Limits of emission quantum yield determination

Abstract

The development of new fluorescent molecules and dyes requires precise determination of their emission efficiency, which ultimately defines the potential of the developed materials. For this, the photoluminescence quantum yield (QY) is commonly used, given by the ratio of the number of emitted and absorbed photons, where the latter can be determined by subtraction of the transmitted signal by the sample and by a blank reference. In this work, we show that when the measurement uncertainty is larger than 10% of the absorptance of the sample, the QY distribution function becomes skewed, which can result in underestimated QY values by more than 200%. We demonstrate this effect in great detail by simulation of the QY methodology that implements an integrating sphere, which is widely used commercially and for research. Based on our simulations, we show that this effect arises from the non-linear propagation of the measurement uncertainties. The observed effect applies to the measurement of any variable defined as Z = X/Y , with Y = U − V , where X, U and V are random, normally distributed parameters. For this general case, we derive the analytical expression and quantify the range in which the effect can be avoided.

Quantum Yield Bias in Materials With Lower Absorptance

“…S9 [41]). From this measurement, assuming a normal distribution of photon counts, we find an experimental uncertainty of 0.3%, which indicates a very precise measurement (we note that, in the limit of the low fluxes, one needs to take into account a Poisson distribution of photons, which, however, yields the same result [29]). We then compute QY values by taking random combinations of these values of N s and N ref into Eq.…”

“…(2), are expressed in terms of the probability, p x (Fig. S7 [29,41]), that emission and excitation light reach the detector port via multiple reflections inside the IS. In the RTS simulation, different photon paths are individually considered in a realistic IS setup, yielding solutions even for nonuniform photon distributions and IS geometries; this allows for more exact modeling of the setup (Figs.…”

“…4 Comparison of the experimental dependence of the PL QY of R6G on the single-pass absorptance (gray symbols) with simulated values from the AM (black line) and RTS (red symbols) approaches. For comparison, a peak value of the QY probability distribution [29] is also shown in the presence of measurement uncertainty in number of photons of α = 0.3% (green line).…”

“…The QY distribution function is then given by the ratio of two normal distributions, for which we have derived an analytical expression in Ref. [29]. As shown in Fig.…”

“…This limit is crucial because the absorption is directly linked to many experimental parameters, e.g., sample concentration, excitation wavelength, or volume, that may be varied in the study of a material. However, two effects have not yet been generally implemented in the QY methodology: first, signal offsets and nonlinearities for weak signals, which have been discussed only within the framework of IS measurements of absorption [7]; and, second, a systematic bias in QY measurement that occurs due to the skewed and even bimodal shape of the QY probability distribution function [29,30]. Importantly, this distribution function no longer has a defined meaning [30], making the situation even more complex.…”