Upgrade to Pro — share decks privately, control downloads, hide ads and more …

Planning time-resolved experiments: kinetic modelling

Planning time-resolved experiments: kinetic modelling

Presented at the Time-Resolved I19 Workshop at Diamond Light Source.

Jonathan Skelton

January 22, 2023
Tweet

More Decks by Jonathan Skelton

Other Decks in Science

Transcript

  1. Dr Jonathan Skelton Department of Chemistry, University of Manchester ([email protected])

    Planning time-resolved experiments: kinetic modelling
  2. Acknowledgements Dr Jonathan Skelton i19 TR Workshop, 24th Jan 2023

    | Slide 2 ... plus many others, too numerous to mention
  3. Overview i19 TR Workshop, 24th Jan 2023 | Slide 3

    Dr Jonathan Skelton o Solid-state linkage isomerism o Photocrystallography o Kinetics: JMAK theory • The decay process • The excitation process • Steady-state behaviour • Numerical simulations o Summary: key questions to ask o Time-resolved experiment https://bit.ly/3ZWTayo
  4. Solid-state linkage isomerism i19 TR Workshop, 24th Jan 2023 |

    Slide 4 Dr Jonathan Skelton https://chem-is-you.blogspot.com/2013/05/chemistry-of-d-and-f-block-origin-of.html
  5. Solid-state linkage isomerism i19 TR Workshop, 24th Jan 2023 |

    Slide 5 Dr Jonathan Skelton SO2 (sulphoxide) NO (nitrosyl) NO2 - (nitrite) N2 (“dinitrogen”)
  6. Solid-state linkage isomerism i19 TR Workshop, 24th Jan 2023 |

    Slide 6 Dr Jonathan Skelton L. E. Hatcher et al., Phys. Chem. Chem. Phys. 20, 5874 (2018), DOI: 10.1039/C7CP05422J
  7. Photocrystallography i19 TR Workshop, 24th Jan 2023 | Slide 7

    Dr Jonathan Skelton Images: L. E. Hatcher and M. R. Warren
  8. Photocrystallography i19 TR Workshop, 24th Jan 2023 | Slide 8

    Dr Jonathan Skelton
  9. Photocrystallography i19 TR Workshop, 24th Jan 2023 | Slide 9

    Dr Jonathan Skelton L. E. Hatcher et al., Phys. Chem. Chem. Phys. 20, 5874 (2018), DOI: 10.1039/C7CP05422J
  10. Kinetics: JMAK theory i19 TR Workshop, 24th Jan 2023 |

    Slide 10 Dr Jonathan Skelton Slow initial rate: waiting for nuclei to form Fast transformation: existing nuclei grow and new nuclei form Slow final rate: little untransformed phase for nuclei to continue to grow https://www.tf.uni-kiel.de/matwis/amat/iss/kap_8/illustr/s8_4_3b.html
  11. Kinetics: JMAK theory i19 TR Workshop, 24th Jan 2023 |

    Slide 11 Dr Jonathan Skelton Can be described by the JMAK equation: 𝛼 𝑡 = 𝛼∞ + (𝛼0 − 𝛼∞ )𝑒−𝑘𝑡𝑛 where: 𝛼 𝑡 𝛼0 /𝛼∞ 𝑘 𝑛 = = = = fraction transformed initial/final fractions rate constant Avrami exponent https://www.tf.uni-kiel.de/matwis/amat/iss/kap_8/illustr/s8_4_3b.html
  12. JMAK: the 𝒌 and 𝒏 parameters i19 TR Workshop, 24th

    Jan 2023 | Slide 12 Dr Jonathan Skelton 0.0 0.2 0.4 0.6 0.8 1.0 0 10 20 30 40 50 60 α(t) t [s] k = 0.01 k = 0.1 k = 1 0.0 0.2 0.4 0.6 0.8 1.0 0 10 20 30 40 50 60 α(t) t [s] n = 1 n = 2 n = 3 n = 4 𝛼0 = 1, 𝛼∞ = 0, 𝑛 = 1 𝛼0 = 1, 𝛼∞ = 0, 𝑘 = 10-2 s−𝑛
  13. JMAK: the Avrami exponent 𝒏 i19 TR Workshop, 24th Jan

    2023 | Slide 13 Dr Jonathan Skelton Initial 𝑛 = 1 (0D growth) 𝑛 = 2 (1D growth) 𝑛 = 4 (3D growth) 𝑛 = 3 (2D growth)
  14. The decay process i19 TR Workshop, 24th Jan 2023 |

    Slide 14 Dr Jonathan Skelton Decay corresponds to 𝛼𝑡=0 = 1 and 𝛼𝑡=∞ = 0: 𝛼 𝑡 = 𝑒−𝑘dec𝑡𝑛 L. E. Hatcher et al., Phys. Chem. Chem. Phys. 20, 5874 (2018), DOI: 10.1039/C7CP05422J
  15. Temperature dependence i19 TR Workshop, 24th Jan 2023 | Slide

    15 Dr Jonathan Skelton The 𝑘dec as a function of temperature usually follows the Arrhenius law: 𝑘dec 𝑇 = 𝐴exp − 𝐸A 𝑅𝑇 → ln 𝑘dec 𝑇 = ln 𝐴 − 𝐸A 𝑅 1 𝑇 L. E. Hatcher et al., Phys. Chem. Chem. Phys. 20, 5874 (2018), DOI: 10.1039/C7CP05422J
  16. Metastable state lifetime i19 TR Workshop, 24th Jan 2023 |

    Slide 16 Dr Jonathan Skelton Substitute 𝑘dec (𝑇) into JMAK equation, set 𝛼 = 0.5 and solve for 𝑡: 𝑡 𝛼 = 0.5 = − 1 𝐴 ln 0.5 exp 𝐸A 𝑅𝑇 1 𝑛 1 s 10 s 1 min 1 hr 1 day L. E. Hatcher et al., Phys. Chem. Chem. Phys. 20, 5874 (2018), DOI: 10.1039/C7CP05422J
  17. The excitation process i19 TR Workshop, 24th Jan 2023 |

    Slide 17 Dr Jonathan Skelton Excitation corresponds to 𝛼𝑡=0 = 0 and 𝛼𝑡=∞ = 1: 𝛼 𝑡 = 1 − 𝑒−𝑘exc𝑡𝑛 L. E. Hatcher et al., Phys. Chem. Chem. Phys. 20, 5874 (2018), DOI: 10.1039/C7CP05422J
  18. The excitation process i19 TR Workshop, 24th Jan 2023 |

    Slide 18 Dr Jonathan Skelton L. E. Hatcher et al., Phys. Chem. Chem. Phys. 20, 5874 (2018), DOI: 10.1039/C7CP05422J MS occupation after 120 s illumination w/ four different xtals
  19. Steady-state behaviour i19 TR Workshop, 24th Jan 2023 | Slide

    19 Dr Jonathan Skelton For a typical linkage isomer system, we have: o A strongly temperature-dependent decay rate 𝑘dec o A weakly temperature-dependent (i.e. approximately constant) excitation rate 𝑘exc Competing processes result in three temperature regimes: o Low 𝑇: 𝑘dec << 𝑘exc → 𝛼 = 1 (complete excitation) o High 𝑇: 𝑘dec >> 𝑘exc → 𝛼 = 0 (no excitation) o Intermediate 𝑇: 𝑘dec ≈ 𝑘exc → 0 < 𝛼 < 1 (steady state) Can measure the steady-state occupation as a function of temperature by collecting structures under continuous illumination
  20. Steady-state behaviour i19 TR Workshop, 24th Jan 2023 | Slide

    20 Dr Jonathan Skelton L. E. Hatcher et al., Phys. Chem. Chem. Phys. 20, 5874 (2018), DOI: 10.1039/C7CP05422J “metastable limit”
  21. Numerical simulations i19 TR Workshop, 24th Jan 2023 | Slide

    21 Dr Jonathan Skelton Cannot predict steady-state behaviour analytically -> need numerical simulations 𝑡 = 0 𝛼 = 𝛼0 𝑡dec ′ = Τ −ln𝛼 𝑘dec Τ 1 𝑛 ∆𝛼 dec = exp −𝑘dec 𝑡dec ′ + ∆𝑡 𝑛 − 𝛼 Excitation active? 𝑡 = 𝑡 + ∆𝑡 𝛼 = 𝛼 + ∆𝛼 dec + ∆𝛼 exc ∆𝛼 exc = 0 𝑡exc ′ = Τ −ln 1 − 𝛼 𝑘exc Τ 1 𝑛 ∆𝛼 exc = 1 − exp −𝑘exc 𝑡exc ′ + ∆𝑡 𝑛 − 𝛼 𝑡 = 𝑡max ? 𝑡 = 𝑡 𝛼(𝑡) = 𝛼 Update params? Predicted 𝑡, 𝛼(𝑡) Y N N Y N Y
  22. Numerical simulations 1 i19 TR Workshop, 24th Jan 2023 |

    Slide 22 Dr Jonathan Skelton L. E. Hatcher et al., Phys. Chem. Chem. Phys. 20, 5874 (2018), DOI: 10.1039/C7CP05422J
  23. Numerical simulations 2 i19 TR Workshop, 24th Jan 2023 |

    Slide 23 Dr Jonathan Skelton L. E. Hatcher et al., Phys. Chem. Chem. Phys. 20, 5874 (2018), DOI: 10.1039/C7CP05422J Each simulation started with 𝛼 = 0 and run in three segments: 1. 𝑡 = 0-2 mins: no excitation → nothing happens 2. 𝑡 = 2-4 mins: excitation switched on → excites towards steady state 3. 𝑡 = 4-24 mins: excitation switched off → steady-state population decays
  24. Numerical simulations 3 i19 TR Workshop, 24th Jan 2023 |

    Slide 24 Dr Jonathan Skelton L. E. Hatcher et al., Phys. Chem. Chem. Phys. 20, 5874 (2018), DOI: 10.1039/C7CP05422J 180 s pulse
  25. Summary: key questions to ask Dr Jonathan Skelton o Can

    we measure the kinetics of the process we want to study? • Performed low-𝑇 (“slow”) photocrystallography experiments on a lab machine and extrapolated to higher 𝑇 o Can we estimate a “ballpark” lifetime for the excited state? • Can derive from JMAK kinetic fits; ranges from ~days at 𝑇 = 200 K to ~1s at 300 K o Can we use our data to plan any other aspects of the experiments? • Can use fairly simple numerical simulations parameterised by kinetic measurements to: 1) predict behaviour during a simulated pump/probe experiment; and 2) suggest experimental parameters e.g. excitation time and measurement temperature i19 TR Workshop, 24th Jan 2023 | Slide 25
  26. Time-resolved experiment i19 TR Workshop, 24th Jan 2023 | Slide

    26 Dr Jonathan Skelton
  27. Time-resolved experiment i19 TR Workshop, 24th Jan 2023 | Slide

    27 Dr Jonathan Skelton Our workflow: 1. Preliminary experiments: o Decay curves at 𝑇 = 240-270 K o Excitation curve at 𝑇 = 150 K o Steady-state occupation between 𝑇 = 250-300 K 2. Kinetic fitting to derive 𝐴 and 𝐸A for decay and estimate 𝑘exc 3. Numerical simulations to select 𝑡exc /𝑡dec and estimate 𝑇 for given 𝑡cyc 4. Time-resolved measurement at estimated 𝑇 + automatic processing to determine rough 𝛼 𝑡 - inspect result and raise/lower 𝑇 as required 5. Data fitting using numerical simulations to extract 𝑘exc and 𝑘dec from each TR dataset
  28. Preliminary measurements i19 TR Workshop, 24th Jan 2023 | Slide

    28 Dr Jonathan Skelton
  29. Numerical simulations i19 TR Workshop, 24th Jan 2023 | Slide

    29 Dr Jonathan Skelton 𝑡cyc = 170 s 𝑡cyc = 34 s 𝑡cyc = 14 s 𝑡cyc = 22 s 𝑡cyc = 108 s L. E. Hatcher et al., Nature Comms. Chem. 5, 102 (2022), DOI: 10.1038/s42004-022-00716-1
  30. TR results 1 i19 TR Workshop, 24th Jan 2023 |

    Slide 30 Dr Jonathan Skelton
  31. TR results 2 i19 TR Workshop, 24th Jan 2023 |

    Slide 31 Dr Jonathan Skelton Data from lab (Ph-SCXRD), DLS (Ph-SCXRD) and DLS (TR) L. E. Hatcher et al., Nature Comms. Chem. 5, 102 (2022), DOI: 10.1038/s42004-022-00716-1
  32. TR results 3 i19 TR Workshop, 24th Jan 2023 |

    Slide 32 Dr Jonathan Skelton L. E. Hatcher et al., Nature Comms. Chem. 5, 102 (2022), DOI: 10.1038/s42004-022-00716-1
  33. Follow up: Timepix tests i19 TR Workshop, 24th Jan 2023

    | Slide 33 Dr Jonathan Skelton L. E. Hatcher et al., Nature Comms. Chem. 5, 102 (2022), DOI: 10.1038/s42004-022-00716-1 Single module, (-2 1 0) reflection
  34. Thankyou for listening! Any questions?