**3. Experimental section**

Infrared spectroscopy is an experimental technique able to detect the absorption of infrared radiation by the matter [20]. Characteristic vibrational states may be attained by the mol‐ ecule at the frequencies characteristic for each component molecular group. They can be mea‐ sured as an absorption spectrum, i.e., a plot of the absorbed intensity of the applied radiation, expressed as absorbance, as a function of its frequency, measured in terms of wave number (cm−1). The infrared spectrum is characteristic for any molecule to such an extent that it may be considered the molecule fingerprint. For a molecule that consists of N atoms, there are (3N‐6) ways in which the molecule can vibrate, or (3N‐5), if it is linear, therefore, it is reason‐ able to expect that complex molecules or mixture of substances could originate complex IR spectra, difficult to analyze and to interpret. Nevertheless, some moieties of the molecules, the so‐called functional groups, display one or more absorption infrared bands at specific frequencies, slightly influenced by the surrounding parts of the molecule. In such a way, it is possible to identify the chemical groups responsible for such features even though the mol‐ ecule is not known.

FTIR spectrophotometers use the technique of Michelson interferometry to simultaneously sample a range of frequencies. The IR beam emitted by the source is collected by a beam split‐ ter and divided into two beams each one of half intensity with respect to the original beam. One is falling on the moving mirror and the other one on the fixed mirror. The light beams reflected by the moving and the fixed mirrors are combined generating a complex interfero‐ gram, as a function of the position of the moving mirror. The resulting interferogram is sub‐ jected to Fourier analysis to generate a spectrum, i.e., a plot of intensity versus frequency. Absorption spectra are obtained by measuring the interferograms with a sample and with the empty sample cell (blank) in the beam, being the interferogram intensity

$$I\_{\text{interface}}(t) = k \stackrel{\leftrightarrow}{\int} I\_{\text{beam}}(\nu) e^{i2\pi t} \, d\nu \tag{1}$$

where *k* is a constant, *I*beam the intensity of the beams and ν the wave number. From the inter‐ ferogram, the intensity of the beams can be calculated by inverse Fourier transforming the resulting interferograms

$$I\_{ham}(\nu) = \ k \stackrel{\leftrightarrow}{\int} I\_{int}(t)e^{-i2\pi nt} \, dt \tag{2}$$

The IR absorption spectrum is calculated as the logarithm of the intensity quotient of blank to sample.

### **3.1. Equipment and materials**

related to different local H bonding structure. In the paper of Onori and Santucci [15] and Mallamace et al. [16], the best fit deconvolution of the band was performed in the study of, respectively, AOT hydrated micelles and lysozyme at different temperatures to investigate

Pure water ν(OH) band (3800–2800 cm−1) cannot be fitted by a single Gaussian line, but can be deconvoluted into components, usually assigned to different sets of molecules. Following the central limit theorem stating that the distribution of the sum (or average) of a large number of independent, identically distributed variables will be approximately nor‐ mal, regardless of the underlying distribution, the component number could be enormously large. However, the structural constraints settled on the basis of the number and strength of hydrogen bonds in different arrangements avoids effects of overfitting, allowing the break‐ down of the band up to a maximum of six sub‐bands in dependence on the model assumed to describe water system. The structure of *ν*(OH) band is described in details by Schmidt and Miki [17] and directly related to the O‐H bond lengths: variations in the bond lengths are caused by the influence of the surrounding hydrogen‐bonded network of water molecules and affect position and width of the components bands. According to this view, from the higher wave number region towards the lower one, the first peak (3680 cm−1) can be attrib‐

the vapor state. The three intermediate components contribute 85% to the total signal, indi‐ cating that the majority of water molecules have a local hydrogen‐bonded network which

O) is responsible for the envelope of the two low wave number bands. The peak position of each band was related to O–H bond length. The values were calculated by transforming the frequency and full‐width half‐maximum values of the *ν*(OH) band components using

In recent times, we have developed a technique operating the removal from the spectrum of the features due to the spurious vibrational bands unrelated to water by means of the operation of subtraction of the "dry sample" spectrum, i.e., the spectrum of the sample gently dehydrated to expel as much solvent as possible without affecting the molecule structure [9, 10, 19]. The cleaned band obtained by such procedure can be treated as a water ν(OH) band and therefore compared with the corresponding band of pure water and analyzed by decon‐ volution in component bands, each one related to different hydrogen bond engagements and

Infrared spectroscopy is an experimental technique able to detect the absorption of infrared radiation by the matter [20]. Characteristic vibrational states may be attained by the mol‐ ecule at the frequencies characteristic for each component molecular group. They can be mea‐ sured as an absorption spectrum, i.e., a plot of the absorbed intensity of the applied radiation, expressed as absorbance, as a function of its frequency, measured in terms of wave number (cm−1). The infrared spectrum is characteristic for any molecule to such an extent that it may

O molecules as confirmed by theoretical calculations. Solid clusters (6–10

O molecules behaving as in

uted to monomer‐like vibration, due to free O–H vibration of H2

structural dynamical transitions.

194 Fourier Transforms - High-tech Application and Current Trends

includes 3–7 H2

Badger's rule [18].

H2

lengths.

**3. Experimental section**

Any standard commercial Fourier transform infrared spectrophotometer can be used to per‐ form the experiments described in the present paper. We have used two kinds of equipment: BOMEM DA8 and Jasco 420 FTIR spectrophotometers operating in the 4000–400 cm−1 range, at temperature close to ambient (290–300 K). Each spectrum was measured by acquiring 128 scans at 2 cm−1 spectral resolution.

The samples were thin films obtained by depositing aqueous solutions (*c* = 10–40 mg/ml) on CaF<sup>2</sup> windows and allowing them to dry in air under ambient conditions. The film smeared on the calcium fluoride platelets was assembled in a sealed sample cell consisting in a dry box equipped with IR transparent CaF<sup>2</sup> windows. In the box were inserted (1) a vessel containing a saturated salt solution suitable to assess the opportune relative humidity (RH) to which the sample has to be equilibrated; (2) the sample prepared as a film smeared on a CaF<sup>2</sup> platelet, vertically positioned in such a way as to allow for transmission measurements (**Figure 1**). The box, avoiding any contact of the sample with the external atmosphere, was inserted in the sample chamber of the FTIR spectrophotometer.

**Figure 1.** Sketch of the sample holder employed to attain the desired hydration degree in the samples. The samples were obtained as films of macromolecule solution smeared on the vertical CaF<sup>2</sup> platelet, allowed to dry in air before to expose them to the moist ambient in the box. Different relative humidity was achieved in the inner ambient of the box by saturated salt solutions put in the vessel placed on the box base and assembled together with the sample.

Blank measurements were recorded on the sample holder in order to subtract the contribu‐ tion of the CaF<sup>2</sup> platelet on which the sample was deposited and the spectrum of the dry box CaF<sup>2</sup> windows.

### **3.2. Experimental procedures and analysis of water sorption**

The protein film together with the salt solution suitable to keep it at the desired humidity level was assembled in the sample holder for 1–2 days before to submit it to the measurements. **Table 1** lists the salts employed for preparing salt solutions able to provide in the desiccator water activities *a*w ranging between 0.06 and 0.97.

The change in the hydrating solution was performed in a dry box under a controlled N<sup>2</sup> atmo‐ sphere. The lowest hydration value was reached by maintaining the sample in an oven at about 80°C for 2 h. This sample was called the "dry" sample.

Fitting operation of the OH stretching and Amide bands was performed according to Gaussian curves starting from a second derivative analysis [21]. In particular, the OH‐stretching mode band (*ν* ~3400 cm−1*)* was analyzed following the approach, adopted in the literature to describe the solvent role of water and deconvoluted into components, which, in principle, might be related to different hydrogen‐bond distances [17]. A twofold analysis was performed on the *ν*(OH) band. First, the spectra of the samples collected by decreasing (desorption run) and increasing (adsorption run) the ambient relative humidity were compared and analyzed with


**Table 1.** Salts employed for saturated salt solutions necessary to accomplish the controlled activities *aw* in the box where the macromolecule films were equilibrated before FTIR measurements.

Blank measurements were recorded on the sample holder in order to subtract the contribu‐

**Figure 1.** Sketch of the sample holder employed to attain the desired hydration degree in the samples. The samples

expose them to the moist ambient in the box. Different relative humidity was achieved in the inner ambient of the box by

saturated salt solutions put in the vessel placed on the box base and assembled together with the sample.

The protein film together with the salt solution suitable to keep it at the desired humidity level was assembled in the sample holder for 1–2 days before to submit it to the measurements. **Table 1** lists the salts employed for preparing salt solutions able to provide in the desiccator

sphere. The lowest hydration value was reached by maintaining the sample in an oven at

Fitting operation of the OH stretching and Amide bands was performed according to Gaussian curves starting from a second derivative analysis [21]. In particular, the OH‐stretching mode band (*ν* ~3400 cm−1*)* was analyzed following the approach, adopted in the literature to describe the solvent role of water and deconvoluted into components, which, in principle, might be related to different hydrogen‐bond distances [17]. A twofold analysis was performed on the *ν*(OH) band. First, the spectra of the samples collected by decreasing (desorption run) and increasing (adsorption run) the ambient relative humidity were compared and analyzed with

The change in the hydrating solution was performed in a dry box under a controlled N<sup>2</sup>

**3.2. Experimental procedures and analysis of water sorption**

were obtained as films of macromolecule solution smeared on the vertical CaF<sup>2</sup>

196 Fourier Transforms - High-tech Application and Current Trends

about 80°C for 2 h. This sample was called the "dry" sample.

water activities *a*w ranging between 0.06 and 0.97.

platelet on which the sample was deposited and the spectrum of the dry box

atmo‐

platelet, allowed to dry in air before to

tion of the CaF<sup>2</sup>

windows.

CaF<sup>2</sup>

respect to the other spectral features (Amide bands). Second, the OH stretching band was resolved, by a curve fitting approach, in Gaussian components. The goal in the method is to decompose the feature into three component bands which can be assigned to three different sets of hydrogen bond strength. The Gaussian component amplitude, converted into water amounts, can be used to plot sorption isotherm curves [22]. The relative amounts of water in the three different structural forms were expressed in terms of the area of each peak by assuming that the sum of the areas of the peaks is proportional to the total amount of water in the protein. The corresponding H bond lengths were evaluated by employing Nakamoto plots [23].

Water sorption isotherms were obtained as the sorbed water vapor amount versus water vapor activity *a*w at fixed temperature [22]. The water content of the sample was spectropho‐ tometrically determined from the ν(OH) band amplitude subtraction of the spectrum of the same sample fully dehydrated ("dry" sample). In this way, any contribution to the band of N–H and C–H stretching vibrations, occurring in the same wave number range, was system‐ atically eliminated. Due to the thin thickness of the samples, layered as film and the very low water content (0.97–0.06 gwater/gdry sample), the very small change in the optical path produced by dehydrating the sample does not affect significantly the spectra intensity. Adaptation of Beer's law was successively used to rescale the intensity of the "cleaned" *ν*(OH) bands, in accordance with the approach proposed in the literature to study various hydrated biomate‐ rials [24]. To quantify the integrated absorbance in terms of water surface coverage, we can assume a modified form of Beer‐Lambert' law

$$\tilde{A} = \prescript{}{b}{\text{ and }} \text{ad } \text{v = } \varepsilon \left( \nu\_{\text{MAX}} \right) \overline{\text{c}} d \tag{3}$$

where *A*˜ is the integrated absorbance of the component band, *ε* (*νMAX*) is the molar absorp‐ tivity at wave number ν*MAX* corresponding to the peak of the band (L mol−1 cm−1), *c*¯ is the concentration of the absorbing species (mmol/cm<sup>3</sup> or, equivalent mol/L) and *d* is the average thickness of the absorbing species film, that is, adsorbed water, in centimeters [9].

For water, it is possible to evaluate the molar absorptivity *ε*(ν) at fixed wave number [24]: for example, one can evaluate ε (3600 cm−1) = 1.647 L mol−1 cm−1. By assuming the path length *d* as the thickness of a film of water, the corresponding amount of the water content can be con‐ verted in concentration *c*¯ of water, assumed as only absorbing species. The concentration *c*¯ in each sample prepared at each hydration degree can be evaluated and employed to normalize the amplitude of the subcomponents in the ν(OH) band. The desorption‐adsorption branches of the isotherm curves were therefore obtained for each Gaussian component. As a rule, the desorption experiments were performed by starting from the highest *a*w value (*a*w = 0.97) and accomplished before the adsorption one, to avoid possible damages in the samples produced by dehydration treatments.
