Influence of the Real Background Signal on the Linearity of the Stern-Volmer Calibrationfor the Determination of Molecular Oxygen with Optical Sensors

Denis Badocco, Andrea Mondin, Alberto Fusar, Gabriella Favaro, and Paolo Pastore*Department of Chemical Sciences, UniVersity of Padua, Via Marzolo 1, 35131 Padua, Italy

ReceiVed: May 29, 2009; ReVised Manuscript ReceiVed: July 15, 2009

The role of light emission components unrelated to the Stern-Volmer (SV) kinetic model, in the curvatureof the Stern-Volmer model, was evidenced and the discrepancy often encountered between calibrations withlight intensity, I, and luminescence lifetime,τ, was explained by means of mathematical models applied toexperimental data. Sensing membranes prepared embedding tris-4,7-diphenyl-1,10-phenanthroline (Ru(dpp)),platinum(II) meso-tetraphenylporphyrin (PtTPP), and palladium(II) meso-tetra(pentafluorophenyl)porphyrin(PdFTPP) in a polysulfone matrix were used to confirm the proposed theory. Multisite hypotheses or othercorrection procedures must be invoked only after a careful evaluation of the background light really presentin the system. A new form of the SV equation having the advantage to obtain the K′SV and the effectivebackground with a simple unweighted regression method was proposed and compared to the “classical” SVrequiring the knowledge of the background and a weighted regression. Experimental results confirmed thetheory for what concerns the concentration limit for the determination of oxygen which may be theoreticallydetermined. Ru(dpp)OS, PtTPP, and PdFTPP membranes may determine oxygen mixtures up to 100, 60.7,and 19.0%, respectively, with a resolution of 2%. Narrower working intervals are explorable if better resolutionis required.

Introduction

Oxygen optical sensors are more and more attractive thanconventional amperometric devices, because, in general, they havea faster response time, they do not consume oxygen, and they areless easily poisonable.1 Thin films containing oxygen-sensitiveluminophores are widely used as in pressure-sensitive paintsbecause of their high sensitivity.2,3 Sensor operation is usually basedon the quenching of luminescence in the presence of oxygen.Luminophores commonly used are transition metal complex likeruthenium phenanthrolines4-6 and metal porphyrins (MP)7 becauseof their long lifetimes and strong absorption in the blue-violet regionof the spectrum, which is compatible with common high-brightnesslight-emitting diodes. These transition metal complexes are usuallyembedded in various polymeric matrices prepared as thin layermembranes deposited onto suitable holders by spin- or dip-coatingtechniques. The use of the Langmuir-Blodgett deposition tech-nique8 allowed also the preparation of compact and ordinate thinfilms for obtaining stereoselective sensors for application in foodcontrol.9-11 The oxygen-quenching process is described by theStern-Volmer equations:

and

where I and τ are the fluorescence intensity and excited-statelifetime of the fluorophore, respectively. I0 and τ0 denote the

absence of oxygen, K′SV the Stern-Volmer constant and %O2 theoxygen percent. The oxygen amount may be determined bymeasuring either the emission intensity12 or the lifetime of theluminophore. Lifetimes can be determined from the decay curve13

or by phase-modulation measurements.14 Lifetime measurementsare more accurate; they are not influenced by signal drift but requiremore complicated instrumentation and measurements. On the otherhand, light intensity measurement is simpler and may be useful tobuild simpler and cheaper oxygen sensors. One of the aspects notyet completely understood is the nonlinearity of the SV calibrationexperimentally encountered in many cases.15 Some authors ex-plained this behavior with a multisite emitting model, either 2- and3-site models16 or with log Gaussian models.17 Moreover, nonuni-form decays were treated with various fitting procedures18,19 butthey cannot correctly distinguish a single Gaussian distribution oflifetimes and a sum of two exponentials or a bimodal Gaussiandistribution and a sum of at least three exponentials.19-21 Thus, adescription based on discrete lifetime components should only beregarded as truly representing discrete molecular states if supportedby supplementary data. A simpler model for describing thenonexponential luminescence decay was developed by Lippitschet al.,19 who considered the interaction of the luminophore withthe nonuniform environment provided by the hosting polymer. Alsoin this case, however, some deviations from linearity remainedunexplained.

In this paper we propose an explanation of this behavior, atleast for some experimental cases, on the basis of a morecomplete rationalization of the nature of the optical response.We will demonstrate the role of the background correction inthe curvature of the SV and also in the discrepancy oftenencountered between calibrations with I and τ.22 We willdemonstrate that the common practice to make a simplebackground correction by testing the membrane without thelumunophore is a mistake because this choice does not accountfor some processes like self-absorption of the label, and the

* To whom correspondence should be addressed. E-mail:paolo.pastore@unipd.it.

RI )I0

I- 1 ) K′SV,I ·% O2 (1)

Rτ )τ0

τ- 1 ) K′SV,τ ·% O2 (2)

J. Phys. Chem. C 2009, 113, 15742–1575015742

10.1021/jp9050676 CCC: $40.75 2009 American Chemical SocietyPublished on Web 08/06/2009

presence of unquenchable emitted light. These events mayproduce unexpected experimental inconsistencies leading to thecited inequality between the light intensity and with the lifetimeratios, I0/I * τ0/τ. Theoretical considerations will furnish themathematical models to explain the experimental data obtainedwith three test polysulfone-based membranes. Sensing mem-branes will be prepared by embedding tris-4,7-diphenyl-1,10-phenanthroline (Ru(dpp)),23,24 platinum(II) meso-tetraphenylpor-phyrin (PtTPP),24 and palladium(II) meso-tetra(pentafluo-rophenyl)porphyrin (PdFTPP)24 characterized by quite differentlifetimes.2,25 Moreover, they have suitable absorption/emissionwavelength so that they have large Stokes shifts, reasonableluminescence quantum yields, and relatively good thermal,chemical, and photochemical stability. The mathematical/experimental approach indicates the optimal oxygen concentra-tion working intervals for the three tested membranes.

Materials and Methods

Reagents. Platinum(II) chloride and 5,10,15,20-tetraphenyl-21H,23H-porphyrin, ruthenium(III) chloride trihydrate (99.98%)and 4,7-diphenyl-1,10-phenanthroline (dpp),26,27 sodium octane-sulfonate (Na-OS), CHCl3 anhydrousg 99%, polysulfone (PSF)d ) 1.24 g/L, MN ) 16.000, MW ) 35 000, and 5,10,15,20-tetrakis(pentafluorophenyl)-21H,23H-porphyrinpalladium(II)were obtained from Aldrich Products. Ultrapure water wasobtained with a Millipore Plus System (Milan, Italy, resistivity18.2 MΩ cm-1). Ru(dpp)OS and PtTPP were synthesizedaccording to refs 27 and 28, respectively.27,28

Procedures. Preparation of Oxygen-SensitiWe Membranes.The polysulfone membranes investigated were prepared by dip-coating onto a glass support (10 × 30 × 1 mm) under nitrogenatmosphere. The substrates were previously washed with waterand soap, rinsed with water and with isopropanol, and then driedunder nitrogen flow. The membranes were obtained by dissolv-ing a suitable amount of the metal complex and polysulfone in10 g of dry chloroform. The optimized conditions for the dip-coating deposition are reported in Table 1.

After the chloroform had evaporated, membranes were driedat room temperature for 1 h. The membrane thickness wasdetermined by ellipsometric measurement. Membranes weretested at 25.0 °C, P ) 1 atm.

Instrumentation and Characterization of Materials. OxygenOptical Sensor. The oxygen sensor built in our laboratory wasdescribed elsewhere.29 The excitation source is a Bivar,LED5UV40030 high-brightness violet LED (angle 30°, spectraloutput peaks at 406 nm) or a high-brightness blue LED (Nichia,NSPE590, angle 15°) whose spectral output peaks at 464 nm,or a blue violet laser diode (SHARP, GH04P21A2GE 105 mW,maximum emission 405 nm, half-intensity width 2 nm). Lightemitted from the membrane passed through a homemade long-wave-pass filter (cutoff 570 nm, prepared depositing on apolyester film suitable amount of three DEKA glass paints) andfocused onto a Hammamatsu S1223 photodiode detector(Hamamatsu, Middlesex, UK). The signal output was directedto a LeCroy Wave Surfer 44xs, 450 MHz, oscilloscope (Geneva,

Switzerland). Lifetimes were determined from pulsed irradiationrealized with a Thurby Thandar Instruments TGP110 pulsegenerator. Gas mixtures were prepared by mixing suitableamounts of nitrogen and oxygen. Oxygen and nitrogen wereflown via Alicat Scientific mass flow controllers (code MC-100-SCC-D, calibrated for O2 and N2) into the sensor cell andmixed via a homemade mixer. Calibration of mass flowcontrollers was controlled with a PBI Dansensor O2 analyzer(Milan, Italy) measuring the oxygen percentage after mixing.A Perkin-Elmer lambda 25 UV-vis spectrophotometer was usedto determine the absorbance spectra of the luminophoresincorporated in membranes or dissolved in CHCl3: for themeasurements in CHCl3 a quartz cuvette was used, whilemeasurements on membranes were done by inserting a mem-brane holder in a slit perpendicular to the incident beam. A dip-coating deposition of the membrane implies the coverage ofboth sides of the glass support so that one of them was removedwith acetone after drying, before absorbance measurement todetermine its thickness. Emission spectra were recorded with aAndor Newton CCD cooled by a Peltier cooler at -70 °Cchamber coupled to a Shamrock 3031-B grating. Measures wererecorded using a gain of 4×, 128 electron multiplier 128×, slit10 µm, and averaging 100 acquisitions. Background andcalibration using a Ar/Hg lamp occurred once a day. Thicknessesmeasurements were done with a spectroscopic ellipsometer mod.Alpha-SE (J.A. Woollam Co. Inc.).

Laser Pulse Experiments. The temperature effect presentwhen a continuous laser LED source is used is resolved bypulsing the laser emission and by sampling emissions at theend of the pulse period, when the signal reached a steady-statecondition. The pulse width and the rest time were 3 ms and0.5 s long, respectively, for the PdFTPP membrane and 0.5 msand 0.5 s for Ru(dpp)OS and PtTPP. The sampling time wasmade in the last 10% of the pulse width. Responses were averageof 1000 pulses.

Theory

Nature of the Experimental Light Emission in an OpticalSensor. The SV equation works with the light intensity, I,coming from the following kinetic scheme:

where hν and hν′ are the photon energies absorbed and emitted,respectively; kabs, kf

0 are the absorption and emission rateconstants; ki represents all the nonradiative decays; kq is thequenching rate constant. Now the question is: does the detectorread the emitted light required by this mechanism? The generalanswer is no. The recorded light depends also on the membranenature and on the instrumental setup. The experimental emittedlight read by the photodiode at the ith experiment may betherefore defined as

TABLE 1: Membrane Preparation Parameters

label Ru(dpp)OS PtTPP PdFTPP

concn (µmol g-1 (PSF)) 20 20 10extraction velocity (cm min-1) 2.5 1.5 1.5support glass glass glassPSF concn (g mL-1 (CHCl3)) 0.2 0.2 0.2immersion velocity (cm min-1) 12 12 12deposition under N2 N2 N2

M + hν f M* kabs

M* f M + hν′ kf0

M* f M + heat ki

M* + O2 f M + O2 kq

Iiex ) ai(I + INQ) + Ii

B - IAbs (3)

Determination of Molecular Oxygen J. Phys. Chem. C, Vol. 113, No. 35, 2009 15743

in the presence of oxygen and

in the absence of oxygen (0 < ai < 1 is a constant depending onthe system geometry as the photodiode does not collect all theemitted light). Ii

NQ is the nonquenchable light coming from theluminophore; Ii

B is the background light emission and IiAbs is

the light absorbed by the luminophore inside the membrane.Ii

B, in turn, is composed of two contributions: one is thephotodiode background current, Ii

PTD, and the other is thenonfilterable light coming from the light source, Ii

NF.

The constant ai may be eliminated by normalizing the lightintensity and obtaining the corrected SV equation.

By rearranging eq 6 we obtain a new form of the SV equationthat accounts for the real background of the membrane:

where ∆Iiex ) I0,i

ex - Iiex ) ai(I0 - I) ) ai∆I and Ii

S ) aiINQ -IAbs. If ai is constant IS and IB do not depend on “i”, we mayplot Ii

ex - IB vs ∆Iiex/(% O2) so that 1/K′SV and IS may be obtained

as slope and intercept, respectively. Equation 7 is a new formof the SV equation. It has the advantage to obtain the K′SV andthe effective background with a simple unweighted regressionmethod. On the contrary, the “classical” SV requires theknowledge of the background and a weighted regression. It isimportant to notice that if the experimental data are linearaccording to eq 7 then there is no need of multisite hypothesesor other correction procedures.16-21 The correctness of the SVkinetic model is confirmed. To our knowledge, all authorsneglect the IS contribution and plot (I0

ex - IB)/(Iex - IB) vs %O2. The error made by neglecting IS may be defined as

Consequently from eq 6 we obtain

Figure 1 reports eq 9 with nine xS values for K′SV ) 0.14(PtTPP membrane). For xS < 0 and xS > 0 eq 9 produces positive(curves 1-4) and negative (curves 6-9) deviations fromlinearity, respectively. These deviations are more accentuatedfor larger K′SV and % O2 values. Curve 5 is linear as xS ) 0.These results demonstrate that if the IS value is not consideredwhen really present, the SV is not linear. In particular, with the

chosen K′SV an error % xS of (0.5% is sufficient to observecurved calibrations; that is, a curvature is significant for |xSK′SV|> 7 × 10-4.

Statistical Aspects of the Fitting Procedures for Eq 7. As∆Ii

ex/(% O2) is not a deterministic variable, the standardapproach to the regression procedure is not valid as ∆Ii

ex is noterror free. Anyway, from the errors propagation theory we maydemonstrate that the variance of the ordinates, sIi

ex-IB2 , is largerthan that of abscissas, s∆Ii

ex/(%O2)2 , for % O2 > 1 so that we may

consider the least-squares regression a good approximation for% O2 > 1. A safer approach, especially for sensors dedicated tolow concentrations (% O2 < 1), may be obtained with the robustnonparametric regression.30,31

Statistical Aspects of the Fitting Procedures for Eq 6. TheSV model corrected for IS is a composed measurement account-ing for (I0

ex - IB - IS)/(Iex - IB - IS) - 1, and its error, sRI)

s((I0ex-IB-IS)/(Iex-IB-IS) - 1), must be estimated from the errors

propagation assuming s ) sI0) sI ) sIB ) sIS.

This equation clearly indicates that more precise measurementsare obtained with low K′SV ·% O2 values. When the calibrationsensitivity is sufficiently low (K′SV ·% O2 < 1), precisionbecomes independent of % O2 and the regression may be notweighted. For a given membrane (that is for a given K′SV) eq10 indicates that the sRI

increases with % O2, so that theregression must be weighted with32

The model becomes

where P1w and P2w are intercept and slope of the weightedmodel,33 respectively. The SV model is correct only if the P1w

value is statistically equal to zero.

I0,iex ) ai(I0 + INQ) + Ii

B - IAbs (4)

IiB ) Ii

NF + IiPTD (5)

I0,iex - Ii

B + IAbs - ai · INQ

Iiex - Ii

B + IAbs - ai · INQ

)I0

I) 1 + K′SV ·% O2

(6)

Iiex - Ii

B ) 1K′SV

∆Iiex

% O2+ Ii

S (7)

% xs ) 100IS/(I0ex - IB) (8)

I0

I)

I0ex - IB

Iex - IB)

1 + K′SV ·% O2

1 + xSK′SV ·% O2(9)

Figure 1. Plot of eq 9 with K′SV ) 0.14 (PtTPP membrane) with %xS ) -4, -2, -1, -0.5, 0.0, 0.5, 1, 2, and 4 (curves 1 to 9,respectively).

sRI)

√2s

I - IB - IS1 + (I0 - IB - IS

I - IB - IS )2

)

√2s

I0 - IB - IS(1 + K′SV ·% O2)√1 + (K′SV ·% O2)

2 (10)

wi )1

sRI

2(11)

RI ) P1w + P2w ·% O2 (12)

15744 J. Phys. Chem. C, Vol. 113, No. 35, 2009 Badocco et al.

Working Interval of the Classic SV Equation. As theresponse, I, is not linear with % O2, the sensitivity, dI/d % O2,decreases with % O2 so that, at large % O2, measurements areless accurate, and consequently, at what % O2 variation, ∆%O2, produces a significant ∆Iex value? The condition for which∆Iex is no more significant may be obtained with a t test:

where sy/x2 is the estimate of the regression variance relative to

eq 7 with n data and tR,n-2 is the t-Student with R ) 0.5 andn - 2 degrees of freedom. In this equation we used sy/x asestimate of σI. The ∆Iex value may be computed from thederivative of the SV equation:

If ∆% O2 is the required resolution value, R, combining eqs13 and 14 we obtain the maximum % O2 for that resolution.

with g ) I0/(tR,n-2[2/n]1/2sy/x)1/2. The plot % O2max vs K′SV,

parametric in R, is reported in Figure 2. All the membraneshave very similar g values, g ) 17.3 (1.3). For pK′SV ) -0.3,0.9, and 1.75, close to those of our membranes (PdFTPP, PtTPP,and Ru(dpp)OS), the % O2

max is 19.0, 60.7, and 100, respectively,when the required resolution is R ) 2%. For better resolutionsthese values decrease (see data relative to R ) 0.5%, forinstance).

Considerations on the Lifetime-Based SV. It is suitable topoint out that the SV in terms of lifetime, τ, may be alsoobtained by correcting the exponential fitting with τi

S:

This originates the equivalent form to eq 7:

In this equation, anyway, the correction term τiS cannot be

interpreted as lifetimes are not additive and this makes eq 17highly improbable. It is possible to obtain a lifetime-basedsensible model by considering the emission areas during thetime decay after the switch off of the exciting light pulse. Thatemission profile may be interpreted as the sum of manymonoexponential decays hypothetically due to nonquenchablesites (INQ), to background decay (IF - IABS) depending on theelectrical circuit time constant, τcirc. This is represented by thefollowing equation

The emission area may be obtained by integrating eq 18:

and then, for a generic % O2

In the absence of O2

From eqs 1 and 2 we obtain:

and after a few rearrangements we obtain

This is equivalent to eq 7. It is possible to obtain K′SV,τ and AF

as fitting parameters and, by combining eq 22 with eq 6 weformulate the “true” SV equation in terms of lifetime.

The term “true” indicates that, in this form, the SV furnishesthe correct τ0/τ ratio. Many authors observed the discrepancy

Figure 2. % O2max vs K′SV. Upper oxygen concentration limit, % O2

max,detectable with the SV for a resolution, R ) ∆% O2 ) 0.5, 1.0, 1.5and 2.0, with g ) 17.3 (see eq 15).

∆Iex

sy/x√2/n) tR,n-2 (13)

∆Iex )I0K′SV∆% O2

(1 + K′SV ·% O2)2

(14)

% O2max ) 1

K′SV(g√K′SVR - 1) + R (15)

τ0,iex - τi

S

τiex - τi

S)

τ0

τ) 1 + K′SV ·% O2 (16)

τiex )

∆τiex

K′SV ·% O2+ τi

S (17)

I(t) ) Ie-kt + ∑i

Iie-kit + IPTD (18)

Aex ) ∫0

∞(I(t) - IPTD) dt ) ∫0

∞Ie-kt dt +

∫0

∞ ∑i

Iie-kit dt (19)

Aex ) Iτ + ∑i

Iiτi ) Iτ + INQτ0 + (IF - IABS)τcirc )

Iτ + AF (20)

A0ex ) I0τ0 + AF (21)

A0ex - AF

Aex - AF)

I0τ0

Iτ) (1 + K′SV,I ·% O2)(1 + K′SV,τ ·% O2)

(22)

Aex )A0

ex - AF

(1 + K′SV,I ·% O2)(1 + K′SV,τ ·% O2)+ AF

(23)

τ0

τ)

A0ex - AF

Aex - AF

Iex - IB - IS

I0ex - IB - IS

) 1 + K′SV,τ ·% O2

(24)

Determination of Molecular Oxygen J. Phys. Chem. C, Vol. 113, No. 35, 2009 15745

between the SV in terms of I and τ25,34 while others observedno discrepancies at all.35 In this section we indicated possiblecauses and in the next one these hypotheses will be experimen-tally demonstrated.

Results and Discussion

Characterization of Ru(dpp)OS, PtTPP, and PdFTPP inCHCl3 and in Polysulfone. Figure 3 reports normalizedemission and absorption spectra of Ru(dpp)OS, PtTPP, andPdFTPP in PSF (a-c continuous line). Absorption spectra ofthe three complexes obtained in CHCl3 are also reported (dottedline) together with the normalized background spectra obtainedby irradiating a luminophore-free membrane (signals wereproperly filtered). Table 2 reports the absorption/emissioncharacteristic parameters of PtTPP and PdFTPP in CHCl3 andin PSF. The reported ε values were computed from themembrane thickness measured by ellipsometry (1.75(0.30) µm,

2.53(0.30) µm, and 2.80(0.14) µm for Ru(dpp)OS, PtTPP, andPdFTPP, respectively). The data of the Ru(dpp)OS complexhave been already published.29 In this context it is useful toresume them: an absorption band at 452 nm with a half-heightwidth of 109 nm in PSF is present; in CHCl3 this band has ablue shift of 7 nm. The emission peak in PSF is at 608 nm.The εCHCl3 value computed with eight concentration levels is38 300 dm3 mol-1cm-1. The emission spectra of the metalporphyrin complexes exhibit the typical multiple band aspect:the main Soret’s (or B(0,0)) band, the Q(1,0) and Q(0,0) bandsvisible both in PSF and in CHCl3. Also in this case theεCHCl3values relative to the three peaks were computed with eightconcentration levels. The found values are comparable to thoseobtained by other authors in different solvents.24 The ε valuesof Soret’s band are statistically equivalent in CHCl3 and in PSFwhile it is significantly larger in PSF for the Q bands.24 PtTPPhas an increase of 6 nm of the half-height width. The εQ(1,0)/εQ(0,0) ratios of the same MP, obtained in CHCl3 and in PSF aresimilar. The fluorinated MP has the largest ratio as describedby other authors36,37 who rationalized the effects of the substit-uents in the MP on the π-π* transitions. The ν[B(0.0)-Q(0.0)] splitfor PtTPP is 6361 cm-1 in CHCl3 and 6148 cm-1 in PSF. Theν[B(0.0)-Q(0.0)] split for PdFTPP is 6487 cm-1 in CHCl3 and 6310cm-1 in PSF. The increase is 213 and 177 cm-1 for PtTPP andPdFTPP, respectively. Both MP’s have a very similar emissionprofiles showing two bands: the most intense at 650 nm, andthe other at 720 nm. They are assigned to the triplet state of theQ bands.38 The normalized emission profiles in the presenceand in the absence of O2 are coincident as expected by theory.Backgrounds are different but all of them begin at 550 nm owingto the chosen filter. As the Ru(dpp)OS excitation spectrumpartially overlaps the emission one, a self-absorption effect maybe present. On the other hand, MP does not have excitation/emission overlaps but have two absorption peak at 500-550nm so that the background spectra may be altered. In otherwords, the background is correlated to the chosen luminophoreso that it cannot be measured with a “blank” membrane builtwithout the luminophore. This fact must be accounted for toevaluate the correct background.29 Its value must be obtainedwith the real sensing membrane, in the presence of luminophore.

Role of the Background for the Correct Interpretationof the SV Equation. The usual oxygen calibration with theSV approach would lead to the plots of Figure 4a. Clearcurvatures are evidenced for the two MP complexes. Figure 4breports the experimental Ii

ex - IB vs ∆Iiex/% O2 of three sensors,

according to eq 7. All membranes have linear behavioraccording to the corrected SV model. As reported in the Theorysection, both robust and parametric regression models furnishstatistically equivalent estimates of IS and K′SV as demonstratedby slopes and intercept values reported in Table 3. A test madeon the intercept indicates that IS is statistically unequal to zerofor all the considered membranes. PtTPP and PdFTPP mem-branes have % xS ) -5.0 and % xS ) -5.9 respectively. Thesenegative values may be justified by the absorption spectradescribed in Figure 3. In particular, % xS of PdFTPP is morenegative than % xS of PtTPP as expected by the εQ(0.0)

PdFTPP/εQ(0.0)PtTPP

= 8 ratio (PdFTPP absorbs more than PtTPP). On the contrary,the Ru(dpp)OS membrane has % xS ) +10.7 which is muchhigher than blank. We interpreted this result with the presenceof caged emitting sites not reachable by oxygen and thereforeunquenchable. Both differences are significant and they changethe SV calibration profile from linear to curved, as demonstratedin the Theory section. The |xSK′SV| value of Ru(dpp)OS is1.5 × 10-3 so that its calibration appears almost linear while

Figure 3. Emission and absorption spectra of (a) Ru(dpp)OS, (b)PtTPP, and (c) PdFTPP in PSF (continuous line). Absorption spectraof the three complexes obtained in CHCl3 (dotted line).

15746 J. Phys. Chem. C, Vol. 113, No. 35, 2009 Badocco et al.

the other two membranes have |xSK′SV| values largely greaterthan 7 × 10-4 (6.5 × 10-3 and 1.1 × 10-1 for PtTPP andPdFTPP, respectively) and justify the curvature experimentallyfound in Figure 4 a.

The SV corrected for the IS term according to eq 6 isrepresented in Figure 4c. Table 4 reports the regressionparameters obtained with both parametric and weighted para-metric regressions. The weight, wi ) 1/(sRI

2 ), was obtained withvarious % O2 and by means of sRI

and according to eq 10. AnF-test on the regression variance indicated outlayer data. TheRu(dpp)OS has only one outlayer for % O2 ) 100, PtTPPexhibits outlayers for % O2 > 50 and PdFTPP has outlayers for% O2 > 20. From the knowledge of the K′SV value we maydetermine the limits of application of the SV calibration. FromFigure 1, and with a resolution of 2% the limit % O2values forthe studied membranes are 100, 60.7, and 19.0% for Ru(dpp)OS,PtTPP, and PdFTPP, respectively. The existence of a % O2

theoretical maximum value justifies the presence of outlayerswhich are due to the lack of light intensity reading accuracy inthe indicated concentration intervals. The determination coef-ficient very close to unity (R2 g 0.999) confirms the linearmodel. From Table 4 it is evident that only the regressionparameters obtained with the weighted model are comparableto those in Table 3, and consequently, wi cannot be neglected.The case of the PtTPP membrane is a clear example. In fact,the classic regression approach furnishes a K′SV value muchlarger than the expected one and an intercept much lower than0 (-0.264) indicating a procedural error. For PdFTPP the errorproduces effects on the slope. For the Ru(dpp)OS membrane,the low calibration sensitivity renders the results similar for thetwo regression modes adopted.

SV Linearity and Consistency between I0/I and τ0/τCalibrations. In this section we will demonstrate that theinconsistency between the I0/I and τ0/τ calibration reported byvarious authors25,34 in many cases is only apparent. The use ofunique light source and filters for all membranes was adoptedto compare the different sensors. We chose the UV laser LED(λmax ) 395 nm) because its high power allows (1) to accuratelymeasure lifetimes and (2) to excite also the Ru(dpp)OS. Adrawback of the UV laser LED is anyhow evidenced in Figure5a, where the normalized emission profiles, for the PtTPPmembrane, produced with the UV laser LED are compared tothose obtained with the UV LED. Each step refers to increasing% O2 values alternated to pure N2. The UV laser LED loses23.4% of the signal in 2.2 h compared to the 0.9% of the UVLED. The calibration sensitivity increases from 0.133 (UV LED)to 0.189 (UV laser LED). Analogous behavior was obtainedfor the other two membranes. Although membranes are ther-mostated, the experimental system cannot discharge the heatproduced by the laser leading to the observed behavior. This isconfirmed by Figure 5b in which the emission profile obtainedwith the laser source is steeper as a result of an increase of theoxygen diffusion coefficient caused by the temperature increase.The two curves relative to the UV LED refer to experimentsperformed before and after the laser one. Their substantialidentity indicates that the laser does not modify the membranestructure. The temperature effect problem may be resolved by

TABLE 2: Absorption/Emission Characteristic Parameters of PtTPP and PdFTPP in CHCl3 and in PSF

λB(0.0)max (nm) λQ(1.0) (nm) λQ(0.0) (nm)

complex structure λemm (nm) εB(0.0)/103 (M-1 cm-1) εQ(1.0)/103 (M-1 cm-1) εQ(0.0)/103 (M-1 cm-1) εQ(1.0)/εQ(0.0) ν[B(0.0)-Q(0.0)] (cm-1)

PtTPP CHCl3 402 510 539 3.7 6361101 (0.1) 10.2 (0.1) 2.45 (0.01)

PSF 652 405 511 540 4.0 6148102 (14) 12.9 (2) 3.3 (1.2)

PdFTPP CHCl3 407 520 553 1.0 6487265 (0.1) 22.3 (0.1) 19.7 (0.1)

PSF 661 410 521 554 1.1 6310252 (38) 28.2 (4.2) 25.7 (3.5)

Figure 4. (a) Usual representation of the SV plot with backgroundsubtraction. The straight lines represent the linear fitting of the firstfew data points for each membrane. (b) Experimental data plottedaccording to eq 7 for Ru(dpp)OS (0), PtTPP (4), and PdFTPP (O)(parametric regression). The intercept represents an estimate of IS.Regression parameters are in Table 3. (c) Experimental data plottedaccording to the SV model corrected with IS (weighted parametricregression). Regression parameters are in Table 4.

Determination of Molecular Oxygen J. Phys. Chem. C, Vol. 113, No. 35, 2009 15747

pulsing the laser emission and by sampling emissions at theend of the pulse period, when the signal reached a steady-statecondition. The results are reported in Figure 6a-c showing thenormalized decay profiles in logarithmic scale as a function oftime for various % O2. In this plane all the decays at low % O2

values are linear, demonstrating a monoexponential behavior.The curve fitting with a monoexponential model in the absenceof oxygen allows to estimate the lifetime, τ0, of the lumino-phores: 5.5, 83.3, and 1010 µs for Ru(dpp)OS, PtTPP, andPdFTPP, respectively. The inset of the figure reports the sampledsignal. All the data are resumed in Figure 6d where both theSV calibration in terms of I (uncorrected for IS, empty symbols)and τ (obtained from the monoexponential fitting, blacksymbols) are plotted. In the condition adopted the two calibrationmodes are not coincident. The same result is obtained also witha two-exponential fitting.

Let us apply the theoretical consideration above-reported.Figure 7a,b reports the calibrations in terms of I and emissionarea, Aex, according to eqs 7 and 23, respectively (regressionparameters are reported in Table 5). The % xs values experi-mentally obtained agree with those obtained with different lightsources. In particular, 10.5 for the Ru(dpp)OS is obtained alsowith the blue LED, demonstrating that an unquenchablecontribution is present. The values for the other membranes arenegative but their absolute value is in both cases lower. This isconsistent with the fact that with the laser source the IB/I0 ratiois lower with respect to the UV LED source. Both regressions

on I and A point out IS and AF contributions and allow to estimatethe K′SV value as regression parameter. The found K′SV valueswith I and A, reported in Table 5, are statistically equivalentand are equivalent to those reported in Table 4, demonstratingthe correctness of the experimental choice: the pulse allows themembrane to maintain the temperature set up. Knowing IS andAF, it is now possible to obtain the new SV calibrationsaccording to eqs 12 and 24. The results are reported in Figure8. It is evident that both calibrations in terms of I and τ arenow linear and quite close one another. The results are reportedin Table 6. Data obtained with I are more accurate than thoseobtained with A.

Conclusions

In this paper we demonstrated that experimental dataobtained from oxygen optical sensors can be conditioned bylight sources not considered in the SV kinetic model. Theymay influence the SV plot and must be suitably evaluated toobtain good quality data. We demonstrated this fact for threereal sensors based on different luminophores: tris-4,7-diphenyl-1,10-phenanthroline (Ru(dpp), platinum(II) meso-tetraphenylporphyrin (PtTPP), and palladium(II) meso-tetra(pentafluorophenyl)porphyrin, (PdFTPP) embedded in apolysulfone matrix. Experimental data, interpreted withmathematical functions, demonstrated that the curvature fromlinearity and the discrepancy between data obtained with light

TABLE 3: Parametric and Nonparametric Regressions Relative to the Three Membranes Reported in Figure 4b

membrane regression I0ex - IB (V) IS (V) sIS (V) 1/K′SV s1/K′SV

K′SV % xs R2

Ru(dpp)OS parametric 0.131 0.017 0.005 72.5 1.2 0.0138 0.9961robust 0.014 73.0 0.0137 10.7 0.9991

PtTPP parametric 0.443 -0.0226 0.0095 7.47 0.07 0.134 0.9992robust -0.0223 7.47 0.134 -5.0 0.9992

PdFTPP parametric 0.480 -0.026 0.0012 0.536 0.006 1.87 0.9995robust -0.029 0.554 1.81 -5.9 0.9998

TABLE 4: Parametric and Weighted-Parametric Regressions (RI ) P1w + P2w ·% O2) Relative to the Three MembranesReported in Figure 4c

label regression P1w sP1P2w sK′SV

R2

Ru(dpp)OS parametric 0.013 0.019 0.0138 0.0003 0.997weighted parametric 0.0004 0.003 0.0137 0.0004 0.999

PtTPP parametric -0.264 0.18 0.1437 0.0033 0.996weighted parametric 0.0087 0.025 0.1332 0.0024 0.997

PdFTPP parametric 0.012 0.02 1.77 0.025 0.995weighted parametric 0.001 0.020 1.82 0.012 0.999

Figure 5. (a). Normalized emission profiles coming from the UV and UV laser LED sources by increasing the % O2 value, alternated to pure N2.(b) Particulars of the first step of (a), transition from % O2 ) 100 to 0 (100% N2). Experimental conditions: PtTPP membrane; T ) 25 °C; P ) 1atm; % O2 after the third step ) 0.5, 1, 1.5, 2.5, 3.5, 5, 7.5, 10, 15, 20, 30, 40, and 50.

15748 J. Phys. Chem. C, Vol. 113, No. 35, 2009 Badocco et al.

emission intensity, I, and in excited-state lifetime, τ, are onlyapparent and due to the background emission. Consequently,multisite emission hypotheses or other correction proceduresthat appeared in the literature must be invoked only after acareful evaluation of the background light really present in

the system. After corrections, the sensors’ behavior was thatforeseen by the SV theory. Equation 7 is a new form of theSV equation. It has the advantage to obtain the K′SV and theeffective background with a simple unweighted regressionmethod. On the contrary, the “classical” SV requires the

Figure 6. Normalized decay profiles in logarithmic scale as a function of time for various % O2 values for Ru(dpp)OS (a), PtTPP (b), and PdFTPP(c). Inset: signal in the last 10% of the pulse width for various % O2 values. (d) SV calibration plots in terms of I (uncorrected for IS, emptysymbols) and (from monoexponential fitting, black symbols). % O2 values as in Figure 3.

Figure 7. (a) Regressions of the experimental data according to eq 12 to obtain the IS value. (b) Regressions of the experimental data accordingto eq 24 to obtain the AF value.

TABLE 5: Regression Parameters Relative to Figure 7a,b

method label F-test n/ntot K′SV,I sK′SV,IIS (mV) sIS (mV) R2 I0 (mV) % xs

I Ru(dpp)OS 12/13 0.014 0.001 0.178 0.090 0.997 2.05 10.5PtTPP 12/15 0.136 0.004 -0.039 0.009 0.9998 4.59 -0.86PdFTPP 11/15 1.79 0.06 -0.071 0.009 0.998 3.56 -2.05

method label F-test n/ntot K′SV,τ sK′SV,τ AF (mV ·µs) sAF (mV ·µs) R2 A0 (mV ·µs) % AF

A Ru(dpp)OS 12/13 0.0135 0.0009 0.36 0.30 0.994 11 3.4PtTPP 12/15 0.140 0.003 11.7 2.0 0.9994 389 3.0PdFTPP 10/15 1.79 0.03 32.6 23.2 0.9993 3523 1.0

Determination of Molecular Oxygen J. Phys. Chem. C, Vol. 113, No. 35, 2009 15749

knowledge of the background and a weighted regression.Moreover, the reported results demonstrated that a concentra-tion limit for the determination of oxygen may be theoreti-cally determined and experimentally found.

Acknowledgment. We gratefully acknowledge the CLR srl(Rodano-Milan, Italy) for funding this research. Moreover, wegratefully thank Dr. Paolo Roverato and Mr. Lorenzo Dainese.

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JP9050676

Figure 8. SV calibration plots in terms of I and τ according to eq 12(black symbols) and eq 24 (empty symbols). % O2 values as in Figure 3.

TABLE 6: Weighted Parametric Regressions Relative toCalibrations in Figure 8

membrane SV P1w sP1wK′SV sK′SV

R2

Ru(dpp)OS I 0.0001 0.0061 0.0136 0.0004 0.9991τ -0.021 0.044 0.015 0.002 0.96

PtTPP I -0.004 0.011 0.144 0.001 0.9997τ -0.046 0.058 0.134 0.004 0.991

PdFTPP I 0.07 0.11 1.799 0.049 0.996τ -0.022 0.087 1.68 0.09 0.990

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