Nonresonant holeburning in the Terahertz range: Brownian oscillator model

The response to the field sequence of nonresonant hole burning, a pump-wait-probe experiment originally designed to investigate slow relaxation in complex systems, is calculated for a model of Brownian oscillators, thus including inertial effects. In the overdamped regime the model predictions are very similar to those of the purely dissipative stochastic models investigated earlier, including the possibility to discriminate between dynamic homogeneous and heterogeneous relaxation. The case of underdamped oscillations is of particular interest when low-frequency excitations in glassy systems are considered. We show that also in this situation a frequency selective modification of the response should be feasable. This means that it is possible to specifically address various parts of the spectrum. An experimental realization of nonresonant holeburning in the Terahertz regime therefore is expected to shed further light on the nature of the vibrations around the so-called boson peak.     

Dynamic Kerr effect responses in the terahertz range

Dynamic Kerr effect measurements provide a simple realization of a nonlinear experiment. We propose a field-off experiment where an electric field of one or several sinusoidal cycles with frequency omega is applied to a sample in thermal equilibrium. Afterwards, the evolution of the polarizability is measured. If such an experiment is performed in the terahertz range it might provide valuable information about the low-frequency dynamics in disordered systems. We treat these dynamics in terms of a Brownian oscillator model and calculate the Kerr effect response. It is shown that frequency-selective behavior can be expected. In the interesting case of underdamped vibrational motion we find that the frequency dependence of the phonon damping can be determined from the experiment. Also the behavior of overdamped relaxational modes is discussed. For typical glassy materials we estimate the magnitude of all relevant quantities, which we believe will be helpful in experimental realizations.     

A theoretical analysis of the effect of solvent on the Kerr constant of dilute polymer solutions

A new model in which solvent molecules are regarded as discrete particles is used for investigating the influence of solvent orientation near a polymer chain and of the anisotropy of the internal electric field on the Kerr effect in a polymer solution. The relation derived for the Kerr constant consists of two parts containing nine terms each in the general case (the physical meaning of the terms is briefly discussed). Relations for the above effect in a nonpolar isotropic solvent, and explicit calculations of the Kerr constant for a simple model of a rigid polymer molecule are given.     

Characterizing polymers with heterogeneous micro‐ and macrostructures

The potentially extreme heterogeneity of polymer micro‐ and macrostructures has been demonstrated and a means for characterizing them has been suggested. To ensure that all possible microstructures, such as diad stereosequences in vinyl homopolymers and monomer sequences in copolymers, including their locations along polymer chains, that is, all macrostructures, are represented, it became necessary to generate samples with huge quantities (many many tons) of constituent polymer chains. This suggested a practical need for distinguishing between polymer samples with chains that have homogeneous and heterogeneous populations of micro‐ and macrostructures. A combination of high resolution ¹³C‐nuclear magnetic resonance to determine the types and amounts of constituent short‐range microstructures, and dilute solution electrical birefringence or Kerr effect measurements to locate them along the polymer chains has been suggested, and may be able to achieve this distinction. This combination of techniques is required to reduce the innumerably large numbers of different possible polymer macrostructres whose Kerr constants would have to be calculated, for comparison to the observed values. The ability to determine polymer macrostructures is critical to the development of relevant, more meaningful, and therefore, improved structure–property relations for polymer materials. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 409–414     

Effect of stereogenic centers on the self-sorting, depolymerization, and atropisomerization kinetics of porphyrin-based aggregates

We present our results on the mixing of different porphyrin molecules in supramolecular assemblies. Herein, chiral amplification experiments reveal the subtle role of the structural (mis)match between these monomers. We show that according to the "sergeant-and-soldiers" principle, a chiral porphyrin "sergeant" efficiently mixes with achiral "soldiers" in the same helical aggregate and strongly biases its handedness. However, when we mix two porphyrin enantiomers in a majority-rules experiment, no chiral amplification is observed at all, which is due to their narcissistic self-sorting into conglomerate-like aggregates. The mixing between two enantiomers in the same stack only occurs in a diluted-majority-rules experiment, in which enantiomeric mixtures of sergeants are diluted with achiral soldiers. The different outcomes of these chiral amplification phenomena are verified by modeling studies that reveal high mismatch penalties, which are ascribed to the high stereocenter loading of 12 methyl groups onto the monomers. Mixed-metal chiral amplification experiments between copper- and zinc-porphyrins show the same distinction in their mixing behavior, which is further supported by fluorescence measurements. The selective removal of chiral Zn-porphyrins from these mixed-metal systems is performed with the Lewis base quinuclidine that depolymerizes the Zn-porphyrins upon axial ligation. This extraction process proceeds at different time scales, depending on the mixed state: slow extraction kinetics for the mixed sergeant-and-soldiers and diluted-majority-rules systems and an instant extraction for the phase-separated majority-rules system. By simultaneously monitoring the supramolecular chirality during extraction, a chiral memory effect is observed for both mixed systems that show slow extraction kinetics. For the sergeant-and-soldiers system, the remaining supramolecular backbone contains achiral monomers only, which give rise to a long lasting chiral memory with slow, entropy-driven atropisomerization. Yet in case of the diluted-majority-rules system, the remaining backbone contains a mixture of achiral and chiral monomers in its unpreferred helicity; giving rise to a short chiral memory, in which the fast atropisomerization is enthalpy-driven due to the high mismatch penalty.     

Interaction between Peroxy Radicals and Acetaldehyde on Solid Surfaces and Its Role in the Oxidation of Aldehydes

Heterogeneous interaction between peroxy radicals and acetaldehyde in a capillary reactor treated with boric acid was studied. The possibility of a reaction occurring between adsorbed peroxy radicals and acetaldehyde was confirmed. Based on a comparison of these data and those obtained for other surfaces along with the ignition and slow oxidation of aldehydes in reactors with identical surfaces, it was concluded that the oxidation of aldehydes includes not only a homogeneous component but a heterogeneous component as well.     

Infrared spectra of homogeneous and heterogeneous proton-bound dimers in the gas phase

Infrared multiphoton dissociation spectra of three homogeneous and two heterogeneous proton-bound dimers were recorded in the gas phase. Comparison of the experimental infrared spectra recorded in the fingerprint region of the proton-bound dimers with spectra predicted by electronic structure calculations shows that all modes which are observed contain motion of the proton oscillating between the two monomers. The O-H-O asymmetric stretch for the homogeneous dimers is shown to occur at around 800 cm-1. As expected, the O-H-O asymmetric stretching modes for the heterogeneous proton-bound dimers are observed to shift to significantly higher energy with respect to those for the homogeneous proton-bound dimers due to the asymmetry of the O-H-O moeity. This shift is shown to be predictable from the difference in proton affinities between the two monomers. Density functional predictions of the infrared spectra based on the harmonic oscillator model are demonstrated to predict the observed spectra of the homogeneous proton-bound dimers with reasonable accuracy. Calculations of the structure and infrared spectrum of protonated diglyme at the B3LYP/6-31+G** level and basis also agree well with an infrared spectrum recorded previously. For both heterogeneous proton-bound dimers, however, the predicted spectra are blue-shifted with respect to experiment.     

Heterogeneous and homogeneous reduction of benzyl phenyl ether

By analyzing the kinetics of heterogeneous (electrode) and homogeneous reduction for benzyl phenyl ether it was found that toluene and phenol are formed via the transfer of two electrons and the breaking of the PhO-Bz bond. It was shown that electron transfer constitutes the slow stage in heterogeneous and homogeneous reduction. The homogeneous transfer coefficient was approximately 0.5, which represents a significant difference from the heterogeneous value.A. E. Arbuzov Institute of Organic and Physical Chemistry, Kazan's Scientific Center, Russian Academy of Sciences, 420083 Kazan'. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 8, pp. 1760–1765, August, 1992.     

Surfactant adsorption on solid surfaces: recognition between heterogeneous surfaces and adsorbed surfactant aggregates

We study the possibility of the recognition of surface heterogeneities with surfactant adsorption by performing Monte Carlo simulations. It is found that when each patch size of a heterogeneous surface is capable of being commensurate with the size of aggregates adsorbed on the constituent homogeneous surfaces, the adsorption isotherm of the system will display both adsorption characteristics for each homogeneous surface. Otherwise, one or more adsorption characteristics will be spoiled or destroyed. Therefore, the adsorption isotherm of surfactants on a heterogeneous surface provides a signal of recognition.     

Parallels between multiple population-period transient spectroscopy and multidimensional coherence spectroscopies

We have recently shown that homogeneous and heterogeneous kinetics can be distinguished by experiments that compare the evolution of the population of a state over two time intervals [E. van Veldhoven et al., ChemPhysChem 8, 1761 (2007)]. This paper elaborates on the analogy between these multiple population-period transient spectroscopy (MUPPETS) experiments and more familiar spectroscopies based on the evolution of coherences. Using a modified inverse-Laplace transform, a standard kinetics decay is re-expressed as a "rate spectrum." A nonexponential decay creates a linewidth in this spectrum. Mechanisms for line broadening in rate spectra are compared to those for line broadening in frequency-domain spectra. Homogeneous and heterogeneous kinetics are defined precisely and are shown to be the counterparts of homogeneous and inhomogeneous line broadenings in frequency-domain spectra. Homogeneous line broadening mechanisms are further divided into equilibrium and nonequilibrium mechanisms, with equilibrium mechanisms more prevalent in frequency spectra and nonequilibrium mechanisms more prevalent in rate spectra. Spectral representations of two-dimensional MUPPETS experiments are developed that are equivalent to two-dimensional coherence spectroscopies. In particular, spectra equivalent to hole-burning and to correlation spectra are defined. Frequency-domain spectra are often modeled as an inhomogeneous distribution of identical homogeneous line shapes. A parallel homogeneous-heterogeneous model for kinetics is defined. Within this model, MUPPETS has sufficient information to completely separate the homogeneous and heterogeneous contributions to a nonexponential decay, even when the homogeneous contribution is nonexponential.     

From hygrophilic to superhygrophobic: theoretical conditions for making high-contact-angle surfaces from low-contact-angle materials

The possibility of making high-contact-angle, rough surfaces from low-contact-angle materials has recently been suggested and demonstrated. A thermodynamic analysis of this possibility in terms of feasibility and stability is presented. It turns out that only roughness topographies that conform to a feasibility condition which is developed in the present paper can support this phenomenon. Even under conditions that support the phenomenon, the high-contact-angle state may not be stable, and transition from the heterogeneous (Cassie-Baxter) wetting regime to the homogeneous (Wenzel) regime with a lower contact angle may occur. In addition, it is suggested to use the general terms hygrophilic and hygrophobic (based on the Greek prefix hygro- that means liquid) to describe low- and high-contact-angle surfaces, respectively.     

Molecular dynamics investigation with the time resolved optical Kerr effect on the CS2-C6H6 mixtures

An investigation of the molecular dynamics in pure liquids and in mixtures through the technique of time resolved optical Kerr effect is performed. The samples studied were the mixtures of carbon disulfide (CS(2)) with benzene (C(6)H(6)). The molecular dynamics of the pure liquids is briefly discussed while the main results are obtained for the mixtures. A slow dynamics component is observed for the optical heterodyne detected optical Kerr effect transient decaying exponentially with time constants on picosecond time scale. The fast subpicosend time relaxations are analyzed in terms of the nondiffusive component of the spectral response that is associated with the molecular dynamics. The modifications of the spectrum are quantified, and the explanation of the observed changes is given in terms of the structural interaction configurations that produced changes in the intermolecular potential within which the molecules execute librational motions.     

Solvent dynamics effect in condensed-phase electron-transfer reactions

Channel-based reaction-diffusion equations are solved analytically for two electron transfer (ET) models, where the fast inner-sphere coordinate leads to an ET reaction treated by Fermi's golden rule, and the slow solvent coordinate moves via diffusion. The analytic solution has let us derive an ET rate constant that modifies the Marcus-Jortner formula by adding a constant alpha which we call a dynamic correction factor. The dynamic correction factor measures the effect of solvent friction. When the relaxation of solvent dynamics is fast, the dynamic correction can be neglected and the ET rate constant reduces to the traditional Marcus-Jortner formula. If the solvent dynamic relaxation is slow, the dynamic correction can be very large and the ET rate can be reduced by orders of magnitude. Using a generalized Zusman-Sumi-Marcus model as a starting point, we introduce two variants, GZSM-A and GZSM-B, where in model A, only one quantum mode is considered for inner-sphere motion and in model B, a classical mode for inner-sphere motion is added. By comparing the two models with experimental data, it is shown that model B is better than model A. For the solvents that have a relaxation time ranging between 0 and 5 ps, our result agrees fairly well with experimental data; for the solvents that have a relaxation time ranging between 5 and 40 ps, our result deviates from the experimental values. After introducing an adjustable scaling index in the effective time correlation function of the reaction coordinate, good agreement is achieved between the experiment and the theory for model B for all of the solvents studied in this paper.     

The structure of O/W microemulsions formulated with alkylglucosides

By following a method proposed by Kahlweit, an equilibrium diagram was determined in O/W quaternary microemulsions. These systems were formed by octanol (cosurfactant)/water/octane (oil)/alkylglucoside (surfactant). The experiment study was performed at two different temperatures (25°C and 50°C). The objective of this study work was to determine the structure of these lower microemulsions and to study the influence of the cosurfactant. Hence, different experimental techniques were employed: light scattering (static and dynamic), Kerr effect (static and dynamic), viscosity and refractometric measurements. It was concluded that the surfactant volume fraction in equilibrium with micelles is 0.044 and the micelle shapes are revolution ellipsoids.     

Surface Organometallic Chemistry for Single-site Catalysis and Single-atom Catalysis

Although driven by different research interests, single-site catalysts and single-atom catalysts are both believed to be model systems bridging homogeneous and heterogeneous catalysis. The two concepts are similar but different. In this review, we will first explain the difference between single-atom catalysis and single-site catalysis, in terms of their goals, synthetic methods and coordination structures of corresponding catalysts. Then, we will introduce the surface organometallic chemistry method, a method traditionally used for synthesizing single-site catalyst. We will explain why it might benefit the single-atom catalysis community. At last, the choice of support to accommodate the method for synthesizing single-atom catalysts will be discussed.     

Thermodynamic anomalies in a lattice model of water

We investigate a lattice-fluid model of water, defined on a three-dimensional body centered cubic lattice. Model molecules possess a tetrahedral symmetry, with four equivalent bonding arms, aiming to mimic the formation of hydrogen bonds. The model is similar to the one proposed by Roberts and Debenedetti [J. Chem. Phys. 105, 658 (1996)], simplified in that no distinction between bond "donors" and "acceptors" is imposed. Bond formation depends both on orientation and local density. In the ground state, we show that two different ordered (ice) phases are allowed. At finite temperature, we analyze homogeneous phases only, working out phase diagram, response functions, the temperature of maximum density locus, and the Kauzmann line. We make use of a generalized first-order approximation on a tetrahedral cluster. In the liquid phase, the model exhibits several anomalous properties observed in real water. In the low temperature region (supercooled liquid), there are evidences of a second critical point and, for some range of parameter values, this scenario is compatible with the existence of a reentrant spinodal.     

Various methods for enhancement in heterogeneous catalysed biodiesel production reaction rate

The biodiesel can be produced by transesterification and esterification reaction with edible and non-edible oil respectively. These reactions are catalysed by both homogeneous and heterogenous catalyst. The transesterification reactions for heterogeneous catalysts proceed at a relatively slow rate. The heterogeneous reaction mixture constitutes a three-phase system, oil/alcohol/catalyst therefore the mass transfer limitation controls the reaction rate. In the present study Tetra-hydrofuran, Hexane and Heptane as co-solvent have been tested for the transesterification and esterification reaction. Tetra-hydrofuran, assists in decreasing the mass transfer between the oil and methanol phases. Tetra-hydrofuran was found to be the best co-solvent. It also represents that the presence of Tetra-hydrofuran only enhance the solubility of phases not final equilibrium yield. Results are compared with homogeneous and heterogeneous catalysed reaction. Ultrasonic irradiation influenced the mixing of the reaction mixture and resulted in higher yields, for each co-solvent case.     

Heterogeneous and homogeneous nucleation compared: rapid nucleation on microscopic impurities

We use computer simulation to calculate the rates of both homogeneous nucleation and heterogeneous nucleation on microscopic impurities. We do so in perhaps the simplest model of fluids and magnets: the two-dimensional Ising model. We expect our results to be qualitatively applicable to many simple and complex fluids. We find that heterogeneous nucleation on an impurity that is not only microscopic but also as small as possible, that is, a single fixed spin, is more than four orders of magnitude faster than homogeneous nucleation. The rate of heterogeneous nucleation then increases by a factor of approximately five for each additional fixed spin in the impurity. These results suggest that impurities as small as single molecules can result in homogeneous nucleation being irrelevant due to heterogeneous nucleation on these microscopic impurities being much faster.     

Analysis of the approximate slow invariant manifold method for reactive flow equations

The Approximate Slow Invariant Manifold method of Singh, Powers and Paolucci is a useful method for addressing model reduction in systems of reactive flow equations. It exploits separations of time scales between slow and fast species, and it generalizes the Intrinsic Low-Dimensional Manifold method, which was developed for model reduction in the context of reaction kinetics, to systems with diffusive and active transport. In this article, we present a mathematical analysis of the Approximate Slow Invariant Manifold method in the context of systems of reaction–diffusion equations with slow and fast reaction kinetics. Beginning with systems of two species (one slow and one fast), and then treating general systems with multiple slow and fast species, we explicitly determine the accuracy of the Approximate Slow Invariant Manifold method. We find that it is correct up to and including the terms of first order in the small parameter that measures the separation of the kinetics time scales, and that it captures many of the terms at second order, as well. Our analysis includes precise statements of the errors at second order, and we find that these are proportional to the slow components of the reaction–diffusion equation, as well as to the curvature of the critical manifold. We illustrate the results analytically on two prototypical examples, the Michaelis–Menten–Henri model with diffusion of the slow species and the Davis–Skodje model in which both the slow and fast species diffuse.     

Numerical study of a fragile three-dimensional kinetically constrained model

We numerically study the three-dimensional generalization of the kinetically constrained east model, the north-or-east-or-front (NEF) model. We characterize the equilibrium behavior of the NEF model in detail, measuring the temperature dependence of several quantities: alpha-relaxation time, distributions of relaxation times, dynamic susceptibility, dynamic correlation length, and four-point susceptibility. We show that the NEF model describes quantitatively experimental observations over an exceptionally wide range of time scales. We illustrate this by fitting experimental data obtained both in the mildly supercooled regime by optical Kerr effect and close to the glass transition by dielectric spectroscopy.