stability of pah clusters

Stability of PAH clusters

Sébastien Zamith, Ming-Chao Ji, Jean-Marc L’Hermite, Christine Joblin,

Léo Dontot, Mathias Rapacioli and Fernand Spiegelman

Zhen et al. ApJ 863 128 (2018)


PAH clusters as models for carboneous nanograins.

Destruction of such nanograins: route for formation of large complex PAHs?

Delaunay et al, J. Phys. Chem. Lett., 6, 1536-1542 (2015)

Are these PAH clusters stable?


• Cationic pyrene clusters studied using

• Mass spectrometry techniques and

• Phase Space Theory to deduce

• Dissociation energies

n(Py)

1016HC:Pyrene

PAH = polyaromatic hydrocarbons

• Experimental setup

• Experimental results

• Phase Space Theory

• Dissociation energies

• Conclusion

Outline

Can also be used to observe the spontaneous thermal evaporation of

mass selected clusters.

Experimental setup

Experimental setup initially designed to perform collisions between

mass selected clusters and atomic or molecular vapor (attachment cross-

section, fragmentation cross-section, nanocalorimetry, …).

Experimental setup

• Gaz aggregation source

0 50 100 150 200 250 300 350 400

161.0 161.5 162.0 162.5 163.0 163.50

2000

4000

6000

8000

n=5

n=4

n=3

Time of flight (µs)

n=2

(Py)+

n

-2 uma

-1 uma

+2 uma

Inte

nsity (

arb

. u

.)

Time of flight (µs)

+1 uma

Cluster production

Small pure Pyrene clusters

Cluster production

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

mass (amu)

0 10 20 30 40

n


Large pure pyrene clusters



Mixed water-pyrene clusters

Cluster production

0 400 800 1200 1600 2000

m/z

(H2O)mH+

(Py)n+

(Py)n(H2O)m+

Experimental setup

n(Py)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

mass (amu)

0 10 20 30 40

n

• Gaz aggregation source, n = 1-40

• Thermalization : T = 25-300 K

Experimental setup

Large number of collisions with the helium buffer gaz Canonical distribution of internal energies Ei

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

mass (amu)

0 10 20 30 40

n

• Transfer to the high vacuum part

Experimental setup

Internal energies Ei, microcanonical evolution 0 1000 2000 3000 4000 5000 6000 7000 8000 9000

mass (amu)

0 10 20 30 40

n

n

• Mass selection and slowing down

Experimental setup

Internal energies Ei, microcanonical evolution

Experimental setup

n

Internal energies Ei, microcanonical evolution

• Free flight

• Products analyzed by TOF mass spectrometry

Experimental setup

156 158 160 162 164 166 168 170

T = 166 K

T = 121 K

ToF (µs)

T = 217 K

156 158 160 162 164 166 168 170

ToF (µs)

156 158 160 162 164 166 168 170

ToF (µs)

156 158 160 162 164 166 168 170

T = 166 K

T = 121 K

ToF (µs)

T = 217 K

156 158 160 162 164 166 168 170

ToF (µs)

156 158 160 162 164 166 168 170

ToF (µs)

eV22@(Py) : Example 11

Ratio I/I0

I = parent peak intensity I0 = sum of parent + fragment peaks

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

156 158 160 162 164 166 168 170

T = 166 K

T = 121 K

ToF (µs)

T = 217 K

156 158 160 162 164 166 168 170

ToF (µs)

156 158 160 162 164 166 168 170

ToF (µs)

eV22@(Py) : Example 11

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/I 0

T (K)


Evolution of the mass spectra of mass selected clusters with initial temperature. As the temperature is raised, appearance of fragments due to evaporation

I = I0e-W(T)t ?

thermalization

t1 t2 t3 t4


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:

ii EnEn ,,1

thermalization

t1 t2 t3 t4





0.0 0.5 1.0 1.5 2.0 2.5 3.0

Eint

(eV)

After t1, population of size n might no longer be at

temperature T

new, non-canonical, distribution of internal energies

thermalization

t1 t2 t3 t4





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

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

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.)

PST evaporation rates

)()12(

),(),(

i

f

iENJh

JEGJEW

)1(0

JJBE

DEEE

rot

rotif






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.)


)()12(

),(),(

i

f

iENJh

JEGJEW

)1(0

JJBE

DEEE

rot

rotif

Only one adjustable parameter


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

t1 t2 t3 t4

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 25

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 40

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 35

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 30

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 20

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 19

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 18

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 17

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 16

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 15

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 14

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 13

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 12

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 11

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 10

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 9

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 8

25 50 75 100 125 150 175 200 225 250 275 3000.75

0.80

0.85

0.90

0.95

1.00

I/Io

T (K)

n = 7

25 50 75 100 125 150 175 200 225 250 275 3000.95

0.96

0.97

0.98

0.99

1.00

I/Io

T (K)

n = 6

25 50 75 100 125 150 175 200 225 250 275 3000.95

0.96

0.97

0.98

0.99

1.00

I/Io

T (K)

n = 5

25 50 75 100 125 150 175 200 225 250 275 3000.95

0.96

0.97

0.98

0.99

1.00

I/Io

T (K)

n = 4

25 50 75 100 125 150 175 200 225 250 275 3000.95

0.96

0.97

0.98

0.99

1.00

I/Io

T (K)

n = 3

25 50 75 100 125 150 175 200 225 250 275 3000.95

0.96

0.97

0.98

0.99

1.00

I/Io

T (K)

n = 2

Black squares: values deduced from the reproduction of the

experimental curves using PST

0 5 10 15 20 25 30 35 40 45 500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

D

n (

eV)

Size n

Dissociation energies



Only lower limit for n=2

0 5 10 15 20 25 30 35 40 45 500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

D

n (

eV)

Size n






Bulk: DHvap ~ 0.93 eV @ 298 K

0 5 10 15 20 25 30 35 40 45 500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

D

n (

eV)

Size n

0 5 10 15 20 25 30 35 40 45 500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

D

n (

eV)

Size n






Neutral like evolution

0 5 10 15 20 25 30 35 40 45 500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

D

n (

eV)

Size n






Dilution of

charge resonance stabilization

as size increases


0 5 10 15 20 25 30 35 40 45 500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

D

n (

eV)

Size n




Red triangles: DFTB calculation (cf Rapacioli et al.)



Dilution of


as size increases


• 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

Conclusion

• Apart from the dissociation energy, no free parameters for the PST.

Too good to be true?

• At least, effective evaporation rates are obtained

Conclusion

0 1 2 3 4 5 6 70

20

40

60

80

100

Cro

ss s

ection

(Å

2)

Ecm

(eV)

(Py)+

2 - 1 Py

Conclusion

• Preliminary data on CID cross-section measurements: dissociation energies compare well with evaporation data.

Laser vaporization cluster source

Molecular aggregation source

Quadrupole Trap T ~4 - 300 K

ICR cell ~10 K, ~10-11 mbar

(PAH)n+

(H2O)mH+

Mixed PAH-H2O

aggregates

PIRENEA 2 Setup

thermalization

t1 t2 t3 t4


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

0 200 400 600 800 1000 1200 1400

(H2O)

n(Py)

+

2

(H2O)

nPy

+

masse (uma)

Py+

(H2O)

nH

+ Small pure Pyrene clusters.


Mixed water-pyrene clusters

Cluster production

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:


r

L

r

CrVeff

2)(

22

4

4







rrelv

f

relrxrrelvfv

rrelvrrelv dEdEdEJEG

JEENEEEENENdEdEdEEEEP

),(

),,()()(),,(

21

From the PST we also get the probability of energy partition among the

fragments:

)()12(

),(),(

i

f

iENJh

JEGJEW

)1(0

JJBE

DEEE

rot

rotif



Red triangles: DFTB calculation (cf Rapacioli et al.)

Bulk: DH0vap ~ 0.93 eV @ 298 K

0 5 10 15 20 25 30 35 40 45 500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

D

n (

eV)

Size n



Dilution of


as size increases

Bulk: DH0vap ~ 0.93 eV @ 298 K

25303540

0.000

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.0

2 4 6 8 10 12 14 16 18 20

0

1

2

3

4

i, o

rig

ina

l si

ze n

+i

Cluster size n

T = 250 K

Initial size contributions

Simulated TOF mass spectra

156 158 160 162 164 166 168 170

TOF (µs)

Monte Carlo integration

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

on average we have:

i Tk

i

B

i

e

E

1

P(J,T) = probability to have the total angular momentum J in the parent

cluster.

Tk

BJ

B

BeJTk

BJP

2

24)(

High temperature or low B limit used

To compare with the experiment we need to integrate over distributions:

J

dETJPTEP ),(),(

Vibrational harmonic frequencies

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.

harmonic frequencies from DFTB for the tetramer

-10 0 10 20 30 40 50 60 70 80

0

500

1000

1500

2000

2500

3000

frequency (

cm

-1)

mode

Using these, the heat capacity of bulk pyrene can be reproduced:

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 3000

5

10

15

20

25

30

C (

kB/m

ole

cu

le)

T (K)

Bulk (Exp)

Py+

500:

frequency factor = 0.96

frequency factor = 1.00

Vibrational harmonic frequencies

Moments of inertia and rotational constants

For the PST calculation the rotational constant B is needed. I

B2

2

The moment of inertia are taken as the geometrical average of the 3

main moments: 3321 IIII

Squares: DFTB calculation

Line : 3/5

1)()( nPyIPyI n

0 5 10 15 20 25 30 35 40

0

10000

20000

30000

40000

mom

ent in

ert

ie (

um

a.Å

2)

n5/3

G

Linear Fit G

Equation y = a + b*x

Weight No Weighting

Residual Sum of Squares

841076.94201

Pearson's r 0.9992

Adj. R-Squar 0.99807

Value Standard Err

GIntercept -386.6998 264.06523

Slope 1035.0141 18.5796

If clusters evaporate after the second Wiley

McLaren acceleration and before the reflectron (t4),

they end up in the “secondary” fragment peak.

If they evaporate after the reflectron they can not be

distinguished from the parent peak.

156 158 160 162 164 166 168 170

T = 166 K

T = 121 K

ToF (µs)

T = 217 K

156 158 160 162 164 166 168 170

ToF (µs)

156 158 160 162 164 166 168 170

ToF (µs)

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


0 1 2 3 4 5 6 70

20

40

60

80

100

Cro

ss s

ection (

Å2)

Ecm

(eV)

(Py)+

2 - 1 Py


0 1 2 3 4 5 6 70

20

40

60

80

100

Cro

ss s

ection (

Å2)

Ecm

(eV)

Tth = 25K, Ar

(Py)+

3 - 1 Py

(Py)+

3 - 2 Py


0 1 2 3 4 5 6 70

50

100

(Py+

4) - 1 Py

(Py)+

4 - 2 Py

(Py)+

4 - 3 Py

Cro

ss s

ection (

Å2)

Ecm

(eV)

Blue stars: theory

Red squares: values deduced from the reproduction of the

experimental curves using PST (CID).

0 1 2 3 4 5 6 7 8 9 10

0.6

0.7

0.8

0.9

1.0

1.1

Dn (

eV

)

Taille

stability of pah clusters

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