Analytical Chemistry Chemical Cytometry Quantitates Superoxide

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electrodes in various conditions, in chronoamperometry 18 and cyclic voltammetry. 19 The mapping of concentration profiles was alsoperformedintheirvicinityusingamethodalreadydescribed. 18-23 At the same time, we proposed a theoretical model to evaluate the influence of natural convection on mass transport in still media. 18 The good agreement observed between theory and experiments demonstrated the validity of this model over a wide range of experimental conditions. 18,22-26 The purpose of this study is then to take the benefit of this model to delineate the experimental conditions that allow convection-free regimes to be observed in dynamic and steady-state regimes. These conditions are better presented in a zone diagram showing the influence of all the parameters: time scale of the experiment, electrode radius, and thickness of the convection-free domain. Comparison with experimental data will also serve to illustrate the relative contributions of convection and diffusion at electrodes of different sizes performing under the steady-state regime. MODEL OF NATURAL CONVECTION The influence of convection on the electrode responses can be quantified from deviations of their diffusive currents or from alteration of their diffusion layers. Under pure diffusional conditions, the concentration profile of a species at a disk electrode is given by integration of Fick’s second law: 10 ∂c(r, z, t) ∂t ) D( ∂2c(r, z, t) ∂r 2 + ∂2c(r, z, t) ∂z 2 + 1 ∂c(r, z, t) r ∂r ) (1) where r describes the radial position normal to the axis of symmetry at r ) 0 and z describes the linear displacement normal to the plane of the electrode at z ) 0. D is the diffusion coefficient. For a chronoamperometric experiment, the pertinent boundary conditions are t < 0; r, z g 0; c(r, z, t) ) c° (2) t g 0; r e r 0 ; c(r,0,t) ) 0 (3) r, z f ∞; c(r, z, t) ) c° (4) The current is readily obtained from integration of the concentration gradients at the electrode surface with (18) Amatore, C.; Szunerits, S.; Thouin, L.; Warkocz, J. S. J. Electroanal. Chem. 2001, 500, 62–70. (19) Amatore, C.; Pebay, C.; Thouin, L.; Wang, A. F. Electrochem. Commun. 2009, 11, 1269–1272. (20) Amatore, C.; Pebay, C.; Scialdone, O.; Szunerits, S.; Thouin, L. Chem.sEur. J. 2001, 7, 2933–2939. (21) Amatore, C.; Szunerits, S.; Thouin, L.; Warkocz, J. S. Electroanalysis 2001, 13, 646–652. (22) Amatore, C.; Knobloch, K.; Thouin, L. Electrochem. Commun. 2004, 6, 887– 891. (23) Baltes, N.; Thouin, L.; Amatore, C.; Heinze, J. Angew. Chem., Int. Ed. 2004, 43, 1431–1435. (24) Rudd, N. C.; Cannan, S.; Bitziou, E.; Ciani, L.; Whitworth, A. L.; Unwin, P. R. Anal. Chem. 2005, 77, 6205–6217. (25) Amatore, C.; Sella, C.; Thouin, L. J. Electroanal. Chem. 2006, 593, 194– 202. (26) Amatore, C.; Knobloch, K.; Thouin, L. J. Electroanal. Chem. 2007, 601, 17–28. 6934 Analytical Chemistry, Vol. 82, No. 16, August 15, 2010 r0 ∂c(r, z, t) i )(2πnFD∫ r ∂r (5) 0 ∂z In still solutions, natural convection operates perpendicularly to the electrode surface. It is based on microscopic motions of the solution except in the very near vicinity of the electrodes, where it vanishes. Experimentally, the resulting velocity field is extremely difficult to estimate. Moreover, it is almost impossible to master mathematically since it depends on many parameters which are not easy to control (vibrations, temperature gradients, movement of the cell atmosphere, etc.). However, beyond these difficulties, we demonstrated successfully that, for electroactive species, the influence of natural convection can be assimilated to that of an apparent diffusion coefficient depending on the orthogonal distance z from the electrode plane. 18 Moreover, since the electrochemical perturbation affects only the viscous sublayer adjacent to the electrode, we showed that Dapp could be evaluated by z Dapp ) D( 1 + 1.522( δconv) 4 ) where δconv is the thickness of the convection-free layer. This is the only parameter introduced into the model to account for the effects of natural convection. It is possible to evaluate its influence on the electrode response by replacing D by Dapp in eq 1 and solving numerically the new mass transport equation in association with the same boundary conditions (eqs 2-4). EXPERIMENTAL SECTION All the solutions were prepared in purified water (Milli-Q, Millipore). A 10 mM concentration of K4Fe(CN)6 (Acros) was dissolved in 1 M KCl (Aldrich), which was used as the supporting electrolyte. Reciprocally 2 mM FcCH2OH (Acros) was prepared in 0.1 M KNO3 (Fluka). The diffusion coefficients were DFe ) (6.0 ± 0.5) × 10 -6 cm 2 s -1 27 for Fe(CN)6 4- / Fe(CN)6 3- and DFc ) (7.6 ± 0.5) × 10 -6 cm 2 s -1 for FcCH2OH/ FcCH2OH + . The working electrodes were Pt disk electrodes of 12.5, 25, 62.5, 125, 250, and 500 µm radii. They were obtained from the cross section of Pt wires (Goodfellow) sealed into soft glass. The reference electrode was a Ag/AgCl electrode, and the counter electrode was a platinum coil. A scanning electrochemical microscope (910B CH Instruments) was used to establish the concentration profiles. The amperometric probe was a Pt disk electrode of submicrometric dimension (∼500 nm radius). Its fabrication and the related procedure to map the concentrations have already been reported. 23 For Fe(CN)6 4- /Fe(CN)6 3- experiments, the working electrode was biased at +0.6 V/ref on the oxidation plateau of Fe(CN)6 4- . The probe was biased at +0.6 V/ref to collect Fe(CN)6 4- or -0.1 V/ref to collect Fe(CN)6 3- . For FcCH2OH/FcCH2OH + experiments, the working electrode was biased at +0.25 V/ref. In this case, the probe was biased at +0.25 V/ref to collect FcCH2OH and -0.1 V/ref to collect FcCH2OH + . The mass transport equation was solved numerically in the conformal space adapted to the geometry of a microdisk elec- (27) Amatore, C.; Szunerits, S.; Thouin, L.; Warkocz, J.-S. Electrochem. Commun. 2000, 2, 353–358. (6)
trode 28 by a finite element using Comsol Multiphysics software. The thickness of the convection-free layer, δconv, was determined before each experiment by chronoamperometry as described previously. 18 RESULTS AND DISCUSSION An important property of disk ultramicroelectrodes is that their diffusion layers develop with time until reaching a steady-state limit imposed by hemispherical-type diffusion. However, natural convection may interfere with the mass transport as soon as the thickness of the expanding diffusion layer becomes comparable to δconv. In such a case, a steady-state regime is still achieved but is then controlled by the respective contributions of diffusion and natural convection. Depending on the electrode radius, r0, and the thickness of the convection-free layer, δconv, two situations may be encountered, whether the diffusion at the electrode surface is planar or not. Indeed, at short time scales, the thickness of the diffusion layer is considerably smaller than the electrode radius. The electrodes then behave as electrodes of infinite dimensions, and planar diffusion operates. In that particular situation, the Cottrell equation applies with i planar )( nFADc° √πDt for electrodes of surface area A. Using the Nernst formulation, eq 7 is similar to that given in hydrodynamic electrochemical methods: 10 i )( nFADc° δ where δ ) (πDt) 1/2 . Therefore, natural convection interferes significantly with the mass transport as soon as δconv ≈ (πDt) 1/2 . Whenever this condition is not met, the diffusion layer may develop, possibly reaching a hemispherical behavior until being eventually limited by δconv. However, since diffusion and natural convection occur together in steady-state regimes, their contributions in mass transport remain difficult to comprehend. To solve this problem, one needs first to investigate the concentration profiles established under the pure diffusional steady-state regime, i.e., without any influence of natural convection. In such a case, solution of eq 1 shows that most of the concentration gradients operate over a distance comparable to the electrode radius (Figure 1A). Concentration along the z axis (Figure 1B) varies according to c 2 z ) arctan( c° π r0) The diffusion layer presents a hemispherical shape, and the steady-state current is given by: (7) (8) (9) i hemisph )(4nFr 0 Dc° (10) (28) Amatore, C.; Fosset, B. J. Electroanal. Chem. 1992, 328, 21. Figure 1. Steady-state concentration profile simulated at a disk electrode without considering the influence of natural convection: (A) 2D concentration profile with isoconcentration lines ranging from c/c° ) 0.1 to c/c° ) 0.9. (B) Concentration profile along the vertical axis of symmetry. Using the Nernst formulation again, comparison between eqs 8 and 10 leads to an equivalent diffusion layer thickness, δ ) πr0/ 4. This thickness differs slightly from δz, which may be obtained by extrapolating the concentration gradient at z ) 0, r ) 0 along the z axis. Indeed, when z f 0, the concentration profile at r ) 0 tends to (Figure 1B) c 2 z ) c° π r0 (11) which gives δz ) πr0/2. The difference in the δ and δz values results from the nonradial distribution of diffusion fields at disk electrodes. Concentration gradients are higher at the electrode edges than at the center (Figure 1A). Since δ is evaluated from the integration of concentration gradients over the whole electrode surface (eq 5), it is necessarily smaller than δz. In the following, the variation of these two parameters will provide an accurate estimation of the influence of natural convection, either from the current (i.e., through δ) or from the alteration of concentration profiles in the z direction (i.e., through δz), where natural convection prevails. Analytical Chemistry, Vol. 82, No. 16, August 15, 2010 6935
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Anal. Chem. 2010, 82, 6745-6750 Let
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purchased from Invitrogen-Molecular
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Figure 3. Electropherograms of TPP-
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Anal. Chem. 2010, 82, 6751-6755 Res
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(pH 8.0) with cysteine and cystamin
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Figure 4. Ion mobility mass spectra
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GOx glucose + O298 gluconic acid +
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coater at 2000 rpm for 20 s, and th
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Figure 5. Comparison of cyclic volt
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in channels with either no grooves
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indicators of atmospheric processin
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Figure 1. GC/MS total ion chromatog
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Table 2. Concentrations and Stable
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on a substrate are preferred. 20-24
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Figure 4. SERS analysis of NAADP co
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Anal. Chem. 2010, 82, 6775-6781 Hig
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tion, 2 µL of proprionaldehyde wer
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Figure 4. Analysis of 2a by HPLC-MS
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eaction of 1a with PBH can be condu
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Numerous references had demonstrate
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Figure 1. TEM images of the prepare
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Figure 4. Schematic representation
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esult in a big SPR signal change wi
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also reduces chemical noise, which
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Table 1. Extraction Yields, Liquid
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scanning of AMPP amides of the anal
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Anal. Chem. 2010, 82, 6797-6806 δ
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Figure 1. Schematic view of the pre
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from the specimen and enclosed in a
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Figure 4. (A) IRMS mass-44 chromato
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Table 3. Ambient Measurement Result
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Anal. Chem. 2010, 82, 6807-6813 Dir
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Polymerase (1 U per sample). Reacti
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of which was constant for all ampli
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analytically useful signals at less
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carbon black and RP-C18 for the ext
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solution in an equal volume, and 1
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Table 2. Concentrations and Ratios
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Anal. Chem. 2010, 82, 6821-6829 Mac
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mg/mL protein, followed by separati
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Figure 2. Productivity of SEQUST an
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Figure 4. High-resolution MS/MS spe
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Figure 6. Characterization of PSMs
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containing T-T mismatches. 23 Based
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Figure 1. Extinction spectra of sol
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Figure 3. (A) The value of Ex650 nm
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Figure 5. Extinction spectra and co
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wished to explore the dehydration o
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constant medium for separation; we
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Figure 2. Standards of (Pi)n, n ) 1
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Figure 5. Quantitative calibration
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Anal. Chem. 2010, 82, 6847-6853 Met
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Figure 1. 226 Ra spectrum by liquid
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Table 1. Counting Properties and De
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Table 3. Analysis of 226 Ra in Sedi
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mercial microarray scanner and fabr
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Figure 2. Optical transmission meas
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Figure 5. Volcano plots detailing t
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data as well. The 41 genes in Table
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corresponding compound if its chemi
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Figure 1. Schematic illustration of
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Table 1. Absolute Quantification Re
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ment. Therefore, the long-time drea
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Figure 1. Chemically actuated micro
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Figure 2. Influence of a surfactant
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Figure 5. Device to eject and mix s
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Anal. Chem. 2010, 82, 6877-6886 Imm
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NaCl, phosphate buffer saline (PBS)
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Figure 2. Product ion mass spectra
Page 139 and 140: -70 °C resolved the problem, givin
Page 141 and 142: Table 1. Intraday Precision and Acc
Page 143 and 144: Anal. Chem. 2010, 82, 6887-6894 Fer
Page 145 and 146: Figure 1. Infrared spectra of (A) u
Page 147 and 148: Figure 3. Cyclic voltammograms obta
Page 149 and 150: Figure 6. Calculated charge from ch
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Page 153 and 154: Table 1. Chemical Structure, pKa Va
Page 155 and 156: pH with a tilted baseline (Figure 1
Page 157 and 158: Table 2. Linearity and Detection Li
Page 159 and 160: ascorbic acid (AA), uric acid (UA),
Page 161 and 162: the multielement capabilities, the
Page 163 and 164: RESULTS AND DISCUSSION Sulfur Detec
Page 165 and 166: Table 2. Molecular Properties and C
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Page 169 and 170: dilution and hybridization buffer.
Page 171 and 172: solution under appropriate incubati
Page 173 and 174: Figure 4. Standardization curve for
Page 175 and 176: Anal. Chem. 2010, 82, 6919-6925 Ele
Page 177 and 178: the ×10 objective, to have a large
Page 179 and 180: Figure 2. With a suitable removal o
Page 181 and 182: the NB signal in a much better foot
Page 183 and 184: Scheme 1. Reactions of Selenium Rea
Page 185 and 186: Figure 2. (a) ESI-MS spectrum showi
Page 187 and 188: Figure 4. (a) ESI-MS spectrum showi
Page 189: Anal. Chem. 2010, 82, 6933-6939 Dif
Page 193 and 194: Figure 4. Comparison between simula
Page 195 and 196: Figure 6. Comparison between simula
Page 197 and 198: educed in the vicinity of double bo
Page 199 and 200: Figure 2. Normalized product ion ab
Page 201 and 202: Figure 4. EID (a) and IRMPD (b) of
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Page 205 and 206: Figure 1. Schematic flowchart showi
Page 207 and 208: difference, ppm compound Table 1. I
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Page 211 and 212: Figure 5. Extracted ion current ESI
Page 213 and 214: m/z 1172.935 was observed for Ser14
Page 215 and 216: linked products via affinity tags.
Page 217 and 218: Scheme 2. Fragmentation Mechanism o
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Page 223 and 224: Figure 5. (A) MALDI-TOF/TOF product
Page 225 and 226: Anal. Chem. 2010, 82, 6969-6975 Ana
Page 227 and 228: Figure 3. Equilibrium response as a
Page 229 and 230: Figure 6. The average measured resp
Page 231 and 232: for the fill time, and we find that
Page 233 and 234: nucleotide tails. 3-5 Thus, the amo
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Page 239 and 240: Anal. Chem. 2010, 82, 6983-6990 Imp
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Figure 2. Configuration editor wind
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Figure 4. Dependencies between volu
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Since the time for liquid expulsion
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Anal. Chem. 2010, 82, 6991-6999 Int
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Figure 1. Representation of the Car
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Table 2. Capillary Electrophoresis
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Figure 4. (A) Typical raw electroph
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field. DNA profiles were delivered
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Another approach to handle this lim
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(principal components, PCs) in whic
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Figure 5. Relevant score plots and
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CONCLUSIONS In this paper we have i
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electroactive-species loaded liposo
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Figure 2. Qdot-based FLFTS response
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Figure 6. Fluorescence imaging of Q
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Anal. Chem. 2010, 82, 7015-7020 Sel
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Table 1. Effect of 1 D-LC Condition
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Figure 3. Peak-production rate vers
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Anal. Chem. 2010, 82, 7021-7026 Cel
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luciferase (T7 control vector) was
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Figure 3. Inhibitory effects of luc
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Anal. Chem. 2010, 82, 7027-7034 Pat
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Electrochemistry. Electrochemical m
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Figure 2. SEM images of Au substrat
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Table 3. Film Thickness Measurement
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Anal. Chem. 2010, 82, 7035-7043 Qua
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Figure 1. (A) FL spectra of BSPOTPE
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Figure 4. (A) Variation in the FL i
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Figure 6. (A) FL spectra of BSPOTPE
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Scheme 1. Proposed Mechanism for Fl
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one or more drawbacks including poo
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Figure 2. Free fluorophores do not
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Anal. Chem. 2010, 82, 7049-7052 Dev
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Figure 2. Comparative analysis of d
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