Dr Jonathan Skelton Department of Chemistry, University of Manchester ([email protected]) Planning time-resolved experiments: kinetic modelling 

Acknowledgements Dr Jonathan Skelton i19 TR Workshop, 24th Jan 2023 | Slide 2 ... plus many others, too numerous to mention 

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 

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 

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

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 

Photocrystallography i19 TR Workshop, 24th Jan 2023 | Slide 7 Dr Jonathan Skelton Images: L. E. Hatcher and M. R. Warren 

Photocrystallography i19 TR Workshop, 24th Jan 2023 | Slide 8 Dr Jonathan Skelton 

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 

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 

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 

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 

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) 

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 

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 

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 

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 

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 

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 

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” 

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 

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 

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 

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 

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 

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

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 

Preliminary measurements i19 TR Workshop, 24th Jan 2023 | Slide 28 Dr Jonathan Skelton 

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 

TR results 1 i19 TR Workshop, 24th Jan 2023 | Slide 30 Dr Jonathan Skelton 

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 

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 

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 

Thankyou for listening! Any questions?