Since
Sørensen and Bjerrum defined the pH scale, we have relied
on two methods for determining pH, the colorimetric or the electrochemical.
For pH electrodes, calibration is easy as a linear response is observed
in the interesting pH range from 1 to ∼12. For colorimetric
sensors, the response follows the sigmoidal Bjerrum diagram of an
acid–base equilibrium. Thus, calibration of colorimetric sensors
is more complex. Here, seven pH responsive fluorescent dyes based
on the same diazaoxatriangulenium (DAOTA) fluorophore linked to varying
receptor groups were prepared. Photoinduced electron transfer (PeT)
quenching from appended aniline or phenol receptors generated the
pH response of the DAOTA dyes, and the position of the pK
a value of the dye was tuned using the Hammett relationship
as a guideline. The fluorescence intensity of the dyes in a sol–gel
matrix environment was measured as a function of pH in universal buffer,
and it was found that the dyes behave as perfect pH responsive probes
under these conditions. The response of optical pH sensors is nonlinear
and was found to be limited to 2–3 pH units for a precision
of 0.01 pH unit. As sensors with a broader sensitivity range can be
achieved by mixing multiple dyes with different pK
a values, mixtures of dyes in solution were investigated,
and a broad range pH sensor with a precision of 0.006 pH units over
a range of 3.6 pH units was demonstrated. Further, approximating the
sensor response as linear was considered, and a limiting precision
for this approach was determined. As the responses of the pH responsive
DAOTA dyes were found to be ideally sigmoidal and as the six dyes
were shown to have pK
a values scattered
over a range from ∼2 to ∼9, this allows for design of
a broad range optical pH sensor in the pH range from 1 to 10. This
hypothesis was tested using quaternary mixtures of the different DAOTA
dyes, and these were found to behave as a direct sum of the individual
components. Thus, while linear calibration is limited to a precision
of 0.02 in a range of 2–3 pH units, calibration using ideal
sigmoidal functions is possible in the range of 1–10 with a
precision better than 0.01, and as good as 0.002 pH units.