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1 Supportg formato O-demad degraftg ad the study of molecular eght ad graftg desty of poly(methyl methacrylate) brushes o flat slca substrates Roha atl, Salomo Turgma Cohe, Jří Šrogl, Douglas Ksero 3, Ja Gezer,* Departmet of Chemcal ad Bomolecular Egeerg orth Carola State Uversty Ralegh, orth Carola Departmet of Chemcal Egeerg Ketterg Uversty Flt, Mchga US Army Research Offce Research Tragle ark, orth Carola * correspodg author: Ja Gezer (a_gezer@csu.edu)

2 Effect of TBAF o polymer molecular eght We tested hether TBAF has a effect o the molecular eght of MMA. To that ed, e performed cotrol SEC expermets usg pure THF solvet, THF cotag a hgh cocetrato of TBAF, ad MMA (stadard sytheszed by aoc polymerzato; M 4 kda) soluto cotag varous cocetratos of TBAF at 50C for 4 hours. The results (cf. Fgure S) demostrate that the eluto tme of MMA s ot affected by the presece of TBAF ad that the molecular eght dstrbuto of MMA eluted from TBAF solutos of varous cocetratos s detcal to that of MMA THF solvet oly. Fgure S. DRI sgal as a fucto of eluto tme SEC collected from pure THF (black), THF th 0. M TBAF (red), MMA stadard (gree), MMA stadard mmersed 0.0 M soluto of TBAF (blue), ad MMA stadard mmersed 0. M soluto of TBAF (mageta). Determg the molecular eght dstrbuto of polymers We have performed sze excluso chromatography (SEC) expermets to test the loest sestvty of the DRI detector to determe uambguously the molecular eght dstrbuto (MWD) our samples. I these tests, e used polystyree (S) stadards (commercally avalable from Fluka) as ell as S ad MMA specmes prepared by free radcal polymerzato (FR), atom trasfer radcal polymerzato (ATR) ad reverse ATR (RATR).

3 Fgure S. (ma) Eluto curves as determed by the DRI detector for S stadards (sytheszed by aoc polymerzato ad obtaed from Fluka, th a omal umber average molecular eght of 70 kda) as a fucto of polymer cocetrato THF. (left set) tegrated area uder the S eluto peak as a fucto of S cocetrato THF. (rght set) ormalzed DRI sgal obtaed by dvdg the ra DRI sgal by the S peak tegrated area (cf. set o left) as a fucto of S eluto tme. The SEC expermets ere carred out usg polymer solutos THF order to maxmze the refractve dex cotrast betee the polymer ad the solvet. For stace, the refractve dces of polystyree (S) ad poly(methyl methacrylate) (MMA) are.59 ad.49, respectvely. The refractve dex of THF s ad that of toluee s We tested the sestvty of the dfferetal refractve dex (DRI) detector by passg polystyree solutos THF of varous cocetratos through the SEC. The samples featured both S stadards (prepared by aoc polymerzato ad obtaed from Fluka) as ell as S ad MMA specmes prepared by free radcal polymerzato, ATR ad reverse ATR (RATR). We determed that the mmum cocetrato of polymer solute THF s 0. mg/ml. At ths cocetrato the SEC eluto peaks dd ot exhbt ay dstorto due to sestvty lmt (cf. Fgure S ad Fgure S3) ad provded cosstetly the same values of the frst momet of the MWD,.e., the umber average molecular eght, M, as ell as the polydspersty dex (DI). For a substrate of dmesos 4. cm x 4. cm th MMA layer

4 (assumg bulk desty of.8 g/cm 3 ) the thckess of a flm correspodg to ml of 0. mg/ml soluto s 48 m. Ths s the mmum adequate thckess requred for a measuremet from a sgle sample. Fgure S3. (left colum) Eluto curves for varous S ad MMA samples as a fucto of the cocetrato THF. (rght colum) The umber average molecular eght (M, red symbols) ad the polydspersty dex (DI, blue symbols) of the respectve samples as a fucto of S cocetrato THF. The yello area deotes the rage of polymer cocetratos that are safe to use for MWD aalyss. Molecular eght dstrbuto determed from expermet We use the MWDs measured expermetally by SEC to determe the umber average degree of polymerzato ( ),.e., the st momet of the dstrbuto, the eght average degree of polymerzato ( ),.e., the d momet of the dstrbuto, ad the DI. DRI SEC measures the eght fracto dstrbuto of -mers as a fucto of the umber repeat uts each -mer,.e., =fx( ). From ths:

5 , (S), (S) DI, (S3) ote that DI s related to the stadard devato of a dstrbuto () va 5 / (S4) I the follog secto e provde mathematcal descrpto of several models that descrbe the molecular eght dstrbutos terms of eght fractos of a x-mer, x (x). osso dstrbuto The oso () dstrbuto descrbes the MWD a truly lvg polymerzato (.e., o termato or cha trasfer). The geeral form of the dstrbuto s gve by Equato (S5): v e v.! (S5) I Equato (S5), v s defed as: v. (S6) The DI s defed as: DI. v (S7) ote that because (x-)!=(x), Equato (S5) ca also be rtte as: v e v. (S8) Schulz-Zmm dstrbuto The Schulz-Zmm (SZ) dstrbuto s based o a model for cha polymerzato ad s sometmes called the most probable dstrbuto. As put, the SZ dstrbuto fucto uses, ad ether or the DI. ote that the aforemetoed quattes are coected: k DI. (S9) k

6 Whe oe defes k ad p as: k, (S0) DI k p, (S) DI oe ca sho that: k, (S) p k. (S3) p The eght fracto of a x-mer,.e., x (x), s gve by: k p k k exp p exp. (S4) k k k k k Equato (S4) s cosstet th the IUAC defto of the Schulz Zmm dstrbuto. 6 ATR dstrbuto Zhu ad coorkers recetly preseted a theory for molecular eght dstrbuto ATR. 7 Whle ths model has bee developed for bulk CSTR, e use t here as ell assumg that codtos the CSTR are roughly fulflled (.e., the cocetratos of the moomers ad the reactve speces are costat). I surface-tated polymerzato e ork th a large excess of moomers; e further assume that the cocetrato of the actve speces s costat f o termato takes place. I ths model, hch assumes that o termato takes place, the probablty that a radcal ll propagate s gve by: k pm M k XC. (S5) k p d I Equato (S5), [M] ad [XC] are the cocetratos of the moomer ad the deactvator (.e., metal halde), respectvely, ad k p ad k d are the reacto costats for propagato ad deactvato, respectvely. Whe e defe z as the umber of actvato cycles, e obta: z. (S6) z. (S7) DI. (S8) z

7 The eght fracto of a -mer s gve by: 0 z! z e. (S9) here z>0 ad <. Both z ad are used as a put. Further expadg the sum Equato (S9), oe obtas: 0 0! z!!!! z. (S0) The sum gve by Equato (S0) ca be expressed as: )z ( ;; F!!! z!!! 0. (S) here F (a;b;z) s (Kummer cofluet) hypergeometrc fucto. Fally, by combg Equato (S9) th Equato (S) oe arrves at: )z ( ;; F! e z. (S) Wesslau dstrbuto The Wesslau (W) dstrbuto s a dfferetal molecular eght dstrbuto smlar to Schulz- Zmm dstrbuto, both of hch are derved from a geeral form of most probable dstrbuto: 0 / l exp, (S3) here DI l l, (S4) 4 exp 0. (S5) The Wesslau dstrbuto s referred to as log ormal dstrbuto. Aother example of a log ormal dstrbuto s the so-called Lasg-Kraemer dstrbuto. Schulz-Flory dstrbuto The IUAC defto of the Schulz Flory (SF) dstrbuto s: 8 p p. (S6)

8 I Equato (S6) p s a emprcally-determed adustable parameter. Oe ca rte: 9 p exp p. (S7) Thus for k= ad kog that ()= oe ca recover (S6) from combg (S4) ad (S7). Ths dstrbuto mples that shorter polymers are favored over loger oes. Smth et al dstrbuto Thee dstrbuto due to Smth et al (S) 0 s used for lvg polymerzato th propagato, termato ad cha trasfer, here: R p. (S8) R p R t R tr I Equato (S8), the parameter represets the probablty that the cha ll propagate rather tha termate. Further: DI, (S9) or DI. (S30) The 3 A A. (S3) I Equato (S3), A s the fracto of polymer molecules formed by dsproportoato ad cha-trasfer reactos. Thus for A= termato occurs oly by dsproportoato hle for A=0 termato takes place by combato. The expresso the frst bracket Equato (S3) s mathematcally detcal to that obtaed for codesato (.e., step groth) polymerzato: p p, (S3) except o usg p stead of. I Equato (S3) p s defed as the extet of reacto (or the fracto of groups that have reacted or equvaletly the probablty of that a partcular group has reacted). ote also the smlarty betee the expresso the frst bracket o Equato (S3) ad the defto of gve by the Schulz-Flory dstrbuto,.e., Equato (S6). Specfcally, he replacg th -p Equato (S3) oe ca recover Equato (S6). Recall the defto of p for the Schulz-Flory dstrbuto, p s assumed to be a emprcally-determed adustable parameter. Ths s dfferet from the defto of p gve by Equato (S3). Replacg p th -p Equato (S3) also recovers Equato (S6). Hece, cauto has to be take th regard to the physcal meag ad defto of p all cases.

9 Modelg expermetal MWD We test ho ell are the MWD determed expermetally by SEC represeted by each of the aforemetoed models. I our aalyss, e do ot use the osso s dstrbuto for true lvg polymerzato because the fts ere of poor qualty. To obta the best ft to the expermetal data, e employ to approaches. These feature fttg the data usg the Kolmogorov-Smrov dstace statstc ad the ch-squared approach. The Kolmogorov-Smrov (K-S) dstace statstc s obtaed by comparg the cumulatve dstrbutos fuctos of the expermetal ad model molecular eght dstrbutos. 3 Oce the to cumulatve dstrbutos are obtaed, the K-S statstc s defed as the maxmum absolute dfferece betee the to: K S max D(),D(),D(3),...D( ), (S33) here D(x) s gve by: x max max x max D (x). (S34),exp ermet,mod el I Equato (S34),,expermet ad,model represet the value of the cumulatve dstrbuto for the -mer. I addto, for each data set ad each model e evaluate the stadard ch-squared value,, defed as: 4 max,exp ermet,exp ermet,mod el, (S35) Of the to methods, the ch-squared test s less preferred because bg the observatos ths maer results a loss of formato. I cotrast, the K-S method s more rgorous because t teds to fd the best ft to the expermetal data hle matag the formato about the fuctoal form gve by each respectve model. Depedece of graftg desty o brush polydspersty The graftg desty of surface-achored polymers s defed as: h A, (S36) M here h s the dry flm thckess, ρ s the bulk desty, A s Avogadro s umber, ad M s the average molecular eght. M s gve by: M M, (S37) 0 here M 0 s the moomer molecular eght ad s the umber average degree of polymerzato, gve by:

10 X, (S38) X here X s umber of polymers havg a degree of polymerzato of. From mass coservato t follos that h s obtaed by dvdg the total volume of polymer all uts the flm (V polymer ) by the sample area (A): V h polymer A. (S39) V polymer s a product of the volume of a moomer (V 0 ) ad the total umber of segmets preset: V V X. (S40) polymer 0 By sertg the expressos gve by Equatos (S37)-(S40) to Equato (S36), oe obtas: V 0 X A X X M 0 A. (S4) Assumg that the desty of a polymer s equal to the desty of a moomer, oe obtas: M 0 V0 A. (S4) Fally, after some algebra oe obtas: X. (S43) A Equato (S43) recovers the defto of the graftg desty as a total umber of polymers,.e., the umerator Equato (S43), per ut area. Equato (S43) demostrates that the graftg desty of polymer brushes does ot deped o the molecular eght dstrbuto (.e., polydspersty) of the polymer brushes as log as the umber of polymer brushes tated does ot crease after the polymerzato commeced. Dscusso of modelg the SEC curves I the paper e preseted the polymer eght fracto as a fucto of the umber average degree of polymerzato for MMA brushes gro va surface-tated ATR th Cu (II) /Cu (I) =0.00 for varous reacto tmes (cf. Fgure 5). The expermetal data ere modeled usg the Schulz-Zmm (SZ), ATR, Wesslau (W), Schultz-Flory (SF), ad Smth et al (S)

11 models. The fts ere obtaed by mmzg the K-S statstc ad the value of the K-S statstc at the mmum as take as a measure of the qualty of the ft. The results of the fts ere preseted Fgure 6, here e plotted the DI vs.. The results obtaed dcated that the SZ, ATR, ad W models performed very ell; the values of ad DI obtaed from the models matched very closely the expermetal values of the same quattes. I cotrast, the SF ad S models, hle they dd capture the geeral shape of the MWD profles, faled to reproduce quattatvely the expermetal values of ad DI. Here e preset plots smlar to those Fgure 5 ad Fgure 6 for the remag Cu (II) /Cu (I) ratos. Specfcally, Fgures S4, S6, ad S8 e plot the polymer eght fracto as a fucto of the umber average degree of polymerzato for MMA brushes gro va surface-tated ATR th Cu (II) /Cu (I) =0, 0.005, ad 0.05, respectvely. Expermetally measured data as ell as best fts to the aforemetoed models are provded. Fgures S5, S7, ad S9 dsplay the depedece of DI o for expermetal data as ell as the values obtaed from the best fts. Just as for the case Cu (II) /Cu (I) =0.00, the fts to the remag Cu (II) /Cu (I) cocetratos reveal that the SZ, ATR, ad W models ft the expermetal data quattatvely ell. The SF ad S models do ot descrbe the expermetal data ell. For completeess, e also clude the fts usg the ch-squared approach to MWDs from MMA brushes gro from slca surfaces usg ATR th Cu (II) /Cu (I) =0.00 for varous reacto tmes. ote that the fts obtaed by the K-S method are plotted Fgure 5 ad Fgure 6. The models due to SZ, ATR, W, SF, ad S approaches are plotted Fgure S0. The DI vs. depedece s preseted Fgure S. The treds see Fgure S match those dscussed earler th regard to Fgure 6. I spte of ths agreemet, the K-S method s preferred fttg the data because t captures the fuctoal form of the varous models better tha the ch-squared approach, as dscussed earler.

12 Fgure S4. Weght fracto of MMA chas ( ) degrafted from flat surfaces (black les) as a fucto of umber average degree of polymerzato ( ) for MMA brushes gro for a) 6, b) 9, c) 6, d) 0, ad e) 4 hrs th Cu (II) /Cu (I) =0 (see expermetal secto for detals). The expermetal data ere ftted usg the Kolmogorov-Smrov (K-S) method to dstrbutos featurg the models of Schulz-Zmm (red), ATR (gree), Wesslau (blue), Schulz-Flory (cya), ad Smth et al (mageta).

13 Fgure S5. olydspersty dex (DI) vs. umber average degree of polymerzato ( ) for MMA chas degrafted from flat surfaces (black star) gro for a) 6, b) 9, c) 6, d) 0, ad e) 4 hrs th Cu (II) /Cu (I) =0 (see expermetal secto for detals). The expermetal data ere ftted usg the Kolmogorov-Smrov (K-S) method to dstrbutos featurg the models of Schulz-Zmm (red square), ATR (gree crcle), Wesslau (blue up-tragle), Schulz-Flory (cya do-tragle), ad Smth et al (mageta-damod).

14 Fgure S6. Weght fracto of MMA chas ( ) degrafted from flat surfaces (black les) as a fucto of umber average degree of polymerzato ( ) for MMA brushes gro for a), b) 6, c) 0, ad d) 4 hrs th Cu (II) /Cu (I) =0.005 (see expermetal secto for detals). The expermetal data ere ftted usg the Kolmogorov-Smrov (K-S) method to dstrbutos featurg the models of Schulz-Zmm (red), ATR (gree), Wesslau (blue), Schulz-Flory (cya), ad Smth et al (mageta).

15 Fgure S7. olydspersty dex (DI) vs. umber average degree of polymerzato ( ) for MMA chas degrafted from flat surfaces (black star) gro for a), b) 6, c) 0, ad d) 4 hrs th Cu (II) /Cu (I) =0.005 (see expermetal secto for detals). The expermetal data ere ftted usg the Kolmogorov-Smrov (K-S) method to dstrbutos featurg the models of Schulz-Zmm (red square), ATR (gree crcle), Wesslau (blue up-tragle), Schulz-Flory (cya do-tragle), ad Smth et al (mageta-damod).

16 Fgure S8. Weght fracto of MMA chas ( ) degrafted from flat surfaces (black les) as a fucto of umber average degree of polymerzato ( ) for MMA brushes gro for a), b) 6, c) 0, ad d) 4 hrs th Cu (II) /Cu (I) =0.05 (see expermetal secto for detals). The expermetal data ere ftted usg the Kolmogorov-Smrov (K-S) method to dstrbutos featurg the models of Schulz-Zmm (red), ATR (gree), Wesslau (blue), Schulz-Flory (cya), ad Smth et al (mageta).

17 Fgure S9. olydspersty dex (DI) vs. umber average degree of polymerzato ( ) for MMA chas degrafted from flat surfaces (black star) gro for a), b) 6, c) 0, ad d) 4 hrs th Cu (II) /Cu (I) =0.05 (see expermetal secto for detals). The expermetal data ere ftted usg the Kolmogorov-Smrov (K-S) method to dstrbutos featurg the models of Schulz-Zmm (red square), ATR (gree crcle), Wesslau (blue up-tragle), Schulz-Flory (cya do-tragle), ad Smth et al (mageta-damod).

18 Fgure S0. Weght fracto of MMA chas ( ) degrafted from flat surfaces (black les) as a fucto of umber average degree of polymerzato ( ) for MMA brushes gro for a) 6, b) 9, c), d) 6, e) 0, ad f) 4 hrs th Cu (II) /Cu (I) =0.00 (see expermetal secto for detals). The expermetal data ere ftted usg the ch-squared ( ) method to dstrbutos featurg the models of Schulz-Zmm (red), ATR (gree), Wesslau (blue), Schulz-Flory (cya), ad Smth et al (mageta).

19 Fgure S. olydspersty dex (DI) vs. umber average degree of polymerzato ( ) for MMA chas degrafted from flat surfaces (black star) gro for a) 6, b) 9, c), d) 6, e) 0, ad f) 4 hrs th Cu (II) /Cu (I) =0.00 (see expermetal secto for detals). The expermetal data ere ftted usg the ch-squared ( ) method to dstrbutos featurg the models of Schulz-Zmm (red square), ATR (gree crcle), Wesslau (blue up-tragle), Schulz-Flory (cya do-tragle), ad Smth et al (mageta-damod).

20 Refereces () Bradup, J.; Immergut, E. H.; Grulke, E. A. olymer Hadbook; Joh Wley & Sos: e York, 999; pp V/9 V/95. () Bradup, J.; Immergut, E.; Grulke, E. olymer Hadbook; Joh Wley & Sos: e York, 999; pp V/87 V/89. (3) Sgma Aldrch (accessed Feb 4, 05). (4) Sgma Aldrch (accessed Feb 4, 05). (5) Hemez,. C.; Lodge, T.. olymer Chemstry; d Edto.; Taylor & Fracs: Boca Rato, FL, USA, 007, pp 8. (6) Schulz Zmm dstrbuto (accessed Feb 4, 05). (7) Masta, E.; Zhou, D.; Zhu, S. Modelg Molecular Weght Dstrbuto ad Effect of Termato Cotrolled Radcal olymerzato: A ovel ad Trasformatve Approach. J. olym. Sc. art A olym. Chem. 04, 5, (8) Most probable dstrbuto ( macromolecular assembles) (accessed Feb 4, 05). (9) Grulke, E. A. olymer rocess Egeerg; TS ublshg Compay: Lexgto, KY, USA, 994, pp 75. (0) Smth, W. B.; May, J. A.; Km, C. W. olymer Studes by Gel ermeato Chromatography. J. olym. Sc. art A- 966, 4, () Oda, G. rcples of olymerzato; Joh Wley & Sos: Hoboke, J, USA, 004, pp 90. () ater,. C.; Colema, M. M. Essetals of olymer Scece ad Egeerg; DEStec publcatos: Lacaster, A, USA, 009, pp 9. (3) Hollader, M.; Wolfe, D. A. oparametrc Statstcal Methods; Wley-VCH Verlag GmbH & Co. KGaA: Chcester, UK, 999, pp (4) Greeood,. E.; kul, M. S. A Gude to Ch-Squared Testg; Wley-VCH Verlag GmbH & Co. KGaA: e York, 996.