Analytical Chemistry Chemical Cytometry Quantitates Superoxide

Figure 6. The average measured response time, τmeas, is independent
of the volume fraction of absorbed analyte, φ, and thus the
analyte activity. This response time, however, is strongly analyte
dependent, enabling discrimination between analytes having nearly
identical chemical affinities such as toluene and undecane. At low
concentrations (where the slope of the response curve is low) and
for long response times, sensor drift becomes an issue and response
times are difficult to reliably measure; such is the case for low
concentrations of undecane.
variations, we normalized the response time of each sensor to
agree with that of an arbitrarily chosen reference sensor, by
exposing the sensors to a mesitylene activity of 0.058, which
resulted in a swelling of 0.005. These renormalized time scales
were then used to determine both the average response time
to an analyte and the associated measurement error in terms
of the standard deviation. The dimensionless correction factors
ranged from 0.6 to 1.3.
To determine if it is a reasonable assumption that the variation
in the measured response time is caused by variations in sensor
thickness, we made 10 chemiresistors on a glass slide using
methods and materials identical to those for the originals. Sensor
thickness measurements, made with a Nikon mm-800 measuring
microscope with a quadra-chek 200 advanced digital readout
system, give a sensor thickness of 216 ± 26 µm. The average
response time, τ meas, of the original five sensors to mesitylene
at an activity of 0.058 was 48 ± 13 s. Using this average response
time and the average composite thickness of the newly made
sensors (i.e., 216 µm), we calculate a measured diffusion
coefficient of 4.5 × 10 -2 cm 2 /s. From this diffusion coefficient
we computed the predicted response times for the 10 new
sensors, yielding 48 ± 8 s. Therefore, the variation in response
times that we measured for the original sensors is similar to
the variation in response time that we predict from the newly
made sensors. It should be noted that this measured diffusion
coefficient is not a true diffusion coefficient because it is
calculated from τmeas, which is a convolution of the actual
diffusion time scale and the time scale from the flow cell fill
time as we will discuss in the following section.
An accurate determination of the sorption kinetics ideally
requires that the flow cell fill time is fast compared to the sorption
kinetics. In the following we will determine this fill time from the
measured sorption kinetics and use this value to extract the true
sorption kinetics from the measured values. The true sorption
time can then be compared to the flow cell fill time to determine
whether this fast fill time condition is met in our experiments.
Flow Cell Fill Time. After the inlet stream starts to deliver
an analyte of fixed activity to the flow cell, the analyte activity
rises continuously, due to the finite volume of pure nitrogen that
must be displaced. The transient analyte activity can be obtained
by modeling the flow cell as a continuously stirred tank and is of
the form
a(t) ) a ∞ (1 - e -t/τf ) (8a)
In terms of the volume fraction of the vapor this is
φ vap (t) ) φ vap (∞)(1 - e -t/τf ) (8b)
The characteristic time for the flow cell to reach a steady-state
concentration is given by τf ) Vf/F, where Vf is the volume of
the flow cell and F is the volumetric flow rate of nitrogen from
the inlet stream.
Convolution of Time Scales. The measured composite
swelling in Figure 4 is a convolution of the increase in the analyte
vapor activity in the flow cell and the diffusive kinetics, which for
simplicity we take to be of the form φ(t) ) φ∞(1 - e -t/τ d) for a
step increase in the analyte activity at t ) 0. Using eq 5, the
expression is
t dφvap (t)
φ(t) ) K∫ 0
t)s dt [1 - e-(t-s)/τd ]ds (9)
Using eq 8a to evaluate the derivative gives
φ(t) ) Kφvap (∞) t
τ ∫ e
0
f
-s/τf -(t-s)/τd [1 - e ]ds (10)
A straightforward integration leads to the final expression for the
sorption kinetics”
φ(t) ) Aφvap (∞)[ 1 - τd e
τd - τf -t/τd +
τ f
e
τd - τf -t/τf]
(11)
The measured lifetime can then be computed from this equation,
and the surprisingly simple result is
τmeas ) 1 ∞
φ ∫ [1 - φ(t)] dt ) τ
0
d + τf ∞
(12)
The true diffusion time can thus be obtained from the measured
time by τd ) τmeas s τf. (The case where τd = τf leads to division
by zero in eq 11. This division looks troublesome, but can be
handled by defining τd ) τf(1 + ε) and carefully taking the limit
as ε f 0.)
Corrected Sorption Times. The correction of the measured
sorption times for the flow cell fill time requires a determination
of the fill time. The fill time can be extracted from the measured
sorption times themselves, through a limiting process, as we will
now describe. To obtain accurate measured sorption times, we
first average these measured times over all analyte activities to
obtain a mean response time we call τjmeas. This averaging is valid,
because the measured sorption time is independent of the
Analytical Chemistry, Vol. 82, No. 16, August 15, 2010
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