Quanta-
φ
rev. C (23 Apr 2010)
Theory of Operation
1-7
For the example given above for rhodamine 101 (
υ
= 93.01%),
σ
rel
= 0.007 and
σ
abs
=
0.654 %.
Consider that:
These values can be used to diagnose trends in the precision and accuracy of
, es-
pecially when evaluated under conditions where the sample concentration or quan-
tum efficiency is being systematically varied. An example is with a quenching ex-
periment or when titrating the sample concentration to minimize reabsorption (inner
filter) effects.
The error-propagation routine is normalized to the
L
a
and
L
c
integration conditions
as a general rule. This is because the
E
a
and
E
c
values (which are typically less in-
tense) are normally collected under conditions of longer integration time or higher
excitation power so that these values must be divided by a constant factor in the eq-
uation for
υ
.
The largest absolute source of error in the
υ
measurement is likely to be in the larg-
er
L
a
and
L
c
values. Therefore HORIBA Scientific recommends that you carefully
consider the required integration time and excitation-power conditions for the
E
a
and
E
c
values to prevent the larger noise-levels in
L
a
and
L
c
from ―swamping out‖
the smaller fluorescence area signal value.
This is a particularly important prob-
lem with the ratiometric nature of the
equation, because the larger source of
error is in the denominator.
Self-absorption and inner-filter effects
The measurement of
υ
, as an absolute value, is strongly influenced by the sample con-
centration. Relative changes and observed values of
υ
can be easily complicated by
concentration-related artifacts. Because
υ
is determined by the number of photons ab-
sorbed, the concentration must be measured under the ―Beer-Lambert‖ criterion of a li-
near relationship between OD and sample concentration.
One important effect of increasing sample concentration is ―self-absorption‖, a depres-
sion in the bluer edge of the emission spectral region, where it overlaps with the redder
edge of the excitation or absorbance spectrum.
HORIBA Scientific recommends the following practical considerations to avoid self-
absorption:
Adjust the sample concentration so that, when plotting absorption (A) or optical
density (OD) against concentration, a linear plot appears. Generally this occurs at
the
λ
peak
when OD < 0.1, and better around 0.05.
When possible, make multiple measurements while varying the sample concentra-
tion (OD), to determine if (and when) observed
υ
and
E
c
area fall in a linear region
when plotted against sample concentration or OD.
Plot the ―normalized‖
E
c
spectral areas, and evaluate their integrated areas relative
to the sample OD, to determine if the blue edges are depressed in a manner syste-
matically related to the OD. For compounds with
υ
< 100%, and narrow Stokes
shifts between the excitation spectrum and emission spectrum, the relative areas
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