Stability of PAH clusters
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(2) Stability of PAH clusters PAH clusters as models for carboneous nanograins. Destruction of such nanograins: route for formation of large complex PAHs?. Zhen et al. ApJ 863 128 (2018) Delaunay et al, J. Phys. Chem. Lett., 6, 1536-1542 (2015). Are these PAH clusters stable?.
(3) Stability of PAH clusters • Cationic pyrene clusters (Py). n. studied using. • Mass spectrometry techniques and. • Phase Space Theory to deduce. • Dissociation energies. Pyrene : C16H10 PAH = polyaromatic hydrocarbons.
(4) Outline • Experimental setup. • Experimental results • Phase Space Theory • Dissociation energies • Conclusion.
(5) Experimental setup. Experimental setup initially designed to perform collisions between mass selected clusters and atomic or molecular vapor (attachment crosssection, fragmentation cross-section, nanocalorimetry, …).. Can also be used to observe the spontaneous thermal evaporation of mass selected clusters..
(6) Experimental setup. • Gaz aggregation source.
(7) Cluster production. 8000. (Py). n=3. + n. 6000. Small pure Pyrene clusters. Intensity (arb. u.). n=4 4000. +1 uma -1 uma. 2000. -2 uma +2 uma. n=5 0 161.0. 0. 50. 100. 150. 161.5. 162.0. 162.5. 163.0. 163.5. Time of flight (µs). n=2. 200. 250. Time of flight (µs). 300. 350. 400.
(8) Cluster production. n 0. 10. 20. 30. 40. Small pure Pyrene clusters Large pure pyrene clusters. 0. 1000. 2000. 3000. 4000. 5000. mass (amu). 6000. 7000. 8000. 9000.
(9) Cluster production. (Py)n+. (Py)n(H2O)m+ (H2O)mH+ 0. 400. 800. 1200. m/z. 1600. 2000. Small pure Pyrene clusters Large pure pyrene clusters Mixed water-pyrene clusters.
(10) Experimental setup. • Gaz aggregation source, n = 1-40 n. 0. 10. 20. 30. 40. (Py) n. 0. 1000. 2000. 3000. 4000. 5000. mass (amu). 6000. 7000. 8000. 9000.
(11) Experimental setup. • Thermalization : T = 25-300 K n. 0. 10. 20. 30. 40. Large number of collisions with the helium buffer gaz Canonical distribution of internal energies Ei 0. 1000. 2000. 3000. 4000. 5000. mass (amu). 6000. 7000. 8000. 9000.
(12) Experimental setup. • Transfer to the high vacuum part n. 0. 0. 10. 1000. 2000. 20. 3000. 4000. 30. 5000. mass (amu). 6000. 40. 7000. 8000. 9000. Internal energies Ei, microcanonical evolution.
(13) Experimental setup. n. • Mass selection and slowing down. Internal energies Ei, microcanonical evolution.
(14) Experimental setup. n. • Free flight. Internal energies Ei, microcanonical evolution.
(15) Experimental setup. T = 121 K 156. 158. 160. 162. 164. 166. 168. 170. 166. 168. 170. 166. 168. 170. ToF (µs). • Products analyzed by TOF mass spectrometry. T = 166 K 156. 158. 160. 162. 164. ToF (µs). T = 217 K 156. 158. 160. 162. 164. ToF (µs).
(16) Experimental results Evolution of the mass spectra of mass selected clusters with initial temperature. As the temperature is raised, appearance of fragments due to evaporation. T = 121 K 156. 158. 160. 162. 164. 166. 168. 170. 166. 168. 170. 166. 168. 170. ToF (µs). T = 166 K 156. 158. 160. 162. 164. ToF (µs). T = 217 K 156. 158. 160. 162. 164. ToF (µs). Example: (Py)11 @ 22 eV. Ratio I/I0 I = parent peak intensity I0 = sum of parent + fragment peaks.
(17) Experimental results Evolution of the mass spectra of mass selected clusters with initial temperature. As the temperature is raised, appearance of fragments due to evaporation. T = 121 K 156. 158. 160. 162. 164. 166. 168. 170. 1.00. ToF (µs) 0.95. T = 166 K 158. 160. 162. 164. 166. 168. 170. ToF (µs). I/I0. 156. 0.90. 0.85. 0.80. T = 217 K 156. 158. 160. 162. 164. 166. 168. 170. ToF (µs). Example: (Py)11 @ 22 eV. 0.75 25. 50. 75. 100. 125. 150. 175. 200. 225. 250. 275. 300. T (K). I = I0e-W(T)t ?.
(18) Experimental results t1. t2. t3. t4. thermalization. At the thermalizer exit: - Cluster size distribution - Canonical distribution of internal energies Ei After the propagation time t1, the population of size n will have contributions from the evaporation of larger sizes:. n 1, Ei. . n, Ei.
(19) Experimental results t1. t2. t3. t4. thermalization. At the thermalizer exit: - Cluster size distribution - Canonical distribution of internal energies Ei. After t1, population of size n might no longer be at temperature T new, non-canonical, distribution of internal energies 0.0. 0.5. 1.0. 1.5. Eint (eV). 2.0. 2.5. 3.0.
(20) Experimental results t1. t2. t3. t4. thermalization. At the thermalizer exit: - Cluster size distribution - Canonical distribution of internal energies Ei Depending on where evaporation takes place, it might not be observed. Experimental results reproduced by simulating the propagation in the setup with evaporation probabilities evaluated at each time step Model for evaporation rates.
(21) PST evaporation rates Ingredients of the Phase Space Theory: - initial internal energy of the parent Ei - density of states of the parent N(E) - total number of states of the fragments G(E,J) - conservation of angular momentum. W ( Ei , J ) . G( E f , J ). E f Ei Erot D. h(2 J 1) N ( Ei ). Erot B0 J ( J 1). Approximations: - only vibrational harmonic frequencies considered - all species considered as spherical tops - ion-polar interaction between the neutral fragment and the charged cluster. Energy partition among the fragments Harmonic frequencies and moments of inertia from DFTB calculation (cf Rapacioli et al.).
(22) PST evaporation rates Ingredients of the Phase Space Theory: - initial internal energy of the parent Ei - density of states of the parent N(E) - total number of states of the fragments G(E,J) - conservation of angular momentum. W ( Ei , J ) . Only one adjustable parameter. G( E f , J ). E f Ei Erot D. h(2 J 1) N ( Ei ). Erot B0 J ( J 1). Approximations: - only vibrational harmonic frequencies considered - all species considered as spherical tops - ion-polar interaction between the neutral fragment and the charged cluster. Energy partition among the fragments Harmonic frequencies and moments of inertia from DFTB calculation (cf Rapacioli et al.).
(23) PST evaporation rates t1. t2. t3. t4. Generate initial population of size n (cascaded evaporations use of dissociation energies of sizes n+1, n+2, …) (t1) Calculate clusters trajectories with evaporation probabilities (t2, t3, t4) Generate TOF mass spectra vs initial temperature Compare with experiment, adjust dissociation energy.
(24) 0.95. 0.95. 0.95. 0.90. 0.90. 0.90. n = 40. I/Io. 1.00. I/Io. 1.00. I/Io. 1.00. n = 35. n = 30. 0.85. 0.85. 0.85. 0.80. 0.80. 0.80. 0.75 25. 50. 75. 100. 125. 150. 175. 200. 225. 250. 275. 0.75 25. 300. 50. 75. 100. 125. T (K). 150. 175. 200. 225. 250. 275. 0.75 25. 300. 0.95. 0.95. 0.90. 0.90. 0.90. n = 25. I/Io. 0.95. I/Io. 1.00. I/Io. 1.00. n = 20 0.85. 0.85. 0.80. 0.80. 0.80. 75. 100. 125. 150. 175. 200. 225. 250. 275. 0.75 25. 300. 50. 75. 100. 125. T (K). 150. 175. 200. 225. 250. 275. 0.75 25. 300. 0.95. 0.90. 0.90. 0.90. I/Io. 0.95. I/Io. 0.95. I/Io. 1.00. n = 18. n = 17 0.85. 0.85. 0.80. 0.80. 0.80. 100. 125. 150. 175. T (K). 200. 225. 250. 275. 300. 0.75 25. 50. 75. 100. 125. 150. 175. T (K). 175. 200. 225. 250. 275. 300. 50. 75. 100. 125. 150. 175. 200. 225. 250. 275. 300. 200. 225. 250. 275. 300. n = 16. 0.85. 75. 150. T (K). 1.00. 50. 125. T (K). 1.00. 0.75 25. 100. n = 19. 0.85. 50. 75. T (K). 1.00. 0.75 25. 50. T (K). 200. 225. 250. 275. 300. 0.75 25. 50. 75. 100. 125. 150. 175. T (K).
(25) 0.95. 0.95. 0.95. 0.90. 0.90. 0.90. n = 15. I/Io. 1.00. I/Io. 1.00. I/Io. 1.00. n = 14. n = 13. 0.85. 0.85. 0.85. 0.80. 0.80. 0.80. 0.75 25. 50. 75. 100. 125. 150. 175. 200. 225. 250. 275. 0.75 25. 300. 50. 75. 100. 125. T (K). 150. 175. 200. 225. 250. 275. 0.75 25. 300. 0.95. 0.95. 0.90. 0.90. 0.90. n = 12. I/Io. 0.95. I/Io. 1.00. I/Io. 1.00. n = 11 0.85. 0.85. 0.80. 0.80. 0.80. 75. 100. 125. 150. 175. 200. 225. 250. 275. 0.75 25. 300. 50. 75. 100. 125. 150. 175. 200. 225. 250. 275. 0.75 25. 300. 0.95. 0.95. 0.90. 0.90. 0.90. I/Io. 0.95. I/Io. 1.00. I/Io. 1.00. n=9. n=8 0.85. 0.85. 0.80. 0.80. 0.80. 100. 125. 150. 175. T (K). 200. 225. 250. 275. 300. 0.75 25. 50. 75. 100. 125. 150. 175. T (K). 175. 200. 225. 250. 275. 300. 50. 75. 100. 125. 150. 175. 200. 225. 250. 275. 300. 200. 225. 250. 275. 300. n=7. 0.85. 75. 150. T (K). 1.00. 50. 125. T (K). T (K). 0.75 25. 100. n = 10. 0.85. 50. 75. T (K). 1.00. 0.75 25. 50. T (K). 200. 225. 250. 275. 300. 0.75 25. 50. 75. 100. 125. 150. 175. T (K).
(26) 1.00. 1.00. 1.00. 0.99. 0.99. 0.99. n=6. 0.98. I/Io. 0.98. I/Io. I/Io. 0.98. n=5. n=4. 0.97. 0.97. 0.97. 0.96. 0.96. 0.96. 0.95 25. 50. 75. 100. 125. 150. 175. 200. 225. 250. 275. 0.95 25. 300. 50. 75. 100. 125. T (K) 1.00. 0.99. 0.99. 200. 225. 250. 275. 300. I/Io. n=3 0.97. 0.97. 0.96. 0.96. 50. 75. 100. 125. 150. 175. T (K). 200. 225. 250. 275. 300. 0.95 25. n=2. 50. 75. 100. 125. 150. 175. T (K). 0.95 25. 50. 75. 100. 125. 150. 175. T (K). 0.98. 0.98. I/Io. 175. T (K). 1.00. 0.95 25. 150. 200. 225. 250. 275. 300. 200. 225. 250. 275. 300.
(27) Dissociation energies 1.2 1.1 1.0 0.9 0.8. Dn (eV). 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0. 5. 10. 15. 20. 25. 30. 35. 40. 45. 50. Size n. Black squares: values deduced from the reproduction of the experimental curves using PST.
(28) Dissociation energies 1.2 1.1 1.0 0.9 0.8. Dn (eV). 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0. 5. 10. 15. 20. 25. 30. 35. 40. 45. 50. Size n. Black squares: values deduced from the reproduction of the experimental curves using PST Only lower limit for n=2.
(29) Dissociation energies 1.2 1.1 1.0. Bulk: DHvap ~ 0.93 eV @ 298 K. 0.9 0.8. Dn (eV). 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0. 5. 10. 15. 20. 25. 30. 35. 40. 45. 50. Size n. Black squares: values deduced from the reproduction of the experimental curves using PST Only lower limit for n=2.
(30) Dissociation energies 1.2 1.1 1.0. Bulk: DHvap ~ 0.93 eV @ 298 K. 0.9 0.8. Neutral like evolution. Dn (eV). 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0. 5. 10. 15. 20. 25. 30. 35. 40. 45. 50. Size n. Black squares: values deduced from the reproduction of the experimental curves using PST Only lower limit for n=2.
(31) Dissociation energies 1.2 1.1 1.0. Bulk: DHvap ~ 0.93 eV @ 298 K. 0.9 0.8. Neutral like evolution. Dn (eV). 0.7 0.6. Dilution of charge resonance stabilization as size increases. 0.5 0.4 0.3 0.2 0.1 0.0 0. 5. 10. 15. 20. 25. 30. 35. 40. 45. 50. Size n. Black squares: values deduced from the reproduction of the experimental curves using PST Only lower limit for n=2.
(32) Dissociation energies 1.2 1.1 1.0. Bulk: DHvap ~ 0.93 eV @ 298 K. 0.9 0.8. Neutral like evolution. Dn (eV). 0.7 0.6. Dilution of charge resonance stabilization as size increases. 0.5 0.4 0.3 0.2 0.1 0.0 0. 5. 10. 15. 20. 25. 30. 35. 40. 45. 50. Size n. Black squares: values deduced from the reproduction of the experimental curves using PST Only lower limit for n=2 Red triangles: DFTB calculation (cf Rapacioli et al.).
(33) Conclusion • We have observed the thermal evaporation of pyrene clusters, n=2-40 • Experimental results successfully reproduced using PST • Dissociation energies deduced, in good agreement with theory and bulk value.
(34) Conclusion • Apart from the dissociation energy, no free parameters for the PST. Too good to be true? • At least, effective evaporation rates are obtained.
(35) Conclusion • Preliminary data on CID cross-section measurements: dissociation energies compare well with evaporation data. 100. (Py)+2 - 1 Py. Cross section (Å2). 80. 60. 40. 20. 0 0. 1. 2. 3. 4. Ecm (eV). 5. 6. 7.
(36) PIRENEA 2 Setup Laser vaporization cluster source Quadrupole Trap T ~4 - 300 K. Molecular aggregation source. ICR cell ~10 K, ~10-11 mbar. (PAH)n+ Mixed PAH-H2O aggregates (H2O)mH+.
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(38) Experimental results t1. t2. t3. t4. thermalization. For a size n @ 22 eV, we have:. t1 = D/v0 = 20 µs @ 200 K t2 = 24n µs t3 = 25 n µs t4 = 25 n µs. D = distance between the exit of the thermalizer and the first Wiley-McLaren = 8 cm v0 = thermal velocity of helium. Similar time spent in the different parts of the setup Similar evaporation probability at each experimental stage.
(39) Cluster production. Py+. Small pure Pyrene clusters.. (H2O)nH+ (H2O)nPy+ (H2O)n(Py)+2. Large pure pyrene clusters Mixed water-pyrene clusters. 0. 200. 400. 600. 800. masse (uma). 1000. 1200. 1400.
(40) PST evaporation rates The version of PST used here contains the constraint that total angular momentum is conserved, and that in the reverse process the associating product must overcome the maximum of the centrifugal barrier which defines the position of the transition state (loose transition state). The interaction between the products is represented by an effective central potential of the form:. C4 L2 2 Veff (r ) 4 r 2r.
(41) PST evaporation rates Ingredients of the Phase Space Theory: - initial internal energy of the parent Ei - density of states of the parent N(E) - total number of states of the fragments G(E,J) - conservation of angular momentum. W ( Ei , J ) . G( E f , J ) h(2 J 1) N ( Ei ). E f Ei Erot D Erot B0 J ( J 1) From the PST we also get the probability of energy partition among the fragments: P( Ev , Erel , Er )dEv dErel dEr . N1 ( Ev ) N 2 ( E f Ev Erel Er ) N x ( Er , Erel , J ) G( E f , J ). dEv dErel dEr.
(42) Dissociation energies 1.2 1.1 1.0. Bulk: DH0vap ~ 0.93 eV @ 298 K. 0.9 0.8. Neutral like evolution. Dn (eV). 0.7 0.6. Dilution of charge resonance stabilization as size increases. 0.5 0.4 0.3 0.2 0.1 0.0 0. 5. 10. 15. 20. 25. 30. 35. 40. 45. 50. Size n. Black squares: values deduced from the reproduction of the experimental curves using PST Red triangles: DFTB calculation (cf Rapacioli et al.) Bulk: DH0vap ~ 0.93 eV @ 298 K.
(43) Initial size contributions T = 250 K. 4. 0.000 10.00. i, original size n+i. 3. 20.00 30.00. 2. 40.00 50.00 60.00. 1. 70.00 80.00. 0. 90.00 100.0. 2. 4. 6. 8. 10. 12. 14. Cluster size n. 16. 18. 20 25303540.
(44) Simulated TOF mass spectra. 156. 158. 160. 162. 164. TOF (µs). 166. 168. 170.
(45) Monte Carlo integration To compare with the experiment we need to integrate over distributions:. P(E, T )P( J , T )dE J. P(E,T) = probability to have an internal energy E in the parent cluster. Number occupation ni of each vibration randomly picked up so that i on average we have:. E i. e. i k BT. 1. P(J,T) = probability to have the total angular momentum J in the parent cluster.. 4 B 2 J e P( J ) k BT . . BJ 2 k BT. High temperature or low B limit used.
(46) Vibrational harmonic frequencies 3000. -1. frequency (cm ). 2500. 2000. 1500. harmonic frequencies from DFTB for the tetramer. 1000. 500. 0 -10. 0. 10. 20. 30. 40. 50. 60. 70. 80. mode. Vibrational harmonic frequencies calculated for neutral pyrene and cationic clusters of sizes 1, 2, 3 and 4. To extrapolate for larger sizes n: Intramolecular frequencies = cation + (n-1) neutrals Intermolecular frequencies = linear interpolation between 13 cm-1 and the lowest cationic frequency..
(47) Vibrational harmonic frequencies Using these, the heat capacity of bulk pyrene can be reproduced: 30. Bulk (Exp) + 500. Py :. C (kB/molecule). 25. frequency factor = 0.96 frequency factor = 1.00. 20. 15. 10. 5. 0 0. 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300. T (K).
(48) Moments of inertia and rotational constants 2 For the PST calculation the rotational constant B is needed. B 2I The moment of inertia are taken as the geometrical average of the 3 main moments: 3. I I1 I 2 I 3. G Linear Fit G. moment inertie (uma.Å2). 40000. 30000. Squares: DFTB calculation 20000. 10000. Equation. y = a + b*x. Weight Residual Sum of Squares Pearson's r. No Weighting 841076.942 01. Adj. R-Squar. Value G. Standard Err. Intercept. -386.6998. 264.06523. Slope. 1035.0141. 18.5796. 0 0. 5. 10. 15. 20. 25 5/3. n. 30. 5/ 3 ) I ( Py ) n n 1. Line : I ( Py. 0.9992 0.99807. 35. 40.
(49) T = 121 K 156. If clusters evaporate after the second Wiley McLaren acceleration and before the reflectron (t4), they end up in the “secondary” fragment peak.. 158. 160. 162. 164. 166. 168. 170. 166. 168. 170. 166. 168. 170. ToF (µs). T = 166 K 156. 158. 160. If they evaporate after the reflectron they can not be distinguished from the parent peak.. 162. 164. ToF (µs). T = 217 K 156. 158. 160. 162. 164. ToF (µs).
(50) Clusters production. Clusters are produced in a gas aggregation source. Ionization by either : - a discharge electrode, I 100µA, V 1 kV - an electron gun, I = 2.5 A, V = -100 V.
(51) Experimental results 100. (Py)+2 - 1 Py. Cross section (Å2). 80. 60. 40. 20. 0 0. 1. 2. 3. 4. Ecm (eV). 5. 6. 7.
(52) Experimental results 100. Tth = 25K, Ar (Py)+3 - 1 Py (Py)+3 - 2 Py. Cross section (Å2). 80. 60. 40. 20. 0 0. 1. 2. 3. 4. Ecm (eV). 5. 6. 7.
(53) Experimental results 100. (Py+4) - 1 Py (Py)+4 - 2 Py. Cross section (Å2). (Py)+4 - 3 Py. 50. 0 0. 1. 2. 3. 4. Ecm (eV). 5. 6. 7.
(54) 1.1. 1.0. Dn (eV). 0.9. 0.8. 0.7. 0.6 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Taille. Blue stars: theory Red squares: values deduced from the reproduction of the experimental curves using PST (CID)..
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