Warning !

Soas is no longer maintained. You are strongly encouraged to switch to its successor, QSoas

Principle

As an alternative to a simple linear baseline, usually guided by a part of the sweep where the faradaic current is zero (the $ i=0$ range), I provide here a simple non-linear baseline, guided by both the $ i=0$ range and by a part of the sweep where the faradaic current has reached a limiting value (the $ i=i_{\rm lim}$ range), as illustrated in Figure [*]. Note that if a ``swichy'' voltammogram is analyzed, the limiting current is that of the plateau, not the maximal (peak) current[4].

In Figure [*]A, each pair of squares defines an interval, one in the $ i=0$ region, and the other in the $ i=i_{\rm lim}$ part of the voltammogram (empty and filled symbols, subscripts $ 1$ and $ 2$, respectively). For both ranges, the average potentials $ x_j$, $ j=0$ or $ {\rm lim}$, currents $ y_j$ and slopes $ \partial y/\partial x\vert _{x=x_j}=y'_j$ are measured.

In the range $ x_0>x>x_{\rm lim}$, a second order polynomial baseline ( $ y=ax^2+bx+c$) is calculated so that (i) it goes through the points of coordinates ($ x_0,y_0$) and ( $ x_{\rm lim},y_{\rm lim}-i_{\rm
lim}$), and (ii) its slopes at these positions ($ 2ax_j+b$) match the values of $ y'_j$. $ a$, $ b$, and $ c$, which define the polynomial baseline, and $ i_{\rm lim}$, are therefore the unique solution of the linear set of equations:

\begin{equation*}\left [\begin {array}{cccc} x_0^2 & x_0 & 1 & 0  \noalign{\me...
...p } y'_0  \noalign{\medskip } y'_{\rm lim} \end {array}\right ]\end{equation*} (1)

$ a=(y'_{\rm lim}-y'_0)/[2(x_{\rm lim}-x_0)]$, $ b=(x_{\rm lim}y'_0-x_0y'_{\rm lim})/(x_{\rm lim}-x_0)$, $ c=[x_0^2(y'_0+y'_{\rm lim})+2y_0(x_{\rm lim}-x_0)-2x_0x_{\rm lim}y'_0]/[2(x_{\rm lim}-x_0)]$, $ i_{\rm lim}= (x_0-x_{\rm lim})(y'_0-y'_{\rm lim})/2+y_{\rm lim}-y_0$.

In the ranges $ x>x_0$ and $ x<x_{\rm lim}$, the baseline is linearly extrapolated.



Warning !

Soas is no longer maintained. You are strongly encouraged to switch to its successor, QSoas
Christophe Leger 2009-02-24