Size-dependent melting of PAH nano-clusters: A molecular dynamic study

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1 Size-dependent melting of PAH nano-clusters: A molecular dynamic study Dongping Chen, Tim Totton, and April 2013

2 PAH mobility: current questions The internal structure of a soot particle is poorly understood. Limited knowledge about how mobile PAHs are within a soot particle. Liquid-like clusters were observed in series of experiments. Why?

3 Source of particle rounding Developing an understanding of soot particle mobility is essential to improve current soot model B3 flame [1] particle rounding due to mass addition only particle rounding due to PAH mobility only particle rounding due to both mechanisms [1] B. Zhao, Z. Yang, Z. Li, M. V. Johnston, and H. Wang. Proceedings of the Combustion Institute, 30(1): , 2005

4 Molecular dynamics Solve classical equations of motion based on atomistic force field which defines potential of system U(X) F ( X ) = U ( X ) = MX ( t) Force field split into intermolecular and intramolecular contributions Intermolecular described by form of PAHAP potential.

5 Intermolecular Potentials Use atom-atom potentials Approximated as sum of all pairwise atomic interactions between molecules U = U R, ab ab A A< B a A b B ( Ω ) ab R ab (molecule A atoms a and molecule B with atoms b)

6 Melting hypotheses (1) D β ~ γ sv, γ lv,h f δ is the thickness of the liquid layer

7 Melting hypotheses (2) Homogeneous melting hypothesis T cm /T BM Liquid nucleation and growth hypothesis Liquid skin melting hypothesis D -1 (nm -1 ) An illustration of different melting hypotheses

8 Melting criteria (1) The caloric curve exhibits a jump indicating absorption of latent heat. Coronene50 cluster Melting point T cm =465K NOTE: bulk T BM of coronene is 711K which is 250K higher than that of coronene50 cluster. This phenomenon is known as Melting-point depression

9 Melting criteria (2) Fluctuations in nearest neighbour distance Define nearest neighbour distance of molecule A: Fluctuations in R A,min :

10 Melting criteria (3) To explicitly describe the local melting, the cluster was divided into concentric shells with the same thickness (3.5 Å) 1 st shell 2 nd shell 3 rd shell 4 th shell 5 th shell Let S = {molecule indices A} δ s Coronene50 cluster Average distance from centre of mass (COM)

11 Investigated clusters Molecules from pyrene up to circumcoronene. Pyrene (C 16 H 10 ) Coronene (C 24 H 12 ) Size from 50 to 500. Ovalene (C 32 H 14 ) Hexabenzocoronene (C 42 H 18 ) Circumcoronene (C 54 H 18 ) Coronene50 cluster Coronene100 cluster

Simulation setup SA Equilibrium (NVT) Production (NVT) EM Packing The The Perform Randomly conformation equilibrated simulated energy packing annealing is conformation further minimisation molecule

12 Simulation setup SA Equilibrium (NVT) Production (NVT) EM Packing The The Perform Randomly conformation equilibrated simulated energy packing annealing is conformation further minimisation molecule equilibrated (SA) is method again step and to for form is simulated remove used least the to cluster-like the 3 produce in ns 1 ns a under production relatively abnormal structure a particular proper artificial (PACKMOL) run from temperature starting force where [1] due conformation the to T data while previous is the collected. ( step initial ns). velocities are assigned from a Maxwell distribution at T. [1] L. Martínez, R. Andrade, E. G. Birgin, J. M. Martínez. Packmol: A package for building initial configurations for molecular dynamics simulations. Journal of Computational Chemistry, 30(13): , 2009.

13 Coronene cluster: energy plot 605K 540K 490K 615K 465K 515K indicates the melting point of different size of nano-clusters A single point represents an average value of 1 ns production trajectory.

14 Coronene cluster: Plots of fluctuation in nearest neighbour distance This flat curve indicates all the molecules within these cluster are in the same energy state. Surface melting Increase T This cluster melts at this T (465K). δ s Melting point from the energy criteria is also 465K. Both criteria predict the same melting point. Coronene50 cluster

15 Coronene cluster: Plots of fluctuation in nearest neighbour distance δ s Coronene50 cluster Coronene80 cluster Coronene100 cluster

16 Melting curve for coronene Fixed intercept=1.0, fit slope only fit both intercept and slope By fitting the linearity between melting point and the reciprocal of cluster size, the predicted bulk melting point is slightly higher (3.1%) than the true value.

17 Melting animations Coronene 50 cluster 400K

18 Melting animations Coronene 50 cluster 465K

Layer separation Separation molecules Average layer separation (Å) C 16 H 10 3.66 C 24 H 12 3.6 C 32 H 14 3.59 C 42 H 18 3.

6 Å, and they decrease with the increase of the size of molecule. Ovalene50 cluster Comparison 3.50 Å (diesel soot) [1] 3.

19 Layer separation Separation molecules Average layer separation (Å) C 16 H C 24 H C 32 H C 42 H C 54 H NOTE: Average layer separations are around 3.6 Å, and they decrease with the increase of the size of molecule. Ovalene50 cluster Comparison 3.50 Å (diesel soot) [1] 3.35 Å (Graphite) [1] S. Mosbach, M.S. Celnik, A. Raj, M. Kraft, H.R. Zhang, S. Kubo, K. Kim, Towards a detailed soot model for internal combustion engines, Combust. Flame 156 (6) (2009)

20 Conclusions PAH clusters show a size-dependent melting behaviour. The melting point predicted by the isotropic PAHAP potential yield a good agreement with experimental observation. Small stacks are the basic building block of PAH nano-clusters.

21 Layer separation (1) Ovalene50 cluster at low temperature state 10 6 Front view Back view

22 Layer separation (2) Ovalene50 cluster molecule Average molecule in stacks (#) Max size of stacks (#) C 16 H 10 3~4 6 C 24 H C 32 H C 42 H C 54 H Source: clusters with 50 molecules

23 MD intermolecular potential Isotropic version fitted to PAHAP for use with MD code U ab = G exp f [ α ( R ρ )] 6 ( R ) ab ab C R ab ab 6 6 ab + ab qaq R ab b Coronene (C 24 H 12 ) [1] U inter = A A< B a A b B U ab More accurate than standard potentials [1] Tim Totton, Alston Misquitta, and, Physical Chemistry Chemical Physics, 14, (2012)

Soot - Developing anisotropic potentials from first principles for PAH molecules. Tim Totton, Alston Misquitta and Markus Kraft 12/11/2009

Soot - Developing anisotropic potentials from first principles for PAH molecules. Tim Totton, Alston Misquitta and 12/11/2009 HRTEM images of soot Some evidence for different soot structures based on different