1. Introduction

The optical extinction of liquid water increases strongly in the ultraviolet wavelength region due to electronic absorption and Rayleigh scattering. Published UV spectra [1–6] show differences in extinction up to two orders of magnitude, where the data by Quickenden and Irvin [1] are referred as the extinction spectra of the purest liquid water. The absorption originates from the tail of the $\tilde{X}$→$\tilde{A}$ electronic transition with a maximum at 7.4 eV (167.5 nm) in the gas phase and is broadened and blue shifted with a maximum at 8.3 eV (149.4 nm) in the liquid phase of water [7].

Further studies on the optical properties of water concentrated on the application of the Urbach rule to the absorption band and the temperature dependence of the liquid water absorption in the UV region. The Urbach rule [8] states that the extinction near the absorption edge is an exponential function of photon energy at a defined temperature. The Urbach constant for liquid water was first reported by Onaka and Takahashi [9], and later by Williams et al. [10].

There have been several studies of the temperature dependence of the optical extinction of liquid water in the UV spectral region [7,11–13]. All studies reveal a redshift of the ultraviolet absorption band occurring with increasing water temperature. Furthermore, Marin et al. [7] investigated the influence of the density on the extinction behavior of water in a range between 0.10 - 0.36 g cm⁻³ at 400 °C. Above the water critical temperature T_c = 374 °C a fall in density leads to a blueshift of the UV absorption band.

Pope and Fry [14] as well as Sogandares and Fry [15] used highly purified water (specific conductivity: 0.056 µS cm⁻¹) to determine the absorption spectrum of liquid water in the near UV and visible spectral domain. The absorption values of Pope and Fry are commonly referred as state-of-the-art in the visible and near UV [16] with minimum water absorption of 0.0044 ± 0.0006 m⁻¹ at 418 nm [14] (measurements performed using an integrating cavity absorption meter [17]).

Table 1 gives a compact overview of the above mentioned studies on the optical properties of liquid water. The purity of water is generally a result of the remaining impurities, which can be measured as the sum parameters TOC (total organic carbon) for organic impurities and specific conductivity for ionic impurities. In the majority of the mentioned water studies neither specification [9–13] nor the purification procedure were described in detail [7,9,13] or the amount of purification was not sufficient [9–13]. Only Quickenden and Irvin [1] included an oxidation procedure in the form of an oxidative distillation to produce highly purified water. Consequently, the optical properties measured could be influenced by the organic impurities. Furthermore, Table 1 indicates that only in two studies [1,7] has the dissolved oxygen absorbing UV light [18] been removed. The cleaning, the extinction and the reflection of the optical cells are other critical points. Residual contaminations on the surfaces of the used cells could lead to errors in determining the optical properties of water. The optical surfaces have to be cleaned thoroughly and the extinction and the reflection of the optical windows have to be measured or corrected, respectively. In some cases [7,9,10,13] no corrections for extinction or reflections of the cell material were made. In other cases [1,11,12] window extinction and reflections were corrected.

Table 1. Overview on published UV extinction studies on pure liquid water

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In the present work we reinvestigated the optical extinction down to 181 nm of the clearest ultrapure water. Our study represents the first study to measure the extinction of ultrapure water at such short wavelength. Our water samples were the purest so far by the means of TOC levels and specific conductivity (Table 1). Corrections for the extinction and reflections of the cell material were included. Furthermore, with the measured intrinsic absorption edge at the electronic transition the Urbach constant was determined for ultrapure water. A double exponential fit of such ultrapure water is presented. The Rayleigh scattered light was calculated with updated parameters showing the correct wavelength dependence for the first time. Additionally, we investigated the temperature dependence of our water samples.

2. Experimental

The ultrapure water was produced by a lab water system (Ultra Clear TWF UV plus TM system with El-Ion CEDI Cell, Siemens) using a combination of filtration, reverse osmosis, deionization by ion exchange, continuous electro-deionization, UV-oxidation and ultrafiltration (details of the purification process can be found in appendix A). A further cleaning step with a double quartz distill under nitrogen atmosphere did not improve the lab analysis nor the UV spectra of our water.

To characterize our water samples, TOC (Total Organic Carbon) and conductivity were measured (details can be found in appendix B). Online TOC levels of 2.6 ± 0.7 ppb were found. Furthermore, the contents of ionic impurities, especially UV absorbing anions, were determined by ion chromatography: 0.5 ± 0.14 µg L⁻¹ fluoride, 0.9 ± 0.5 µg L⁻¹ chloride, 1.6 ± 0.5 µg L⁻¹ sulfate, 1.0 ± 0.6 µg L⁻¹ sodium, 0.2 ± 0.4 µg L⁻¹ potassium, 0.14 ± 0.3 µg L⁻¹ calcium, and 0.06 ± 0.05 µg L⁻¹ zinc. Phosphate, nitrate, magnesium, iron, copper, nickel, cadmium, and manganese were lying below detection limit.

Measurements of extinction spectra in the UV range between 193 and 340 nm were taken with a double beam scanning spectrophotometer (V-660, Jasco, data pitch of 0.5 nm, spectral bandwidth of 1 nm), modified with nitrogen flushing (avoiding oxygen absorption, 700 mL min⁻¹) and equipped with a more sensitive photomultiplier (R955, Hamamatsu) for wavelengths below 200 nm. The increasing contribution of stray light prevented accurate measurements below 193 nm.

For the determination of the water extinction between 181 nm and 193 nm an in-house developed vacuum UV single beam spectrophotometer with a spectral resolution of 1.3 nm was used. The light of a 30 W arc deuterium lamp was collected and collimated by a concave mirror. The collimated light beam passed the sample and was then focused by another concave mirror to a slit. The light was then spectrally dispersed by a concave flat-field grating (Carl Zeiss Jena) and imaged on a photodiode array (Hamamatsu, 512 pixels). The entire system was housed in a polycarbonate box and flushed with nitrogen at the same level as the aforementioned spectrometer.

For the extinction measurements rectangular cuvettes with PTFE stoppers (110-QS, Hellma) and temperature controlled cells (165-QS, Hellma) made of fused silica (Suprasil). We used two sets of cuvettes for the two measurements ranges: (i) 181 nm…193 nm: of thicknesses 1, 2, 5, 10 mm; (ii) 193 nm…340 nm: of thicknesses 1, 2, 5, 10 cm. Before every measurement the respective cuvette was cleaned and measured empty. Details of the cleaning procedure and the temperature controlling of the cuvettes can be found in appendix C.

The UV measurements started by taking the base line to compensate light intensity between sample and reference path without cuvettes. Due to extinction drifts up to ± 0.001 the base line was recorded every hour. All measurements in both spectrometers were run against nitrogen as reference. After measuring the cleaned cuvettes filled with nitrogen, they were filled with water and measured. The extinction of the cuvettes and the Fresnel loses have been included by the following procedure: The extinction E was calculated by the extinction difference of the water filled and the nitrogen filled cuvettes leading to Eq. (1):

where ε is the molar extinction coefficient of water, c is the concentration, d is the path length, R_AS and R_WS are the reflection coefficients of air-Suprasil and water-Suprasil interfaces, respectively. This equation accounts for the Fresnel losses (right terms of the right-hand part of Eq. (1)) at the two interfaces (water-Suprasil interface, air-Suprasil interface). The Fresnel losses themselves have been calculated by using the material dispersion of Suprasil [19], water [20], and air [21]. The spectral distribution of the resulting Fresnel extinction E_FL can be approximated by a polynomial fitting function E_FL = 109.15 λ⁵ + 174.65 λ⁴ – 111.75 λ³ + 35.912 λ² – 5.8511 λ + 0.4237, which holds between 180 and 400 nm.

3. Results and discussion

Linear extinction: Different purification procedures lead to different water extinction spectra with a variation of up to two orders of magnitude (inset Fig. 1). These variations could be caused by remaining impurities within the water which could cause artificial extinction not from the actual water. The spectrum of our ultrapure water at 25 °C measured according to the procedure above between 181 to 340 nm (green curve in Fig. 1) shows a very good overlap with the data from Quickenden and Irvin [1] (blue curve in Fig. 1) which is referred as state-of-the-art for the extinction of ultrapure water. Our measurement extends this limit further down to 181 nm, clearly resolving the absorption edge at short wavelength and thus giving information about the UV extinction of ultrapure water down to wavelengths not accessed before. Between 215 and 300 nm a minor deviation between our result and that of Quickenden can been seen with a maximum difference of 0.9 10⁻⁴ at 270 nm, which we attribute to the usage of different spectrometers. Independent of different spectral measurement devices used, our water samples show a particular smaller amount of impurities compared to the work of Quickenden as the specific conductivity of our sample is about 8 times smaller than those in Ref [1]. (our sample: 0.055 µS cm⁻¹, Quickenden: 0.43 µS cm⁻¹). Therefore our measurements represent the state-of-the-art measurements of the Rayleigh contribution to the extinction of ultrapure water.

 

Fig. 1 Measured extinction spectra of ultrapure water of the present work (green) and of Quickenden and Irvin (blue) [1]. The dashed grey vertical line corresponds to the shortest wavelength measured in [1] (the greenish bar indicates the region not measured by Quickenden and Irvin). The dashed curves (3) and (4) represent the nonlinear fitting function and the calculated Rayleigh scattering contribution, respectively. Inset: Published ultraviolet extinction spectra of ultrapure and pure water. The numbers in the square brackets next to the curves relate to the corresponding reference. The red curve is the Rayleigh scattering contribution calculated by Quickenden and Irvin [1].

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Fig. 2 Spectral distribution of the decadic extinction temperature coefficients (dE/dT) of ultrapure water; (temperature range: 10 to 30 °C; red solid curve: mean values from the experiment; black error bars refer to three standard deviations). The red dashed line results from interpolating our curve towards shorter wavelengths allowing to compare our findings with those of Weeks et al [12].

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This survey clearly shows that the extinction spectrum of ultrapure water in the wavelength range from 200 to 340 nm is strongly sensitive to impurities resulting from incomplete removing of inorganic, organic and gaseous contaminations during the handling and purification procedures.

The measured values for the decadic extinction of water in the deep UV (181 to 187 nm) were slightly lower than those reported by Stevenson [11] (Table 2), whereas this difference cannot result from the small temperature difference of 0.5 °C. The most likely explanation of the slightly higher extinction in Ref [11] is the presence of an additive extinction of residual impurities caused by the not sufficient mono distillation to purify water. Compared to other authors our values are approximately 10% higher (1.46 cm⁻¹ at 185 nm) than those reported by Barret and Mansell [13] and approx. 12% lower (1.80 cm⁻¹ at 184.9 nm) than those reported by Weeks [12]. The higher extinction values of Weeks [12] could result from additive extinction of organic impurities due to the missing oxidative step and of not removed dissolved oxygen. A comparison of the values reported by Barret and Mansell [13] to other published data and to our values is problematic as the data acquisition procedure and the water purification process are inadequately described. Weeks [12] compared his measured values to those reported by Barret and Mansell [13] and discuss that an inaccurate wavelength calibration of Barret and Mansell [13] could be the reason for the discrepancy. Halman and Patzer [22] obtained a similar value of the extinction (1.47 cm⁻¹) at 184.9 nm as Barret and Mansell [13]. The measurements [13] were taken against empty cells and a necessary correction of the higher Fresnel losses was not discussed.

Table 2. Comparison of the extinction values between 181 and 187 nm of our measurements and those reported in [11]

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The determined values of the decadic extinction for ultrapure water can be fitted by the sum of two exponential functions given by the following Eq. (2):

with the fitting parameters listed in Table 3.This function is valid in the wavelength range between 181 and 340 nm and can be straightforwardly used for many applications such as a standard reference spectrum for ultrapure water quality control.

Table 3. Fitting coefficients of the UV extinction of ultrapure water using Eq. (2)

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An exponential dependence of the decadic extinction of ultrapure water can be concluded by Fig. 1 and the exponential fit (Eq. (2)). The absorption edge of water therefore follows the Urbach rule, given by the empirical Eq. (3):

where E is the decadic extinction, hυ is the photon energy of the incident radiation, and E₀, υ₀, and σ are constants characteristic of the material under investigation.

The Urbach rule [8] declares that the decadic extinction E near the absorption edge is an exponential function of photon energy at a defined temperature. This exponential behavior is observed in the low energy tail of absorption bands of many solids and is correlated to the substance disorder which can be of structural, compositional, or thermal origin [23].

The measured extinction between 6.41 and 6.85 eV (181 to 193 nm) was used to determine the Urbach constant σ for ultrapure water. By plotting the decadic extinction E versus photon energy hυ we obtained the slope C = σ/k_b*T = 13.1167 (eV)⁻¹ and calculated σ = 0.337 at 25 °C. The Urbach constant was reported by Williams at el. as 0.36 at 24 °C [10] and by Onaka and Takahashi as 0.3 at room temperature [9].

The residual extinction in the range between 200 and 340 nm could be explained by Rayleigh scattering. Therefore, we calculated the Rayleigh scattering contribution based on the method used in [1]. The light loss due to Rayleigh scattering can be expressed by the decadic extinction E_RS:

where k_b is the Boltzmann constant, n is the real part of the refractive index at the wavelength λ, β_T is the isothermal compressibility of liquid water, (∂n/∂p)_T is the pressure derivative of n at constant temperature T, and ρ is the depolarization ratio for scattered light.

Here we use the most recent available parameters and the full material dispersion down to 180 nm. Values for n and for (∂n/∂p)_T as functions of wavelength were calculated by the Sellmeier equation given in [24] and by their pressure derivatives (inset Fig. 3). Figure 3 in appendix D shows the excellent agreement of the calculated refractive indices with measured values by Dalmon and Masamura [20] down to 180 nm. The depolarization ratio ρ is presumably wavelength dependent [25,26] but no data is available for such short wavelength. Hence, the average value ρ = 0.108 (436 nm and 546 nm) from [27] was used in our calculation. Furthermore, β_T = 4.52472 10⁻¹⁰ N⁻¹ m² (25°C) [28], k_b = 1.38054 10⁻²³ J K⁻¹, and T = 298.15 K were used to determine E_RS.

 

Fig. 3 Comparison of the material dispersion of ultrapure water given by Masamura [20] (measurement) and by Weiss [24] (calculation) at environmental pressure. Inset: Comparison of pressure derivatives dn/dp at 25 °C. The blue curve represents the values of Quickenden [1] calculated by an extrapolation based on the material parameters in the visible spectral domain reported by Kratohvil et al. [27]. Qickenden and Irvin [1] used four values from [27] for dn/dp at 365, 405, 436, and 546 nm and linearly extrapolated these values down to 190 nm.

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Our calculated values for E_RS at 25 °C (Fig. 1) are lower by factors of 2.2 (190 nm) to 2.6 (320 nm) compared to [1] due to the more accurate parameters. The slope of the Rayleigh scattering curve calculated in this work fits better with the long red tail of the absorption edge of ultrapure water than the values of Quickenden and Irvin [1]. A match to the experimental results can only be achieved if an unrealistic depolarization ratio of 0.7 is assumed. Quickenden and Irvin [1] demonstrated that the amount of extinction in the tail of the water absorption edge above 200 nm could not originate only by Rayleigh scattering using Eq. (4) for calculation. Possible explanations [1,7] for the higher experimental extinction could be (i) a broad, weak, electronic absorption, (ii) a breakdown of the Urbach rule, (iii) possible extinction of residual impurities in water, and (iv) preresonance of Rayleigh scattering. Many organic impurities absorb light in the ultraviolet wavelength region with molar extinction coefficients typically in the range between 10² and 10⁵ cm⁻¹/(mol L⁻¹) [29]. An impurity with an extinction coefficient of 10³ cm⁻¹/(mol L⁻¹) and a concentration of 10⁻⁶ mol L⁻¹ would generate an extinction of 10⁻³ cm⁻¹ which lies higher than the measured values for ultrapure water above 220 nm. Due to the sophisticated and highly accurate purification steps we used to produce the cleanest type of water, the in-depth literature survey (Tab. 1) and the comparison to the data of Quickenden [1] an influence of impurities on our measured spectra can be excluded. Marin et al. [7] calculated the extinction of water in the presence of resonant scattering theoretically and showed that the observed water extinction cannot be explained by resonant Rayleigh scattering. Consequently, it can be assumed that the tail of the water absorption edge is a scattering artifact and does not belong to the water absorption band [1,7].

Temperature dependence: Water spectra were collected at different temperature in the range between 10 and 30 °C. An increasing temperature leads to increased water extinction due to a spectral shift of the absorption edge. A linear spectral band shift of 0.066 ± 0.0038 nm K⁻¹ (−0.00236 ± 4.1*10⁻⁵ eV K⁻¹) was observed. The spectral shift differs from [7] by 5 10⁻⁴ eV K⁻¹, probably because of the larger temperature range used here. Rayleigh scattering even with incorporation of resonance, broadening effects resulted from changes in the solvation environment, or vibrational hot band absorptions cannot describe the measured spectral shift with increasing temperature [7]. The observed shift can be caused by a decrease in the average electronic transition energy.

The change of the water extinction depending on temperature at a defined wavelength can be described empirically for a small temperature range by Eq. (5):

with the temperature coefficient β:

where dE/dT is the decadic extinction temperature coefficient and T₀ = 25 °C is the reference temperature, respectively. The linear dependences of the extinction upon temperature over 10 to 30 °C are shown in Fig. 4 in appendix D. From the wavelength depending slopes of the linear temperature dependencies of the water extinction, the spectral distribution of dE/dT was obtained (Fig. 2).

 

Fig. 4 Dependency of water extinction on temperature at three predefined wavelengths (red: 187 nm, blue: 190nm, green: 195 nm). The points represent the measurement data and the solid lines are linear fits.

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Our measured data can be fitted in the range between 187 and 200 nm with the fitting function dE/dT = 7.54955*10⁻⁷ λ⁴ – 5.97617*10⁻⁴ λ³ + 0.1774 λ² – 23.40698 λ + 1158.15784 (R² = 0.9998). Literature data for the extinction temperature coefficient in UV wavelength region was only found in [12], where dE/dT was measured at 184.9 nm between 20 and 35 °C. Weeks et al. [12] determined dE/dT near 25 °C to 0.051 ± 0.001 cm⁻¹ K⁻¹ (slope at 25 °C of Fig. 2 in [12]) which is more than twice the value we calculated with our fitting function shown in Fig. 2 (0.023 cm⁻¹ K⁻¹ at 184.9 nm). The higher value of Weeks et al. could result from the extinction temperature dependence of possible impurities due to the missing oxidative step in the water purification process and of the not removed dissolved oxygen. Extinction temperature coefficients in the visible and near infrared wavelength region near the maximal absorptions (higher overtone and combination transitions) were determined to be up to about three orders of magnitude lower than the UV values obtained [30–32].

4. Conclusions

We have presented the optical properties of the clearest ultrapure water investigated so far in the ultraviolet. We have extended the start-of-the-art extinction values of Quickenden and Irvin [1] towards shorter wavelengths by 15 nm (down to 181 nm), allowing to redefine a straightforward-to-use double-exponential fitting function for the extinction of ultrapure water in the deep UV (at 25 °C). Our calculated Rayleigh scattered contribution using updated material parameters reproduces the evolution of the extinction in the range between 205 nm and 340 nm much better than others reported in the literature. We reveal the Urbach constant and determine the spectral distribution of extinction temperature coefficient of such ultrapure water in the deep UV for the first time. This coefficient allows to noninvasively determine the temperature of water just by measuring the UV extinction, which is useful in cases thermo elements are problematic to employ or where miniaturized spectrometer such as liquid core waveguides are considered [33].