Average Internal Energy Research Articles

Fragmentation lifetimes and the internal energy of sputtered clusters

We have compared the distribution of internal energies and fragmentation rate constants determined experimentally for sputtered Fe n + cluster ions with theoretical Molecular Dynamics computer simulations. It is found that the experimental data and the simulation are complementary with respect to the fragmentation time scale involved. While the experiment is sensitive to fragmentation times of nanoseconds and above, the simulation can provide information about the time interval ranging from femtoseconds to about one nanosecond. From the experimental data, it is found that the distribution of fragmentation rates as a function of time after the emission of the clusters follows a power law rather than an exponential decay, thus indicating a broad distribution of fragmentation rate constants. From the simulation, we conclude that this dependence continues down into the sub-nanosecond time range with, however, increasing exponent as the times get shorter. Around fragmentation times at or below 10 −12 s, the rate distribution levels off due to a maximum possible rate constant of the order of the vibrational frequency of the cluster. The fragmentation rate constants are connected with the internal energy distribution of the sputtered clusters by means of statistical RRK theory. While the average internal energy determined by experiment and simulation agree quite well, significant differences are found in the width of the respective distributions, the origin of which is attributed to the different times scales explored by both techniques.

Singly- and doubly-negative carbon clusters in sputtering: Energy spectra, abundance distributions and unimolecular fragmentation

The emission of singly- and doubly-charged negative cluster ions in sputtering of graphite by 14.5 keV Cs+ ion bombardment was investigated by mass spectrometry. Specifically, for anionic Cn− (n⩽23) and CsCn− (n⩽11) and dianionic Cn2− (n⩽39) species the emission-energy spectra were recorded and their abundance distributions as a function of cluster size n were determined. The energy spectra provided evidence for cluster decomposition in the ion accelerating region of the spectrometer corresponding to a time scale from some 10−10 s to several 10−8 s. The abundance of these fragment ions are similar to those of the parent ions in terms of the dependence on the size n and their absolute magnitudes converge with increasing cluster size. Due to energetic ejection events, the clusters are sputtered with high internal energies; they cool by unimolecular decomposition. The most probable fragmentation process for Cn− appears to be by evaporation of a neutral C2 molecule. For these decay reactions, the fragmentation-time distributions were derived from the appropriate parts of the energy spectra; they were found to scale exponentially with time. From these data the average lifetimes τ for these unimolecular decompositions were determined. For Cn− the lifetimes slightly increase with n: τ∼8×10−9 s at n=6 to τ∼5×10−8 s at n=25. Similar values are found for CsCn−, whereas for the dianionic clusters Cn2− they are shorter, τ∼(5–7)×10−9 s for n=12–18. Estimates of internal energies, Eint, of sputtered Cn− clusters were derived from these lifetimes, employing statistical theories of unimolecular decomposition; values of Eint increase with cluster size n for 5⩽n⩽25, whereas the average internal energy per constituent atom, Eint/n amounts to ∼1 eV in that range.

Experimental and Monte Carlo Simulation Studies of the Thermodynamics of Polyethyleneglycol Chains Grafted to Lipid Bilayers

Experimental measurements of the affinity of binding of fluorescent acylated polyethyleneglycol (PEG) conjugates to bilayers containing varying levels of phosphatidylethanolamine-PEGs (PE-PEGs) have been combined with Monte Carlo simulations to investigate the properties of the polymer chains at a PEG-grafted lipid interface. The affinity of binding of such conjugates to large unilamellar phosphatidylcholine/phosphatidylethanolamine (9:1) vesicles decreases 27-fold as the size of the coupled PEG chain increases from 1 to 114 monomer units. Incorporation of increasing amounts of PE-PEG2000 or PE-PEG5000 into the vesicles progressively reduces the affinity of binding of acylpeptide-PEG2000 or -PEG5000 conjugates. Monte Carlo simulations of surfaces with grafted PEG chains revealed no significant dependence of several characteristic properties of the polymer chains, including the average internal energy per polymer and the radii of gyration, on the grafting density in the range examined experimentally. The average conformation of a surface-grafted PEG2000 or PEG5000 chain was calculated to be fairly extended even at low grafting densities, and the projected cross-sectional areas of the grafted PEG chains are considerably smaller than those predicted on the basis of the estimated Flory radius. The experimental variation of the binding affinity of acylated conjugates for bilayers containing varying mole fractions of PE-PEG2000 or -PEG5000 is well explained by expressions treating the surface-grafted PEG polymers either as a van der Waals gas or as a system of rigid discs described by scaled particle theory. From the combined results of our experimental and simulation studies we conclude that the grafted PEG chains exist in a “mushroom” regime throughout the range of polymer densities examined experimentally and that the diminished affinity of binding of acylated-PEG conjugates to bilayers containing PE-PEGs results from occlusion of the surface area accessible for conjugate binding by the mobile PE-PEG polymer chains.

Internal energy of sputtered clusters: The influence of bombarding conditions

We have investigated the internal (vibrational) excitation of nascent clusters formed during sputtering of metal surfaces. On one hand, theoretical model calculations were performed by Molecular Dynamics computer simulation using the MD/MC-CEM many body interaction potential. On the other hand, experimental data were collected by studying the fragmentation lifetimes of sputtered cluster ions on time scales of 10−9–10−6 s after their ejection and conversion of the resulting lifetime distributions into the distributions of internal energies. It is found that sputtered clusters possess average internal energies of about 1 eV per constituent atom, corresponding to vibrational temperatures of several thousand K. Special emphasis was put on the influence of the bombarding conditions on these results. Surprisingly, neither the nature or kinetic energy of the primary ions nor the bond strength of the ejected clusters seem to significantly influence the average internal energy.

Ultrafast studies of the photodissociation of the acetone 3s Rydberg state at 195 nm: Formation and unimolecular dissociation of the acetyl radical

Ultrafast deep UV mass-resolved photoionization spectroscopy has been used to investigate the photodissociation dynamics of the 3s Rydberg state of acetone. Single photon excitation at 193–195 nm is followed by single photon (at 260 nm) and two photon (at 390 nm) ionization and the signal is measured for both the acetone and acetyl photoions. The acetone Rydberg state lifetime determined from both single and two photon detection is surprisingly long, 4.7±0.2 ps. The higher probe energy for two photon ionization results in a lower minimum acetyl internal energy for ionization, so that part of the measured signal is due to neutral acetyl dissociation dynamics rather than only dissociative ionization of excited state acetone (which is the case for single photon ionization at 260 nm). The secondary dissociation rate of the neutral acetyl intermediate is measured, clearly establishing that photodissociation via the first Rydberg state of acetone occurs by a sequential dissociation mechanism. The acetyl dissociation occurs with a characteristic time of 3.1±0.5 ps. Based on RRKM (Rice–Ramsperger–Kassel–Marcus) calculations, this suggests an average acetyl internal energy of ∼25 kcal/mole. The long lifetime of the 3s Rydberg state suggests that the dissociation dynamics may be described in terms of a fully statistical dissociation mechanism.

The Melting Phase Transition in Small Carbon Dioxide Clusters

Small isolated carbon dioxide clusters have been studied by canonical and microcanonical Molecular Dynamics simulation. The phenomenon of “dynamical coexistence” between solidlike and liquidlike forms of the (CO2)13 cluster was found, in a finite energy range. An animation of this phenomenon is shown. Coexistence is associated with bimodality in the probability distribution of the short-time averaged internal kinetic energy of the system in the microcanonical ensemble. This phenomenon has also been observed in (CO2)12,14. It is interpreted in terms of the energy distribution of the Potential Energy Surface minima. This statistical mechanics tool enables to understand why dynamical coexistence has also been observed in previous works on (Ar)13 and (N2)13 but not in the case of (Ar)8,14 and (SF6)13.

A Statistical Thermodynamic Model for Studying Energy Band Structure of Semiconductor Heterostructures

Advances in the science and technology of device quality semiconductor microstructures opened new directions in the making of heterojunction devices which are much faster than the conventional silicon devices. In order to fully appreciate the potantial electronic and optoelectronic applications of heterostructures there are material issues that must be fully investigated. One of the most important issues is the understanding and determination of the discontinuity in the energy band structure of the heterostructure at its interface and has received world wide interest among the device physicists and engineers over the three decades [1]. These energy band offsets affect various device properties such as the injection efficiency of heterojunction bipolar transistors (HBTs) and the carrier confinement in the recently developed modulation doped field effect transistors (MODFETs)[2]. A statistical thermodynamic model is presented to study the band offsets and temperature and strain induced nonlinearities in the band structure of lattice matched and pseudomorphic heterostructures. The model uses an average internal reference energy level (obtained using the universal tight bonding theory [3]), at which the bonding (valence-like) and antibonding (conduction-like) states are equal, to define the thermodynamic equilibrium for a heterostructure at any temperature and strain. Use of such internal reference level allows one to incorporate the effects of third nearest neighboor interactions on the band offset calculations. The temperature and strain induced nonlinear effects on the band structure is calculated by using two universal statistical thermodynamic postulates [4]: (i) The free electrons and holes are electrically charged weakly interacting quasi-chemical particles; (ii) The electron-hole pairs are generated by the charge transfer from the bonding (antibonding) states toantibonding (bonding) states in tetrahedrally coordinated semiconductors and semimetals. It is shown that there is a good agreement between the model predictions and experimental data for the band offsets and temperature and pressure induced nonlinearities in the energy bandgaps of lattice matched AlGaAs/GaAs and HgCdTe/CdTe heterostructures for over wide range of temperatures and pressures. It is also shown that in the HgTe/CdTe system, the applied pressure moves up the energy of \Gamma_{6c} antibonding states above the energy of the \Gamma_{8v} bonding states and HgTe becomes a diamond type semiconductor above certain pressure with finite bandgap. Above the transition pressure of 25 Kbar, the band alignment at the HgTe/CdTe interface transforms from type III to conventional type I.

Dynamical effects of reagent vibrational excitation in the Cl + C 2H 6( ν5 = 1) → HCl + C 2H 5 reaction

The title reaction is investigated using a photoinitiated technique that allows for the measurement of HCl product vibrational and rotational distributions using resonance enhanced multiphoton ionization (REMPI), the determination of center-of-mass scattering through core extraction, and the deduction of the average internal energy of the C 2H 5 product from HCl spatial anisotropy. Vibrational excitation of the ethane reagent is shown to produce only a 5% to 10% increase in integral reactivity. Production of forward-scattered HCl ( v = 1) is observed, which is similar to the behavior of the chemically related Cl + CH 4 ( ν 3 = 1) reaction.

Time-resolved photodissociation of p-bromotoluene ion as a probe of ion internal energy

The unimolecular dissociation of the p-bromotoluene radical cation was studied by using Fourier transform ion cyclotron resonance spectrometry. The parent ions were prepared by charge-transfer reactions of toluene- d 8 ions with p-bromotoluene. The toluene- d 8 radical cations were produced by two-photon ionization at 266 nm. The photodissociation was accomplished by 532 nm. The p-bromotoluene ion dissociates to C 7H 7 + with a loss of Br via one- and two-photon processes. The structures of the C 7H 7 + products were identified by ion-molecule reactions. The dissociation rates were measured by time-resolved photo-dissociation (TRPD) spectroscopy. The C 7H 7 + products from one-photon dissociation (1PD) were reactive toward toluene- d 8 and yielded CD 3C 6D 4CH 2 +, indicating the benzyl ion structure. No unreactive tropylium ions were detected from 1PD. The rate constant of 1PD obtained at the internal energy of 2.43 eV was combined with the photoelectron-photoion coincidence data reported in the internal energy range 2.75–3.33 eV to estimate the activation parameters for the lowest barrier process that led to the benzyl ion exclusively. The two-photon dissociation (2PD) resulted in both the benzyl and tropylium ions with the branching ratio, [benzyl +]/[tropylium +] = 92/8. It appears that the tropylium ion results from the isomerization of the p-tolyl ion produced by 2PD via a direct C-Br cleavage. The TRPD spectroscopy was used as a thermometric probe of the average internal energy of the parent ions produced by electron impact. The rates of 1PD were compared as a function of cooling time and pressure to examine the energy cooling processes. The effect of radiative heating of an ICR cell by hot filament on the dissociation rate was also examined.

Dynamics for the Cl+C2H6→HCl+C2H5 reaction examined through state-specific angular distributions

Photolysis of Cl2 initiates the title reaction at a sharply defined collision energy of 0.24±0.03 eV. Nascent product rotational state distributions for HCl (v=0) are determined using resonance enhanced multiphoton ionization (REMPI), center-of-mass scattering distributions are measured by the core-extraction technique, and the average internal energy of the C2H5 product is deduced from the dependence of the core-extracted signal on the photolysis polarization. The HCl product has little rotational excitation, but the scattering distribution is nearly isotropic. Although seemingly contradictory, both of these features can be accounted for by using the simple line-of-centers model presented to explain earlier results for the Cl+CH4 reaction. In contrast to the Cl+CH4 reaction, the data suggest that the Cl+C2H6 reaction proceeds through a loosely constrained transition-state geometry. The reactions of atomic chlorine with ethane, C2H6, and perdeuteroethane, C2D6, yield virtually identical results. These findings, along with the low energy deposited by the reaction into the ethyl product (200±120 cm−1), demonstrate that the alkyl fragment acts largely as a spectator in this hydrogen abstraction reaction.

Thermodynamics of a free SU q(2) fermionic system

We calculate the partition function, average occupation number and internal energy for an SU q (2) fermionic system and compare this model at T = 0 with the ordinary fermionic, q = 1, case. At low temperatures and q ⪢ 1 we find the chemical potential μ to have the same temperature dependence as the Fermi case. For q ⪡ 1, the function μ( T) has in addition a linear dependence on T.

Fragmentation of cluster ions in SIMS: cluster distributions over lifetime, excitation energy and kinetic energy release

Ta n + clusters ( n≤8) have been produced by the sputtering of Xe + ions with energy of 9 keV. For sputtered clusters Ta n + (4≤ n≤8) the lifetime distributions and the internal energy distributions were determined. The average lifetimes and the average internal energies were obtained by the treatment of corresponding experimental distributions. The average internal energy per constituent atom is about ⋍ 1.8 ± 0.3 eV/atom and this value depends weakly on cluster size. The kinetic energy release (KER) distributions of the sputtered fragmented clusters were also measured. Within the framework of Klots's model of “evaporation ensemble” the dissociation energies of Ta n + (4≤ n≤7) clusters have been calculated by using KER-distributions.

Average activation energies of low-energy fragmentation processes of protonated peptides determined by a new approach.

An attempt was made to estimate the average activation energies of low-energy fragmentation processes of protonated oligopeptides by combining RRKM theory and the results of electrospray ionization/surface induced dissociation (ESI/SID). The average internal energy was assumed to be deposited by three processes: thermal energy gained in the heated capillary of the electrospray source, energy gain in the capillary-skimmer region of the electrospray source, and energy deposition by collision with the surface. The latter fraction was calculated based on the position of the ESI/SID fragmentation of efficiency curves and the ratio of kinetic to internal energy conversion in SID. Using the average internal energy estimated from the experimental results, the average activation energies were evaluated by applying RRKM theory. The application of this approach for protonated leucine enkephalin resulted in an average activation energy of 36 +/- 5 kcal/mol for the lowest energy decompositions. The approach has also been applied to several other peptides in the mass range of 200-1200 Da, yielding average activation energies in the range of 35-47 kcal/mol.

Computer simulation of the supercritical carbon dioxide fluid (II) internal energy and structure of carbon dioxide system containing one benzene molecule

Using potential models based on ab initio quantum chemical calculations, we study a supercritical CO 2 fluid containing one benzene molecule using Monte Carlo simulations. First, molecular average internal energy is calculated for the whole system and for the first solvation shell of the benzene molecule. This analysis shows that the CO 2 molecules in the first solvation shell have a large energetic stabilization owing to the shape of the solute. In addition to the stabilization, the solute-solvent interactions in the first solvation shell show large fluctuations for both the in-plane and out-of-plane parts. Secondly, an orientational distribution function is defined to investigate the CO 2 fluid structure. This function indicates that the CO 2CO 2 intermolecular configuration has a large dependence on the temperature of the system for both the whole system, and for the first solvation shell of the solute. Moreover, the benzene molecule is confirmed to control the mutual arrangement between neighboring CO 2 molecules.

Unimolecular Dissociation Kinetics of Benzene Cluster Ions

Abstract The “unimolecular” dissociation processes of benzene cluster ions prepared by resonant 2-photon ionization (R2PI) of neutral clusters were investigated by using a time-of-flight mass spectrometer equipped with a reflectron. The dissociation rates were determined for fast-decay processes (kfast) in the acceleration region and slow dissociations (kslow) in the drift region of the spectrometer. The ejection of one neutral molecule was a dominant dissociation channel of small (C6H6)n+ in the drift region; in addition, the ejection of two molecules was observed for n − 2 ≥ 14. These size-specific dissociation channels and the size dependence of the kslow values imply a closing of the first shell of (C6H6)n+ at n = 14. The magnitude of both kfast and kslowwas found to be independent of the excess energy upon R2PI, suggesting rapid cooling of the nascent hot ions by prompt dissociation within the laser focus. For slow dissociation within a well-defined time window, the measured values of kslow were compared with those calculated according to a statistical theory of unimolecular reaction. The comparison deduced the average internal energies of (C6H6)n+ at ca. 1 μs after preparation.

Evolution of ion internal energy during collisional excitation in the Paul ion trap: A stochastic approach

A first-order model is developed for collisional activation as effected via resonance excitation and helium buffer gas in the Paul ion trap. For an ion population at steady-state under specified experimental conditions, the kinetic theory of ion transport in gases is first used to calculate an effective temperature shown to be identical to the internal temperature for molecular ions in an atomic gas. The evolution of the ion internal energy is then followed by a random walk simulation designed to be representative of the actual collisional energy transfer process, except ion losses due to dissociation and reactive processes during collisional activation are excluded. During the simulation, inelastic ion-neutral collisions increase the average ion internal energy via small energy changes (both positive and negative) until a steady-state condition is reached in which excitation and deexcitation processes are balanced. Histogramming the simulated data reveals a Boltzmann-type internal energy distribution whose average internal energy is the same as that calculated for a true Boltzmann distribution at the same internal temperature.

Collisional Deactivation of CDCl3 Excited with a TEA CO2 Laser

The decay of infrared fluorescence from IR multiphoton excited CDCl3 was studied as a function of incident fluence and pressure of added Ar. The decays were exponential and allowed for the calculation of the average energy transferred per collision, 〈〈ΔE〉〉, with Ar and with CDCl3, as a function of the average internal energy of excited CDCl3 using a direct method. Identical information was obtained following the inversion procedure developed by Barker et al. (Int. Rev. Phys. Chem. 1993, 12, 2, 305). Both sets of values agree well for a single value of the internal energy. The experimental results were also modeled using a master equation formulation to obtain 〈ΔE〉d, confirming the predictive power of the model calculations. The increase of temperature of the gas mixture and its effect on the IR fluorescence signal were also analyzed.

Direct variational solutions to the Grad-Schluter-Shafranov equation

A direct variational method based on an energy principle is applied to obtain approximate magnetohydrodynamic equilibria for tokamak plasmas. The geometry of the nested magnetic flux surfaces is specified by a model that includes displacement, elongation and triangularity effects. The radial dependence in flux coordinates is described by a consistent set of trial functions which allows analytical calculation of the flux-surface averaged internal energy density of the plasma. Approximate solutions of the variational problem are obtained for arbitrary aspect-ratio tokamaks using a one-parameter optimization procedure.

Reaction window in the single-electron capture by ammonia dications

Single-electron capture (SEC) by NH32+ with rare gases (He, Ne, Ar, Kr, Xe) and benzene, NH32+ + G → NH3+ + G+, has been investigated using a forward geometry double-focusing mass spectrometer. The SEC cross-section goes through a maximum within a reaction window centered at an exothermicity of approximately 4.5 eV. This correspondes to a target-projectile distance for the charge transfer of about 3.2 Å. The average internal energy of NH3+-ions resulting from SEC has been obtained both via translational energy gain measurements and via an analysis of the daughter ion spectra. The agreement between both methods is satisfactory and shows that the lower the ionization energy of the target, the more probable the excitation of NH3+ to the à 2E state. With benzene (ionization energy = 9.25 eV) as the target gas, however, the excess energy is converted partly to internal energy of C6H6+, leading most probably to the D̃ 2B2u, Ẽ 2B1u and F̃ 2A1g states of C6H6+. A model based on the Landau-Zener non-adiabatic formalism, including one entrance channel (NH32+ + G) and two exit channels (NH3+ X̃ 2A2″ + G+ and NH3+ à 2E + G+) accounts qualitatively for the observed results in the case of exothermic single-electron capture. This model is not appropriate for slightly exothermic or endothermic charge transfer, i.e., in the present case, for the Ne and He target gases.

Internal energy distribution of benzene molecular ions in surface‐induced dissociation

AbstractThe so‐called ‘deconvolution’ method has been used to determine the internal energy distribution of molecular ions of an organic compound, benzene, excited by collisions with self‐assembled monolayer surfaces formed on gold. The average internal energy was found to increase linearly with the laboratory collision energy. The kinetic energy–internal energy (T–V) conversion was 17% for the octadecanethiolate monolayer and 28% for the 2‐(perfluorooctyl)‐ethanethiolate monolayer surface. The results are similar to those obtained for metal carbonyl projectiles, though they indicate somewhat higher energy conversion. In addition, excitation of the projectile ion well beyond 20 eV internal energy is observed.