Simultaneous All-Optical Determination of Molecular Concentration and Extinction Coefficient

Abstract

Absolute molecular number concentration and extinction coefficient are simultaneously determined from linear and nonlinear spectroscopic measurements. This method is based on measurements of absolute femtosecond pump-probe signals. Accounting for pulse propagation, we present a closed form expression for molecular number concentration in terms of absorbance, fluorescence, absolute pump-probe signal, and laser pulse parameters (pulse energy, spectrum, and spatial intensity profile); all quantities are measured optically. As in gravimetric and coulometric determinations of concentration, no standard samples are needed for calibration. The extinction coefficient can then be determined from the absorbance spectrum and the concentration. For fluorescein in basic methanol, the optically determined molar concentrations and extinction coefficients match gravimetric determinations to within 10% for concentrations from 0.032 to 0.540 mM, corresponding to absorbance from 0.06 to 1. In principle, this photonumeric method is extensible to transient chemical species for which other methods are not available.

Implantable Nanosensors: Toward Continuous Physiologic Monitoring

“…There are three general analyte recognition routes; reversibly non-reactive, reversibly reactive, and irreversible reactive 78 . Small molecule recognition elements such as crown ether or calixarene ionophores exemplify reversibly non-reactive recognition as they bind and release an ion of interest with no chemical reaction.…”

Not All β-Sheets Are the Same: Amyloid Infrared Spectra, Transition Dipole Strengths, and Couplings Investigated by 2D IR Spectroscopy

“…The spectrum of a calibrant molecule with known transition dipole strength is used to eliminate dependence of the measurement on experimental parameters, such as laser fluence and spatial overlap of laser pulses. 27 The transition dipole of the protein is calculated as the ratio of signal strengths shown in eq 1, where ΔOD sample and ΔOD calibrant are the intensities of the 2D IR spectra of the sample and calibrant, OD sample and OD calibrant are the OD of the sample and calibrant, and $false|{\overrightarrow{\mu }}_{\text{calibrant}}{|}^2$ is the transition dipole strength of the calibrant. By using a calibrant molecule with a similar anharmonicity and line width to the protein vibrational transitions we are studying, the effects of the overlapping bleach and excited state absorption cancel (to a reasonable approximation) when taking the ratio of signals described in eq 1.…”

“…Our method of measuring transition dipole strengths relies on the fact that the 2D IR signal is proportional to c × | μ⃗ | 4 ; by taking the ratio of the 2D IR and linear signals we obtain a measurement of | μ⃗ | 2 that is independent of concentration. The spectrum of a calibrant molecule with known transition dipole strength is used to eliminate dependence of the measurement on experimental parameters, such as laser fluence and spatial overlap of laser pulses . The transition dipole of the protein is calculated as the ratio of signal strengths shown in eq , where ΔOD sample and ΔOD calibrant are the intensities of the 2D IR spectra of the sample and calibrant, OD sample and OD calibrant are the OD of the sample and calibrant, and | μ⃗ calibrant | 2 is the transition dipole strength of the calibrant.…”

Pulse Propagation Effects in Optical 2D Fourier-Transform Spectroscopy: Theory

“…It successfully reproduces optical density effects on the integrated two-pulse photon echo signal decay rate and beam geometry distortions of relative cross-peak amplitudes in 2DFT infrared spectra . 2DFT spectra calculated using the 3DFT method at waiting times long compared to dipole dephasing dynamics connect to expressions for absolute pump–probe signal size , and to experimentally tested expressions for product 2D peak shapes …”

“…However, in order to take advantage of this additional information, one must avoid or account for distortions of the signal caused by the absorptive and dispersive nature of the sample. − Avoidance relegates experimental work to sample optical densities (OD) less than 0.1 where such distortions are typically below 10%, allowing 2DFT spectra to be modeled at the 10% level by ignoring spatial pulse propagation effects at the cost of reduced signal size. In contrast, nonlinear optical signals are typically maximized at optical densities near 0.7, where propagation effects are significant and must be accounted for. − For linear optics, neglect of propagation distortions corresponds to a restriction that the exponential in Beer’s law can be described by a Taylor series expansion that is truncated after the zeroth and first order terms. Because the signal-to-noise ratio of linear absorption spectra is typically optimized at optical densities between 0.3 and 0.7 , where the first-order Taylor series is a poor approximation to the exponential, transmittance spectra are almost always converted to an extinction coefficient using the Beer–Lambert law before modeling.…”