Bimodal Energy Distribution Research Articles

Non-vanishing boundary effects and quasi-first-order phase transitions in high dimensional Ising models

In order to gain a better understanding of the Ising model in higher dimensions we have made a comparative study of how the boundary, open versus cyclic, of a d-dimensional simple lattice, for d=1,…,5, affects the behaviour of the specific heat C and its microcanonical relative, the entropy derivative −∂2S/∂U2.In dimensions 4 and 5 the boundary has a strong effect on the critical region of the model and for cyclic boundaries in dimension 5 we find that the model displays a quasi-first-order phase transition with a bimodal energy distribution. The latent heat decreases with increasing systems size but for all system sizes used in earlier papers the effect is clearly visible once a wide enough range of values for K is considered.Relations to recent rigorous results for high dimensional percolation and previous debates on simulation of Ising models and gauge fields are discussed.

Growth and melting of droplets in cold vapors

A model has been developed to investigate the growth of droplets in a supersaturated cold vapor taking into account their possible solid-liquid phase transition. It is shown that the solid-liquid phase transition is nontrivially coupled, through the energy released in attachment, to the nucleation process. The model is based on the one developed by J. Feder, K. C. Russell, J. Lothe, and G. M. Pound [Adv. Phys. 15, 111 (1966)], where the nucleation process is described as a thermal diffusion motion in a two-dimensional field of force given by the derivatives of a free-energy surface. The additional dimension accounts for droplets internal energy. The solid-liquid phase transition is introduced through a bimodal internal energy distribution in a Gaussian approximation derived from small clusters physics. The coupling between nucleation and melting results in specific nonequilibrium thermodynamical properties, exemplified in the case of water droplets. Analyzing the free-energy landscapes gives an insight into the nucleation dynamics. This landscape can be complex but generally exhibits two paths: the first one can generally be ascribed to the solid state, while the other to the liquid state. Especially at high supersaturation, the growth in the liquid state is often favored, which is not unexpected since in a supersaturated vapor the droplets can stand higher internal energy than at equilibrium. From a given critical temperature that is noticeably lower than the bulk melting temperature, nucleation may end in very large liquid droplets. These features can be qualitatively generalized to systems other than water.

Vibrational−Rotational Energy Distributions in the Reaction O− + D2 → OD + D−

The D(+) transfer reaction between O(-) ((2)P) and D(2) to form OD and D(-) was studied using the crossed molecular beam technique at collision energies of 1.55 and 1.95 eV. The reaction appears to proceed by a direct mechanism through large impact parameters. At both collision energies, more that 70% of the excess energy is partitioned into product translation. At the lower collision energy, the OD products are formed in the ground vibrational state with a bimodal rotational energy distribution. At the higher collision energy, both v' = 0 and 1 products are formed; ground vibrational state products have a mean rotational energy of 0.05 eV, corresponding to J' approximately 6. In contrast, OD products formed in v' = 1 are formed with significant rotational excitation, with the most probable J' approximately 15. The bimodal rotational distribution is rationalized in terms of trajectories that sample two potential surfaces coupled by a conical intersection in the vicinity of the [O...DD](-) intermediate that correlate to (OD(-),D) or (OD,D(-)) products.

Roaming Dynamics in Formaldehyde-d2 Dissociation

State-resolved photodissociation dynamics of formaldehyde-d(2), i.e., D(2)CO, at energies slightly above the deuterium atom elimination channel have been studied both experimentally and theoretically. The results showed a clear bimodal distribution of energy into molecular photofragments. Substantial translational excitation of products at high rotational levels of CO was observed together with the D(2) cofragment in moderately excited vibrational levels, whereas rather small translational energy release of CO in low rotational levels was matched by a large degree of vibrational excitation in the D(2) molecule. An analogous distribution of energy in two distinct channels has been recently observed under similar conditions in H(2)CO photolysis and attributed to two different dissociation pathways, namely, a pathway via the conventional transition state geometry and the previously unobserved pathway, deemed "roaming". Our experimental and theoretical data indicated that the same two dissociation pathways were responsible for the bimodal energy distribution into the molecular fragments resulting from the photolysis of D(2)CO. Energy partitioning into molecular products was compared between photolysis of H(2)CO and D(2)CO at energies slightly above the H/D atom abstraction threshold.

Phase coexistence in melting aluminum clusters

The internal energy distributions for melting aluminum cluster cations with 100, 101, 126, and 127 atoms have been investigated using multicollision induced dissociation. The experimental results can be best fit with a statistical thermodynamic model that incorporates only fully solidlike and fully liquidlike clusters so that the internal energy distributions become bimodal during melting. This result is consistent with computer simulations of small clusters, where rapid fluctuations between entirely solidlike and entirely liquidlike states occur during the phase change. To establish a bimodal internal energy distribution, the time between the melting and freezing transitions must be longer than the time required for equilibration of the energy distribution (which is estimated to be around 1-2 micros under our conditions). For Al(100)(+) and Al(101)(+), the results indicate that this criterion is largely met. However, for Al(126)(+) and Al(127)(+), it appears that the bimodal energy distributions are partly filled in, suggesting that either the time between the melting and freezing transitions is comparable to the equilibration time or that the system starts to switch to macroscopic behavior where the phase change occurs with the two phases in contact.

Investigation of the adsorption mechanism of a peptide in reversed phase liquid chromatography, from pH controlled and uncontrolled solutions

The single-component equilibrium adsorption of the tripeptide Leucyl-Leucyl-Leucine (LLL) on a high-efficiency Jupiter Proteo column ( C 12 ) was investigated experimentally and modeled theoretically. The experimental equilibrium isotherms of LLL for adsorption on a C 12 packing material from an aqueous solution of methanol (48%) and trifluoroacetic acid (0.1%) were measured by frontal analysis (FA). The FA measurements were done with two solutions, one in which the pH was controlled, the other in which it was not. Two solutions of LLL in the mobile phase were prepared (4.3 and 5.4 g/L) and their pH measured (2.94 and 2.88), respectively. The first solution was titrated with TFA to match the pH of the mobile phase (2.03), so its pH was controlled. The pH of the other solution was left uncontrolled. In both cases the isotherms could be modeled by a bi-Langmuir equation, a choice consistent with the bimodal affinity energy distribution (AED) obtained for LLL. The isotherm parameters derived from the inverse method (IM) of isotherm determination under controlled pH conditions (by fitting calculated profiles to experimental breakthrough profiles) are in a good agreement with those derived from the FA data. Under uncontrolled pH conditions, the application of IM suggests the coexistence of two different adsorption mechanisms. According to the isotherm parameters found by these three methods (FA, AED and IM), the C 12 -bonded silica can adsorb around 500 and 70 g/L of LLL under controlled and uncontrolled pH conditions, respectively. The adsorption of LLL on the C 12 material strongly depends on the pH of the mobile phase and on the quantity of TFA added, which plays the role of an ion-pairing agent.

Energy distribution of bombarding ions in plasma etching of dielectrics

In plasma etching for microelectronics fabrication, a sheath electric field accelerates ions into the substrate so they strike at normal incidence, contributing energy and reactive species to enable anisotropic etch profiles. The energy of the bombarding ions is typically controlled coarsely with a sinusoidal bias voltage applied to the substrate electrode, producing a broad bimodal ion energy distribution (IED) at the substrate. By systematically tailoring the shape of the waveform, the energies and relative fluxes of the two IED peaks are varied independently over a 100–500 eV range in a fluorocarbon-based helicon plasma, while silicon dioxide and photoresist etch rates are monitored. A 100 eV IED peak was combined with a higher energy peak, with the energy and relative flux of the high energy group as variables in the experiment. A relatively small contribution of high energy ions is found to lead to considerable etch rate enhancement, higher than predicted by a linear combination of single-peak etch rates at the two energies. Because high energy ion bombardment is known to suppress fluorocarbon deposition, it seems likely that changes in surface chemical composition in their presence enhances the contribution of lower energy ions to etching reactions.

Chemical Dynamics Simulation of Ne Atom Scattering off a Squalane Surface

A chemical dynamics simulation was performed to study collisions between neon (Ne) atoms and a liquid squalane (2,6,10,15,19,23-hexamethyltetracosane) surface. Ten thousand trajectories were calculated, with an incident energy of 10 kcal/mol, incident polar angle 45° with respect to the surface normal, and random azimuthal angle. The final energy distribution, angular distribution, and impact sites were determined and analyzed. The incident Ne atoms have short residence times on the surface with most atoms successfully scattering within 3−7 ps. Due to thermal fluctuations of the surface, the incident energy is dissipated efficiently, and more than 60% of the initial energy of the Ne atoms is transferred with three or more “kicks” on the surface. For in-plane scattered Ne atoms with a final polar angle of 45°, the energy transfer is 58% ± 8%, which is in good agreement with the experimental value of 60% (J. Chem. Phys. 1993, 99, 7056). A bimodal energy distribution is observed for both in-plane and out-of-...

Calculation of Protein Heat Capacity from Replica-Exchange Molecular Dynamics Simulations with Different Implicit Solvent Models

The heat capacity has played a major role in relating microscopic and macroscopic properties of proteins and their disorder-order phase transition of folding. Its calculation by atomistic simulation methods remains a significant challenge due to the complex and dynamic nature of protein structures, their solvent environment, and configurational averaging. To better understand these factors on calculating a protein heat capacity, we provide a comparative analysis of simulation models that differ in their implicit solvent description and force-field resolution. Our model protein system is the src Homology 3 (SH3) domain of alpha-spectrin, and we report a series of 10 ns replica-exchange molecular dynamics simulations performed at temperatures ranging from 298 to 550 K, starting from the SH3 native structure. We apply the all-atom CHARMM22 force field with different modified analytical generalized Born solvent models (GBSW and GBMV2) and compare these simulation models with the distance-dependent dielectric screening of charge-charge interactions. A further comparison is provided with the united-atom CHARMM19 plus a pairwise GB model. Unfolding-folding transition temperatures of SH3 were estimated from the temperature-dependent profiles of the heat capacity, root-mean-square distance from the native structure, and the fraction of native contacts, each calculated from the density of states by using the weighted histogram analysis method. We observed that, for CHARMM22, the unfolding transition and energy probability density were quite sensitive to the implicit solvent description, in particular, the treatment of the protein-solvent dielectric boundary in GB models and their surface-area-based hydrophobic term. Among the solvent models tested, the calculated melting temperature varied in the range 353-438 K and was higher than the experimental value near 340 K. A reformulated GBMV2 model of employing a smoother molecular-volume dielectric interface was the most accurate in reproducing the native conformation and a two-state folding landscape, although the melting transition temperature did not show the smallest deviation from experiment. For the lower-resolution CHARMM19/GB model, the simulations failed to yield a bimodal energy distribution, yet the melting temperature was observed to be a good estimate of higher-resolution simulation models. We also demonstrate that a careful analysis of a relatively long simulation is necessary to avoid trapping in local minima and to find a true thermodynamic transition temperature.

Impact of an error in the column hold-up time for correct adsorption isotherm determination in chromatography: II. Can a wrong column porosity lead to a correct prediction of overloaded elution profiles?

The adsorption isotherm was determined for phenol in methanol/water on a C-8 stationary phase using frontal analysis in staircase mode, assuming different total column porosities, from 1 to 87%. Each set of adsorption isotherm data, with a certain column porosity, was fitted to various adsorption models and the generated parameters were used to calculate overloaded elution band profiles that were compared with experiments. It was found that the bi-Langmuir model had an optimum fit for a porosity that corresponds well with the value found experimentally. The adsorption energy distribution (AED) calculations and error analysis confirmed a bimodal energy distribution. It was also found that band profiles can be accurately predicted with a quite arbitrary chosen porosity, under prerequisite that a wrong but flexible adsorption model is chosen instead of the correct one. The latter result is very useful for quick optimizations of preparative separations where the exact value of the column porosity is not available.

Bimodal energy distributions in the scattering of Ar + ions from modified surfaces at hyperthermal energies

Collisions of Ar + ions with three different surfaces have been studied by mass and energy resolved ion-scattering spectrometry. Kinetic energy distributions of scattered ions measured as a function of ion energy and scattering angle show two energetically and spatially distinct peaks corresponding to a low energy loss process and a very high energy loss process. The low energy loss peak is interpreted as due to the interaction of the Ar + ions with the self-assembled monolayer surface acting as a bulk surface.

Limits of the numerical estimation of the adsorption energy distribution from adsorption isotherm data using the expectation-maximization method

The limits of the use of the expectation-maximization (EM) method for the study of the heterogeneity of adsorbent surfaces were tested by calculating the adsorption energy distribution of systems having known degrees of heterogeneity. Connecting on-line two different columns allows the simulation of a heterogeneous system. The two columns used were endcapped, C 18-bonded silica used as stationary phases and having different degrees of C 18 chain coverages (0.42 and 2.03 μ mol/m 2). The adsorption constants of phenol measured by frontal analysis (FA) are significantly different on these two columns. On each column, the adsorption behavior was best accounted for by a bi-Langmuir isotherm model, corresponding to a heterogeneous surface with a bimodal energy distribution. The difference between the adsorption energies on the weak adsorption sites of the two columns is 1.5 kJ/mol. The energy difference of their high energy sites is 2.2 kJ/mol. The EM method can readily distinguish between adsorption sites having energies that differ by more than 5 kJ/mol after more than 10 million iterations, but it cannot distinguish between adsorption sites for which this energy difference is less than 2 kJ/mol, even after 100 million iterations. For highly heterogeneous systems, (e.g., those with more than three different types of adsorption sites), the EM program does not converge necessarily towards the actual energy distribution function but toward a simpler one, having fewer adsorption sites that are almost equally spaced in the energy space. This failure of the EM program is related to the fact that, despite the excellent precision of the FA measurements ( < 1%), any series of adsorption data can be represented by several distinct AEDs. Thus, the degree of heterogeneity of RPLC adsorbents determined with the EM method might often be minimized, resulting in erroneous values of the isotherm parameters.

Energy distributions of positive and negative ions during magnetron sputtering of an Al target in Ar∕O2 mixtures

The ion flux obtained during reactive magnetron sputtering of an Al target in Ar∕O2 gas mixtures was studied by energy-resolved mass spectrometry, as a function of the total and O2 partial pressures. The positive ions of film-forming species exhibited bimodal energy distributions, both for direct current and radio frequency discharges, with the higher energy ions most likely originating from sputtered neutrals. For the negative oxygen ions a high-energy peak was observed, corresponding to ions formed at the target surface and accelerated towards the substrate over the sheath potential. As the total pressure was increased the high-energy peaks diminished due to gas-phase scattering. Based on these results, the role of energetic bombardment for the phase constituent of alumina thin films are discussed.

Time-resolved mass and energy spectral investigation of a pulsed polymerising plasma struck in acrylic acid

This paper details an electrical diagnostic study of the discharge used in the pulsed plasma polymerisation of acrylic acid. The capacitively coupled RF discharge was operated at a frequency of 1 kHz and a pressure of 1.3 Pa. Using a retractable deposition-protected Langmuir probe the time-resolved electron temperature, density and plasma potential in the bulk were obtained. The time-resolved ion energy distribution functions (IEDFs) relative to ground potential for a selection of masses ( m/ z = 19, 55, 73) and the mass spectra (2–100 amu) have been measured by the energy-resolved mass spectrometer using an improved double gating technique. In both the “on” and “off” times of the pulse, the IEDFs for the heavier mass ions are characterised by a single peak ( E p – hereafter – the energy which corresponds with the peak intensity), the position and width of which are determined by the time-dependent plasma potential V p and its distribution across the plasma to the spectrometer, while a weakly bimodal ion energy distribution is present in the IEDF for m/ z = 19 in the “on” time. In the steady “on” time, the relative ion flux (detector count rate) of each species and the energy corresponding to the peak intensity in the IEDFs are constant, the latter ( E p ∼ 47 eV) correlating very well to the probe measured plasma potential. At pulse initiation, V p rises to values > 90 V, however, these energies are not detected in IEDF with our time resolution of 10 μs. In the “off” time, this energy falls with a two-fold decay time, initially sharply to ∼ 23 eV (at the first measured point which was made 1 μs after beginning of the “off” period) and then slowly in the next 150 μs to ∼ 17–18 eV closer to the end of the cycle. The elevation of the E p well above ground is in contrast to that usually observed in pulsed Ar discharges (∼ 10 V higher), due to in this case, charging of the acrylic acid deposited materials on the walls. The time-history of the integrated area under the IEDFs reveals that after the initiation of the “on” time the concentration N of lighter species rises more quickly than the heavier ones. In the “off” time, however, although N 19 becomes negligible after 50 μs, N 73 decreases more quickly than N 55 which is still non-zero at 150 μs. The time resolved mass-spectral reveal the general mass dependency in the concentration rise and fall times of the detected species.

Adsorption of the enantiomers of 3-chloro-1-phenyl-propanol on silica-bonded chiral quinidine carbamate

The interactions of 3-chloro-1-phenyl-propanol with a quinidine carbamate-bonded chiral stationary phase under NPLC conditions were studied by measuring the adsorption isotherm data of its enantiomers by frontal analysis, modeling these data with a suitable isotherm model, and comparing the experimental overloaded elution band profiles with those calculated with this isotherm and the equilibrium dispersive model of liquid chromatography. The affinity energy distribution was calculated from the adsorption isotherm data. The results show that the surface of the adsorbent is heterogeneous and exhibits a bimodal adsorption energy distribution. This fact is interpreted in terms of the presence of two different types of adsorption sites on the stationary phase, nonselective and enantioselective sites. Albeit the bi-Langmuir isotherm model successfully accounts for the single-component data corresponding to both enantiomers, the competitive bi-Langmuir isotherm model does not allow an accurate prediction of the overloaded band profiles of the racemic mixture. Thermodynamic data are drawn for explanation. Some aspects of the retention mechanism are discussed in the light of the data obtained.

Adsorption isotherms of the fullerenes C 60 and C 70 on a tetraphenylporphyrin-bonded silica

The single-component adsorption isotherms of the C 60 (from 0 to 15 g/L) and C 70 (from 0 to 8 g/L) buckminsterfullerenes on a tetraphenylporphyrin-bonded silica were acquired by frontal analysis, using a solution of toluene–1-methylnaphthalene (40:60, v/v) as the mobile phase. The best isotherm model derived from the fitting of these adsorption data was the bi-Langmuir model, a choice supported by the bimodal affinity energy distribution (AED) obtained for C 60. The isotherm parameters derived from the inverse method (IM) of isotherm determination (by fitting calculated profiles to experimental overloaded band profiles of C 60 and C 70) are in very good agreement with those derived from the FA data. According to the isotherm parameters found by these three methods (FA, AED, IM), the tetraphenylporphyrin-bonded silica can adsorb 54 and 42 mmol/L of C 60 and C 70 fullerenes, respectively, a result that is consistent with the relative molecular size of these two compounds. The 20% lower surface accessibility for C 70 is compensated by a three times higher equilibrium constant on the low-energy sites, giving a selectivity α C 70 / C 60 = 3.6. Large volumes (0.2, 0.8 and 1.7 mL) of mixtures of C 60 (3.2 g/L) and C 70 (1.3 g/L) were injected and their elution profiles compared to those calculated from the competitive bi-Langmuir model derived from the single-component isotherm data. A good agreement is obtained between calculated and experimental profiles, which supports the two-site adsorption mechanism derived from the single-component adsorption data. The measurements of the influence of the pressure on the retention of C 60 and C 70 demonstrate that the partial molar volumes of the two buckminsterfullerenes are 12 mL/mol larger in the stationary than in the mobile phase.

Retention of ionizable compounds in reversed-phase liquid chromatography. Effect of the ionic strength of the mobile phase and the nature of the salts used on the overloading behavior.

The retention mechanism of the protonated cation in propranolol chloride on C18-Xterra was investigated using mobile phases of various compositions. Accurate adsorption data were measured by frontal analysis, with a mixture of methanol and water (25% methanol), with no salt, as the mobile phase. The experimental isotherm has at least two inflection points, at concentrations of about 0.2 and 6.0 g/L, respectively. This precludes the modeling of these data with a simple convex-upward isotherm (e.g., Langmuir). The adsorption energy distribution or relationship between the number of sites on the adsorbent surface and the energy of adsorption on these sites was calculated by assuming Moreau isotherm behavior (S-shaped isotherm). This model has never been applied to describe the surface heterogeneity of any RPLC adsorbent. The calculation converged toward a bimodal energy distribution. Accordingly, the bi-Moreau model is the simplest theoretical model accounting for the adsorption data of propranolol from a mobile phase without salt. The complex-overloaded band profiles of propranolol measured in the presence of increasing concentrations of a supporting salt (KCl) in the mobile phase demonstrate that the same isotherm model applies also under these conditions, as was merely assumed in a previous work. The elution band profiles of propranolol calculated with the bi-Moreau isotherm model for solutions of salts of different natures (CaCl2, CsCl, Na2SO4) in the same mobile phase agree very well with the experimental band profiles.

Spatial and temporal variations in wave characteristics across a reef platform, Warraber Island, Torres Strait, Australia

A field experiment was conducted at Warraber Island, Torres Strait, Australia to investigate spatial and temporal variations in wave characteristics and energy across a mesotidal coral reef platform. Measurements of water depth were obtained using five pressure sensors deployed across a 2.7-km section of reef flat from July 3–5, 2001. The reef surface was uneven and consisted of an outer reef flat, a central reef flat depression, an inner reef ramp, a palaeo-reef surface and the shoreline. Water levels decreased landward across the platform with tide ranges at the shoreline being almost 50% lower than at the outer reef flat. Rising and falling tides were characterised by a bimodal energy distribution with both short-period (0–3 s) and wind (3–8 s) waves present. Higher water levels were dominated by wind waves. The highest waves occurred at high tides associated with nocturnal tidal cycles with Hs decreasing from 0.5 to 0.2 m from the outer reef flat to the shoreline. Wave energy at swell (8–20 s) and infragravity (>20 s) frequencies was negligible across the reef platform although there was evidence of wave groups at higher water levels.Reef geometry and changes in water level determine the magnitude of wave energy on the reef platform. Up to 85–95% of incident wave energy is attenuated by the central reef flat depression at high and low tide, respectively, and strong linear relationships exist between Hs and h at all locations. Both wave height and wave type are strongly depth dependent. Critical reef rim depths required to produce Hs of a given size vary spatially across the reef rim due to variations in reef topography. A distinct depth related threshold exists at which short-period and wind wave dominance reverses. Over a 14-day spring-neap tidal cycle, the time of occurrence of wave action diminishes across the reef platform to the shoreline. Larger waves (Hs=0.2 m) occur for only 9% of time at the outer reef flat and for less than 0.5% over the remaining reef platform. This implies that on mesotidal reef platforms, sediment entrainment and transport are severely constrained under normal wave energy conditions and significant change is likely restricted to extreme events.

A washboard with moment of inertia model of gas-surface scattering.

A washboard with moment of inertia (WBMI) model for gas atom scattering from a flexible surface is proposed and applied. This model is a direct extension of the washboard model [J. Chem. Phys. 92, 680 (1990)] proposed for gas atom scattering from relatively rigid, corrugated surfaces. In addition, a moment of inertia is incorporated in the original washboard model to describe the flexibility of softer, more highly corrugated surfaces such as polymer or liquid surfaces. The moment of inertia of the effective surface object introduces a dependence of the efficiency of energy transfer on the position and direction of impact, a feature that has been shown to be critical by molecular dynamics simulations. The WBMI model is solved numerically by Monte Carlo integration, which makes the implementation of multiple impacts between a colliding atom and the surface very efficient. The model is applied to Ne and Ar atoms scattering from an alkylthiolate self-assembled monolayer surface and reproduces the major results obtained by classical trajectory simulation of the same system, i.e., a bimodal translation energy distribution P(E(f)) with the low-energy component well-fit with a Boltzmann distribution, but with a temperature that may (Ar) or may not (Ne) be the same as the surface temperature. This indicates that the WBMI model, with well-motivated physical assumptions and simplified interaction, reveals many of the major aspects of the gas-surface collision dynamics, though it does not take into account the real-time dynamics explicitly.

Determination of the single component and competitive adsorption isotherms of the 1-indanol enantiomers by the inverse method

The inverse method of isotherm determination consists in calculating the numerical values of the coefficients of an isotherm model that give a set of chromatographic profiles in best possible agreement with the set of experimental profiles available. This method was applied to determine the adsorption isotherms of the 1-indanol enantiomers on a cellulose tribenzoate chiral stationary phase. Both single-component and competitive isotherms were determined by using no more than one or two overloaded band profiles. The isotherms determined from the overloaded band profiles agreed extremely well with the isotherms determined by frontal analysis. Several isotherm models were used and tested. The best-fit isotherm was selected by means of statistical evaluation of the results. The results show that the adsorption is best characterized with a model describing heterogeneous adsorption with bimodal adsorption energy distribution.