Supporting information for: Large Protonation-Gated Photochromism of an OPE-Embedded Difurylperfluorocyclopentene

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1 Eletrni Supplementary Material (ESI) fr Physial Chemistry Chemial Physis. This jurnal is the Owner Sieties 015 1/9 Supprting infrmatin fr: Large Prtnatin-Gated Phthrmism f an OPE-Embedded Difurylperflurylpentene Janni Wlf, $, Thmas Huhn *,$ and Ulrih E. Steiner $ $ ahbereih Chemie, Universität Knstanz, D Knstanz, Germany; Present address: Slar & Phtvltais Engineering Researh Center, King Abdullah University f Siene and Tehnlgy, Thuwal , Saudi Arabia. Crrespnding Authr * thmas.huhn@uni-knstanz.de. Cntent: 1. System f equatins fr alulating the equilibrium nentratins f the speies B, BH, HA and A -. Absrbane/Absrbane diagrams fr the spetral hange n titratin f S by TAH 3. Simulated spetra f the three prtlyti frms 4. Defining a ph nn-aq in a nn-aqueus aprti slvent 5. Calulatin f the fratins f the prtlyti frms during frward and bak titratin 6. Derivatins f the ph dependent quantum yields f individual prtlyti frms BH, 1

2 /9 1. System f equatins fr alulating the equilibrium nentratins f the speies B, BH, BH, HA and A - Here the symbl B fr the base applies t either f the phthrmi frms S and S. A [BH ] = K1[HA] (S1) A [BH ] = K[HA] (S) [BH ] [ ] 0 = B BH [BH ] (S3) 0 [ ] [HA] = HA [A ] (S4) [ HA] = [ HA] BH BH 0 (S5). Absrbane/Absrbane diagrams fr the spetral hange n titratin f S by TAH igure S1 Absrbane vs. absrbane diagrams fr the wavelengths f strngest spetral hange during titratin f S by TAH (f. Spetra in igure 1).

3 3/9 3. Simulated spetra f the three prtlyti frms Absrbane Absrbane Wavelength [nm] Wavelength [nm] Absrbane Absrbane Wavelength [nm] Wavelength [nm] igure S Simulated spetra f the three prtlyti frms S (blak), S H (blue) and S (red) fr H representative values f the equilibrium nstants K 1 and K. In all ases, the fit f A λ ([TAH] 0 ) is equally gd. In ase f the fit values K 1 = K = 0.08 the spetrum f BH is best entered between thse f B and BH. In this ase it is als shwn that the spetrum f S H is lse t a linear mbinatin f the spetra f S and S H (dashed blue urve). 4. Defining a ph nn-aq fr a nn-aqueus aprti slvent In water, prtlyti equilibria are related t slvated prtns H, usually written as H 3 O, but ften just dented H. r example fr a general base B B H BH (S6) Arding t the law f mass atin, the equilibrium nentratins f B and BH are determined by the equilibrium nstant K B and the prtn nentratin [H ]: K B 3

4 4/9 BH = ph KB[H ] = KB 10 (S7) The aidity r prtnating pwer f the slutin is desribed by the ph defined as: ph aq = lg H (S8) In nn-aqueus aprti slvents that annt be prtnated, the prtns are dnated by the undissiated aid: K B B HA BH A (S9) Hene the rati f equilibrium nentratins f B and BH is given by: BH [HA] = K B (S10) [A ] Cnsequently, fr a given aid HA, the aidity in a nn-aqueus aprti slvent may be defined by the rati [HA]/[A - ]. Hene the systemati generalizatin f the definitin f ph fr a nn-aqueus aprti slvent ntaining the aid HA wuld be: [HA] ph nn aq = lg [A (S11) ] and the nentratin rati f aid t base frm is again uniquely determined by ph nn-aq. BH phnn aq = KB 10 (S1) [ B] This nept is similar t the Hammet H 0 funtin in superaid media. [S1,S] 5. Calulatin f fratins f prtlyti frms during frward and bak titratin In the fllwing, base B represents either f the tw phthrmi frms S and S with its speifi equilibrium nstants. The definitins: [BH ] ph b1 = K110 (S13) [BH ] ph b = K10 (S14) [BH ] are useful t represent the fratins f the varius prtlyti frms: 1 X = 1 b bb (S15) Y tt 1 1 [BH ] 1 b b 1 = (S16) bb tt 1 1 [BH ] bb 1 Z = (S17) tt 1 b1 bb 1 Nte that, depending n the ase, the nentratin tt refers t [S ] tt r [S ] tt. Using these fratins, the absrbane at any wavelength is represented as: 4

5 5/9 ( λ, ) ( λ) ( λ) Y ( λ) A ph = A X A A Z (S18) 1 3 with the definitins [ ] [ ] [ ] A = ε B A = ε B A = ε B (S19) 1 B tt BH tt 3 BH tt where the ε i represent the mlar extintins effiients f the varius speies and the ptial path length. 6. Derivatins f the ph dependent quantum yields f individual prtlyti frms The time-dependene f the sum [ S ] tt f the nentratins f the pen frms is desribed by equatin ((S0)): d [ S ] [ ] SH SH S S tt ε εs H ε A S H = I0 ( 1 10 ) ΦS Φ Φ SH SH dt V A A A (S0) ε [S H ] S H S [S ] ε S H ε S H ΦS Φ Φ SH SH A A A where I 0 is the phtn flux density, the illuminated area f the uvette, V the (stirred) vlume f the sample slutin, A the ttal absrbane at the wavelength f irradiatin, the varius ε parameters the mlar absrptin effiients f the respetive speies, and the ptial path length. Using the definitins in Setin 5 abve and the expressin fr the phtkineti fatr pk equatin (S0) an be simplified t: pk A = (S1) A 1 10 Substituting yields: tt d [ S ] by: [ S ] dt tt {( Φ Φ, Φ, 3 )[ S ] = I A X A Y A Z V 1 pk 0 S,1 SH SH tt ( ΦS A )[ ],1 X Φ A SH, Y Φ A SH,3Z S } tt (S) [ S ] = [ S ] [S ] (S3) tt tt tt d [ S ] dt tt {( Φ Φ )[ ] SH, Φ Φ Φ Φ S SH SH SH = I A X A Y A Z A X A Y A Z V 1 pk 0 S,1,3 S,1,,3 tt ( ΦS A )[ ],1 X Φ A SH, Y Φ A SH,3Z S } tt (S4) 5

6 6/9 Within eah kineti run at a given ph nn-aq, the expressins in the rund brakets f equatin (S4) are nstant. They represent the analgues f the pseud quantum yield Q in a phtreversible reatin with ne prtlyti speies nly. Defining Q = Q Q with ( ΦS A,1 X Φ A,3 ) ( S SH,Y Φ A Φ SH Z A,1 X Φ A SH, Y Φ A SH,3Z) = Q = Φ A X Φ A Y Φ A Z SH Q = Φ A X Φ A Y Φ A Z S,1 SH,,3 S,1,,3 SH SH (S5) (S6) (S7) the phtkineti rate law simplifies t: d [ S ] dt tt = I0 Q[ ] Q[ ] V { S S } 1 pk tt tt (S8) The send term in parentheses is related t the PSS by: Q[ S] Q[ S ] Thus, equatin (S8) an be written as Sine [ ], tt d [ S ] dt tt = tt, pss (S9) = I Q{ [ S] [ S ] } (S30) V tt, 1 pk 0 tt tt, pss S is linearly related t the absrbane at any wavelength, an equatin f the frm f equatin (S30) is als valid fr the absrbane A at the bservatin wavelength f hie: da 1 = pki0 Q{ A Apss} (S31) dt V Reslving equatin (S9) fr yields an equatin suitable fr the experimental determinatin f : Q = tt, pss Q[ S ] /[ S] tt (S3) Arding t equatin (S5) Q is btained as Q = Q Q (S33) In igure S3, we shw three fit versins assuming different values f K K,1 =K, equal t 0.06, 0.08, 0.1. In eah fit, the value f φs is fixed t a value f , suh that the Q value in slutin withut aid is exatly reprdued. The tw ther quantum yields φ, and φ were left as free fitting S H S H parameters. 6

7 7/9 r K = 0.06, the fit urve learly rises t early when passing ph nn-aq = 0 t the negative diretin. This is due t the fat that the ntributin f S H must mpensate fr the late rise f the ntributin f S H Table S1 Data used t fit the individual quantum yields fr the ring-lsing ismerizatin f the prtlyti frms f S indued by irradiatin with 313 nm light. a equiv TAH n [S] tt Q A 583 at PSS %pen in PSS Q 313 ph nn-aq 10 6 b X Y Z a Here, all alulatins were arried ut assuming K,1 = K, = b Calulated n the basis f equatins (S1)-(S5) and equatin (S11). Theretial effiients alulated arding t equatins (S6) (S10). T fit the ph nn-aq dependene f Q 313 arding t equatin (S6), the fllwing absrbanes f the individual prtlyti speies f S were used: A S = 0.706, A = 0.704, and A = S H whih is due t an bviusly t lw basiity f S H fr the K value hsen. Hwever, then S H already ntributes t muh in the verlapping regin f S and S H. On the ther hand, fr K = 0.10, a negative quantum yield must be assumed fr S H t mpensate the t early rising f the ntributin f S H appearing as a nsequene f an bviusly smewhat t high basiity f S and S H. S H The value f K = 0.08 lies just in between the tw latter ases and thus prvides the best fit. Atually, here t, the quantum yield fr S H is slightly negative, if mplete freedm is admitted fr the fit f φ, and φ S H H. It is demnstrated in igure S3, that setting φ t zer wuld nt signifiantly affet S S H the qualitiy f the fit, and that the upper limit f φ S H belw a value f 0.01., set by the experimental auray, wuld be learly 7

8 8/9 ph nn-aq ph nn-aq ph nn-aq igure S3 its f the ph nn-aq dependene f the bserved partial pseud quantum yield Q (blak data pints), alulated fr three ases f K,1 = K, values. Blak lines: ttal simulated value f Q, magenta lines: ntributins f S, saled by a fatr f 10 fr better visibility, blue lines: ntributins f S H, red lines: ntributins f S H. The fits were fred t reprdue the data pint in nn-aidified slutin exatly, thereby fixing the quantum yield fr S t φ S = The ther quantum yields were 8

9 9/9 btained frm a free least squares fit using Mathematia. In ase f K 1 = K, = 0.08, the effet f a quantum yield adaptatin fr S H is als shwn: φ S H = (free fit, slid blue line fr ntributin f S H t Q, slid blak line fr ttal value f Q ), φ S H = 0.0 (set value, brken blue hrizntal line fr ntributin f S H t Q, lwer brken blak line fr ttal value f Q ), φ S = 0.01 H (set value, upper brken blue line fr ntributin f S H t Q, upper brken blak line fr ttal value f Q ). The fit f the ring-pening phtkinetis fr irradiatin at 313 nm is shwn in igure S4. igure S4 Partitining f pseud quantum yield fr the ring-pening ismerizatin at 313 nm int ntributins f individual prtlyti frms f S (magenta), S H (blue) and S (red) f the lsed H frm as a funtin f ph nn-aq. Red dts represent measured data pints. The blak urve represents the best fit f the dataset with the fllwing parameters: AS = 0.507, A S H φ φs H S = 0.007, = 0.001, φs H ph nn-aq = 0.543, A S H = Errr margins f quantum yields ±30%. = 0.570, Referenes: S1) Hammett, L. P.; Deyrup, A. J., J. Am. Chem. S. 193, 54, S) Hammett, L. P., Physial rgani hemistry: reatin rates, equilibria, and mehanisms. MGraw Hill Bk Cmpany,