On the shattering of clusters by surface impact heating

Impact of composite soft-rigid elastic projectiles: A numerical study

We study by numerical simulation the impact of a one-dimensional composite projectile, composed of two superposed homogeneous parts, on an infinitely rigid and massive wall. The coefficient of restitution and the contact time are systematically measured as functions of the contrasts of mass and stiffness between the two parts. For purely elastic parts, these quantities show complex trends associated with different dynamics of the deformation waves propagating inside the projectile. A significant portion of the initial kinetic energy can be trapped in the deformation modes: the coefficient of restitution is lowest, about 0.2, when there is a strong stiffness contrast between the two parts and the stiff and soft parts are at the leading and trailing edges of the projectile respectively. In this case, we highlight the presence of multiple bounces, whose number increases as the proportion of the soft part increases. Finally, viscoelastic parts can be implemented in the same numerical framework to successfully recover the results obtained in real composite projectile impact experiments [D'Angelo et al., Phys. Rev. E 103, 053005 (2021)2470-004510.1103/PhysRevE.103.053005].

Impact dynamics of composite elastorigid projectiles onto solid surfaces

We investigate the impact of composite objects. They consist of a soft layer on top of a rigid part with a hemispherical impacting end. The coefficient of restitution (e) of such objects is studied systematically as a function of the mass ratio and of the nature of the materials. For rather elastic materials, the coefficient of restitution is a nonmonotonic function of the mass ratio and exhibits important variations. The dynamics of the impact can be characterized by several bounces depending on the ratios between the four timescales at play. These include the duration of contact of the rigid part with the substrate and the time for the elastic waves to travel back and forth in the soft layer. In that sense, describing these projectiles requires one to take into account both the Hertzian theory of contact and the elastic waves described by Saint-Venant's approach.

Experimental and theoretical investigation of overall energy deposition in surface-induced unfolding of protein ions

Recent advances in native mass spectrometry have enabled its use to probe the structure of and interactions within biomolecular complexes. Surface-induced dissociation, in which inter- and intramolecular interactions are disrupted following an energetic ion-surface collision, is a method that can directly interrogate the topology of protein complexes. However, a quantitative relationship between the ion kinetic energy at the moment of surface collision and the internal energy deposited into the ion has not yet been established for proteins. The factors affecting energy deposition in surface-induced unfolding (SIU) of protein monomers were investigated and a calibration relating laboratory-frame kinetic energy to internal energy developed. Protein monomers were unfolded by SIU and by collision-induced unfolding (CIU). CIU and SIU cause proteins to undergo the same unfolding transitions at different values of laboratory-frame kinetic energy. There is a strong correlation between the SIU and CIU energies, demonstrating that SIU, like CIU, can largely be understood as a thermal process. The change in internal energy in CIU was modeled using a Monte Carlo approach and theory. Computed values of the overall efficiency were found to be approximately 25% and used to rescale the CIU energy axis and relate nominal SIU energies to internal energy. The energy deposition efficiency in SIU increases with mass and kinetic energy from a low of ∼20% to a high of ∼68%, indicating that the effective mass of the surface increases along with the mass of the ion. The effect of ion structure on energy deposition was probed using multiple stages of ion activation. Energy deposition in SIU strongly depends on structure, decreasing as the protein is elongated, due to decreased effective protein-surface collisional cross section and increased transfer to rotational modes.

Ghost peaks observed after atmospheric pressure matrix-assisted laser desorption/ionization experiments may disclose new ionization mechanism of matrix-assisted hypersonic velocity impact ionization

RATIONALE

Understanding the mechanisms of matrix-assisted laser desorption/ionization (MALDI) promises improvements in the sensitivity and specificity of many established applications in the field of mass spectrometry. This paper reports a serendipitous observation of a significant ion yield in a post-ionization experiment conducted after the sample had been removed from a standard atmospheric pressure (AP)-MALDI source. This post-ionization is interpreted in terms of collisions of microparticles moving with a hypersonic velocity into a solid surface. Calculations show that the thermal energy released during such collisions is close to that absorbed by the top matrix layer in traditional MALDI. The microparticles, containing both the matrix and analytes, could be detached from a film produced inside the inlet capillary during the sample ablation and accelerated by the flow rushing through the capillary. These observations contribute some new perspective to ion formation in both laser and laser-less matrix-assisted ionization.

METHODS

An AP-MALDI ion source hyphenated with a three-stage high-pressure ion funnel system was utilized for peptide mass analysis. After the laser had been turned off and the MALDI sample removed, ions were detected during a gradual reduction of the background pressure in the first funnel. The constant-rate pressure reduction led to the reproducible appearance of different singly and doubly charged peptide peaks in mass spectra taken a few seconds after the end of the MALDI analysis of a dried-droplet spot.

RESULTS

The ion yield as well as the mass range of ions observed with a significant delay after a completion of the primary MALDI analysis depended primarily on the background pressure inside the first funnel. The production of ions in this post-ionization step was exclusively observed during the pressure drop. A lower matrix background and significant increase in relative yield of double-protonated ions are reported.

CONCLUSIONS

The observations were partially consistent with a model of the supersonic jet from the inlet capillary accelerating detached particles to kinetic energies suitable for matrix-assisted hypersonic-velocity impact ionization.

Tandem mass spectrometry in an electrostatic linear ion trap modified for surface-induced dissociation

A variety of ion traps are used in mass spectrometry. A key feature shared by most of them is the ability to perform tandem mass spectrometry (MS/MS). The Orbitrap is perhaps the most notable ion trap in which MS/MS has yet to be performed. An electrostatic linear ion trap (ELIT) is analogous to an orbitrap in that ions are trapped using solely electrostatic fields. However, the relatively simple ion motion within an ELIT facilitates analysis of fragment ions produced within the device. In this report, we describe an ELIT to which we have added a target for surface induced dissociation (SID). When combined with our previously described method for isolating a precursor ion trapped in an ELIT,1 this apparatus enables MS/MS to be performed. Measurement of product ion m/z is facilitated by the fact that the ELIT is isochronous over the energy range of 1850-2000 eV so that changes to ion energy during SID do not cause major m/z shifts. We demonstrate MS/MS by isolating and dissociating each compound in a four component mixture of tetraalkylphosphonium cations. We also discuss the optimization of collision energy and the length of time that the SID target is available for collision, two parameters that are important in the performance of these experiments.

Collision induced dissociation of doubly-charged ions: Coulomb explosion vs. neutral loss in [Ca(urea)]2+ gas phase unimolecular reactivity via chemical dynamics simulations

In this paper we report different theoretical approaches to study the gas-phase unimolecular dissociation of the doubly-charged cation [Ca(urea)](2+), in order to rationalize recent experimental findings. Quantum mechanical plus molecular mechanical (QM/MM) direct chemical dynamics simulations were used to investigate collision induced dissociation (CID) and rotational-vibrational energy transfer for Ar + [Ca(urea)](2+) collisions. For the picosecond time-domain of the simulations, both neutral loss and Coulomb explosion reactions were found and the differences in their mechanisms elucidated. The loss of neutral urea subsequent to collision with Ar occurs via a shattering mechanism, while the formation of two singly-charged cations follows statistical (or almost statistical) dynamics. Vibrational-rotational energy transfer efficiencies obtained for trajectories that do not dissociate during the trajectory integration were used in conjunction with RRKM rate constants to approximate dissociation pathways assuming complete intramolecular vibrational energy redistribution (IVR) and statistical dynamics. This statistical limit predicts, as expected, that at long time the most stable species on the potential energy surface (PES) dominate. These results, coupled with experimental CID from which both neutral loss and Coulomb explosion products were obtained, show that the gas phase dissociation of this ion occurs by multiple mechanisms leading to different products and that reactivity on the complicated PES is dynamically complex.

A comparative study of cluster-surface collisions: Molecular-dynamics simulations of (H2O)1000 and (SO2)1000

A classical molecular-dynamics study of (H2O)1000 and (SO2)1000 clusters impacting with velocities between 6 x 10(2) and 8 x 10(3) ms at normal incidence on a repulsive target is presented. Using the ratio of total kinetic energy to total binding energy of the cluster as a scaling parameter, a general description of the fragmentation dynamics as well as the final fragment size distributions is achieved for the different systems. With increasing ratio, the angular distribution of the emitted monomers rapidly shifts from isotropic to anisotropic. At the highest investigated velocities, a tendency to recover more isotropic distributions is observed. Comparable transient compression of the impacting cluster is reached, on the other hand, for the same, unscaled collision velocities in both systems. For both H2O and SO2 the obtained internal temperatures of the cluster fragments are found to be independent of impact energy and close to the boiling temperature of the respective systems.

Mechanical Simulation of the Pressure and the Relaxation to Thermal Equilibrium of a Hot and Dense Rare Gas Cluster

A cold atomic cluster can be very rapidly heated and compressed by a hypersonic impact at a hard surface. The impact can be simulated by computing a classical trajectory for the motion of the atoms. By suddenly confining the hot and dense cluster within a rigid container, it is possible to monitor the time evolution of the force acting on the faces of the container. It is found that the pressure computed this way very rapidly decays to a time-independent value. After a somewhat longer time, this value reproduces the value for the pressure computed as the sum of the kinetic and internal pressures. This agreement is expected for a system in equilibrium. These observations support the conclusion that there is a fast relaxation to thermal equilibrium in these essentially hard-sphere systems. The deviation from equilibrium is primarily due to the propagation of shock waves within the cluster. The equilibrium pressure can reach up to the megabar range.

Activation of large ions in FT-ICR mass spectrometry

The advent of soft ionization techniques, notably electrospray and laser desorption ionization methods, has enabled the extension of mass spectrometric methods to large molecules and molecular complexes. This both greatly extends the applications of mass spectrometry and makes the activation and dissociation of complex ions an integral part of these applications. This review emphasizes the most promising methods for activation and dissociation of complex ions and presents this discussion in the context of general knowledge of reaction kinetics and dynamics largely established for small ions. We then introduce the characteristic differences associated with the higher number of internal degrees of freedom and high density of states associated with molecular complexity. This is reflected primarily in the kinetics of unimolecular dissociation of complex ions, particularly their slow decay and the higher energy content required to induce decomposition--the kinetic shift (KS). The longer trapping time of Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) significantly reduces the KS, which presents several advantages over other methods for the investigation of dissociation of complex molecules. After discussing general principles of reaction dynamics related to collisional activation of ions, we describe conventional ways to achieve single- and multiple-collision activation in FT-ICR MS. Sustained off-resonance irradiation (SORI)--the simplest and most robust means of introducing the multiple collision activation process--is discussed in greatest detail. Details of implementation of this technique, required control of experimental parameters, limitations, and examples of very successful application of SORI-CID are described. The advantages of high mass resolving power and the ability to carry out several stages of mass selection and activation intrinsic to FT-ICR MS are demonstrated in several examples. Photodissociation of ions from small molecules can be effected using IR or UV/vis lasers and generally requires tuning lasers to specific wavelengths and/or utilizing high flux, multiphoton excitation to match energy levels in the ion. Photodissociation of complex ions is much easier to accomplish from the basic physics perspective. The quasi-continuum of vibrational states at room temperature makes it very easy to pump relatively large amounts of energy into complex ions and infrared multiphoton dissociation (IRMPD) is a powerful technique for characterizing large ions, particularly biologically relevant molecules. Since both SORI-CID and IRMPD are slow activation methods they have many common characteristics. They are also distinctly different because SORI-CID is intrinsically selective (only ions that have a cyclotron frequency close to the frequency of the excitation field are excited), whereas IRMPD is not (all ions that reside on the optical path of the laser are excited). There are advantages and disadvantages to each technique and in many applications they complement each other. In contrast with these slow activation methods, the less widely appreciated activation method of surface induced dissociation (SID) appears to offer unique advantages because excitation in SID occurs on a sub-picosecond time scale, instantaneously relative to the observation time of any mass spectrometer. Internal energy deposition is quite efficient and readily adjusted by altering the kinetic energy of the impacting ion. The shattering transition--instantaneous decomposition of the ion on the surface--observed at high collision energies enables access to dissociation channels that are not accessible using SORI-CID or IRMPD. Finally, we discuss some approaches for tailoring the surface to achieve particular aims in SID.

Surface-induced dissociation of peptide ions: kinetics and dynamics

Kinetics and dynamics studies have been carried out for the surface-induced dissociation (SID) of a set of model peptides utilizing a specially designed electrospray ionization Fourier Transform ion cyclotron resonance mass spectrometer in which mass-selected and vibrationally relaxed ions are collided on a orthogonally-mounted fluorinated self-assembled monolayer on Au [111] crystal. The sampling time in this apparatus can be varied from hundreds of microseconds to tens of seconds, enabling the investigation of kinetics of ion decomposition over an extended range of decomposition rates. RRKM-based modeling of these reactions for a set of polyalanines demonstrates that SID kinetics of these simple peptides is very similar to slow, multiple-collision activation and that the distribution of internal energies following collisional activation is indistinguishable from a thermal distribution. For more complex peptides comprised of several amino acids and with internal degrees of freedom (DOF) of the order of 350 there is a dramatic change in kinetics in which RRKM kinetics is no longer capable of describing the decomposition of these complex ions. A combination of RRKM kinetics and the "sudden death" approximation, according to which decomposition occurs instantaneously, is a satisfactory description. This implies that a population of ions-which is dependant on the nature of the peptide, kinetic energy and sampling time-decomposes on or very near the surface. The shattering transition is described quantitatively for the limited set of molecules examined to date.

Direct dynamics study of N-protonated diglycine surface-induced dissociation. Influence of collision energy

A quantum mechanical and molecular mechanical (QM + MM) direct dynamics classical trajectory simulation is used to study energy transfer and fragmentation in the surface-induced dissociation (SID) of N-protonated diglycine, (gly)2H+. The peptide ion collides with the hydrogenated diamond [111] surface. The Austin Model 1 (AM1) semiempirical electronic structure theory is used for the (gly)2H+ intramolecular potential and molecular mechanical functions are used for the diamond surface potential and peptide/surface intermolecular potential. The simulations are performed at collision energies Ei of 30, 50, 70, and 100 eV and collision angle of 0 degrees (perpendicular to the surface). The percent energy transfer to the peptide ion is nearly independent of Ei, while energy transfer to the surface increases with increase in Ei. A smaller percent of the energy remains in peptide translation as Ei is increased. These trends in energy transfer are consistent with previous trajectory simulations of SID. At each Ei the most likely initial pathway leading to fragmentation is rupture of the +H3NCH2-CONHCH2COOH bond. Fragmentation occurs by two general mechanisms. One is the traditional Rice-Ramsperger-Kassel-Marcus (RRKM) model in which the peptide ion is activated by its collision with the surface, "bounces off", and then dissociates after undergoing intramolecular vibrational energy redistribution (IVR). The other mechanism is shattering in which the ion fragments as it collides with the surface. Shattering is the origin of the large increase in number of product channels with increase in Ei, i.e., 6 at 30 eV, but 59 at 100 eV. Shattering becomes the dominant dissociation mechanism at high Ei.

Collisional activation of peptide ions in FT-ICR mass spectrometry

In the last decade, the characterization of complex molecules, particularly biomolecules, became a focus of fundamental and applied research in mass spectrometry. Most of these studies utilize tandem mass spectrometry (MS/MS) to obtain structural information for complex molecules. Tandem mass spectrometry (MS/MS) typically involves the mass selection of a primary ion, its activation by collision or photon excitation, unimolecular decay into fragment ions characteristic of the ion structure and its internal excitation, and mass analysis of the fragment ions. Although the fundamental principles of tandem mass spectrometry of relatively small molecules are fairly well-understood, our understanding of the activation and fragmentation of large molecules is much more primitive. For small ions, a single energetic collision is sufficient to dissociate the ion; however, this is not the case for complex molecules. For large ions, two fundamental limits severely constrain fragmentation in tandem mass spectrometry. First, the center-of-mass collision energy-the absolute upper limit of energy transfer in a collision process-decreases with increasing mass of the projectile ion for fixed ion kinetic energy and neutral mass. Secondly, the dramatic increase in density of states with increasing internal degrees of freedom of the ion decreases the rate of dissociation by many orders of magnitude at a given internal energy. Consequently, most practical MS/MS experiments with complex ions involve multiple-collision activation (MCA-CID), multi-photon activation, or surface-induced dissociation (SID). This review is focused on what has been learned in recent research studies concerned with fundamental aspects of MCA-CID and SID of model peptides, with an emphasis on experiments carried out with Fourier transform ion cyclotron resonance mass spectrometers (FT-ICR MS). These studies provide the first quantitative comparison of gas-phase multiple-collision activation and SID of peptide ions. Combining collisional energy-resolved data with RRKM-based modeling revealed the effect of peptide size and identity on energy transfer in collisions-very important characteristics of ion activation from fundamental and the analytical perspectives. Finally, the combination of FT-ICR with SID was utilized to carry out the first time-resolved experiments that examine the kinetics of peptide fragmentation. This has lead to the discovery that the time-dependence of ion dissociation varies smoothly up to a certain collision energy, and then shifts dramatically to a time-independent, extensive dissociation. This near-instantaneous "shattering" of the ion generates a large number of relatively small fragment ions. Shattering of ions on surfaces opens up a variety of dissociation pathways that are not accessible with multiple-collision and multiphoton excitation.

Shattering of Peptide ions on self-assembled monolayer surfaces

Time- and collision energy-resolved surface-induced dissociation (SID) of des-Arg(1)- and des-Arg(9)-bradykinin on a fluorinated self-assembled monolayer (SAM) surface was studied by use of a novel Fourier transform ion cyclotron resonance mass spectrometer (FT-ICR MS) specially equipped to perform SID experiments. Time-resolved fragmentation efficiency curves (TFECs) were modeled by an RRKM-based approach developed in our laboratory that utilizes a very flexible analytical expression for the internal energy deposition function capable of reproducing both single- and multiple-collision activation in the gas phase and excitation by collisions with a surface. Both experimental observations and modeling establish a very sharp transition in the dynamics of ion-surface interaction: the shattering transition. The experimental signature for this transition is the appearance of prompt (time-independent) fragmentation, which becomes dominant at high collision energies. Shattering opens a variety of dissociation pathways that are not accessible to slow collisional and thermal ion activation. This results in much better sequence coverage for the singly protonated peptides than dissociation patterns obtained with any of the slow activation methods. Modeling demonstrated that, for short reaction delays, dissociation of these peptides is solely determined by shattering. Internal energies required for shattering transition are approximately the same for des-Arg(1) and des-Arg(9)-bradykinin, resulting in the overlap of fragmentation efficiency curves obtained at short reaction delays. At longer delay times, parent ions depletion is mainly determined by a slow decay rate and fragmentation efficiency curves for des-Arg(1) and des-Arg(9)-bradykinin diverge. Dissociation thresholds of 1.17 and 1.09 eV and activation entropies of -22.2 and -23.3 cal/(mol K) were obtained for des-Arg(1) and des-Arg(9)-bradykinin from RRKM modeling of time-resolved data. Dissociation parameters for des-Arg(1)-bradykinin are in good agreement with parameters derived from thermal experiments. However, there is a significant discrepancy between the thermal data and dissociation parameters for des-Arg(9)-bradykinin obtained in this study. The difference is attributed to the differences in conformations that undergo thermal activation and activation by ion-surface collisions prior to dissociation.

Trapping, reflection, and fragmentation in a classical model of atom-lattice collisions

A classical one-dimensional model of the collision of an atom of mass M with a cold, semi-infinite harmonic lattice comprised of identical atoms of mass m is considered. In the model, the interactions between the incident atom (adatom) and the lattice are described in terms of a truncated parabolic potential by which the adatom is harmonically bound to the lattice at short distances but evolves freely when its distance is larger than a critical length R(c). The dynamics of the adatom colliding with an infinitely cold lattice is studied as a function of the initial velocity of the adatom. In order to determine whether the colliding atom is bound or reflected from the lattice in the asymptotic time limit, "secondary" collision events in which the incident atom leaves and reenters the interaction zone of the lattice are carefully considered. It is demonstrated that secondary collisions anticipated to be important for heavy adatoms (mu=m/M<1) also occur in the case of light adatoms (mu > or = 1). It is shown that the neglect of secondary collisions leads to an underestimation of the lower energy bound for adatom reflection of roughly 10% for mu close to 1. By generalizing the model to allow for the breaking of lattice bonds, the phenomenon of collision-induced lattice fragmentation is investigated.

Coefficient of restitution for one-dimensional harmonic solids

Using a numerical algorithm based on the time evolution of normal modes, we calculate the coefficient of restitution eta for various one-dimensional harmonic solids colliding with a hard wall. We find that, for a homogeneous chain, eta=1 in the thermodynamic limit. However, for a chain in which weaker springs are introduced in the colliding front half, eta remains significantly less than one even in the thermodynamic limit, and the "lost" energy goes mostly into low frequency normal modes. An understanding of these results is given in terms of how the energy is redistributed among the normal modes as the chain collides with the wall. We then contrast these results with those for collisions of one-dimensional harmonic solids with a soft wall. Using perturbation theory, we find that eta=1 for all harmonic chains in the extremely soft wall limit, but that inelasticity grows with increasing chain size in contrast to hard wall collisions.