The absolute sensitivity

The minimum number of spins detectable (Nmin) in EPR is:43

𝑁_𝑚𝑖𝑛= 12𝜋𝑉𝑐𝑘𝐵𝑇𝑠𝛤 𝜇₀𝑔2_𝜇 𝐵2𝑆(𝑆 + 1)𝐻𝑟𝑄𝑈( 𝐹𝑘_𝐵𝑇_𝑑𝑏 𝑃₀ ) 1/2 , (2.22)

where the symbols have the following meaning: Vc - volume of the cavity (TE102 mode

assumed), Γ - line width of the absorption line (half-width half-height), QU - effective

unloaded Q factor of the cavity, Fn - noise factor for sources other than thermal (Fn = 1 for

ideal spectrometer), Td - detector temperature, b - band width of the entire detecting and

amplifying system.

The Nmin equals ca. 1011 spins, when typical values are inserted to the equation, which

depending on the sample volume suggests concentrations of 1-10 nM. None the less, this

Figure 2.11. The sensitivity comparison between one loop one gap LGR (A) and TE102 cavity resonator for 0.1

mM of stable TEMPAMINE radical in aqueous solution in 0.4 mm ID sample tube. Due to the design of the LGR the effective length of the sample inside both of the resonators was the same, and the effective H1 field

48

approximation neglects several sample, resonator and spectrometer related variables and is more akin what EPR spectrometer manufacturers would report.

Equation 2.22 shows the complications related to quantitative investigations in EPR, as the signal is dependent on several parameters. The equation also omits several sample, resonator and EPR spectrometer settings related variables, which will be discussed in Chapter 4, and thus analytical measurements and the quantification of the absolute number of spins in EPR can be extremely challenging. This situation is further complicated by the insertion of the electrochemical cell into the resonator when in situ EC-EPR experiments are performed, a topic covered in the next section.

49

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