The main difference is now the pre-exponential factor has now been described by more physical parameters instead of the experimental factor 
  
    
      
        A
      
    
    {\displaystyle A}
  . One is once again revered to the sources as listed below for a more in-depth and rigorous mathematical derivation and interpretation. Efficiency
The physical properties of electrodes are mainly determined by the material of the electrode and the topology of the electrode. The properties required depend on the application and therefore there are many kinds of electrodes in circulation. The defining property for a material to be used as an electrode is that it be conductive. Any conducting material such as metals, semiconductors, graphite or conductive polymers can therefore be used as an electrode. Often electrodes consist of a combination of materials, each with a specific task. Typical constituents are the active materials which serve as the particles which oxidate or reduct, conductive agents which improve the conductivity of the electrode and binders which are used to contain the active particles within the electrode. The efficiency of electrochemical cells is judged by a number of properties, important quantities are the self-discharge time, the discharge voltage and the cycle performance. The physical properties of the electrodes play an important role in determining these quantities.
In which the 
  
    
      
        λ
      
    
    {\displaystyle \lambda }
   is the reorganisation energy. Filling this result in the classically derived Arrhenius equation

leads to

With A being the pre-exponential factor which is usually experimentally determined, although a semi classical derivation provides more information as will be explained below. This classically derived result qualitatively reproduced observations of a maximum electron transfer rate under the conditions 
  
    
      
        Δ
        
          G
          
            †
          
        
        =
        λ
      
    
    {\displaystyle \Delta G^{\dagger }=\lambda }
  . For a more extensive mathematical treatment one could read the paper by Newton.