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).     

Use of Higher-Order Frequency Response Functions for Identification of Nonlinear Adsorption Kinetics: Single Mechanisms under Isothermal Conditions

The concept of higher-order frequency response functions(FRFs), which is based on Volterra series expansion of nonlinearfunctions, is used for analysis of kinetics of nonlinear adsorptionsystems. Four different kinetic mechanisms: Langmuir kinetics, filmresistance control, micropore diffusion control and pore-surfacediffusion control were analyzed and the results were compared. It wasshown that, contrary to the linear frequency response characteristicfunctions, the higher-order FRFs corresponding to different mechanismsdiffer in shape. This result offers great potential for theidentification of the adsorption-diffusion mechanism governing theprocess. It is shown that the second order FRFs give sufficientinformation for distinguishing different mechanisms.     

Hierarchically structured free-standing hydrogels with liquid crystalline domains and magnetic nanoparticles as dual physical cross-linkers

Here we report a modular strategy for preparing physically cross-linked and mechanically robust free-standing hydrogels comprising unique thermotropic liquid crystalline (LC) domains and magnetic nanoparticles both of which serve as the physical cross-linkers resulting in hydrogels that can be used as magnetically responsive soft actuators. A series of amphiphilic LC pentablock copolymers of poly(acrylic acid) (PAA), poly(5-cholesteryloxypentyl methacrylate) (PC5MA), and poly(ethylene oxide) (PEO) blocks in the sequence of PAA-PC5MA-PEO-PC5MA-PAA were prepared using reversible addition-fragmentation chain transfer polymerization. These pentablock copolymers served as macromolecular ligands to template Fe(3)O(4) magnetic nanoparticles (MNPs), which were directly anchored to the polymer chains through the coordination bonds with the carboxyl groups of PAA blocks. The resulting polymer/MNP nanocomposites comprised a complicated hierarchical structure in which polymer-coated MNP clusters were dispersed in a microsegregated pentablock copolymer matrix that further contained LC ordering. Upon swelling, the hierarchical structure was disrupted and converted to a network structure, in which MNP clusters were anchored to the polymer chains and LC domains stayed intact to connect solvated PEO and PAA blocks, leading to a free-standing LC magnetic hydrogel (LC ferrogel). By varying the PAA weight fraction (f(AA)) in the pentablock copolymers, the swelling degrees (Q) of the resulting LC ferrogels were tailored. Rheological experiments showed that these physically cross-linked free-standing LC ferrogels exhibit good mechanical strength with storage moduli G' of around 10(4)-10(5) Pa, similar to that of natural tissues. Furthermore, application of a magnetic field induced bending actuation of the LC ferrogels. Therefore, these physically cross-linked and mechanically robust LC ferrogels can be used as soft actuators and artificial muscles. Moreover, this design strategy is a versatile platform for incorporation of different types of nanoparticles (metallic, inorganic, biological, etc.) into multifunctional amphiphilic block copolymers, resulting in unique free-standing hybrid hydrogels of good mechanical strength and integrity with tailored properties and end applications.     

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.     

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.     

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.     

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.