ELECTRODE FORMULATION FOR A LI-ION BATTERY AND SOLVENT-FREE METHOD FOR ELECTRODE MANUFACTURING
20230084468 · 2023-03-16
Inventors
- Stephane Bizet (Serquigny, FR)
- Anthony BONNET (COLOMBES CEDEX, FR)
- Oleksandr Korzhenko (Lacq, FR)
- Samuel DEVISME (Serquigny, FR)
Cpc classification
H01M4/13
ELECTRICITY
H01M4/485
ELECTRICITY
H01M4/1393
ELECTRICITY
Y02E60/10
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
H01M4/1391
ELECTRICITY
H01M10/0525
ELECTRICITY
International classification
H01M4/62
ELECTRICITY
H01M10/0525
ELECTRICITY
H01M4/1391
ELECTRICITY
H01M4/1393
ELECTRICITY
H01M4/485
ELECTRICITY
H01M4/583
ELECTRICITY
Abstract
The present invention relates generally to the field of electrical energy storage in rechargeable secondary batteries of Li-ion type. More specifically, the invention relates to an electrode formulation for a Li-ion battery, comprising a binder based on a mixture of fluoropolymers. The invention also relates to a process for preparing electrodes using said formulation, by a technique of solvent-free deposition on a metal substrate. The invention relates finally to an electrode obtained by this process and also to Li-ion secondary batteries comprising at least one such electrode.
Claims
1. A Li-ion battery electrode comprising an active filler for anode or cathode, an electronically conductive filler and a fluoropolymer binder, characterized in that said binder consists of the mixture of: a fluoropolymer A, the melt viscosity of which is greater than or equal to 1000 Pa.Math.s at 232° C. and at a shear of 100 s.sup.−1, and of a fluoropolymer B having a melt viscosity of at least 250 Pa.Math.s lower, at 232° C. and at a shear of 100 s.sup.−1, than that of fluoropolymer A.
2. The electrode of claim 1, wherein said fluoropolymers A and fluoropolymer B contain at least one fluoromonomer chosen from the group consisting of: vinyl fluoride; vinylidene fluoride (VDF); trifluoroethylene (VF3); chlorotrifluoroethylene (CTFE); 1,2-difluoroethylene; tetrafluoroethylene (TFE); hexafluoropropylene (HFP); perfluoro(alkyl vinyl) ethers; perfluoro(1,3-dioxole); perfluoro(2,2-dimethyl-1,3-dioxole) (PDD); the product of formula CF.sub.2═CFOCF.sub.2CF(CF.sub.3)OCF.sub.2CF.sub.2X wherein X is SO.sub.2F, CO.sub.2H, CH.sub.2OH, CH.sub.2OCN or CH.sub.2OPO.sub.3H; CF.sub.2═CFOCF.sub.2CF.sub.2SO.sub.2F; the product of formula F(CF.sub.2)nCH.sub.2OCF═CF.sub.2 wherein n is 1, 2, 3, 4 or 5; the product of formula R.sub.1CH.sub.2OCF═CF.sub.2 wherein R.sub.1 is hydrogen or F(CF.sub.2)m and m is equal to 1, 2, 3 or 4; the product of formula R.sub.2OCF═CH.sub.2 wherein R.sub.2 is F(CF.sub.2)p and p is 1, 2, 3 or 4; perfluorobutyl ethylene (PFBE); 3,3,3-trifluoropropene; and 2-trifluoromethyl-3,3,3-trifluoro-1-propene.
3. The electrode of claim 1, wherein: fluoropolymer A comprises a VDF homopolymer and/or at least one copolymer of vinylidene fluoride (VDF) and hexafluoropropylene (HFP), and fluoropolymer B comprises a VDF homopolymer and/or at least one VDF-HFP copolymer.
4. The electrode of claim 1, wherein said fluoropolymer A has a viscosity of greater than or equal to 1500 Pa.Math.s at a shear of 100 s.sup.−1.
5. The electrode of claim 1, wherein the HFP content of said at least one copolymer of vinylidene fluoride (VDF) and hexafluoropropylene (HFP) of said fluoropolymer A is greater than or equal to 3% and less than or equal to 55% by weight.
6. The electrode of claim 1, wherein the fluoropolymer A consists of a copolymer of vinylidene fluoride (VDF) and hexafluoropropylene (HFP) having an HFP content of greater than or equal to 3% by weight.
7. The electrode of claim 1, wherein the fluoropolymer A consists of a mixture of two or more copolymers of vinylidene fluoride (VDF) and hexafluoropropylene (HFP), the HFP content of each copolymer being greater than or equal to 3% by weight.
8. The electrode of claim 1, wherein the fluoropolymer A is a homopolymer of vinylidene fluoride or a mixture of homopolymers of vinylidene fluoride.
9. The electrode of claim 1, wherein said fluoropolymer B has a viscosity at least 500 Pa.Math.s lower, at 232° C., advantageously at least 750 Pa.Math.s lower, at a shear of 100 s.sup.−1, than that of the polymer A.
10. The electrode of claim 1, wherein the fluoropolymer B is a homopolymer of vinylidene fluoride or a mixture of homopolymers of vinylidene fluoride.
11. The electrode of claim 1, wherein the fluoropolymer B consists of a VDF-HFP copolymer having an HFP content of between 3% and 55% by weight.
12. The electrode of claim 1, wherein the fluoropolymer B consists of a mixture of two or more VDF-HFP copolymers.
13. The electrode of claim 1, wherein said mixture comprises: i. a weight content of fluoropolymer A of greater than or equal to 1% and less than or equal to 20%, and ii. a weight content of fluoropolymer B of less than or equal to 99% and greater than 80%.
14. The electrode of claim 1, wherein said active filler is selected from the group consisting of lithium metal, graphite, silicon/carbon composites, silicon, graphene, fluorographites of CFx type where x is between 0 and 1 and titanates of LiTi.sub.5O.sub.12.
15. The electrode of claim 1, wherein said active filler is selected from the group consisting of LiMO.sub.2 type, of LiMPO.sub.4 type, Li.sub.2MPO.sub.3F type, Li.sub.2MSiO.sub.4 type where M is Co, Ni, Mn, Fe or a combination of these, LiMn.sub.2O.sub.4 type and S.sub.8 type.
16. The electrode of claim 1, having the following composition by weight: 50% to 99.9% of active filler, 0.05% to 25% of conductive filler, 0.05% to 25% of polymer binder, 0 to 5% of at least one additive chosen from the list: plasticizer, ionic liquid, dispersant for the fillers, flow agent for the formulation, fibrillating agent, the sum of all these percentages being 100%.
17. A process for manufacturing the Li-ion battery electrode of claim 1, said process comprising the following steps: mixing the active filler, the fluoropolymer binder and the electronically conductive filler by means of a process which makes it possible to obtain an electrode formulation that can be applied to a metal substrate by a solvent-free process; depositing said electrode formulation on the metal substrate by a solvent-free process so as to obtain a Li-ion battery electrode, and consolidating said electrode by a heat treatment and/or thermomechanical treatment.
18. The process of claim 17, wherein the mixing step is carried out in two steps: mixing the electronically conductive filler and the fluoropolymer polymer binder using a solvent-free process or by co-spraying, to obtain an intimate mixture, then mixing the conductive filler and the polymer binder using a solvent-free process or by co-spraying, to obtain an intimate mixture, then
19. The process of claim 17, wherein said mixing step is carried out by a process selected from the group of: agitation, air-jet mixing, milling of the mixture, high-shear mixing, mixing with a V-mixer, mixing with a screw mixer, double-cone mixing, drum mixing, conical mixing, double Z-arm mixing, mixing in a fluidized bed, in a planetary mixer, extrusion, calendering, and or mechanofusion.
20. The process of claim 17, wherein said solvent-free process is carried out by depositing the electrode formulation on the metal substrate by a process chosen from the following processes: pneumatic spraying, electrostatic spraying, dipping in a fluidized powder bed, dusting, electrostatic transfer, deposition with rotary brushes, deposition with rotary metering rolls, and calendering.
21. The process of claim 17, wherein said solvent-free process is carried out in two steps: a first step which comprises producing a self-supporting film from the electrode formulation which has been premixed using a thermomechanical process, and a second step wherein the self-supporting film is assembled with the metal substrate by a process allying temperature and pressure.
22. The process of claim 17, wherein the consolidation of said electrode is carried out by at least one heat treatment selected from the group of passing through an oven, under an infrared lamp and through a calender with heated rolls.
23. A secondary Li-ion battery comprising an anode, a cathode and a separator, wherein at least one of the anode or cathode comprises the composition of claim 1.
Description
DESCRIPTION OF EMBODIMENTS OF THE INVENTION
[0033] The invention is now described in greater detail and in a nonlimiting manner in the description that follows.
[0034] According to a first aspect, the invention relates to a Li-ion battery electrode comprising an active filler for anode or cathode, an electronically conductive filler and a fluoropolymer binder.
[0035] Characteristically, said binder consists of a mixture of at least two fluoropolymers having different melt viscosities, namely: [0036] a fluoropolymer A, the melt viscosity of which is greater than or equal to 1000 Pa.Math.s at 232° C. and at a shear of 100 s.sup.−1, and [0037] a fluoropolymer B having a viscosity at least 250 Pa.Math.s lower, at 232° C. and at a shear of 100 s.sup.−1, than that of the polymer A.
[0038] According to various embodiments, said electrode comprises the features below, in combination where appropriate. The stated contents are expressed by weight, unless otherwise stated.
[0039] The invention uses fluoropolymers. The term “fluoropolymer” means a polymer including fluorine groups —F. The fluoropolymer contains in its chain at least one monomer chosen from the compounds containing a vinyl group capable of opening in order to polymerize and which contains, directly attached to this vinyl group, at least one fluorine atom, a fluoroalkyl group or a fluoroalkoxy group.
[0040] By way of example of a fluorinated vinyl monomer which is part of the composition of the fluoropolymers A and B, mention may be made of: vinyl fluoride; vinylidene fluoride (VDF); trifluoroethylene (VF3); chlorotrifluoroethylene (CTFE); 1,2-difluoroethylene; tetrafluoroethylene (TFE); hexafluoropropylene (HFP); perfluoro(alkyl vinyl) ethers such as perfluoro(methyl vinyl) ether (PMVE), 5-perfluoro(ethyl vinyl) ether (PEVE) and perfluoro(propyl vinyl) ether (PPVE); perfluoro(1,3-dioxole); perfluoro(2,2-dimethyl-1,3-dioxole) (PDD); the product of formula CF.sub.2═CFOCF.sub.2CF(CF.sub.3)OCF.sub.2CF.sub.2X wherein X is SO.sub.2F, CO.sub.2H, CH.sub.2OH, CH.sub.2OCN or CH.sub.2OPO.sub.3H; the product of formula CF.sub.2═CFOCF.sub.2CF.sub.2SO.sub.2F; the product of formula F(CF.sub.2)nCH.sub.2OCF═CF.sub.2 wherein n is 1, 2, 3, 4 or 5; the product of formula R.sub.1CH.sub.2OCF═CF.sub.2 wherein R.sub.1 is hydrogen or F(CF.sub.2)m and m is equal to 1, 2, 3 or 4; the product of formula R.sub.2OCF═CH.sub.2 wherein R.sub.2 is F(CF.sub.2)p and p is 1, 2, 3 or 4; perfluorobutyl ethylene (PFBE); 3,3,3-trifluoropropene and 2-trifluoromethyl-3,3,3-trifluoro-1-propene.
[0041] The fluoropolymer which is part of the composition of each of the polymers A and B can be: a homopolymer, or a copolymer comprising two more fluormonomers listed above, or else mixtures of homopolymer and of copolymer, or mixtures of two copolymers; it can also comprise non-fluoro comonomers such as ethylene.
[0042] The fluoropolymers A and B can have similar structures (comprising the same monomers), or else can have different structures. According to one embodiment, said binder contains: [0043] a fluoropolymer A which comprises a VDF homopolymer and/or at least one copolymer of vinylidene fluoride (VDF) and hexafluoropropylene (HFP), the melt viscosity of which is greater than or equal to 1000 Pa.Math.s at 232° C. and under a shear of 100 s.sup.−1, and [0044] a fluoropolymer B which comprises a VDF homopolymer and/or at least one VDF-HFP copolymer, said fluoropolymer B having a viscosity at least 250 Pa.Math.s lower, at 232° C. and at a shear of 100 s.sup.−1, than that of the polymer A. According to one embodiment, the fluoropolymer A comprises at least one VDF homopolymer and/or at least one VDF-HFP copolymer having an HFP content of greater than or equal to 1% by weight, preferably greater than or equal to 3%, advantageously greater than or equal to 6%. Said VDF-HFP copolymer has an HFP content of less than or equal to 55%, preferably less than or equal to 50%.
[0045] According to one embodiment, the fluoropolymer A consists of a single VDF-HFP copolymer having an HFP content of greater than or equal to 1%. According to one embodiment, the HFP content of this VDF-HFP copolymer is between 3% and 55%, limits included, preferably between 6% and 50%, limits included.
[0046] According to one embodiment, the fluoropolymer A consists of a mixture of two or more VDF-HFP copolymers, the HFP content of each copolymer being greater than or equal to 1%. According to one embodiment, each of the copolymers has an HFP content of between 3% and 55%, limits included, preferably between 6% and 50%, limits included.
[0047] According to one embodiment, the fluoropolymer A is a vinylidene fluoride (VDF) homopolymer or a mixture of vinylidene fluoride homopolymers.
[0048] According to one embodiment, the fluoropolymer A has a melt viscosity greater than or equal to 1000 Pa.Math.s, preferably greater than or equal to 1500 Pa.Math.s, and advantageously greater than or equal to 2000 Pa.Math.s at 232 ° C. and at a shear of 100 s.sup.−1. The viscosity is measured at 230° C., at a shear gradient of 100 s.sup.−1, using a capillary rheometer or a parallel-plate rheometer in accordance with standard ASTM D3825. The two methods give similar results.
[0049] According to one embodiment, the fluoropolymer B is a mixture of PVDF homopolymer with a VDF-HFP copolymer or else a mixture of two or more VDF-HFP copolymers.
[0050] According to one embodiment, the fluoropolymer B is a vinylidene fluoride (VDF) homopolymer or a mixture of vinylidene fluoride homopolymers.
[0051] According to one embodiment, the fluoropolymer B consists of a single VDF-HFP copolymer having an HFP content of greater than or equal to 1%. According to one embodiment, the HFP content of this VDF-HFP copolymer is between 3% and 55%, limits included, preferably between 6% and 50%, limits included.
[0052] According to one embodiment, the fluoropolymer B has a viscosity at least 250 Pa.Math.s lower, at 232° C. and at a shear of 100 s.sup.−1, than that of the polymer A, and preferentially at least 500 Pa.Math.s lower than that of the polymer A and advantageously at least 750 Pa.Math.s lower than that of the polymer A.
[0053] The fluoropolymers used in the invention can be obtained by known polymerization methods, such as solution, emulsion or suspension polymerization. According to one embodiment, they are prepared by an emulsion polymerization process in the absence of a fluorinated surfactant.
[0054] According to one embodiment, said mixture contains: [0055] i. a weight content of polymer A of greater than or equal to 1% and less than or equal to 20%, preferentially greater than or equal to 5% and less than or equal to 20%, and [0056] ii. a weight content of polymer B of less than or equal to 99% and greater than or equal to 80%, preferably less than or equal to 95% and greater than or equal to 80%.
[0057] The active materials at the negative electrode are generally lithium metal, graphite, silicon/carbon composites, silicon, fluorographites of CF.sub.x type with x between 0 and 1, and titanates of LiTi.sub.5O.sub.12 type.
[0058] The active materials at the positive electrode are generally of the LiMO.sub.2 type, of the LiMPO.sub.4 type, of the Li.sub.2MPO.sub.3F type, of the Li.sub.2MSiO.sub.4 type, where M is Co, Ni, Mn, Fe or a combination of these, of the LiMn.sub.2O.sub.4 type or of the S.sub.8 type.
[0059] The conductive fillers are chosen from carbon blacks, graphites, natural or synthetic, carbon fibers, carbon nanotubes, metal fibers and powders, and conductive metal oxides. They are preferentially chosen from carbon blacks, natural or synthetic graphites, carbon fibers and carbon nanotubes.
[0060] A mixture of these conductive fillers may also be produced. In particular, the use of carbon nanotubes in combination with another conductive filler such as carbon black can have the advantages of reducing the content of conductive fillers in the electrode and of reducing the content of polymer binder on account of a lower specific surface area compared to carbon black.
[0061] According to one embodiment, a polymeric dispersant that is different to said binder is used in a mixture with the conductive filler in order to break up the agglomerates present and to aid the dispersion thereof in the final formulation with the polymer binder and the active filler. The polymeric dispersant is chosen from poly(vinylpyrrolidone), poly(phenylacetylene), poly(meta-phenylene vinylidene), polypyrrole, poly(para-phenylene benzobisoxazole), poly(vinyl alcohol) and mixtures thereof.
[0062] The composition by weight of the electrode is: [0063] 50% to 99% of active filler, preferably from 50% to 99%, [0064] 25% to 0.05% of conductive filler, preferably from 25% to 0.5%, [0065] 25% to 0.05% of polymer binder, preferably from 25% to 0.5%, [0066] 0 to 5% of at least one additive chosen from the list: plasticizer, ionic liquid, dispersant for the conductive fillers, flow agent for the formulation, fibrillating agent such as polytetrafluoroethylene (PTFE),
the sum of all these percentages being 100%.
[0067] The invention also relates to a process for producing a Li-ion battery electrode, said process comprising the following steps: [0068] mixing the active filler, the polymer binder, the conductive filler and any additives by means of a process that makes it possible to obtain an electrode formulation that can be applied to a metal support by a solvent-free process; [0069] depositing said electrode formulation on the metal substrate by a “solvent-free” process so as to obtain a Li-ion battery electrode and [0070] consolidating said electrode by a heat treatment (application of a temperature ranging up to 50° C. above the melting temperature of the polymer, without mechanical pressure) and/or thermomechanical treatment such as calendering.
[0071] A “solvent-free” process is understood as meaning a process in which there is no need for a step of evaporation of residual solvent downstream of the deposition step.
[0072] Another embodiment of the process for producing an electrode comprises the following steps: [0073] mixing the active filler, the polymer binder and the conductive filler by means of a process that makes it possible to obtain an electrode formulation, the constituents of which are mixed homogeneously; [0074] producing a self-supporting film of the formulation by means of a thermomechanical process such as extrusion, calendering or thermocompression; [0075] depositing the self-supporting film on the metal substrate by a calendering or thermocompression process, and [0076] consolidating said electrode by a heat treatment and/or thermomechanical treatment such as calendering for example, the latter step being optional if the preceding step already achieves a sufficient degree of adhesion and/or porosity.
[0077] Step of Preparing the Electrode Formulation
[0078] The polymers A and B are in the form of a powder, the mean particle size of which is between 10 nm and 1 mm, preferentially between 50 nm and 500 μm and even more preferentially between 50 nm and 50 μm.
[0079] The fluoropolymer powder may be obtained by various processes. The powder may be obtained directly by an emulsion or suspension synthetic process by drying by spray-drying or by freeze-drying. The powder may also be obtained by milling techniques, such as cryomilling. On completion of the powder production step, the particle size can be adjusted and optimized by selection or screening methods.
[0080] According to one embodiment, the polymers A and B are introduced at the same time as the active and conductive fillers at the time of the mixing step.
[0081] According to another embodiment, the polymers A and B are mixed together before mixing with the active and conductive fillers. For example, a mixture of polymers A and B can be produced by co-spraying of the latices of polymers A and B to obtain a mixture in powder form. The mixture thus obtained can, in turn, be mixed with the active and conductive fillers.
[0082] Another embodiment of the mixing step consists in proceeding in two steps. Firstly, either polymer A or polymer B or both are mixed with a conductive filler by a solvent-free process or by co-spraying. This step makes it possible to obtain an intimate mixture of the binder and the conductive filler. Then, in a second step, the binder and the conductive filler, which have been premixed, and the optional fluoropolymer not yet used are mixed with the active filler. The mixing of the active filler with said intimate mixture is carried out using a solvent-free mixing process, to obtain an electrode formulation.
[0083] Another embodiment of the mixing step consists in proceeding in two steps. First, either polymer A or polymer B or both are mixed with an active filler by a solvent-free process or a process of spraying a liquid containing the binder and/or the conductive filler onto a fluidized powder bed of the active filler. This step makes it possible to obtain an intimate mixture of the binder and the active filler. Then, in a second step, the binder, the active filler and the optional optional fluoropolymer not yet used are mixed with the conductive filler.
[0084] Another embodiment of the mixing step consists in proceeding in two steps. Firstly, an active filler is mixed with a conductive filler by a solvent-free process. Then, in a second step, either the two polymers A and B are mixed at the same time with the premixed active filler and conductive filler, or the polymers A and B are mixed one after the other with the premixed active filler and conductive filler.
[0085] Solvent-free mixing processes for the various constituents of the electrode formulation include, without this being an exhaustive list: mixing by agitation, air-jet mixing, high-shear mixing, mixing with a V-mixer, mixing with a screw mixer, double-cone mixing, drum mixing, conical mixing, double Z-arm mixing, mixing in a fluidized bed, mixing in a planetary mixer, mixing by mechanofusion, mixing by extrusion, mixing by calendering, mixing by milling
[0086] Other mixing processes include mixing options that employ a liquid such as water, for example spray drying (co-spraying) or a process of spraying a liquid containing the binder and/or the conductive filler onto a fluidized powder bed of the active filler.
[0087] At the end of this mixing step, the formulation obtained may undergo a final step of milling and/or screening and/or selection in order to optimize the size of the particles of the formulation in preparation for the step of deposition on the metal substrate.
[0088] The formulation in powder form is characterized by the bulk density. It is known in the art that low-density formulations are very restrictive in terms of the uses and applications thereof. The main components contributing to the increase in density are carbon-based additives such as carbon black (bulk density of less than 0.4 g/cm.sup.3), carbon nanotubes (bulk density of less than 0.1 g/cm.sup.3), polymer powders (bulk density of less than 0.9 g/cm.sup.3). A combination of the low-density components in order to obtain an additive combining polymer binder/electron conductor/other additive is recommended in order to improve the premixing step downstream of the deposition of the formulation described above. Such a combination can be produced by the following methods: [0089] a) dispersion of the components in water or the organic solvent, followed by elimination of the solvent (co-spraying, freeze-drying, extrusion/compounding in the presence of the solvent or of water); [0090] b) dry or “wet” co-milling using a known milling method such as a ball or bead mill, followed by a drying step if necessary.
Such a method is particularly advantageous for the significant increase of the bulk density.
[0091] Step of Depositing Said Electrode Formulation on a Support
[0092] According to one embodiment, the end of the mixing step, the electrode is manufactured by means of a solvent-free powder coating method, by depositing the formulation on the metal substrate by a process of pneumatic spraying, electrostatic spraying, dipping in a fluidized powder bed, dusting, electrostatic transfer, deposition with rotary brushes, deposition with rotary metering rolls, calendering.
[0093] According to one embodiment, at the end of the mixing step, the electrode is manufactured by a two-step solvent-free powder coating process. A first step is carried out which consists in producing a self-supporting film from the formulation which has been premixed by means of a thermomechanical process such as extrusion, calendering or thermocompression. Then this self-supporting film is assembled with the metal substrate by a process combining temperature and pressure such as calendering or thermocompression.
[0094] The metal supports of the electrodes are generally made of aluminum for the cathode and of copper for the anode. The metal supports may be surface-treated and have a conductive primer with a thickness of 5 μm or more. The supports may also be carbon fiber woven or nonwoven fabrics.
[0095] Step of Consolidating the Electrode
[0096] The consolidation of said electrode is effected by a heat treatment, by passage through an oven, under an infrared lamp, through a calender with heated rollers or through a press with heated plates. Another alternative consists of a two-step process. First of all, the electrode is subjected to a heat treatment in an oven, under an infrared lamp or by contact with heated plates without pressure. A step of compression at ambient or elevated temperature is then carried out by means of a calender or a plate press. This step makes it possible to adjust the porosity of the electrode and to improve adhesion on the metal substrate.
[0097] The invention also relates to a Li-ion battery electrode produced by the process described above.
[0098] According to one embodiment, said electrode is an anode.
[0099] According to one embodiment, said electrode is a cathode.
[0100] The invention also provides a Li-ion secondary battery comprising a negative electrode, a positive electrode and a separator, wherein at least one electrode is as described above.