J. Phys. Chem. C 2009, 113, 20467–20475
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Calibration Models under Dynamic Conditions for Determining Molecular Oxygen with Optical Sensors on the Basis of Luminescence Quenching of Transition-Metal Complexes Embedded in Polymeric Matrixes Denis Badocco, Andrea Mondin, Alberto Fusar, and Paolo Pastore* Department of Chemical Sciences, UniVersity of Padua, 1 Via Marzolo 1, 35131 Padua, Italy ReceiVed: June 29, 2009; ReVised Manuscript ReceiVed: September 25, 2009
Three oxygen-sensitive polysulfone-based membranes employing ruthenium tris(4,7-diphenyl-1,10-phenanthroline)octylsulfonate (Ru(dpp)OS), 5,10,15,20-tetraphenyl-21H,23H-porphyrin platinum(II) (PtTPP), and 5,10,15,20-tetrakis(pentafluorophenyl)-21H,23H-porphyrin palladium(II) (PdFTPP) were prepared and tested with different calibration approaches. The three luminescent labels were chosen for their different lifetimes giving the dimensionless Stern-Volmer (SV) constant, K′SV, of 0.0176(0.0001), 0.146(0.001), and 1.768(0.014) for Ru(dpp)OS, PtTPP, and PdFTPP, respectively. The usual SV calibration approach, model I, was compared to two alternative dynamic models on the basis of the light emission profile. Model II was based on the inflection point, and model III was based on a suitable integral of the light emission profile. Regression parameters were determined, and their physical meanings were explained with digital simulation techniques enlightening the nature of the chosen approaches. Sensitivity, precision, and working interval of the three membranes were studied. Model I fails for high oxygen percentage values, %O2 (depending on luminophore nature), while the other two work well in the whole 0-100 %O2 range. Model I works up to 98%, 50%, and 25% oxygen with Ru(dpp)OS, PtTPP, and PdFTPP, respectively. Model II is more sensitive than model I for %O2 < 60%, < 6%, and < 2% for Ru(dpp)OS, PtTPP, and PdFTPP membranes, respectively. Precision of model I is almost constant as foreseen for a linear model. Averaged experimental precision values of 3.5, 0.7, and 0.4% were found for Ru(dpp)OS, PtTPP, and PdFTPP, respectively. An averaged dimensionless kinetic constant valid for all membrane typologies was determined. It allowed the evaluation of the membrane thickness. Introduction Many papers have been published about the molecular oxygen determination by fluorescence quenching of suitable transition metal complexes embedded in various polymeric matrices. Luminophores commonly used are ruthenium phenanthrolines complexes (RuPhC)1-3 because of their long lifetimes and strong absorption in the blue-violet region of the spectrum, which is compatible with common high-brightness light-emitting diodes. Also, porphyrins4 have attracted much attention as promising materials because of their interesting properties as optoelectronic,5-8 electron transfer,9 catalysis,10 nonlinear optics,11 photodynamic therapy,12 and molecular semiconductors.13 Their metal complexes (MPoC) play a relevant role in biological processes including photosynthesis and respiration.14 MPhC and MPoC may be embedded in various polymeric materials including plastic polymers, sol-gels, and hybrids to obtain oxygen permeable sensors.1-3,15,16 Recent studies demonstrated the possibility to use MPoC as sensing probes for organic compounds.17,18 Dendritic compounds have been also reported because of their more intense emission and longer excited-state lifetime than nonmodified complexes.19,20 They are usually prepared as thin-layer membranes deposited onto suitable holders by spin- or dip-coating techniques. The use of the Langmuir-Blodgett (LB) deposition technique21 allowed also the preparation of compact and ordinate thin films for obtaining stereoselective sensors for application in food control.22-24 * To whom correspondence should be addressed. Phone: (+)39 49 8275182. Fax: (+)39 49 8275175. E-mail:
[email protected].
The Stern-Volmer (SV) equation is the general tool to monitor molecular oxygen by using fluorescence quenching, but its precision depends on the nature of the sensing membrane, that is, on the lifetime of the luminescent label together with the nature of the host polymer (permeability). The measured observables are the emission intensity and the luminophore lifetime which is usually determined by a mono- or multiexponential fitting15,25,26 or with distribution models applied to the quenching constant.27 Moreover, the SV calibration may be obtained with phase-shift measurements.28 Lifetime measurements usually give more accurate results; they are not influenced by signal drift, system geometry, or physical variations of the detection apparatus (temperature variation of the photodiodes, for instance), but they require more complicated instrumentation. On the other hand, light intensity measurement is simpler and may be useful to build simpler and cheaper oxygen sensors. All the cited methods are based on static measurement of luminescence, but, in this paper, we will demonstrate that useful information may be obtained under dynamic conditions recording the light emission profile on passing from pure nitrogen to a generic oxygen mixture. In particular, the usual SV calibration model (model I),29 based on the light intensity ratio, I0/I, will be compared to two other models. One model is based on the light emission profile and on its inflection point (model II); the other is based on a suitable integral of the light emission profile (model III). The three models will be used to monitor three polysulfone-based sensitive membranes employing ruthenium tris(4,7-diphenyl-1,10-phenanthroline)octylsulfonate (Ru(dpp)OS), 5,10,15,20-tetraphenyl-21H,23H-porphyrin platinum(II) (PtTPP), and 5,10,15,20-tetrakis(pentafluorophenyl)-21H,23H-
10.1021/jp906059m CCC: $40.75 2009 American Chemical Society Published on Web 11/02/2009
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TABLE 1: Membrane Preparation Parameters label concentration (µmol g-1 (PSF)) extraction velocity (cm min-1) support PSF concentration (g mL-1 (CHCl3)) immersion velocity (cm min-1) deposition under
Ru(dpp)OS PtTPP PdFTPP 20 5
20
10 1.5
glass 0.2 12 N2
working interval. In the present paper, we obtain two calibration models characterized by the regression parameters P1 and P2. These parameters are physically interpreted by considering the steady-state approximation applied to the excited species M* and by assuming the following kinetic scheme:
M + hν f M* M* f M + hν′
porphyrin palladium(II) (PdFTPP) whose excited states have quite different lifetimes.17,30 The chosen host matrix, polysulfone, is less used than polystyrene and ethyl cellulose, for instance, but it produced linear SV calibration for the three probes. This fact simplifies the mathematical description of the alternative calibration models developed in this work. Digital simulation will help to understand the nature of the physical constants defined in the model equations enlightening the meaning of the chosen approaches. Experimental Section Reagents. Platinum(II) chloride, 5,10,15,20-tetraphenyl21H,23H-porphyrin, ruthenium(III) chloride trihydrate (99.98%), 4,7-diphenyl-1,10-phenanthroline (dpp), sodium octylsulfonate (Na-OS), CHCl3 anhydrous g 99%, polysulfone (PSF) (d ) 1.24 g/L, MN: 16.000, MW: 35 000), and 5,10,15,20-tetrakis(pentafluorophenyl)-21H,23H- porphyrin palladium(II) were obtained from Aldrich Products. Ultrapure water was obtained with a Millipore Plus System (Milan, Italy, resistivity 18.2 MΩ cm-1). Ru(dpp)OS and PtTPP were synthesized according to a previously reported procedure.31,32 Procedures: Preparation of Oxygen-Sensitive Membranes. The PSF membranes investigated were prepared by dip-coating onto a glass support (10 × 30 × 1 mm) under nitrogen atmosphere. The substrates were previously washed with water and soap, were rinsed with water, were rinsed with isopropanol, and then were dried under nitrogen flow. The membranes were obtained by dissolving a suitable amount of the metal complex and PSF in 10 g of dry chloroform. The optimized conditions for the dip-coating deposition are reported in Table 1.33,34 After the chloroform had evaporated, membranes were dried at room temperature for 1 h. Membranes were tested at 25 °C. Instrumentation: Oxygen Optical Sensor. The oxygen sensor built in our laboratory was described elsewhere.35 Its excitation source is a Bivar LED5UV40030 high-brightness violet LED (angle 30°, spectral output peaks at 406 nm) or a high-brightness blue LED (Nichia, NSPE590, angle 15°) whose spectral output peaks at 464 nm. Light emitted by the membrane passed through a Kodak N°21 Wratten gelatin filter long wave pass gel filter (cutoff 570 nm) and focused onto a Hammamatsu S1223 photodiode detector (Hamamatsu, Middlesex, United Kingdom). Oxygen and nitrogen were mixed and flown via a homemade mass flow controller into the sensor cell. The signal output was directed to a LeCroy Wave Surfer 44xs, 450 MHz, oscilloscope (Geneva, Switzerland). Gas mixtures were prepared by mixing suitable amounts of nitrogen and oxygen. The exact composition was determined after mixing with a PBI Dansensor O2 analyzer (Milan, Italy). Results and Discussion This section is divided into two parts. In the first one, we derive the equations describing the calibration models II and III alternative to the SV model I; in the second one, the three models are compared in terms of sensitivity, precision, and
M* f M + heat M* + O2 f M + O2 In this scheme, hν and hν′ are the photon energies absorbed and emitted, respectively. Calibration Model II: Inflection Point Position of Emission Profiles. It is well-known29 that the SV calibration model I may be represented as
RI )
I0 - 1 ) P1 + P2 · %O2 I
(1)
In this model, the regression parameters P1 and P2 represent ′ values, respectively. The SV equation is a the 0 and the KSV general tool to monitor the molecular oxygen by using fluorescence quenching, but its precision depends on the nature of the sensing membrane, that is, on the lifetime of the luminescent label together with the nature of the host polymer (permeability). The equation describing the oxygen diffusion inside the polymeric membrane is the usual second Fick’s law. Here, it is written in terms of oxygen percent in a mixture, %O2(x, t), located at the spatial coordinate x along the membrane thickness and at temporal coordinate t:
∂%O2(x, t) ∂2%O2(x, t) ) DO2 · ∂t ∂x2
(2)
(DO2 is the oxygen diffusion coefficient). When oxygen comes out of the membrane, this differential equation has the following analytical solution:28,36
%O2(x, t) ) %O2 ·
[
∞
∑
( )]
4 1 -kn · t nπx · sin e π n)1 n 2L
(3)
%O2 represents the initial oxygen composition at equilibrium at 1 atm. It is homogeneous along the membrane of thickness, L. The constant kn is defined as
kn )
n 2 · π 2 D O2 · 2 4 L
(4)
In each infinitesimal membrane layer, dx, the luminescence quenching by %O2(x, t) is ∂I(x, t) so that, by means of the SV equation with ∂I0 ) I0 · dx/L, we obtain
∂I0 ′ · %O2(x, t) ) 1 + KSV ∂I(x, t)
(5)
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In integral form
kγ =
I(t) )
I0 · L
dx ∫0L 1 + KSV ′ · %O2(x, t)
(6)
I(t) ≈
I0 · L
∫0L
dx ′ · %O2 · 1 + KSV
4h -kt · t ·e π
) I0 ′
4h
(7)
1 + e-kt · t+ln(KSV · %O2 · π ) This equation represents a sigmoid which may be linearized as
(
ln
)
( 4hπ ) + ln(K′
γflex = ln
By assuming n ) 1 and sin((π · x)/(2 · L)) ) h in eq 3, and k1 ) kt, the integral (eq 6), after some handling, may be approximated to
I0 - 1 ) -kt · t + γflex ) -kγ · γ + γflex I(t)
(8)
with kγ and γflex ) kt · tflex slope and intercept, respectively. These two parameters are defined by approximated equations obtainable from eq 7
π2 = 2.47 4 SV · %O2)
(9)
(10)
The γflex parameter is the dimensionless time position of the sigmoid inflection point. The parameters in the right part of eq 8 are dimensionless through DO2/L2. The simple approximated eq 7 will be now verified by simulation. Figure 1a reports the I(t) profiles numerically obtained37 with ′ and switching from pure oxygen to pure nitrogen. various KSV In Figure 1b, the profiles of Figure 1a in logarithmic form are drawn (continuous line) together with their fittings (dotted lines) obtained with eq 8 versus the dimensionless time, γ (the model was applied in the 0.2 < γ < 2 interval). All regressions have determination coefficients equal to unity demonstrating the correctness of the linear model that is the correctness of the approximations to obtain eq 7 in the chosen interval. It is evident that the initial part of the simulated curves is not well fitted at ′ values. It is important to observe that all slopes are large KSV very similar indicating that (1) they are independent of K′SV and that (2) all the emission shapes are equal (they are only shifted). ′ . Its dependence is For this reason, γflex clearly depends on KSV ′ (Figure 1c, open circles), linear in the plot γflex versus pKSV and eq 11 represents the regression equation.
Figure 1. (a) Simulated dimensionless emission intensity of an optical oxygen sensor on passing from pure nitrogen to pure oxygen and back for ′ values; (b) ln ((I0)/(I) - 1) vs γ (continuous line) and linear fitting regression according to eq 7; (c) γflex and residuals vs pKSV ′ (linear fitting 15 KSV parameters of eq 11); (d) kγ vs pKSV ′ .
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′ (R2 ) 0.9994) γflex ) 3.863(0.022) - 2.116(0.013) · pKSV (11) This equation is equivalent to eq 10 for %O2 ) 100. The generalized form for all oxygen mixtures is the following where decimal logarithms are converted to natural.
′ · %O2) γflex ) -0.369 + 0.919 · ln(KSV
(12)
Model II may consequently be written as
γflex ) P1 + P2 · ln(%O2)
(13)
where P1 ) -0.369 + P2 · ln(KSV ′ ) and P2 ) 0.919. Contrary to model I, the calibration sensitivity is independent of the membrane nature as P2 is constant. P1 actually contains information about the membrane type; P2 is a constant indicating that transient emission profiles of all membranes have exactly the same shape. In other words, the transient profile is independent of the membrane nature. In Figure 1c, the residuals are also reported (black circles). Their values are low although not stochastic. We wrote above that the slopes, kγ, in Figure 1b were essentially equal. Figure 1d shows the variation of kγ with pK′SV. Its variation is between 2.17 and 2.37 with an average of jkγ ) 2.25(0.09). This value is close to that predicted by eq 9 (2.467). Under this limit, we may consider jkγ as independent of the used luminophore and of the membrane nature and structure. The knowledge of jkγ allows to determine, for instance, the membrane thickness by recording a single light emission profile and knowing the oxygen diffusion coefficient.
L=
jkγ DO2 · kt
L2 = L1
kt1
(15)
kt2
It must be evidenced that eqs 14 and 15 usually hold, in the absence of internal filter effect.34,36 In the present case, we verified the absence of the internal filter effect from intensity measurements recorded at various dye concentrations. Calibration Model III: Emission Areas. Figure 1a describes the simulated emission profiles associated to various KSV ′ values. Figure 2a represents the simulated emission profiles at constant KSV ′ values (KSV ′ ) 0.15) and for various %O2. The area, A, above the profiles for γ g 0 (the shaded area of curve 1 was drawn as an example) is related to the oxygen amount inside the membrane. In particular, considering the transition from oxygen mixtures to pure nitrogen we may write
A)
∫0∞
(I0 - I) · dγ I0
(16)
In Figure 2b, circles indicate the areas of all the simulated curves as a function of the %O2 in the mixture. As for model II, we derive the equation of the physical model associated to the observable “area”, A, to fit the data in Figure 2b. From eq 16 and eq 8, we obtain
A)
∫0∞
(I0 - I) · dγ ) I0
∫0∞
(
)
e-kγ · γ+γflex · dγ 1 + e-kγ · γ+γflex
(17)
(14)
The advantage of this approach with respect to the thickness measurement by VIS spectroscopy previously adopted34 is that, in this case, the molar extinction coefficient is not needed. The repeatability of the membrane thickness may be evaluated by comparing various membranes without the knowledge of DO2 according to
The solution of this integral is
A)
1 · ln(1 + eγflex) kγ
(18)
From eq 12, we obtain
Figure 2. (a) Fourteen emission profiles vs γ for KSV ′ ) 0.150 at various %O2. The shaded area, relative to curve 1, is reported as an example of the considered observable. (b) Areas obtained from simulated profiles (symbols) and fitting curve from eq 19. Regression characteristics: χ2/ν ) 3.3 × 10-6 and R2 ) 0.99997.
Models for Determining Molecular Oxygen
A)
1 ′ · %O2)0.92) · ln(1 + 0.69 · (KSV kγ
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(19)
The correctness of this model may be verified by fitting the areas obtained from simulated profiles with eq 19 using kγ and ′ as regression parameters and %O2 as the independent KSV ′ ) 0.158. The fitting is variable. We obtain kγ ) 2.19 and KSV very good as demonstrated by the continuous line in Figure 2b characterized by χ2/ν ) 3.3 × 10-6 and R2 ) 0.99997. The found kγ value is identical to the theoretical one obtainable from ′ ) 0.15. The KSV ′ value is 5% larger than Figure 1d with KSV the theoretical one. Model III eq 19 may be finally expressed as
A ) P1 · ln(1 + P2 · %O0.92 0 )
(20)
′ )0.92 are the In this equation, P1 ) (1)/(kγ) and P2 ) 0.69 · (KSV regression parameters for fitting the experimental data. In model III, the meaning of the parameters P1 and P2 is analogous to the P2 and P1 of model II, respectively. Comparison among Calibration Sensitivities of the Three Models. The aim of this paragraph is to compare the three models in terms of calibration sensitivities, Si. Sensitivity is the first derivative of the model equations with respect to %O2. Model I:
SRI )
| |
d(RI) ′ ) KSV d%O2
(21)
Model II:
Sγ )
| |
dγflex 0.919 ) d%O2 %O2
(22)
Figure 3. Comparison among the sensitivities, S, of the three models. Zone A: SRI > Sγ > SA; zone B: Sγ > SRI > SA. The three membranes are individuated by their pKSV ′ individuating three %O2 (squares) so that model I is more sensitive with Ru(dpp)OS for %O2 > 60, with PtTPP for %O2 > 6, and with PdFTPP for %O2 > 2. The plus symbol indicates %O2 ) 20 (air) where pKSV ′ ) 1.34.
In this case, sensitivity strongly depends on the membrane nature (KSV ′ ). The three sensitivities may be compared as follows. ′ · %O2 > 0.919, that is, for pKSV ′ < (a) SRI > Sγ is true for KSV log((%O2)/(0.919)) (b) Sγ > SA is always true ′ · %O2 > 1.2 · 10-7 (that is, (c) SRI > SA is true for KSV experimentally always true) In c, the inequality is always true as 1.2 · 10-7 implies to work ′ ) 0.01. The three with %O2 lower than 1.2 · 10-5 for KSV ′ ) log((%O2)/ comparisons may be visualized by plotting pKSV (0.919)) versus %O2 (Figure 3). This function, representing SRI ) Sγ, cuts the plane into zones A and B characterized by the following inequalities. Zone A:
SRI > Sγ > SA
Model III:
′ )0.92 · %O-0.08 0.63 · (KSV 2 dA SA ) ) d%O2 jkγ · (1 + 0.69 · (KSV ′ · %O2)0.92)
|
|
Zone B:
(23) The sensitivity of model I depends on the membrane characteristics. In particular, high sensitivity is associated to high KSV ′ value. On the contrary, in model II, Sγ is independent of membrane and luminophore nature. Moreover, it is inversely proportional to the oxygen concentration. In model III, SA depends on both KSV ′ and %O2. When KSV ′ · %O2 is sufficiently large, SA depends only on %O2.
SA =
0.919 jkγ · %O2
(24)
This fact implies that for large %O2 the calibration plot is independent of the used membrane and luminophore as for model II. At low %O2
′ )0.92 · %O-0.08 0.63 · (KSV 2 SA = jkγ
(25)
Sγ > SRI > SA Model I is more sensitive in zone A, and model II is more sensitive in zone B. The three membranes used in this paper are represented in Figure 3 with their pK′SV values, namely, pK′SV ′ = 0.8 for PtTPP, and pKSV ′ = 0.3 = 1.8 for Ru(dpp)OS, pKSV for PdFTPP (gray squares). The %O2 at which one method becomes more sensitive than the other is represented by the quoted %O2. In other words, we may say that sensitivity of model I is always greater than the other two for %O2 > 60 for Ru(dpp)OS, for %O2 > 6 for PtTPP, and for %O2 > 2 for PdFTPP. Consequently, if we have to work close to %O2 ) ′ > 20, it is better to use model II with membranes having pKSV 1.34 (Ru(dpp)OS for instance), while if we have membranes with pKSV ′ < 1.34, model I is preferable (porphyrins, for instance). Comparison among Precisions of the Three Models. In this paragraph, we will compute the %O2 measurement precision, s%O2, of the three models. Precision depends on the chosen model and on the precision of the experimental RI, γflex, and A parameters.
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Precision of Model I. In Model I, RI is a composed measurement ((I0/I) - 1), and its error, sRI ) s(I0/I)-1, may be estimated from the errors propagation assuming s ) sI0 ) sI.
sRI )
s · I
() 1+
I0 I
2
)
s ′ · %O2) · √1 + (1 + KSV ′ · %O2)2 (26) · (1 + KSV I0
This equation indicates that more precise measurements are obtained with low KSV ′ · %O2. For a given membrane (that is, ′ ), eq 26 indicates that the standard deviation of for a given KSV RI increases with the %O2 value so that the regression must be weighed with38
wi ) 1/sRI2
(27)
RI ) P1w + P2w · %O2
(28)
The model becomes
where P1w and P2w are intercept and slope of the weighed model, respectively. The precision is defined by38
(
sy/x,w 1 sxˆ0 ) · + P2w m · wxˆ0
1
∑ wi
+
(xˆ0 - jxw)2
∑ wi · (xi - jxw)2
)
1/2
(29)
where xˆ0 is the discriminated %O2 value; jxw is the mean value weighed on all the used %O2 levels; xi is the %O2 level of the ith measurement; sy/x,w is the standard deviation of the regression accounting for the weighed dispersion of the data; sxˆ0 ) s%O2 is the precision; and m is the RI measurement repetition number. Precision of Models II and III. The estimate of the sγflex relative to model II must be obtained from the experimental profile fitting procedure of the γflex parameter. The estimate of the sA relative to model III may be obtained only by repeating the measurement at the same %O2 value. Experimental Check of the Models. Experimental Emission Profiles. Figure 4 reports the experimental profiles obtained with the three membranes by varying the %O2 amount. All profiles were corrected for the background intensity, IB, and were normalized. The three used luminophores are characterized by quite different lifetimes so that the relevant membranes have ′ , and so the three models are compared different values of KSV in a wide KSV ′ range. Ru(dpp)OS (KSV ′ ) 0.0176) and PtTPP ′ ) 0.146) based membranes quench 62.9% (curve 11 in (KSV Figure 4a) and 96.1% (curve 15 in Figure 4b) of emitted light, respectively, when saturated with %O2 ) 100. PdFTPP exhibits ′ ) 1.77). Light emission is much higher sensitivity (KSV completely quenched with %O2 g 20 (Figure 4c), and %O2 ) 0.7 lowers light emission by 54.1%. Experimental Application of Model I. In Figure 5, the usual SV calibration mode is reported (model I). All data in the plot were corrected for IB and were normalized before applying the weighed fitting. An F-test on the regression variance (sy/x) determined outlayers (circled data in Figure 5). Ru(dpp)OS exhibits only one outlayer for %O2 ) 98. PtTPP exhibits outlayer data for %O2 > 50. PdFTPP exhibits outlayers for %O2
Figure 4. Experimental, normalized emission profiles vs %O2 for Ru(dpp)OS (a), PtTPP (b), and PdFTPP (c). Data were corrected for IB. For the Ru(dpp)OS membrane, %O2 ) 5.6,10.4, 19.5, 27.8, 40.3, 48.7, 59.5, 70.7, 80.3, 90.5, 98.4. For the PtTPP membrane, %O2 ) 0.7, 1.2, 1.6, 2.5, 3.5, 5.1, 7.4, 9.9, 14.8, 20.0, 30.8, 40.0, 49.7, 74.7, 100.0. For the PdFTPP membrane, %O2 ) 0.7, 0.9, 1.1, 1.5, 2.0, 3.0, 4.0, 5.0, 7.4, 9.9, 20.2, 34.8, 50.1, 76.0, 100.0.
> 25 (data outside the plot area). Other authors obtained wider intervals by using more sophisticated instrumentation.39 The weight (w) associated to the various %O2 values must be computed with the errors propagation law knowing sRI and assuming s ) sI0 ) sI ) sIB.
√2 · s sRI ) · I - IB
( ) 1+
I0 - IB I - IB
2
(30)
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J. Phys. Chem. C, Vol. 113, No. 47, 2009 20473 independent of the nature of the membrane as expected. Moreover, they are close to the theoretical value of 0.919. The difference is due both to experimental errors and to the linear approximation adopted in the theoretical model. The estimate of KSV ′ may be obtained from the already discussed P1w ≈ -0.369 + P2w · ln(K′SV). We obtain K′SV ) 0.018, 0.135, and 1.85 for Ru(dpp)OS, PtTPP, and PdFTPP, respectively. These values are very close to that obtained with model I so that we may conclude that we correctly interpreted the physical nature of the parameters P1w and P2w. Figure 6a indicates that curve shapes are equal and that they are only shifted owing to the different pKSV ′ values, therefore,
′ ∆P1w ≈ -2.116 · ∆pKSV
Figure 5. Weighed parametric regressions with prediction bands for Ru(dpp)OS (O), PtTPP (0), and PdFTPP (4) membranes. Statistical data are in Table 1. Circled data are outlayers.
(31)
As the curve shape is independent of the luminophore and polymer nature, the most suitable sensing membrane will be prepared for the chosen application. Figure 6b reports the curve fitting of the PdFTPP membrane as an example. The regression quality is very good as indicated by the fitting parameters (R2 g 0.99998 and χ2/ν e 4.36 · 10-6). The first-order kinetic rate constant values are 0.110(0.0013) s-1, 0.397(0.017) s-1, and 0.351(0.010) s-1 for Ru(dpp)OS, PtTPP, and PdFTPP, respectively. The low standard deviation found indicated that these rate constants are typical of the membrane. If all the membranes have the same permeability, it is possible to obtain the ratio of the membrane thickness
The weighed regression parameters are reported in Table 2. On the basis of the outlayer data, the working intervals are %O2 ) 98, 50, and 25 for Ru(dpp)OS, PtTPP, and PdFTPP, respectively. Experimental Application of Model II. Figure 6a represents γflex versus %O2. The γflex values are obtained from the experimental emission profile curve fitting of the three membranes through eq 13. Prediction bands are also reported. The great advantage of this model with respect to model I is that all data points lay inside the prediction bands so that it is very stable in the whole 0-100%O2 range. It is independent of the ′ . The luminophore nature as calibration is independent of KSV P2w values reported in Table 3 are similar so that they are
TABLE 2: Statistical Data of the Weighed Parametric Regressions of the Three Membranes label
regression model
P1w
sP1w
P2w
sP2w
F-testa
R2
Ru(dpp)OS PtTPP PdFTPP
RI ) P1w + P2w · %O2
0.0004 0.0001 0.063
0.0004 0.001 0.073
0.0176 0.146 1.768
0.0001 0.001 0.014
10/11 12/15 11/15
0.9990 0.9994 0.9995
a
The F-test column reports the nonoutlayer data used for regression.
Figure 6. (a) Parametric regressions with prediction bands obtained with model II for Ru(dpp)OS (O), PtTPP (0), and PdFTPP (4). Regression parameters are reported in Table 2. (b) Fitted profiles (bold line) overlapped the experimental data of PdFTPP.
TABLE 3: Regression Parameters of Model IIIa
a
label
regression model
P1w
sP1w
P2w
sP2w
R2
Ru(dpp)OS PtTPP PdFTPP
γflex ) P1w + P2w · ln(%O2)
-3.80 -2.15 0.13
0.04 0.03 0.03
0.86 0.89 0.85
0.03 0.03 0.03
0.9990 0.9993 0.9991
See Figure 6a.
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LRu ) LPtTPP
kPtTPP ) kRu
0.397 ) 1.9 0.110
Badocco et al.
(32)
The absolute thickness may be obtained with eq 14 knowing the oxygen diffusion coefficient (4.04 · 10-8 cm2 s-1).40 Our Ru(dpp)OS, PtTPP, and PdFTPP membranes have thicknesses of 6.4(0.3), 3.4(0.3), and 3.6(0.3) µm, respectively. Membranes produced with the same dip-coating conditions have statistically identical thickness demonstrating the robustness of the preparation procedure. Experimental Application of Model III. Figure 7a represents A versus %O2. The A values were obtained from the integral of the experimental emission profile of the three membranes (eq 16 with time in seconds). Regression curves were obtained with eq 19, and their statistical parameters are reported in Table 4. From eq 19, in dimensional form, we may write P1 ) 1/kt. The obtained kt values are 0.17(0.01), 0.38(0.01), and 0.34(0.01) for Ru(dpp)OS, PtTPP, and PdFTPP, respectively, and they are comparable to those obtained with model II. The F-test did not evidence any outlayers so that, as in model II, we have the ′ values advantage to discriminate also large %O2. The KSV derived from P2 are 0.04(0.01), 0.17(0.01), and 2.2(0.1) for Ru(dpp)OS, PtTPP, and PdFTPP, respectively. They are of the same order of magnitude as those computed with model I and are slightly larger than the reference values owing to the approximated eq 19. For a practical use, model III, expressed in eq 19, may be simplified as follows
A ) P1 · ln(1 + P2 · %O2)
(33)
Comparison among Precisions of the Experimental Models. Figure 8 reports the experimental precision s%O2versus %O2 of the three calibration models applied to the three membranes. The precision of model I is almost constant as foreseen by a linear model. The Ru(dpp)OS membrane precision shows a slight increase. Averaged experimental precision values of 3.5, 0.7, and 0.4% were found for Ru(dpp)Os, PtTPP, and PdFTPP,
respectively, so that precisions improve by increasing the calibration sensitivity. A very precise membrane works in a narrower working range. The oblique segments reported in Figure 8 indicate the upper %O2 calibration limits. Models II and III have increasing s%O2values with %O2 as expected. On the basis of the working interval, models II and III are preferable because they span the whole 0-100%O2 interval. Moreover, at low oxygen concentration, they are always more precise than model I. On the other hand, model I is more precise for very sensitive membranes such as the porphyrin-based ones at %O2 g 10 for PtTPP and %O2 g 6 for PdFTPP as foreseen by the inversion of calibration sensitivity described in Figure 3. ′ We have to distinguish two cases: (1) low and (2) large KSV values. ′ values, models II and III are always better (1) At low KSV than model I in the whole 0-100 %O2 interval (see Figure 8a relative to the Ru based luminophore). ′ values, models II and III are always better (2) At large KSV than model I at low %O2 values and are the worst for large concentration (see Figure 8b and c relative to the Pd and Pt-based luminophores). Anyway, model I cannot work at large oxygen concentrations owing to lack of sensitivity. Conclusions Two calibration approaches, alternative to the SV one, for the determination of gaseous molecular oxygen with optical polysulfone-based sensors, employing Ru(dpp)OS, PtTPP, and PdFTPP, were presented. Both approaches are dynamic and are based on the light emission profile produced by a variation of oxygen concentration through the sensing layer. One is based on the emission profile inflection point (model II: γflex = P1 + P2 · ln(%O2)); the other is based on a suitable integral of the light emission profile (model III: A ) P1 · ln(1 + P2 · %O20.92)). The comparison with the classical SV calibration approach (model I) was done in terms of calibration sensitivity, precision, and %O2 working interval. Calibration sensitivities are in the sequence model I > model II > model III or model II > model I > model III depending on
Figure 7. (a) Parametric regressions with prediction bands obtained with model III for Ru(dpp)OS (O), PtTPP (0), and PdFTPP (4); A ) (kjγ · Aex)/ P1. Regression parameters are reported in Table 3. (b) Profiles in terms of 1 - I(t)/I0 relative to the experimental data of PdFTPP.
TABLE 4: Regression Parameters of Model III label Ru(dpp)OS
PtTPP PdFTPP
regression model
A ) P1 · ln(1 + P2 · %O0.92 0 )
P1
sP 1
P2
s P2
R2
5.88
0.31
0.038
0.003
0.999
2.63 2.99
0.08 0.05
0.136 1.459
0.009 0.071
0.999 0.999
Models for Determining Molecular Oxygen
J. Phys. Chem. C, Vol. 113, No. 47, 2009 20475 mathematical form than the SV one but have demonstrated more robustness and more precision in a wider concentration interval. Acknowledgment. We gratefully acknowledge the CLR s.r.l. (Rodano-Milan, Italy) for funding this research. References and Notes
Figure 8. Precisions, s%O2, vs %O2 obtained with calibration models I-III. Membrane: (a) Ru(dpp)OS, (b) PtTPP, and (c) PdFTPP.
the luminophore nature and on the %O2 value. Model II is more sensitive than model I for %O2 < 60, < 6, and < 2, for Ru(dpp)OS, PtTPP, and PdFTPP membranes, respectively. Concerning precision, models II and III are preferable than the classic model I at low %O2 values which exhibits averaged experimental precisions of 3.5, 0.7, and 0.4% for Ru(dpp)OS, PtTPP, and PdFTPP, respectively. Model I works well up to %O2 ) 98, 50, and 25 with Ru(dpp)OS, PtTPP, and PdFTPP, respectively. The other two models work in the whole 0-100% interval. A dimensionless kinetic constant, jkγ ) 2.25(0.09), valid for all membrane typologies was determined. It allowed the evaluation of the membrane thickness. A disadvantage of models II and III is that the complete emission profile is required. On the basis of the simplified kinetic model, the regression parameters of the two proposed models have been correlated by the SV constant. The two models have a more complicated
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