SUPPORTING INFORATION Zwitterionic Polymerization: A Kinetic Strategy for the Controlled Synthesis of Cyclic Polylactide Wonhee Jeong, Eun Ji Shin, Darcy A. Culin,, James L. Hedric, and Robert. Waymouth,* Department of Chemistry, Stanford University, Stanford, CA 9435 IB Almaden Research Center, 65 Harry Road, San Jose, CA 952 Current address: Ashland Performance aterials, 52 Blazer Parway, Dublin, OH 437 Table of Contents. Experimental procedures S2 2. Simulation methods S4 3. Absolute molecular weight determination S6 4. Hall s trial method S7 5. Experimental and simulation results for the echanistic odel II S8 6. echanistic odel with initiation (first order in ) and propagation (second order in ) (echanistic odel II-) S9 7. Calculation of monomer conversion in the sequential polymerization S S
. Experimental procedures General Considerations. All reactions and polymerizations were performed in a drybox or with Schlen techniques under nitrogen. H nuclear magnetic resonance (NR) spectra were recorded at room temperature on a 5 Hz spectrometer, with shifts reported in parts per million downfield from tetramethylsilane and referenced to the residual solvent pea. Gel permeation chromatography (GPC) was performed in tetrahydrofuran (THF) at a flow rate of. ml/min or a mixture of acetonitrile and dichloromethane (4: by volume) at a flow rate of.5 ml/min on a Waters chromatograph equipped with four 5 μm Waters columns (3 mm x 7.7 mm) connected in series. A Viscote S358 refractive index detector and Viscote GPCmax autosampler were employed. The system was calibrated using monodisperse polystyrene standards (Polymer Laboratories). aterials. Tetrahydrofuran (THF) was distilled from sodium/benzophenone and degassed three times via freeze-pump-thaw cycles. Dichloromethane was passed through columns of activated alumina, distilled from calcium hydride (CaH 2 ), and degassed. Carbon disulfide (CS 2 ) was purchased from Aldrich and distilled from CaH 2. D,L-Lactide (rac-lactide) was supplied from Purac, and purified by drying it over CaH 2 in a THF solution, and subsequent sublimations. The monomer was stored in a drybox under nitrogen.,3,5-trimethylbenzene (mesitylene) was purchased from Aldrich and purified by distillation over CaH 2. Deuterated chloroform (CDCl 3 ) was purchased from Acros and used as received. Anhydrous methanol was purchased from Aldrich and used as received.,3- dimesitylimidazol-2-ylidene (Ies) was prepared according to the literature procedure. Representative procedure for polymerization of rac-lactide with Ies. In a drybox, a solution of Ies (.6 mg, 3.46 x -3 mmol) in THF (8 μl) (from a stoc solution) was added to a stirred solution of rac-lactide (5. mg,.348 mmol) and mesitylene (4.7 mg,.339 mmol; an internal standard) in THF (.5 ml) (from a stoc solution). The reaction mixture was stirred for the desired reaction time at room temperature. CS 2 (. ml,.7 mmol) was added to terminate the reaction. The solvent was removed and the crude polymer was analyzed by H NR spectroscopy and GPC. When S2
needed (Entry 9-2 in Table ), polymerizations were performed on a large scale, and the polymers were precipitated with a copious amount of anhydrous methanol. Representative procedure for sequential polymerization of rac-lactide with Ies. In a drybox, a solution of Ies (2.2 mg, 6.92 x -3 mmol) in THF (.6 ml) (from a stoc solution) was added to a stirred solution of rac-lactide ( mg,.696 mmol) in THF (. ml) (from a stoc solution). The reaction mixture was stirred for 6 s at room temperature. Then, a solution of rac-lactide (2 mg,.39 mmol) in THF (. ml) (from a stoc solution) was added and stirring was continued for 3 s at room temperature. CS 2 (.2 ml, 3.4 mmol) was added to terminate the reaction. The solvent was removed and the crude polymer was analyzed by H NR spectroscopy and GPC. S3
2. Stochastic simulation methods The molecular size and size distribution of chains could be studied by means of stochastic simulations of polymerization reactions. 2, 3 First, let us define the rate parameters of initiation, propagation, depropagation, and cyclization for a chain with DP (degree of polymerization; DP ) as follows: ratei 2 = i (S) ratep = (S2) i rated = d (S3) ratec = c (S4) = ratei = ratep + rated + ratec when DP = when DP > (S5) where i, p, d, and c are the rate constants of initiation, propagation, depropagation, and cyclization, respectively. Then, the average life time of chains is given by A time increment (Δt) for each step of the simulation is given by t av =. (S6) f t t = f t tav = (S7) where f t is an adjustable parameter ( < f t < ) for both accuracy and efficiency of modeling. For all chains of interest, a uniform random number (RN; < RN < ) is generated. The life time of i chain is calculated by using ln RN t i =. (S8) If Δt i > Δt, then no transformation for i chain occurs. When Δt i < Δt and DP i =, initiation happens. When Δt i < Δt and DP i >, another uniform random number (RN2; < RN2 < ) is generated, and a type of transformation that occurs is determined according to the following probabilities of propagation, depropagation, and cyclization. S4
ratep P P = (S9) rated P D = (S) ratec P C = (S) After finishing transformations of all chains, values of t,, I, and DP i are updated and recorded for analysis. Based on this algorithm, a computational program was written in Fortran 77. L'Ecuyer s method was utilized to generate random numbers. Using the program and rate coefficients determined from experiments, stochastic simulations of chains at various s and I s were performed with a f t of.. S5
3. Absolute molecular weight determination Poly(lactide)s were analyzed by Gel Permeation Chromatography (GPC) using a triple detection system (Viscote, Houston, TX). Polystyrene standards were used to calibrate the system. The rightangle light scattering (RALS) method was used to determine absolute molecular weights of polymers. Correction for any angular dissymmetry factor in the RALS data was performed in the TriSEC software using the viscometer signal. The angular dissymmetry correction is negligible because the polymers studied are relatively small (< 5 nm) compared to the laser wavelength (6 nm). The eluent was a mixture of acetonitrile and dichloromethane (4/ by volume) at a flow rate of.5 ml/min. The concentration of a crude sample was determined utilizing the specific refractive index increment (dn/dc =.2) reported for poly(rac-lactide)s. 4 The second virial coefficient (A 2 =. -3 ml mol g -2 ) reported for poly(rac-lactide)s was used to calculate the absolute molecular weights. 4 S6
S7 4. Hall s trial method 5 + + = + p i p i p i p p I dt d dt d ln I ln I ln I ln (S2) ) Choose a trial value of p. 2) Calculate the left-hand side (LHS) of eq (S2). 3) Plot the LHS versus. 4) Fit the observed data. 5) Obtain i by using the slope. 6) Predict trial I using the i, p, and y-intercept determined. 7) Repeat the procedure from ) to 6) until trial I I is minimized. Figure S. Fitting of the inetic data based on Hall s method using eq (S2). The y-axis is the left-hand side of eq (S2).
5. Experimental and simulation results for the echanistic odel II Figure S2. First-order inetic plots of the polymerization data at some s and I s. The lines are numerically calculated based on the echanistic odel II using the rate constants ( p = 9.2 ( - s - ) and i =.788 ( -2 s - )) determined at =.6 and I =.6. The degree of polymerization (DP) can be calculated using eq (3). (a) (b) Figure S3. (a) Numerical results for the evolution of molecular weight based on the echanistic odel II the numerical results using the rate constants ( p = 9.2 ( - s - ) and i =.788 ( -2 s - )) determined at =.6 and I =.6. (b) Experimental results. S8
6. echanistic odel with initiation (first order in ) and propagation (second order in ) (echanistic odel II-) Scheme S. Polymerization with initiation (first order in ) and propagation (second order in ). For Scheme S, the rates of initiator and monomer conversion are written as d I - = i I (S3) dt d 2 - = i I + p ( I I ). (S4) dt Numerical fitting of the lactide polymerization data at =.6 and I =.6 below 7% conversion using eq (S3) and (S4) yields p = 2.4 7 ( -2 s - ) and i = 5.56-7 ( - s - ). Figure S4. First-order inetic plots of the polymerization data at some s and I s. The lines are numerically calculated based on the echanistic odel II- using the rate constants ( p = 2.4 7 ( - 2 s - ) and i = 5.56-7 ( - s - )) determined at =.6 and I =.6. S9
The degree of polymerization (DP) can be calculated using eq (3). (a) (b) Figure S5. (a) Numerical results for the evolution of molecular weight based on the echanistic odel II- using the rate constants ( p = 2.4 7 ( -2 s - ) and i = 5.56-7 ( - s - )) determined at =.6 and I =.6. (b) Experimental results. S
7. Calculation of monomer conversion in the sequential polymerization Let us define the following variables : the amount of monomer in the beginning (in mol) 2 : the amount of monomer added to the mixture at t (in mol) total = + 2 conv : conversion at t (in %) conv 2 : conversion between t and 2 t (in %) conv total : conversion at 2 t (in %). Then, the monomer conversion during the second polymerization, conv 2, is given by conv 2 = tot 2 conv tot conv conv + (S5) where conv is estimated from independent homopolymerizations (See Table ). Table S. onomer Conversion during the Second Polymerization. S
References () Arduengo, A. J., III; Dias, H. V. R.; Harlow, R. L.; Kline,. J. Am. Chem. Soc., 992, 4, 553. (2) Szymansi, R.; Baran, J. acromol. Theory Simul. 22,, 836. (3) atyjaszewsi, K.; Szymansi, R.; Teodorescu,. acromolecules 994, 27, 7565. (4) Kang, S.; Zhang, G.; Aou, K.; Hsu, S. L.; Stidam, H. D. J. Chem. Phys. 23, 8, 343. (5) Beste, L. F.; Hall, H. K., Jr. J. Phys. Chem. 964, 68, 269. S2