Nonexponential Kinetics Research Articles

Non-exponential structural relaxation, anomalous light scattering and nanoscale inhomogeneities in glasses

Light scattering from glasses in the glass transition region exhibits an anomalous Rayleigh scattering. We observe a maximum in the scattering intensity vs. temperature during heating. It is shown that this behavior is consistent with the presence of nanometer scale inhomogeneities (density fluctuation) which relax at differing rates. Recent observations of anomalous light scattering were carried out on strong glass formers and fragile glass formers. In all cases a hysteresis effect is seen in the light scattering between heating and cooling each sample from room temperature through the glass transition region. From these measurements we suggest that this could be the source of non-exponential structural relaxation kinetics. A model based upon the modified Tool-Narayanaswamy model is found to be in agreement with the calculations based on the experimental results.

Non-exponentiality in electron transfer kinetics: Static versus dynamic disorder models

Non-exponential electron transfer kinetics in complex systems are often analyzed in terms of a quenched, static disorder model. In this work we present an alternative analysis in terms of a simple dynamic disorder model where the solvent is characterized by highly non-exponential dynamics. We consider both low and high barrier reactions. For the former, the main result is a simple analytical expression for the survival probability of the reactant. In this case, electron transfer, in the long time, is controlled by the solvent polarization relaxation—in agreement with the analyses of Rips and Jortner and of Nadler and Marcus. The short time dynamics is also non-exponential, but for different reasons. The high barrier reactions, on the other hand, show an interesting dynamic dependence on the electronic coupling element,V el.

Nonexponential relaxation in fully frustrated models

We study the dynamical properties of the fully frustrated Ising model. Due to the absence of disorder the model, contrary to spin glass, does not exhibit any Griffiths phase, which has been associated to non-exponential relaxation dynamics. Nevertheless we find numerically that the model exhibits a stretched exponential behavior below a temperature T_p corresponding to the percolation transition of the Kasteleyn-Fortuin clusters. We have also found that the critical behavior of this clusters for a fully frustrated q-state spin model at the percolation threshold is strongly affected by frustration. In fact while in absence of frustration the q=1 limit gives random percolation, in presence of frustration the critical behavior is in the same universality class of the ferromagnetic q=1/2-state Potts model.

Physical Aging in Supercooled Glycerol: Evidence for Heterogeneous Dynamics?

Several recent experiments on glycerol and other supercooled liquids have suggested that dynamically heterogeneous domains in the liquid are responsible for the nonexponential structural relaxation dynamics observed near the glass transition. In addition, it appears that the exchange of domain types may occur much more slowly than intradomain relaxation, at least in some cases. By examining a simple model of a dynamically heterogeneous liquid, we show that these ultraslow domain-exchange dynamics should be apparent at long times in nonequilibrium, physical aging experiments where the distribution of domains is perturbed. We recently observed such an ultraslow tail in the physical aging dynamics of the Brillouin shift for supercooled glycerol, following a rapid quench to a temperature below the glass transition (Miller, R. S.; MacPhail, R. A. J. Chem. Phys. 1997, 106, 3393); here we describe physical aging experiments carried out at two additional final temperatures. Unfortunately, the precision in the newer measurements at long times is not sufficient for us to resolve an ultraslow component. However, the broad distribution of relaxation times that characterizes the aging dynamics is consistent with the presence of such a tail and is much broader than the distribution for the equilibrium supercooled liquid. While our new experiments are ambiguous as to the nature of this broadening and the ultraslow tail, we believe the notion that the physical aging process can be sensitive to spatially heterogeneous dynamics is important, and we suggest further experiments designed to address this issue.

Combination of Pressure and Temperature Dependent Measurements: A Simple Access to Intrinsic Thermal Activation Energies

Intrinsic activation energies E0 # for different adiabatic photoreactions have been derived by combining pressure and temperature dependent time-resolved fluorescence data. This procedure allows the division of the observable activation energy Eobs # into a diffusive barrier Ed # induced by the solvent viscosity and an intrinsic part E0 , due to the intramolecular reaction coordinate, and furthermore, the procedure corrects for polarity effects on the rate constant. When applied to the kinetics of charge transfer state formation in DMABN (N,N-dimethylaminobenzonitrile), it establishes the barrierless nature of the excited state hypersurface in the investigated solute/solvent systems. This case of a negligible intrinsic activation energy is characterized by nonexponential kinetics whereas a comparable case with barrier, the excimer formation in DIPHANT, an intramolecular 9-phenylanthracene excimer molecule, shows exponential decays. For this system in polydimethylsiloxane (S1000), an intrinsic thermal barrier of 17 kJ/mol was determined.

A phenomenology of relaxor ferroelectrics

We propose a phenomenological theory for the dielectric properties of relaxor ferroelectrics based on the assumption that the polar clusters distributed in highly polarizable host lattice are responsible for the relaxor behavior. Two major differences between relaxors ferroelectrics and conventional orderdisorder ferroelectrics have been employed for the theory: i) the existence of the broad distribution of local fields experienced by each polar cluster; ii) the existence of the distribution of relaxation times giving rise to non-exponential non-critical kinetics which may compete with the critical slowing down near the ferroelectric phase transition. We illustrate numerically predictions of the theory for the dielectric response for relaxors with incipient ferroelectric order like PMN or K 1-x L ix T a O3 (x < 0.022), and for relaxors undergoing true first order ferroelectric phase transitions like PST or PLZT.

Application of diffuse reflectance laser-flash photolysis to the study of aromatic probes in β-cyclodextrin solid complexes

Time-resolved diffuse reflectance laser-flash photolysis techniques were employed to study the photochemistry of benzil, naphthalene, and pyrene within β-cyclodextrin solid complexes. The photochemistry of benzil and naphthalene is dominated by their triplet state. In the case of pyrene, the formation of radical cations and radical anions is observed, in addition to the signals due to the triplet state. In all three cases triplet excited states exhibit non-exponential (multi-component) kinetics. Analysis of triplet decays by means of lifetime distributions shows that quenching by oxygen is significantly restricted within β-cyclodextrin solid complexes. This result is attributed to the protection offered by the cyclodextrin cavity, which limits the space available for diffusion and contact of reactants.

Nonexponential kinetics of a single tRNAPhe molecule under physiological conditions.

The fluorescence decay functions of individual, specifically labeled tRNAPhe molecules exhibit nonexponential character as a result of conformational dynamics occurring during the measurement on a single molecule. tRNAPhe conformational states that interchange much more slowly are evidenced by the distribution of lifetimes observed for many individual molecules. A structural model for the nonexponential decay indicates that the tRNAPhe-probe adduct fluctuates between two states, one of which provides conditions that quench the probe fluorescence.

Communications between distant sites on supercoiled DNA from non-exponential kinetics for DNA synapsis by resolvase

To determine how distant sites on supercoiled DNA communicate with each other, the mechanism of site-specific recombination by resolvase was analysed by using a rapid-reaction quench-flow device to study the kinetics of individual steps in the reaction pathway. Three sets of measurements revealed the rates for: (1) the initial binding of the protein to its target sites on the DNA; (2) the synapsis of the two DNA-protein complexes; (3) the overall process of recombination. The binding of the protein to the DNA was complete within 50 milliseconds while recombination required 500 seconds. Surprisingly, synapsis spanned this entire time range: some DNA molecules gave synaptic complexes within ten milliseconds after the initial binding, while others took over 100 seconds. The departure from exponential behaviour may be due to each molecule of DNA having to undergo different conformational fluctuations in order to juxtapose the recombinational sites. From polymer physics theory, the rate of synapsis ought to vary with either the size of the DNA molecule or the length of DNA between the recombinational sites, depending on the nature of the fluctuations, but plasmids of different sizes and with different spacings between the sites all gave the same rates for synapsis. This observation cannot be reconciled with current models for encounters of distant sites on supercoiled DNA. However, the superhelical axis in the DNA molecules used here will be branched at one or more positions and the encounters may arise from the motion of a single branch relative to the remainder of the chain. Alternatively, the non-exponential kinetics for synapsis may be due to multiple re-arrangements of non-productive complexes following DNA juxtaposition.

Random walk models for DNA synapsis by resolvase

During site-specific recombination by resolvase, the protein binds to two sites on a supercoiled DNA molecule and the loaded sites then interact with each other to form a synaptic complex. The kinetics of synapsis show non-exponential behaviour extending over five log units of time and are independent of the length of the DNA molecule and the length of DNA between the sites. In this study, numerical models were developed in order to account for how fluctuations in the structure of supercoiled DNA might lead to the juxtaposition of distant sites in a manner consistent with the experimental data on synapsis by resolvase. Models where the juxtaposition arises from fluctuations around branch points in the superhelix failed to match the data: they yielded non-exponential kinetics but only over two log units of time and they predicted longer synapsis times for both larger DNA molecules and larger inter-site spacings. In another model, one fraction of the juxtaposition events gives rise directly to the productive complex while the remaining fraction initially yields a non-productive complex: the latter molecules undergo no further fluctuations until the abortive synapse dissociates at the end of a delay period. This model again failed to match the experimental data. However, the inclusion of three sorts of non-productive complexes, each with a different delay constant, led to progress curves that concurred with the data. Schemes were also developed to account for the juxtaposition of three sites at a branch point in supercoiled DNA.

Critical Dynamics and Cluster Dynamics of the 3D ±JIsing Spin-Glass Model in Its `Griffiths Phase'

Non-exponential slow dynamics in the `Griffiths phase' of the three-dimensional (3D) ± J Ising spin-glass model is studied by means of Monte Carlo simulation. The distribution of relaxation times averaged over samples, \bar P ( x ) with x = lnτ, is calculated from spin auto-correlation functions simulated. It is found that \bar P ( x ) consists of two branches. The cross-over value between the branches, x c , diverges as T → T c , T c being the spin-glass transition temperature. Therefore τ c (= e x c ) is regarded as the critical relaxation time associated with the onset of the spin-glass order at T c , and the branch of \bar P ( x ) at x x c causes the unusual slow dynamics peculiar to spin glasses. Various aspects of \bar P ( x ) of this branch examined are consistent with the following picture; compact regions with less frustrations than the system as a whole are thermally fluctuating ...

On the Origin of Heme Absorption Band Shifts and Associated Protein Structural Relaxation in Myoglobin following Flash Photolysis

The role of the protein structural change monitored by absorption band shifts following flash photolysis of CO from myoglobin is discussed in terms of structure-function relationships. Evidence is presented that the Soret band shift does not depend primarily on the covalent linkage of the heme iron to the protein by using the mutation H93G(L) in which the proximal histidine 93 is replaced by glycine and an exogenous ligand L, which coordinates the heme iron but is not covalently bound to the globin. While CO rebinding kinetics depend strongly on the nature of the exogenous ligand L in H93G(L), the magnitude and time evolution of the Soret band shift in a viscous buffer on the nanosecond time scale are hardly perturbed in all cases studied. Comparison of the Soret band and charge transfer Band III shifts demonstrates that both have a similar time dependence on the nanosecond to microsecond time scale following flash photolysis in viscous solvents. We conclude that the nonexponential kinetics of protein relaxation probed by transient absorption band position shifts involves primarily distal coordinates prior to ligand escape. This result agrees with earlier measurements of Soret band shifts in distal pocket mutants of myoglobin (1). We suggest that the band shifts are primarily a response to changes in the electrostatic field around the heme (a transient Stark shift) associated with changes in protein structure that occur following ligand photodissociation.

Radical pair kinetics in a magnetic field

Exact analytical expressions for the evolution of a non-diffusing spin-correlated radical pair in a strong magnetic field are presented. The recombination of singlet and triplet pairs at different rates, and the coherent evolution caused by magnetic interactions, lead to radical pair concentrations which are the sum of four time-dependent terms : two decaying exponentials and two exponentially damped oscillations. The predicted time dependence is used to illuminate the recombination dynamics of the primary radical pair in photosynthetic bacterial reaction centres. Although mono-exponential decay is expected ˜ 20 ns after the formation of each individual radical pair, the inhomogeneous distribution of Larmor frequencies of the two electron spins leads to non-exponential kinetics and different time constants for the disappearance of singlet and triplet pairs, and the formation of singlet and triplet recombination products.

Radical pair kinetics in a magnetic field

Exact analytical expressions for the evolution of a non-diffusing spin-correlated radical pair in a strong magnetic field are presented. The recombination of singlet and triplet pairs at different rates, and the coherent evolution caused by magnetic interactions, lead to radical pair concentrations which are the sum of four time-dependent terms : two decaying exponentials and two exponentially damped oscillations. The predicted time dependence is used to illuminate the recombination dynamics of the primary radical pair in photosynthetic bacterial reaction centres. Although mono-exponential decay is expected ˜ 20 ns after the formation of each individual radical pair, the inhomogeneous distribution of Larmor frequencies of the two electron spins leads to non-exponential kinetics and different time constants for the disappearance of singlet and triplet pairs, and the formation of singlet and triplet recombination products.

Scaling law for the non-exponential ligand rebinding of CO in myoglobin

The non-exponential kinetics of the rebinding in myoglobin is simulated by universal functions such as a Havriliak-Negami function, a rational approximation or a modified stretched exponential all of which depend on time via a scaling variable (t/τ 1 2 (T)) β(T). For the scaling parameters, the half-decay time τ 1 2 and the exponent β the temperature dependence including tunneling effects are analyzed. It is shown that the scaling properties imply temperature-dependent distributions of activation energies and the existence of a critical temperature T ∗ ∼ 170–190 K above which no positive static distribution exists.

Photoluminescence in pyridine-based polymers: Role of aggregates

We present a study of the morphology dependence of the photoluminescence (PL) properties of the pyridine-based polymers poly(p-pyridyl vinylene), poly(p-pyridine), and poly(p-pyridyl vinylene p-phenylene vinylene) (PPyVPV). The photoluminescence of solution samples is characterized by high quantum efficiency (g70% in PPyVPV), weak coupling to vibrational modes (Huang-Rhys parameter \ensuremath{\sim}0.5) and a single-exponential decay (radiative lifetime \ensuremath{\sim}1 ns). On the other hand, film samples display strongly redshifted, featureless emission with low quantum yield (20%) and highly nonexponential decay dynamics. Through consideration of absorption and excitation spectra, the ``site-selectivity'' of the PL, and the concentration dependence of the PL spectrum, we demonstrate that the redshifted film spectra are a result of the formation of low-energy aggregate sites due to strong interchain interactions. Time-resolved measurements suggest a longer radiative lifetime for the aggregate vs solution, leading to the lower efficiency. Aggregate formation is found to be morphology dependent, and is minimal in ``powder'' samples which are precipitated after polymerization. \textcopyright{} 1996 The American Physical Society.

Excited state dynamics of bacteriorhodopsin revealed by transient stimulated emission spectra

The femtosecond photoisomerization of bacteriorhodopsin (bR), pumped at either 550 nm or 405 nm, was probed between 640 nm and 950 nm. The 550 nm pump spectra exhibit net gain signals peaking at > 950 nm. A transient absorption is proposed to partially cancel the emission. The 405 nm pump transients exhibit nonexponential kinetics and display this new absorption, due to the presence of hot molecules. The absence of time dependence of the shape of the stimulated emission spectra is inconsistent with conventional models invoking low-frequency motion out of the Franck-Condon region following excitation. The time independence is reminiscent of the photoisomerization of cis-stilbene.

Erratum: Non-Poisson statistics of reactive events and nonexponential kinetics

Erratum: Non-Poisson statistics of reactive events and nonexponential kinetics

Nonexponential ligand rebinding of CO and O 2 in myoglobin controlled by fluctuations of the protein

The kinetics of first-order processes which depend on a fluctuating coordinate are studied analytically. The fluctuations are described as uncorrelated jumps with an arbitrary time distribution between jumps. As an example, the nonexponential ligand rebinding kinetics in proteins is analyzed in the adiabatic limit where the reaction is controlled by the motion along the reaction coordinate. A new powertime law is deduced for the rebinding at low temperatures.

‘‘False tunneling’’ and multirelaxation time nonexponential kinetics of electron transfer in polar glasses

Classical electron transfer in polar glasses is described by a theory based on a model microscopic Hamiltonian which includes the discreteness and randomness of the glassy polar modes with distinct orientation. When configurational dynamics is fast, the reaction is described by exponential kinetics with a rate constant of non-Arrhenius type. The temperature dependent rate constant resembles the tunneling rate, despite the classical transfer of the electron. This effect is called ‘‘false tunneling.’’ In this limit the possibility of a self-acceleration of the reaction is pointed out. When configurational dynamics is very slow the reaction kinetics are nonexponential with multirelaxation time behavior. The reaction is shown to be almost insensitive to temperature change pointing out on a possible explanation of a broad temperature-independent range in the ‘‘rate constant’’ in an electron transfer in cytochrome c oxidation in chromatium. At short times, the reaction accelerates compared to the exponential behavior, while at long times it becomes slower. For strongly exothermic reactions the kinetics are always slower than an exponential decay.