Abstract

Capillaries with a high-index fluorescent coating represent a new type of whispering-gallery-mode (WGM) microcavity sensor. By coating silicon quantum dots (Si-QDs) onto the channel wall of a microcapillary, a cylindrical microcavity forms in which the optical confinement arises from the index contrast at the interface between the QD layer and the glass capillary wall. However, the ability to functionalize the QD layer for biosensing applications is an open question, since the layer consists of a mixture of Si-QDs embedded in a glassy SiOx matrix. Here, we employ a polyelectrolyte (PE) multilayer approach to functionalize the microcapillary inner surface and demonstrate the potential of this refractive index sensing platform for label-free biosensing applications, using biotin-neutravidin as a specific interaction model.

© 2015 Optical Society of America

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2015 (1)

A. François, T. Reynolds, and T. M. Monro, “A fiber-tip label-free biological sensing platform: a practical approach toward in-vivo sensing,” Sensors (Basel) 15(1), 1168–1181 (2015).
[Crossref] [PubMed]

2014 (4)

A. Meldrum and F. Marsiglio, “Capillary-type microfluidic sensors based on optical whispering gallery mode resonances,” Reviews in Nanoscience and Nanotechnology 3(3), 193–209 (2014).
[Crossref]

W. R. Wong, O. Krupin, S. D. Sekaran, F. R. Mahamd Adikan, and P. Berini, “Serological diagnosis of dengue infection in blood plasma using long-range surface plasmon waveguides,” Anal. Chem. 86(3), 1735–1743 (2014).
[Crossref] [PubMed]

M. D. Baaske, M. R. Foreman, and F. Vollmer, “Single-molecule nucleic acid interactions monitored on a label-free microcavity biosensor platform,” Nat. Nanotechnol. 9(11), 933–939 (2014).
[Crossref] [PubMed]

S. Lane, J. Chan, T. Thiessen, and A. Meldrum, “Whispering gallery mode structure and refractometric sensitivity of fluorescent capillary-type sensors,” Sens. Actuators B Chem. 190, 752–759 (2014).
[Crossref]

2013 (7)

K. J. Rowland, A. François, P. Hoffmann, and T. M. Monro, “Fluorescent polymer coated capillaries as optofluidic refractometric sensors,” Opt. Express 21(9), 11492–11505 (2013).
[Crossref] [PubMed]

S. M. Grist, S. A. Schmidt, J. Flueckiger, V. Donzella, W. Shi, S. Talebi Fard, J. T. Kirk, D. M. Ratner, K. C. Cheung, and L. Chrostowski, “Silicon photonic micro-disk resonators for label-free biosensing,” Opt. Express 21(7), 7994–8006 (2013).
[PubMed]

Y. Zhi, T. Thiessen, and A. Meldrum, “Silicon quantum-dot-coated microspheres for microfluidic refractive index sensing,” J. Opt. Soc. Am. B 30(1), 51–56 (2013).
[Crossref]

Y. Zhi, C. P. K. Manchee, J. W. Silverstone, Z. Zhang, and A. Meldrum, “Refractometric sensing with silicon quantum dots coupled to a microsphere,” Plasmonics 8(1), 71–78 (2013).
[Crossref]

Y. Zhi, T. Thiessen, and A. Meldrum, “Silicon quantum dot coated microspheres for microfluidic refractive index sensing,” J. Opt. Soc. Am. B 30(1), 51–56 (2013).
[Crossref]

S. McFarlane, C. P. K. Manchee, J. Silverstone, J. G. C. Veinot, and A. Meldrum, “Feasibility of a fluorescent-core microcapillary for biosensing applications,” Sens. Lett. 11(8), 1513–1518 (2013).
[Crossref]

S. McFarlane, C. P. K. Manchee, J. W. Silverstone, J. G. C. Veinot, and A. Meldrum, “Synthesis and operation of fluorescent-core microcavities for refractometric sensing,” J. Vis. Exp. 73(73), e50256 (2013), doi:.
[Crossref] [PubMed]

2012 (3)

L. Weiss, A. Tazibt, A. Tidu, and M. Aillerie, “Water density and polarizability deduced from the refractive index determined by interferometric measurements up to 250 MPa,” J. Chem. Phys. 136(12), 124201 (2012).
[Crossref] [PubMed]

P. Preechaburana, M. C. Gonzalez, A. Suska, and D. Filippini, “Surface Plasmon Resonance Chemical Sensing on Cell Phones,” Angew. Chem. Int. Ed. Engl. 51(46), 11585–11588 (2012).
[Crossref] [PubMed]

J. W. Silverstone, S. McFarlane, C. P. K. Manchee, and A. Meldrum, “Ultimate resolution for refractometric sensing with whispering gallery mode microcavities,” Opt. Express 20(8), 8284–8295 (2012).
[Crossref] [PubMed]

2011 (2)

C. P. K. Manchee, V. Zamora, J. W. Silverstone, J. G. C. Veinot, and A. Meldrum, “Refractometric sensing with fluorescent-core microcapillaries,” Opt. Express 19(22), 21540–21551 (2011).
[PubMed]

E. Wijaya, C. Lenaerts, S. Maricot, J. Hastanin, S. Habraken, J.-P. Vilcot, R. Boukherroub, and S. Szunerits, “Surface plasmon resonance-based biosensors: From the development of different SPR structures to novel surface functionalization strategies,” Curr. Op. Sol. St. M. 15(5), 208–224 (2011).
[Crossref]

2010 (2)

M. Charlebois, A. Paquet, L. S. Verret, K. Boissinot, M. Boissinot, M. G. Bergeron, and C. N. Allen, “Toward Automatic Label-Free Whispering Gallery Modes Biodetection with a Quantum Dot-Coated Microsphere Population,” Nanoscale Res. Lett. 5(3), 524–532 (2010).
[Crossref] [PubMed]

G. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. Mei, and O. G. Schmidt, “Rolled-up optical microcavities with subwavelength wall thicknesses for enhanced liquid sensing applications,” ACS Nano 4(6), 3123–3130 (2010).
[Crossref] [PubMed]

2009 (4)

P. Bianucci, J. R. Rodriguez, C. M. Clements, J. G. C. Veinot, and A. Meldrum, “Silicon nanocrystal luminescence coupled to whispering gallery modes in optical fibers,” J. Appl. Phys. 105(2), 023108 (2009).
[Crossref]

H. T. Beier, G. L. Coté, and K. E. Meissner, “Whispering gallery mode biosensors consisting of quantum dot-embedded microspheres,” Ann. Biomed. Eng. 37(10), 1974–1983 (2009).
[Crossref] [PubMed]

J. Ladd, A. D. Taylor, M. Piliarik, J. Homola, and S. Jiang, “Label-free detection of cancer biomarker candidates using surface plasmon resonance imaging,” Anal. Bioanal. Chem. 393(4), 1157–1163 (2009).
[Crossref] [PubMed]

M. Piliarik and J. Homola, “Surface plasmon resonance (SPR) sensors: approaching their limits?” Opt. Express 17(19), 16505–16517 (2009).
[Crossref] [PubMed]

2008 (8)

I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express 16(2), 1020–1028 (2008).
[Crossref] [PubMed]

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[Crossref] [PubMed]

S. Pang, R. E. Beckham, and K. E. Meissner, “Quantum dot-embedded microspheres for remote refractive index sensing,” Appl. Phys. Lett. 92(22), 221108 (2008).
[Crossref] [PubMed]

A. François and M. Himmelhaus, “Optical biosensor based on whispering gallery mode excitations in clusters of microparticles,” Appl. Phys. Lett. 92(14), 141107 (2008).
[Crossref]

A. Weller, F. C. Liu, R. Dahint, and M. Himmelhaus, “Whispering gallery mode biosensors in the low-Q limit,” Appl. Phys. B 90(3-4), 561–567 (2008).
[Crossref]

Y. Panitchob, G. S. Murugan, M. N. Zervas, P. Horak, S. Berneschi, S. Pelli, G. Nunzi Conti, and J. S. Wilkinson, “Whispering gallery mode spectra of channel waveguide coupled microspheres,” Opt. Express 16(15), 11066–11076 (2008).
[Crossref] [PubMed]

A. Tsortos, G. Papadakis, K. Mitsakakis, K. A. Melzak, and E. Gizeli, “Quantitative determination of size and shape of surface-bound DNA using an acoustic wave sensor,” Biophys. J. 94(7), 2706–2715 (2008).
[Crossref] [PubMed]

H. Zhu, I. M. White, J. D. Suter, and X. Fan, “Phage-based label-free biomolecule detection in an opto-fluidic ring resonator,” Biosens. Bioelectron. 24(3), 461–466 (2008).
[Crossref] [PubMed]

2007 (9)

H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express 15(15), 9139–9146 (2007).
[Crossref] [PubMed]

C.-D. Chen, S.-F. Cheng, L.-K. Chau, and C. R. Wang, “Sensing capability of the localized surface plasmon resonance of gold nanorods,” Biosens. Bioelectron. 22(6), 926–932 (2007).
[Crossref] [PubMed]

I. Teraoka and S. Arnold, “Whispering-gallery modes in a microsphere coated with a high-refractive index layer: polariza-tion-dependent sensitivity enhancement of the resonance-shift sensor and TE-TM resonance matching,” J. Opt. Soc. Am. B 24(3), 653–659 (2007).
[Crossref]

I. M. White, S. I. Shapova, H. Zhu, J. D. Suter, S. Lacey, P. Zhang, H. Oveys, L. Brewington, J. Gohring, and X. Fan, “Applications of the liquid core optical ring resonator platform,” Proc. SPIE 6757, 675707 (2007).
[Crossref]

C. M. Hessel, E. J. Henderson, and J. G. C. Veinot, “An investigation of the formation and growth of oxide-embedded silicon nanocrystals in hydrogen silsesquioxane-derived nanocomposites,” J. Phys. Chem. C 111(19), 6956–6961 (2007).
[Crossref]

H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express 15(15), 9139–9146 (2007).
[Crossref] [PubMed]

E. Nuhiji and P. Mulvaney, “Detection of unlabeled oligonucleotide targets using whispering gallery modes in single, fluorescent microspheres,” Small 3(8), 1408–1414 (2007).
[Crossref] [PubMed]

P. Zijlstra, K. L. van der Molen, and A. P. Mosk, “Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere,” Appl. Phys. Lett. 90(16), 161101 (2007).

I. Teraoka and S. Arnold, “Coupled whispering gallery modes in a multilayer-coated microsphere,” Opt. Lett. 32(9), 1147–1149 (2007).
[Crossref] [PubMed]

2006 (2)

H. Zhu, J. D. Suter, I. M. White, and X. Fan, “Aptamer Based Microsphere Biosensor for Thrombin Detection,” Sensors (Basel Switzerland) 6(8), 785–795 (2006).
[Crossref]

G. Schweiger and M. Horn, “Effect of changes in size and index of refraction on the resonance wavelength of microspheres,” J. Opt. Soc. Am. B 23(2), 212–217 (2006).
[Crossref]

2005 (1)

D. E. Gómez, I. Pastoriza-Santos, and P. Mulvaney, “Tunable whispering gallery mode emission from quantum-dot-doped microspheres,” Small 1(2), 238–241 (2005).
[Crossref] [PubMed]

2004 (1)

V. Bosio, F. Dubreuil, G. Bogdanovic, and A. Fery, “Interactions between silica surfaces coated by polyelectrolyte multilayers in aqueous environment: comparison between precursor and multilayer regime,” Colloids Surf. A Physicochem. Eng. Asp. 243(1-3), 147–155 (2004).
[Crossref]

2003 (2)

P. Vermette, T. Gengenbach, U. Divisekera, P. A. Kambouris, H. J. Griesser, and L. Meagher, “Immobilization and surface characterization of NeutrAvidin biotin-binding protein on different hydrogel interlayers,” J. Colloid Interface Sci. 259(1), 13–26 (2003).
[Crossref] [PubMed]

S. F. Cheng and L. K. Chau, “Colloidal gold-modified optical fiber for chemical and biochemical sensing,” Anal. Chem. 75(1), 16–21 (2003).
[Crossref] [PubMed]

2001 (2)

2000 (2)

K. Johansen, R. Stålberg, I. Lundström, and B. Liedber, “Surface plasmon resonance: instrumental resolution using photo diode arrays,” Meas. Sci. Technol. 11(11), 1630–1638 (2000).
[Crossref]

I. Barinaga-Rementeria Ramírez, L. Ekblad, and B. Jergil, “Affinity partitioning of biotinylated mixed liposomes: effect of charge on biotin--NeutrAvidin interaction,” J. Chromatogr. B Biomed. Sci. Appl. 743(1-2), 389–396 (2000).
[Crossref] [PubMed]

1999 (3)

J. J. Cras, C. A. Rowe-Taitt, D. A. Nivens, and F. S. Ligler, “Comparison of chemical cleaning methods of glass in preparation for silanization,” Biosens. Bioelectron. 14(8-9), 683–688 (1999).
[Crossref]

C. Rosano, P. Arosio, and M. Bolognesi, “The X-ray three-dimensional structure of avidin,” Biomol. Eng. 16(1-4), 5–12 (1999).
[Crossref] [PubMed]

V. Lefèvre-Seguin, “Whispering-gallery mode lasers with doped silica microspheres,” Opt. Mater. 11(2-3), 153–165 (1999).
[Crossref]

1997 (1)

G. Decher, “Fuzzy nanoassemblies: toward layered polymeric multicomposites,” Science 227(5330), 1232–1237 (1997).
[Crossref]

1993 (1)

P. Allongue, V. Costa-Kieling, and H. Gerische, “Etching of Silicon in NaOH Solutions,” J. Electrochem. Soc. 140(4), 1009–1018 (1993).

1992 (1)

G. Decher and J. Schmitt, “Fine-tuning of the film thickness of ultrathin multilayer films composed of consecutively alternating layers of anionic and cationic polyelectrolytes,” Prog. Coll. Pol. Sci. S 89, 160–164 (1992).

1986 (1)

G. Y. Onoda and E. G. Liniger, “Experimental determination of the random-parking limit in two dimensions,” Phys. Rev. A 33(1), 715–716 (1986).
[Crossref] [PubMed]

1980 (1)

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of Structure Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44(7), 475–478 (1980).
[Crossref]

1973 (1)

1965 (1)

1957 (1)

S. A. Greenberg, “The depolymerisation of silica in sodium hydroxide solutions,” J. Phys. Chem. 61(7), 960–965 (1957).
[Crossref]

Aillerie, M.

L. Weiss, A. Tazibt, A. Tidu, and M. Aillerie, “Water density and polarizability deduced from the refractive index determined by interferometric measurements up to 250 MPa,” J. Chem. Phys. 136(12), 124201 (2012).
[Crossref] [PubMed]

Allen, C. N.

M. Charlebois, A. Paquet, L. S. Verret, K. Boissinot, M. Boissinot, M. G. Bergeron, and C. N. Allen, “Toward Automatic Label-Free Whispering Gallery Modes Biodetection with a Quantum Dot-Coated Microsphere Population,” Nanoscale Res. Lett. 5(3), 524–532 (2010).
[Crossref] [PubMed]

Allongue, P.

P. Allongue, V. Costa-Kieling, and H. Gerische, “Etching of Silicon in NaOH Solutions,” J. Electrochem. Soc. 140(4), 1009–1018 (1993).

Arnold, S.

Arosio, P.

C. Rosano, P. Arosio, and M. Bolognesi, “The X-ray three-dimensional structure of avidin,” Biomol. Eng. 16(1-4), 5–12 (1999).
[Crossref] [PubMed]

Baaske, M. D.

M. D. Baaske, M. R. Foreman, and F. Vollmer, “Single-molecule nucleic acid interactions monitored on a label-free microcavity biosensor platform,” Nat. Nanotechnol. 9(11), 933–939 (2014).
[Crossref] [PubMed]

Barber, P. W.

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of Structure Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44(7), 475–478 (1980).
[Crossref]

Barinaga-Rementeria Ramírez, I.

I. Barinaga-Rementeria Ramírez, L. Ekblad, and B. Jergil, “Affinity partitioning of biotinylated mixed liposomes: effect of charge on biotin--NeutrAvidin interaction,” J. Chromatogr. B Biomed. Sci. Appl. 743(1-2), 389–396 (2000).
[Crossref] [PubMed]

Beckham, R. E.

S. Pang, R. E. Beckham, and K. E. Meissner, “Quantum dot-embedded microspheres for remote refractive index sensing,” Appl. Phys. Lett. 92(22), 221108 (2008).
[Crossref] [PubMed]

Behrens, S. H.

S. H. Behrens and D. G. Grier, “The charge of glass and silica surfaces,” J. Chem. Phys. 115(14), 6716–6721 (2001).
[Crossref]

Beier, H. T.

H. T. Beier, G. L. Coté, and K. E. Meissner, “Whispering gallery mode biosensors consisting of quantum dot-embedded microspheres,” Ann. Biomed. Eng. 37(10), 1974–1983 (2009).
[Crossref] [PubMed]

Benner, R. E.

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of Structure Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44(7), 475–478 (1980).
[Crossref]

Bergeron, M. G.

M. Charlebois, A. Paquet, L. S. Verret, K. Boissinot, M. Boissinot, M. G. Bergeron, and C. N. Allen, “Toward Automatic Label-Free Whispering Gallery Modes Biodetection with a Quantum Dot-Coated Microsphere Population,” Nanoscale Res. Lett. 5(3), 524–532 (2010).
[Crossref] [PubMed]

Berini, P.

W. R. Wong, O. Krupin, S. D. Sekaran, F. R. Mahamd Adikan, and P. Berini, “Serological diagnosis of dengue infection in blood plasma using long-range surface plasmon waveguides,” Anal. Chem. 86(3), 1735–1743 (2014).
[Crossref] [PubMed]

Berneschi, S.

Bianucci, P.

P. Bianucci, J. R. Rodriguez, C. M. Clements, J. G. C. Veinot, and A. Meldrum, “Silicon nanocrystal luminescence coupled to whispering gallery modes in optical fibers,” J. Appl. Phys. 105(2), 023108 (2009).
[Crossref]

Bogdanovic, G.

V. Bosio, F. Dubreuil, G. Bogdanovic, and A. Fery, “Interactions between silica surfaces coated by polyelectrolyte multilayers in aqueous environment: comparison between precursor and multilayer regime,” Colloids Surf. A Physicochem. Eng. Asp. 243(1-3), 147–155 (2004).
[Crossref]

Boissinot, K.

M. Charlebois, A. Paquet, L. S. Verret, K. Boissinot, M. Boissinot, M. G. Bergeron, and C. N. Allen, “Toward Automatic Label-Free Whispering Gallery Modes Biodetection with a Quantum Dot-Coated Microsphere Population,” Nanoscale Res. Lett. 5(3), 524–532 (2010).
[Crossref] [PubMed]

Boissinot, M.

M. Charlebois, A. Paquet, L. S. Verret, K. Boissinot, M. Boissinot, M. G. Bergeron, and C. N. Allen, “Toward Automatic Label-Free Whispering Gallery Modes Biodetection with a Quantum Dot-Coated Microsphere Population,” Nanoscale Res. Lett. 5(3), 524–532 (2010).
[Crossref] [PubMed]

Bolaños Quiñones, V. A.

G. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. Mei, and O. G. Schmidt, “Rolled-up optical microcavities with subwavelength wall thicknesses for enhanced liquid sensing applications,” ACS Nano 4(6), 3123–3130 (2010).
[Crossref] [PubMed]

Bolognesi, M.

C. Rosano, P. Arosio, and M. Bolognesi, “The X-ray three-dimensional structure of avidin,” Biomol. Eng. 16(1-4), 5–12 (1999).
[Crossref] [PubMed]

Bosio, V.

V. Bosio, F. Dubreuil, G. Bogdanovic, and A. Fery, “Interactions between silica surfaces coated by polyelectrolyte multilayers in aqueous environment: comparison between precursor and multilayer regime,” Colloids Surf. A Physicochem. Eng. Asp. 243(1-3), 147–155 (2004).
[Crossref]

Boukherroub, R.

E. Wijaya, C. Lenaerts, S. Maricot, J. Hastanin, S. Habraken, J.-P. Vilcot, R. Boukherroub, and S. Szunerits, “Surface plasmon resonance-based biosensors: From the development of different SPR structures to novel surface functionalization strategies,” Curr. Op. Sol. St. M. 15(5), 208–224 (2011).
[Crossref]

Brewington, L.

I. M. White, S. I. Shapova, H. Zhu, J. D. Suter, S. Lacey, P. Zhang, H. Oveys, L. Brewington, J. Gohring, and X. Fan, “Applications of the liquid core optical ring resonator platform,” Proc. SPIE 6757, 675707 (2007).
[Crossref]

Chan, J.

S. Lane, J. Chan, T. Thiessen, and A. Meldrum, “Whispering gallery mode structure and refractometric sensitivity of fluorescent capillary-type sensors,” Sens. Actuators B Chem. 190, 752–759 (2014).
[Crossref]

Chang, R. K.

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of Structure Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44(7), 475–478 (1980).
[Crossref]

Charlebois, M.

M. Charlebois, A. Paquet, L. S. Verret, K. Boissinot, M. Boissinot, M. G. Bergeron, and C. N. Allen, “Toward Automatic Label-Free Whispering Gallery Modes Biodetection with a Quantum Dot-Coated Microsphere Population,” Nanoscale Res. Lett. 5(3), 524–532 (2010).
[Crossref] [PubMed]

Chau, L. K.

S. F. Cheng and L. K. Chau, “Colloidal gold-modified optical fiber for chemical and biochemical sensing,” Anal. Chem. 75(1), 16–21 (2003).
[Crossref] [PubMed]

Chau, L.-K.

C.-D. Chen, S.-F. Cheng, L.-K. Chau, and C. R. Wang, “Sensing capability of the localized surface plasmon resonance of gold nanorods,” Biosens. Bioelectron. 22(6), 926–932 (2007).
[Crossref] [PubMed]

Chen, C.-D.

C.-D. Chen, S.-F. Cheng, L.-K. Chau, and C. R. Wang, “Sensing capability of the localized surface plasmon resonance of gold nanorods,” Biosens. Bioelectron. 22(6), 926–932 (2007).
[Crossref] [PubMed]

Cheng, S. F.

S. F. Cheng and L. K. Chau, “Colloidal gold-modified optical fiber for chemical and biochemical sensing,” Anal. Chem. 75(1), 16–21 (2003).
[Crossref] [PubMed]

Cheng, S.-F.

C.-D. Chen, S.-F. Cheng, L.-K. Chau, and C. R. Wang, “Sensing capability of the localized surface plasmon resonance of gold nanorods,” Biosens. Bioelectron. 22(6), 926–932 (2007).
[Crossref] [PubMed]

Cheung, K. C.

Chrostowski, L.

Clements, C. M.

P. Bianucci, J. R. Rodriguez, C. M. Clements, J. G. C. Veinot, and A. Meldrum, “Silicon nanocrystal luminescence coupled to whispering gallery modes in optical fibers,” J. Appl. Phys. 105(2), 023108 (2009).
[Crossref]

Costa-Kieling, V.

P. Allongue, V. Costa-Kieling, and H. Gerische, “Etching of Silicon in NaOH Solutions,” J. Electrochem. Soc. 140(4), 1009–1018 (1993).

Coté, G. L.

H. T. Beier, G. L. Coté, and K. E. Meissner, “Whispering gallery mode biosensors consisting of quantum dot-embedded microspheres,” Ann. Biomed. Eng. 37(10), 1974–1983 (2009).
[Crossref] [PubMed]

Cras, J. J.

J. J. Cras, C. A. Rowe-Taitt, D. A. Nivens, and F. S. Ligler, “Comparison of chemical cleaning methods of glass in preparation for silanization,” Biosens. Bioelectron. 14(8-9), 683–688 (1999).
[Crossref]

Dahint, R.

A. Weller, F. C. Liu, R. Dahint, and M. Himmelhaus, “Whispering gallery mode biosensors in the low-Q limit,” Appl. Phys. B 90(3-4), 561–567 (2008).
[Crossref]

Dale, P. S.

Decher, G.

G. Decher, “Fuzzy nanoassemblies: toward layered polymeric multicomposites,” Science 227(5330), 1232–1237 (1997).
[Crossref]

G. Decher and J. Schmitt, “Fine-tuning of the film thickness of ultrathin multilayer films composed of consecutively alternating layers of anionic and cationic polyelectrolytes,” Prog. Coll. Pol. Sci. S 89, 160–164 (1992).

Ding, F.

G. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. Mei, and O. G. Schmidt, “Rolled-up optical microcavities with subwavelength wall thicknesses for enhanced liquid sensing applications,” ACS Nano 4(6), 3123–3130 (2010).
[Crossref] [PubMed]

Divisekera, U.

P. Vermette, T. Gengenbach, U. Divisekera, P. A. Kambouris, H. J. Griesser, and L. Meagher, “Immobilization and surface characterization of NeutrAvidin biotin-binding protein on different hydrogel interlayers,” J. Colloid Interface Sci. 259(1), 13–26 (2003).
[Crossref] [PubMed]

Donzella, V.

Dubreuil, F.

V. Bosio, F. Dubreuil, G. Bogdanovic, and A. Fery, “Interactions between silica surfaces coated by polyelectrolyte multilayers in aqueous environment: comparison between precursor and multilayer regime,” Colloids Surf. A Physicochem. Eng. Asp. 243(1-3), 147–155 (2004).
[Crossref]

Ekblad, L.

I. Barinaga-Rementeria Ramírez, L. Ekblad, and B. Jergil, “Affinity partitioning of biotinylated mixed liposomes: effect of charge on biotin--NeutrAvidin interaction,” J. Chromatogr. B Biomed. Sci. Appl. 743(1-2), 389–396 (2000).
[Crossref] [PubMed]

Fan, X.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[Crossref] [PubMed]

I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express 16(2), 1020–1028 (2008).
[Crossref] [PubMed]

H. Zhu, I. M. White, J. D. Suter, and X. Fan, “Phage-based label-free biomolecule detection in an opto-fluidic ring resonator,” Biosens. Bioelectron. 24(3), 461–466 (2008).
[Crossref] [PubMed]

I. M. White, S. I. Shapova, H. Zhu, J. D. Suter, S. Lacey, P. Zhang, H. Oveys, L. Brewington, J. Gohring, and X. Fan, “Applications of the liquid core optical ring resonator platform,” Proc. SPIE 6757, 675707 (2007).
[Crossref]

H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express 15(15), 9139–9146 (2007).
[Crossref] [PubMed]

H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express 15(15), 9139–9146 (2007).
[Crossref] [PubMed]

H. Zhu, J. D. Suter, I. M. White, and X. Fan, “Aptamer Based Microsphere Biosensor for Thrombin Detection,” Sensors (Basel Switzerland) 6(8), 785–795 (2006).
[Crossref]

Fery, A.

V. Bosio, F. Dubreuil, G. Bogdanovic, and A. Fery, “Interactions between silica surfaces coated by polyelectrolyte multilayers in aqueous environment: comparison between precursor and multilayer regime,” Colloids Surf. A Physicochem. Eng. Asp. 243(1-3), 147–155 (2004).
[Crossref]

Filippini, D.

P. Preechaburana, M. C. Gonzalez, A. Suska, and D. Filippini, “Surface Plasmon Resonance Chemical Sensing on Cell Phones,” Angew. Chem. Int. Ed. Engl. 51(46), 11585–11588 (2012).
[Crossref] [PubMed]

Flueckiger, J.

Foreman, M. R.

M. D. Baaske, M. R. Foreman, and F. Vollmer, “Single-molecule nucleic acid interactions monitored on a label-free microcavity biosensor platform,” Nat. Nanotechnol. 9(11), 933–939 (2014).
[Crossref] [PubMed]

François, A.

A. François, T. Reynolds, and T. M. Monro, “A fiber-tip label-free biological sensing platform: a practical approach toward in-vivo sensing,” Sensors (Basel) 15(1), 1168–1181 (2015).
[Crossref] [PubMed]

K. J. Rowland, A. François, P. Hoffmann, and T. M. Monro, “Fluorescent polymer coated capillaries as optofluidic refractometric sensors,” Opt. Express 21(9), 11492–11505 (2013).
[Crossref] [PubMed]

A. François and M. Himmelhaus, “Optical biosensor based on whispering gallery mode excitations in clusters of microparticles,” Appl. Phys. Lett. 92(14), 141107 (2008).
[Crossref]

Gengenbach, T.

P. Vermette, T. Gengenbach, U. Divisekera, P. A. Kambouris, H. J. Griesser, and L. Meagher, “Immobilization and surface characterization of NeutrAvidin biotin-binding protein on different hydrogel interlayers,” J. Colloid Interface Sci. 259(1), 13–26 (2003).
[Crossref] [PubMed]

Gerische, H.

P. Allongue, V. Costa-Kieling, and H. Gerische, “Etching of Silicon in NaOH Solutions,” J. Electrochem. Soc. 140(4), 1009–1018 (1993).

Gizeli, E.

A. Tsortos, G. Papadakis, K. Mitsakakis, K. A. Melzak, and E. Gizeli, “Quantitative determination of size and shape of surface-bound DNA using an acoustic wave sensor,” Biophys. J. 94(7), 2706–2715 (2008).
[Crossref] [PubMed]

Gohring, J.

I. M. White, S. I. Shapova, H. Zhu, J. D. Suter, S. Lacey, P. Zhang, H. Oveys, L. Brewington, J. Gohring, and X. Fan, “Applications of the liquid core optical ring resonator platform,” Proc. SPIE 6757, 675707 (2007).
[Crossref]

Gómez, D. E.

D. E. Gómez, I. Pastoriza-Santos, and P. Mulvaney, “Tunable whispering gallery mode emission from quantum-dot-doped microspheres,” Small 1(2), 238–241 (2005).
[Crossref] [PubMed]

Gonzalez, M. C.

P. Preechaburana, M. C. Gonzalez, A. Suska, and D. Filippini, “Surface Plasmon Resonance Chemical Sensing on Cell Phones,” Angew. Chem. Int. Ed. Engl. 51(46), 11585–11588 (2012).
[Crossref] [PubMed]

Gorodetsky, M. L.

Greenberg, S. A.

S. A. Greenberg, “The depolymerisation of silica in sodium hydroxide solutions,” J. Phys. Chem. 61(7), 960–965 (1957).
[Crossref]

Grier, D. G.

S. H. Behrens and D. G. Grier, “The charge of glass and silica surfaces,” J. Chem. Phys. 115(14), 6716–6721 (2001).
[Crossref]

Griesser, H. J.

P. Vermette, T. Gengenbach, U. Divisekera, P. A. Kambouris, H. J. Griesser, and L. Meagher, “Immobilization and surface characterization of NeutrAvidin biotin-binding protein on different hydrogel interlayers,” J. Colloid Interface Sci. 259(1), 13–26 (2003).
[Crossref] [PubMed]

Grist, S. M.

Habraken, S.

E. Wijaya, C. Lenaerts, S. Maricot, J. Hastanin, S. Habraken, J.-P. Vilcot, R. Boukherroub, and S. Szunerits, “Surface plasmon resonance-based biosensors: From the development of different SPR structures to novel surface functionalization strategies,” Curr. Op. Sol. St. M. 15(5), 208–224 (2011).
[Crossref]

Hale, G. M.

Hastanin, J.

E. Wijaya, C. Lenaerts, S. Maricot, J. Hastanin, S. Habraken, J.-P. Vilcot, R. Boukherroub, and S. Szunerits, “Surface plasmon resonance-based biosensors: From the development of different SPR structures to novel surface functionalization strategies,” Curr. Op. Sol. St. M. 15(5), 208–224 (2011).
[Crossref]

Henderson, E. J.

C. M. Hessel, E. J. Henderson, and J. G. C. Veinot, “An investigation of the formation and growth of oxide-embedded silicon nanocrystals in hydrogen silsesquioxane-derived nanocomposites,” J. Phys. Chem. C 111(19), 6956–6961 (2007).
[Crossref]

Hessel, C. M.

C. M. Hessel, E. J. Henderson, and J. G. C. Veinot, “An investigation of the formation and growth of oxide-embedded silicon nanocrystals in hydrogen silsesquioxane-derived nanocomposites,” J. Phys. Chem. C 111(19), 6956–6961 (2007).
[Crossref]

Himmelhaus, M.

A. François and M. Himmelhaus, “Optical biosensor based on whispering gallery mode excitations in clusters of microparticles,” Appl. Phys. Lett. 92(14), 141107 (2008).
[Crossref]

A. Weller, F. C. Liu, R. Dahint, and M. Himmelhaus, “Whispering gallery mode biosensors in the low-Q limit,” Appl. Phys. B 90(3-4), 561–567 (2008).
[Crossref]

Hoffmann, P.

Homola, J.

M. Piliarik and J. Homola, “Surface plasmon resonance (SPR) sensors: approaching their limits?” Opt. Express 17(19), 16505–16517 (2009).
[Crossref] [PubMed]

J. Ladd, A. D. Taylor, M. Piliarik, J. Homola, and S. Jiang, “Label-free detection of cancer biomarker candidates using surface plasmon resonance imaging,” Anal. Bioanal. Chem. 393(4), 1157–1163 (2009).
[Crossref] [PubMed]

Horak, P.

Horn, M.

Huang, G.

G. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. Mei, and O. G. Schmidt, “Rolled-up optical microcavities with subwavelength wall thicknesses for enhanced liquid sensing applications,” ACS Nano 4(6), 3123–3130 (2010).
[Crossref] [PubMed]

Ilchenko, V. S.

Jergil, B.

I. Barinaga-Rementeria Ramírez, L. Ekblad, and B. Jergil, “Affinity partitioning of biotinylated mixed liposomes: effect of charge on biotin--NeutrAvidin interaction,” J. Chromatogr. B Biomed. Sci. Appl. 743(1-2), 389–396 (2000).
[Crossref] [PubMed]

Jiang, S.

J. Ladd, A. D. Taylor, M. Piliarik, J. Homola, and S. Jiang, “Label-free detection of cancer biomarker candidates using surface plasmon resonance imaging,” Anal. Bioanal. Chem. 393(4), 1157–1163 (2009).
[Crossref] [PubMed]

Johansen, K.

K. Johansen, R. Stålberg, I. Lundström, and B. Liedber, “Surface plasmon resonance: instrumental resolution using photo diode arrays,” Meas. Sci. Technol. 11(11), 1630–1638 (2000).
[Crossref]

Kambouris, P. A.

P. Vermette, T. Gengenbach, U. Divisekera, P. A. Kambouris, H. J. Griesser, and L. Meagher, “Immobilization and surface characterization of NeutrAvidin biotin-binding protein on different hydrogel interlayers,” J. Colloid Interface Sci. 259(1), 13–26 (2003).
[Crossref] [PubMed]

Kiravittaya, S.

G. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. Mei, and O. G. Schmidt, “Rolled-up optical microcavities with subwavelength wall thicknesses for enhanced liquid sensing applications,” ACS Nano 4(6), 3123–3130 (2010).
[Crossref] [PubMed]

Kirk, J. T.

Krupin, O.

W. R. Wong, O. Krupin, S. D. Sekaran, F. R. Mahamd Adikan, and P. Berini, “Serological diagnosis of dengue infection in blood plasma using long-range surface plasmon waveguides,” Anal. Chem. 86(3), 1735–1743 (2014).
[Crossref] [PubMed]

Lacey, S.

I. M. White, S. I. Shapova, H. Zhu, J. D. Suter, S. Lacey, P. Zhang, H. Oveys, L. Brewington, J. Gohring, and X. Fan, “Applications of the liquid core optical ring resonator platform,” Proc. SPIE 6757, 675707 (2007).
[Crossref]

Ladd, J.

J. Ladd, A. D. Taylor, M. Piliarik, J. Homola, and S. Jiang, “Label-free detection of cancer biomarker candidates using surface plasmon resonance imaging,” Anal. Bioanal. Chem. 393(4), 1157–1163 (2009).
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Lane, S.

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Papadakis, G.

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P. Bianucci, J. R. Rodriguez, C. M. Clements, J. G. C. Veinot, and A. Meldrum, “Silicon nanocrystal luminescence coupled to whispering gallery modes in optical fibers,” J. Appl. Phys. 105(2), 023108 (2009).
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W. R. Wong, O. Krupin, S. D. Sekaran, F. R. Mahamd Adikan, and P. Berini, “Serological diagnosis of dengue infection in blood plasma using long-range surface plasmon waveguides,” Anal. Chem. 86(3), 1735–1743 (2014).
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Shopova, S. I.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
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S. McFarlane, C. P. K. Manchee, J. Silverstone, J. G. C. Veinot, and A. Meldrum, “Feasibility of a fluorescent-core microcapillary for biosensing applications,” Sens. Lett. 11(8), 1513–1518 (2013).
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S. McFarlane, C. P. K. Manchee, J. W. Silverstone, J. G. C. Veinot, and A. Meldrum, “Synthesis and operation of fluorescent-core microcavities for refractometric sensing,” J. Vis. Exp. 73(73), e50256 (2013), doi:.
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J. W. Silverstone, S. McFarlane, C. P. K. Manchee, and A. Meldrum, “Ultimate resolution for refractometric sensing with whispering gallery mode microcavities,” Opt. Express 20(8), 8284–8295 (2012).
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K. Johansen, R. Stålberg, I. Lundström, and B. Liedber, “Surface plasmon resonance: instrumental resolution using photo diode arrays,” Meas. Sci. Technol. 11(11), 1630–1638 (2000).
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X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
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P. Preechaburana, M. C. Gonzalez, A. Suska, and D. Filippini, “Surface Plasmon Resonance Chemical Sensing on Cell Phones,” Angew. Chem. Int. Ed. Engl. 51(46), 11585–11588 (2012).
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X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
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H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express 15(15), 9139–9146 (2007).
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H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express 15(15), 9139–9146 (2007).
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Talebi Fard, S.

Taylor, A. D.

J. Ladd, A. D. Taylor, M. Piliarik, J. Homola, and S. Jiang, “Label-free detection of cancer biomarker candidates using surface plasmon resonance imaging,” Anal. Bioanal. Chem. 393(4), 1157–1163 (2009).
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L. Weiss, A. Tazibt, A. Tidu, and M. Aillerie, “Water density and polarizability deduced from the refractive index determined by interferometric measurements up to 250 MPa,” J. Chem. Phys. 136(12), 124201 (2012).
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Thiessen, T.

Tidu, A.

L. Weiss, A. Tazibt, A. Tidu, and M. Aillerie, “Water density and polarizability deduced from the refractive index determined by interferometric measurements up to 250 MPa,” J. Chem. Phys. 136(12), 124201 (2012).
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A. Tsortos, G. Papadakis, K. Mitsakakis, K. A. Melzak, and E. Gizeli, “Quantitative determination of size and shape of surface-bound DNA using an acoustic wave sensor,” Biophys. J. 94(7), 2706–2715 (2008).
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P. Zijlstra, K. L. van der Molen, and A. P. Mosk, “Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere,” Appl. Phys. Lett. 90(16), 161101 (2007).

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S. McFarlane, C. P. K. Manchee, J. W. Silverstone, J. G. C. Veinot, and A. Meldrum, “Synthesis and operation of fluorescent-core microcavities for refractometric sensing,” J. Vis. Exp. 73(73), e50256 (2013), doi:.
[Crossref] [PubMed]

S. McFarlane, C. P. K. Manchee, J. Silverstone, J. G. C. Veinot, and A. Meldrum, “Feasibility of a fluorescent-core microcapillary for biosensing applications,” Sens. Lett. 11(8), 1513–1518 (2013).
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P. Bianucci, J. R. Rodriguez, C. M. Clements, J. G. C. Veinot, and A. Meldrum, “Silicon nanocrystal luminescence coupled to whispering gallery modes in optical fibers,” J. Appl. Phys. 105(2), 023108 (2009).
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M. Charlebois, A. Paquet, L. S. Verret, K. Boissinot, M. Boissinot, M. G. Bergeron, and C. N. Allen, “Toward Automatic Label-Free Whispering Gallery Modes Biodetection with a Quantum Dot-Coated Microsphere Population,” Nanoscale Res. Lett. 5(3), 524–532 (2010).
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E. Wijaya, C. Lenaerts, S. Maricot, J. Hastanin, S. Habraken, J.-P. Vilcot, R. Boukherroub, and S. Szunerits, “Surface plasmon resonance-based biosensors: From the development of different SPR structures to novel surface functionalization strategies,” Curr. Op. Sol. St. M. 15(5), 208–224 (2011).
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A. Weller, F. C. Liu, R. Dahint, and M. Himmelhaus, “Whispering gallery mode biosensors in the low-Q limit,” Appl. Phys. B 90(3-4), 561–567 (2008).
[Crossref]

White, I. M.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[Crossref] [PubMed]

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H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express 15(15), 9139–9146 (2007).
[Crossref] [PubMed]

I. M. White, S. I. Shapova, H. Zhu, J. D. Suter, S. Lacey, P. Zhang, H. Oveys, L. Brewington, J. Gohring, and X. Fan, “Applications of the liquid core optical ring resonator platform,” Proc. SPIE 6757, 675707 (2007).
[Crossref]

H. Zhu, J. D. Suter, I. M. White, and X. Fan, “Aptamer Based Microsphere Biosensor for Thrombin Detection,” Sensors (Basel Switzerland) 6(8), 785–795 (2006).
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Wijaya, E.

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Figures (9)

Fig. 1
Fig. 1

of the capillary and the experimental setup. In the cross-sectional diagram of the capillary, the refractive indices m1, m2, and m3 refer to the analyte, fluorescent layer, and capillary wall, respectively. Radius “b” is measured to the QD layer while “a” is the capillary’s original inner radius (i.e., prior to QD layer deposition). The white wave represents a WGM electric field profile.

Fig. 2
Fig. 2

Diagram of the polyelectrolyte surface functionalization for the biosensing experiments corresponding to steps 1-10 below. The NaOH-treated glass surface has a polyelectrolyte trilayer, with the final PAH layer capturing biotin.

Fig. 3
Fig. 3

(a) Fluorescence image of the capillary channel. The red glow is due to the QD emission. The representative slit direction (perpendicular to the channel) is diagrammed. (b) A typical WGM emission spectrum over the range from 760 to 780 nm.

Fig. 4
Fig. 4

WGM wavelength shift as a function of NaOH etching time. As the QD film becomes thinner, the WGMs gradually blueshift. The upper-right inset shows sensorgrams for the water-to-ethanol transition at different etching times. The sensitivity of a single fluorescent microcavity observed at many different etching times is shown in the lower-left inset.

Fig. 5
Fig. 5

(a) Calculated 2D electric field amplitude for an n = 1, l = 310 TM mode for a 50-μm diameter capillary with 500-nm-thick QD film (marked by the black lines). Only part of the circumference is shown. (b) 1D intensity profile for the same conditions as in (a). The discontinuities in the field profile are due to the TM boundary conditions. The sensitivity of this structure is calculated from Eq. (4) to be 23.7 nm/RIU.

Fig. 6
Fig. 6

Sensorgram showing the deposition of alternating layers of PAH (red points) and PSS (yellow), followed by cleaning with 10 M NaOH solution (pink). Water is in blue, labeled a to e. The inset shows representative spectra corresponding to steps a and e.

Fig. 7
Fig. 7

Sensorgram showing the 13-step functionalization and biosensing experiment. The numbers label the steps according to the list given in Section 2. The key step is (12), corresponding to the specific binding of neutravidin.

Fig. 8
Fig. 8

(a) Sensorgram for control sample 1. The sequence is identical to that in Fig. 7, except that the neutravidin (step 12) had been pre-biotinylated before being pumped into the microcavity. (b) Sensorgram for control sample 2. Here, there is a slight redshift (grey points, step 12), likely due to a small amount of electrostatic binding of neutravidin to the PAH layer.

Fig. 9
Fig. 9

Sensorgrams for neutravidin binding, for four different concentrations. These data show only step 12 of the reaction process; for each data set the capillary was cleaned with 10 M NaOH and steps 1-11 were performed prior to the running the neutravidin solution. The black lines are fits using first-order reaction kinetics (Eq. (8). The inset shows kobs plotted against the neutravidin concentration, along with a linear fit.

Equations (9)

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T l (r)={ a l J l ( m 1 k 0 r ), rb b l H l (2) ( m 2 k 0 r )+ H l (1) ( m 2 k 0 r ), r<ba d l H l (1) ( m 3 k 0 r ), r>a }
m 2 H l (1) '( m 3 k 0 a ) m 3 H l (1) ( m 3 k 0 a ) = b l H l (2) '( m 2 k 0 a )+ H l (1) '( m 2 k 0 a ) b l H l (2) ( m 2 k 0 a )+ H l (1) ( m 2 k 0 a ) ,
b l = m 1 J l ( m 1 k 0 b ) H l (1) '( m 2 k 0 b ) m 2 J l '( m 1 k 0 b ) H l (1) ( m 2 k 0 b ) m 1 J l ( m 1 k 0 b ) H l (2) '( m 2 k 0 b )+ m 2 J l '( m 1 k 0 b ) H l (2) ( m 2 k 0 b ) .
S TM = λ 0 ( 2 k 1 2 ) m 1 3 ( k 0 2 + ( k 0 * ) 2 ) b | a l | 2 ( d J l * ( m 1 k 0 r ) dr b J l ( m 1 k 0 b )+ J l * ( m 1 k 0 b ) d J l ( m 1 k 0 r ) dr b )+ k 0 2 + ( k 0 * ) 2 k 0,1 2 I 1 [ I 1 m 1 2 + I 2 m 2 2 + I 3 m 3 2 ] ,
I 1 = 0 m 1 k 0,1 b x | a l J l ( x ˜ ) | 2 dx I 2 = m 2 k 0,1 b m 2 k 0,1 a x | b l H l (2) ( x ˜ )+ H l (1) ( x ˜ ) | 2 dx . I 3 = m 3 k 0 a x | d l H l (1) ( x ˜ ) | 2 dx
σ p = δλ λ 0 ε 0 a( m 2 2 m 1 2 ) α ex
α n = ε n 1 ε n +2 3M ε 0 N A ρ n
R t = R 0 [ 1exp( k obs t ) ]
k obs = k a [ B ]+ k d

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