Nonlinear frequency response analysis: a recent review and perspectives

The nonlinear frequency response analysis (NFRA) can be seen as an extension of electrochemical impedance spectroscopy. NFRA gives a full and detailed representation of the system response and can establish a connection between model parameters and the experimentally observed phenomena. In this article, different theoretical NFRA approaches and the most recent application examples are discussed. A simple electrochemical example is used to showcase the benefits and disadvantages of analyzing the system response by using different approaches. In addition, it was shown how to extract experimental harmonic values and analyze them.     

Ionization energies of hypervalent Li2F,Li2Cl and Na2Cl molecules obtained by surface ionization electron impact neutralization mass spectrometry

Ionization energies of hypervalent Li(2)F, Li(2)Cl and Na(2)Cl molecules detected by surface ionization electron impact neutralization mass spectrometry are reported. The ionization energies were 3.78 +/- 0.2 eV for Li(2)F, 4.93 +/- 0.2 eV for Li(2)Cl, and 4.21 +/- 0.2 eV for Na(2)Cl. The ionization energies (IE) agree with theoretical ionization energies calculated by ab initio methods, supporting the theoretical prediction that Li(2)F has a hyperlithiated configuration in which the odd electron delocalizes over the two lithiums and with photoionization measurement. The first ionization energy of Na(2)Cl was experimentally confirmed earlier and for Li(2)Cl as well.8 We have developed and used this new approach for the problem--in the present work ions were first formed by surface ionization, followed by electron attachment (neutralization).     

CO2-laser photoacoustic detection of heavy water vapour. Basic principles

A CO₂-laser cw system and a photoacoustic detection apparatus, based on a nonresonant gas cell, was constructed and built. Coincidences of D₂O absorption with several laser lines were observed. The strongest absorption was observed with the line at 9.26 m, which was used in the experiments. Samples of deuterated water in the range from 10 to 100% deuterium were used to examine the behaviour of the photoacoustic signal under conditions of varying deuterium content and total vapour pressure. A principal calibration procedure with respect to this is proposed. The behaviour of the system on buffer gas introduction was examined with hydrogen and dry air. Self-buffering of water vapour is also discussed on the basis of the results.     

Nonlinear Frequency Response of Nonisothermal Adsorption Systems

A general method for the investigation of adsorption kinetics of nonlinear,nonisothermal systems, based on frequency response analysis, ispresented. It is based on the definition of higher-order frequency response functions (FRFs) on the adsorber and on the particle level. FRFs on the adsorber level can be estimated from experimentally measuredadsorber FR and used to calculate FRFs on the particle level,which can be further used for model identification, by comparison withtheoretical particle FRFs. The general procedure for calculation of particle FRFs from those of adsorber is given. Also, the generalprocedure for theoretical derivation of particle FRFs is given andillustrated with an example of nonisothermal adsorption governed bymicropore diffusion and film resistance heat transfer, as well as theprocedure for calculating unmeasured adsorber FRFs, which isillustrated with an example of a batch adsorber with volume modulation.     

Photoacoustic study of CO2-laser coincidences with absorption of some organic solvent vapours

Detection of specific molecules in the atmosphere is motivated by the need for monitoring the emission of industrial pollutants. CO₂-laser photoacoustic (PA) spectroscopy was used here to obtain coincidence spectra of the vapours of three organic solvents: trichloroethylene (TCE), benzene, and dioxan. Spectra of coincidences were obtained as a function of total pressure, adding dry air to the vapour of the solvents up to 1000 mbar.A narrow cavity photoacoustic cell with window acoustic buffers was built for improved sensitivity, and is reported here.The vapour molecules studied do have some significant absorption in the CO₂-laser region, or close to it, but that fact does not necessarily lead to usable coincidences with the narrow laser lines. The results reveal several prominent coincidences that can be used for practical purposes, especially in the case of trichloroethylene.     

Discrimination between adsorption isotherm models based on nonlinear frequency response results

A number of criteria are established for distinguishing between different adsorption isotherm types. These criteria are defined based on the adsorption isotherm derivatives up to the third order, which, on the other hand, can be estimated from nonlinear frequency response data. The criteria for five favourable (Langmuir, Freundlich, Sips, Toth and Unilan) isotherms and two complex isotherms (BET and quadratic) are presented. These criteria enable unique identification of the underlying adsorption isotherm relation if the values of the local first, second and third order isotherm derivatives at several points are known. The method is applied to experimental data from our previous publications, for one case of a favourable and one case of a complex isotherm.     

Nonlinear FR-ZLC method for investigation of adsorption equilibrium and kinetics

A new method for investigation of adsorption equilibrium and kinetics, named Nonlinear Frequency Response-Zero Length Column (NFR-ZLC) method, is introduced. It combines the advantages of the Nonlinear FR method (the potential to identify a model corresponding to the most probable kinetic mechanism and to estimate the equilibrium and kinetic parameters of the identified model) and of the ZLC method (the potential to derive direct information about the processes on the particle level, by eliminating the influence of the adsorber). The frequency response functions of a ZLC system, up to the third order, and for three simple kinetic mechanisms (film resistance control, micropore diffusion control and pore-surface diffusion control) are derived and simulated. The procedure for estimation of the equilibrium and kinetic parameters is defined and illustrated based on numerical simulations.     

Detailed structural elucidation of polyesters and acrylates using Fourier transform mass spectrometry

The detailed structural characterization of complex polymer architectures, like copolymers and polymer mixtures, by mass spectrometry presents a challenge. Even though soft ionization analyses revolutionized the characterization of large molecules and provided a means for determining the polymer’s molecular weight distribution, polydispersity, and end groups, full microstructure elucidation and monomer sequencing by soft ionization alone is not possible. The combination of high-resolution Fourier transform mass spectrometry (FTMS) and tandem mass spectrometry (MSⁿ) provides a powerful analytical tool for addressing these challenges. This tool was used in our work to separate and identify the products of polymerization between 12-hydroxystearic acid (HSA) and stearic acid (SA), to provide precise information about the exact location of caprolactones on the Tris(2-hydroxyethyl)isocyanurate (THEIC) molecule, and to sequence a glycidyl methacrylate/methyl methacrylate (GMA/MMA) copolymer. The results highlight the value of ultrahigh resolution and tandem mass spectrometry for fine structural characterization and sequencing of polymers.     

Estimation of single solute adsorption isotherms applying the nonlinear frequency response method using non-optimal frequencies

In order to estimate single solute adsorption isotherms, the nonlinear frequency response (FR) of a chromatographic column is analyzed experimentally and evaluated using the concept of higher order frequency response functions (FRFs) based on the Volterra series and generalized Fourier transform. In this case study, it has been investigated the adsorption of ethyl benzoate on octadecyl silica from a mixture of methanol and water (60:40) as a solvent. Experiments are performed using a standard gradient HPLC unit. For estimation of adsorption isotherms by the nonlinear FR method the column inlet concentration is changed in a nearly sine waveform around several steady-state concentrations. Using this method the first three local derivatives of a single solute adsorption isotherm are estimated from the low frequency asymptotes of the corresponding functions, i.e. the phase and first order derivative of the FRFs. For an accurate estimation of isotherm coefficients periodical experiments should be preformed for frequencies below a certain critical frequency. This is the frequency needed for approaching the low frequency asymptotic behaviour of the corresponding functions close enough, so that errors due to the non-feasibility of experiments with zero frequency can be neglected. Unfortunately, depending on the properties of the system, it can happen (as for the system investigated here) that experiments for the critical frequency would be too long and cannot be realized. In order to study the loss of accuracy of the nonlinear FR method, when it is applied for non-optimal frequencies, experiments are performed for frequencies approximately one order of magnitude higher than the critical frequency required to evaluate the FRF phases. The obtained isotherm model coefficients are compared with the ones estimated using conventional frontal analysis as a reference method. The isotherms determined by two methods are similar, however a closer look reveals that peaks predicted under overloading conditions differ.