The equation you have written is valid for any potential, not only for the ocp.

No correlation can be found between ocpand pzc.

As you well say, only in the ideal case in which you can prepare a clean surface and then immerse it in an electrolyte, will the ocp coincide with the pzc, but only instantaneously, because there will always be some kind of reaction (e.g., oxidation by traces of oxygen in the solution) that will inject charge into the surface.

You must also take into account that, in the case of a carbon electrode that you are considering, the chemical modification of the surface would be equivalent to specific adsorption on a metal electrode, and you will have to considered two different pzc: the potential of zero total carge (pztc), and the potential of zero free charge (pzfc). The former includes both the charge in the electrical double layer and that involved in forming the chemisorption (specific adsorption) bonds, while the latter refers only to the charge corresponding  to the electrical double layer. Only the pztc can be determined experimentally using electrochemical methods. If you change the degree of functionalization of your carbon surface, you will change both the pztc and the pzfc.

in the field of corrosion we try to correlate the inhibition by adsorption, OCP and PZC

ocp is different from PZC

The equation you have written is valid for any potential, not only for the ocp.

No correlation can be found between ocpand pzc.

As you well say, only in the ideal case in which you can prepare a clean surface and then immerse it in an electrolyte, will the ocp coincide with the pzc, but only instantaneously, because there will always be some kind of reaction (e.g., oxidation by traces of oxygen in the solution) that will inject charge into the surface.

You must also take into account that, in the case of a carbon electrode that you are considering, the chemical modification of the surface would be equivalent to specific adsorption on a metal electrode, and you will have to considered two different pzc: the potential of zero total carge (pztc), and the potential of zero free charge (pzfc). The former includes both the charge in the electrical double layer and that involved in forming the chemisorption (specific adsorption) bonds, while the latter refers only to the charge corresponding  to the electrical double layer. Only the pztc can be determined experimentally using electrochemical methods. If you change the degree of functionalization of your carbon surface, you will change both the pztc and the pzfc.

There are two possible sources contributing to the surface charge of an oxidized graphite electrode. The first one is by the application of an external voltage and the second one is by changing the activity of the potential determine ion(s) and in this case proton is the major pdi. Therefore the surface charge contributed from external potential and pdi is independent from each other that they can not be related to each other quantitatively.

let us see the concept of mixed potential proposed by Lingane

OCP arises due to the a number of anodic and cathodic reactions occuring at the interface There is no net flow of currrent

if the interface is ideally polarizable the OCP is due to the large capacitance

Then double layer capacitance predominates 

Then  qm need not be equal to q s ( The charges on  side one and side 2)

but in the case of PZC   q1  = q2 Thisis iso electric point

For polarizabale electrode such as a dropping electrode, the electrical double layer structure is well per the two Lippmann equation. However, for electrode such as an oxidized graphite, its surface potential can be induced by changing the pH (as H+ and OH- can be the pdi). The electrical double layer surrounding an externally charged oxidized graphite electrode will be altered by changing pH of the solution. 

i gave a little thought

in the case of ideally polarizable electrode OPC is due to perfect capacitor

charges on both sides equal

in the case of PZC the charges on both sides equal

in that case ocp+pzc

Thanks everybody for contributing in the discussion. I feel that a wide and scattered range of points has been mentioned above that makes the clear tracking of the main idea and question difficult. Therefore, I would like to put a short introduction like description here linking various ideas mentioned by other people and also trying to highlight the aim of the question. Further enlightenment of this question and its possible answer, could depend on the origin and source of arousal of the two terms under question; OCP and PZC.

Open Circuit Potential (OCP) was basically defined and explained by the people interested in galvanic circuits (cells) where, the potential difference between the terminal members of a sequence of conductors joined together as an open circuit (zero current passing through the circuit) is the algebraic sum of all Galvani potentials at the individual interfaces. The Galvani potential at each interface is the difference of the inner potentials of the two sides of the interface. Regarding the point of interest of the people of this field, that has been the galvanic circuits (presence of faradic reactions), the condition of equilibrium of the charged particles at the interface has been considered as a consequence of a balance between the chemical potential (μ) of the reaction (or let’s say the diffusion driving force enabling the movement of charged species across the interface) which encourages further advance of the reaction and the electrostatic forces appearing on the interface upon the gradual advance of the reaction, hampering its further advance due to formation of an electric field on the charged interface, attracting back the left charged species. Therefore, the Electrochemical Potential of the charged species has been defined as the summation of their chemical and electric/electrostatic potentials in any individual electrode and the equilibrium has been defined as the point where this electrochemical potential of the charged species becomes equal at either side of the interface.

On the other hand, the concepts of double layer potential as well as potential of zero charge has been explored and explained by the people basically interested in non-faradic aspects of the interfacial phenomena. Therefore, the electron density distribution on the solid electrode surface and the attraction of ions of the electrolyte to the interface to balance it, build up specific layers of charge and accordingly a potential difference. Along with the above type of potential build-up due to physisorption, if the nature of solid electrode and the electrolyte allows, chemisorption of some species to the electrode surface can also influence the surface charge and shift the balance, thus resulting in a different interfacial potential. Eventually, the PZC is referred to a potential level that if applied externally to the electrode, all the original accumulated charge is neutralized and the surface charge density becomes zero or minimized. There is also a pH based representation of the PZC but only for systems in which H+/OH− are the potential-determining ions (and it is thus apparent that this representation is of more importance for those interested in chemisorption based alteration of surface potential).

According to above, it is seen that probable contributions of faradic and non-faradic reactions to PZC and OCP, respectively, has been disregarded. This becomes particularly important when a question like the one we are talking about now, arises.

If we assume that there are some factors affecting both, experimentally measured OCP and PZC (like surface chemistry and functional groups that I believe are not only affecting the PZC, but also the OCP), then a direct consequence of changing those factors (like the extent of surface functional groups, for instance, say increasing the degree of surface oxidation), will be the change of both OCP and PZC in a similar way.

I emphasize that I do not think I have meant under some certain conditions OCP and PZC can coincide. In fact, I believe such coincidence requires a material that possesses zero surface charge at its equilibrium conditions in an electrolyte (at its OCP) or in other words, does not show any double layer behavior. Therefore, the question is if OCP and PZC show any similarity in the way they change or can be changed by other parameters.

Please also keep the pH out of the discussion and instead use the equivalent potential or potential change just to avoid confusion and for keeping the potential as the only matter of concern here.

 Agree. pH is only applicable if H+/OH- are pdi species. Any ions that can be adsorbed on the electrode surface can also behave as pdi. See for example the article attached.

Question: Therefore, the question is if OCP and PZC show any similarity in the way they change or can be changed by other parameters.

Answer: Probably not because these are two different charging mechanisms that yield the same surface property of potential change. OCP by externally circuit (polarizable) and PZC (reversible) which acquires its surface charge via:  (1) specific adsorption, lattice substitution (crystal defect) and surface ionization processes (See Werner Stumm and James J. Morgan, Aquatic Chemistry: Chemical Equilibria and Rates in Natural Water, 3rd Ed. Johne Wiley, Chapter 9, especially from page 549-568.

Thanks Chin-Pao for helping with this.

In fact I am not sure if have understood well what you meant by "... two different charging mechanisms ... OCP by externally circuit (polarizable) ..." . I believe these two are not charging mechanisms, they are both just potentials each indicative of some charging mechanism.

Further, I do not think OCP has something to do with "externally circuit". Indeed, as its name suggest, it is measured when the external circuit is "open" and neither a potential nor a current can be applied externally to the system and the net current passing through the interface is also zero. 

And finally, I couldn't understand why should not we be able consider the surface charge caused by the surface functionalities as a contribution to OCP when we are measuring it simply via a three electrode st-up.

Thanks

The interface at the OCP conditions too has surface charges;

if you consider the interface as a perfect capacitor then charges come

now Q=C/V

In the case of ideally non polarisable interface electron transfer matters over charge

Prof. Muralidharan:

1. Agree that the term "mechanism" is not a proper term to describe the origin of surface charges. But this is a minor consideration.

2. OCP by your definition is the potential of standard EMF of a specific REDOX reaction. For examples, Fe3+ + e = Fe2+; Eo = 0.772 V vs.NHE.  At OCP =0.772 V, the activity of Fe3+ and Fe2+ in the solution is {Fe3+} = {Fe2+}. This is a typical Nernstian equation. I am not sure if OCP can be defined as such. I am thinking about OCP as one measurable at the electrode/electrolyte interface such as Hg/NaCl, Pt/NaCl etc that the OCP is established by polarization.

3. If OCP is established externally by polarization, then OCP and ZPC can be related to each other quantitatively by the principle of electroneutrality, that is: OCP + ZPC must always be equal to ZERO.

Can you explain OCP with some examples according to your definition?

Mr. Mazdak Hashempour, I have one question.

How does the molar concentration (eg. 0.1M and 1M of HClO4) of electrolyte shift the potential window of the double layer regime of gold electrode?

And one question that I would like to raise here is that how do you measure OCP and PZC?

to measure  OCP connect the WE  and RE to a high impedence voltmeter

to calculate PZC do a capacitane measurement at different applied voltages it should be purely Non faradic precess

thanks

thanks