Kinetic Asymmetry Research Articles

Growth Mode Diagram for the Epitaxial Growth on the Vicinal Surface of Strained Si (001)

We present the linear stability analysis for the epitaxial thin film growth on the vicinal surface of strained Si and the growth mode diagrams of the epitaxial growth under various operation conditions. Competition between step-step elastic interactions and the asymmetry of incorporation of adatoms from the terraces to step edge is considered. Force monopoles at steps and their interaction lead to it on the vicinal surface while kinetic asymmetry of the adatom incorporation at steps due to Ehrlich-Schwoebel barrier prevents the step bunching instability. Growth mode on the vicinal surface is determined by the competition between elastic step-step interactions and Ehrlich-Schwoebel barrier.

The Two ATP Binding Sites of Cystic Fibrosis Transmembrane Conductance Regulator (CFTR) Play Distinct Roles in Gating Kinetics and Energetics

Cystic fibrosis transmembrane conductance regulator (CFTR), a member of the ABC (ATP binding cassette) transporter family, is a chloride channel whose activity is controlled by protein kinase–dependent phosphorylation. Opening and closing (gating) of the phosphorylated CFTR is coupled to ATP binding and hydrolysis at CFTR's two nucleotide binding domains (NBD1 and NBD2). Recent studies present evidence that the open channel conformation reflects a head-to-tail dimerization of CFTR's two NBDs as seen in the NBDs of other ABC transporters (Vergani et al., 2005). Whether these two ATP binding sites play an equivalent role in the dynamics of NBD dimerization, and thus in gating CFTR channels, remains unsettled. Based on the crystal structures of NBDs, sequence alignment, and homology modeling, we have identified two critical aromatic amino acids (W401 in NBD1 and Y1219 in NBD2) that coordinate the adenine ring of the bound ATP. Conversion of the W401 residue to glycine (W401G) has little effect on the sensitivity of the opening rate to [ATP], but the same mutation at the Y1219 residue dramatically lowers the apparent affinity for ATP by >50-fold, suggesting distinct roles of these two ATP binding sites in channel opening. The W401G mutation, however, shortens the open time constant. Energetic analysis of our data suggests that the free energy of ATP binding at NBD1, but not at NBD2, contributes significantly to the energetics of the open state. This kinetic and energetic asymmetry of CFTR's two NBDs suggests an asymmetric motion of the NBDs during channel gating. Opening of the channel is initiated by ATP binding at the NBD2 site, whereas separation of the NBD dimer at the NBD1 site constitutes the rate-limiting step in channel closing.

Dynamic phase transitions in electromigration-induced step bunching

Electromigration-induced step bunching in the presence of sublimation or deposition is studied theoretically in the attachment-limited regime. We predict a phase transition as a function of the relative strength of kinetic asymmetry and step drift. For weak asymmetry the number of steps between bunches grows logarithmically with bunch size, whereas for strong asymmetry at most a single step crosses between two bunches. In the latter phase the emission and absorption of steps is a collective process which sets in only above a critical bunch size and/or step interaction strength.

Effects of transport and phase equilibrium on fast, nearly irreversible reactive extraction

Integration of reaction and separation can be exploited to drive reversible reactions in the direction of the desired product using multiphase flow contacting. In the case of nearly irreversible, fast reactions, however, the dynamics of the product have little influence on the reactor efficiency in say liquid–liquid reactive extraction. A similar intensification in reaction efficiency to reactive separation can be achieved by exploiting phase equilibrium or asymmetry in mass transfer rates of the reactants. Here, a model for two-layer biphasic flow and homogeneous reaction is proposed for co-current reactive extraction, demonstrating that localization and intensification of reaction occurs in the region between the entrance and crossover. Crossover occurs if the reactant in stoichiometric deficit preferentially populates the reacting phase due to sufficient imbalance in either mass transfer coefficients or phase equilibrium. We develop an infinite Peclet number (convection dominates over bulk diffusion) model that indicates that crossover occurs when 1 > u 0 v 0 > 1 κ u 2 + 1 κ u 1 h U 1 κ v 2 + 1 κ v 1 h V for fast, irreversible reactions. u 0 and v 0 are initial charges to the tubular reactor, the κ 's are mass transfer coefficients for each side of the fluid interface and the h 's are Henry's Law coefficients for reactants U and V . The interpretation of this formula is that if v 0 > u 0 , then crossover will occur if the overall mass transfer rate of U is faster than the overall mass transfer rate for V . Downstream of the crossover point, the reactant in stoichiometric excess also dominates the reacting phase due to relative exhaustion of the more-mobile component. A finite Peclet number theory for fast, irreversible reaction shows that the above formula is a conservative limit for crossover—if it holds, crossover will occur regardless of the Peclet number. A formula for the larger parametric region for crossover with finite Peclet number is derived. Verification that crossover is achieved is found by finite-element numerical analysis of the full governing equations. Both theory and numerical analysis predict localization and intensification of the reaction due to crossover. Crossover sets the length scale as approximately two and a half crossover lengths for completed reaction for sufficiently high Peclet number with strong kinetic asymmetry. The theory predicts that taking the ratio of inlet concentrations S = u 0 / v 0 to be the critical value at fixed physical parameters for mass transfer and phase equilibrium maximizes localization and reactor efficiency. Similarly, the kinetic asymmetry should be as large as possible to exploit the benefits of crossover.

Influence of functional bracing on the kinetics of anterior cruciate ligament-injured knees during level walking

Use of functional knee braces has been suggested to provide protection and to improve kinetic performance of the knee in anterior cruciate ligament-injured patients. However, the efficacy of knee bracing in achieving these goals is still controversial. The purpose of this study was to examine the immediate effects of functional bracing on the three-dimensional kinetics of the knee in individuals with anterior cruciate ligament injuries during level walking. Fifteen anterior cruciate ligament-deficient and 15 anterior cruciate ligament-reconstructed subjects were each fitted with a DonJoy Goldpoint brace and walked at a self-selected pace, first without and then with the brace. Kinematic and kinetic data were measured and three-dimensional joint moments and angular impulses at the knee were calculated and compared between bracing conditions and between limbs. Functional knee bracing did not significantly affect the kinetics of the unaffected knees for either group. Bracing significantly increased the peak abductor moments in anterior cruciate ligament-deficient knees and reduced the bilateral kinetic asymmetry in the coronal plane. For the anterior cruciate ligament-reconstructed group, bracing increased peak moments and impulses of the abductors and extensors. It also reduced bilateral kinetic asymmetry in the sagittal and coronal planes. Effects of the knee brace were apparent in the coronal plane for both anterior cruciate ligament-deficient and anterior cruciate ligament-reconstructed patients, and in the sagittal plane for anterior cruciate ligament-reconstructed patients. Functional bracing can be recommended for anterior cruciate ligament-reconstructed patients to assist in achieving better bilateral kinetic symmetry during gait. For anterior cruciate ligament-deficient patients, apart from bracing, additional emphasis on the rehabilitative training for better kinetic knee performance in the sagittal plane is needed.

Kinetic asymmetry in female runners with and without retrospective tibial stress fractures

Gait asymmetry may be linked to the tendency for runners to sustain chronic overuse injuries. This paper compares gait asymmetry in female runners who have never sustained a running-related injury to those who have sustained unilateral tibial stress fractures. The symmetry index was used to characterize asymmetry in the kinetics of both subject groups. There were three aims to this study: (1) to report natural levels of asymmetry for healthy, never-injured female runners, (2) to compare asymmetry levels between never-injured runners and those who have sustained stress fractures, and (3) to examine the kinetics between the involved and uninvolved limbs of runners who have sustained stress fractures. In all three aims, peak medial, lateral, braking, vertical impact, and vertical ground reaction forces, average and peak instantaneous vertical loading rates, and peak shock were examined. In the never-injured runner group, natural levels of asymmetry ranged from 3.1% for peak vertical ground reaction force up to 49.8% for peak lateral ground reaction force. Symmetry indices were not significantly different in the runners who had previously sustained stress fractures. The involved limb of the previously injured runners demonstrated higher values for braking and vertical impact ground reaction force and peak shock. Interestingly, these runners appeared to have bilaterally-elevated lateral ground reaction forces and loading rates as compared to the never-injured group, although this was not statistically tested. This suggests that previously injured runners may be closer to the injury threshold and, thus, more susceptible. Asymmetry may simply influence the side on which they become injured.

Kinetic Asymmetry In Female Runners With And Without Retrospective Tibial Stress Fractures

The tendency for a runner to become injured on a particular side is not well understood. It has been suggested that it may be due, in part, to asymmetry in their mechanics. PURPOSE The purposes of this study were (1) to compare the levels of kinetic asymmetry in runners who have previously sustained a tibial stress fracture (TSF) and those who have not (CON) and (2) to compare loading parameters between the involved and uninvolved sides of the TSF runners. It was hypothesized that the TSF group would be more asymmetric than the CON group and that they would exhibit greater loading on the involved side. METHODS Twenty-five CON and 24 TSF subjects were eligible for this study. CON subjects reported to have never sustained a running injury. TSF subjects were included if they had sustained one or more tibial stress fractures on a single side of their body. Subjects were asked to run along a 25 meter runway at a speed of 3.65 m/s (± 5%), striking a force platform (Bertec Corp., Worthington, OH) at its center. Data were sampled at 960 Hz. The speed was monitored with photoelectric cells placed 2.86 m apart. Five trials were collected for both the left and right sides. Any trials indicative of targeting were discarded. The same type of neutral running shoe was worn by each subject during data collection. Peak medial, lateral, braking, vertical impact, and vertical ground reaction forces, average and instantaneous vertical loading rates, and peak shock were measured in each subject. Symmetry Index (SI) was used to quantify asymmetry: SI = (XL – XR)/0.5*(XL+ XR). A 1-tailed, independent t-test was used to compare SI values between the TSF and CON groups. A 1-tailed, dependent t-test was used to compare loading values between the involved and uninvolved sides of the TSF group. RESULTS SI values were not significantly different between the CON and TSF groups for any of the parameters. The peak vertical impact ground reaction force and peak shock were both significantly higher on the involved side in the TSF subjects (p = 0.04 and 0.02 respectively). CONCLUSIONS These results indicate that while CON and TSF subjects have similar levels of asymmetry, those in the TSF group may have elevated loading values, bilaterally, that predispose them to injury.

Non-equilibrium effects on fast reactions in a heterogeneous batch reactor

Recent studies by the authors of the heterogeneous catalysis of fast binary reactions have taken a dynamical systems approach, assuming that fast enough reactions are confined to a manifold upon which surface equilibrium holds. This approximation makes substantial simplification possible, for instance in the case of a batch reactor, it allows a naturally sixth order system to be approximated by a two dimensional manifold for the dynamics of two modified Thiele moduli. Nevertheless, a proper assessment of how much faster must the velocity of surface reaction be than the velocity of mass transfer to the catalytic surface before the quasi-equilibrium on the surface holds should be made. In this paper, a theory for the systematic correction to infinitely fast reactions is made for large but finite velocity reactions. It is compared to full numerical solutions to the model equations. Recommendations about the regime of applicability of the quasi-equilibrium approximation are made. In general, the predictions of the quasi-equilibrium theory hold for ratios of mass transfer coefficients to reaction velocity ξ of less than 1 / 1000 , with qualitative agreement in regimes of less than 1 / 100 . The general trend, however, is that the stronger the kinetic asymmetry between the mass transfer coefficients of the reactants, the slower the reaction rate can be and still have the quasi-equilibrium theory hold. A perturbation analysis demonstrates that the quasi-equilibrium theory is a regular limit of the fast non-equilibrium theory. In the irreversible case, a matched asymptotic analysis gives the same prediction for the switch time from effective surface depletion of one reagent to the other as the quasi-equilibrium theory. Furthermore, it gives an estimate of the smoothing out of the transition zone with a temporal width of ξ 1 / 2 . It should be noted that the continual drive for improved catalyst activities inevitably leads to mass transfer limited reactions, and thus this regime is not uncommon.

Stability of a circular epitaxial island

The morphological stability of a single, epitaxially growing, circular adatom island with a radially symmetric adatom distribution is studied using a Burton–Cabrera–Frank type island dynamics model. Various kinds of boundary conditions for the adatom density that include the thermodynamic equilibrium value, line tension, and attachment–detachment kinetics, and different velocity formulas with or without the one-dimensional “surface” diffusion are examined. Rigorous analysis shows that the circular island is always stable if its normalized area A is larger than a critical value. If A is less than such a critical value, and if neither the line tension nor surface diffusion is present, then there exists a critical wavenumber k c = k c( A) such that the island is only stable for wavenumbers less than k c. When the line tension or surface diffusion is present, small islands are always stable. In particular, the Bales–Zangwill instability for straight steps due to the kinetic asymmetry does not exist for small circular islands.

Epitaxial Growth Without Slope Selection: Energetics, Coarsening, and Dynamic Scaling

We study a continuum model for epitaxial growth of thin films in which the slope of mound structure of film surface increases. This model is a diffusion equation for the surface height profile h which is assumed to satisfy the periodic boundary condition. The equation happens to possess a Liapunov or “free-energy” functional. This functional consists of the term |Δ h|2, which represents the surface diffusion, and - log (1 + |∇ h|2), which describes the effect of kinetic asymmetry in the adatom attachment-detachment. We first prove for large time t that the interface width---the standard deviation of the height profile---is bounded above by O(t1/2), the averaged gradient is bounded above by O(t1/4), and the averaged energy is bounded below by O(- log t). We then consider a small coefficient ε2 of |Δ h|2 with ε = 1/L and L the linear size of the underlying system, and study the energy asymptotics in the large system limit ε → 0. We show that global minimizers of the free-energy functional exist for each ε > 0, the L2-norm of the gradient of any global minimizer scales as O(1/ε), and the global minimum energy scales as O( log ε). The existence of global energy minimizers and a scaling argument are used to construct a sequence of equilibrium solutions with different wavelengths. Finally, we apply our minimum energy estimates to derive bounds in terms of the linear system size L for the saturation interface width and the corresponding saturation time.

Asymétries chronométriques, cinétiques et cinématiques de l'initiation de la marche chez un sujet hémiplégique

Objective. – To investigate the temporal, kinetic and kinematic asymmetry of gait initiation in one subject with hemiplegia with an equinus varus foot. Material and methods. – A kinetic analysis with two AMTI ® force plates and a kinematic analysis with an ELITE ® optoelectronic system of gait initiation were performed in one subject with hemiplegia. Results. – The duration of the gait initiation phases was asymmetrical. The monopodal phase was shorter when the affected lower limb was supporting than when the healthy one was supporting. The propulsion resulted from the force exerted on the healthy lower limb. The distribution of body weight on the lower limbs was asymmetrical. Body weight support was more important on the healthy side than on the affected side. Maximal extension of the ankle on the hemiplegic side occurred during the swing phase. Ground clearance was increased by elevating the knee higher on the affected side than on the healthy side during the swing phase. Initial contact with the floor was performed with the foot flat on the affected side. Conclusion. – This preliminary study has shown that gait initiation in one subject with hemiplegia was asymmetrical in kinetics and kinematics. The results concerning kinematics have not been reported previously for gait initiation in subjects with hemiplegia. The study of gait initiation should allow for better understanding postural and movement control strategies developed by patients with hemiplegia.

Finite element method for epitaxial island growth

We present an adaptive finite element method for epitaxial island growth. The problem consists of an adatom diffusion equation on terraces of different height; boundary conditions on steps including the kinetic asymmetry in the adatom attachment and detachment; and the normal velocity law for the motion of the steps determined by a two-sided flux, together with diffusion of edge-adatoms along the steps. The problem is solved using two independent meshes: a two-dimensional mesh for the adatom diffusion and a one-dimensional mesh for the boundary evolution. Some applications demonstrating the influence of the Ehrlich–Schwoebel and inverse Ehrlich–Schwoebel barrier and the anisotropy are shown.

Finite element method for epitaxial growth with attachment–detachment kinetics

An adaptive finite element method is developed for a class of free or moving boundary problems modeling island dynamics in epitaxial growth. Such problems consist of an adatom (adsorbed atom) diffusion equation on terraces of different height; boundary conditions on terrace boundaries including the kinetic asymmetry in the adatom attachment and detachment; and the normal velocity law for the motion of such boundaries determined by a two-sided flux, together with the one-dimensional “surface” diffusion. The problem is solved using two independent meshes: a two-dimensional mesh for the adatom diffusion and a one-dimensional mesh for the boundary evolution. The diffusion equation is discretized by the first-order implicit scheme in time and the linear finite element method in space. A technique of extension is used to avoid the complexity in the spatial discretization near boundaries. All the elements are marked, and the marking is updated in each time step, to trace the terrace height. The evolution of the terrace boundaries includes both the mean curvature flow and the surface diffusion. Its governing equation is solved by a semi-implicit front-tracking method using parametric finite elements. Simple adaptive techniques are employed in solving the adatom diffusion as well as the boundary motion problem. Numerical tests on pure geometrical motion, mass balance, and the stability of a growing circular island demonstrate that the method is stable, efficient, and accurate enough to simulate the growing of epitaxial islands over a sufficiently long time period.

Thin film epitaxy with or without slope selection

Two nonlinear diffusion equations for thin film epitaxy, with or without slope selection, are studied in this work. The nonlinearity models the Ehrlich–Schwoebel effect – the kinetic asymmetry in attachment and detachment of adatoms to and from terrace boundaries. Both perturbation analysis and numerical simulation are presented to show that such an atomistic effect is the origin of a nonlinear morphological instability, in a rough-smooth-rough pattern, that has been experimentally observed as transient in an early stage of epitaxial growth on rough surfaces. Initial-boundary-value problems for both equations are proven to be well-posed, and the solution regularity is also obtained. Galerkin spectral approximations are studied to provide both a priori bounds for proving the well-posedness and numerical schemes for simulation. Numerical results are presented to confirm part of the analysis and to explore the difference between the two models on coarsening dynamics.

Kinetic energy distribution and anisotropy of fragment ions from SF 6 by photoexcitation of a sulfur 2p-electron

The kinetic energy (KE) distribution and asymmetry parameter β have been studied for photofragmentation of SF 6 near the sulfur 2p ionization edges at 170–208 eV. The relative ion yield at KE > 5 eV is higher in the post-edge than in the pre-edge region, whereas β is lower by ∼0.06 in the post-edge region. These results are ascribed to LVV Auger decay occurring above the edges. At KE > 2 eV the distribution curve for core excitation to the (2t 1u) −1(6a 1g) 1 state resembles that for valence-electron ionization, suggesting participation of shake-up satellite states in production of fast F + ions.

Nearly irreversible, fast heterogeneous reactions in premixed flow

When heterogeneous chemical reaction is sufficiently fast, transport of reactants becomes limiting. In a fixed bed reactor, macroscopic concentration gradients cannot be eliminated as a factor limiting the rate of reaction, possibility coupling to the mesoscopic mass transfer of reactants to the surface of the catalyst as limiting, if the reaction does not occur inside a porous support. A theory for strictly irreversible binary reaction is developed that shows the possibility of regimes of kinetic asymmetry in which a crossover point occurs internally in the reactor, demarking a region of high supersaturation in which the surface is effectively depleted of one reagent, followed by a region of rapidly decaying supersaturation, where the surface is effectively depleted of the other reagent. The parametric dependence of this crossover point is given in terms of a transcendental equation which depends on operating parameters (superficial velocity and inlet concentrations) and ratios of transport properties of the reagents. These solutions are corroborated by full nonlinear numerical computations of the boundary value problem, for the case when asymmetric mass transfer coefficients admit the possibility that the mode of operation switches from relative surface depletion of one reactant to depletion of the other in a binary reaction. It is shown that X indicates the region of greatest molecular efficiency in the reactor, and if operating parameters are so chosen such that X is large, high conversion is achieved in the precrossover region. The modified Thiele modulus analysis of the numerical solutions identifies the crossover point and the region of greatest product formation.

The light subunit of system b(o,+) is fully functional in the absence of the heavy subunit.

The heteromeric amino acid transporters are composed of a type II glycoprotein and a non-glycosylated polytopic membrane protein. System b(o,+) exchanges dibasic for neutral amino acids. It is composed of rBAT and b(o,+)AT, the latter being the polytopic membrane subunit. Mutations in either of them cause malfunction of the system, leading to cystinuria. b(o,+)AT-reconstituted systems from HeLa or MDCK cells catalysed transport of arginine that was totally dependent on the presence of one of the b(o,+) substrates inside the liposomes. rBAT was essential for the cell surface expression of b(o,+)AT, but it was not required for reconstituted b(o,+)AT transport activity. No system b(o,+) transport was detected in liposomes derived from cells expressing rBAT alone. The reconstituted b(o,+)AT showed kinetic asymmetry. Expressing the cystinuria-specific mutant A354T of b(o,+)AT in HeLa cells together with rBAT resulted in defective arginine uptake in whole cells, which was paralleled by the reconstituted b(o,+)AT activity. Thus, subunit b(o,+)AT by itself is sufficient to catalyse transmembrane amino acid exchange. The polytopic subunits may also be the catalytic part in other heteromeric transporters.

Kinetic length, step permeability, and kinetic coefficient asymmetry on the Si(111) (7×7) surface

The island nucleation position at the critical terrace width for step flow on the Si(111) $(7\ifmmode\times\else\texttimes\fi{}7)$ surface has been measured with low-energy electron microscopy. These data allow for the kinetic length, which is indicative of the rate-limiting step, to be evaluated and provide compelling new evidence that steps are impermeable. The assessment of step kinetic coefficient asymmetry and its potential for effecting growth instabilities depends crucially upon the kinetic length and step permeability. Step attachment is found to be favored from the terrace trailing an advancing step.

Transport, trapping and interfacial transfer of electrons in dye-sensitized nanocrystalline solar cells

The physical and chemical processes taking place in dye-sensitized solar cells (DSC) are reviewed. In order to achieve high power efficiencies under solar irradiation, it is essential to incorporate kinetic asymmetry into the design of DSCs. Electron transfer to the redox mediator should be slow from the nanocrystalline oxide and fast from the regenerating electrode. This asymmetry can be achieved by the choice of redox electrolyte as well as by selective use of electrocatalysis to accelerate electron transfer at one contact and suitable blocking layers to retard electron transfer at the other interfaces. In the discussion of the processes that determine the efficiency of DSCs, particular emphasis is placed on the role of electron trapping in determining the rates of electron transport and interfacial electron transfer. The prospects for improving the performance of DSCs are discussed in a quantitative framework based on current understanding of the cells.

Oscillatory driving of crystal surfaces: a route to controlled pattern formation.

We show that the oscillatory driving of crystal surfaces can induce pattern formation or smoothening. Depending on driving conditions, step bunching and meandering, mound formation, or surface smoothening may be seen in the presence of a kinetic asymmetry at the steps or kinks. We employ a step model to calculate the induced mass flux along misoriented surfaces, which accounts for surface dynamics and stability. Slope selection, surface metastability, and frequency-dependent surface stability are found. Quantitative predictions for pattern formation on metal surfaces in an electrolyte are provided.