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] 1 2 ANALYTICAL SCIENCES OCTOBER 2015, VOL. 31 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) 2 ANALYTICAL SCIENCES OCTOBER 2015, VOL. 31 3 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) 3 4 ANALYTICAL SCIENCES OCTOBER 2015, VOL. 31 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). 4 .