Electrode design

Abstract

Electrodes of a double-layer capacitor are designed so that sub-capacitors formed at each electrode are stressed substantially equally at the rated voltage of the double-layer capacitor. In an exemplary embodiment, each electrode includes a current collector and an active electrode layer, such as a layer of activated carbon. The electrodes are held apart by a porous separator, and the assembly is immersed in an electrolyte. The thicknesses of the active electrode layers differ, resulting in asymmetrical construction of the capacitor. Different thicknesses cause the sub-capacitors to have different capacitances. When voltage is applied to the double-layer capacitor, the voltage is divided unequally between the unequal sub-capacitors. Properly selected thicknesses allow the voltages at the sub-capacitors to stress equally each sub-capacitor. The rated voltage of the double-layer capacitor can then be increased without overstressing the sub-capacitors.

1 . A method of selecting thicknesses of active electrode layers of a double-layer capacitor, the method comprising: 
 determining a positive voltage limit for a first sub-capacitor formed at a positive electrode of the double-layer capacitor and a negative voltage limit for a second sub-capacitor formed at a negative electrode of the double-layer capacitor;    dividing the positive voltage limit by the negative voltage limit to obtain a first ratio of the second sub-capacitor to the first sub-capacitor;    setting relative thicknesses of active electrode layer at the positive electrode and active electrode layer at the negative electrode so that capacitance of the second sub-capacitor is substantially equal to a product of the first ratio and the capacitance of the first sub-capacitor.    
   
   
       2 . A method of selecting thicknesses of active electrode layers in accordance with  claim 1 , wherein the step of setting relative thicknesses comprises: 
 determining a first normalized sub-capacitance of the first sub-capacitor;    determining a second normalized sub-capacitance of the second sub-capacitor;    dividing the first normalized sub-capacitance by the second normalized sub-capacitance to obtain a specific proportionality constant; and    choosing the relative thicknesses so that a ratio of thickness of the active electrode layer at the negative electrode to thickness of the active electrode layer at the positive electrode is substantially equal to a product of the first ratio and the specific proportionality constant.    
   
   
       3 . A method of selecting thicknesses of active electrode layers in accordance with  claim 2 , wherein the step of determining a positive voltage limit and a negative voltage limit comprises using an equidistant selection method.  
   
   
       4 . A method of selecting thicknesses of active electrode layers in accordance with  claim 2 , wherein the step of determining a positive voltage limit and a negative voltage limit comprises using an equal reliability selection method.  
   
   
       5 . A method of selecting thicknesses of active electrode layers in accordance with  claim 2 , wherein the step of determining a positive voltage limit and a negative voltage limit comprises using cyclic voltammetry measurements.  
   
   
       6 . A method of selecting thicknesses of active electrode layers in accordance with  claim 2 , wherein the step of determining a first normalized sub-capacitance comprises measuring the first normalized sub-capacitance of the first sub-capacitor, and the step of determining a second normalized sub-capacitance comprises measuring the second normalized sub-capacitance of the second sub-capacitor.  
   
   
       7 . A method of selecting thicknesses of active electrode layers in accordance with  claim 2 , wherein: 
 the step of determining a first normalized sub-capacitance comprises applying an analytical capacitance model to physical properties of electrolyte of the double-layer capacitor and of material of the active electrode layers; and    the step of determining a second normalized sub-capacitance comprises applying the analytical capacitance model to the physical properties of electrolyte of the double-layer capacitor and of material of the active electrode layers.    
   
   
       8 . A method of selecting thicknesses of active electrode layers in accordance with  claim 7 , wherein the physical properties used in the analytical model comprise sizes of cations and anions of the electrolyte.  
   
   
       9 . A method of selecting thicknesses of active electrode layers in accordance with  claim 8 , wherein the physical properties used in the analytical model further comprise sizes of pores of the material of the active electrode layers.  
   
   
       10 . A method of selecting thicknesses of active electrode layers in accordance with  claim 7 , wherein the electrolyte comprises an aqueous electrolytic solution, and the physical properties used in the analytical model comprise sizes of cations and anions of the aqueous electrolytic solution.  
   
   
       11 . A method of constructing a double-layer capacitor, the method comprising: providing active electrode layers; 
 providing an electrolyte; and    immersing the active electrode layers in the electrolyte;    wherein the step of providing active electrode layers comprises: 
 determining a positive voltage limit for a first sub-capacitor formed at a positive electrode of the double-layer capacitor and a negative voltage limit for a second sub-capacitor formed at a negative electrode of the double-layer capacitor;  
 dividing the positive voltage limit by the negative voltage limit to obtain a first ratio of the second sub-capacitor to the first sub-capacitor; and  
 setting relative thicknesses of active electrode layer at the positive electrode and active electrode layer at the negative electrode so that capacitance of the second sub-capacitor is substantially equal to a product of the first ratio and the capacitance of the first sub-capacitor.  
   
   
   
       12 . A method of constructing a double-layer capacitor in accordance with  claim 11 , wherein the step of setting relative thicknesses comprises: 
 determining a first normalized sub-capacitance of the first sub-capacitor;    determining a second normalized sub-capacitance of the second sub-capacitor;    dividing the first normalized sub-capacitance by the second normalized sub-capacitance to obtain a specific proportionality constant; and    choosing the relative thicknesses so that a ratio of thickness of the active electrode layer at the negative electrode to thickness of the active electrode layer at the positive electrode is substantially equal to a product of the first ratio and the specific proportionality constant.    
   
   
       13 . A method of constructing a double-layer capacitor in accordance with  claim 12 , wherein the step of determining a positive voltage limit and a negative voltage limit comprises using an equidistant selection method.  
   
   
       14 . A method of constructing a double-layer capacitor in accordance with  claim 12 , wherein the step of determining a positive voltage limit and a negative voltage limit comprises using an equal reliability selection method.  
   
   
       15 . A method of constructing a double-layer capacitor in accordance with  claim 12 , wherein the step of determining a positive voltage limit and a negative voltage limit comprises using cyclic voltammetry measurements.  
   
   
       16 . A method of constructing a double-layer capacitor in accordance with  claim 12 , wherein the step of determining a first normalized sub-capacitance comprises measuring the first normalized sub-capacitance of the first sub-capacitor, and the step of determining a second normalized sub-capacitance comprises measuring the second normalized sub-capacitance of the second sub-capacitor.  
   
   
       17 . A method of constructing a double-layer capacitor in accordance with  claim 12 , wherein: 
 the step of determining a first normalized sub-capacitance comprises applying an analytical capacitance model to physical properties of electrolyte of the double-layer capacitor and of material of the active electrode layers; and    the step of determining a second normalized sub-capacitance comprises applying the analytical capacitance model to the physical properties of electrolyte of the double-layer capacitor and of material of the active electrode layers.    
   
   
       18 . A method of constructing a double-layer capacitor in accordance with  claim 17 , wherein the physical properties used in the analytical model comprise sizes of cations and anions of the electrolyte.  
   
   
       19 . A method of constructing a double-layer capacitor in accordance with  claim 18 , wherein the physical properties used in the analytical model further comprise sizes of pores of the material of the active electrode layers.  
   
   
       20 . A method of constructing a double-layer capacitor in accordance with  claim 17 , wherein the electrolyte comprises an aqueous electrolytic solution, and the physical properties used in the analytical model comprise sizes of cations and anions of the aqueous electrolytic solution.