FTIR spectra of acetone-chloroform system with various component ratios were investigated within the spectral range 3950–4550 cm^{−1}. Methods of multivariate curve resolution were applied to decompose the FTIR spectra into specific components of different composition. A method of decomposition based on structural model of solution which contains acetone, chloroform, and complex acetone/chloroform (1 : 1) was proposed. Results of both approaches are in good agreement within the range of measuring error.

Acetone-chloroform mixture is a prominent example of a system with a pronounced negative deviation from ideal solution behavior. So it has been the subject of many theoretical and experimental researches [

Infrared spectroscopy is powerful tool of investigation of liquid systems [

The purpose of this work is quantitative analysis of acetone-chloroform mixture using model-free and model-based multivariate regression approaches.

FTIR transmission spectra were measured with Thermo Scientific spectrometer Nicolet 6700 with a spectral resolution of 4 cm^{−1}. Optical path length of the quartz cell was 1 mm. The heating of the sample almost did not occur during the measurements due to small value of absorption coefficient at excitation frequency. The temperature of liquid samples was 25

Resolution methods decompose mathematically a global mixed instrumental response into the pure contributions due to each component in the system [^{
T}, each of them including the pure response profiles of the ^{
T}
^{
T} often refer to concentration profiles and spectra (hence their names).

With the measurement matrix

The mathematical decomposition of a single data matrix ^{
T}-type matrices can reproduce the original data set with the same fit quality. But some of the obtained solutions do not have any physical meaning. In plain words, the correct reproduction of the original data matrix can be achieved by using response profiles differing in shape (rotational ambiguity) or in magnitude (intensity ambiguity) from the sought (true) ones [

There are many methods of decomposition experimental matrix ^{
T} matrices optimally fitting the experimental data matrix ^{
T}.

Complete resolution of a two-way data set without ambiguities is only possible in some favorable cases where selectivity [

Boundaries of feasible solutions are related to rotational matrices

The goal is calculation of matrices

The method needs firstly the estimation of one of the feasible solutions within the range of all possible solutions, for instance, using alternating least squares with constraints [

As it was mentioned above, multivariate curve resolution is model-free analysis and its solutions are not unique. Unlike this, model-based analysis gives unique solution and basic parameter of the process, that is, the rate constant and the equilibrium constant in equilibrium investigations [

We can use the structural model of mixture for equilibrium studies. It is well known that the dissolution of one substance in another is accompanied by the formation of molecular complexes arising due to the intermolecular interaction [

If we know structural model of mixture and values of components concentrations before mixing, we can estimate the matrix of concentrations. We could get elements of matrix

Hence, we can find the matrix of spectral profiles

Firstly, we need to find

FTIR transmission spectra (Figure ^{−1}. This spectral range was chosen due to the weak absorption of overtones and composite frequencies in Near-IR region. Weak absorption value allows using the liquid cell with a relatively large value of the optical beam path (1 mm). Measurements in Mid-IR region require to use the optical beam path around 10–25

IR absorbance spectra of acetone-chloroform mixtures with different component ratios.

Our approach is based on a three-component MCR-ALS analysis of the FTIR spectra of water-methanol solutions. During ALS optimization nonnegativity, unimodality, and closure constraints were applied. We found that three components are required to obtain a good fit to the data (accuracy better than 1%). The “pure” components were identified as “free acetone (C_{3}H_{6}O)” and “free chloroform (CHCl_{3}),” and the third component as “acetone-chloroform complex.” The graphical user interface (GUI) in the MATLAB environment developed by Jaumot et al. [

We used MCR-BANDS GUI [^{
T}) and the concentrations (

Boundaries of concentration (a) and spectral profiles (b) of “pure” components obtained by MCR-BANDS analysis (

It is possible to consider acetone-chloroform mixture as ternary. There is no doubt as to formation of equimolar complex _{
2} complex [

The equilibrium constant

We hold total volume of components before mixing constant:

Substituting

We can obtain volume fraction of

We solved (

Concentration (a) and spectral profiles (b) of “pure” components obtained by model-based analysis (

We compared the resolved results by model-based analysis concentration profiles with those obtained by MCR-ALS. The result of comparison is shown in Figure

The result of comparison of resolved concentration profiles using model of mixture (solid curves) and boundaries of MCR solutions (dotted curves).

The analysis of FTIR spectra at different acetone concentrations in acetone-chloroform system using MCR-ALS method was carried out. It can give very necessary information about complex formation in this mixture. Three-component model of the mixture was chosen for the analysis. MCR-BANDS technique was used to obtain the band boundaries of MCR-ALS solutions.

The most difficult aspect of model-based approach is the determination of correct model. The process of fitting several models and comparing the results can be tedious. Three-component model of the mixture was used successfully for model-based approach to decomposition of spectra. Despite simplifying model usage, the concentration profiles obtained by model-free and model-based approaches are in good agreement within the range of measuring error.

Both approaches should be used in decomposition liquid mixture vibrational spectra. The model-free analysis can be invaluable in supporting the model choice.

The authors declare that there is no conflict of interests.