The conductivity is known to be a characteristic parameter of bulk materials rather than surface materials.   If the surface layer  consists of  a  multi-monolayers, naturally, the surface layer would have conductivity.   In this case, the conductivity of the surface layer probably lower than the conductivity of the bulk materials of the substrate due to the present of porosity, surface defects, as so on.    

Trully, i have a similar opinion. Can this be supported by references for specific electrolytes?

Dear Dmitry

I knew for fact that the anodized surface layer of Al2O3 is a porous layer as compared to  the bulk substrate.   The Al2O3 has a lower conductivity than the substrate.  

It might be helpful,refer to the following:

K.Habib,” Measurement of surface resistivity and surface conductivity of anodised aluminium by optical interferometry techniques”, Optics and Laser Technology, Vol.44 (2012) 318-321.

Dear Dmitry,

As we know the role of the solid electrolyte is to conduct oxide ion (O2-) or proton ion from cathode to anode. So that 'the working distance b/w the electrodes can be minimized' if use the solid electrolyte as in the form of a thin film (ranging from 2 micron to 50 nm) rather than as bulk. Moreover, the low dimensionality (2D nanostructures) would be favorable for increasing homo interfaces (ie grain boundaries) through which the ionic transport can be enhanced in the nanocrystalline thin films.

Find attachments for the references. 

Hope this would help you. Good luck.

Thank you

Regards

S. Ajtih Kumar