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In contrast to primary batteries,secondary batteries are rechargeable.One of the earliest is the lead-acid battery invented by the Frenchman Gaston Planté in 1859.This type of battery is still the most widely used in other cars.The cathode consists of lead dioxide (PbO2) and solid lead.Other commonly used rechargeable batteries are NiCd,NiMH and Li-Ion.Due to its importance.
Marcus' theory of electron transfer
The Marcus theory was originally proposed by Nobel Laureate Rudolph A.Marcus and explains the rate at which electrons move from one chemical species to another,For this article,this can be seen as a "jump" from an electrode ” to species in solvent and vice versa. We can formulate the problem as calculating the transfer rate of electrons from the donor to the acceptor.The potential energy of the system is a function of the translational,rotational and vibrational coordinates of the reacting species and surrounding medium molecules,collectively referred to as the reaction coordinates.The abscissa of the right figure indicates these.From the classical electron transfer theory,if a non-adiabatic process and a parabolic potential energy are assumed, the expression for the reaction rate constant (reaction probability) can be calculated by finding the point of intersection (Qx).One important thing to note is that when Marcus came up with the theory he noticed that electron transfer must obey the law of conservation of energy and the Frank-Condon principle.Doing this and then rearranging this results in expressing the free energy of activation in terms of the total free energy of the reaction.
Efficiency 
The physical properties of the electrodes are mainly determined by the materials of the electrodes and the topology of the electrodes. The required properties depend on the application, so a wide variety of electrodes are available in circulation.A decisive property of a material used as an electrode is that it is electrically conductive.Therefore, any conductive material such as metals,semiconductors, graphite, or conductive polymers can be used as electrodes.Often electrodes are made of a variety of materials,each with a specific task.Typical ingredients are active materials used as oxidizing or reducing particles,conductive agents to improve the conductivity of the electrodes,and binders used to contain the active particles within the electrodes.The efficiency of an electrochemical cell is judged by a number of properties,important quantities being self-discharge time,discharge voltage and cycle performance.The physical properties of the electrodes play an important role in determining these quantities.Important properties of electrodes are:resistivity, specific heat capacity (c_p),electrode potential and hardness.Of course, for technical applications,the cost of materials is also an important factor.Values of these properties for some commonly used materials at room temperature (T = 293 K).
Surface effects
The surface topology of the electrode is an important factor in determining the efficiency of the electrode.Due to contact resistance, the efficiency of the electrode will be reduced.Therefore,in order to create an efficient electrode,it is important to design it so that the contact resistance is minimized.
