Determination of a spatial distribution of the permeability of an electrochemical - cell electrode

Abstract

A method for producing an electrochemical cell is provided, the method including determining a spatial distribution (k.sub.x,y.sup.f) of a parameter of interest (k) representative of a permeability of a diffusion layer of at least one electrode of a reference electrochemical cell in operation, the determining being performed by defining a spatial distribution (T.sub.x,y.sup.c) of a set-point temperature (T.sup.c) within the cell in operation, by measuring a spatial distribution (D.sub.x,y.sup.r) of a first thermal quantity (D.sup.r) representative of local removal of heat, by estimating a spatial distribution (Q.sub.x,y.sup.e) of a second thermal quantity (Q.sup.e) representative of local production of heat (Q.sup.e), and by determining the spatial distribution (k.sub.x/y.sup.f) depending on the estimated spatial distribution (Q.sub.x,y.sup.e), and the method further including producing the electrochemical cell based on the reference electrochemical cell and in which the parameter of interest (k) has the determined spatial distribution (k.sub.x,y.sup.f).

Claims

1. A method for producing an electrochemical cell, comprising: providing a reference electrochemical cell including two electrodes separated from each other by an electrolyte and placed between two bipolar plates configured to supply reactive species to the two electrodes and to remove heat produced by the reference electrochemical cell in operation, and having a spatial distribution of local temperature values within the reference electrochemical cell in operation such that at least one local temperature value is greater than or equal to a preset maximum local temperature value, at least one electrode of the two electrodes including a diffusion layer configured to ensure diffusion of the supplied reactive species as far as the electrolyte, and the diffusion layer having a parameter of interest (k) representative of a permeability of the diffusion layer, the parameter of interest (k) being spatially distributed with an initial distribution (k.sub.x,y.sup.i); determining a spatial distribution (k.sub.x,y.sup.f) of the parameter of interest (k) for the reference electrochemical cell in operation by: defining a spatial distribution (T.sub.x,y.sup.c) of a set-point temperature (T.sup.c) within the reference electrochemical cell in operation, the spatial distribution (T.sub.x,y.sup.c) being such that the local temperature values are lower than the preset maximum local temperature value, measuring a spatial distribution (D.sub.x,y.sup.r) of a first thermal quantity (D.sup.r) representative of local removal of heat within the reference electrochemical cell in operation, estimating a spatial distribution (Q.sub.x,y.sup.e) of a second thermal quantity (Q.sup.e) representative of local production of heat within the reference electrochemical cell in operation, the estimating depending on the defined spatial distribution (T.sub.x,y.sup.c) of the set-point temperature (T.sup.c) and on the measured spatial distribution (D.sub.x,y.sup.r) of the first thermal quantity (D.sup.r), such that an effective temperature of the reference electrochemical cell in operation is substantially equal to the defined spatial distribution (T.sub.x,y.sup.c) of the set-point temperature (T.sup.c), and determining the spatial distribution (k.sub.x,y.sup.f) of the parameter of interest (k) for the reference electrochemical cell in operation, depending on the estimated spatial distribution (Q.sub.x,y.sup.e) of the second thermal quantity (Q.sup.e); and producing the electrochemical cell, based on the reference electrochemical cell and in which the parameter of interest (k) has the determined spatial distribution (k.sub.x,y.sup.f).

2. The method according to claim 1, wherein the two bipolar plates are formed from two sheets that are bonded to each other, each sheet including embossments forming, at external faces thereof, a circuit configured to distribute the reactive species, the embossments of the two sheets together forming at internal faces that are opposite the external faces, a cooling circuit including cooling channels in fluid communication with one another between an inlet and an outlet of the cooling circuit.

3. The method according to claim 1, wherein the determining the spatial distribution (k.sub.x,y.sup.f) of the parameter of interest (k) further depends on a preset overall electrical power value of the reference electrochemical cell in operation.

4. The method according to claim 1, wherein the estimating the spatial distribution (Q.sub.x,y.sup.e) of the second thermal quantity (Q.sup.e) includes: generating a mesh of a cooling circuit of at least one bipolar plate among the two bipolar plates of the reference electrochemical cell, which is configured to permit flow of a head-transfer fluid therethrough, and simulating numerically by computer the second thermal quantity (Q.sup.e) on the generated mesh, by solving a discrete numerical model expressing the second thermal quantity (Q.sup.e) as a function of the local temperature values and of the first thermal quantity (D.sup.r).

5. The method according to claim 1, wherein the first thermal quantity (D.sup.r) is a measured effective local flow rate of a heat-transfer fluid flowing in a cooling circuit of a bipolar plate among the two bipolar plates of the reference electrochemical cell, and the second thermal quantity (Q.sup.e) is a local heat flux produced by the reference electrochemical cell in operation.

6. The method according to claim 5, wherein the determining the spatial distribution (k.sub.x,y.sup.f) of the parameter of interest (k) includes: estimating a spatial distribution (I.sup.e) of a density of an electrical signal produced by the reference electrochemical cell in operation from the estimated spatial distribution (Q.sub.x,y.sup.e) of the produced local heat flux, and determining the spatial distribution (k.sub.x,y.sup.f) of the parameter of interest (k) from the spatial distribution (I.sup.e) of the density of the electrical signal.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Other aspects, aims, advantages and characteristics of the invention will become more clearly apparent on reading the following detailed description of preferred embodiments thereof, which description is given by way of nonlimiting example and with reference to the appended drawings, in which:

(2) FIG. 1a is a schematic cross-sectional representation of an exemplary electrochemical cell, and FIG. 1b is a schematic representation illustrating the correlational relationship between the spatial distribution of heat production and the spatial distribution of heat removal the result of which is the spatial distribution of the temperature of the electrochemical cell in operation;

(3) FIG. 2 is a flowchart of a method for determining the spatial distribution of the electrical resistance of the electrochemical cell according to a first embodiment;

(4) FIG. 3 is a flowchart of a method for determining the spatial distribution of the electrical resistance of the electrochemical cell according to a second embodiment;

(5) FIG. 4 is an example of a mesh of the cooling circuit, in which each mesh cell includes a local heat production term Q.sub.i,j.sup.e, a local heat removal term D.sub.i,j.sup.r, and a temperature T.sub.i,j.sup.c;

(6) FIG. 5a is an exemplary spatial distribution of the effective temperature of a reference electrochemical cell in operation, for which cell the permeability of the diffusion layers of the electrodes is spatially uniform, and FIG. 5b is an exemplary spatial distribution of the effective temperature of an electrochemical cell for which the permeability of the diffusion layers has a spatial distribution determined using the method of the first embodiment.

DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS

(7) In the figures and in the rest of the description, references that are the same represent identical or similar components. Moreover, the various embodiments and variants are not mutually exclusive and can be combined with one another. Unless indicated otherwise, the terms substantially, about and of the order of mean to within 10%.

(8) The various embodiments and variants will be described with reference to a fuel cell and in particular to a PEM (proton exchange membrane) hydrogen fuel cell the cathode of which is supplied with oxygen and the anode of which with hydrogen. However, the invention is applicable to any type of fuel cell, and in particular to those operating at low temperatures, i.e. temperatures below 200 C., and to electrochemical electrolyzers.

(9) FIG. 1a partially and schematically illustrates an exemplary electrochemical cell 1 belonging to a stack of cells of a PEM fuel cell. The cell 1 includes an anode 10 and a cathode 20 that are separated from each other by an electrolyte here comprising a polymer membrane 30, the electrodes 10, 20 being placed between two bipolar plates 40, 50 that are suitable for bringing reactive species to the electrodes and for removing the heat produced during the electrochemical reaction.

(10) The bipolar plates include a circuit 41 for distributing hydrogen, which circuit is located on an anodic side, and a circuit 51 for distributing oxygen, which circuit is located on a cathodic side. They are here formed from two metal sheets 2a, 42b; 52a, 52b, that are joined to one another by welded zones or spot welds and pressed so as to form the distributing circuits. The arrangement of the embossments also allows a cooling circuit 43, 53 to be produced inside the plates, through which a heat-transfer fluid may flow without making contact with the electrodes. Other bipolar-plate technologies may be used, for example the plates may be produced from a filled composite, for example a composite filled with graphite, the embossments of which are produced by molding.

(11) Each electrode 10, 20 includes a gas diffusion layer (GDL) 11, 21 placed in contact with one of the bipolar plates 40, 50 and an active layer 12, 22 located between the membrane 30 and the diffusion layer 11, 21. The active layers 12, 22 are the site of electrochemical reactions. They include materials allowing the oxidation and reduction reactions at the respective interfaces of the anode and cathode with the membrane to take place. More precisely, they may include a catalyst, for example platinum particles, placed on an electrically conductive support, for example a carbon-containing matrix, and an ionomer ensuring the protonic conductivity, Nafion for example. The diffusion layers 11, 21 are made from a porous material that permits the diffusion of the reactive species from the distributing circuit of the bipolar plates to the active layers, and the diffusion of the products generated by the electrochemical reaction to the same distributing circuit. They have a given porosity that defines a permeability k.

(12) The porosity of a diffusion layer is defined as the ratio of the volume of the pores of the porous material to the total volume of the material. It is conventionally comprised between 10% and 90%, and is generally about 80%. The permeability k represents the capacity of the layer to let a fluid pass through under the effect of a pressure gradient, such as expressed by Darcy's law:

(13) $\begin{array}{cc}\stackrel{.fwdarw.}{P}=-\frac{}{k}\stackrel{.fwdarw.}{U}& \left(1\right)\end{array}$
where {right arrow over (P)} is the pressure gradient, the viscosity of the fluid, k the permeability of the diffusion layer and {right arrow over (U)} the Darcy velocity, which depends on flow rate and on cross-sectional area perpendicular to the flow.

(14) FIG. 1b schematically shows the spatial distribution of the temperature T of the electrochemical cell as the resultant of a correlational relationship between the spatial distribution of a heat production source term, in other words a quantity representative of the production of heat by the cell, such as the produced heat flux Q, and the spatial distribution of a quantity representative of the removal of the heat produced, for example the mass flow rate D of the heat-transfer fluid in the cooling circuit.

(15) Thus, contrary to the teaching of the prior-art document cited above, it is not enough to increase the uniformity of the distribution of production of heat Q and therefore of the distribution of the heating of the cell to make the distribution of the effective temperature T of the cell uniform. Specifically, it is important to take into account both the possible presence of local nonuniformities in the heat-production term Q and the possible presence of local nonuniformities in the heat-removal term D.

(16) The local production of heat, or more precisely the local produced heat flux Q, is directly proportional to the local electrical power production, or more precisely to the local current density I, as expressed by the relationship between their respective spatial distributions:
Q.sub.x,y=I.sub.x,y(H/2FU.sub.x,y)(2)
where H is the enthalpy of the electrochemical reaction, F is Faraday's constant, and U.sub.x,y is the spatial distribution of the local voltage of the cell, the enthalpy and voltage possibly being considered to be almost uniform at every point of the cell. Thus, the production of heat is impacted by any nonuniformity due to fluidic parameters (dimensions of the circuits for distributing reactive species, etc.), electrochemical parameters (local properties of the electrodes and of the membrane, etc.) but also electrical parameters (electrical resistances of the various components of the cell, the resistivities of the materials for example and the contact resistances between the components of the cell, etc.), which parameters all influence the current-density distribution.

(17) The removal of heat via the flow of heat-transfer fluid may also exhibit local nonuniformities especially due to minor head losses in the cooling circuit. These head losses are a result of the dimensions of the cooling circuit as produced during the production of the bipolar plates, and may lead to the formation of zones of high flow rate or of low flow rate within the cooling circuit.

(18) In the context of the invention, it is sought to adapt the spatial distribution of a parameter of interest influencing the production of electrical power, and therefore of thermal energy, so that the spatial distribution of the effective temperature of the cell in operation corresponds to that of a set-point temperature, while taking into account the spatial distribution of the effective heat removal that the electrochemical cell exhibits.

(19) The parameter influencing the production of electrical power is here a parameter representative of the permeability of the diffusion layer of at least one electrode of the electrochemical cell. The value of this parameter of interest influences current density I.sub.x,y locally insofar as it determines the amount of reactive species able to diffuse locally as far as the active layer. The parameter of interest may thus be the permeability k, which is defined as the capacity of a porous medium to be passed through by a fluid under the effect of a pressure gradient, and which is expressed in darcies or in m.sup.2. It may also be a question of any equivalent parameter, such as porosity , a permeability coefficient K defined as the ratio of the permeability k to the viscosity of the fluid, or a fluidic diffusion coefficient. It will be noted that the relationship between permeability and porosity is especially expressed by the Kozeny-Carman equation (see for example Feser et al., Experimental characterization of in-plane permeability of gas diffusion layers, Journal of Power Sources, 162:1226-1231, 2006). It will be understood here that the lower the local permeability (for example because of a low porosity), the lower the speed with which reactive species pass through the diffusion layer and hence the lower the amount of reactive species able to reach the active layer. This results in a decrease in the local current density exchanged by the cell and therefore in the local produced heat flux. Conversely, the higher the local permeability (especially because of a high porosity), the higher the speed and therefore the amount of reactive species able to reach the active layer. This therefore leads to an increase in the local current density exchanged by the cell and therefore in the local produced heat flux.

(20) By the temperature of the cell, what is meant is local temperature, i.e. the spatial distribution of the temperature of any one of the components of the cell, for example one of the bipolar plates or even one of the electrodes. The temperature of the cell may thus correspond to the spatial distribution of the temperature of the heat-transfer fluid in the cooling circuit. The effective temperature of the cell is the spatial distribution of the temperature of the cell in operation, at the polarization point defined by the voltage of the cell U.sub.tot and the current I.sub.tot, i.e. the local current density I.sub.x,y integrated over the entire area of the cell.

(21) By parameter representative of heat removal, what is meant is a parameter the value of which represents the capacity of the cell to remove locally produced heat. It may in particular be a question of the local mass or volume flow rate of the heat-transfer fluid flowing in the cooling circuit.

(22) By spatial distribution of a parameter, what is meant is the local value of this parameter at every point in the cell, or more precisely, at every point (x,y) in a plane parallel to the cell in the what is called active zone corresponding to the areal extent of the active layers of the electrodes.

(23) Thus, an electrochemical cell the permeability of which is spatially distributed with the distribution thus determined will have an effective temperature, or temperature during operation of the cell, substantially equal to the set-point temperature. This set-point temperature advantageously has a spatial distribution that is substantially uniform scalarwise or gradientwise. By uniform scalarwise, what is meant is that the local value of the temperature is substantially constant. By uniform gradientwise, what is meant is that the local temperature gradient is substantially constant. The local temperature values may however not be constant while remaining below preset maximum local values. The cell then does not contain zones of excess temperature, or hotspots, that on the one hand may increase the rate of the degradation reactions of the components of the cell, and on the other hand may generate mechanical stresses liable to degrade the mechanical strength of the components of the cell. The lifetime of the electrochemical cell is then preserved. By hotspot, what is for example meant is a zone of the cell that contains a temperature peak or a temperature-gradient peak. More precisely, a hotspot may be a zone where the difference between the local temperature and the inlet temperature of the cooling circuit is larger than the product of a coefficient and the temperature difference between the inlet and outlet of the cooling circuit, the coefficient possibly being about 1.2 to 3 or more, and preferably being about 1.5. By way of example, for a temperature of 77 C. at the inlet of the cooling circuit and of 80 C. at the outlet of the circuit, and for a coefficient equal to 1.5, a hotspot is a zone of the cell in which the local temperature exceeds 81.5 C.

(24) FIG. 2 is a flowchart of a method for determining the spatial distribution of the parameter of interest representative of the permeability of an electrode, according to a first embodiment. In this example, the parameter of interest is the permeability k of a diffusion layer of an electrode of the cell, for example the cathodic diffusion layer, the value k.sub.x,y of which has a direct influence on the local electrical current density I.sub.x,y exchanged locally during the electrochemical reaction and therefore on the local produced heat flux Q.sub.x,y.

(25) Generally, according to this first embodiment, an optimized spatial distribution k.sub.x,y.sup.f of the permeability k is determined from an estimation of the spatial distribution T.sub.x,y.sup.e of a difference T.sup.e between an effective temperature T.sup.r of the cell in operationin which cell the permeability is spatially distributed with a given initial distributionand a preset set-point temperature T.sup.c. It is then possible to modify the permeability k of the diffusion layer so that it has the optimized distribution k.sub.x,y.sup.f, so that the effective temperature T.sup.r of the modified cell is substantially equal to the set-point temperature T.sup.c.

(26) In a first step 110, a reference electrochemical cell is defined within which the permeability k of the cathodic diffusion layer is spatially distributed with an initial distribution k.sub.x,y.sup.f. The cell has a structure identical or similar to that described with reference to FIG. 1. The initial spatial distribution k.sub.x,y.sup.f of the permeability k may be substantially uniform, i.e. here it has a value that is substantially constant at every point in the active zone.

(27) In a step 120, a spatial distribution T.sub.x,y.sup.c of a set-point temperature T.sup.c of the reference cell when the latter is in operation and producing a total current density I.sub.tot for a given voltage U.sub.tot is defined. To the first order, the set-point temperature T.sup.c of the cell may correspond to a temperature of the heat-transfer fluid in the cooling circuit, the distribution of this temperature then especially depending on its values at the inlet T.sub.e.sup.c and outlet T.sub.s.sup.c of the cooling circuit. By way of illustration, the inlet temperature may be set beforehand, for example to 75 C., and the outlet temperature may be estimated from the thermal power P.sub.th to be removed, the latter corresponding to the electrical power P.sub.e=I.sub.tot.U.sub.tot delivered during operation of the cell. The thermal power P.sub.th is estimated by integrating over the active zone the local produced heat flux Q.sub.x,y obtained from relationship (2). The outlet temperature T.sub.s.sup.c is then estimated by correlating the thermal power P.sub.th estimated beforehand with the average total flow rate <D.sub.tot> of the heat-transfer fluid in the cooling circuit, by means of the heat capacity c.sub.p of the heat-transfer fluid. It is then possible to define the spatial distribution T.sub.x,y.sup.c of the set-point temperature T.sup.c from the values of the temperature of the heat-transfer fluid at the inlet T.sub.e.sup.c and outlet T.sub.s.sup.c of the cooling circuit, the distribution T.sub.x,y.sup.c advantageously being uniform gradientwise, i.e. the local set-point temperature gradient is substantially constant.

(28) In a step 130, a spatial distribution T.sub.x,y.sup.r of a first thermal quantity representative of the temperature of the cell in operation is obtained. The first thermal quantity is here the effective temperature T.sup.r of the electrochemical cell when it is operating under the same operating conditions as those considered in step 120. This distribution T.sub.x,y.sup.r is not estimated but is the result of a measurement by experimental or numerical means. It may thus be obtained by experimental measurement of an electrochemical cell having the same properties as the reference cell defined in step 110, for example by means of an S++ board sold by S++ Simulation Services, including an invasive plate inserted between two bipolar plates and suitable for measuring a spatial distribution of temperature. The distribution T.sub.x,y.sup.r of effective temperature may also be obtained by numerical simulation using an electrochemical cell model, for example that described in the publication by Robin et al., Development and experimental validation of a PEM fuel cell 2D model to study heterogeneities effects along large area cell surface, International Journal of Hydrogen, 40, 2015, 10211-10230, or even the model described in the publication by Inoue et al. Numerical analysis of relative humidity distribution in polymer electrolyte fuel cell stack including cooling water, J. Power Sources 162 (2006) 81-93.

(29) The distribution T.sub.x,y.sup.r of the effective temperature T.sup.r obtained by experimental or numerical measurement thus takes into account local nonuniformities in the produced heat flux, which depends on local current density, and local nonuniformities in heat removal, which especially depends on the local flow rate of the heat-transfer fluid in the cooling circuit.

(30) In a step 140, the spatial distribution of a second thermal quantity is estimated, here a quantity T.sup.e representative of a local difference between the effective temperature T.sup.r and the set-point temperature T.sup.c. This quantity of local difference T.sup.e is estimated from the spatial distribution T.sub.x,y.sup.c of the set-point temperature T.sup.c defined in step 120 and from the spatial distribution T.sub.x,y.sup.r, of the effective temperature T.sup.r measured in step 130. It may be a question of the difference between the local value of the effective temperature and that of the set-point temperature, or of a ratio of these values, inter alia. Here, the term-to-term difference between the distributions of the effective temperature and set-point temperature are considered: T.sub.x,y.sup.e=T.sub.x,y.sup.rT.sub.x,y.sup.c.

(31) Next, in a step 150, the spatial distribution k.sub.x,y.sup.f of the permeability parameter of interest k is determined depending on the spatial distribution T.sub.x,y.sup.e of the local difference T.sup.e.

(32) According to a first variant, a correctional coefficient is firstly calculated, the spatial distribution of which is proportional term-to-term to that T.sub.x,y.sup.e of the local difference T.sup.e. By way of example, the correctional coefficient varies continuously between a minimum value and a maximum value, as the local difference varies between a substantially zero value and a maximum value, respectively. The minimum value of the correctional coefficient may here be substantially comprised between 0 and 0.75, or even between 0 and 0.5, and for example be substantially equal to 0, 0.1, 0.2 or 0.3, and the maximum value may be substantially equal to unity. Next, the spatial distribution k.sub.x,y.sup.f of the permeability k may be determined by correlation, for example by a term-to-term multiplication, of the initial spatial distribution k.sub.x,y.sup.i of the permeability k with the spatial distribution of the correctional coefficient. Thus, in the zones of the cell where the difference T.sup.e between the effective temperature and the set-point temperature has a maximum value, i.e. in the zones called hotspots, the initial local value k.sub.x,y.sup.f of the permeability k is multiplied by the local value of the correctional coefficient, which is for example equal to 0.25 or even less. Thus, the permeability has a new local value that is decreased with respect to the initial local value, thereby decreasing the amount of reactive species able to diffuse as far as the active layer, thereby leading to a decreased local current density and therefore a decreased produced heat flux.

(33) According to a second variant, firstly at least one zone Z.sub.i of the cell in which the difference T.sup.e has a value above a preset threshold value is identified, the threshold value for example being representative of a hotspot. Next, the spatial distribution k.sub.x,y.sup.f of the permeability k is determined by modifying the initial spatial distribution k.sub.x,y.sup.i in the identified zone Z.sub.i depending on the local value of the difference T.sup.e in this zone. By way of example, the initial spatial distribution k.sub.x,y.sup.i may be modified locally using a correctional coefficient the value of which is proportional to that of the difference T.sup.e in this zone. As in the first variant, the correctional coefficient varies continuously between a minimum value and a maximum value, for example between 0.25 and 1.

(34) Thus, a spatial distribution k.sub.x,y.sup.f of the permeability k of the diffusion layer is obtained. It is then possible to modify the initial distribution k.sub.x,y.sup.f of the permeability k of the diffusion layer of the cathode of the reference cell so that it is the same as the new distribution determined in step 150. The cell thus optimized then has, in operation, an effective temperature the spatial distribution of which is substantially equal to that of the set-point temperature. Insofar as the distribution of the set-point temperature is advantageously uniform, the cell in operation has an effective temperature the distribution of which is also substantially uniform, thus allowing the lifetime of the cell to be preserved.

(35) FIG. 3 is a flowchart of a method for determining the spatial distribution of a parameter of interest representative of the permeability of a diffusion layer of at least one electrode of an electrochemical cell, according to a second embodiment. In this example, the parameter of interest is the permeability k of the diffusion layer, here the cathode, the value of which has a direct influence on the electrical current density produced locally during the electrochemical reaction.

(36) Generally, according to this second embodiment, the spatial distribution k.sub.x,y.sup.f of the permeability k is determined from the estimation of the spatial distribution of the production of heat necessary to obtain the spatial distribution of a set-point temperature, while taking into account the spatial distribution of a thermal quantity representative of the effective heat removal in the cell. It is then possible to modify the initial distribution of the permeability of the diffusion layer so that it has an optimized spatial distribution, so that the effective temperature is then substantially equal to the set-point temperature. The electrochemical cell, the parameter of interest of which is spatially distributed with the optimized distribution, has in operation a temperature substantially equal to the set-point temperature. Unwanted new hotspots or new temperature nonuniformities are not formed.

(37) This approach, which is what may be referred to as an electrochemical and no longer essentially thermal approach, is particularly advantageous when at least one bipolar plate, or even both bipolar plates, of the electrochemical cell are formed from sheets that are bonded to one another and that contain embossments that define a two-dimensional cooling circuit. The embossments of each sheet, in the faces referred to as the external faces of the sheets, i.e. the faces oriented toward an electrode, define a circuit for distributing reactive species. In the internal faces, i.e. the faces opposite the external faces, the embossments form a cooling circuit through which a heat-transfer fluid is intended to flow. The cooling circuit is what is called linear when the cooling channels do not communicate with one another, i.e. when the heat-transfer fluid, between the inlet and outlet of the cooling circuit, cannot substantially pass from one cooling channel to another. The cooling circuit is what is called two-dimensional when the cooling channels communicate with one another, so as to form a two-dimensional fluidic network that is non-linear. This is especially the case when the distributing channels of a sheet are not parallel to those of the other sheet.

(38) In a first step 210, a reference electrochemical cell is defined, or supplied, within which the permeability k of the cathodic diffusion layer is spatially distributed with an initial distribution k.sub.x,y.sup.f. The initial spatial distribution k.sub.x,y.sup.f of the permeability k may be substantially uniform scalarwise, so that its local value is substantially constant at every point in the active zone. The cell has a structure that is identical or similar to that described with reference to FIG. 1 and this step is similar or identical to the step 110 described above. The considered electrochemical cell then has, in operation, a spatial distribution of temperature at least one local value of which is higher than or equal to a preset maximum local value. The latter may be constant or differ depending on the considered point of the electrochemical cell. This step may include: a phase of experimentally prototyping or numerically modeling an electrochemical cell; a phase of measuring the spatial distribution of the temperature within the electrochemical cell in operation; then a phase of comparing the measured spatial distribution of the temperature to a preset spatial distribution of a maximum temperature. The local values of this spatial distribution of maximum temperature are the what are called preset maximum local values.

(39) When at least one local value of the measured temperature is higher than or equal to a corresponding preset maximum local value, i.e. at one and the same position within the spatial distribution, the electrochemical cell is then supplied, i.e. considered, for the following steps of the determining method.

(40) In a step 220, a spatial distribution T.sub.x,y.sup.c of a set-point temperature T.sup.c of the reference cell when the latter is in operation and producing a total current density I.sub.tot for a given voltage U.sub.tot is defined. This step is similar or identical to the step 120 described above. The local values of the spatial distribution of the set-point temperature are lower than corresponding maximum local values.

(41) Optionally, it is advantageous to specify the spatial distribution T.sub.x,y.sup.c of the set-point temperature T.sup.c as a function of the spatial distribution of the concentration of reactive species in the active zone between the inlet and outlet of the corresponding distributing circuit. Specifically, the consumption of reactive species within the active zone of the cell leads to a gradual decrease in the concentration of reactive species along the distributing circuit. This gradual decrease results in a decrease in the local current density produced by the cell and therefore in the local production of heat, thereby leading to the formation of nonuniformities in the temperature of the cell. To compensate for this gradual decrease in the production of heat, it is advantageous to define a set-point temperature that takes into account the decrease in the concentration of reactive species, so that the effective temperature of the cell in operation corresponds to the set-point temperature, the latter advantageously having a uniform spatial distribution. To do this, the spatial distribution {tilde over (T)}.sub.x,y.sup.c of the specified set-point temperature {tilde over (T)}.sup.c may for example be written:
{tilde over (T)}.sub.x,y.sup.c=T.sub.x,y.sup.c+K.sup.i.[max(c.sub.x,y.sup.i)c.sub.x,y.sup.i](3)
where c.sub.x,y.sup.i is the spatial distribution of the concentration c.sup.i in reactive species i, for example in oxygen, and K.sup.i is a positive constant, for example close to 1, which may be subsequently adjusted. The spatial distribution c.sub.x,y.sup.i of the concentration may be estimated to the first order from the routing of the channels of the distributing circuit of the reactive species in question and by assuming a uniform consumption throughout the active zone. It may also be more accurately determined by numerical or experimental measurement of the spatial distribution of the current density in a cell that is similar or identical to the reference cell, which allows the spatial distribution of the concentration of the reactive species to be deduced. Other relationships (3) may be used to specify the spatial distribution of the set-point temperature while taking into account the spatial variation in the concentration of reactive species. Thus, a spatial distribution {tilde over (T)}.sub.x,y.sup.c of the set-point temperature {tilde over (T)}.sup.c is obtained that thus allows a distribution of the effective temperature of the cell to be obtained the uniformity of which is improved.

(42) Moreover, optionally and possibly complementarily with the step of specifying the set-point temperature described above, it is advantageous to specify the spatial distribution T.sub.x,y.sup.c of the set-point temperature T.sup.c as a function of the spatial distribution .sub.x,y of the relative humidity in the distributing circuits. The relative humidity is defined conventionally as the ratio of the partial pressure P.sub.H2O of the water vapor contained locally in the gas flowing through the distributing circuit to the saturated vapor pressure P.sub.sat. The relative humidity has an effect on the electrochemical response. Thus, to compensate for the local variation in relative humidity, it is advantageous to define a set-point temperature that compensates for this local variation, for example for local humidification or dehumidification of the pores of the diffusion layers, so that the effective temperature of the cell in operation has a uniform spatial distribution. To do this the spatial distribution {tilde over (T)}.sub.x,y.sup.c of the specified set-point temperature {tilde over (T)}.sup.c may for example be written:
{tilde over (T)}.sub.x,y.sup.c=T.sub.x,y.sup.c+K.sup..[.sub.x,y/.sub.in](4)
where .sub.x,y is the spatial distribution of the relative humidity in the distributing circuit, .sub.in is the relative humidity at the inlet of the distributing circuit, and K.sup. is a positive constant, for example close to 1, which may be subsequently adjusted. The distribution .sub.x,y of the relative humidity may be estimated to the first order from the routing of the channels of the distributing circuit in question and by assuming a uniform current density throughout the active zone. It may also be more accurately determined by numerical or experimental measurement of the spatial distribution of the current density in a cell that is similar or identical to the reference cell, which allows the spatial distribution of the relative humidity to be deduced. Other relationships (4) may be used to specify the spatial distribution of the set-point temperature from the spatial variation in relative humidity. Thus, a spatial distribution {tilde over (T)}.sub.x,y.sup.c of the set-point temperature {tilde over (T)}.sup.c is obtained that thus allows a distribution of the effective temperature of the cell to be obtained the uniformity of which is improved.

(43) In a step 230, a spatial distribution D.sub.x,y.sup.r of a first thermal quantity representative of the removal of heat D.sup.r within the cell in operation is obtained. The first thermal quantity is here the mass flow rate D.sup.r of heat-transfer fluid in the cooling circuit. This distribution D.sub.x,y.sup.r is not estimated but is the result of a measurement by experimental or numerical means. It may thus be obtained by experimental measurement of an electrochemical cell having the same properties as the reference cell defined in step 210, for example by means of a particle image velocimetry (PIV) technique or any other suitable technique, carried out on a cooling circuit having the same dimensional characteristics as that of the reference cell. The distribution D.sub.x,y.sup.r of the mass flow rate D.sup.r may also be obtained by numerical simulation using a flow simulation software package such as FLUENT or COMSOL for example.

(44) In a step 240, the spatial distribution Q.sub.x,y.sup.e of a second thermal quantity Q.sup.e is estimated from said spatial distribution T.sub.x,y.sup.c of the set-point temperature T.sup.c defined in step 220 and from said spatial distribution D.sub.x,y.sup.r of the heat-transfer fluid flow rate D.sup.r obtained in step 230. The second thermal quantity is representative of the local production of heat and here corresponds to the local heat flux Q.sup.e that the heat-transfer fluid removes D.sup.r to obtain the set-point temperature T.sup.c.

(45) To do this, as illustrated in FIG. 4, the cooling circuit is discretized into a two-dimensional or three-dimensional, here two-dimensional, mesh each mesh cell of which is an elementary volume (i,j) passed through by the heat-transfer fluid. Thus, each mesh cell (i,j) of the distributing circuit has two known quantities: the local set-point temperature T.sub.i,j.sup.c and the local flow rate D.sub.i,j.sup.r of the heat-transfer fluid; and a quantity to be determined: the local produced heat flux Q.sub.i,j.sup.e. Next, the amount of heat and fluid transferred between the mesh cell in question and the adjacent mesh cells is calculated by determining, on the one hand, the temperature differences and, on the other hand, the flow rates of the heat-transfer fluid at the four facets of the mesh cell in question. This calculation may be carried out by numerical simulation by computer, on said mesh. This amounts to solving a discrete numerical model expressing the second thermal quantity, namely here the local heat flux, as a function of local temperature and of the first thermal quantity, namely here the local flow rate of the heat-transfer fluid. The numerical model, which is what is referred to as an electrochemical model, may be expressed by relationship (7).

(46) The temperature differences at the four facets of the mesh cell (i,j) may be calculated in the following way:
T.sub.i,j.sup.1=T.sub.i,j.sup.cT.sub.i,j+1.sup.c(5-1)
T.sub.i,j.sup.2=T.sub.i,j.sup.cT.sub.i1,j.sup.c(5-2)
T.sub.i,j.sup.3=T.sub.i,j.sup.cT.sub.i+1,j.sup.c(5-3)
T.sub.i,j.sup.4=T.sub.i,j.sup.cT.sub.i,j1.sup.c(5-4)

(47) The flow rates of the heat-transfer fluid at the four facets of the mesh cell (i,j) may be obtained by predicting the mass flow rate D.sub.i,j.sup.r (here a vectorial datum) onto the vectors e.sub.x and e.sub.y passing through the mesh cells (i1,j), (i,j) and (i+1,j), and through the mesh cells (i,j1), (i,j) and (i,j+1), respectively:
d.sub.i,j.sup.1=(D.sub.i,j.sup.r.e.sub.y+D.sub.i,j+1.sup.r.e.sub.y)/2(6-1)
d.sub.i,j.sup.2=(D.sub.i,j.sup.r.e.sub.x+D.sub.i1,j.sup.r.e.sub.x)/2(6-2)
d.sub.i,j.sup.3=(D.sub.i,j.sup.r.e.sub.x+D.sub.i+1,j.sup.r.e.sub.x)/2(6-3)
d.sub.i,j.sup.4=(D.sub.i,j.sup.r.e.sub.y+D.sub.i,j1.sup.r.e.sub.y)/2(6-4)

(48) By convention, the local flow rate d.sub.i,j is considered to be positive when the fluid enters into the mesh cell (i,j) and negative when the fluid exits therefrom.

(49) Lastly, the spatial distribution Q.sub.x,y.sup.e of the heat flux Q.sup.e produced by the cell is calculated from the relationship:
Q.sub.x,y.sup.eQ.sub.i,j.sup.e=.sub.k=1.sup.4d.sub.i,j.sup.k.c.sub.p.T.sub.i,j.sup.k(7)

(50) Thus, the spatial distribution of the heat flux Q.sup.e that the cell must produce for the effective temperature distribution to correspond to that of the set-point temperature is obtained, the distribution of the effective mass flow rate of the heat-transfer fluid in the distributing circuit being known.

(51) In a step 250, the spatial distribution k.sub.i,j.sup.f of the permeability k is determined depending on the spatial distribution Q.sub.x,y.sup.e of the produced heat flux Q.sup.e. To do this, it is possible to firstly estimate the spatial distribution of the density of an electrical signal produced by the cell in operation, for example a current density I.sup.e, from the estimated spatial distribution Q.sub.x,y.sup.e of the produced heat flux Q.sup.e. Insofar as the produced heat flux Q.sup.e is approximately proportional to the current density I.sup.e, the latter may be determined from the relationship:

(52) $\begin{array}{cc}{I}_{x,y}^e=Q_{x,y}^e.Math.\frac{I_{\mathrm{tot}}}{Q_{\mathrm{tot}}}& \left(8\right)\end{array}$
where I.sub.tot is the total current density delivered by the electrochemical cell in operation, and Q.sub.tot is the total produced heat flux, which is obtained by integrating the spatial distribution Q.sub.x,y.sup.e over all the active area.

(53) Next, the new spatial distribution k.sub.x,y.sup.f of the permeability k is determined from the local density of the electrical current I.sub.x,y.sup.e. To do this, one approach consists in determining the minimum k.sub.min and maximum k.sub.max values of the permeability of the cathodic diffusion layer. It may be a question of an experimental measurement of a cell sample having the same properties as those of the reference cell, or of a measurement by numerical simulation. Next, the spatial distribution k.sub.x,y.sup.f is calculated, for example using the relationship:

(54) $\begin{array}{cc}{k}_{x,y}^f=\max \left(k_{\max },k_{\min }\frac{I_{\max }^e}{I_{x,y}^e}\right)& \left(9\right)\end{array}$
where I.sub.max.sup.e is the maximum value of the local current density I.sub.x,y.sup.e. The local permeability thus varies linearly between the minimum k.sub.min and maximum k.sub.max values as a function of the local value of the current density I.sup.e. Of course, any other law, for example a polynomial, exponential or logarithmic law, causing the local permeability to vary so that the maximum value k.sub.max corresponds to a maximum local current density and vice versa, may be used. The minimum k.sub.min and maximum k.sub.max values may be preset depending on the overall electric power UI wanted for the electrochemical cell, where U is the electrical voltage and I the electrical current density measured across the terminals of the cell.

(55) Thus, a spatial distribution k.sub.x,y.sup.f of the permeability k taking into account the distribution of production of electrical power I.sup.e and therefore of thermal energy Q.sup.e, and which ensures the effective temperature of the cell in operation corresponds to the set-point temperature T.sup.c, has been determined, while also taking into account the effective removal D.sup.r of heat by the cooling circuit. Insofar as the set-point temperature is advantageously spatially uniform, a cell at least one of the electrodes of which includes a diffusion layer the permeability k of which is distributed with the spatial distribution k.sub.x,y.sup.f thus determined has, when it is operating at the polarization point U.sub.tot and I.sub.tot, an effective temperature the spatial distribution of which is uniform.

(56) FIG. 5a illustrates an exemplary spatial distribution of the effective temperature of an electrochemical cell in operation, in the case where the diffusion layers have a substantially uniform permeability. Three zones of excess temperature, or hotspot zones, are present. In this example, the current density is 0.5 A/cm.sup.2, the pressure is 1.5 bar and the temperature of the heat-transfer fluid at the outlet of the cooling circuit is 80 C. The relative humidity is 50% at the anode and cathode. The stoichiometry is 1.5 at the anode and 1.8 at the cathode. The diffusion layer has an average thickness of 246 m and a porosity of 0.76.

(57) FIG. 5b illustrates the spatial distribution of the effective temperature of the same electrochemical cell in operation, in the case where at least one diffusion layer has a permeability with the spatial distribution modified according to the first embodiment of the method (FIG. 2). It will be noted that the temperature distribution is substantially uniform and does not contain zones of excess temperature.

(58) A method for producing an electrochemical-cell electrode will now be described, here the cathode of the cell. An electrochemical cell that is identical or similar to the reference cell defined in steps 110 and 210 is considered. It includes two electrodes separated from each other by an electrolyte and placed between two bipolar plates suitable for bringing reactive species to the electrodes and for removing the heat produced by the cell in operation. The electrodes each include a diffusion layer and an active layer. The cathode here has a diffusion layer the permeability k of which is spatially distributed with an initial distribution k.sub.x,y.sup.f. Using the method described above with reference to FIGS. 2 and 3, a spatial distribution k.sub.x,y.sup.f of the permeability of the cathodic diffusion layer is determined. Next, in a step 160 (FIG. 2) or 260 (FIG. 3), the cathode is produced in such a way that the permeability k of the diffusion layer has the determined spatial distribution k.sub.x,y.sup.f.

(59) Thus, the permeability k of the diffusion layer is modified locally so as to form nonuniformities in the spatial distribution k.sub.x,y with a view to correcting the nonuniformities in the effective temperature of the cell in operation with respect to a set-point temperature. By way of example, the permeability of the diffusion layer is decreased locally in zones in which the effective temperature of the cell is liable to be above the set-point temperature. Thus, since the local quantity of reactive species capable of diffusing as far as the active layer is decreased, thereby consequently decreasing the local current density and therefore the local produced heat flux. Thus, the effective temperature of the cell corresponds locally to the set-point temperature.

(60) To achieve this, the diffusion layer is, by way of example, impregnated with a sealant in the identified zones Z.sub.i of excess temperature. The sealant may comprise, by way of example, TiO.sub.2 or colloidal silica, or even calcium carbonate. The amount of sealant impregnated locally into the diffusion layer may thus modify the porosity thereof in order thus to obtain a local permeability k.sub.Zi having the desired value.

(61) The sealant may be an ink including water, for example in an amount of 92% to 98%, PTFE, so as to obtain the hydrophobicity desired for the diffusion layer, for example in an amount of 0.5% to 3%, a dispersant, for example triton X-100, for example in an amount of 0.3%, and TiO.sub.2, to seal the pores of the porous material of the diffusion layer and for example in an amount of 1% to 5%. The amount of sealant having impregnated the diffusion layer locally made thus decrease the porosity thereof from the initial value, for example 80%, to 20% or even less, for example 10% or 0%, thereby correspondingly impacting permeability. Thus a local decrease in the porosity of the diffusion layer from 70% to 10% has been observed to lead to a decrease of about 2 C. in the zone in question.

(62) The sealant may be deposited on the surface of the diffusion layer of the cathode, in an identified zone Z.sub.i of excess temperature, by any deposition technique known to those skilled in the art, screen printing for example. Thus, a screen-printing screen is produced that forms a mesh of through-apertures, for example of a few square centimeters area. The apertures are obturated in order to keep only certain apertures intended to ensure the deposition of the sealant in the identified zones Z.sub.i. Next, the screen is placed on the diffusion layer, for example on the side of the layer opposite the active layer, then the sealant is deposited on the diffusion layer through the screen-printing screen. After the screen has been removed, only the zones Z.sub.i are impregnated with the sealant. The amount of sealant may be adjusted by carrying out a plurality of successive depositions in the same zones Z.sub.i, while ensuring that the product deposited in a preceding step has been able to infiltrate into the diffusion layer. A drying step is provided to evaporate the water of the sealant.

(63) Thus, the diffusion layer has a permeability, or porosity, the value of which varies locally. In at least one zone Z.sub.i, the local value of the permeability or porosity is lower than the average value of the permeability or porosity outside this zone Z.sub.i.

(64) Particular embodiments have just been described. Alternative variants and various modifications will be apparent to the person skilled in the art.