Classical molecular dynamics simulations of fusion and fragmentation in fullerene-fullerene collisions
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Classical molecular dynamics simulations of fusion andfragmentation in fullerene–fullerene collisions
Alexey Verkhovtsev , , a b , Andrei V. Korol , and Andrey V. Solov’yov , c MBN Research Center, Altenh¨oferallee 3, 60438 Frankfurt am Main, Germany Instituto de F´ısica Fundamental, CSIC, Serrano 113-bis, 28006 Madrid, Spainthe date of receipt and acceptance should be inserted later
Abstract
We present the results of classical molecular dynamics simulations of collision-induced fusionand fragmentation of C fullerenes, performed by means of the MBN Explorer software package. Thesimulations provide information on structural differences of the fused compound depending on kinematicsof the collision process. The analysis of fragmentation dynamics at different initial conditions shows thatthe size distributions of produced molecular fragments are peaked for dimers, which is in agreement witha well-established mechanism of C fragmentation via preferential C emission. Atomic trajectories of thecolliding particles are analyzed and different fragmentation patterns are observed and discussed. On thebasis of the performed simulations, characteristic time of C emission is estimated as a function of collisionenergy. The results are compared with experimental time-of-flight distributions of molecular fragmentsand with earlier theoretical studies. Considering the widely explored case study of C –C collisions, wedemonstrate broad capabilities of the MBN Explorer software, which can be utilized for studying collisionsof a broad variety of nanoscale and biomolecular systems by means of classical molecular dynamics. Recent years have witnessed extensive development of ex-perimental and theoretical methods for the analysis ofstructure and dynamics of Meso-Bio-Nano (MBN) sys-tems. Irradiation and collision experiments have become afrequently used tool to explore the internal structure anddynamical properties of such diverse systems. As a result,a number of processes occurring in collisions of atoms,ions and atomic clusters with complex molecular targets,biomolecules included, have been studied [1–3].Particular attention has been devoted to the investi-gation of irradiation- and collision-induced processes in-volving carbon fullerenes, including electron capture andionization of C [4–6]; fusion and fragmentation of C induced by ion impact [7–11] or collisions with surfaces[12, 13]; fusion, fragmentation and charge transfer inducedby fullerene–fullerene collisions [14–21]; fission of C irra-diated with short intense laser pulses [22], and the forma-tion of collective electron excitations due to photon [23–25], electron [26–28] and ion [29, 30] impact.Recent advances in the understanding of ion/atom in-teractions with isolated polycyclic aromatic hydrocarbons(PAHs), fullerenes and their clusters were discussed in a a e-mail: [email protected] b On leave from A. F. Ioffe Physical-Technical Institute,194021 St. Petersburg, Russia c On leave from A. F. Ioffe Physical-Technical Institute,194021 St. Petersburg, Russia recent review [31]. Apart from well-known statistical frag-mentation of carbon systems leading to evaporation of C dimers, specific non-statistical fragmentation channels re-sulting in a prompt single-atom atom knockout have beenobserved [32–37].A considerable progress has also been achieved in ex-perimental studies of collision-induced processes involvingbiomolecular systems. The latter targets were consideredeither in form of isolated biomolecules in the gas phaseor as clusters containing up to several tens of molecules.The biomolecular targets have been characterized by anincreasing complexity, starting from water molecules andgoing to nucleobases, nucleosides and nucleotides, aminoacids and protein segments [38–40]. Most of the experi-ments performed dealt with protons or multiply chargedions of carbon and oxygen, i.e. the projectiles which areof current interest for ion-beam cancer therapy [41, 42].The amount of accumulated experimental data on col-lision of atoms, ions and atomic clusters with MBN sys-tems generally exceeds the corresponding outcomes of the-oretical and/or numerical analysis. To a great extent, thisdisbalance can be attributed to the problems in finding ef-ficient theoretical and computational methods which allowone to accurately describe the collision-induced dynamicsin large molecular systems with many internal degrees offreedom. It is therefore highly desirable to develop a singletheoretical and computational tool for modeling collision-induced processes involving different nanoscale systems.This has become possible with the development of MBN Verkhovtsev, Korol, and Solov’yov: Classical MD simulations of fusion and fragmentation of fullerenes
Explorer software package [43, 44]. The software supportsthe most advanced molecular dynamics (MD) simulationsfor a large variety of complex molecular systems. Withthese methods, one can simulate and study many differentdynamical processes that occur in molecular systems, in-cluding different collision and collision-induced processes.By randomizing the initial conditions and carrying outmultiple MD simulations, one can generate sets of datafor the statistical analysis of the outcome of the collisionprocess. This approach can be used, for example, for car-rying out the analysis of mass-spectra of the resulting frag-ments appearing in the course of collision. Apart from thestatistical analysis, MD simulations allow one to visual-ize resulting atomic trajectories and explore the temporalevolution of different molecular fragments.A large number of force fields supported by MBN Ex-plorer, together with its flexible and efficient MD algo-rithms, allow one to model collision-induced dynamics ofthe ionic subsystem of the colliding complexes of varioustypes and internal structures, in broad range of collisionenergies, and in various environmental and thermodynam-ical conditions. The important general feature of collisionsinvolving MBN systems arising from the fact that theycan be characterized not only by the collision energy, butalso by temperature. The colliding systems can be pre-equilibrated at a given temperature and then the kineticenergy of the colliding objects can be fixed at some desir-able value. During the collision, part of the kinetic energycan be transferred to the internal degrees of freedom ofthe colliding systems and be equilibrated there. As a re-sult, they may change their temperature, which may leadto the alteration of their internal structure, as well as toevaporation, fragmentation and multi-fragmentation pro-cesses.In this paper, we study collision-induced fusion andfragmentation of C fullerenes by means of classical MDsimulations performed with MBN Explorer [43]. C –C collisions have been widely studied experimentally, andthere are data on the probability of fullerene fusion and onthe production of smaller clusters due to subsequent frag-mentation [14, 16, 45]. By considering this widely exploredcase study, we aim to demonstrate the main capabilitiesof the software that is suitable for studying collisions of abroad variety of MBN systems. The analysis of fragmenta-tion dynamics shows that the size distributions of molecu-lar fragments produced are peaked for dimers, reflecting awell-established preferential C emission. Apart from that,the simulations provide information on structural aspectsof the fused compound at different kinematic conditionsof the collision. Finally, the atomic trajectories of the col-liding particles are analyzed to explore the dynamics ofthe collision events. On the basis of the performed sim-ulations, characteristic time of C emission is estimatedas a function of collision energy. The results are comparedwith experimental time-of-flight distributions of molecularfragments and with earlier theoretical studies. MD simulations have been performed for the microcanon-ical (
N V E ) ensemble of particles, where the number ofparticles N , the volume V , and the total energy E of thesystem were kept constant. Integration of Newton’s equa-tions of motion was done using the velocity Verlet algo-rithm. To assure conservation of the total energy, we useda small integration time step δt = 0 . × ×
300 ˚A simulation box and were separated by the distance of50 ˚A at the initial time moment. The large size of thesimulation box was chosen to decrease the probability ofinteraction between small molecular fragments producedafter the collision. The simulations were performed for sev-eral collision energies and for different values of the impactparameter. The center-of-mass collision energy was var-ied from 30 eV (corresponding to collision velocity v =40 ˚A/ps) up to about 370 eV ( v = 140 ˚A/ps). We con-sidered 15 values of the impact parameter, ranging from0 ˚A (coaxial binary collision) up to 7 ˚A, which is approxi-mately equal to the diameter of C (gliding collision).In order to reflect the statistical nature of the fusionand fragmentation processes, we performed 2000 simula-tions (80 simulations for a given collision energy with dif-ferent values of the impact parameter). The simulationtime for each run was 10 ps that is of the same order ofmagnitude as in many previous computational studies offullerene fusion and fragmentation performed by means ofclassical and quantum MD simulations [13, 46–51]. In eachsimulation run, the fullerenes were randomly oriented withrespect to each other. The input geometries were set up bymeans of MBN Studio [52, 53] – a graphical user interfaceto MBN Explorer. The quantitative information on timeevolution of the fragments produced (i.e., the number offragments of each type) has been obtained directly fromthe output of the simulations. For each collision energy,ensemble-averaged fragment size distribution was calcu-lated by summing up the data from each individual tra-jectory and normalizing the resulting value to the totalnumber of fragments.We employed the Brenner (reactive empirical bond-order, REBO) potential for carbon systems [54]. It is amany-body potential which depends on the number ofnearest neighbors and contains two-body and angle-depen-dent three-body contributions. The Brenner potential, al-ongside with a similar many-body potential developed byTersoff [55], has been widely used for studying stabilityand structural properties of many carbon systems, includ-ing fullerenes [47, 56–58] and nanotubes [59–62]. Recently,these potentials were also utilized to study single and mul-tiple atom knockouts from PAHs, fullerenes and their clus-ters (see Ref. [31] and references therein).The total potential energy of a system in the Brennerpotential framework reads as U tot = 12 X i X i = j f c ( r ij ) [ U R ( r ij ) − b ij U A ( r ij )] , (1) erkhovtsev, Korol, and Solov’yov: Classical MD simulations of fusion and fragmentation of fullerenes 3 where r ij is the distance between atoms i and j , and f c ( r ij ) is the cutoff function which limits the interactionof an atom to its nearest neighbors. It is defined as f c ( r ij ) = , r ij ≤ R
12 + 12 cos (cid:18) π r ij − R R − R (cid:19) , R < r ij ≤ R , r ij > R (2)with R , being the parameters which determine the rangeof the potential. This function has a continuous value andderivative for all r ij , and goes from 1 to 0 in a small re-gion between R and R , which are chosen to restrict thepotential to nearest neighbors.The functions U R ( r ij ) and U A ( r ij ) are the repulsiveand attractive terms of the potential, respectively. Theyare defined as U R ( r ij ) = D e S − h −√ S β ( r ij − R e ) i U A ( r ij ) = D e SS − " − r S β ( r ij − R e ) , (3)where D e , S , β and R e are parameters.The factor b ij in Eq. (1) is the so-called bond orderterm, which is defined as: b ij = X k = i,j f c ( r ik ) g ( θ ijk ) − δ . (4)Here, the function g ( θ ijk ) depends on the angle θ ijk be-tween bonds formed by pairs of atoms ( i, j ) and ( i, k ).This function has the following form: g ( θ ijk ) = a (cid:20) c d − c d + (1 + cos θ ijk ) (cid:21) , (5)where a , c and d are parameters of the potential.The utilized parameters of the Brenner potential arelisted in Table 1. Table 1.
Parameters of the Brenner [54] potential usedin the calculations. D e (eV) 6.325 a R e (˚A) 1.315 c S d β (˚A − ) 1.5 R (˚A) 1.7 δ R (˚A) 2.0 Let us now quantify the fusion and fragmentation prod-ucts resulting from the collision of two C fullerenes atdifferent collision velocities and impact parameters. In this Figure 1.
The average size of molecular products pro-duced in C -C collisions as a function of the collisionenergy. The collision products, including different molec-ular fragments as well as non-fragmented C moleculesand fused C compounds, were recorded after 10 ps ofthe simulations. Open and filled squares describe the sim-ulations performed at the fullerene initial temperature of0 K and 2000 K, respectively. Other symbols represent ex-perimental data from Refs. [16, 45]. In the experiments,an average temperature of the colliding fullerenes was es-timated around 2000 K.work, collision products have been analyzed in the endof 10 ps-long simulations. Fragmentation of fullerenes wasalso simulated on a few-picosecond timescale in many pre-vious studies employing classical and quantum MD ap-proaches (see, e.g., Refs. [46–51]). Most of these simu-lations were conducted for about 2 − molecules and fused C compounds.Open squares in Figure 1 represent the results ob-tained at the zero temperature of fullerenes. Illustrativesnapshots of the corresponding structures at different col-lision energies are presented in the upper panel of Fig. 2.Figure 1 shows that the maximal average size of molec-ular products and hence the maximal fusion probabilityis obtained at collision energies of about 200 eV, whichis significantly higher than experimental results obtainedfor C +60 + C collisions [16, 45] (shown by blue and green Verkhovtsev, Korol, and Solov’yov: Classical MD simulations of fusion and fragmentation of fullerenes triangles). One should note that in the experiments, anaverage temperature of the colliding fullerenes was esti-mated around 2000 K [16].In order to better match the experimental conditions,we performed simulations where the fullerenes were givenan initial temperature of 2000 K. As a result, each ther-mally excited molecule had an initial internal kinetic en-ergy of about 30 eV. Different initial structures and ve-locities used for the collision simulations were obtainedfrom a 10 ns-long constant-temperature simulation of asingle C molecule being at T = 2000 K. In this simula-tion, temperature control was achieved by means of theLangevin thermostat with a damping time of 0.1 ps. Notethat similar simulations performed at different fullerenetemperatures suggest that C resembles its intact cage-like structure up to T ≈ T = 2000 K are shownin Fig. 1 by filled squares. In agreement to what is knownin the literature [46–48], a non-zero initial temperatureof the fullerenes gives a much better agreement with theexperimental results. Taking into account that statisticaluncertainty of the calculated average size of collision prod-ucts is about 10%, the calculated numbers agree well withthe experimental data. We found that the largest averageproduct size and hence the highest probability of fusion isfor collisions with energies of about 90-120 eV, which is sig-nificantly lower than the value of about 200 eV simulatedat zero initial temperature. The fusion barrier decreasesdue to the thermal energy stored in the fullerenes.Earlier works [17, 50] concluded that classical MD sim-ulations usually provide much larger values for the energywindow for the fusion reaction as compared to the en-ergy window observed experimentally. In the analysis pre-sented above, we demonstrated that classical MD is anadequate approach which can reflect the main features ofthe collision-induced processes if the initial internal en-ergy of the projectile and the target is taken into account.Some disagreement between the simulation results and ex-perimental data can be attributed to the way how theinitial temperature was assigned to each fullerene. In ex-periments [15, 16], the target fullerene was heated up toabout 800 K in the scattering cell, while the temperatureof the projectile was estimated to be as high as 3000 K[16, 17]. Accounting for the different initial temperaturesof the projectile and the target may improve the agree-ment between the theoretical results and experiment evenfurther.The above-presented analysis was performed for thecollision of two neutral C fullerenes, while collisions be-tween a singly-charged and a neutral system, C +60 –C ,were studied experimentally [16, 45]. To explore the ef-fect of an excess charge on the collision dynamics, we per-formed simulations of C +60 –C collisions for selected col-lision energies (91, 151 and 186 eV) at the initial fullerenetemperature of 2000 K. The positive charge was uniformly Figure 2.
Different isomers of C formed after 5 ps asa result of fusion of two C fullerenes at different collisionenergies. The energies are indicated for each case study.The upper row shows the structures which were simulatedat zero fullerene temperature, while the lower row corre-sponds to the fullerene temperature of 2000 K. The struc-tures were rendered with MBN Studio software [52].distributed over the projectile, so that each carbon atomcarried a partial charge of +0 . e . In the new set ofsimulations, we have not observed any statistical differ-ence from the results obtained for the two neutral molecules.These results suggest that the effect of including charge inthe simulations is very small and can thus be neglected.Charge effects may have a stronger impact on the collisiondynamics in the case when one of the colliding moleculeshas a higher charge state or both molecules are charged[20, 65]. This is an interesting question that can be ad-dressed in detail in further studies.One should note that in the simulations of the C +60 –C collisions, minor effects of charge redistribution havebeen observed. Despite this, all the small fragments whichhave been produced were electrically neutral, with eitherzero or small partial charge on different atoms. The ef-fects of charge redistribution can be elaborated in greaterdetail by means of irradiation-driven molecular dynamics(IDMD), that is a novel approach for modeling irradia-tion or collision-driven chemical transformations of com-plex molecular systems [66]. However, this is a separatescientific problem which we do not aim to consider in thiswork.Figure 1 demonstrates that at low collision energies(below about 100 eV), the average collision product sizedecreases. It happens because of the increasing probabil-ity of non-reactive inelastic scattering of two fullerenes,which does not lead to fusion. The complete fusion of twoC into one C structure was observed at T = 0 K atthe energy of 120 eV (see Figure 2b). This is in agree-ment with the results of density-functional tight-binding(DFTB) MD simulations [67] which showed that the ener-gies higher than 100 eV are needed to form a single-cageC . In this energy region, the fusion process results inthe formation of elongated peanut-shaped structures.As known from the earlier theoretical studies [67, 68],at lower energies, the two molecules tend to form a cova-lently bonded dimer (C ) , and this process occurs when erkhovtsev, Korol, and Solov’yov: Classical MD simulations of fusion and fragmentation of fullerenes 5 the collision energy is not high enough to break more thanone or a few bonds. DFTB MD simulations [68] predictedthat the threshold collision energy for this process is about60 eV. One should note, however, that we observed a sig-nificant probability of forming a covalently bonded dimereven at the energy of 30 eV. This observation correspondsto the results of earlier classical MD simulations using theTersoff potential, which gave higher formation probabili-ties of covalently bonded (C ) dimers than within theDFTB method (see the Supplemental Material in [68]),and predicted the kinetic energy threshold as low as 15 eV.This feature was attributed to the fact that the Tersoffpotential overestimates the bonding between sp and sp carbon atoms. The Brenner potential, which we have em-ployed in this work, may have a similar deficiency.In Figure 2, we compare the structure of a C com-pound formed as a result of the fullerene fusion. The struc-tures are shown for three collision energies, namely 67 eV(panels (a,d)), 120 eV (b,e) and 186 eV (c,f), for both 0 Kand 2000 K initial temperature of the colliding fullerenes(upper and lower panels, respectively). As discussed above,simulations performed at zero temperature and low colli-sion energy result in the formation of a dumbbell struc-ture (a). The simulations at the same energy but at a finitefullerene temperature result in the formation of a closed-cage peanut-like structure (d). A similar structure wasobtained as a result of simulations performed at 0 K and120 eV energy (b). This compound is highly deformed butstill represents a closed-cage structure. On the contrary,in the simulations at 2000 K and 120 eV, the energy de-posited into the system is enough to break the fullerenecage (e). This structure resembles the “pretzel phase”, ob-served in earlier MD simulations of the C melting at T ≈ melt-ing at temperatures above 5000 K [63].It is now commonly accepted that an abrupt decreaseof the fusion signal, observed experimentally at the colli-sion energies around 200 eV, is an indication of the rapidloss of the fullerene structure and the onset of a multi-fragmentation regime, leading to the production of manysmall-size fragments [15, 16]. In order to describe the multi-fragmentation process in more detail, we have analyzedthe formation of small fragments (C , C , C , C ) as afunction of the center-of-mass collision energy. The corre-sponding probabilities are shown in Figure 3. These prob-abilities were defined as a ratio of the number of C –C fragments formed after 10 ps, to the total number offragments produced. Open symbols describe the results ofsimulations performed at the zero initial temperature ofcolliding fullerenes, while filled symbols describe the caseof T = 2000 K. It is seen that the formation probabilitiesshow different trends for different fragments. The prob-ability of the dimer formation rapidly increases in both Figure 3.
Comparison of the probabilities of smallfragments (C – C ) formation in the C –C colli-sions as a function of the collision energy. The fragmentswere recorded after 10 ps of the simulations. Open andfilled symbols describe the simulations performed at thefullerene initial temperature of 0 K and 2000 K, respec-tively.cases, confirming that C emission is the leading statisti-cal channel of fullerene fragmentation at moderate colli-sion energies. The probabilities for a single carbon atomand a tetramer formation gradually saturate with increas-ing the collision energy. However, the probability for C formation also increases with energy, especially in the caseof nonzero fullerene temperature simulations. This obser-vation correlates with the results of earlier TB-MD simula-tions [51] which studied radiation-induced fragmentationof C . In the cited work, it was shown that C becomesthe most probable pathway of the C fragmentation atincreasing excitation energy.To analyze in more detail the impact of the fullereneinitial temperature on the fragmentation dynamics, weplotted the size distribution of larger fragments, up to C ,formed in the end of 10 ps-long simulations. The resultsof this analysis are shown in Figure 4. The simulationsperformed at zero initial temperature of fullerenes (upperpanel) show that at the collision energy of 225 eV, onlya few fragmentation events have been observed, while atthe energy of 270 eV a phase transition has taken placeleading to multi-fragmentation of the fullerenes and theformation of multiple small-size fragments. The results ofsimulations at T = 2000 K fullerene temperature (lowerpanel) demonstrate that the phase transition takes placeat lower collision energy. Our analysis shows that in thiscase, the multi-fragmentation regime starts at the colli-sion energy of about 185 eV. As discussed above, the mostprominent effect of the fullerene finite temperature is anincrease in the number of C and C fragments. The datashown in Fig. 4 demonstrate that at 315 eV collision en-ergy the relative number of larger fragments is about 3-6%of the total number of fragments produced, and these val-ues are almost independent on the initial energy stored inthe system. Verkhovtsev, Korol, and Solov’yov: Classical MD simulations of fusion and fragmentation of fullerenes
Figure 4.
Number of C – C fragments, normalizedto the total number of fragments produced after 10 ps,for the center-of-mass collision energies of 225, 270 and315 eV. The upper and the lower panels show the resultsobtained at the 0 K and 2000 K temperature of collidingfullerenes, respectively.It is known that the size distribution of small frag-ments C n , produced in collisions involving fullerene mole-cules, follows a n − λ power law [51, 69]. Having taken intoaccount that the simulated distributions of fragments arepeaked at n = 2, we have fitted the results for n ≥ λ = 1 . ± .
04, which is close to thevalue of 1.54, obtained in earlier MD statistical trajectorysimulations at 500 eV center-of-mass collision energy [70].Apart from the statistical analysis of molecular frag-ments produced in the collisions, MD simulations providea possibility to visualize resulting atomic trajectories andexplore the temporal evolution of different molecular frag-ments. To illustrate this, we analyzed four representativetrajectories obtained at 226 eV center-of-mass collision en-ergy at 2000 K. Figure 5 shows how the size of the largestmolecular product has been evolving in the course of simu-lation. The two colliding fullerenes have fused into a singlecompound after the first 0.4 ps of the simulations as illus-trated by a sharp jump in the number of atoms comprisingthe largest product from 60 to 120. However, the subse-quent evolution of this system is quite different in the fourconsidered trajectories: the lifetime of the fused compoundvaries between about 1 and 3.3 ps and the fragmentationchannels are also rather different. For instance, in trajec-tory 1 (solid black curve) a C tetramer was emitted firstat about 3.7 ps, and the resulting C molecule dissoci-ated into two large fragments containing 77 and 39 atoms.The former fragment emitted a small carbon molecule andthen also disintegrated into two large products formed by Figure 5.
Time evolution of the size of the largest molec-ular product during a 10-ps simulation. Four representa-tive atomic trajectories are shown by different lines.
Figure 6.
Characteristic time of emission of C frag-ments at different collision energies at 2000 K. This quan-tity was defined as a lifetime of the fused C compoundbefore fragmenting into C + C or C − x + C + C x products. The data extracted from the simulations areshown by symbols, while the dashed line shows a linearleast-squares fit.45 and 27 atoms. After another fragmentation event, thelargest molecule recorded after 10 ps of the simulation hasonly 33 atoms. On the contrary, trajectory 4 (dotted greencurve) has been evolving in a completely different way: nofragmentation into large products has been observed butthe fused C compound sequentially emitted two dimersand two trimers, so that the final structure recorded after10 ps consists of 110 atoms.The information stored in the atomic trajectories canbe used to explore the dynamics of the collision events. Inparticular, one can analyze characteristic times of emissionof fragments of a given size. We have monitored emissionof the most frequently produced fragmentation products,C dimers, at different collision energies at 2000 K; the re-sults of this analysis are shown in Figure 6. The emissiontime was defined as a lifetime of the fused C compound erkhovtsev, Korol, and Solov’yov: Classical MD simulations of fusion and fragmentation of fullerenes 7 before fragmentation into C + C or C − x + C + C x products. One can see that at collision energies of about100 −
150 eV, i.e., before the multi-fragmentation takesplace, C fragments are produced in small numbers andmostly within a time window of 5 −
10 ps after the twofullerenes had collided. With an increase of the collisionenergy, the dimers start to eject from the system muchfaster. At the center-of-mass collision energy of 315 eV,C fragments are produced in much larger numbers on asub-picosecond time scale, thus indicating the multifrag-mentation regime. One can expect that with a further in-crease of collision energy, the fragments will be producedeven faster, on the order of several tens of femtoseconds.Note that similar behavior was also observed for otherabundantly produced fragments like single carbon atomsand C molecules. This work has been devoted to the investigation of C fullerene collisions and collision-induced fusion and frag-mentation processes by means of classical molecular dy-namics simulations performed with the MBN Explorersoftware package. The simulations were performed in abroad range of collision energies, thus allowing to modelthe formation of covalently-bonded dumbbell structures,closed-cage C compounds, open-cage structures, as wellas sequential emission of small-size molecular fragmentsand rapid multi-fragmentation. We demonstrated that clas-sical molecular dynamics is capable of describing the mainfeatures of the collision-induced processes if the initial in-ternal energy of the projectile is taken into account.We analyzed the fragmentation dynamics and showedthat the size distributions of molecular fragments pro-duced are peaked for dimers, reflecting a well-known sta-tistical channel of C fragmentation via emission of car-bon dimers. The performed atomistic simulations providedinformation on structural aspects of the fused compoundat different collision energies and thermal energy of thecolliding molecules. Our results have been compared withwell-established experimental results on time-of-flight dis-tributions of molecular fragments. The simulation resultshave been found in agreement with the experimental dataand the results of earlier theoretical studies. We demon-strated that, apart from statistical analysis of producedfragments, molecular dynamics simulations performed withMBN Explorer allow one to analyze temporal evolutionof these fragments. In this work, we studied the tempo-ral evolution of several atomic trajectories and evaluatedthe characteristic time of emission of the most abundantlyproduced fragment, the C dimer.Performing this analysis, we presented some of the ca-pabilities of MBN Explorer to model collisional processesinvolving a broad range of Meso-Bio-Nano systems. Al-though it is not possible to cover many different case stud-ies in a single paper, we note that by means of this tool,it is possible to model collision-induced processes withmany different nano- and biological systems. A broad va-riety of interatomic potentials, including many-body po- tentials for multicomponent systems, and the CHARMMmolecular mechanics potential for organic and biomolecu-lar systems, are implemented in the software, allowing forall-atom modeling of composite materials and nano-biointerfaces. MBN Explorer provides also the tools to themultiscale modeling of collisions in which the dynamics ofMeso-Bio-Nano systems is accompanied by the random,local quantum transformations of the system (such as ion-ization or charge transfer) induced in the system dur-ing the collision process. Recently, such possibilities havebeen implemented through the reactive force field [71]and the irradiation-driven molecular dynamics approach[66]. The latter represents a classical molecular dynamicswith the superimposed random processes of local quan-tum transformations related to the irradiation conditions.All these features allow modeling of the collision phenom-ena involving a broad variety of nanoscale and biomolecu-lar systems, including such widely studied systems likePAHs, novel materials like boron-nitride fullerenes andnanotubes, metallic nanoalloys, collisions with surfaces,and many more. A detailed analysis of the processes oc-curring in these systems is of great current interest butgoes well beyond the scope of a single paper. Therefore,this analysis will be continued in future works. Acknowledgements
AV acknowledges the support by the European Commis-sion through the FP7 Initial Training Network “ARGENT”(grant agreement no. 608163).
Author contribution statement
AV performed the calculations, analyzed the results anddrafted the manuscript. All authors participated in thediscussion of the results, provided valuable comments, andcontributed to the revision of the manuscript.
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