Mechanistic Insights into the Alternating Copolymerization of Epoxides and Cyclic Anhydrides Using a (Salph)AlCl and Iminium Salt Catalytic SystemClick to copy article linkArticle link copied!
- Megan E. Fieser
- Maria J. Sanford
- Lauren A. Mitchell
- Christine R. Dunbar
- Mukunda Mandal
- Nathan J. Van Zee
- Devon M. Urness
- Christopher J. Cramer
- Geoffrey W. Coates
- William B. Tolman
Abstract
Mechanistic studies involving synergistic experiment and theory were performed on the perfectly alternating copolymerization of 1-butene oxide and carbic anhydride using a (salph)AlCl/[PPN]Cl catalytic pair. These studies showed a first-order dependence of the polymerization rate on the epoxide, a zero-order dependence on the cyclic anhydride, and a first-order dependence on the catalyst only if the two members of the catalytic pair are treated as a single unit. Studies of model complexes showed that a mixed alkoxide/carboxylate aluminum intermediate preferentially opens cyclic anhydride over epoxide. In addition, ring-opening of epoxide by an intermediate comprising multiple carboxylates was found to be rate-determining. On the basis of the experimental results and analysis by DFT calculations, a mechanism involving two catalytic cycles is proposed wherein the alternating copolymerization proceeds via intermediates that have carboxylate ligation in common, and a secondary cycle involving a bis-alkoxide species is avoided, thus explaining the lack of side reactions until the polymerization is complete.
Introduction
Results and Discussion
Initiation
Polymerization Kinetics
cond. # | BO/CPMA exptlb | BO:CPMA theor | initial rate (×10–4 M s–1)c | kobs (×10–5s–1)d |
---|---|---|---|---|
1 | 5.0(5) | 500:100 | 2.3(3) | 2.5(6) |
2 | 4.4(4) | 475:100 | 2.3(1) | 2.9(2) |
3 | 3.4(5) | 400:100 | 2.0(5) | 3.2(5) |
4 | 2.8(1) | 300:100 | 1.5(2) | 3.0(3) |
5 | 1.8(1) | 200:100 | 1.1(1) | 3.4(7) |
6 | 6.1(4) | 475:75 | 2.0(4) | 2.4(6) |
7 | 10(1) | 475:50 | 2.1(6) | 3.3(4) |
The target concentration for 1 equiv of (salph)AlCl was 19 mM (13 μmol in ∼700 μL measured total volume). A constant 1:0.9 ratio of (salph)AlCl:[PPN]Cl was used. Each condition was measured in triplicate, with average values listed.
Determined by 1H NMR using an internal standard.
Calculated initial rate at 20% conversion of anhydride.
Calculated using the equation d[Pol]/dt = kobs[BO] in the COPASI fitting software.
Synthesis and Reactivity of Intermediates
Mechanistic Hypotheses and Evaluation by Theory
Conclusions
Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b09079.
Experimental and computational details, including Figures S1–S54, Tables S1–S21, and Scheme S1 (PDF)
Terms & Conditions
Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.
Acknowledgment
Funding for this project was provided by the Center for Sustainable Polymers, an NSF Center for Chemical Innovation (CHE-1413862). This work made use of the NMR facility at Cornell University which is supported, in part, by the NSF under award number CHE-1531632. The authors acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing resources that contributed to the research results reported within this paper. We also thank the Minnesota NMR Center and the UMN Chemistry NMR Center for their assistance with kinetics experiments and Kiley Schmidt for assistance with the TOC graphic.
References
This article references 34 other publications.
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- 30Hoops, S.; Sahle, S.; Gauges, R.; Lee, C.; Pahle, J.; Simus, N.; Singhal, M.; Xu, L.; Mendes, P.; Kummer, U. Bioinformatics 2006, 22, 3067– 3074 DOI: 10.1093/bioinformatics/btl485Google Scholar30https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28Xht1OgsrvK&md5=ff340a6c0c48f525a92a50c983aa1dddCOPASI - A COmplex PAthway SImulatorHoops, Stefan; Sahle, Sven; Gauges, Ralph; Lee, Christine; Pahle, Juergen; Simus, Natalia; Singhal, Mudita; Xu, Liang; Mendes, Pedro; Kummer, UrsulaBioinformatics (2006), 22 (24), 3067-3074CODEN: BOINFP; ISSN:1367-4803. (Oxford University Press)Motivation: Simulation and modeling is becoming a std. approach to understand complex biochem. processes. Therefore, there is a big need for software tools that allow access to diverse simulation and modeling methods as well as support for the usage of these methods. Results: Here, we present COPASI, a platform-independent and user-friendly biochem. simulator that offers several unique features. We discuss numerical issues with these features; in particular, the criteria to switch between stochastic and deterministic simulation methods, hybrid deterministic-stochastic methods, and the importance of random no. generator numerical resoln. in stochastic simulation.
- 31
We hypothesize that the nonzero intercept of the indicated linear fit results from slow initiation at low concentrations of cocatalysts.
There is no corresponding record for this reference. - 32Burés, J. Angew. Chem., Int. Ed. 2016, 55, 2028– 2031 DOI: 10.1002/anie.201508983Google Scholar32https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XmslGitw%253D%253D&md5=c278522341f44c6474bf6dfac3aca01aA Simple Graphical Method to Determine the Order of a Reaction in CatalystBures, JordiAngewandte Chemie, International Edition (2016), 55 (6), 2028-2031CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)A graphical anal. to elucidate the order in catalyst is presented. This anal. uses a normalized time scale, t [cat]Tn, to adjust entire reaction profiles constructed with concn. data. The method is fast and simple to perform because it directly uses the concn. data, therefore avoiding the data handling that is usually required to ext. rates. Compared to methods that use rates, the normalized time scale anal. requires fewer expts. and minimizes the effects of exptl. errors by using information on the entire reaction profile.
- 33
According to this method, the decay of CPMA was plotted against the normalized time scale, t[Cat]N, where t is time, [Cat] is the initial concentrations of both the catalyst and cocatalyst, (salph)AlCl and [PPN]Cl, and N is the order. The three conditions were plotted against possible reaction orders of zero, first, and second, on the normalized time scale, with the best overlay found for the first-order case (Figure S20).
There is no corresponding record for this reference. - 34Martinsen, A.; Songstad, J. Acta Chem. Scand. 1977, 31, 645– 650 DOI: 10.3891/acta.chem.scand.31a-0645Google ScholarThere is no corresponding record for this reference.
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References
This article references 34 other publications.
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- 11Jeon, J. Y.; Eo, S. C.; Varghese, J. K.; Lee, B. Y. Beilstein J. Org. Chem. 2014, 10, 1787– 1795 DOI: 10.3762/bjoc.10.18711https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhs1als7vL&md5=644a3409f0a1958f2906507ce54d6a66Copolymerization and terpolymerization of carbon dioxide/propylene oxide/phthalic anhydride using a (salen)Co(III) complex tethering four quaternary ammonium saltsJeon, Jong Yeob; Eo, Seong Chan; Varghese, Jobi Kodiyan; Lee, Bun YeoulBeilstein Journal of Organic Chemistry (2014), 10 (), 1787-1795, 9 pp.CODEN: BJOCBH; ISSN:1860-5397. (Beilstein-Institut zur Foerderung der Chemischen Wissenschaften)The (salen)Co(III) complex 1 tethering four quaternary ammonium salts, which is a highly active catalyst in CO2/epoxide copolymns., shows high activity for propylene oxide/phthalic anhydride (PO/PA) copolymns. and PO/CO2/PA terpolymns. In the PO/PA copolymns., full conversion of PA was achieved within 5 h, and strictly alternating copolymers of poly(1,2-propylene phthalate)s were afforded without any formation of ether linkages. In the PO/CO2/PA terpolymns., full conversion of PA was also achieved within 4 h. The resulting polymers were gradient poly(1,2-propylene carbonate-co-phthalate)s because of the drift in the PA concn. during the terpolymn. Both polymns. showed immortal polymn. character; therefore, the mol. wts. were detd. by the activity (g/mol-1) and the no. of chain-growing sites per 1 [anions in 1 (5) + water (present as impurity) + ethanol (deliberately fed)], and the mol. wt. distributions were narrow (Mw/Mn, 1.05-1.5). Because of the extremely high activity of 1, high-mol.-wt. polymers were generated (Mn up to 170,000 and 350,000 for the PO/PA copolymn. and PO/CO2/PA terpolymn., resp.). The terpolymers bearing a substantial no. of PA units (fPA, 0.23) showed a higher glass-transition temp. (48 °C) than the CO2/PO alternating copolymer (40 °C).
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- 13Mundil, R.; Hošt’álek, Z.; Šedenková, I.; Merna, J. Macromol. Res. 2015, 23, 161– 166 DOI: 10.1007/s13233-015-3022-413https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXjsFWlsLY%253D&md5=6b63f0ccb58c02d0772a4e0915d34e20Alternating ring-opening copolymerization of cyclohexene oxide with phthalic anhydride catalyzed by iron(III) salen complexesMundil, Robert; Host'alek, Zdenek; Sedenkova, Ivana; Merna, JanMacromolecular Research (2015), 23 (2), 161-166CODEN: MRAECT; ISSN:1598-5032. (Polymer Society of Korea)A series of three iron(III) salen complexes was synthesized and successfully used for copolymn. of cyclohexene oxide and phthalic anhydride. Catalytic systems based on an iron(III) salen complex in combination with 4-(dimethylamino)pyridine (DMAP) or bis(triphenylphosphine)iminium chloride (PPNCl) cocatalysts produced purely alternating copolymer with narrow molar mass distributions. [N,N'-Bis(3,5-di-tert-butylsalicylidene)-1,2-cyclohexylenediamine] iron(III) chloride was the most active complex and afforded the copolymer even in the absence of the cocatalysts. Other iron complexes were completely inactive in absence of a cocatalyst. Both DMAP and PPNCl alone were able to catalyze the copolymn., affording purely alternating copolymers in good yields.
- 14Si, G.; Zhang, L.; Han, B.; Duan, Z.; Liu, B.; Dong, J.; Li, X.; Liu, B. Polym. Chem. 2015, 6, 6372– 6377 DOI: 10.1039/C5PY01040C14https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhtF2rsrbI&md5=554e491ed3840953902cf60db349b5e1Novel chromium complexes with a [OSSO]-type bis(phenolato) dianionic ligand mediate the alternating ring-opening copolymerization of epoxides and phthalic anhydrideSi, Gaoshan; Zhang, Li; Han, Bing; Duan, Zhongyu; Li, Boqian; Dong, Jincheng; Li, Xiangqing; Liu, BinyuanPolymer Chemistry (2015), 6 (35), 6372-6377CODEN: PCOHC2; ISSN:1759-9962. (Royal Society of Chemistry)Four new homogeneous chromium complexes with [OSSO]-type bis(phenolato) dianionic ligand catalysts for the ring-opening copolymn. of phthalic anhydride (PA) and epoxides are reported. Through the structure design, the ligand with a cyclohexylene ring backbone of the chromium complexes is quite beneficial to improving the activity. Of all the cocatalysts employed, DMAP is the most efficient. 1H NMR spectra of the copolymers confirmed the alternating microstructures. This is the first example of a well-defined metal complex with a soft Lewis base as donor for the efficient copolymn. of anhydride and epoxides. Addnl., we demonstrate that poly(4-VCHO-alt-PA) can be conveniently functionalized using a robust free-radical mediated thiol-ene reaction of the pendant vinyl groups.
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- 17Liu, J.; Bao, Y.-Y.; Liu, Y.; Ren, W.-M.; Lu, X.-B. Polym. Chem. 2013, 4, 1439– 1444 DOI: 10.1039/C2PY20842C17https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXit1Wjt7k%253D&md5=c03496278e8e3610481259586dded1d6Binuclear chromium-salan complex catalyzed alternating copolymerization of epoxides and cyclic anhydridesLiu, Jie; Bao, Yuan-Ye; Liu, Ye; Ren, Wei-Min; Lu, Xiao-BingPolymer Chemistry (2013), 4 (5), 1439-1444CODEN: PCOHC2; ISSN:1759-9962. (Royal Society of Chemistry)Mono- and bi-nuclear chromium(iii)-salan complexes are efficient catalysts for the alternating copolymn. of terminal epoxides [such as epichlorohydrin (ClPO) and glycidyl Ph ether (GO)] and cyclic anhydrides [e.g. maleic anhydride (MA) and succinic anhydride (SA)] to afford the corresponding copolymers with >99% ester content. The binuclear complex c bearing a binaphthol linker showed significantly higher activity than the mononuclear chromium-salan complexes a and b. For example, the catalytic activities (based on chromium concn.) of complex c for MA/ClPO and MA/GO copolymns. are 4.1 and 7.1 times that of complex a, resp. An intramol. bimetallic synergistic effect, in which the alternating chain-growth and dissocn. of propagating copolymer species take turns at the two metal ions of the binuclear catalyst c, was suggested to make a contribution to the enhanced catalytic activity. Importantly, when using the binuclear complex c as a catalyst for MA/(S)-GO copolymn., a highly regioregular ring-opening step was obsd. with a concomitant >99% retention of configuration at the methine carbon center of epoxide incorporated into the polyester.
- 18Liu, D.-F.; Zhu, L.-Q.; Wu, J.; Wu, L.-Y.; Lu, X.-Q. RSC Adv. 2015, 5, 3854– 3859 DOI: 10.1039/C4RA08969C18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhvF2rsr7E&md5=52235343fc5df512be893b67a812c3bfRing-opening copolymerization of epoxides and anhydrides using manganese(III) asymmetrical Schiff base complexes as catalystsLiu, Deng-Feng; Zhu, Lu-Qun; Wu, Jing; Wu, Li-Ying; Lu, Xing-QiangRSC Advances (2015), 5 (5), 3854-3859CODEN: RSCACL; ISSN:2046-2069. (Royal Society of Chemistry)Based on a series of asym. Schiff base H2Ln (n = 1-4) ligands with different electronic and steric effects, a series of [Mn(Ln)Cl] complexes were obtained and shown to be effective catalysts in cyclohexene oxide and maleic anhydride, cyclohexene oxide and phthalic anhydride, styrene oxide and maleic anhydride or styrene oxide and phthalic anhydride ring-opening copolymns. Through the structure design, the input of the electron-withdrawing Br substituent para to the phenoxide group of the complexes is quite beneficial to the improved activities. Moreover, both steric and electronic effects of a suitable MeO substituent at the ortho position of the phenoxide group have much more influence on the formation of alternating ring-opening copolymers than that of selected reaction conditions.
- 19Biermann, U.; Sehlinger, A.; Meier, M. A. R.; Metzger, J. O. Eur. J. Lipid Sci. Technol. 2016, 118, 104– 110 DOI: 10.1002/ejlt.20140063119https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXkvVWqtLs%253D&md5=d146572af9e75cf2dc53a7e2ace8612aCatalytic copolymerization of methyl 9,10-epoxystearate and cyclic anhydrides under neat conditionsBiermann, Ursula; Sehlinger, Ansgar; Meier, Michael A. R.; Metzger, Juergen O.European Journal of Lipid Science and Technology (2016), 118 (1), 104-110CODEN: EJLTFM; ISSN:1438-7697. (Wiley-VCH Verlag GmbH & Co. KGaA)The solvent-free copolymn. of Me 9,10-epoxystearate 1 with different cyclic anhydrides, such as phthalic anhydride 2, succinic anhydride 3, maleic anhydride 4, or the Diels-Alder-adduct 5 of Me α-eleostearate and maleic anhydride, using a (salen)CrIIICl-catalyst and n-Bu4NCl as co-catalyst is demonstrated. In this way, polyesters (Mn = 2000-10,000 g/mol) with low glass transition temps. were formed. The reaction is characterized by sustainable aspects, for instance, the use of starting materials derived from renewable resources (>60%), low catalyst loadings, and no added solvent. The alternating ring-opening copolymn. of epoxides such as Me-9,10-epoxystearate with various cyclic acid anhydrides such as phthalic anhydride and succinic anhydride, resp., afford polyesters of narrow mol. wt. distributions using a (salen)CrIIICl catalyst in the presence of n-Bu4NCl. The pending long chain alkyl groups introduced in the polyesters by the fat derived substrates attribute amorphous properties to the polymers. Various fatty epoxides are easily available and open up the possibility for the synthesis of new highly branched polyesters.
- 20DiCiccio, A. M.; Longo, J. M.; Rodríguez-Calero, G. G.; Coates, G. W. J. Am. Chem. Soc. 2016, 138, 7107– 7113 DOI: 10.1021/jacs.6b03113There is no corresponding record for this reference.
- 21Liu, D.; Zhang, Z.; Zhang, X.; Lü, X. Aust. J. Chem. 2016, 69, 47– 55 DOI: 10.1071/CH15162There is no corresponding record for this reference.
- 22Sanford, M. J.; Peña Carrodeguas, L.; Van Zee, N. J.; Kleij, A. W.; Coates, G. W. Macromolecules 2016, 49, 6394– 6400 DOI: 10.1021/acs.macromol.6b01425There is no corresponding record for this reference.
- 23Van Zee, N. J.; Sanford, M. J.; Coates, G. W. J. Am. Chem. Soc. 2016, 138, 2755– 2761 DOI: 10.1021/jacs.5b1288823https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XisFylsrY%253D&md5=7c18d752293d0bb7f5048eba0a283be6Electronic Effects of Aluminum Complexes in the Copolymerization of Propylene Oxide with Tricyclic Anhydrides: Access to Well-Defined, Functionalizable Aliphatic PolyestersVan Zee, Nathan J.; Sanford, Maria J.; Coates, Geoffrey W.Journal of the American Chemical Society (2016), 138 (8), 2755-2761CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)The synthesis of well-defined and functionalizable aliph. polyesters remains a key challenge in the advancement of emerging drug delivery and self-assembly technologies. Herein, we investigate the factors that influence the rates of undesirable transesterification and epimerization side reactions at high conversion in the copolymn. of tricyclic anhydrides with excess propylene oxide using aluminum salen catalysts. The structure of the tricyclic anhydride, the molar ratio of the aluminum catalyst to the nucleophilic cocatalyst, and the Lewis acidity of the aluminum catalyst all influence the rates of these side reactions. Optimal catalytic activity and selectivity against these side reactions requires a careful balance of all these factors. Effective suppression of undesirable transesterification and epimerization was achieved even with sterically unhindered monomers using a fluorinated aluminum salph complex with a substoichiometric amt. of a nucleophilic cocatalyst. This process can be used to synthesize well-defined block copolymers via a sequential addn. strategy.
- 24Nejad, E. H.; van Melis, C. G. W.; Vermeer, T. J.; Koning, C. E.; Duchateau, R. Macromolecules 2012, 45, 1770– 1776 DOI: 10.1021/ma2025804There is no corresponding record for this reference.
- 25(a) Darensbourg, D. J.; Yarbrough, J. C. J. Am. Chem. Soc. 2002, 124, 6335– 6342 DOI: 10.1021/ja012714vThere is no corresponding record for this reference.(b) Darensbourg, D. J.; Yarbrough, J. C.; Ortiz, C.; Fang, C. C. J. Am. Chem. Soc. 2003, 125, 7586– 7591 DOI: 10.1021/ja034863eThere is no corresponding record for this reference.(c) Darensbourg, D. J.; Mackiewicz, R. M.; Rodgers, J. L.; Phelps, A. L. Inorg. Chem. 2004, 43, 1831– 1833 DOI: 10.1021/ic0352856There is no corresponding record for this reference.(d) Darensbourg, D. J.; Mackiewicz, R. M. J. Am. Chem. Soc. 2005, 127, 14026– 14038 DOI: 10.1021/ja053544fThere is no corresponding record for this reference.(e) Darensbourg, D. J.; Yeung, A. D. Polym. Chem. 2015, 6, 1103– 1117 DOI: 10.1039/C4PY01322K25ehttps://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhvVWit7bL&md5=6bb233b581283809a9d26fff5f130c5cKinetics of the (salen)Cr(III)- and (salen)Co(III)-catalyzed copolymerization of epoxides with CO2, and of the accompanying degradation reactionsDarensbourg, D. J.; Yeung, A. D.Polymer Chemistry (2015), 6 (7), 1103-1117CODEN: PCOHC2; ISSN:1759-9962. (Royal Society of Chemistry)The (salen)Cr(III)- and (salen)Co(III)-catalyzed copolymn. reactions between a variety of epoxides with CO2 were studied by computational methods, and these findings were compared with exptl. observations. The displacement of a polymeric carbonate by an epoxide, followed by epoxide ring-opening, was found to be the overall rate detg. step (δG† = 22-27 kcal mol-1), whereas carboxylation of the metal-bound alkoxide is fast (δG† = 6-8 kcal mol-1). Chromium(III)-catalyzed systems have higher free energy barriers than cobalt(III) systems, consistent with the fact that (salen)Cr(III)-catalyzed polymn. reactions have to be performed at higher temps.; such differences were attributed to enthalpy. The metal-bound polymer carbonate and alkoxide backbiting reactions generally have higher barriers than when unbound, due to the terminal oxygen atoms reduced nucleophilicity. Homopolymn. of epoxides to give polyether defects was negligible in both chromium- and cobalt-catalyzed systems. This is due to carboxylation (metal-bound or metal-free) being competitive, and because displacement of a polymeric alkoxide from the metal center by an epoxide is strongly endergonic.(f) Chisholm, M. H.; Zhou, Z. J. Am. Chem. Soc. 2004, 126, 11030– 11039 DOI: 10.1021/ja0394232There is no corresponding record for this reference.
- 26Han, B.; Zhang, L.; Liu, B.; Dong, X.; Kim, I.; Duan, Z.; Theato, P. Macromolecules 2015, 48, 3431– 3437 DOI: 10.1021/acs.macromol.5b00555There is no corresponding record for this reference.
- 27Nakano, K.; Hashimoto, S.; Nozaki, K. Chem. Sci. 2010, 1, 369– 373 DOI: 10.1039/c0sc00220h27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXpvFegsb0%253D&md5=f8d231975f44d7e717b2b673800029bbBimetallic mechanism operating in the copolymerization of propylene oxide with carbon dioxide catalyzed by cobalt-salen complexesNakano, Koji; Hashimoto, Shinichi; Nozaki, KyokoChemical Science (2010), 1 (3), 369-373CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)Dinuclear Co-salen complexes (R,R)-(S,S)-1-4 were synthesized and compared with their mononuclear counterpart rac-5 to suggest that a bimetallic mechanism is in charge for the alternating copolymn. of propylene oxide with CO2 in the absence of onium salt while a monometallic mechanism is more probable in its presence.
- 28Robert, C.; Schmid, T. E.; Richard, V.; Haquette, P.; Raman, S. K.; Rager, M.-N.; Gauvin, R. M.; Morin, Y.; Trivelli, X.; Guérineau, V.; Del Rosal, I.; Maron, L.; Thomas, C. M. J. Am. Chem. Soc. 2017, 139, 6217– 6225 DOI: 10.1021/jacs.7b01749There is no corresponding record for this reference.
- 29Martínez, L. E.; Leighton, J. L.; Carsten, D. H.; Jacobsen, E. N. J. Am. Chem. Soc. 1995, 117, 5897– 5898 DOI: 10.1021/ja00126a048There is no corresponding record for this reference.
- 30Hoops, S.; Sahle, S.; Gauges, R.; Lee, C.; Pahle, J.; Simus, N.; Singhal, M.; Xu, L.; Mendes, P.; Kummer, U. Bioinformatics 2006, 22, 3067– 3074 DOI: 10.1093/bioinformatics/btl48530https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28Xht1OgsrvK&md5=ff340a6c0c48f525a92a50c983aa1dddCOPASI - A COmplex PAthway SImulatorHoops, Stefan; Sahle, Sven; Gauges, Ralph; Lee, Christine; Pahle, Juergen; Simus, Natalia; Singhal, Mudita; Xu, Liang; Mendes, Pedro; Kummer, UrsulaBioinformatics (2006), 22 (24), 3067-3074CODEN: BOINFP; ISSN:1367-4803. (Oxford University Press)Motivation: Simulation and modeling is becoming a std. approach to understand complex biochem. processes. Therefore, there is a big need for software tools that allow access to diverse simulation and modeling methods as well as support for the usage of these methods. Results: Here, we present COPASI, a platform-independent and user-friendly biochem. simulator that offers several unique features. We discuss numerical issues with these features; in particular, the criteria to switch between stochastic and deterministic simulation methods, hybrid deterministic-stochastic methods, and the importance of random no. generator numerical resoln. in stochastic simulation.
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We hypothesize that the nonzero intercept of the indicated linear fit results from slow initiation at low concentrations of cocatalysts.
There is no corresponding record for this reference. - 32Burés, J. Angew. Chem., Int. Ed. 2016, 55, 2028– 2031 DOI: 10.1002/anie.20150898332https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XmslGitw%253D%253D&md5=c278522341f44c6474bf6dfac3aca01aA Simple Graphical Method to Determine the Order of a Reaction in CatalystBures, JordiAngewandte Chemie, International Edition (2016), 55 (6), 2028-2031CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)A graphical anal. to elucidate the order in catalyst is presented. This anal. uses a normalized time scale, t [cat]Tn, to adjust entire reaction profiles constructed with concn. data. The method is fast and simple to perform because it directly uses the concn. data, therefore avoiding the data handling that is usually required to ext. rates. Compared to methods that use rates, the normalized time scale anal. requires fewer expts. and minimizes the effects of exptl. errors by using information on the entire reaction profile.
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According to this method, the decay of CPMA was plotted against the normalized time scale, t[Cat]N, where t is time, [Cat] is the initial concentrations of both the catalyst and cocatalyst, (salph)AlCl and [PPN]Cl, and N is the order. The three conditions were plotted against possible reaction orders of zero, first, and second, on the normalized time scale, with the best overlay found for the first-order case (Figure S20).
There is no corresponding record for this reference. - 34Martinsen, A.; Songstad, J. Acta Chem. Scand. 1977, 31, 645– 650 DOI: 10.3891/acta.chem.scand.31a-0645There is no corresponding record for this reference.
Supporting Information
Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b09079.
Experimental and computational details, including Figures S1–S54, Tables S1–S21, and Scheme S1 (PDF)
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