POLARISATION

A) Theoretical
	If an external source drives current i through an electrode-electrolyte interface the kinetic equilibrium condition (see Eq. 5) in the text Electrode Potentials) does not hold. The current balance is then:

									1)

 Consequently, that one of the the currents carried by component j whose direction agrees with direction of i becomes larger, while the opposite one becomes smaller than the exchange current and their difference must give i. Clearly, the electrode potential  must differ from its equilibrium value. The difference  called overpotential (referred as overvoltage in some cases) :

			 = (i) - equilibrium						2)

	The overpotential due to the externally driven current provides the electrode-electrolyte system with an additional amount of electrochemical potential:

										3)

which is used to speed up the rate limiting step of the process series. The processes involved in current i are as follows:
	i)   chemical reaction in the bulk solution, producing the active componenent 		(this is not always a part of the consecutive process system);
	ii)  diffusional mass transfer of the active component to the interface;
	iii) adsorption of the active component on surface of the electrode;
	iv) transfer of the active component into/from the electrode;
	v)  desorption of the active component from surface of the electrode;
	vi) diffusional mass transfer of the active component from the interface.
Any of these processes may be the slowest one that is the rate limiting step.
	We confine ourselves to process iv) as rate limiting because this is always the case in or near to equilibrium, and we are interested in measuring the exchange current. (At large overpotentials both the adsorption and the transfer processes are fast and diffusion becomes rate limiting step. We will enter this region during the measurement but do not evaluate it.)
	The additional amount of electrochemical potential is distributed between the molar Gibbs energy changes of the processes of transference into and from the electrode. One of the transfer processes can be referred as anodic and the opposite one as cathodic
The transfer process is anodic if it is oxidative: cations leave the electrode or electrons enter it. Contrarily, the transfer process is cathodic if it is reductive: cations enter the electrode or electrons leave it.
	The ratio of distribution  is called  transfer coefficient. It expresses the Gibbs energy change of the anodic process divided by the additional amount of electrochemical potential. Its value must be 01, usually 0,30,6. Thus the electrochemical potential of the reduced form of component j (it is the reduced form which takes part in the anodic process!) can be given by

								4a)

and that of its oxidized form is
							4b)

Subscript eq indicates the equilibrium value.
	Formally, the process of transference can be regarded as a redox reaction whose rate v is governed by mass action kinetics:

										5)

Superscript n is the order of component j in the reaction.
As the transferred particles carry electric charges, reaction rate can be converted to current by multiplication with the charge transferred (zjF) and the surface of the electrode. Exchange current can be written:

						6)

	Activity of component j can be expressed from electrochemical potential (see Eqs. 2) and 8) in the text Electrode Potentials):

								7)

This activity can be written in Eqs. 5) and 6). As nan and ncat are constants, the standard chemical potential  and the equilibrium electric potential  are constants at given temperature, pressure and composition, they all can be included in rate constant k. Doing this, exchange current takes the form:

									8)

Rate constants are the same both in anodic and in cathodic direction in this form, so subscripts an and cat have been omitted.
As any point of the current-electrochemical potential field may be an equilibrium point, Eq. 8) must be valid in nonequilibrium situations, too, however with nonequilibrium electrochemical potentials. In such a case anodic and cathodic currents are:

									9a)
									9b)

After writing the electrochemical potentials form Eqs. 4) in Eqs. 9) and taking the anodic current as positive, the two currents can be substituted in Eq. 1). Finally, by means of Eq. 8) we obtain :

				10)

	The measurable (net) current is a difference of  two oppositely signed exponentials, resembling somewhat to a hyperbolic sine function, and just like with that, it is practically straight in its middle (around equilibrium) region. The linear term in MacLaurin's expansion gives:

									11)

This middle linear region continues with exponential regions on its both sides, as either   (if  0) or (1-) (if  0) is considerably larger than 25.6mV (that is RT/zF  on 25C),  then the contribution of the opposite current in Eq. 10) becomes negligible.
	The exponential regions are usually followed by diffusional regions where diffusion is becoming the rate limiting step. Current tends to its highest value that is to the rate of charge transfer by the diffusion. As diffusion takes place in the liquid film adhered to the electrode surface and the thickness of this film depends on Reynolds number, diffusional limit current depends on stirring rate.

B) Equipment
	We are going to polarize a quinhydrone electrode we are familiar with from a previous measurement. 

	An electrolyte of steady pH and saturated by quinhydrone is stirred by a magnetic stirrer in a thermostated vessel. 
	Three identical flat platinum rings are immersed to serve as electrodes. The middle one should be polarized and measured (working electrode). An other one is needed to get a closed electric circuit (auxiliary or counter electrode; it will be polarized in the opposite direction but it is not measured). These two electrodes are connected to a current generator. Both the sign and the intensity of the current can be controlled. 
	The third electrode holding its equilibrium potential during the measurement serves as reference. 
	A voltmeter of high input impedance measures the voltage between the working and the reference electrodes that is the overpotential.
Carrying out the measurement oppositely, controlling electrode potential and measuring current, is more advantageous but more expensive as well. Of course, one gets the same polarization graph  in this way, however, the measurement is faster and the electrode potentials where by-processes are disturbingly fast can be avoided.

C) Experimental
	The aim of this work is to measure a polarization cycle, to determine the exchange current and the transfer coefficient.
	1. Start the thermostate and fill the vessel with 0.1M HCl solution. Saturate it with quinhydrone and turn on the magnetic stirrer.
	2. Immerse the glass rode holding the platinum rings. Take care that each ring be covered by the electrolyte and the stirrer do not collide with the glass rode. The current generator output marked   has to be connected to the working electrode and the other output to the auxiliary electrode. The voltmeter input marked V has to be connected to the working electrode while the other input (marked COM) to the reference electrode.
	3. If temperature has been settled begin to polarize in cathodic direction (switch in position -). Increase current gradually and read overpotential.
	4. As neither the position nor the number of revolutions is steady at a magnetic stirrer, the Reynolds number is unsteady, too, and so the diffusional limiting current; one measures unsteady overpotentials in the diffusional region. From the current where overpotential is not steady any more, decrease current gradually and read overpotentials again, back to the origin.
	5. Change the switch to position + and do the measurement in anodic direction as it was written under 3. and 4.
	6. With the aid of a big beaker, wash the cell, the electrodes and the stirrer rode with distilled water.
	7. Plot the graph  i -  (polarization graph). Read the slope of the linear region and calculate exchange current by means of Eq. 11).
	8. Plot the graph log i -   (Tafel graph). It should give straight lines of common intersection in the exponential regions of the polarization graph. Read the intersection (it is log i) and calculate exchange current again. Read the slopes of the straight lines and calculate -t és 1- making use of Eq. 10).
	9. However stoichiometry of the redoxi reaction between quinone and hydroquinone claims it to be a two electron process, the kinetics is of one electron. The two electrones are transferred in two steps, and the rate limiting of them is always the first one. Alas, the first one in one direction is the second one in the opposite direction, so  -t and 1- do not belong to the same elementary process pair! Their sum may differ from 1.