Standard synthesis of formazine and influence of stirring
Figure 1 displays three repeated syntheses of formazine at 100 % relative concentration and 25 °C (i.e., 4000 FTU). Here, the formation of formazine occurs approximately 2.5 h after initial mixing of the stock solutions, leading to a turbid suspension. The sharp increase of turbidity at this point in time is assumed to indicate the beginning of the precipitation of formazine.
After approximately 5 h, the reduced scattering coefficient as well as the reflected intensity I
R reached a plateau. The reduced scattering coefficient indicates a reproducibility of about 4 % (single standard deviation) at 24 h, whereas the reflected intensity at this time, obtained by the turbidity probe, varies by factor of approximately 2. This strongly disagrees with the stated reproducibility of formazine suspensions of about 1 % [11, 18].
Since PDW measurements indicate that formazine can be reproducibly formed, it is likely that the turbidity probe measurements are highly dependent on the surrounding conditions. Even though the probe was implemented in the reaction vessel as reproducible as possible, surface reflections from the jacketed beaker, stirrer bar, etc. seem to affect the obtained reflected intensities. Additionally, also the surrounding light has an influence on the detected reflected intensities for the chosen experimental setup. Both effects not only cause problems while calibrating such turbidity probes, but also limit the applicability of these probes in any process environment, since the effect of the measurement geometry and other external influences is significant. Due to the inconsistency of the reflected intensities for the replicated formazine formations, all turbidity data are given in arbitrary units and are not expressed (“calibrated”) in FTUs.
Comparing the precipitation onset, a different starting time between the turbidity probe and PDW spectroscopy can be noted. The delay of the reduced scattering coefficient in comparison to the turbidity probe is about 15 to 25 min in Fig. 1. This is caused by a certain minimal turbidity level needed for successful PDW experiments, i.e., material exhibiting multiple light scattering and therefore requiring a higher scatterer concentration. Accordingly, before the polymer precipitation sets in at approximately 2.5 h, only signal noise is obtained by PDW spectroscopy (Fig. 1, dotted lines). These false signals are identified by extremely large deviations between experimentally obtained amplitude and phase of the PDW and their fits during data analysis. Hence, data points are discarded for χ
2 values of >100 (sum of the squared deviations between experimental data and fit) . For the turbidity probe, also trends are observed before the precipitation onset, probably again due to the above-stated geometric effects and external light sources.
In the ISO 7027, it is described that the formazine suspension should be prepared without stirring over 24 h after initial mixing. Figure 2 displays two repeated syntheses without stirring. While the precipitation onset time and initial values of μ
s′ and I
R are similar to the data shown in Fig. 1, strong variations are detected after around 10 h, which are very likely related to sedimentation effects.
The influence of stirring is shown in Fig. 3, where the stirrer was switched on and off alternatingly in one of the batches from Fig. 2 after 24 h. Immediately after stirring for the first time, the partly sedimented suspension is resuspended and constant reduced scattering coefficients and reflected intensities at the expected levels are measured. In contrast, stopping stirring reinitiates sedimentation, with pronounced effects on both optical probes for longer settling times (e.g., after 28 h in Fig. 3). But also after long settling times resuspension seems feasible (stirrer on at 42 h in Fig. 3). However, the absolute values of μ
s′ and I
R here (0.179 mm−1 at 690 nm and 6.3 103 at 860 nm, respectively) differ from the ones at the initial plateau period (0.169 mm−1 at 690 nm and 5.1 103 at 860 nm).
If resuspension is not fully reproducible or if the polymer undergoes permanent alteration remains unclear. However, despite the regulations stated in the ISO 7027, the experimental observations indicate that the synthesis of formazine should be performed under continuous stirring, allowing also for better temperature control. Furthermore, it has to be stressed that any protocol for a turbidity probe calibration with formazine should include its controlled resuspension. All further syntheses of formazine presented in this work were realized under stirring.
Temperature dependence of formazine synthesis
The ISO 7027 requests a reaction temperature of (25 ± 3) °C. Besides homogenous temperature distribution within the reaction vessel (stirring), the supposedly long reaction time of 24 h implies active temperature control. To evaluate the temperature influence on the formazine synthesis, the reaction temperature was varied systematically (Fig. 4).
Increasing temperatures cause significantly earlier onsets of the formazine precipitation, observed by both measurement technologies. At 24 h, the obtained experimental values of I
R and μ
s′ vary. The standard deviation in Fig. 4 at 24 h is approximately 4 % for μ
s′ without clear temperature dependence (data not shown). In contrast to turbidity measurements, PDW spectroscopy is not affected by ambient light. Therefore, the variation of 4 % in μ
s′, also seen in repeated measurements at the same temperature, is attributed mostly to the reproducibility of the formazine synthesis itself. However, limitations of reproducibility within the experimental setup may still have an influence on PDW spectroscopy. For the turbidity probe trends, very high noise is obtained at around 8 h. This is caused by sunlight entering the lab during sunset. Similar effects are observed 12 h later (sunrise), where again I
R is affected. For the chosen turbidity measurement setup, this clearly indicates how substantially such experiments can be biased by external influences.
Figure 5 displays the clouding onset time of the formazine precipitation (t
start) as function of the reaction temperature. An exponential decay is observed, indicating that the clouding onset represents a certain reaction state during the formazine synthesis. Linearization based on an Arrhenius approach yields a remarkable linearity (Fig. 5 inset). The activation energy calculated from the slopes is (94.0 ± 1.2) kJ mol−1 (by PDW spectroscopy) and (95.2 ± 5.8) kJ mol−1 (by turbidity measurement). These values are close to the typical range for condensation reactions of formaldehyde (50–83 kJ mol−1 [30, 31]).
Concentration dependence of formazine synthesis
Figure 6 displays μ
s′ and I
R as function of time for a simultaneous variation of the relative concentration of the reactants, ranging from 5 to 333 %. Increasing concentrations result in larger experimental values for μ
s′ and I
R at 24 h.
In addition, it also can be noted that the clouding onset time varies systematically, with earlier formazine precipitation at higher concentrations (Fig. 7). The experimental relation of c
rel vs. t
start can be described by an exponential decay function of the form c
rel = A exp(−B t
start). Including an additional y-axis intercept could yield the solubility of formazine in water at 25 °C. However, its precise determination would require experiments at low concentrations (e.g., c
rel = 5 % and lower). For the fits given in Fig. 7, the data set of c
rel = 5 % has not been used due to the significant error in the associated value of t
start at that concentration for both experimental methods. Besides the experimentally obtained concentration dependence of the clouding onset time, it remains to be discussed what further type of kinetic information can be obtained from the concentration influence.
In contrast, the experimental data obtained at 24 h show a linear relation with changing relative concentration (Fig. 8). Since the slope of μ
s′ as function of concentration is strongly affected by particle size, changes in particle dimension would lead to a non-linear behavior, even for moderate particle concentrations investigated here [12, 26]. Thus, the linearity suggests that only the concentration of formazine particles, but not their structure or size is affected. In Fig. 8, PDW spectroscopy data is also shown for wavelengths of 690 and 906 nm for a first spectral evaluation. Even though the overall fit quality is low (e.g., compare to Fig. 10, with polystyrene as scatterer), some conclusions can be drawn. For PDW spectroscopy, repeated experiments result in similar reduced scattering coefficients and therefore good reproducibility of the formazine synthesis. Furthermore, for PDW spectroscopy, the obtained y-axis intercept is close to zero ((−0.0106 ± 0.0133) mm−1 for 690 nm and (−0.0051 ± 0.0120) mm−1 for 906 nm).
This is not the case for the turbidity data. Here, a significant y-axis intercept is noted (I
rel = 0) = 9.8 102), with I
R = 2.0 103 for clear water being even higher (this data point was not included in the linear regression). In addition, the poor reproducibility of I
R trends (cf. Fig. 1) is also noted at other concentrations. On the contrary, the chosen turbidity probe can proportionally measure the influence of concentration up to the maximal possible concentration of c
rel = 333 %. With respect to the ISO 7027, this indicates that also higher FTUs than 4000 (i.e., c
rel = 100 %) could be realized for instrument calibrations on the basis of formazine.
The experimentally obtained mean absorption coefficient from PDW spectroscopy for all relative concentrations was determined to approximately (5.4 ± 2.9) 10−4 mm−1 and (6.2 ± 2.9) 10−3 mm−1 for 690 and 906 nm, respectively, exhibiting no systematic tendencies (data not shown). They are in the range of the absorption coefficients of pure water at these wavelengths (cf. Fig. 11).
Quantification of high turbidities
Heterogeneous chemical, physical, or biotechnological processes quite often exhibit much stronger light scattering than can be represented by formazine as calibration standard. For example, at c
rel = 333 % PDW spectroscopy measures reduced scattering coefficients of less than 1 mm−1 at various wavelengths (cf. Fig. 8). In reality, experimental values of more than 1000 mm−1 have been obtained (e.g., for aqueous TiO2 suspensions, data not shown). To evaluate to what extent turbidity process probes can address also higher turbidities, i.e., at which values a signal saturation for I
R sets in, further concentration series with polystyrene suspensions have been performed.
Figure 9 shows reflected intensities at two different wavelengths for a polystyrene suspension at volume fractions below 0.005. Already above very low concentrations (volume fraction Φ
PS of approximately 0.0014), a deviation from the linear fit can be noted for both wavelengths. At this concentration, the turbidity signal starts to saturate (for the chosen polystyrene suspension). With respect to the reflected intensity, this saturation starts at around 1.7 104 for a wavelength of 860 nm (max. I
R for formazine at c
rel = 333 % was 1.2 104 at 860 nm, cf. Fig. 8). In comparison to Fig. 8, a linear detection range can clearly be determined, limiting the use of turbidity probes in highly turbid systems.
Accordingly, the turbidity probe is insensitive to higher concentrations (Fig. 10). Here, results from the turbidity probe are compared with PDW spectroscopy in a way that the individual linear regressions are mostly in parallel for very low concentrations (by y-axis scaling). As can be seen from PDW spectroscopy measurements, I
R values of up to 4.5 105 at 516 nm should be expected for the highest polystyrene volume fraction. Instead, I
R saturates at approximately 1 104 at that wavelength. In contrast, PDW spectroscopy provides increasing reduced scattering coefficients over the entire investigated concentration range. It has to be stressed that the increase in μ
s′ is actually non-linear towards higher volume fractions, which can be described by so-called dependent light scattering and which is a material property, not a measurement limitation . While high turbidities do not limit the application space of PDW spectroscopy, the theoretical requirement of μ
s′ > > μ
a  at the experimental wavelength is critical for low turbidities. The inset in Fig. 10 displays the experimental μ
s′ for the polystyrene concentration series in double-logarithmic scale. As anticipated, deviations occur towards very low particle concentrations. For the investigated suspension, a lower measurement range limit for the reduced scattering coefficient of approximately 0.05 mm−1 can be identified which translates here to a polystyrene volume fraction of approximately 1.6 10−4. However, for quite a number of processes investigated with PDW spectroscopy, too low turbidity has not been of relevance [12, 13].
For practical considerations, the obtained findings imply that the saturation level of a turbidity sensor should always be estimated in order to define the suitable concentration range. This has to be performed with the material under investigation or at least with materials of equivalent optical properties. In contrast, for PDW spectroscopy as process analytical technology, a certain degree of turbidity is always needed. Though a threshold of approximately 0.05 mm−1 for μ
s′ was found, this value may be different if significant light absorption occurs at the experimental wavelength used.
The calibration-free and wavelength-dependent separation of light absorption and light scattering is a fundamental benefit of PDW spectroscopy. Figure 11 displays reflected intensities from the turbidity probe and absorption as well as reduced scattering coefficients from PDW spectroscopy as a function of wavelength for two polystyrene concentrations. In addition, absorption coefficients of pure water [32–39] are shown.
As anticipated, the reduced scattering coefficient increases with higher concentration and with lower wavelength. Such a trend is not found in the reflected intensities. Besides the saturation effect, the spectrum represents the emission/detection characteristics of the light source and the detector within the spectrometer. To measure the typical increase of light scattering towards smaller wavelengths, the experimental turbidity setup would need to be calibrated with respect to the light source, detector, and all other optical elements (e.g., fibers). For practical consideration, this may cause additional concerns (e.g., aging of the light source, constant light coupling into the fiber-optical cables, wavelength-dependent light losses due to fiber bending, etc.). In contrast, the wavelength-dependent reduced scattering coefficient is very helpful for process monitoring in systems of particles, droplets, or cells where concentration and size varies simultaneously. As a consequence, besides the saturation and calibration problem of a turbidity probe, multiwavelength measurements are highly recommended for turbidity measurements as well as for PDW spectroscopy.
The absorption coefficient in Fig. 11 scales over three orders of magnitude for the aqueous polystyrene suspension. Particularly for the wavelength range above 700 nm, the experimental values approach the absorption coefficient of pure water. However, below 700 nm, a higher absorption than pure water is observed, which is attributed to the increasing concentration of organic material in the suspension.
The concentration dependence of the absorption coefficient at 515 and at 982 nm is shown in Fig. 12 in more detail. For not too small absorption coefficients, a linear relation with the volume fraction Φ
PS is found as anticipated. Extrapolating the linear trends to zero volume fraction (i.e., pure water), absorption coefficients of (0.0451 ± 0.0003) mm−1 at 982 nm and (6.3 10−5 ± 1.5 10−5) mm−1 at 515 nm are found. They are in good agreement to the literature data [32–39], as can be also seen in Fig. 12. The non-linear deviation towards larger absorption coefficients at very low volume fractions is regarded as a measurement artifact. At these low concentrations, the required condition μ
s′ > > μ
a is not fulfilled. Interestingly, this deviation from linearity occurs already at higher volume fractions for the wavelength of 982 nm in comparison to 515 nm. This can be explained by the significantly higher light scattering at 515 nm (cf. Fig. 11), allowing for the determination of absorption coefficients also in very low concentrated systems.
Extrapolating the linear trends in Fig. 12 to a volume fraction of 1 (i.e., theoretically pure polystyrene), absorption coefficients of (−0.0011 ± 0.0063) mm−1 at 982 nm and (0.0228 ± 0.0005) mm−1 at 515 nm are found. However, since absorption reference data for the vis/NIR region for polystyrene seems not to be available, here it is only referred to the organic fraction within the aqueous polystyrene suspension.
Considerations about calibration standards
Based on the concentration dependence as observed by PDW spectroscopy for the formazine suspension (cf. Fig. 8), changing the relative target concentration by 1 % causes a shift of the reduced scattering coefficient of 1.07 % at 690 nm and of 1.05 % at 906 nm. Similarly, having the concentration 5 % off the target induces a change of 5.33 % at 690 nm and of 5.26 % at 906 nm in μ
s′. With respect to repeatability, for the three trials investigated here, as well as for syntheses at different temperatures ±4 % from the average μ
s′ (single standard deviation) was obtained at 24 h. For the turbidity probe implemented here, the influence of the surrounding conditions caused severe problems in the repeatability, accounting to deviations of more than ±36 % at 24 h. Therefore, the reproducibility of the formazine synthesis itself is not the limiting factor for quantitative measurements.
For the polystyrene suspension investigated here, much stronger light scattering is observed than what can be achieved with a formazine suspension (e.g., factor of approximately 35 for μ
s′ at 690 nm). In addition, polystyrene provides the advantage of changing the slope of μ
PS) by adjusting its particle size. This is of benefit if calibration standards with different turbidity dynamics are required. Since even at maximal relative concentration of c
rel = 333 % the formazine suspension exhibits reduced scattering coefficients of only approximately 0.6 mm−1 (depending on the wavelength), it is of very limited use for calibrating probes for the application in concentrated heterogeneous processes. Here, far more turbid calibration material is needed. Though the reproducible production of such material may be more complex (e.g., providing polystyrene particles with always the same particle size distribution), its optical certification may be helpful. In particular, separating light absorption and light scattering, as it is achieved, e.g., by the calibration-free approach of PDW spectroscopy, would allow for new calibration materials. Instead of requiring materials with highly reproducible formation protocols, nearly any dilutable turbid suspension could act as reference material, as long as its optical properties are characterized.