Carbonyl Groups. University of Chemical Technology, Beijing , PR China;

Transcription

1 Electroc Supplemetary Materal (ESI) for Physcal Chemstry Chemcal Physcs Ths joural s The Ower Socetes 0 Supportg Iformato A Theoretcal Study of Structure-Solublty Correlatos of Carbo Doxde Polymers Cotag Ether ad Carboyl Groups Megj Xu a, Ja Che b, Che Zhag a, Zhogje Du *a ad Jaguo M *c a The Key Laboratory of Carbo Fber ad Fuctoal Polymers, Mstry of Educato, Bejg Uversty of Chemcal Techology, Bejg 0009, PR Cha; b State Key Laboratory of Chemcal Egeerg, Departmet of Chemcal Egeerg, Tsghua Uversty, Bejg 00084, Cha; c Laboratory of Computatoal Chemstry, Departmet of Chemcal Egeerg, Bejg Uversty of Chemcal Techology, Bejg 0009, Cha Computatoal Method. The Geerator Matrx Method * Correspodg authors: duzj@mal.buct.edu.c; mjg@mal.buct.edu.c

2 Electroc Supplemetary Materal (ESI) for Physcal Chemstry Chemcal Physcs Ths joural s The Ower Socetes 0 The secod ad the fourth momets ad r 4 r betwee the two pots the Koyama dstrbuto fucto are calculated through the geerator matrx method. For the Cartesa coordate system, suppose the supplemetary agle of bod vector l ad l + to be θ each macromolecule cha, ad set = α γ. The summato of the two stes α ad γ ca be expressed as r = l = () where l = ( l,0,0)', l s the bod legth ad ' meas trasposg. Let T deote the matrx of the trasformato betwee referece frames + ad. For smplcty, the er rotato of bod s supposed to be fully free, ad depedet betwee each other, thus T cosθ sθ 0 = () The square of the magtude of the cha vector r betwee stes α ad γ ca be wrtte as r r r l l l l l = = j = j + = j= j> = = = + ' ltt + Tj lj l j>= = (3) Here l ' s the trasposed form of bod vector l. The geerator matrx wth rows s G = ( l T l ), (4) ' G = ( l l ), (5) ' ' ' lt l G = 0 T l ( < < ) 0 0 (6)

3 Electroc Supplemetary Materal (ESI) for Physcal Chemstry Chemcal Physcs Ths joural s The Ower Socetes 0 Therefore r =Π G (7) = ad the secod momet ca be symbolzed by = Π r G G G = (8) wth ' l T l G = 0 T l ( < < ) 0 0 (9) Set A ad B to be j ad k l order matrx, respectvely. The drect product A B s k jl order matrx, whch has the elemet AjB the th row ad jth colum. Correspodgly, the expresso of 4 r s obtaed 4 =Π( ) Π = = r G G G (0) The fourth momet ca be gve the hgh order tesor form r = G ΠG G 4 = (). Itramolecular Correlato Fuctos For smplcty, PEC acts as a example. The repeat ut of PEC cotas sx stes. As show Fgure, the stes A, B, C, D, E ad F correspod to the CH, ether oxyge, carboyl carbo, ether oxyge, emthylee ad carboyl oxyge, respectvely. Accordgly, depedet tramolecular correlato

4 Electroc Supplemetary Materal (ESI) for Physcal Chemstry Chemcal Physcs Ths joural s The Ower Socetes 0 fuctos betwee the lke stes as well as the ulke stes were obtaed after some tedous algebrac summatos. They were gve as follows (due to the symmetry structure of PEC, depedet tramolecular correlato fuctos could be reduced to 3 depedet tramolecular correlato fuctos) N ˆ ˆ Ω ( k) =Ω ( k) = + ( N ) ˆ ω ( k) () AA EE AA = 5 N ˆ ˆ Ω ( k) =Ω ( k) = + ( N ) ˆ ω ( k) (3) BB DD BB = 5 N ˆ Ω ( k) = + ( N ) ˆ ω ( k) (4) CC CC = 5 N ˆ Ω ( k) = + ( N ) ˆ ω ( k) (5) FF FF = 5+ N ˆ ˆ Ω ( k) =Ω ( k) = ˆ ω ( k) + ( N ) ˆ ω ( k) + ˆ ω ( k) [ ] (6) AB DE AB = AB = 5+ AB = 5 N ˆ ˆ Ω ( k) =Ω ( k) = ˆ ω ( k) + ( N ) ˆ ω ( k) + ˆ ω ( k) [ ] (7) AC CE AC = AC = 5+ AC = 5 N ˆ ˆ Ω ( k) =Ω ( k) = ˆ ω ( k) + ( N ) ˆ ω ( k) + ˆ ω ( k) [ ] (8) AD BE AD = 3 AD = 5+ 3 AD = 5 3 N ˆ Ω ( k) = ˆ ω ( k) + ( N ) ˆ ω ( k) + ˆ ω ( k) [ ] (9) AE AE = 4 AE = 5+ 4 AE = 5 4 N ˆ ˆ Ω ( k) =Ω ( k) = ˆ ω ( k) + ( N ) ˆ ω ( k) + ˆ ω ( k) [ ] (0) AF EF AF = 3 AF = 5+ 3 AF = 5 N ˆ ˆ Ω ( k) =Ω ( k) = ˆ ω ( k) + ( N ) ˆ ω ( k) + ˆ ω ( k) [ ] () BC CD BC = BC = 5+ BC = 5

5 Electroc Supplemetary Materal (ESI) for Physcal Chemstry Chemcal Physcs Ths joural s The Ower Socetes 0 N ˆ Ω ( k) = ˆ ω ( k) + ( N ) ˆ ω ( k) + ˆ ω ( k) [ ] () BD BD = BD = 5+ BD = 5 N ˆ ˆ Ω ( k) =Ω ( k) = ˆ ω ( k) + ( N ) ˆ ω ( k) + ˆ ω ( k) [ ] (3) BF DF BF = BF = 5+ BF = 5 N ˆ Ω ( k) = ˆ ω ( k) + ( N ) ˆ ω ( k) (4) CF CF = CF = Reduced X-ray Scatterg Itesty The so called reduced X-ray scatterg testy s defed by I k = k k f k ( ) ( ) ( ) (5) here, k s scatterg vector, ad k = 4 π s θ / λ, λ s the wavelegth of the scattered radato, θ s the scatterg agle, k ( ) s the scatterg testy per ste, ad f ( k) s the scatterg factor squared averaged over all stes wrtte the form α α α= f ( k) = x f ( k) (6) I whch s the umber of stes wth a repeat ut of polymer, x α ad fα ( k) are the mole fracto ad scatterg factors of the stes, respectvely. The scatterg factors of dfferet stes ca be calculated followg Narte s method 4 b α k /(6 π ) (7) = f ( k) = a e + c α α α The costats a α, b α ad c α are also take from referece. The k ( ) ca be wrtte terms of k ( ) = f ( k) f ( ks ) ( k)/ (8) α γ

6 Electroc Supplemetary Materal (ESI) for Physcal Chemstry Chemcal Physcs Ths joural s The Ower Socetes 0 Here the S ( k) s determed usg the followg equatos S ( k) = ω ( k) + ρ h ( k) (9) α ad ρα s the ste desty of type α 4. Destes for Polymers at Dfferet Temperatures The destes for PEO, PPO, PVAc, PEC, PPC at dfferet temperatures are gve Table. Refereces P. J. Flory, Macromolecules, 974, 7, 38. A. H. Narte, J. Chem. Phys., 979, 70, 99.

7 Electroc Supplemetary Materal (ESI) for Physcal Chemstry Chemcal Physcs Ths joural s The Ower Socetes 0 Table. Destes for polymers at dfferet temperatures T (K) ρ (g/cm 3 ) PEO PPO PVAc PEC PPC

8 Electroc Supplemetary Materal (ESI) for Physcal Chemstry Chemcal Physcs Ths joural s The Ower Socetes 0 CH O C O CH A B C F D E O Fgure. Graphc represetato of PEC