Overall Enhancement Equation for SERS

We will define SERS as the case where the major enhancement contributions come from EM effects and an adsorption-induced charge transfer (CT) resonances. In this case, the contribution to enhanced scattering of molecules not adsorbed on the metal surface should be small with respect to those in the first layer since, firstly, the EM enhancement factors are larger on the surface and, secondly, the charge transfer resonance can only occur at the surface, i.e., for a chemisorbed species. The CT polarizability can be 10 to 10 times larger than the NR polarizability. Accordingly, we write the SERS scattering intensity equation as 

In order to determine experimentally the enhancement produced by the surface effect, the enhanced scattering intensity is divided by the scattering intensity of molecules totally outside the enhancement range of the metal surface and the ratio normalized for the number of scattering molecules involved. For an electrode/solution interface with a nonoptically absorbing species, the SERS enhancement ratio, Gsers is 

Electrochemical techniques such as chronocoulometry, integrated cyclic voltammetry curves, or differentiating double-layer capacity measurements as a function of bulk concentrations can be used to estimate FA however, these types of determinations may still be in error since they measure the total number of surface species, while the number of molecules at active sites which exhibit both the EM and CT effects may be much smaller. Thus, the estimates of Gsers 10 to 10 found at pretreated Ag, for example, may err on the low side if special active sites are involved in SERS. It has been estimated that only 3% of the surface sites are SERS active.  

The experimental enhancement ratio, Gsers for the nonoptically absorbing molecules also can be expressed in terms of theoretically defined parameters  

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