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
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
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 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
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
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
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 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
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
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
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
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
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
| 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