Estimating Ph at the Air/Water Interface with a Confocal
ANALYTICAL SCIENCES OCTOBER 2015, VOL. 31 1 2015 © The Japan Society for Analytical Chemistry
Supporting Information
Estimating pH at the Air/Water Interface with a Confocal
Fluorescence Microscope
Haiya YANG, Yasushi IMANISHI, Akira HARATA†
Department of Molecular and Material Sciences, Interdisciplinary Graduate School of
Engineering Sciences, Kyushu University, 6-1 Kasugakoen, Kasuga-shi, Fukuoka 816-8580,
Japan
† To whom correspondence should be addressed.
Email: [email protected]
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Mathematical relationship between fluorescence peak wavenumbers and pH for a fluorescent
pH indicator
In a confocal fluorescence microscope, the probe volume is confined in an elongated cylindrical
shape with radius and height . If the position of the surface is defined to be exactly at the
symmetrical plane horizontally intersecting the cylinder, the probe area and probe volume are
and for the surface observation, while they are zero and for the bulk
observation, respectively. For a component i, the ratio of fluorescent intensity detected for the
surface observation with respect to the bulk observation can be given as
(S1)
where and represent the efficiencies of fluorescence excitation detection per
fluorescent molecule at the surface and in the bulk solution, respectively; is the surface
density, and is the bulk concentration. Because , Eq. (S1) is deformed into
; (S2)
when , a surface-selective observation for this surface-active component at the water
surface is available.17
In this case, and at a low concentration limit, the pH-dependent fluorescence spectrum of
the surface-adsorbed pH indictor is given by
, (S3)
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where is proportionality constant for the equipment, is the excitation laser power, is
the fluorescence photo frequency, A and B are acid and basic forms of the pH indicator,
respectively. Here, it is assumed that fluorescent spectra of the both acid and basic forms are pH
independent. At a low concentration limit, where , Eq. (S3) is deformed into
(S4)
where is the fraction of the acid form in the solution’s surface region.
The pH-dependent fluorescent spectrum of the bulk indicator is given by
, (S5)
where is the fraction of the acid form in the solution’s bulk region.
At the fluorescence maxima, we have both for surface (x=surf) and
bulk (x=bulk). For simplicity, the fluorescence spectrum shapes around the fluorescence
maxima are assumed to be ( ), so that , and
we get
, (S6)
where
(S7)
and
. (S8)
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The values of can be determined through Eq. (5) after obtaining the values of
, , and with surface tension measurements. is a
known value. Both and are assumed to be 1.
Therefore, a mathematical relationship between fluorescence peak wavenumbers and pH is
clearly understood through Eq. (S6), Eq. (S7), and Eq. (S8).
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