The generalized transition state method

Current theories of unimolecular reaction rates are based on the transition state method which replaces internal reactant dynamics by an assumption of internal equilibrium. The present work is devoted to the development of generalized transition state method which allows effects such as nonergodicity and non-exponential decay to be accounted for within a simple theoretical framework. The derivation is quantum mechanical and not limited by any weak perturbation assumption. An effective hamiltonian is constructed for the reactant dynamics. The loss of amplitude due to reaction is accounted for by a dissipative term in the hamiltonian which is obtained on a phenomenological basis. The diagonalization of the hamiltonian allows the decay of reactant state to be predicted. The decay information is then used to set up a non-markovian master equation which in turn yields the rate coefficient for the reaction. The accuracy of the method is tested in one-dimensional model calculations in which particular attention is paid to decay by quantum mechanical tunneling through a potential barrier.     

Complex Franck—Condon overlap integral in nonradiative decays

Considering the nuclear coordinate (Q) dependence of the electronic energy denominator appearing in the virbonic coupling matrix element, a complex Franck—Condon overlap integral which is needed in order to evaluate the nonradiative decay rate constant not only in the weak coupling but also in the strong coupling case is derived. The real part of the overlap integral plays an important role in the weak coupling case. The imaginary part is originated from the potential energy surface crossing regions and, consequently, contributes to the nonradiative decay rate constant in the strong coupling case. When the Q-dependence of the electronic energy denominator is neglected, the complex overlap integral leads to the results ontained by using the usual Herzberg—Teller expansion method. It is shown that the complex integral is expressed by the optical Franck—Condon overlap integral multiplied by a correction factor when the nonradiative decay from the vibrationless state is considered.     

Factors affecting the stability of foamed concentrated emulsions

This paper attempts to quantify the stability of three-phase systems generated by aerating concentrated water-in-oil emulsions. In such materials, which we call foamed emulsions, the continuous phase is itself a two-phase system. In this work, we modify and extend the method originally proposed by Iglesias et al. (Colloids and Surfaces A, 98 (1995) 167–174) to viscous three-phase foams. The modified method involves imparting a destabilising force to the sample to make the foam short-lived and measuring the change in height as a function of decay time. The change of height during decay represents the rate at which gas is evolved from the foamed emulsion and is logarithmic with time. The data treatment yields two values, the decay constant and half-life, which are used as a means of measuring and comparing stability. Two distinct decay mechanisms (smooth decay and catastrophic collapse) operate in foamed emulsions that are subjected to oscillations. For a given decay mechanism, the decay constant is an intrinsic property of the foamed emulsion and is independent of the imposed oscillations. Experimental results indicate that different bubble stabilising surfactants and emulsion morphology significantly affect the foam stability, and that the stability is inversely related to the initial expansion. Examination of the gas–emulsion interface shows a segregation of droplets, with smaller droplets found preferentially at the gas–emulsion interface.     

Excitation-emission-lifetime analysis of multicomponent systems—II. Synthetic model data

To determine the efficacy of three-dimensional principal component factor analysis (PCFA) for extracting non-exponential decay parameters from multicomponent data, we have constructed synthetic data matrices which mimic the possible outcomes of experiments in the nanosecond time domain with copper porphyrins. Our results demonstrate that PCFA is capable of determining non-exponential time decay in systems with two and three emitting species. The accuracy of the rate constants determined by this method is limited by the accuracy of the non-linear Marquardt algorithm that we have used for the final fits. Although extremely overlapped components have been resolved using this method, degeneracy in one of the dimensions is problematic.     

Foam production--ratio between foaminess and rate of foam decay

Foams are usually characterized by the foaminess of their surfactant solutions and the rate of foam decay. These two properties have been described many times separately in the literature. There is a certain correlation between them, which can vary depending on the type and the concentration of the surfactants, the method of foam generation, etc. We suggest with this work a new parameter unifying foaminess and rate of foam decay. The foam production is a parameter, which is a ratio between foaminess and rate of foam decay. It was shown an example how foaminess, rate of foam decay and foam production depends on C/CMC (C - surfactant concentration, CMC - critical micelle concentration) of aqueous solutions of sodium octylsulfate (SOS). In addition, it has been stressed that a number of scientific problems on transient foams can be solved by means of the approach pointed out by this study. An example, for which the foam production depends on the way of foam generation, is given. A new criterion for assessing the ability of the surfactants to stabilize foams has been suggested. Thus, the stronger surfactants do not always produce more stable transient foams than the weaker ones, as usually is assumed.     

Kinetic stability of complex molecular clusters

This investigation is concerned with modeling the evaporation, or decay, of n-nonane molecular clusters. We use a unique cluster decay model that was first developed to estimate the decay time scale of argon clusters using molecular-dynamics simulations. In this study we seek to enhance the model so that it represents a more complex cluster decay dynamic, suitable for n-nonane clusters. Experimental measurements of nucleation rates of n-nonane droplets have been used to deduce the rate at which a molecule escapes from the cluster. Typically for an n-nonane cluster containing 40 molecules, at an experimental temperature of 225 K, the empirical decay time, which is the inverse of the decay rate, is estimated to be 50 ns. For this time scale, the direct observation of n-nonane cluster decay from a molecular-dynamics trajectory is not feasible, since decay events are so rare. However, the cluster decay model uses a combination of molecular dynamics and stochastic dynamics in order to resolve the problem associated with long decay time scales. The model is based on a Langevin treatment that views cluster decay as single-particle escape from a confining potential of mean force. It is used to predict kinetic decay times of n-nonane clusters. We discover this result differs significantly from a classically derived decay time scale determined from a continuum thermodynamic treatment of the population balance equations of clusters. However, the dynamically generated results obtained from the kinetic decay model compare more favorably than the classical results with the empirical decay times that are deduced from experimental measurements of n-nonane clusters.     

准弹性光散射研究苯乙烯-二乙烯基苯共聚超微粒的溶液性质

本文用光子相关光谱技术研究了聚苯乙烯-二乙烯基苯(PSt-DVB)共聚超微粒的溶液性质.该微粒的浓度涨落时间相关函数在波矢为q时,有指数衰减形式,其衰减速率г=q~2D_t.在精确的实验误差范围内,衰减速率的变化率为零。用累积量方法解析散射场的一阶时间相关方程,得到了作为浓度和温度函数的微粒扩散常数.与流体办学方程结合,计算出了微粒的流体力学尺寸.通过实验也确定了微粒在良溶剂中的分子形态.     

Cooperative motion in amorphous polymers; application to the study of free-radical migration in solids

A Monte Carlo method has been used for studying the effect of the motion of some submolecular structures on the migration of radical centres and on the free-radical decay and its dependence on density. Motions of crank, crankshaft, kink, and double kink type are considered. A cooperative type of motions is also taken into account. The results show that cooperative motions support diffusion of radical centres and thus also the free-radical decay but, at higher densities, the cooperation of motions is restricted. The density of the system, where the decay of radicals is followed, affects the rate of the decay, its increase causes radical decay retardation. This is in line with the high pressure effect, which also retards the radical decay rate.     

Rotational dynamics of solvated carbon dioxide studied by infrared, Raman, and time-resolved infrared spectroscopies and a molecular dynamics simulation

Rotational dynamics of solvated carbon dioxide (CO(2)) has been studied. The infrared absorption band of the antisymmetric stretch mode in acetonitrile is found to show a non-Lorentzian band shape, suggesting a non-exponential decay of the vibrational and/or rotational correlation functions. A combined method of a molecular dynamics (MD) simulation and a quantum chemical calculation well reproduces the observed band shape. The analysis suggests that the band broadening is almost purely rotational, while the contribution from the vibrational dephasing is negligibly small. The non-exponential rotational correlation decay can be explained by a simple rotor model simulation, which can treat large angle rotations of a relatively small molecule. A polarized Raman study of the symmetric stretch mode in acetonitrile gives a rotational bandwidth consistent with that obtained from the infrared analysis. A sub-picosecond time-resolved infrared absorption anisotropy measurement of the antisymmetric stretch mode in ethanol also gives a decay rate that is consistent with the observed rotational bandwidths.     

Energy dependent decay rates of Lennard-Jones clusters for use in nucleation theory

Decay rates of small clusters (containing between 10 and 40 Lennard-Jones atoms) are determined by molecular dynamics simulations. The cluster is defined by the condition that the atoms must lie within a specified distance of their center of mass, and initial isothermal states are generated using a Metropolis Monte Carlo method. Plots of the logarithm of the survival fraction against time are found to be nonlinear, indicating that the decay of constant temperature clusters is non-Markovian and depends on the collision rate with a thermalizing gas. However, when the clusters are banded according to their energies, exponential decay is seen. The energy dependent decay rates from simulations agree to within a factor of 2 with those estimated from equilibrium considerations (using free energies from thermodynamic integration and assuming a Gaussian energy distribution), indicating that clusters defined in this way can be used in Markovian rate equations. During nucleation, the cluster energy distribution is shifted from its equilibrium value, leading to a reduction in the nucleation rate by a temperature dependent factor of 100 or more, in the absence of a thermalizing carrier gas.     

Rotational diffusion of colloidal particles near confining walls

We study the rotational diffusion of a spherical colloid confined in a narrow channel between parallel plane hard walls. The walls damp translational diffusion much more than rotational diffusion so that there is expected to be little translation-rotation coupling. Using a recent calculation of the nonisotropic rotational mobilities arising from the hydrodynamic interactions with the walls, we set up the rotational Smoluchowski equation for either a particle with a permanent dipole moment or a polarizable particle with axisymmetric polarizabilities subject to an external electric field. Using the Smoluchowski equation dynamics we calculate the time-correlation functions of orientation that are measured in depolarized light scattering for the cases of no external field, external field normal to the walls, and external field parallel to the walls. The decay of correlations is shown to be given by a weighted sum of decaying exponentials and can be characterized by an initial and a mean characteristic decay time. The weights and decay rates of each component and the characteristic decay times are studied numerically for a range of field strengths. The nonisotropic rotational mobilities make these decay times highly sensitive to the distance of the particle from the confining walls. This position dependence can be used as a method of measuring the rotational mobilities or, conversely, the rate of decay of correlations can be used as a probe of particle position between the confining walls.     

A study of surface dynamics of polymers. III. Surface dynamic stabilization by plasma polymerization

As demonstrated in Part II of this series of studies, the hydrophobic character of CF₄ plasma-treated Nylon 6 and poly(ethylene terephthalate) (PET) decay with time of water immersion, and the rate of decay can be used as a measure for the surface mobility of (substrate) polymers. The same method of using fluorine-containing moieties introduced by CF₄ plasma treatment as surface labeling is applied to investigate the influence of a thin layer of plasma polymer of methane applied onto the surface of those polymers. An ultrathin layer of plasma polymer provides a barrier to the rotational and diffusional migration of the introduced chemical moieties from the surface into the bulk of the film. The influence of operational parameters of plasma polymerization on the surface dynamic stability are examined by measuring the decay rate constants for (subsequently) CF₄ plasma-treated samples. The rate constant was found to decrease sharply with increasing value of plasma energy input manifested by J/kg monomer, and no decay was observed as the energy input reached a threshold value (about 6.5 GJ/kg for PET, about 7.0 GJ/kg for Nylon 6), indicating that unperturbable surfaces can be created by means of plasma polymerization.     

Diffusion and trapping in a suspension of spheres with simultaneous reaction in the continuous phase

Much progress has been made in modeling the reaction of Brownian particles with spherical traps. Previously, work has focused on the effective reaction rate of systems of particles that diffuse freely until they are trapped by spheres in the dispersion. A particularly effective and efficient method to describe the reacting system is based on first-passage time distributions, from which an effective reaction rate coefficient of the suspension can be determined. The analysis presented here addresses reaction and diffusion in systems in which particles can undergo reaction in the continuous phase as well as reaction at the sphere surface. The first-passage method is extended to allow reaction or decay of the diffusing species in the continuous phase. The diffusion path is divided into a series of first-passage regions and is considered the probability of the particle being consumed in each of these regions. This allows the determination of the total reaction rate of the suspension (continuous phase reaction plus trapping) and the relative consumption rate in each phase. The extended method is applied to a model system of concentric spheres with a known continuum solution. It is shown to be accurate for consumption of reactant in the continuous phase from approximately 0 to approximately 100%. The method then is applied to a suspension of spheres.     

Monte Carlo approach to the decay rate of a metastable system with an arbitrarily shaped barrier

A path integral Monte Carlo method based on the fast-Fourier transform technique combined with the important sampling method is proposed to calculate the decay rate of a metastable quantum system with an arbitrary shape of a potential barrier. The contribution of all fluctuation actions is included which can be used to check the accuracy of the usual steepest-descent approximation, namely, the perturbation expansion of potential. The analytical approximation is found to produce the decay rate of a particle in a cubic potential being about 20% larger than the Monte Carlo data at the crossover temperature. This disagreement increases with increasing complexity of the potential shape. We also demonstrate via Langevin simulation that the postsaddle potential influences strongly upon the classical escape rate.     

Pressure dependence of free radical decay in irradiated isotactic polypropylene

Free radicals were generated in isotactic polypropylene by gamma-irradiation. The samples were annealed at pressures between 1 and 8000 atm and temperatures between 60 and 110°. The concentration of free radicals was estimated by the ESR method. The rate constants of free radical decay were determined for various pressures and temperatures. The rate constant of free radical decay decreases with increasing pressure while the activation energy increases. The relationship between the kinetics of molecular motion and the kinetics of free radical decay is discussed.     

Chlorine‐Enhanced Surface Mobility of Au(100)

Motivated by experimental studies of two‐dimensional Ostwald ripening on Au(100) electrodes in chlorine‐containing electrolytes, we have studied diffusion processes using density functional theory. We find that chlorine has a propensity to temporary form AuCl complexes, which diffuse significantly faster than gold adatoms. With and without chlorine, the lowest activation energy is found for the exchange mechanism. Chlorine furthermore reduces the activation energy for the detachment from kink sites. Kinetic Monte Carlo simulations were performed on the basis of extensive density functional theory calculations. The island‐decay rate obtained from these Monte Carlo simulations, as well as the decay rate obtained from the theoretical activation energies and frequency factors when inserted into analytical solutions for Ostwald ripening, are in agreement with experimental island‐decay rates in chlorine‐containing electrolytes.     

Photon emission from a driven single-molecule source: a renormalization group approach

The photon emission from a single molecule driven simultaneously by a laser and a slow electric radio frequency (rf) field is studied. We use a non-Hermitian Hamiltonian approach which accounts for the radiative decay of a two-level system modeling the single-molecule source. We apply the renormalization group method for differential equations to obtain long time solution of the corresponding Schrodinger equation, which allows us to calculate the average waiting time for the first photon emission. Then, we analyze the conditions for suppression and enhancement of photon emission in this dissipative two-level system. In particular we derive a transcendental equation, which yields the nontrivial rf field control parameters, for which enhancement and suppression of photon emission occurs. For finite values of radiative decay rate an abrupt transition to the state when both situations are indistinguishable is found for certain values of the rf field parameters. Our results are shown to be in agreement with the available experiments [Ch. Brunel et al., Phys. Rev. Lett. 81, 2679 (1998)].     

Radiation chemistry of polyethylene. XIV. Allyl radical decay kinetics in different types of polyethylene

The decay kinetics of the chain allyl free radical has been studied in the following morphological forms of polyethylene (PE): Marlex bulk film, hydrogenated PE, and extended-chain PE. Coupled with previous work on single-crystalline PE it can be seen that the decay rate is greater the more amorphous the sample. In the Marlex bulk film and hydrogenated PE the decay can be interpreted in terms of a simultaneous fast and slow decay process by means of our Q-function equation, but with rising temperature the decay approximates a single rate process. With extended-chain PE the allyl decay rate does not become appreciable until the melting range is approached. The fraction of allyl radicals decaying by the slow process is 2 to 10 times greater than the fraction of fast decaying radicals. The ratio of the fast decay rate constant to that of the slow rate constant is greater for the bulk Marlex film than for the hydrogenated PE. All ratios decrease with rising temperature. For times up to about 150 min the allyl decay in the extended-chain PE accurately follows a single second-order decay law with a time-independent diffusion controlled reaction rate constant.     

Radiolytic unsaturation decay in polyethylene. Part II—the effect of irradiation temperature, thermal history and orientation

The decay rate of vinyl unsaturation in high-density polyethylenes irradiated at temperatures from about 310 to 450 K, changes significantly in the melting range up to the crystalline melting point as does free radical mobility and the polymer crystallinity. However, orienting the polymer, or slow cooling or quenching from the melt, prior to irradiation, do not alter the decay process or its rate, although they do alter the rate of increase of insoluble gel and of elastic modulus in the molten state. It is suggested that, below 340 K, the marked deviations from a first-order decay result from the limited mobility of polymeric free radicals in the crystalline phase and from scavenging, by vinyl groups, segregated into the amorphous phase, of radiolytic hydrogen atoms (H). In the melting range, the mobility of polymeric free radicals increases as the crystallinity decreases, reducing the importance of scavenging, so vinyl decay approximates more closely to a first-order relation. In the melt, the vinyl decay relation is not changed qualitatively by H atom scavenging, but the effective vinyl concentration is lower, so the decay rate drops sharply.     

Cocrystallization Tailoring Multiple Radiative Decay Pathways for Amplified Spontaneous Emission

Amplified spontaneous emission (ASE) is intrinsically associated with lasing applications. Inefficient photon energy transfer to ASE is a long‐standing issue for organic semiconductors that consist of multiple competing radiative decay pathways, far from being rationally regulated from the perspective of molecular arrangements. Herein, we achieve controllable molecular packing motifs by halogen‐bonded cocrystallization, leading to ten times increased radiative decay rate, four times larger ASE radiative decay selectivity and thus remarkable ASE threshold decrease from 223 to 22 μJ cm^?2, albeit with a low photoluminescence quantum yield. We have made an in‐depth investigation on the relationship among molecular arrangements, vibration modes, radiative decay profiles and ASE properties. The results suggest that cocrystallization presents a powerful approach to tailor the radiative decay pathways, which is fundamentally important to the development of organic ASE and lasing materials.