community whose principal economic activity appears to be money-lending. The resentment expressed by Rigord before 1182 is born anew, all the more so as some prominent lay and ecclesiastical authorities in the king's entourage (including Rigord himself) were not happy to see Jews readmitted in 1198. Some of them are no doubt the pope's source of information; they must have painted to him an alarming portrait of Jewish -insolence‖ and its dire consequences, and clearly Innocent was ready to accept their point of view with little hesitation. In the two bulls where he deals with the question of usury, Innocent paints a very dark picture indeed, insisting on the most dramatic examples of a world turned upside down: sacred vessels and other church property in hock to Jews, widows and orphans coldly disinherited, a perverted justice system in which Jewish witnesses are preferred to Christians.

Yet the symptoms of this -insolence‖, for the pope, go well beyond the issues of usury. He cites, as we have seen, numerous examples showing how Jews refuse to accept their subservient place in Christian society. Some involve direct challenges to Christian practice: a synagogue, taller than the neighboring church, where Jews pray so loudly that mass cannot be held next door. Some Jews, claims the pope, openly mock Christian devotion to the crucifix during holy week processions. This -insolence‖ is seen in commercial operations as well, where Jews sell what they consider not good enough for them (be it meat, milk or wine) to Christians, as if to their inferiors. Numerous texts indeed attest to collaboration between Jewish and Christian butchers in cities throughout Europe: as the hind legs of even properly slaughtered animals were not kosher, it made eminent sense to sell the non-kosher meat to Christians. Various Christian writers had addressed this issue before Innocent, most affirming that it was licit to buy such meat from Jews (arguing that Christian willingness to eat all that God has given us was a testimony to the superiority of the new Christian covenant over the old Jewish one); others, like Innocent, frowned on such consumption or prohibited it. 15 One of the principal preoccupations of the pope in these bulls, as we have seen, is the presence of Christian servants in Jewish homes. Jews' employment of Christian servants overturns the hierarchy that must prevail, for Innocent, between the -sons of the crucifiers‖ and those of the Crucified. This had long been an object of legislation in both lay and canon law: various laws of the Theodosian code prohibited Jews from owning Christian slaves (serui); these prohibitions were subsequently oft repeated 16 . The Pope observes that numerous Jews have Christian servants in their homes, performing domestic chores and taking care of their children. This indeed seems to be a widespread phenomenon throughout contemporary Northern European Jewry, as we see in both Latin and Hebrew sources. 17 As with the collaboration between Christian and Jewish butchers, Innocent is fighting deeply entrenched and widely accepted practices, trying to paint them as scandalous in order to justify their abolishment.

Transubstantiation and ritual purity

Most of what we have examined so far is fairly standard in writing and legislation concerning Jews in the late twelfth or early thirteenth centuries: as we have seen, Innocent addresses these issues more forcefully and with greater hostility to Jews than his predecessors, but the general outlines of his Jewish policies are not new. There is one exception to this: Innocent seems to show a preoccupation with purity and with the dangers of pollution that close daily contact with Jews represent to the body of Christendom. It is perhaps no accident that the two passages in these bulls which most clearly evoke such fears both have to do with the Eucharist. It is under Innocent III's pontificate that the fourth Lateran Council (in 1215) establishes the doctrine of the Transubstantiation, according to which the bread and wine of the Eucharist are physically transformed into the flesh and blood of Christ. The doctrine provoked much debate and dissention within the Church and clearly some unease which is reflected here in passages concerning milk and wine.

We have seen that Innocent railed against the employ of Christian servants in Jewish homes. While other churchmen had worried about the spiritual dangers of such cohabitation, which could lead to apostasy, Innocent, in Etsi non displiceat Domino, intones darkly of the -abominations‖ that Jews inflict on their wet-nurses. He explains this more fully in Etsi Iudeos, where he denounces what he presents as a common practice: Jews oblige their Christian wet-nurses to extract some milk into the latrines for three days after they have taken communion. Did some Jews in fact oblige their wet-nurses do perform such a humiliating rite, to mark their contempt for the Eucharist? Or is the pope (or more likely one of his sources of information) making a false accusation which he knows will provoke the ire of his readers? At any case, it is quite unlikely that this was a common practice, as the pope 16 For examples, see http://www.cn-telma.fr/relmin/resultats/?typeRecherche=extraits&MOT_CLE[]=slaves . 17 See Baumgarten, Mothers and Children.

insinuates. Given the difficulty that families had to find wet-nurses in Medieval Europe, it is hard to believe that Jewish parents would deliberately humiliate a woman who provided nourishment to their infants.18 Moreover, Innocent's accusation presupposes, on the part of Jews, a strong disdain for their Christian servants; this does not correspond with the image we find in the Hebrew documentation: on the contrary, we find rabbis arguing about whether, for example, to give a gift to one's Christian servant during Purim19 . Finally, it seems that the emergence of such rumors, and the fact that they were widely accepted (even, here, at the Lateran), has little to do with real-life Jewish practice; it is the fruit of the Christian clerics' theological preoccupations. The supposed fact that Jews oblige their wet nurses to express their milk into the latrines after they have taken communion shows (for the pope) that Jews recognize the power of the Eucharist, a power present even in the milk of these Christian women. It also suggests hostility towards the sacrament: this milk, imbued with the Divine presence, is tossed away in a filthy place. In the same way, host desecration stories will, starting in the thirteenth century, relate that Jews put hosts in latrines or on refuse heaps.20 In a perverse logic, it is believed that Jews recognize Christ's presence in the consecrated host (and, here, even in the milk of women who have taken communion) and that this presence provokes their implacable, eternal and violent hatred. Here again, one is struck by the harsh language in this bull and by the Pope's tendency to spread anti-Jewish rumors: in Etsi non displiceat Domino, he accused them of complicity with thieves and with the murder of innocent Christians.

We have seen how, in Ut esset Cain, Innocent denounces the practice of Jews who make wine, keep the good wine, and sell the rest to Christians: -and with this, now and again, the sacrament of the blood of Christ is performed‖. Here again, the pope expresses his fears concerning the potentially sullying effects of contact between Jews and the species of the Eucharistic sacrament. In both cases, these preoccupations are to be understood in the context of contemporary debates on the doctrine of the Transubstantiation, which is subsequently adopted by the fourth Lateran Council in 1215. This preoccupation, which might seem paradoxical, highlights the hesitations and uncertainties provoked by these debates: why should the purity (or impurity) of the wine matter if the sacrament truly transforms it into the blood of Christ, which by definition should be immune to any corruption?

Conclusions:

These three bulls confirm the portrait that a number of historians paint of Innocent as an uncompromising advocate of reducing contact between Jews and Christians. He is dealing here with common themes among Christian authors who write on Judaism and Jews, but he does so with a vehemence and an aggressiveness rare in earlier papal correspondence. These texts represent a hardening of pontifical rhetoric concerning the Jews, to whom Innocent attributes an implacable hostility towards Christianity and towards Christians, whom they mock and-given the opportunity-kill.

I would nevertheless fall short of Heinrich Graetz's portrayal of Innocent as the chief culprit for the degeneration of Christian-Jewish relations in medieval Europe. Indeed to search for a -turning point‖ between an age of tolerance and one of persecution is simplistic and perhaps pointless. What we do see here, clearly, is the fear and disgust caused by everyday physical interactions between Jews and Christians, which had been and remained frequent. The fear of the corruption of the Eucharistic species by contaminating contact with Jews is present in these letters, as we have seen-and to my knowledge for the first time.

While Innocent makes no accusations of host desecration per se, we see reflected in these letters some of the same concerns that will later lead to full-blown stories of host desecration-one the first and most influential of which will come some eighty years later, in 1290, in Paris. In these stories, as Miri Rubin has shown, supposed Jewish hostility towards the host serves as -proof‖ of the Transubstantiation. This imagined hostility confirms that Jews are the eternal and constant enemies of Christians. This poisonous idea, responsible for the loss of thousands of lives in Jewish communities throughout Europe in the fourteenth and fifteenth centuries, is not yet fully blown in Innocent's bulls. But we see the seeds from which such ideas will sprout.

This publication is part of the research project RELMIN --The Legal Status of Religious Minorities in the Euro-Mediterranean World (5 th -15 th centuries)‖

The research leading to this publication has received funding from the European Research Council under the European Union's Seventh Framework Progamme (FP7/2007-2013) /ERC grant agreement n°249416.

  Before analyzing this bull in greater detail, let me briefly present the two other bulls that interest us here. Innocent sent the second one, Etsi Iudeos, to the Archbishop of Sens and the Bishop of Paris on July 15 th 1205 10 . Innocent returns to the themes of Etsi non displiceat Domino, to which he refers; he also refers to similar letters which he sent to the Duke of Burgundy and the Countess of Troyes. The bull concerns the practice of Christian servants (seruientes) 11 working in Jewish homes, clearly a common occurrence (well attested in Latin and Hebrew documents 12 ), a point which the pope had addressed (as we have seen) in Etsi non displiceat Domino. The pope reiterates the prohibition of employment of Christian seruientes by Jews. Unlike the king, the bishop and archbishop have no legal authority over Jews. The pope thus exhorts them to use the sentence of excommunication against those

Robert Chazan, « Pope Innocent III and the Jews », in J.Moore, ed., Pope Innocent III and his World (Aldershot, 1999), 187-204.

Dyan Elliott, -Pollution, illusion, and masculine disarray: nocturnal emissions and the sexuality of the clergy‖, inKarma Lochrie, et al., eds., Constructing Medieval Sexuality (Minneapolis, 1997), 1-23.

Quoted in David Biale, Blood and Belief : The Circulation of a Symbol between Jews and Christians (Berkeley, 2007), 115.

For the full Latin text of the bull, with English and French translations, commentary and bibliography, see John Tolan, -Etsi non displiceat Domino‖, Notice n° 30385 , RELMIN project, «The legal status of religious minorities in the Euro-Mediterranean world (5 th -15 th centuries)» , Telma Web edition, IRHT, Institut de Recherche et d'Histoire des Textes -Orléans http://www.cn-telma.fr/relmin/extrait30385/.

See David Freidenreich, Foreigners and their Food: Constructing Otherness in Jewish, Christian, and Islamic Law (Berkeley, 2011). I thank David Freidenreich for letting me see his manuscript before publication.

On the difficulties of finding wet-nurses in medieval Europe, see C. Klapisch-Zuber, "Parents de sang, parents de lait: La mise en nourrice a Florence (1300-1500)," Annales de démographie historique

(1983):33-64 ; Baumgarten, Mothers and Children.19 See Baumgarten, Mothers and Children.

M. Rubin, Gentile Tales: The Narrative Assault on Late Medieval Jews(New Haven, 1999).