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Abstract
We present a method to simultaneously measure the film thickness and individual concentrations of two urea derivates (urea ${{\rm CH}_4}{{\rm N}_2}{\rm O}$ and dimethylurea ${{\rm C}_3}{{\rm H}_8}{{\rm N}_2}{\rm O}$) mixed in an aqueous solution at constant temperature using near-infrared (NIR) absorption at multiple specific wavelengths. Fourier transform infrared (FTIR) spectra of aqueous mixtures of urea and dimethylurea solutions were recorded in the 1250–2500 nm wavelength range in thin-layer quartz cuvettes at room temperature. The spectra reveal suitable detection wavelengths, i.e., 1450, 1933, 2200, and 2270 nm, for which both the absorption coefficient and its variation with the species concentration are large enough to achieve satisfactory detection sensitivity and selectivity. For validation measurements, samples were prepared in thin-layer quartz transmission cells with known path lengths and mixture compositions in the range 100–1000 µm and 0–40 wt.%, respectively. Film thickness and mass fractions of both species were determined from measured absorbance ratios in the determined characteristic wavelength bands.
© 2021 Optical Society of America
1. INTRODUCTION
Liquid films in the sub-millimeter thickness range occur in many practical processes. For example, the characterization of fuel films in internal combustion engines is necessary to characterize wall wetting during fuel injection, which causes pollutant emissions [1] (e.g., unburned hydrocarbons and soot). Other examples include the injection of reactants for selective catalytic exhaust gas treatment (SCR) in internal combustion engines and fundamental investigations of spray impingement on surfaces [2]. In many cases, knowledge of the concentration of potential solutes (e.g., salts, urea, sugars) and their variation with ambient conditions are necessary for a complete and quantitative description of wetting, flow, heat transfer, and evaporation on surfaces in detail [3]. Besides these practical applications, aqueous urea solutions play important roles in physiological systems. The concentration of urea in urine can serve as health indicator [4]; urea is part of many skin treatment creams, and aqueous solutions of urea and its derivates are one of the most used protein denaturing agents [5].
Non-intrusive optical diagnostics for the measurement of film thickness and concentrations of multiple solutes would be highly desired for improving the understanding of wall-film formation, evaporation, and degradation processes. Much work has been published on the optical diagnostics of liquid films [6], with only a few measurement techniques available to address these measurement issues in harsh environments. Of those, laser absorption [7–13], shadowgraphy [14], and laser-induced fluorescence (LIF) [15–19] have been successfully applied to measure liquid-film thickness and solute concentration. Although there are strategies to determine the different quantities individually, their integration into easy-to-use compact sensors with multi-parameter sensitivity and fast response (in the sub-millisecond range) is rare.
The near-infrared (NIR) absorption spectrum of liquid water contains some weak and medium-strength broad features resulting from overtone ($2{\nu _1}$ and $2{\nu _3}$) and combination (${\nu _1} + {\nu _3}$) bands around 1450 nm and the combination band (${\nu _1} + {\nu _2}$) around 1900 nm. In the case of aqueous solution, the shape and strength of these features change with solute concentration and, therefore, enable characterization of aqueous solutions. For aqueous urea solutions, these absorption features are affected by the IR activity of NH overtone (around 1470 nm) [20] and combination bands (around 2200 nm) [21]. With increasing urea concentration, the overall absorption feature around 1450 nm is weakened due to a change in volumetric density, while in the 2200 nm region a weak separated urea absorption peak appears between the two stronger water bands. The variation of the absorption spectra as a function of urea concentration provides the basis for the measurement strategy investigated here.
For the selection of optimum wavelength positions for a multi-color absorption sensor, the variation of the absorption spectrum with (combined) urea solute concentration needs to be known. In a previous work of our group [22], we generated a corresponding spectral data base for aqueous urea solutions only (between 0 and 40 wt.% urea) using Fourier transform infrared (FTIR) spectroscopy in the 1250–2500 nm spectral range. In this work, we extend the NIR absorption spectra database to dimethylurea (DMU) at isothermal conditions to provide the spectral information needed for deriving a film thickness and concentration measurement strategy based on multi-wavelength absorbance ratios. Here, several urea/DMU mixture compositions between 0 and 40 wt.% (in 10 wt.% steps) were considered to provide continuous interpolating functions. We validate the measurement concept for solutions prepared in a thin-layer optical cell with known path lengths.
2. BASIC PRINCIPLES
The transmitted intensity through a sample, $I^\lambda$, is described by the Lambert–Beer law:
Taking the ratio of two such logarithmic intensity ratios for different wavelength combinations eliminates the film thickness and reduces the problem to a ratio of absorption coefficient differences for the selected wavelength positions. The absorption coefficients vary with concentration and can be fitted by a plane as function of urea and DMU concentration with the fitting coefficients ${a^\lambda},\;{b^\lambda}$, and ${c^\lambda}$ (cf. Eq. 5); thus,
By repeating this for the other wavelength combinations, both concentrations can be inferred from solving the resulting equation system of two equations with two unknown concentrations. For the known concentrations (i.e., known absorption coefficients), the film thickness can then be derived from Eq. (4),
3. RESULTS
A. Spectral Database
Our previously built database of spectral absorption coefficients of aqueous urea solutions in the NIR from 1250 to 2500 nm [22,23] was extended to a second solute (DMU) to provide parameterized fitting functions for the absorption coefficient of the mixed solution to determine film thickness and two solvent concentrations simultaneously. Urea (U, ${{\rm NH}_2} - {\rm CO} - {{\rm NH}_2}$, 99%) and DMU (${{\rm CH}_3} - {\rm NH} - {\rm CO} - {\rm NH} - {{\rm CH}_3}$, 98%) were supplied by Merck and Alfa Aesar, respectively. NIR spectra were measured with a FTIR spectrometer (Bruker, Vertex 80, spectral resolution ${2}\;{{\rm cm}^{- 1}}$) with a 0.2 mm path length fused-silica cuvette (Specac, GS20502, JGS3) placed in the sample compartment of the spectrometer at room temperature (293 K). Interference fringes in the measured spectra generated by the parallel windows in the small-path-length cell were removed using wavelet transformation, which is a powerful method to reduce signal contributions of unwanted frequencies [24,25]. Spectra of aqueous DMU were measured with concentrations between 0 and 40 wt.%, as well as aqueous solutions with two-component mixtures of urea and DMU with combinations between 0 and 40 wt.% in 10 wt.% steps. Combinations with a total concentration of about 60 wt.% could not be measured as the solution exceeded the solubility limit at room temperature. Spectral variations were investigated using principal component analyses (PCAs) [26]. In this multivariate method, the initial dimension of the spectral dataset is reduced by transforming it to a new coordinate system (the so-called principal components, PCs). These PCs result from linear combinations of the original variables, are orthogonal to each other, and are aligned in a way that the PCs are orientated along the maximum variability in the dataset in successive order. The values characterizing how much each original variable is contributing to the new PC are called loadings and, when plotted over the original variable, reveal the regions in the dataset with the largest variation. The PCA was performed using the “Principal Component Analysis for Spectroscopy” app from Origin Pro. There, the covariance matrix is used for analysis of the data (mean centered, not normalized) for all concentrations.
Figure 1 shows the NIR absorption coefficient of aqueous DMU solutions as function of the DMU mass fraction from 0 (pure water) to 40 wt.% (in steps of 10 wt.%, colored solid lines) at 293 K in the 1250–2500 nm wavelength range. The right $y$ axis (black solid line) shows the loadings of the first PC describing 99.5% of the variation in the dataset.
Fig. 1. Wavelength-dependent absorption coefficient of aqueous dimethylurea solutions with a DMU concentration from 0 to 40 wt.% at 293 K. The black line shows the loadings from principal component analysis of the first PC describing 99.5% of the spectral variation.
Figure 2 shows the NIR absorption coefficient of aqueous urea solutions as function of the urea mass fraction from 0 (pure water) to 40 wt.% (colored solid lines) at 293 K in the wavelength range from 1250 to 2500 nm. The right $y$ axis (black solid line) shows the loadings of the first PC describing 99.6% of the variation in the dataset.
Fig. 2. Wavelength-dependent absorption coefficient of aqueous urea solutions with urea concentrations from 0 to 40 wt.% at 293 K. The black line shows the loadings from principal component analysis of the first PC describing 99.6% of the spectral variation.
In both cases, there are various effects that affect the absorption spectra of DMU solutions including (1) change in the volumetric density of water; (2) water–DMU molecular interactions; and (3) additional spectral features due to absorption by the NH groups [20]. The latter is most prominent in the 2100–2300 nm wavelength range. For urea, this region is strongly affected by NH absorption with two peaks at 2160 and 2200 nm. For DMU, one peak appears at 2270 nm, whereas the 2100–2220 nm wavelength range is only weakly affected by NH absorption.
Figure 3 shows the variation of the absorption spectra of pure water and of aqueous solutions with different concentrations of urea and DMU and the loadings of the first PC describing 89.1% of the spectral variation. For clarity, the spectra at 10 and 30 wt.% DMU (top) and 20 and 40 wt.% DMU (bottom) are shown separately. The obtained spectroscopic database then serves for choosing four suitable wavelength positions that on the one hand provide high sensitivity to the solvent concentration and on the other hand have sufficient absorption strengths for film thickness measurements. For film thicknesses in the range of 100–1000 µm, an absorption coefficient of around ${30}\;{{\rm cm}^{- 1}}$ yields an acceptable signal-to-noise ratio (SNR) in transmission measurements. Strong absorption features of urea and DMU are present around 2200 and 2270 nm, respectively. Therefore, the four chosen detection wavelengths are 1450 and 1933 nm (used for film thickness determination in Eq. 4) and 2200 and 2270 nm (high sensitivity to the urea and DMU concentration, respectively). For film thicknesses of above 1 mm, the 1933 nm water absorption band is too strong for light being transmitted through the sample, which is why, beyond this film thickness, 1800 nm is used instead.
Fig. 3. Wavelength-dependent absorption coefficient of pure water (red) and aqueous solutions containing different concentrations of urea and DMU at 10 and 30 wt.% DMU (top) and 20 and 40 wt.% DMU (bottom) at 293 K. The black curve shows the loadings of the first principal component describing 89.1% of the spectral variation.
Fig. 4. NH absorption band of aqueous solution with 30 wt.% of urea and DMU each. The dashed black line shows the experimental spectrum, and the green line shows a fit function based on three Gaussian profiles, which are displayed as blue lines. The red line shows the absorption coefficient of pure water, used as baseline for the Gaussian profiles.
Fig. 5. Urea and dimethylurea concentration dependence of the NIR absorption coefficient shown at a wavelength of 1450, 1933, 2200, and 2270 nm. The plane is a fit to the data points.
To gain more information about the spectral seperation of the urea and DMU absorption features around 2200 nm, a multi-peak Gaussian fit of the NH absorption region from 2120 to 2320 nm was performed for all two-component urea mixtures investigated. Three Gaussian peaks were used, and the fit yielded peak positions at 2156, 2204, and 2267 nm with respective linedwidths of 32, 67, and 44 nm [full width at half-maximum (FWHM)]. The peak at 2156 nm can be assigned to vibrations originating from CO stretch and CN stretch coupled with ${{\rm NH}_2}$ deformation [20]. The peak at 2204 nm can be assigned to coupled NH stretch and ${{\rm NH}_2}$ rocking vibrations of urea [20], while the peak at 2267 nm can be assigned to the NH stretch vibrations combined with the stretch vibration between NH and the methylgroup (${{\rm CH}_3}$) of DMU [21]. Figure 4 shows the fitted individual Gaussian peaks (blue solid lines) comprising the synthesized spectrum (dashed line) best fitting the measured spectrum (green solid line) for an aqueous solution with 30 wt.% of urea and DMU each, with the red line showing the pure water spectrum in this spectral region.
The variation of the absorption coefficient with concentration is nearly linear and, thus, for a two-component mixture, can be modeled as a plane. Figure 5 shows the urea and DMU concentration dependence of the absorption coefficient $k$ together with a fitted linear dependence in the concentrations (weight percent) of the two urea species:
with the fitting coefficients ${a^\lambda},\;{b^\lambda}$, and ${c^\lambda}$ for both components at wavelength position $\lambda$ (see Table 1). As can be seen in Table 1, at 2270 nm there is a strong DMU and a lower urea dependence, respectively, while this is the other way around at 2200 nm. Therefore, these two wavelengths were chosen for distinguishing between the two urea derivates.
Table 1. Fitting Coefficients of the Measurement Wavelengths Characterizing the Concentration Dependence of the Respective Absorption Coefficients
A third-order polynomial fit including non-linear terms and mixed terms [$f({w_{\rm U}},{w_{{\rm DMU}}}$] was also tried to characterize the variation of the absorption coefficient with urea and DMU concentration. As there are no significant differences in the evaluated data with both fits (less than 3% variation), only the linear fit is shown here.
B. Validation Measurements
To validate the measurement performance, liquid samples were prepared in a cell of known thickness (105, 205, 507, and 967 µm) and at known concentrations of urea and DMU (10, 20, 30, and 40 wt.%), and mixtures of both in 10 wt.% steps at room temperature. The urea and DMU concentration and film thickness were inferred from measured transmittance ratios using the equation system of Eq. (3) (with the wavelengths combinations 1450, 1933, 2200 nm and 1450, 2200, 2270 nm) and Eq. (4) (with the wavelengths combination 1450 and 1933 nm). The transmittance ratios were derived from FTIR spectra with a spectral resolution of ${2}\;{{\rm cm}^{- 1}}$.
Fig. 6. Correlation between measured and given film thickness between 100 and 1000 µm. The upper panel indicates the absolute value of the residuals between measured and given values for mixtures of urea and DMU, distinguished by symbol and color, respectively.
Figures 6–8 show comparisons between the data evaluated from transmission ratios and the given film thickness, urea, and DMU concentration values. The solid straight lines in each graph represent the one-to-one correspondence between both values, with the upper panels indicating the absolute value of the residuals between measured and given parameter values. Each graph shows one of the three simultaneously inferred parameters. In the legend of each graph, the other two parameters are represented by the symbol and by color, respectively. The measurement uncertainty of film thickness and concentration values for both compounds calculated by error propagation based on the parameters in Eqs. (4) and (3) was about 9.4% and 11.4%, respectively. Multiple measurements were performed on different days for all cases shown with results well within the range of the estimated error.
Fig. 7. Correlation between measured and given DMU concentration between 0 and 40 wt.%. The upper panel indicates the absolute value of the residuals between measured and given values for mixtures of urea and DMU, distinguished by symbol and color, respectively.
Fig. 8. Correlation between measured and given urea concentration between 0 and 40 wt.%. The upper panel indicates the absolute value of the residuals between measured and given values for mixtures of urea and DMU, distinguished by symbol and color, respectively.
For the film thickness measurements (Fig. 6), the largest deviation between known and measured value is 8.3% (for the sample with 20 wt.% urea, 20 wt.% DMU and at a sample thickness of 205 µm).
For the DMU measurements (Fig. 7), the largest derivation of known and measured value is 11.1% (for the sample with 40 wt.% urea, with 10 wt.% DMU, and at a sample thickness of 105 µm).
For the urea measurements (Fig. 8), the largest derivation of known and measured value is 8.5% (for the sample with 10 wt.% urea, with 20 wt.% DMU, and at a sample thickness of 967 µm).
Table 2. Manufacturer Data of the Bandpass Filters Used for the Sensor Measurement Simulation
Fig. 9. Transmission profiles of the bandpass filters used for the sensor measurement simulations. Also shown are exemplary spectra of the reference and sample measurement of a sample with 40 wt.% urea and 20 wt.% DMU at 200 µm thickness.
4. STRATEGY FOR A PORTABLE SENSOR
In a previous work of our group, we presented a sensor concept for film thickness and urea concentration measurements based on the NIR absorption of a bandpass filtered broadband light source [22]. Due to the FWHM transmission bandwidth between typically 10 and 13 nm (see Table 2) of the employed filters in that work, the measured transmission intensities are spectrally not as sharply resolved as in the current FTIR measurements (${2}\;{{\rm cm}^{- 1}}$, ${\sim}{0.3}\;{\rm nm}$ in the NIR). To quantify how this affects the measurements in such a filter-based sensor, the FTIR spectral intensities were integrated over commercially available bandpass filter curves, and the layer thicknesses and concentrations were determined with these values using the same ratio method as described above. Figure 9 shows the transmission profiles of the bandpass filters used for this simulation and exemplary spectra of a reference (incident intensity $I_0^\lambda$) and sample measurement (transmitted intensity $I^\lambda$) for a 40 wt.% urea and 20 wt.% DMU sample at 200 µm film thickness. A comparison of the determined film thickness and concentration values using the bandpass filtered measurement wavelengths and the “spectrally sharp” FTIR measurement wavelengths shows a typical variation of around 1% between both methods. This demonstrates good feasibility of a sensor design for simultaneous measurement of layer thickness and concentration of two urea derivatives using, e.g., a broadband fiber coupled light source and appropriate bandpass filters on the detector side. Depending on the desired temporal resolution and available signal intensities, either a time-multiplexed (using a filter wheel and a single detector) [22] or wavelength-multiplexed (a wavelength dispersing grating and five detectors) [27] setup might be realized in a portable instrument.
5. CONCLUSION
A novel optical absorption method for the characterization of aqueous urea/DMU solution thin films was demonstrated via NIR absorption measurements of urea and DMU at concentrations of 0–40 wt.% and film thicknesses of 100–1000 µm at room temperature (293 K). The measurement technique is based on absorption ratios at characteristic NIR wavelengths (1450, 1933, 2200, and 2270 nm) that were selected according to FTIR measurements of absorption spectra of water/urea/DMU solutions in the respective wavelength range of interest of two prominent water bands. The largest measured error in film thickness was 8.3%, in urea concentration 8.5% and in DMU concentration 11.1%. This work presents absorption spectra for water/urea/DMU solutions and the first use of the absorption bands at 2200 and 2270 nm with respective peak absorption coefficients of 40 and ${46}\;{{\rm cm}^{- 1}}$ for the characterization of water/urea/DMU thin films. The suitability of this absorption method for an absorption sensor using a bandpass filtered broadband light source was investigated. For this purpose, transmittances measured by FTIR were integrated over typical bandwidths of commercially available interference filter transmission profiles, and film thicknesses and concentrations were determined with these values. A typical deviation of 1% from the values measured by spectrally sharp FTIR transmissions was determined.
Funding
Deutsche Forschungsgemeinschaft (229633504).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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