Finite Energy Barrier Research Articles

The emergence of cooperative dynamics in polymers as an effect of conformational restrictions: The case of crystallization and an example on heterogeneous confinement

Cooperativity in the segmental dynamics of polymers, as enhanced by crystal confinement, shows up even above the dynamic glass transition. Some related physical aspects are outlined and, on the basis of a statistical mechanical model, these effects are quantitatively analysed. In this model, which extends aspects of the Adam–Gibbs theory for glass formers, the frequency width of the conformational relaxation is intrinsically connected to a finite free energy barrier hindering readjustment. A possible thermodynamic criterion for crystallization arrest then follows from the analysis of dielectric relaxation data available in the literature. Low-temperature cold-crystallized poly(ethylene terephthalate) is then considered in particular; it is found from mechanical and dielectric relaxation analyses that a cooperativity increase accompanies both recrystallization and cooling towards the glass transition temperature. The application of the model to the case of poly(dimethyl siloxane) confined in nanoporous glasses is also illustrated as an example.

Molecular dynamics simulation study of self-diffusion for penetrable-sphere model fluids

Molecular dynamics simulations are carried out to investigate the diffusion behavior of penetrable-sphere model fluids characterized by a finite energy barrier ϵ. The self-diffusion coefficient is evaluated from the time-dependent velocity autocorrelation function and mean-square displacement. Detailed insights into the cluster formation for penetrable spheres are gained from the Enskog factor, the effective particle volume fraction, the mean free path, and the collision frequency for both the soft-type penetrable and the hard-type reflective collisions. The simulation data are compared to theoretical predictions from the Boltzmann kinetic equation and from a simple extension to finite ϵ of the Enskog prediction for impenetrable hard spheres (ϵ→∞). A reasonable agreement between theoretical and simulation results is found in the cases of ϵ∗ ≡ ϵ/k(B)T=0.2, 0.5, and 1.0. However, for dense systems (packing fraction ϕ>0.6) with a highly repulsive energy barrier (ϵ∗ = 3.0), a poorer agreement was observed due to metastable static effects of clustering formation and dynamic effects of correlated collision processes among these cluster-forming particles.

Surface-induced morphology and free-energy pathways in breakup of a nematic liquid crystalline cylinder

We compute the surface-induced morphology and the free-energy pathways as a cylindrical liquid crystalline filament with preferred homeotropic (orthogonal) interface orientation passes through a sequence of growing sinusoidal perturbations and breaks up into droplets. Liquid crystalline morphology is determined using a simulated annealing algorithm [R. K. Goyal and M. M. Denn, Phys. Rev. E, 75, 021704 (2007)] to minimize the Oseen-Frank free energy. A first-order morphological transition with a finite energy barrier is required when the perturbation amplitude exceeds a critical value, and it is possible that progress towards breakup will be kinetically trapped in a varicose cylindrical shape. This result may be related to the apparent kinetic trapping of dispersed nematic 4'-octyl-4-biphenylcarbonitrile in a gel state reported by Inn and Denn [J. Rheol., 49, 887 (2005)].

Orientational multiplicity and transitions in liquid crystalline droplets

Orientation distributions in droplets of liquid crystals with homeotropic anchoring are computed with a simulated annealing algorithm that minimizes the free energy of the Oseen-Frank continuum theory. The droplets exhibit multiple orientational steady states that are separated by finite energy barriers over the entire range of the dimensionless ratio of surface to elastic forces, with maximum transition energy densities of the order of 2000 J/m3 (Pa) for a typical liquid crystalline droplet with a spherical radius of 1 microm. The transition energy densities decrease with elongation to spheroidal droplets with aspect ratios of four or more, indicating that droplet elongation is favored to drive surface-induced transitions.

Confined electrons and holes in Si nanocrystals: Theoretical modeling of the energy spectrum and radiative transitions

We construct the theory of carriers confined in spherical Si quantum dots with finite energy barriers for electrons and holes in the framework of Luttinger Hamiltonian for holes and taking into account the strong anisotropy of the conduction electron effective mass in Si. As a boundary condition for the electron and hole wave functions we use continuity of the wave functions and the current at the boundary of the nanocrystals. We apply this theory for the case of the SiO2 matrix surrounding Si quantum dots. We show that for experimentally relevant quantum dots energy spacings between neighbouring electron and hole levels are of the order of hundreds of meV. Therefore the relaxation of excited electrons and holes is damped.Theoretical calculations of probabilities of various radiative transitions are presented.

Theoretical modeling of excitation and de-excitation processes of Er in SiO 2 with Si nanocrystals

We construct the theory of carriers confined in Si quantum dots with finite energy barriers for electrons and holes in the framework of the multiband effective mass theory. We apply this theory for theoretical modeling of the excitation of erbium inside and outside of Si nanocrystals in SiO 2 matrix due to the Auger process induced by the recombination of a confined electron–hole pair as well as the intraband transitions of “hot” confined carriers. Auger de-excitation processes of the Er 3+ ion leading to the quenching of erbium luminescence are discussed as well.

Modelling sequential protein folding under kinetic control

This study presents a novel investigation of the effect of kinetic control on cotranslational protein folding. We demonstrate the effect using simple HP lattice models and show that the cotranslational folding of proteins under kinetic control has a significant impact on the final conformation. Differences arise if nature is not capable of pushing a partially folded protein back over a large energy barrier. For this reason we argue that such constraints should be incorporated into structure prediction techniques. We introduce a finite surmountable energy barrier which allows partially formed chains to partly unfold, and permits us to enumerate exhaustively all energy pathways. We compare the ground states obtained sequentially with the global ground states of designing sequences (those with a unique global ground state). We find that the sequential ground states become less numerous and more compact as the surmountable energy barrier increases. We also introduce a probabilistic model to describe the distribution of final folds and allow partial settling to the Boltzmann distribution of states at each stage. As a result, conformations with the highest probability of final occurrence are not necessarily the ones of lowest energy. Software available on request.

Dislocation mobility in two-dimensional Lennard–Jones material

In seeking to understand at a microscopic level the response of dislocations to stress, we have undertaken to study as completely as possible the simplest case: a single dislocation in a two-dimensional crystal. The intention is that results from this study will be used as input parameters in larger length scale simulations involving many defects. We present atomistic simulations of defect motion in a two-dimensional material consisting of atoms interacting through a modified Lennard–Jones potential. We focus on the regime where the shear stress is smaller than its critical value, where there is a finite energy barrier for the dislocation to hop one lattice spacing. In this regime motion of the dislocation will occur as single hops through thermal activation over the barrier. Accurate knowledge of the barrier height is crucial for obtaining rates of such processes. We have calculated the energy barrier as a function of two components of the stress tensor in a small system, and have obtained good fits to a functional form with only a few adjustable parameters. We examine prefactors, finite temperature and dynamics.

Fine structure of the exciton groundstate in self-assembled CdSe quantum dots

The fine structure of the heavy-hole exciton in CdSe quantum dots grown on ZnSe by molecular beam epitaxy is studied. The application of a tilted magnetic field allows us to observe all four levels of the ground state simultaneously. The zero-field separation between the optically forbidden and allowed doublets ranges between 1.7 and 1.9 meV and is markedly reduced due to the existence of a wetting layer and the finite energy barrier at the hetero-interface. The energy splitting within the allowed doublet (200 μeV) is substantially larger than for the forbidden states (⩽20 μeV), proving that a dominant contribution arises from the long-ranged part of the electron–hole exchange interaction. The total set of g-factors is derived. A huge anisotropy for the electron is found.

Frozen structural disorder in a pseudospin model with barriers

A pseudospin model for describing structurally disordered crystals is justified and developed. It includes the finite energy barrier between states at the site. A metastable glass state in the model is investigated by the Monte Carlo method. The temperature dependences of the average energy, order parameter, Edwards–Anderson parameter, and autocorrelation function are determined. It is shown that the glass state is maintained to a certain temperature, after which a devitrification occurs. Features are observed in the behavior of the specific heat and susceptibility, and an anomalous slowing of the relaxation in the devitrification region is seen. The role of the energy barrier in the formation of the glassy state is discussed.

Magneto-optical study of the exciton fine structure in self-assembled CdSe quantum dots

We have studied the fine structure of the heavy-hole exciton in CdSe quantum dots grown on ZnSe by molecular beam epitaxy. Applying a tilted magnetic field, all four levels of the ground state are detected simultaneously. The zero-field separation between the optically forbidden and allowed doublets ranges between 1.7 and 1.9 meV and is crucially influenced by the finite energy barrier at the heterointerface as well as the existence of a wetting layer. The energy splitting within the allowed doublet (200 \ensuremath{\mu}eV) is substantially larger than for the forbidden states (\ensuremath{\leqslant} 20 \ensuremath{\mu}eV), demonstrating that a dominant contribution arises from the long-ranged part of the electron-hole exchange interaction. The total set of g factors is derived. A huge anisotropy for the electron is found.

Dislocation Mobility in Two-Dimensional Lennard-Jones Material

AbstractIn seeking to understand at a microscopic level the response of dislocations to stress we have undertaken to study as completely as possible the simplest case: a single dislocation in a two dimensional crystal. The intention is that results from this study will be used as input parameters in larger length scale simulations involving many defects. We present atomistic simulations of defect motion in a two-dimensional material consisting of atoms interacting through a modified Lennard-Jones potential. We focus on the regime where the shear stress is smaller than its critical value, where there is a finite energy barrier for the dislocation to hop one lattice spacing. In this regime motion of the dislocation will occur as single hops through thermal activation over the barrier. Accurate knowledge of the barrier height is crucial for obtaining the rates of such processes. We have calculated the energy barrier as a function of two components of the stress tensor in a small system, and have obtained good fits to a functional form with only a few adjustable parameters.

Stability of the grain configurations of thin films—A model for agglomeration

We have calculated the energy of three distinct grain configurations, namely, completely connected, partially connected, and unconnected configurations, evolving during a spheroidization of polycrystalline thin film by extending a geometrical model due to Miller et al. to the case of spheroidization at both the surface and film-substrate interface. “Stability” diagram defining a stable region of each grain configuration has been established in terms of the ratio of grain size to film thickness versus equilibrium wetting or dihedral angles at various interface energy conditions. The occurrence of spheroidization at the film-substrate interface significantly enlarges the stable region of unconnected grain configuration thereby greatly facilitating the occurrence of agglomeration. Complete separation of grain boundary is increasingly difficult with a reduction of equilibrium wetting angle. The condition for the occurrence of agglomeration differs depending on the equilibrium wetting or dihedral angles. The agglomeration occurs, at low equilibrium angles, via partially connected configuration containing stable holes centered at grain boundary vertices, whereas it occurs directly via completely connected configuration at large equilibrium angles except for the case having small surface and/or film-substrate interface energy. The initiation condition of agglomeration is defined by the equilibrium boundary condition between the partially connected and unconnected configurations for the former case, whereas it can, for the latter case, largely deviate from the equilibrium boundary condition between the completely connected and unconnected configurations because of the presence of a finite energy barrier to overcome to reach the unconnected grain configuration.

Self-consistent rate theory of submonolayer homoepitaxy with attachment/detachment kinetics

The reversible nucleation and growth of two-dimensional islands during the submonolayer stage of epitaxial growth is studied with self-consistent rate equations and kinetic Monte Carlo simulations. In contrast to most previous work, we take account of the effects of both a finite energy barrier to the detachment of atoms from islands and a finite barrier to the incorporation of adatoms into islands. A correct boundary condition for the diffusion field at island edges is derived that takes account of these processes. For small detachment rates, quantitative agreement is obtained between the solutions to the rate theory and the simulations for the average monomer and island densities as a function of coverage. {copyright} {ital 1997} {ital The American Physical Society}

Level crossing along sphaleron barriers.

In the electroweak sector of the standard model topologically inequivalent vacua are separated by finite energy barriers, whose height is given by the sphale\-ron. For large values of the Higgs mass there exist several sphaleron solutions and the barriers are no longer symmetric. We construct paths of classical configurations from one vacuum to a neighbouring one and solve the fermion equations in the background field configurations along such paths, choosing the fermions of a doublet degenerate in mass. As in the case of light Higgs masses we observe the level crossing phenomenon also for large Higgs masses.

Wilson-loop instantons.

Wilson-loop symmetry breaking is considered on a space-time of the form M4 x K, where M4 is a four-dimensional space-time and K is an internal space with nontrivial and finite fundamental group. It is shown in a simple model that the different vacua obtained by breaking a non-Abelian gauge group by Wilson loops are separated in the space of gauge potentials by a finite energy barrier. An interpolating gauge configuration is then constructed between these vacua and shown to have minimum energy. Finally some implications of this construction are discussed.

Spin glasses - A transition in plain ordinary space

We are living a fascinating moment where theorists, faced to ample experimental and (more recent) simulation evidence seem to have little choice other than to accept that the transition which they described, actually occurs in our ordinary space at 3 d. We review here some of the experimental arguments, based on critical measurements performed at equilibrium in the high temperature phase, and we stress the similarities and the differences with superparamagnetism and with an ordinary phase transition. By contrast, the slow relaxations which are observed in the low temperature phase below Tc are interpreted in terms of activation over finite energy barriers and would suggest little more than ordinary superparamagnetism. Some features of the Fulcher law which describes the edge between the equilibrium and the non equilibrium regimes, would allow to conciliate both points of view : it is the critical divergence of the barrier heights, on approaching Tc from above, which is responsible for the fact that the system appears blocked at a temperature Tg(t) slightly larger than Tc for all experiments performed in a finite time t.

Explanation of the freezing temperature in spin glasses

The freezing of spins in the two-dimensional ±J-model [1,2] (anti- and ferromagnetic nearest neighbour bonds between Ising spins) is investigated for the case of a one-spin-flip-dynamic (as used in Monte-Carlo calculations). The phenomenon is caused by the existence of finite energy barriers between the different ground-state valleys. The barrier heights are calculated by a numerical method turning one ground state to its inverse. The freezing temperature is determined by the vanishing of the free energy barriers between the valleys. The corresponding entropy is calculated by the Transfermatrix-Method. The free energy barriers vanish at Tf≂1.3±0.1 in good agreement with the cusp of the susceptibility in Monte-Carlo calculations. The long-time behaviour of spin glasses is governed by the mentioned free energy barriers.

The effects of finite contact energy barriers and traps on space-charge-limited currents in thin insulators

The effects of finite contact energy barriers and small insulator thickness on space-charge-limited currents are investigated. Diffusion effects are implicitly considered. The analysis is extended to include a variety of common trap distributions, and numerical results are given using zinc sulphide as the insulator. The concepts discussed are illustrated by current-voltage characteristics computed from the exact space-charge-limited theory.

Ondes de spin dans un verre magnetique classique

Resume The spin dynamics of a classical very dilute totally disordered Heisenberg spin glass is investigated at low temperatures. At 0 K, it is supposed that the spins are in metastable equilibrium in one of a great number of possible configurations, different configurations being separated by finite energy barriers. It is found that at 0 K, there are spin waves at very long wavelengths k-1⪢R0 (R0, mean spacing between spins). At finite temperatures, there may be excitations involving a few number of spins whose thermal activation would damp the spin waves. Possible domain structure would reduce the existence of spin waves to LM>k-1⪢R0 (LM, mean dimension of domain). The persistence of a residual (very low) mean magnetization has been neglected.