2.1

Liquids Measurements

The experimental methods use to derive the liquids n(v) and k(v) optical constants data were largely derived by Bertie and colleagues^7,14-16 and improvements to these methods have been described by Myers et al.^18-19 While the basic experimental procedure involves making a series of simple liquids transmission measurements, attention to detail is required at every step in order to obtain quantitative values for k (and in turn for n).

The key to quantitative results lies within the multiple path length method of data collection for liquid samples. This approach allows for more accurate analysis where the signal may vary up to four orders of magnitude between the weak and strong absorption bands. In addition, liquid absorbance measurements are now recorded in both the mid-infrared (MIR) and near-infrared (NIR) regions, with data extended¹⁹ out to 10,000 cm^-1. Shorter path length cells are used for MIR measurements where strong absorbance features have become saturated (ABS₁₀ ≥ 2). Such features are usually associated with fundamental modes of vibration and typically lie between 4,000 and 400 cm^-1. Longer path lengths are used for the weaker absorption bands above 4,000 cm^-1. Inclusion of NIR measurements allows for detection of weak absorption features above ca. 5,000 cm^-1 and greatly improves signal-to-noise (S/N).

Two different FTIR spectrometers are used in order to optimize each instrument for their respective spectral region of interest and to increase the efficiency of sample collection time. NIR measurements (10,000-3,000 cm^-1) are recorded on a Bruker Vertex 70 using a quartz tungsten bulb, an extended-range broadband potassium bromide (KBr) beamsplitter and a deuterated triglycine sulfate (DTGS) detector. A Bruker Tensor 27 with a silicon carbide glow bar source, broadband potassium bromide (KBr) beamsplitter and a DTGS detector is used to collect MIR data ranging from 7,800 to 400 cm^-1. An empty sample chamber purged with ultra-high purity nitrogen gas is used as a background (I₀) spectrum. Absorbance spectra are then generated by using the equation A = -log(I/I₀) where I is the sample spectrum. Typically three sets of 128 scans are collected at 2.0 cm^-1 resolution for each sample.

Prior to sample measurements, daily tests are performed to calibrate both the x and y-axes (frequency and transmission values, respectively). The x-axis is calibrated using gas-phase CO₂ and H₂O reference data from the Pacific Northwest National Laboratory (PNNL) IR database²⁰ in comparison to measured absorbance spectra of the sample compartment open to air. The y-axis is calibrated using a MRC Infrared Linearity Standard (MRC-910-NG11 S/N 0108, Middleton Spectral Vision, Middleton, WI) with known transmission values compared at various wavelengths. The sample used as an example in the manuscript is squalene from Alfa Aesar (98% purity).

To provide quantitative values for both n and k, multiple path lengths are used to account for both strong and weak absorption bands. Weaker absorption features above ~4,000 cm^-1 are also detected by employing the MIR-NIR dual measurement protocol. As shown in Figure 1, commercial cells utilized for liquid absorbance measurements are typically made of potassium bromide (KBr) with path lengths ranging from 15 μm to 3,000 μm, but potassium chloride or zinc selenide (for aqueous species) may also be used. To provide accurate results for stronger absorbance bands, shorter path cells are formed by placing the 15 μm cells in a hydraulic press to achieve path lengths down to as short as 1.5 μm. For the MIR at least seven different path lengths are used between 1 and 500 μm. In the NIR 100, 200, 500, 1,000 and 3,000 μm cells are used. For consistency purposes and to aid in the data merging process, the same 100, 200 and 500 μm cells with the same fill are used for both the MIR and the NIR instruments/measurements.

Figure 1:

Instrumentation used to provide quantitative data. A Bruker Tensor 27 or 37 is used to measure absorbance spectra of liquids injected into commercial cells ranging from 15 to 3,000 μm. For saturated bands, cells must be crushed with a hydraulic press to achieve path lengths < 15 μm. Beer’s law is utilized to estimate cell path lengths based on certain bands.

Path length values are initially estimated by measuring the fringe spacing in an empty cell, but further analysis is required to account for changes that may result from cells relaxing after being filled. An iterative approach based on the Beer-Lambert law of absorption is used to determine the ratio of path lengths for various cells from multiple absorbance plots in order to get the best estimate of path lengths.

In addition to the multiple path length approach, multiple burdens (i.e. replicate sample fills and measurements) are used for each path length to provide accurate measurements over a range of varying band strengths. Shorter path lengths are key for the accuracy of strong absorption bands and achieving linearity, while longer path length cells and the extension of collection methods to the near-infrared provide further information about weaker absorbance features. The k vectors are calculated for each absorbance file using²¹ Bertie’s program “RNJ46A” and appropriate regions from each are later merged to provide a composite k vector.

In addition to absorbance measurements, the refractive index of liquid samples is measured using an ATAGO refractometer at seven fixed wavelengths in both the visible and near-IR region. The scalar n values are measured at 480, 486, 546, 589, 644, 656 and 1,550 nm and a modified-Sellmeier equation²² is used to interpolate n at the highest frequency value:

The final n vector is calculated using the composite k vector and the refractive index at the highest frequency value using the Kramers-Kronig relation²¹ per Bertie’s “LZZKTB” program.

2.2

Solids and Bulk Liquid Measurements

The methods used to acquire the hemispherical and diffuse reflectance spectra in the mid-infrared using an integrating sphere have been previously described.^3,4,23,24 An integrating sphere coupled to a spectrometer can be used to measure the reflectance spectra of solids, bulk liquids and samples deposited on various substrates. Briefly, a 75 mm matte gold-coated Bruker A562 integrating sphere accessory with a two-port design is placed in the sample compartment of a Bruker Tensor 37 FTIR, or bolted to a Bruker Optics IR Cube FTIR spectrometer. The spectrometer provides a modulated infrared beam to the sphere which is reflected by a flip mirror located inside the integrating sphere. The flip mirror is used to reflect light directly to the sample at the bottom port or to a point of reference (either top port or side wall) within the sphere. With the mirror pointing down towards the sample port, a 15° angle is formed between the incident light beam and the normal to the sample surface (Figure 2).

Figure 2:

Sketch of the integrating sphere used to take hemispherical (A) and diffuse-only (B) measurements where the gold dome top is removed to allow the specular portion to escape. The black hatched square represents the detector on the axis going into the paper.

Per the two-port design, two sets of spectra can be recorded for each sample: the diffuse-only reflectance spectra (where the specular component is removed) and total (or hemispherical) reflectance spectra. For hemispherical reflectance as shown in Figure 2A, the top gold dome is left in place so that the light comes in from the right, reflects off a mirror and down to the sample where all the reflected light is collected. The specular ray is indicated in the red arrows, while the diffuse components are shown in green. For diffuse-only measurements depicted in Figure 2B, the top gold dome is removed to allow the specular component to escape.

Hemispherical and diffuse-only reflectance spectra were collected using a double-sided, forward-backward acquisition at 4.0 cm^-1 resolution between 7,500 and 500 cm^-1, using a Mertz phase correction and a Blackman-Harris 3-term apodization. The instrument is purged with ultra-high purity N₂ to reduce excess H₂O and CO₂ interferences. A set of standards is measured daily prior to collecting sample spectra to ensure the instrument and its reflectance accessory are performing consistently and optimally.

3.1

Typical case for liquids: Squalene

Squalene is presented as an example in this manuscript where various peak strengths are present throughout the entire spectral range (10,000 to 400 cm^-1, 1.0 to 25.0 μm) and multiple path lengths are necessary to determine accurate k (and therefore n) values. Shorter path lengths are important for maintaining a linear response for the strong bands. The longer path lengths are necessary, however, to detect weaker band strengths above 6,000 cm^-1, in particular to achieve good S/N in this domain. Seven cells with varying path lengths (6.03, 9.23, 19.3, 42.9, 121, 262 and 503 μm) were used for absorbance measurements of squalene for the MIR to account for varying band strengths as demonstrated in Figure 3 (left). Five path length cells were used for the NIR absorbance measurements: 122, 260, 508, 1,024 and 3,055 μm (right). The 122, 260 and 508 μm cells used in the NIR measurements were the same cells from the MIR measurements with the same fill. Since MIR and NIR path lengths are calculated independently from each other and based on their absorbance spectra, marginal differences in values from the same cell may be a result of the cell relaxing or minor differences in the Beer-Law plots, the differences less than 2% in almost all cases. Since two spectrometers are used, a slightly different portion of the liquid cell may be interrogated by the beam. As shown from Figure 3, multiple path lengths are necessary to account for regions of the spectra where peaks become saturated or conversely, where signal is very weak, but a feature is indeed present.

Figure 3:

Example of multiple path lengths used for squalene for the MIR (A) and NIR (B) absorbance measurements. MIR data in this figure are presented from 3,400 cm^-1 to 2,400 cm^-1 while NIR data are presented between 6,200 and 5,200 cm^-1. Seven path lengths were used for the MIR (6.03, 9.23, 19.3, 42.9, 121, 262 and 503 μm) and 5 for the NIR (122, 260, 508, 1,024 and 3,055 μm). The same cells with the same fill of squalene were used for the 121-503 μm path lengths for both instruments.

Figures 3A and 3B demonstrate the importance of using multiple path lengths: For the MIR peak near 3,000 cm^-1 the long path cells (121, 262 and 503 μm) are all off scale with measurements of ABS >3; these data are not used in the fit at these wavelengths. However, the same cells represent good data (linear in response) in the NIR near 5,700 cm^-1, along with two additional long path cells of 1,024 and 3,055 μm. Using such data, individual k vectors were created for each path length cell for both MIR and NIR data and then merged to create a composite k vector for each region. For the NIR three vectors were created and merged by hand to create a final k-vector for the NIR region between 10,000 and 3,601 cm^-1. For the MIR, five composite spectra were created and merged to produce the final MIR k-vector between 7,800 and 400 cm^-1. A more detailed list of the individual k-vectors and their regions is provided in Table 1.

Table 1.

List of cells used to create individual MIR and NIR k-vectors and their corresponding spectral regions.

The refractive index for squalene was calculated at 27 °C at seven wavelengths using an Abbe Refractometer to determine (via interpolation) the n value at the highest recorded IR frequency for both the MIR (7,800 cm^-1) and NIR (10,000 cm^-1). Using a modified-Sellmeier fit, the refractive index was determined via interpolation to be 1.4771 at 10,000 cm^-1 and 1.4730 at 7,800 cm^-1 as seen in Figure 4.

Figure 4:

Plot of measured refractive index values collected with Abbe refractometer (red circles) along with the modified Sellmeier fit (black trace) for squalene at 27 °C. The dashed lines and blue triangles represent where the refractive index at 10,000 cm^-1 and 7,800 cm^-1 was determined from the fit via interpolation.

A composite k-spectrum between 10,000 and 400 cm^-1 was created from the composite MIR and NIR k vectors. The NIR data were used exclusively above 5,577 cm^-1 and the MIR data were used exclusively below 4,853 cm^-1. The overlap region between MIR and NIR data was between 5,577 and 4,853 cm^-1. The KKT per Bertie’s²¹ program “LZZKTB” was used to create a final n vector from the resulting composite k vector and the refractive index at the highest frequency for the spectral region (10,000 cm^-1). The final composite n(v) and k(v) spectra are shown below in Figure 5 across the entire spectral domain. By using multiple path lengths and a two-instrument system to accommodate MIR and NIR measurements, both strong and weak absorption features were detected for squalene and more accurate n(v) and k(v) values were derived across a large spectral range.

Figure 5:

The final n (black trace) and k (red trace) spectra of squalene over 10,000-400cm^-1.

3.2

Modeling spectra based on n(v) and k(v)

Optical constants can be useful in modeling samples that may be encountered in an environment other than bulk liquids. This is important because other than water, the bulk form is rarely encountered for liquids, but rather as thin/thick layers on substrate, droplets, aerosols, etc. Reflectance measurements of liquids are thus more complicated as absorbance, reflectance and refraction of the incident light must all be taken into account. So-called “transflectance” features are prominent in thin layer systems as the incidence light can pass through the sample multiple times. As an example, we have used the n(v) and k(v) values derived above to calculate model spectra of 1 μm and 100 μm layers of squalene on aluminum as seen in Figure 6. To produce these spectra, a commercial thin film modeling and design package (Essential Macleod) was used with an incidence angle of 60°. As shown, spectra can vary drastically based on morphological conditions such as particle size, substrate material, and layer thickness.

Figure 6:

Modeled reflectance spectra of squalene at two different thicknesses on aluminum. Two different polarizations are shown for the reflected light.

3.3

Publicly available data

Currently the optical constants for 57 liquid species spanning a diverse set of organic, inorganic and organophosphorous compounds are available on the NIST website at https://webbook.nist.gov/chemistry/silmarils-liquids-n-k/.^18,24 For this set of compounds, n and k values are available from 7,800 to 400 cm^-1 at 2 cm^-1 resolution. An additional 70 liquids have been measured using the MIR-NIR dual method to extend data out to 10,000 cm^-1. These compounds have been detailed in a previous publication and will be available for download at a later date.¹⁹

In addition to the liquids n/k data, quantitative values for hemispherical and diffuse reflectance is available for download for 130 solid samples on the NIST website (https://webbook.nist.gov/chemistry/silmarils-solids-hrf-drf/).^13,25 The optical constants of solids using quantitative absorption measurements in KBr pellets have also been recorded as outlined by Myers et al.²⁶ Specifically, the n/k values for 70 solids of both inorganic and organic species have been calculated using this method. Due to the limited availability of optical constants for solid compounds, more experiments are required to confirm the validity of the KBr pellet method.