DETERMINATION OF THE SPATIAL DISTRIBUTION OF CATALYTIC ACTIVITY OF AN ELECTRODE OF AN ELECTROCHEMICAL CELL

Abstract

The invention relates to a method for determining a spatial distribution (Wc.sub.x,y.sup.i) of a parameter of interest (Wc) representative of a catalytic activity of an active layer of at least one electrode of an electrochemical cell, comprising steps in which a spatial distribution (Wc.sub.x,y.sup.i) of the parameter of interest (Wc) is determined depending on the spatial distribution (Q.sub.x,y.sup.e) of a second thermal quantity (Q.sup.e) estimated beforehand from the spatial distribution (T.sub.x,y.sup.c) of a set-point temperature (T.sup.c) and from the spatial distribution (D.sub.x,y.sup.r) of a first thermal quantity (D.sup.r).

Claims

1. Method for determining a spatial distribution (Wc.sub.x,y.sup.f) of a parameter of interest (Wc) representative of a catalytic activity of an active layer of at least one electrode of an electrochemical cell, said cell including 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, at least one electrode including an active layer containing at least one catalyst, the active layer being suitable for generating an electrochemical reaction from one of the reactive species, said method comprising: i) providing an electrochemical cell, within which the parameter of interest (Wc) is distributed with an initial spatial distribution (Wc.sub.x,y.sup.i) and for which the spatial distribution of a temperature within the electrochemical cell in operation has at least one local value higher than or equal to a preset maximum local value; ii) defining a spatial distribution (T.sub.x,y.sup.c) of a set-point temperature (T.sup.c) within said electrochemical cell in operation, said distribution being such that the local temperature values are lower than preset maximum local values; iii) measuring a spatial distribution (D.sub.x,y.sup.r) of a first thermal quantity representative of the local removal of heat (D.sup.r) within said electrochemical cell in operation; iv) estimating a spatial distribution (Q.sub.x,y.sup.e) of a second thermal quantity (Q.sup.e) representative of the local production of heat (Q.sup.e) within said electrochemical cell in operation, depending on said spatial distribution (T.sub.x,y.sup.c) of the set-point temperature (T.sup.c) and on said measured spatial distribution (D.sub.x,y.sup.r) of the first thermal quantity (D.sup.r), so that the spatial distribution of the temperature of said electrochemical cell in operation, the first thermal quantity (D.sup.r) of which cell having said measured spatial distribution (D.sub.x,y.sup.r) and the second thermal quantity (Q.sup.e) of which cell having said estimated spatial distribution (Q.sub.x,y.sup.e), is substantially equal to that (T.sub.x,y.sup.c) of the set-point temperature (T.sup.c); and v) determining a spatial distribution (Wc.sub.x,y.sup.f) of the parameter of interest (Wc) depending on the estimated spatial distribution (Q.sub.x,y.sup.e) of the second thermal quantity (Q.sup.e).

2. Determining method according to claim 1, wherein the parameter of interest is the load of catalyst (Wc) in the active layer.

3. Determining method according to claim 1, wherein the spatial distribution (Wc.sub.x,y.sup.f) of the parameter of interest (Wc) is determined so that it has an average value substantially identical to an average value of the initial distribution (Wc.sub.x,y.sup.i).

4. Determining method according to claim 1, wherein the bipolar plates are formed from two sheets that are bonded to each other, each sheet including embossments forming, in what is called an external face, a circuit for distributing a reactive specie, the embossments of the sheets together forming, in what are called internal faces that are opposite the external faces, a cooling circuit including cooling channels that communicate fluidically with one another between an inlet and an outlet of the cooling circuit.

5. Determining method according to claim 1, wherein determining the spatial distribution of the parameter of interest is furthermore carried out depending on a preset value of a parameter representative of an overall electrical power of the electrochemical cell.

6. Determining method according to claim 1, wherein estimating a spatial distribution of the second thermal quantity includes: generating a mesh of a cooling circuit of at least one bipolar plate of the electrochemical cell, through which circuit a heat-transfer fluid is intended to flow; and simulating numerically by computer the second thermal quantity on said mesh, by solving a discrete numerical model expressing the second thermal quantity as a function of the local temperature and of the first thermal quantity.

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

8. Determining method according to claim 7, wherein v) includes: a) estimating a spatial distribution of the density of an electrical signal (I.sup.e) produced by the cell in operation, from said estimated spatial distribution of the produced heat flux (Q.sup.e); and b) determining the spatial distribution of the parameter of interest (Wc), from said spatial distribution of the density of the electrical signal (I.sup.e).

9. Method for producing an electrochemical-cell electrode, comprising: considering a reference electrochemical cell, said cell including 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, at least one electrode including an active layer suitable for generating an electrochemical reaction from one of the reactive species, the active layer having a parameter of interest representative of a catalytic activity (Wc) spatially distributed with an initial distribution (Wc.sub.x,y.sup.i); ii) determining a spatial distribution (Wc.sub.x,y.sup.f) of the parameter representative of catalytic activity (Wc), using the method according to claim 1; and iii) producing said electrode so that the parameter representative of the catalytic activity (Wc) of the active layer thereof has the determined spatial distribution (Wc.sub.x,y.sup.f).

10. Producing method according to claim 9, wherein producing said electrode includes depositing, in at least one zone (Z.sub.i) of the active layer identified beforehand from said determined spatial distribution (Wf.sub.x,y.sup.f) of the parameter representative of catalytic activity (Wc), a catalytic ink having a catalytic load lower than an average catalytic load outside of said zone (Z.sub.i).

11. Producing method according to claim 10, wherein the catalytic ink is deposited by screen printing by means of a screen-printing screen including at least one obturated aperture intended to cover said zone (Z.sub.i) of the active layer.

12. Method for producing an electrochemical cell, comprising: considering a reference electrochemical cell, said cell including 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, at least one electrode including an active layer suitable for generating an electrochemical reaction from one of the reactive species, the active layer having a parameter of interest representative of a catalytic activity (Wc) spatially distributed with an initial distribution (Wc.sub.x,y.sup.i); determining a spatial distribution (Wc.sub.x,y.sup.f) of the parameter of interest (Wc), using the determining method according to claim 1; and producing the electrochemical cell, on the basis of the reference electrochemical cell in which the parameter of interest (Wc) has the determined spatial distribution (Wc.sub.x,y.sup.f).

13. Data storage medium containing instructions for implementing the determining method according to claim 1, these instructions being executable by a processor.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0050] 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:

[0051] 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 temperature spatial distribution of the temperature of the electrochemical cell in operation;

[0052] FIG. 2 a is a flowchart of a method for determining the spatial distribution of the catalytic load of an electrochemical cell according to a first embodiment;

[0053] FIG. 3 a is a flowchart of a method for determining the spatial distribution of the catalytic load of an electrochemical cell according to a second embodiment;

[0054] 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 local temperature T.sub.i,j.sup.c;

[0055] FIG. 5 is an example of a relationship between the power density of a fuel cell as a function of the catalytic load of the electrochemical cells;

[0056] FIG. 6a is an exemplary spatial distribution of the effective temperature of a reference electrochemical cell in operation, for which cell the catalytic load of the active layers of the electrodes is spatially uniform, and FIG. 6b is an exemplary spatial distribution of the effective temperature of an electrochemical cell for which the catalytic load of the active layers has a spatial distribution determined using the method of the first embodiment;

[0057] FIGS. 7a to 7c illustrate three steps of the deposition of a catalytic ink on the surface of an electrochemical-cell active layer by means of a screen-printing screen.

DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS

[0058] In the figures and in the rest of the description, references that are the same represent identical or similar components. In addition, the various components are not shown to scale so as to make the figures clearer. 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%.

[0059] 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.

[0060] 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 by the electrochemical reaction.

[0061] 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 42a, 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.

[0062] 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 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. The active layers 12, 22 are the site of electrochemical reactions. They include materials suitable for allowing the oxidation and reduction reactions at the respective interfaces of the anode and cathode with the membrane. More precisely, they each include an ionomer ensuring the protonic conductivity, for example Nafion, a catalyst for generating the electrochemical reaction, for example platinum, and an electrically conductive carrier, for example a carbon-containing matrix.

[0063] As mentioned above, the catalytic activity of the active layer especially depends on the active surface area of the catalyst, i.e. the surface area of the catalyst capable of making contact with the reactive species, expressed in square centimeters or sometimes in square centimeters per unit weight of catalyst, and the load (or loading or content) of catalyst, expressed in grams per unit area of the cell.

[0064] 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.

[0065] 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.

[0066] 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.

[0067] The removal of heat via the flow of the 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 low flow rate within the cooling circuit.

[0068] 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.

[0069] The parameter influencing the production of electrical power is here a parameter representative of the catalytic activity of the active 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 number of electrons that recombine or protons that are generated at the cathode and anode, respectively, during the electrochemical redox reactions. The parameter of interest is here the load of catalyst Wc or catalytic load. It may also be a question of any equivalent parameter, such as the active surface area of the catalyst. It will be understood here that the lower the local catalyst load Wc.sub.x,y, the lower the local current density I.sub.x,y produced by the cell (and therefore the lower the local flux Q.sub.x,y of produced heat) will be.

[0070] By 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 temperature when the cell is operating at the polarization point defined by the voltage of the cell U.sub.tot and the total current density I.sub.tot, i.e. the local current density I.sub.x,y integrated over the entire area of the cell.

[0071] 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.

[0072] 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.

[0073] Thus, an electrochemical cell the catalytic load 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.

[0074] FIG. 2 a is a flowchart of a method for determining the spatial distribution of the parameter of interest representative of the catalytic activity of an electrode, according to a first embodiment. In this example, the parameter of interest is the catalyst load Wc of an active layer of an electrode of the cell, for example the cathodic active layer, the value Wc.sub.x,y of which has a direct influence on the local electrical current density I.sub.x,y produced locally by the electrochemical reaction and therefore on the local heat flux Q.sub.x,y produced.

[0075] Generally, according to this first embodiment, an optimized spatial distribution Wc.sub.x,y.sup.f of the load of catalyst Wc is determined from the 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 catalytic load is spatially distributed with a given initial distributionand a preset set-point temperature T.sup.c. It is then possible to modify locally the catalytic load Wc of the active layer so that it has the optimized distribution Wc.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.

[0076] In a first step 110, a reference electrochemical cell is defined within which the catalytic load Wc of the cathodic active layer is spatially distributed with an initial distribution Wc.sub.x,y.sup.i. The cell has a structure identical or similar to that described with reference to FIG. 1. The initial spatial distribution Wc.sub.x,y.sup.i of the catalytic load Wc may be substantially uniform, i.e. here it has a value that is substantially constant at every point in the active zone.

[0077] 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.Math.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.e 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.s.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.

[0078] 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 a 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 from an electrochemical cell model, for example that 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.

[0079] 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.

[0080] 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.

[0081] Next, in a step 150, the spatial distribution Wc.sub.x,y.sup.f of the catalytic load Wc is determined depending on the spatial distribution T.sub.x,y.sup.e of the local difference T.sup.e.

[0082] 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 Wc.sub.x,y.sup.f of the catalytic load Wc may be determined by correlation, for example by a term-to-term multiplication, of the initial spatial distribution Wc.sub.x,y.sup.i of the catalytic load Wc 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 Wc.sub.x,y.sup.i of the catalytic load Wc is multiplied by the local value of the correctional coefficient, which is for example equal to 0.25 or even less. Thus, the catalytic load Wc has a new local value that is decreased with respect to the initial local value, which decreases the local current density and therefore the produced heat flux.

[0083] 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 Wc.sub.x,y.sup.f of the catalytic load Wc is determined by modifying the initial spatial distribution Wc.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 Wc.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 and 1.

[0084] Thus, a spatial distribution Wc.sub.x,y.sup.f of the catalytic load Wc of the active layer is obtained. It is then possible to modify the initial distribution Wc of the catalytic load Wc of the cathodic active layer 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.

[0085] FIG. 3 a is a flowchart of a method for determining the spatial distribution of a parameter of interest representative of the catalytic activity of an active layer of at least one electrode of an electrochemical cell, according to a second embodiment. In this example, the parameter of interest is the catalytic load Wc of the active layer, here the cathode, the value of which has a direct influence on the electrical current density exchanged locally during the electrochemical reaction.

[0086] Generally, according to this second embodiment, the spatial distribution Wc.sub.x,y.sup.f of the catalytic load Wc 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 catalytic load Wc of the active 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.

[0087] 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.

[0088] In a first step 210, a reference electrochemical cell is defined, or supplied, within which the catalytic load Wc of the cathodic active layer is spatially distributed with an initial distribution Wc.sub.x,y.sup.i. The initial spatial distribution Wc.sub.x,y.sup.i of the catalytic load Wc 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: [0089] a phase of experimentally prototyping or numerically modelling an electrochemical cell; [0090] a phase of measuring the spatial distribution of the temperature within the electrochemical cell in operation; then [0091] 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.

[0092] 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 the same position within the spatial distribution, the electrochemical cell is then supplied, i.e. considered, for the following steps of the determining method.

[0093] 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.

[0094] 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 specie, 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.Math.[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.sub.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 c.sup.i 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.

[0095] 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 rate of the electrochemical reactions. 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 and dehumidification in the distributing circuits, 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:

{acute over (T)}.sub.x,y.sup.c=T.sub.x,y.sup.c+K.sup..Math.[.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 total-water 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.

[0096] In a step 230, a spatial distribution D.sub.x,y.sup.r of a first thermal quantity representative of the local removal of heat D.sup.r within the electrochemical 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.

[0097] 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 D.sup.r removes to obtain the set-point temperature T.sup.c.

[0098] 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 the 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).

[0099] 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)

The flow rates of the heat-transfer fluid at the four facets of the mesh cell (i,j) may be obtained by projecting 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.Math.e.sub.y+D.sub.i,j+1.sup.r.Math.e.sub.y)/2(6-1)

d.sub.i,j.sup.2=(D.sub.i,j.sup.r.Math.e.sub.x+D.sub.i1,j.sup.r.Math.e.sub.x)/2(6-2)

d.sub.i,j.sup.3=(D.sub.i,j.sup.r.Math.e.sub.x+D.sub.i+1,j.sup.r.Math.e.sub.x)/2(6-3)

d.sub.i,j.sup.4=(D.sub.i,j.sup.r.Math.e.sub.y+D.sub.i,j1.sup.r.Math.e.sub.y)/2(6-4)

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.

[0100] 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.Math.c.sub.p.Math.T.sub.i,j.sup.k(7)

[0101] 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.

[0102] In a step 250, the spatial distribution Wc.sub.x,y.sup.f of the catalytic load Wc 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:

[00001] $\begin{matrix} I_{x, y}^{e} = Q_{x, y}^{e} .Math. \frac{I_{tot}}{Q_{tot}} & (8) \end{matrix}$

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.

[0103] Next, the new spatial distribution Wc.sub.x,y.sup.f of the catalytic load Wc 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 Wc.sub.min and maximum Wc.sub.max values of the load Wc of the active layer. It may be a question of values commonly used in the context of PEM cell stacks. Next, the spatial distribution Wc.sub.x,y.sup.f is calculated, for example using the relationship:

[00002] $\begin{matrix} {Wc}_{x, y}^{f} = \max ({Wc}_{\max}, {Wc}_{\min} .Math. \frac{I_{\max}^{e}}{I_{x, y}^{e}}) & (9) \end{matrix}$

where I.sub.max.sup.e is the maximum value of the local current density I.sub.x,y.sup.e. The local load Wc thus varies linearly between the minimum Wc.sub.min and maximum Wc.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 load Wc to vary so that the maximum value Wc.sub.max corresponds to a maximum local current density and vice versa, may be used. The minimum Wc.sub.min and maximum Wc.sub.max values may be preset depending on the overall electrical 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.

[0104] Alternatively to relationship (9), the spatial distribution Wc.sub.x,y.sup.f is determined from a curve giving the relationship between the current density I and the load Wc. FIG. 5 is an example of such a relationship, which here equivalently relates the power density of a fuel cell in operation to the catalytic platinum load of the electrochemical cells, for an efficiency of 50%. The spatial distribution Wc.sub.x,y.sup.f is determined depending on the spatial distribution I.sub.x,y.sup.e. It will be noted here that the catalytic load may vary from a minimum value of about 0.05 mg/cm.sup.2 to a maximum value of about 0.4 mg/cm.sup.2 to 0.5 mg/cm.sup.2, this leading current density to increase and therefore power to increase from 100 mW/cm.sup.2 to 400 mW/cm.sup.2.

[0105] Thus, a spatial distribution Wc.sub.x,y.sup.f of the load Wc 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 an active layer the catalytic load Wc of which is distributed with the spatial distribution Wc.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.

[0106] FIG. 6a illustrates an exemplary spatial distribution of the effective temperature of an electrochemical cell in operation, in the case where the anodic and cathodic active layers have a substantially uniform catalytic load. Three zones of excess temperature, or hotspot zones, are present, referenced Z.sub.1 to Z.sub.3. The operating conditions in this case are a pressure of 1.5 bar, a temperature of 80 C. at the outlet of the cooling circuit, a relative humidity of 50% at the anode- and cathode-side inlets, and a stoichiometry of 1.8 for the air and 1.5 for the hydrogen.

[0107] FIG. 6b illustrates the spatial distribution of the effective temperature of the same electrochemical cell in operation, in the case where at least one active layer has a catalytic load having the spatial distribution modified according to the first embodiment of the method (FIG. 2) only in one portion of the cell indicated by the dashed lines. It will be noted that, in this portion in which a hotspot Z.sub.2 was present, the temperature distribution is substantially uniform and does not contain zones of excess temperature. In the other portions of the cell, in which the catalytic load was not modified, the hotspots Z.sub.1 and Z.sub.3 are still present.

[0108] 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 an active layer the catalytic load Wc of which is spatially distributed with an initial distribution Wc.sub.x,y.sup.i. Using the method described above with reference to FIG. 2 or 3, a spatial distribution Wc.sub.x,y.sup.f of the catalytic load of the cathodic active layer is determined. Next, in a step 160 (FIG. 2) or 260 (FIG. 3), the cathode is produced in such a way that the catalytic load Wc of the active layer has the determined spatial distribution Wc.sub.x,y.sup.f.

[0109] Thus, the catalytic load Wc of the active layer is modified locally so as to form nonuniformities in the spatial distribution Wc.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 load Wc of the active layer is decreased locally in zones in which the effective temperature of the cell is liable to be above the set-point temperature. Thus, the local current density is decreased, thereby consequently decreasing the local produced heat flux. Thus, the effective temperature of the cell corresponds locally to the set-point temperature.

[0110] To achieve this, on a carrier of the active layer, for example a carbon-containing carrier, a catalytic ink including, by way of illustration, a catalyst, for example 4 g of Pt.sub.3Co, an ionomer, for example 6.4 g of Nafion, water, for example in an amount of 18.5 g, and a solvent, for example 1.5 g of ethanol, is deposited.

[0111] The catalytic ink may be deposited on the surface of the carrier of the active layer of the cathode, in at least one identified zone Z.sub.i of excess temperature, or even on all the surface of the active layer, by any deposition technique known to those skilled in the art, screen printing for example.

[0112] With reference to FIGS. 7a to 7c, in the case where a deposit is produced by screen printing in certain zones of the active layer, a screen-printing screen 60 is produced that forms a mesh of through-apertures 61, for example of a few square centimeters in an area. Certain apertures 62 are obturated to prevent the deposition of catalytic ink in the identified zones Z.sub.i (FIG. 7a). Next, the screen 60 is placed on the carrier of the active layer then the catalytic ink 63 is deposited on the active layer through the screen 60 (FIG. 7b). After the screen has been removed, the active layer includes the catalytic ink 63 on substantially all its surface except for the zones Z.sub.i (FIG. 7c). The amount of catalyst may be adjusted in the zones Z.sub.i by optionally carrying out one or more successive depositions in these zones with a catalytic ink containing a different amount of catalyst from that used in the zones adjacent the zones Z.sub.i.

[0113] Thus, the active layer has a catalytic load the value of which varies locally. In at least one zone Z.sub.i, the local value of the catalytic load is lower than the average value of the load outside this zone Z.sub.i.

[0114] By way of illustration, the zones Z.sub.i in which the catalytic load Wc is modified according to the spatial distribution Wc.sub.x,y.sup.f determined using the determining method described with reference to FIG. 2 or 3 may have an area of about a few hundred square microns to a few square centimeters, for example an area from 400 m.sup.2, which is the typical size of a mesh cell of a screen-printing screen of the type conventionally used, to 110 cm.sup.2, which is half the total area of a cell of 220 cm.sup.2. Of course, these data are here purely illustrative. More precisely, such a zone Z.sub.i has an area ranging from 0.5 cm.sup.2 to 40 cm.sup.2, where 0.5 cm.sup.2 is here the minimum typical size of a mesh cell of a measuring device allowing temperature nonuniformities to be measured, and where 40 cm.sup.2 is the typical size of the measured hotspots. The area of the zones Z.sub.i may thus be about 6 cm.sup.2.

[0115] It has been observed that decreasing the amount of catalyst by 100% in a 216 cm.sup.2 strip allows the local current density to be decreased by 0.3 A/cm.sup.2, this leading to a decrease in the effective local temperature of 2 C. on average. Thus, by extrapolation, it may be assumed that a decrease of 0.1 mg/cm.sup.2 in the amount of platinum in an area of at least 1 cm.sup.2 will cause a decrease in the effective temperature in this zone of 0.5 C.

[0116] The catalytic load may be comprised between 0 and 0.5 mg/cm.sup.2 in the case of platinum for an electrochemical cell for a fuel cell. The catalytic load has a maximum local value outside of the zones Z.sub.i, and a local value in the zones Z.sub.i lower than the nominal value. The nominal average value of the load is comprised between the maximum and minimum local values and corresponds to the average of the local load over the entire area of the active layer. The nominal average value especially depends on the desired total power density. It may thus be about 0.4 mg/cm.sup.2 of platinum. The content of ionomer, for example of Nafion, may be comprised between 2% and 30% of the catalytic load, may preferably be comprised between 7% and 20% and may for example be about 15%.

[0117] It may be advantageous for the determined spatial distribution Wc.sub.x,y.sup.f of the load Wc to have a nominal average value substantially identical to that of the initial distribution Wc.sub.x,y.sup.i, so as not to modify the total power density of the cell in operation. Thus, whereas in the hotspot zones Z.sub.i the spatial distribution Wc.sub.x,y.sup.f has a local value below that of the initial distribution Wc.sub.x,y.sup.i, the local value Wc.sub.x,y.sup.f is increased outside of the zones Z.sub.i. By way of example, to retain an average value of 0.4 mg/cm.sup.2 of platinum over all of the active layer, a decrease of 0.1 mg/cm.sup.2 in a zone Z.sub.i of 6 cm.sup.2 area leads to 0.6 mg being distributed over the rest of the area of the active layer, for example over 214 cm.sup.2 for a cell with an active layer with an area of 220 cm.sup.2.

[0118] Particular embodiments have just been described. Alternative variants and various modifications will be apparent to the person skilled in the art.

DETERMINATION OF THE SPATIAL DISTRIBUTION OF CATALYTIC ACTIVITY OF AN ELECTRODE OF AN ELECTROCHEMICAL CELL

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