Atom transfer versus catalyst transfer: Deviations from ideal Poisson behavior in controlled polymerizations

Accepted Manuscript Atom transfer versus catalyst transfer: Deviations from ideal Poisson behavior in controlled polymerizations EmilyDaniels Weiss, Racquel Jemison, KevinJ.T. Noonan, RichardD. McCullough, Tomasz Kowalewski PII:

S0032-3861(15)30038-0

DOI:

10.1016/j.polymer.2015.06.017

Reference:

JPOL 17913

To appear in:

Polymer

Received Date: 9 January 2015 Revised Date:

10 June 2015

Accepted Date: 11 June 2015

Please cite this article as: Weiss E, Jemison R, Noonan KT, McCullough R, Kowalewski T, Atom transfer versus catalyst transfer: Deviations from ideal Poisson behavior in controlled polymerizations, Polymer (2015), doi: 10.1016/j.polymer.2015.06.017. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Atom Transfer versus Catalyst Transfer: Deviations from Ideal Poisson Behavior in

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Controlled Polymerizations

Emily Daniels Weiss,* a Racquel Jemison,* a Kevin J.T. Noonan, a Richard D. McCullough, b

a

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* These authors contributed equally to this work

Department of Chemistry, Carnegie Mellon University, 4400 5th Ave, Pittsburgh, Pennsylvania,

15213

Harvard School of Engineering and Applied Sciences, 29 Oxford St, Cambridge,

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Massachusetts, 02138

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b

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Tomasz Kowalewski a

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Corresponding Author

Tomasz Kowalewski, [email protected] Keywords

Controlled polymerizations, ATRP, catalyst-transfer polymerization, Grignard metathesis, polymerization kinetics

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Abstract Over the past several years there has been growing interest in a new class of controlled living

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polymerizations jointly referred to as catalyst-transfer polycondensations (CTPs), in which monomers are coupled by a variety of metal-catalyzed metatheses, such as Grignard metathesis polymerization (GRIM). Interest in these processes is primarily driven by their applicability to the synthesis of conjugated polymers for organic electronics. In this article we use computational

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modelling of polymerization reactions to identify inherent factors which cause the widely

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observed deviation of chain length distributions in CTP products from the Poisson distribution expected for ideal living polymerizations. The primary source of these deviations is shown to be related to intermittent deactivation of metathesis pathways which transform the newly added monomer into a chain end capable of further propagation. Maximum departures from ideal

the rate of polymerization. Introduction

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behavior are observed when the rates of processes involved in metathesis are comparable with

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Since its discovery in 1995, atom transfer radical polymerization (ATRP) has become one of the most widely-studied and used types of controlled radical polymerization, and represents one of

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the most significant contributions to the field of synthetic polymer chemistry.1-3 ATRP offers precise

control

over

polymer

composition

allowing

for

highly-complex,

tailored,

macromolecular structures. Hallmarks of ATRP, include a linear relationship between number average molecular weight and conversion due to its living nature, and low dispersity (Ð) which originates from its high rates of deactivation compared to propagation. Not long after the discovery of ATRP and, in fact, just down the hall from the Matyjaszewski lab, McCullough and coworkers responded to Matyjaszewski’s challenge to

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create a living conjugated polymerization process by developing Grignard metathesis polymerization (GRIM). Because GRIM uses metal-catalyzed metathesis processes to add monomer units to the growing chain end, forming new carbon-carbon bonds (based upon work

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by the Corriu and Kumada groups who independently reacted a Grignard reagent and an organic halide catalyzed by Ni or Pd catalysts to couple two alkyl, aryl, or vinyl groups),4 it is also commonly referred to as Kumada catalyst-transfer polycondensation. They demonstrated that

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just like their earlier McCullough method, GRIM polymerization yields highly-regioregular poly(3-alkylthiophenes) (rr-P3ATs) containing almost exclusively 2,5’ (head-to-tail) couplings.5The capability of rr-P3ATs to self-assemble in a highly ordered manner afforded major

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improvements in charge transport, and contributed to the resurgence of interest in the field of organic electronics. They currently serve as benchmark materials in understanding synthetic, structural, transport properties of semiconducting polymers.11-15

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Initially, GRIM polymerization was viewed just as a more practical way to synthesize highly desirable rr-P3ATs. It soon became clear, however, that the process bears considerable similarity to living ionic and controlled radical polymerizations such as ATRP, yielding

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polymers with relatively narrow molecular weight distributions, uncharacteristic for a stepgrowth mechanism typically associated with polycondensation reactions. Other important

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similarities to living polymerizations included the nearly linear dependence of the degree of polymerization (DPn) on conversion degree, concomitant ability to predetermine the DPn of the final product by the monomer to initiator ratio, and good preservation of growing chain end functionality allowing for the creation of block copolymers.7,15-17

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One of the most characteristic features of an ideal living polymerization is narrow molecular weight distributions of the product which can be described by a Poisson distribution





= 1 +






−




 

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with the dispersity index DPw/DPn given as:16 (1)

Thus, for an ideal living system, a polymer with DPn = 50 should exhibit Ð ≈ 1.02. It should be

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pointed out, however, that in both ATRP and CTP systems like GRIM polymerization, values of Ð of 1.2 or greater are commonly observed. 6,8,17,18 The main purpose of the current study was to

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illustrate and explore the origin of this considerable molecular weight distribution broadening. To this end, we have developed and implemented in Mathematica (Wolfram Research, Inc.) a straightforward numerical kinetic model comprised of a large system of ordinary differential equations (ODEs) corresponding to each of the reactions in Schemes 1 (ATRP) and 2 (GRIM).

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The individual ODEs treat the polymeric reaction participants, comprised of different numbers of repeat units, as separate species (e.g. with PBrn in ATRP corresponding to dormant (halogencapped) chains containing n repeat units). For a system comprised of i different macromolecular

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species this yields a system comprised of at least i × N equations, where N is the upper limit chosen in such a way that it is reached only by a vanishingly small fraction of polymer chains.

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To satisfy this condition for ideal living systems with “well-behaved,” relatively narrow distributions, this upper limit must be at least twice the final degree of polymerization, which leads to sets containing hundreds of coupled differential equations. In the past, the massive size of ODE systems necessary to describe polymerization reactions led to the use of approximate methods, such as Galerkin method, which is employed by PREDICI, a commonly used commercial software package.19 However, the processing power of

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modern computers and the availability of efficient numerical ODE solvers embedded in scientific/engineering computation packages such as Mathematica or MATLAB (Mathworks, Inc.) make it practical to rapidly set up and solve large ODE systems on personal computers with

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minimal up-front investments in time and resources. The computations in the study described herein have been carried out with Mathematica, which, owing to its symbolic computer algebra structure, is particularly suitable for setting large equation systems and for effective integration

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of the calculations with post-processing and visualization of results. The primary intent of this study was to identify the factors which could be responsible for the deviations from ideality in

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catalyst transfer polycondensations, and to provide the synthetic chemists with guidelines which would be helpful in elucidating the mechanistic intricacies of this class of polymerizations.

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Modeling Atom Transfer Radical Polymerization

ATRP mechanism and parameters. As shown in Scheme 1, control of polymerization in ATRP relies on reversible deactivation/activation of radicals comprising growing chain ends

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with the aid of a halogen atom shuttled back and forth between the chain end and the metal complex. Familiar kinetic equations which can be used to describe this system with Br as a

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capping halogen and Cu as a catalytic complex are listed in Table 1 as Equations 2-8.

Scheme 1. ATRP mechanism comprised of: the halogenated dormant polymer chain, Pn-Br; the metal-ligand species, Cu1/L; the growing polymer radical species Pn•, which can propagate (governed by kp) or terminate via kt to form the terminated species, Tn. The activation and deactivation rate constants, ka and kd, govern the chain growth control.

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Table 1. Kinetic equations used to model ATRP Monomer





[ ] = − [ ] [• ]

(2)



Smallest radical

[• ]

= −2 



[ • ] [• ] 

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[ ] =  [ ][• ] −  [][ ]

Dormant chains

+  [][  ] −  [ ][ • ]

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−  [ ][  • ]

• [• ] =  [ ] ([([" ]] − [• ]) −  [ ][• ]

All remaining radicals



(3) (4)

(5)

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− 2  [• ] [• ] +  [][ ] 

Cu(I) concentration

[]′

Cu(II) concentration

=  [ ] [• ] 

−  [] [ ]











"

[% ] =   &

(6)



[ ] =  [] [ ] − [ ] [• ]

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• [&• ]["& ]

(7)

(8)

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Terminated chains



For the numerical kinetic model, we simulated ATRP choosing parameters based on

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experimental results of the polymerization of bulk styrene at 110 °C using 1-phenylethyl bromide as an initiator, copper as the metal, and di-4,4’-(5-nonyl)-2,2’-bpy as the ligand.1,2,20,21 To show the effects of initial addition of Cu(II) on ATRP, we employed two Cases, the first in absence of initial Cu(II), and the second with 10 mol% of Cu(II) compared to Cu(I). Table 2. Coefficients used in ATRP simulations Parameter

Abbreviation

Value

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kp

1.6 × 103 M-1s-1

Activation rate constant

ka

0.45 M-1s-1

Deactivation rate constant

kd

1.1 × 107 M-1s-1

Termination rate constant

kt

108 M-1s-1

Initial monomer concentration

[M]0

Initiator concentration

[PBr]0

Initial Cu(I) concentration

[CuBr]0

Initial Cu(II) concentration (Case 1)

[CuBr2]0

Initial Cu(II) concentration (Case 2)

[CuBr2]0

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Propagation rate constant

8.73 M (bulk styrene) 0.1746 M

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0.1746 M

0

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0.01746 M

ATRP simulation results. The overall polymerization “trajectories”, representing the evolution

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of the DP distribution for ATRP simulations for Case 1 (in the absence of initial Cu(II)), and

Figure 1. Evolution of DP distributions with conversion for ATRP Case 1 ([CuBr2]0 = 0 M) (left) and Case 2 ([CuBr2]0 = 0.01746 M) (right). In these and all subsequent plots, the DP distributions are presented in terms of concentration ci (in mM) of all chain species with degree of polymerization DPi. For better readability the discrete distributions are represented in a continuous manner. In contour maps the color corresponds to the concentration according to the scale bar shown on the left. This representation of the evolution of the distribution can be thought of as a “trajectory” of polymerization reaction, which provides an instantaneous “birds eye” view of the entire polymerization. The dotted red lines superimposed on the polymerization trajectories track the values of DPn vs conversion. Plots located to the right of trajectory maps show their “cross-sections” at values of conversion degree highlighted on the contour map with a dotted line, and represent distributions at conversions equal to 0.25 (bottom), 0.6 (middle), and 0.95 conversion (bottom). Insets in plots show the distributions with vertical scale stretched by a factor of 10 to highlight the subtleties related to the presence of low- and high-DP shoulders.

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Case 2 (initial Cu(II) equal to 0.1 of the initial Cu(I) concentration) are shown in Figure 1.

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Plots of DPn and Ð versus conversion degree for Cases 1 and 2 are shown in Figure 2, compared to those of an ideal living polymerization. Change in Cu(I) and Cu(II) concentration for each Case are plotted versus conversion degree in Figure 3. These results were compared to

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those calculated using PREDICI under the same ATRP polymerization conditions, and were

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found to be nearly identical.

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Discussion of ATRP simulation. The contour maps in Figure 1 show the

and increase in DP with % monomer conversion, which, in both Cases 1 and 2, closely follow that of an ideal living

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broadening of molecular weight distributions

number of low molecular weight chains in the

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final distributions is higher. This is apparent

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Figure 3. Copper concentration evolution for Case 1 polymerization. In Case 1, however, the ([CuBr2]0 = 0 M) (red) and Case 2 ([CuBr2]0 = 0.01746 M) (blue).

in the magnified plots of distributions to the

right of the contour maps and the markedly higher Ð at low % conversion (Figure 2,

Figure 2. DPn (top) and Ð (bottom) versus conversion for Case 1 ([CuBr2]0 = 0 M) (red) and Case 2 ([CuBr2]0 = 0.01746 M) (blue) compared to an ideal living polymerization model (black).

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bottom). This phenomenon is well-known in ATRP synthetic practice, and is commonly avoided by adding Cu(II) to the initial reaction.2,21,22 The presence of initial Cu(II) ensures a fast enough kd to prevent coupling of organic radical species which are formed along with Cu(II) in the atom

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transfer step. With enough Cu(II) present for organic radicals to react with, couplings between two organic radicals are not as likely, resulting in narrower distributions and lower Ð. The

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concentration of Cu(I) and Cu(II) are shown in Figure 3, which illustrates the more constant presence of Cu(II) in Case 2, compared to Case 1 which contains very little Cu(II) at low % conversion, allowing for more termination between organic radical species. Using the ATRP simulation as a basis for modeling realistic results, we move on to model polymerization by catalyst transfer. Modeling Catalyst Transfer Polymerization

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GRIM polymerization mechanism and parameters. The original Grignard metathesis polymerization scheme, reported by McCullough, suggested that following reductive elimination, the growing polymer associates nondiffusively with the Ni catalyst. It is now

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recognized that the mechanism proceeds instead via a Ni-polymer π-complex,23-25 The Ni catalyst does not, however remain associated with a single chain end, as substantial evidence exists to support a chain walking process, allowing for bidirectional propagation during CTP.26,27

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Motivated by these reports (as well as those suggesting Ni0 diffusion and catalyst resting states),23,28 and inspired by our understanding of the ATRP mechanism, we consider periods of

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deactivation and subsequent reactivation within the GRIM polymerization mechanism. Including these processes in addition to the known oxidative addition transmetallation, and reductive elimination steps may explain many of the non-ideal characteristics of GRIM.6,8,29,30 Scheme 2 depicts the reaction mechanism for GRIM polymerization, including deactivation of the species

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between the reductive elimination and oxidative addition steps. The corresponding differential

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equations used to implement the numerical model are listed in Table 3 as Equations 9-15.

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Scheme 2. GRIM polymerization mechanism including deactivation/activation of growing chains.

The mechanism in Scheme 2 indicates that the tail-to-tail (T-T) defect inherent in

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polymers prepared by GRIM is always located at the chain end. However, these T-T defects have been shown to occur at other points throughout the chain suggesting that growth can occur at either chain end, presumably due to catalyst walking,.26,27 While this is not explicitly shown in our mechanism, it does not affect the process of adding monomer to the growing chain, and the deactivation step accounts for time when the catalyst is walking along the chain and is unable to propagate.

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Table 3. Kinetic equations used to model GRIM polymerization [ ]′ = −

∗  ' [ ]  [ ] − 2) [*+] [ ] 

(9)

[ ' ] = ) [*+] [ ] − ,- [ ' ]

(10)

' [ ]′ = − [ ] − . [ ] + ,- [" ] +  /0 1

(11)

First monomer attached propagating chain

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Pre-propagating chains



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Monomer

[' ] = 

Monomer-attached propagating chains

∗ ' [ ][ ] −

,- [' ]

(12)

∗ ' [ ][ ]

(13)

[ 0 ]′ =  [ ] −  [ 0 ]

(14)

[*+] = −) [*+][ ]

(15)

[∗ ]′ = . [ ] − 

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Propagating chains Non-propagating chains Nickel catalyst

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The initial Grignard and transmetallation rate constants (kg and ktm, respectively) in the GRIM polymerization model were chosen based on a UV-vis study by Catala and coworkers who reported two separate rates of monomer consumption.31 The rates of reductive elimination

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and oxidative addition (kre and koa, respectively) were inferred from kinetic studies which indicate the rate limiting step in Ni(dppp)Cl2-catalyzed synthesis of poly(3-hexylthiophene) to be

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transmetallation (ktm), as evidenced by a first order rate dependence on both monomer and catalyst.6,8,24,32 Changing the catalyst to Ni(dppe)Cl2 results in zeroth order dependence on monomer concentration and first order dependence on the concentration of catalyst, indicating that reductive elimination is the rate limiting step.23 In the entire set of simulations the value of ktm has been set to unity and used as a reference value for all remaining rate constants. The simulations were carried out over a 21×21×21 grid of rate constant values, which were varied over two orders of magnitude as follows:

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log(kd) = (-2, -1.9, … 0);

log(ka) = log(kd) (0, 0.1, … 2.0);

log(kre) = (-1, -0.9, … 1)

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For simplicity, in the main simulation sweep the value of koa has been set to be equal to kre, even though it is now recognized that in GRIM the reductive elimination is slower than oxidative addition, and is sometimes the rate limiting step in the reaction depending on the The impact of the koa/kre ratio was then explored in additional simulation runs,

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catalyst.

providing support for this simplified assumption for all other simulations.

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Table 4. Coefficients used in GRIM simulations Parameter

Abbreviation

Value

kg

5 M-2 s-1

ktm

1 M-1 s-1

kd

0.01 to 1 s-1

ka

0.01 to 1 × kd

Reductive elimination rate constant

kre

0.1 to 10 s-1

Oxidative addition rate constant

koa

Equal to kre

Initial monomer concentration

[M]0

0.25 M

Nickel concentration

[Ni]0

0.0083 M

Grignard step rate constant Propagation rate constant

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Activation rate constant

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Deactivation rate constant

GRIM simulation results. To approximate experimentally-observed scenarios with broader molecular weight distributions and higher Ð, one could hypothesize that, as in ATRP, a disproportionation

step

may

be

involved

in

GRIM

polymerization,

resulting

in

disproportionation between two polymer chains. While this has been suggested in the literature, it is not likely due to steric factors and can be easily controlled by reducing the temperature of

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the reaction to better stabilize the catalyst.33,34 A significant disproportionation step would also be apparent in plots of polymerization degree versus conversion, which are generally very linear at high conversion degrees. Consequently, we did not account for disproportionation at this point

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in our GRIM calculations.

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Chain initiation profiles. Non-instantaneous initiation was considered as another potential source

of non-ideal behavior. Because Ni(dppp)Cl2 is only marginally soluble in THF, we hypothesized that deviations from ideal living behavior might be induced by the rate at which the catalyst

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dissolves into the reaction mixture, and modeled the release of nickel based on two distinct

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profiles of release rate: constant and linearly decreasing. In both cases the release rates were

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Figure 4. DPn versus conversion for constant Ni(dppp)Cl2 release at kre = 10 (top row), 1 (middle row), and 0.1 (bottom row) for polymerization time equal to tr/t99.9% (0, 0.2, 0.4, 0.6, and 0.8), where tr stands for the release time. Traces for an ideal living polymerization are shown by the shaded traces under the dashed black line in each plot.

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adjusted in such a way that they assured complete release of a fixed amount of catalyst over the

Figure 5. Ð versus conversion for constant Ni(dppp)Cl2 release at kre = 10 (top row), 1 (middle row), and 0.1 (bottom row) for polymerization time equal to tr/t99.9% (0, 0.2, 0.4, 0.6, and 0.8), where tr stands for the release time. Values of Ð for an ideal living polymerization are provided by the shaded traces under the black dashed line in each plot.

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release time tr. Simulations were performed for tr values set according to condition: tr/t99.9% = (0, 0.2, 0.4, 0.6, 0.8), where t99.9% represents the amount of time necessary to reach 99.9% monomer

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conversion. Figures 4-6 show results from the constant catalyst release profile for three values of kre (0.1, 1, and 10). Similar figures for the linearly decreasing release rate profile are included in

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the Supporting Information.

Evolution of DP with conversion is presented in Figure 4 and compared to that of an ideal

living polymerization. Figure 5 shows that delayed release can easily lead to values of Ð in excess of 1.2, especially at high values of kre. Comparison with Figure 4, however, ahows that achieving these values leads to marked deviations from linearity in the evolution of DP with conversion (Figure 4). The origin of these high Ð values is observed in plots of the final weight fraction DP distributions in Figure 6, which also show that delaying the catalyst release results in

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uncharacteristically wide and, in some cases, nearly bimodal distributions. Because delayed nickel release is unlikely to be the sole factor causing deviations from ideal livingness in GRIM, and to prevent these features from confounding other characteristics of the polymerization

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scheme, subsequent numerical model results assume instantaneous catalyst release.

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Figure 6. Final weight fraction DP distributions versus DPn for constant Ni(dppp)Cl2 release at kre = 10 s(top row), 1 s-1 (middle row), and 0.1 s-1 (bottom row) for polymerization time equal to tr/t99.9% (0, 0.2, 0.4, 0.6, and 0.8), where tr stands for the release time.

Deactivation of growing chains: To investigate the effect of chain deactivation, rate constants kd,

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ka, kre, and koa were varied systematically, providing a comprehensive table of results which include distributions of all species at every point in time throughout the polymerization. Included

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in Figures 7-12 are selected arrays of plots, all generated using high rates of deactivation compared to activation (kd = 100 ka). Other kd/ka scenerios are included in the full analysis located in the Supporting Information. Within each set of plots, kd and kre were varied with respect to ktm. Each array of plots is organized from top to bottom in terms of the ratio of rates between reductive elimination and transmetallation, and from left to right in terms of the ratio of rates between deactivation to transmetallation.

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Figure 7. Array of final normalized weight fraction DP distributions for kd/ka= 100. Target DPn (30) is indicated by the black dashed line. Broad, nearly bimodal distributions are observed along the bottomleft/top-right diagonal of the array (highlighted), indicating that the most pronounced distortions occur ∗ when the time scale of the transformation from 234 to 2356 matches the time scale of reversible deactivation/activation.

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The ranges over which kd/ ktm and kre/ ktm were varied are kept consistent throughout Figures 7-12, and highlight three distinct regimes. These can be observed in Figures 7-12 either

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along the diagonal, where kre/ ktm is on the order of 10 × kd/ ktm (where deviations from ideal living behavior are most apparent), and above and below the diagonal where the results reveal a more ideal system. Figure 7 specifically highlights this diagonal of maximum distortion, but it is apparent within all sets of plots, and similar trends emerge in each of the three specified regions. Figures 7-9 are most diagnostic in terms of observing the impact of chain deactivation on molecular weight distributions. Figure 7 contains plots of final weight fraction distributions, and Figure 8 reveals the resulting trends in Ð. An alternate visualization of Ð that encompasses

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information from the array plots in Figure 8 is presented in Figure 9. This figure, which describes only final Ð values, emphasizes the higher Ð values obtained along the diagonal of maximum

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distortion.

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Figure 8. Ð versus conversion compared to an ideal living polymerization (dashed black). Both above and below the diagonal, Ð closely matches that of the anionic polymerization, however along the diagonal, large dispersity values are observed.

Figures 10-12 help elucidate the origins of the increased distribution widths and higher Ð

values observed in Figures 7-9. Contour maps showing the temporal evolution of molecular weight distributions for all species are presented in Figure 10, and reflect our desire to highlight the reaction kinetics. Figure 11, which describes monomer consumption over time, also make kinetic trends evident. Finally, Figure 12 provides concentration evolution with time for each type of growing polymer chain P*, Pm, P, and P†.

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Discussion of GRIM polymerization simulations. The ranges of reaction rate constants over which the plot arrays in Figures 7-12 were chosen highlight the greatest deviations from Poisson distributions and ideal living behavior, occuring along the diagonal where kre/ ktm is comparable

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to kd/ ktm. These trends are most profound when kd is much higher than ka, although plots

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corresponding to other values of kd/ka (which are provided in the Supporting Information), also

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Figure 9. Contour map of final Ð values that vary based on rates of kd and kre compared to ktm. Color indicates the value of Ð at the end of the polymerization (represented by color and indicated for three distinct values), for various ratios of kre and kd compared to ktm. Three values of Ð (1.55, 1.35, and 1.15) are shown, reflecting the common trend of wider distributions along the diagonal.

reveal similar patterns.

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Figure 10. Contour maps showing weight fraction distributions of all chains in terms of DPn vs time. A single plot representing one of the plots within the large array to the right is shown to provide axis and scale information for the array of plots, all of which maintain common axes. The color scale represents concentration of the resulting chains, indicated by the scale bar. Black dashed traces on all plots show the DPn evolution with time.

Above the diagonal, the kd/ ktm ratio is generally low, indicating that the pre-propagating

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chains, P, have less tendency to deactivate, and propagating chains, P*, are the dominant species in the reaction (cf. Figure 12). With little deactivation, the reaction proceeds very much like an exponential decrease of

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ideal living polymerization. This is reflected by the characteristic

monomer concentration with time (Figure 11) and asymptotic increase of DPn to its target value in temporal contour maps (Figure 10). As kre and koa are decreased with respect to ktm (recall that in the adopted computational

scheme kre/koa = 1), approaching the diagonal of maximum distortion, the intermediate species Pm and P spend more time in a “waiting period.” This, in turn, increases the odds that some of them become temporarily deactivated to species P† (cf. Figure 12), which gives the propagating chains

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Figure 11. Monomer concentration versus time. X-axes are scaled to monomer conversion time (indicated in seconds in each plot). The diagonal highlighted in previous figures represents a clear shift in reaction order from first order in monomer concentration above the diagonal to zeroth order below the diagonal.

dynamic advantage and allows them to grow longer, producing a distinct shoulder in chain

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length distributions (cf. Figures 7 and 10). This distortion of distributions becomes most pronounced for combinations of rate constants corresponding to the diagonal of maximum

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perturbation.

In the region below the diagonal of maximum distortion (when kre and koa are low and kd

is high, compared to ktm), nearly all chains are deactivated early and spend the majority of the polymerization in the “waiting period,” evidenced by the high concentration of P† in Figure 12. Monomer is depleted only when chains reactivate, which is very infrequent, resulting in a zeroth order rate dependence on monomer concentration, and a substantial increase in the time required

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Figure 12. Fraction of each species versus time for propagating chains, P* (shaded red); nonpropagating chains, P† (black); monomer attached propagating chains, Pm (blue); and pre-propagating chains, P (green). Above the diagonal, P* dominate, while P† are the predominant species below. Along the diagonal, a wide range of species are present.

to reach total conversion of monomer (cf. Figure 11). The rate of reactivation is solely

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responsible for further progression through the cycle. Because all chains are slowed down equally and monomer addition is substantially arrested, narrow molecular weight distributions

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with low Ð are observed in Figures 7-10. A shift in reaction kinetics between various reaction conditions has been observed before

in the literature. In studies by McNeil and coworkers, dependence on monomer was observed to switch from first to zeroth order when the ligand was changed from dppp to dppe due to differences in the extent of steric contribution from the ligand.25,35 Our model indicates that catalysts with greater affinity for the growing chain and (using the catalyst chain walking

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hypothesis) would be less likely to walk along the growing chain, exist for less time in the deactivated state, leading to more Poisson-like molecular weight distributions. This is also supported by recent studies with Pd catalysts for GRIM by the Stefan group. They suggest that

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complete dissociation of a Pd(0) species from the growing chain results in a slow, step-growth

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polymerization with high Ð values.36

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Rates of oxidative addition and reductive elimination. Throughout our computational scheme, we

have, for simplicity, assumed the rate of oxidative addition to be equal to that of reductive elimination. To determine the impacts of different kre and koa rate constants, we reran the GRIM

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polymerization simulation varying kre beteen 0.10 to 10 times the rate of koa and plotted final

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values of Ð in the style of Figure 9. These plots (each representing a different value of kre/koa) are

Figure 13. Contour maps of final Ð values that vary based on rates of kd and kre compared to ktm. Each plot represents a different value of kre compared to koa, with kre ranging from 0.1 to 10 × koa. These are plotted in the same style as Figure 9, however fewer points were plotted, evidenced by more jagged curves. Note that the plot in row 2, column 3 (where log(kre/koa = 0) is the same as Figure 9, since this is the case where kre equals koa.

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presented in Figure 13. Upon adjusting the kre/koa ratio, the position of the diagonal of maximum distortion is shifted, most significantly along the log(kre/ ktm ) axis. This is likely due to the amount of time it takes for chains to enter and then subsequently exit the “waiting period”

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∗ . With a tenfold increase or decrease in kre compared to koa, the between species P89 and P85

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diagonal shifts up or down, respectively. The simulation was also rerun to account for variation

Figure 14. Contour maps of final Ð values that vary based on rates of kd and kre compared to ktm for a system with initial monomer concentration = 2.0 M. Each plot represents a different value of kre compared to koa, with kre ranging from 0.1 to 10 × koa. These are plotted in the same style as Figure 9, however fewer points were plotted, evidenced by more jagged curves.

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in initial monomer concentration, producing final Ð values shown in Figure 14 (plotted in the same style as Figure 13) for a system with an initial monomer concentration of 2.0 M. An additional plot for a system with an initial monomer concentration of 1.0 M is provided in the

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Supporting Information. The previously-observed diagonal of maximum perturbation is shifted along itself, resulting in higher overall Ð as monomer concentration is increased. This suggests that lower Ð systems may be achieved by decreasing the initial monomer concentration, but that

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the behavior of the overall system is still greatly influenced by chain deactivation, which is

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governed by the affinity of the catalyst for the growing chain end. Conclusions

Using numerical kinetic models, we have produced visualizations of both atom and catalyst transfer polymerizations, which accurately represent results consistent with experimental polymerizations, to examine sources of deviation from ideal living behavior. This modelling

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method has allowed us to investigate parameters affecting Grignard metathesis polymerization, and have led us to support a mechanism for deactivation and subsequent reactivation of growing polymer chains in the GRIM polymerization process. Our results indicate that even for slow

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processes like catalyst-transfer, deactivation and activation of growing polymer chains provides

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significant control over polymerization, and can result in an ideal living process if kinetic rate constants are appropriately controlled by experimental parameters (e.g. catalyst choice, or monomer concentration). Similarities highlighted here between atom-transfer and catalysttransfer, provide insight into GRIM polymerization and other catalyst-transfer processes, that may motivate future inquiry about its mechanism and drive changes that afford greater control over semiconducting polymer design. References

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(1) Wang, J.-S.; Matyjaszewski, K., Controlled/"living" radical polymerization. atom transfer radical polymerization in the presence of transition-metal complexes, Journal of the American Chemical Society 1995, 117, 5614-5615. (2) Matyjaszewski, K.; Xia, J., Atom Transfer Radical Polymerization, Chemical Reviews 2001, 101, 2921-2990. (3) Matyjaszewski, K.; Spanswick, J., Controlled/living radical polymerization, Materials Today 2005, 8, 26-33. (4) Johansson Seechurn, C. C. C.; Kitching, M. O.; Colacot, T. J.; Snieckus, V., Palladium-Catalyzed Cross-Coupling: A Historical Contextual Perspective to the 2010 Nobel Prize, Angewandte Chemie International Edition 2012, 51, 5062-5085. (5) Loewe, R. S.; Khersonsky, S. M.; McCullough, R. D., A Simple Method to Prepare Head-to-Tail Coupled, Regioregular Poly(3-alkylthiophenes) Using Grignard Metathesis, Advanced Materials 1999, 11, 250-253. (6) Sheina, E. E.; Liu, J.; Iovu, M. C.; Laird, D. W.; McCullough, R. D., Chain Growth Mechanism for Regioregular Nickel-Initiated Cross-Coupling Polymerizations, Macromolecules 2004 37, 3526-3528. (7) Loewe, R. S.; Ewbank, P. C.; Liu, J.; Zhai, L.; McCullough, R. D., Regioregular, Head-to-Tail Coupled Poly(3-alkylthiophenes) Made Easy by the GRIM Method:  Investigation of the Reaction and the Origin of Regioselectivity, Macromolecules 2001, 34, 4324-4333. (8) Iovu, M. C.; Sheina, E. E.; Gil, R. R.; McCullough, R. D., Experimental Evidence for the Quasi“Living” Nature of the Grignard Metathesis Method for the Synthesis of Regioregular Poly(3alkylthiophenes), Macromolecules 2005, 38, 8649-8656. (9) Stefan, M. C.; Javier, A. E.; Osaka, I.; McCullough, R. D., Grignard Metathesis Method (GRIM): Toward a Universal Method for the Synthesis of Conjugated Polymers, Macromolecules 2009 42, 30-32. (10) Osaka, I.; McCullough, R. D., Advances in Molecular Design and Synthesis of Regioregular Polythiophenes, Accounts of Chemical Research 2008, 41, 1202-1214. (11) Heuer, H. W.; Wehrmann, R.; Kirchmeyer, S., Electrochromic Window Based on Conducting Poly(3,4-ethylenedioxythiophene)–Poly(styrene sulfonate), Advanced Functional Materials 2002, 12, 8994. (12) De Paoli, M.-A.; Nogueira, A. F.; Machado, D. A.; Longo, C., All-polymeric electrochromic and photoelectrochemical devices: new advances, Electrochimica Acta 2001, 46, 4243-4249. (13) Groenendaal, L.; Zotti, G.; Aubert, P. H.; Waybright, S. M.; Reynolds, J. R., Electrochemistry of Poly(3,4-alkylenedioxythiophene) Derivatives, Advanced Materials 2003, 15, 855-879. (14) Garnier, F.; Yassar, A.; Hajlaoui, R.; Horowitz, G.; Deloffre, F.; Servet, B.; Ries, S.; Alnot, P., Molecular engineering of organic semiconductors: design of self-assembly properties in conjugated thiophene oligomers, Journal of the American Chemical Society 1993, 115, 8716-8721. (15) Zhang, R.; Li, B.; Iovu, M. C.; Jeffries-El, M.; Sauvé, G.; Cooper, J.; Jia, S.; Tristram-Nagle, S.; Smilgies, D. M.; Lambeth, D. N.; McCullough, R. D.; Kowalewski, T., Nanostructure Dependence of FieldEffect Mobility in Regioregular Poly(3-hexylthiophene) Thin Film Field Effect Transistors, Journal of the American Chemical Society 2006, 128, 3480-3481. (16) Hiemenz, P. C.; Lodge, T. P. Polymer Chemistry; 2nd ed.; CRC Press: Boca Raton, FL, 2007. (17) Jeffries-El, M.; Sauve, G.; McCullough, R. D., Facile Synthesis of End-Functionalized Regioregular Poly(3-alkylthiophene)s via Modified Grignard Metathesis Reaction, Macromolecules 2005 38, 1034610352. (18) Yokoyama, A.; Miyakoshi, R.; Yokozawa, T., Chain-growth polymerization for poly(3hexylthiophene) with a defined molecular weight and a low polydispersity, Macromolecules 2004, 37, 1169-1171. (19) Wulkow, M. In Progress in Industrial Mathematics at ECMI 94; Neunzert, H., Ed.; Vieweg+Teubner Verlag, 1996; pp 166-175.

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(20) Patten, T. E.; Xia, J.; Abernathy, T.; Matyjaszewski, K., Polymers with Very Low Polydispersities from Atom Transfer Radical Polymerization, Science 1996, 272, 866-868. (21) Matyjaszewski, K.; Patten, T. E.; Xia, J., Controlled/“Living” Radical Polymerization. Kinetics of the Homogeneous Atom Transfer Radical Polymerization of Styrene, Journal of the American Chemical Society 1997, 119, 674-680. (22) Kajiwara, A.; Matyjaszewski, K.; Kamachi, M., Simultaneous EPR and Kinetic Study of Styrene Atom Transfer Radical Polymerization (ATRP), Macromolecules 1998, 31, 5695-5701. (23) Lanni, E. L.; McNeil, A. J., Mechanistic Studies on Ni(dppe)Cl2-Catalyzed Chain-Growth Polymerizations: Evidence for Rate-Determining Reductive Elimination, Journal of the American Chemical Society 2009, 131, 16573-16579. (24) Lanni, E. L.; McNeil, A. J., Evidence for Ligand-Dependent Mechanistic Changes in NickelCatalyzed Chain-Growth Polymerizations, Macromolecules 2010, 43, 8039-8044. (25) Bryan, Z. J.; McNeil, A. J., Conjugated Polymer Synthesis via Catalyst-Transfer Polycondensation (CTP): Mechanism, Scope, and Applications, Macromolecules 2013. (26) Tkachov, R.; Senkovskyy, V.; Komber, H.; Sommer, J.-U.; Kiriy, A., Random Catalyst Walking along Polymerized Poly(3-hexylthiophene) Chains in Kumada Catalyst-Transfer Polycondensation, J. Am. Chem. Soc. 2010, 132, 7803-7810. (27) Verswyvel, M.; Monnaie, F.; Koeckelberghs, G., AB Block Copoly(3-alkylthiophenes): Synthesis and Chiroptical Behavior, Macromolecules 2011, 44, 9489-9498. (28) Achord, B. C.; Rawlins, J. W., Evidence of Ni(0) Complex Diffusion during Grignard Metathesis Polymerization of 2,5-Dibromo-3-hexylthiophene, Macromolecules 2009, 42, 8634-8639. (29) Miyakoshi, R.; Yokoyama, A.; Yokozawa, T., Synthesis of Poly(3-hexylthiophene) with a Narrower Polydispersity, Macromolecular Rapid Communications 2004, 25, 1663-1666. (30) Yokoyama, A.; Miyakoshi, R.; Yokozawa, T., Chain-Growth Polymerization for Poly(3hexylthiophene) with a Defined Molecular Weight and a Low Polydispersity, Macromolecules 2004, 37, 1169-1171. (31) Lamps, J. P.; Catala, J. M., Real Time Controlled Polymerization Kinetics of 2,5-Dibromo-3decylthiophene Using UV−Vis Spectroscopy: Determination of the Reaction Rate Constants, Macromolecules 2009, 42, 7282-7284. (32) Tkachov, R.; Senkovskyy, V.; Komber, H.; Kiriy, A., Influence of Alkyl Substitution Pattern on Reactivity of Thiophene-Based Monomers in Kumada Catalyst-Transfer Polycondensation, Macromolecules 2011, 44, 2006-2015. (33) Bilbrey, J. A.; Sontag, S. K.; Huddleston, N. E.; Allen, W. D.; Locklin, J., On the Role of Disproportionation Energy in Kumada Catalyst-Transfer Polycondensation, ACS Macro Letters 2012, 1, 995-1000. (34) Miyakoshi, R.; Yokoyama, A.; Yokozawa, T., Development of catalyst-transfer condensation polymerization. Synthesis of π-conjugated polymers with controlled molecular weight and low polydispersity, Journal of Polymer Science Part A: Polymer Chemistry 2008, 46, 753-765. (35) Lanni, E. L.; Locke, J. R.; Gleave, C. M.; McNeil, A. J., Ligand-Based Steric Effects in Ni-Catalyzed Chain-Growth Polymerizations Using Bis(dialkylphosphino)ethanes, Macromolecules 2011, 44, 51365145. (36) Bhatt, M. P.; Magurudeniya, H. D.; Sista, P.; Sheina, E. E.; Jeffries-El, M.; Janesko, B. G.; McCullough, R. D.; Stefan, M. C., Role of the transition metal in Grignard metathesis polymerization (GRIM) of 3-hexylthiophene, J. Mater. Chem. A 2013, 1, 12841-12849.

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Molecular weight distributions in controlled polymerizations were simulated numerically. ATRP and catalyst transfer polymerization were analyzed.

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The possible sources of deviations from Poisson distribution were identified.

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DPn versus conversion for constant (same as manuscript Figure 4) and decreasing Ni(dppp)Cl2 release at kre = 10 (top row), 1 (middle row), and 0.1 (bottom row) for polymerization time equal to tr/t99.9% (0, 0.2, 0.4, 0.6, and 0.8), where tr stands for the release time. Traces for an ideal living polymerization are shown by the shaded traces under the dashed black line in each plot.

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Constant Ni release

Decreasing Ni release

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Ð versus conversion for constant (same as manuscript Figure 5) and decreasing Ni(dppp)Cl2 release at kre = 10 (top row), 1 (middle row), and 0.1 (bottom row) for polymerization time equal to tr/t99.9% (0, 0.2, 0.4, 0.6, and 0.8), where tr stands for the release time. Values of Ð for an ideal living polymerization are provided by the shaded traces under the black dashed line in each plot.

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Constant Ni release

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Final weight distributions versus DPn for constant (same as manuscript Figure 6) and decreasing Ni(dppp)Cl2 release at kre = 10 s-1 (top row), 1 s-1 (middle row), and 0.1 s-1 (bottom row) for for polymerization time equal to tr/t99.9% (0, 0.2, 0.4, 0.6, and 0.8), where tr stands for the release time.

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Constant Ni release

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Arrays of final normalized weight fraction DP distributions for kd/ka= 100 for log(kd/ka) = 0.0, 0.4, 0.8, 0.12, 0.16, and 0.20 (0.20 is the same as manuscript Figure 7). Target DPn (30) is indicated by the black dashed line. Wide, nearly bimodal distributions are observed along the diagonal representing the regions where reaction rate constants are of similar orders, while narrow, Poisson distributions are obtained both above and below the diagonal.

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Ð versus conversion compared to an ideal living polymerization (dashed black) for log(kd/ka) = 0.0, 0.4, 0.8, 0.12, 0.16, and 0.20 (0.20 is the same as manuscript Figure 9). Both above and below the diagonal, Ð closely matches that of the anionic polymerization, however along the diagonal, large dispersity values are observed.

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Contour maps showing weight average distributions of all chains in terms of DPn vs time for log(kd/ka) = 0.0, 0.4, 0.8, 0.12, 0.16, and 0.20 (0.20 is the same as manuscript Figure 10). A single plot representing one of the plots within the large array to the right is shown to provide axis and scale information for the array of plots, all of which maintain common axes. The color scale represents concentration of the resulting chains, indicated by the scale bar. Black dashed traces on all plots show the DPn evolution with time.

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Monomer concentration versus time for log(kd/ka) = 0.0, 0.4, 0.8, 0.12, 0.16, and 0.20 (0.20 is the same as manuscript Figure 11). X-axes are scaled to monomer conversion time (indicated in seconds in each plot). The diagonal highlighted in previous figures represents a clear shift in reaction order from first order in monomer concentration above the diagonal to zeroth order below the diagonal. Traces for an ideal living polymerization are included for comparison (dashed black).

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Fraction of each species versus time for propagating chains, P* (shaded red); non-propagating chains, P† (black); monomer attached propagating chains, Pm (blue); and pre-propagating chains, P (green) for log(kd/ka) = 0.0, 0.4, 0.8, 0.12, 0.16, and 0.20 (0.20 is the same as manuscript Figure 12). Above the diagonal, P* dominate, while P† are the predominant species below. Along the diagonal, a wide range of species are present.

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Contour maps of final Ð values that vary based on rates of kd and kre compared to ktm for systems with initial monomer concentration = 0.25 (same as manuscript Figure 13), 1.0, and 2.0 M (same as manuscript Figure 14). Each plot represents a different value of kre compared to koa, with kre ranging from 0.1 to 10 × koa. These are plotted in the same style as Figure 9 in the manuscript, however fewer points were plotted, evidenced by more jagged curves. Note that the plot in row 2, column 3 (where log(kre/koa = 0) is the same as Figure 9 in the manuscript, since this is the case where kre equals koa.

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