Analytical Chemistry Chemical Cytometry Quantitates Superoxide
Analytical Chemistry Chemical Cytometry Quantitates Superoxide
Analytical Chemistry Chemical Cytometry Quantitates Superoxide
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Figure 4. The volume fraction of absorbed analyte, φ, approaches<br />
its asymptotic value exponentially upon exposure to an analyte, in<br />
this case p-xylene vapors, at an activity of 0.054.<br />
Figure 5. The measured characteristic response time, τmeas, isthe<br />
y intercept of the line obtained by plotting A ) ∫0 t ∆φ(s)/φ∞ ds as a<br />
function of B ) ∆φ(t) ) φ∞ - φ(t).<br />
is a mathematically complex problem, but for practical purposes<br />
the kinetic data can be fit by the simple exponential expression<br />
φ(t) ) φ ∞ (1 - e -t/τmeas ) (5)<br />
Here t is time and τmeas is the measured response time of the<br />
chemiresistor to the analyte in question. Fitting to this form<br />
will prove useful in correcting the observed kinetic data for<br />
the time it takes for the analyte concentration to reach the<br />
steady state in the flow cell. Despite this, we can actually obtain<br />
the response time in a model-independent fashion. To do so,<br />
we simply plot the integral A ) ∫0 t ∆φ(s)/φ∞ ds against B )<br />
∆φ(t)/φ∞, where ∆φ(t) ≡ φ∞ - φ(t). We can operationally define<br />
τmeas as the y intercept of this curve in the limit as ∆φ(t) f 0,<br />
but if eq 5 is a reasonable fit, the result will be a straight line<br />
whose y intercept is easily obtained. The data in Figures 5 are<br />
indeed linear, so eq 5 is actually quite a good description of the<br />
raw kinetic data.<br />
RESULTS<br />
In the following we give the theoretical expression for the true<br />
sorption kinetics, which is shown to be independent of the analyte<br />
activity. We then develop an expression for the measured sorption<br />
kinetics, which is a convolution of the true sorption kinetics and<br />
the kinetics of filling the flow cell. We then show how the flow<br />
cell fill kinetics can be determined from the measured sorption<br />
kinetics and how the fill time can be used to extract the true<br />
6972 <strong>Analytical</strong> <strong>Chemistry</strong>, Vol. 82, No. 16, August 15, 2010<br />
sorption time from the measured time. Both the measured and<br />
true sorption kinetics are shown to be independent of the activity,<br />
but strongly dependent on the analyte saturation vapor pressure.<br />
Predicted Sorption Time. From Raoult’s law, the partial<br />
pressure of a chemical species, P, in a gas is equal to its volume<br />
fraction, φ vap, times the total pressure, or φvap ≡ V/Vtot ) P/Ptot.<br />
Recall that the analyte activity is a ) P/P*; therefore, a ) φvap/<br />
φvap*, where φvap* is the volume fraction of analyte vapor at<br />
saturation. From the linearized form of the Flory-Huggins<br />
equation (eq 3), φ ) a/e 1+� , the partition coefficient, K, is then<br />
K ≡ φ 1<br />
)<br />
φvap φvap *e 1+�<br />
At high inlet stream fluxes the response time of an FSCR is<br />
diffusion limited, and from Fick’s second law of diffusion for the<br />
case of a semi-infinite slab, the sensor’s response time can be<br />
expressed as<br />
τd ∝ K d2 1<br />
)<br />
Dt Dtφvap *e 1+�d2<br />
(6)<br />
(7a)<br />
where d is the thickness of the composite and Dt is the diffusion<br />
coefficient of the analyte into the silicone. Note that even for<br />
analytes of identical chemical affinity there is discrimination<br />
based on sorption kinetics, due to variations in their diffusivity<br />
and saturation volume fraction. From the ideal gas law, the<br />
saturation vapor pressure is given by P* )Fφvap*RT/Mw, so<br />
the sorption time can also be written as<br />
τ d ∝ RT<br />
P*<br />
F<br />
M w D t e 1+�d2<br />
(7b)<br />
The saturation vapor pressure varies over a wide range, so the<br />
sorption kinetics should be a very useful method of discrimination.<br />
Measured Sorption Time. The goal is to determine the true<br />
sorption time, including any dependence this time might have on<br />
the analyte activity. Unfortunately, the measured sorption time is<br />
a convolution of two factors: the time it takes for the analyte<br />
activity in the flow cell to reach its steady-state value (flow cell<br />
fill time) and the true mass sorption time. In a constant-flow-rate<br />
apparatus, and for any particular analyte, neither of these factors<br />
should be dependent on the analyte activity, so the measured<br />
sorption time should be independent of the analyte activity. The<br />
data in Figure 6 show that this is indeed the case and also show<br />
significant differences in the sorption kinetics for different analytes,<br />
as expected. At low concentrations (where the slope of the<br />
response curve is low) and for long response times, sensor drift<br />
becomes an issue and response times are difficult to reliably<br />
measure; such is the case for low concentrations of undecane.<br />
This issue, however, can be addressed by using a sensor with<br />
high sensitivity at low analyte concentrations. 23<br />
The data in Figure 6 are an average for five sensors, each<br />
tested simultaneously in the same flow cell. Because of sensorto-sensor<br />
variations in polymer thickness, each chemiresistor had<br />
a somewhat different response time. For example, the five sensors<br />
exposed to mesitylene at an activity of 0.058 have an average<br />
response time, τmeas,of48± 13 s. To account for these thickness