Chemistry Reference
In-Depth Information
chromatogram is difficult. Its disadvantage is that the differentiation degrades the signal-to-noise ratio, so that
some form of smoothing is required in conjunction with differentiation [3].
13.1.1 Theoretical aspects
13.1.1.1
Basic properties of derivative spectra
For a single-peak spectrum, the first-derivative is a plot of the gradient dS/d
(S being absorbance or
fluorescence or another type of signal) envelope versus wavelength and features a maximum and a
minimum; the vertical distance between these is the amplitude, which is proportional to the analyte
concentrations; theoretically, dS/d
λ
λ
is zero at
λ
max
for the band in the normal spectrum. The second-
derivative spectrum, d
2
S/d
λ
max
of the normal
absorption (or emission) band [4]. In principle, both peak heights (measured from d
2
A/d
λ
2
vs.
λ
, has two maxima with a minimum between them, at
0) are
proportional to the analyte concentration but the amplitude can also be measured by the so-called tangents
method, in which a tangent is drawn to the maxima and the amplitude is measured vertically from the
tangent to the minimum [5]. Other possibilities have been considered [6], and background absorbance of
fluorescence cam be eliminated.
The differentiation discriminates against broad bands, emphasizing sharper features to an extent that
increases with increasing derivative order, because for bands (Gaussian or Lorentzian) the amplitude D
n
of
the n-th derivative is related to the n-th power of the inverse of the band-width, w, of the normal spectrum [7]:
λ
2
=
n
1
⎛⎞
D
∝
⎜
⎝⎠
Thus, for two bands A and B of equal absorbance but different width, the derivative amplitude of the sharper
band (A, for example) is greater than that of the broader (B) by a factor that increases with increasing
derivative order [8,9]:
n
D
w
Dw
⎛⎞
∝
⎜
⎝⎠
nA
,
B
nB
,
A
For this reason, the use of derivative spectra can increase the detection sensitivity [10,11] of minor spectral
features.
For quantitative analysis in UV-visible spectrophotometry, if Beer's law is obeyed for the normal spectrum,
the following equation can be obtained:
n
n
dy
d
ε
=
..
lc
n
n
d
λ
d
λ
where A
=
absorbance,
ε
=
molar absorptivity, l
=
cell path-length and c
=
concentration of the analyte, and
this form the basis of analytical determinations [12].
