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Obtaining Kinetic Information from the Chain-Length Distribution of Polymers Produced by RAFT Dominik Konkolewicz,† Meiliana Siauw,† Angus Gray-Weale,‡ Brian S. Hawkett,† and Se´bastien Perrier*,† Key Centre for Polymers & Colloids, School of Chemistry, The UniVersity of Sydney, NSW 2006, Australia, and School of Chemistry, Monash UniVersity, Victoria 3800, Australia ReceiVed: January 23, 2009; ReVised Manuscript ReceiVed: March 12, 2009
We describe a simple model for the kinetics and chain-length distribution of polymers made by living radical techniques. Living radical methods give good control over the molecular weight of a linear polymer by capping the growing end and forming a dormant chain. The polymer is predominantly capped, and occasionally decaps to form a radical that propagates for a short period before recapping. Our model uses this mechanism to describe the chain-length distribution of polymers made by living radical methods. We focus on oligomers made by reversible addition-fragmentation chain transfer (RAFT) polymerization as model systems. Our model can determine optimal reaction conditions for desired polymer properties and test hypotheses about reaction schemes by using only two parameters, with each parameter related to the kinetics. The first parameter is the mean number of monomers added when a chain decaps. A broad distribution results if many monomers are added upon decapping. The second parameter is the mean number of times a polymer decaps. Many decapping events indicate high monomer conversion. Our model gives kinetic information by directly fitting to an experimental chain-length distribution, which is the reverse of other kinetic models that generate the distribution from rate coefficients. Our approach has also the advantage of being simpler than previously published kinetic schemes, which use many rate coefficients as inputs. Our model was tested against three monomers (acrylic acid, butyl acrylate, and styrene) and two RAFT agents. In each case, we successfully describe the chain-length distribution, and give information about the kinetics, especially the probability of propagation versus deactivation by the RAFT mechanism. This excellent agreement with a priori expectations and quantum calculations makes our model a powerful tool for predicting the structure of polymers obtained by living radical polymerization. SCHEME 1: RAFT Mechanisma
Introduction Radical polymerization can be used to produce both longchain polymers1 and short-chain oligomers2 from a wide variety of vinyl monomers. These polymers have a wide range of applications, including as liquid crystals,3 in molecular electronics,4 as model systems for microphase behavior,5 and in emulsion polymerization.6-8 In free-radical polymerizations the average molecular weight can be varied by changing the concentration of chain transfer agents.9 However, free-radical methods do not give good control over chain-length distribution and hence the properties of the polymer. This is evidenced by the polymer’s polydispersity indices (PDIs), which are typically around 2.9 The PDI is the ratio of the weight-average molecular weight to the number-average molecular weight, and describes the breadth of the distribution. A monodisperse polymer has a PDI of 1, and uncontrolled polymerizations give PDIs of 2 or even higher. Free-radical polymerization cannot, in general, be used to make block copolymers. Living polymerizations, on the other hand, can reduce the polydispersity and improve the control over a polymer’s architecture, give narrow molecular weight distributions, and can be used to make block copolymers.10 Polymers synthesized by living techniques can improve properties such as tensile * To whom correspondence should be addressed. Phone: +61 2 9351 3366. E-mail:
[email protected]. † The University of Sydney. ‡ Monash University.
a
Pj and Pk are polymer chains of some chain length.
strength compared to free-radical synthesized polymers.11 Block copolymers made by living methods have been used as stabilizers in emulsion polymerization,6-8 or alternatively can assist in the manufacture of memory storage devices.11 Anionic polymerization was the first reported living polymerization.10,12 In contrast to free-radical polymerization, anionic polymerization is limited in terms of monomer functionality.10,12 These limitations have been addressed over the past 15 years with the development of living radical polymerization (LRP) methods, which give narrow distributions for a wide variety of monomers. Examples of LRP process are nitroxide-mediated polymerization (NMP),13,14 atom transfer radical polymerization (ATRP),15,16 and reversible addition-fragmentation chain transfer (RAFT) polymerization.17 Each technique gives polymer chains with well-defined molecular weights and narrow distributions for long-chain polymers. RAFT polymerization differs from NMP and ATRP, since it is based on the transfer of activity between polymer chains, rather than reversible deactivation of the growing polymer chains (see Scheme 1). Furthermore, among the living radical polymerization techniques, RAFT is the most versatile, since it can be adapted to the widest range of
10.1021/jp900684t CCC: $40.75 2009 American Chemical Society Published on Web 04/29/2009
Kinetics and Chain-Length Distribution of Polymers monomers at convenient temperatures.18-21 RAFT polymerization has been used to synthesize a variety of polymer architectures, including linear, block, gradient, star, hyperbranched polymers, and oligomers with narrow molecular weight distributions (PDI < 1.2).21-27 In this paper we outline a simple model that gives the chainlength distribution of polymers synthesized by living radical methods, focusing on RAFT. The two key aspects of our model are (i) its simplicitysit focuses on two key reaction steps in living radical polymerization, and as a result is simpler than many kinetic schemes used to describe the chain-length distribution of polymerssand (ii) its excellent description of the chainlength distribution of a variety of oligomerssthe model presented here agrees very well with experiments, and has been shown to agree well with methods based on the commercial PREDICI software.28,29 Our model is an alternative to PREDICI since it can be easily implemented at little to no cost. Our model is based on the most important elements in the chain-length distribution, rather than using details of the reaction that are not crucial to the distribution. It can be used to optimize reaction conditions for a given property, or to verify a given reaction scheme and suggest side reactions. It may also be used to directly extract kinetic information from the chain-length distribution. This approach is unique to our model and differs from most other kinetic methods, which input rate coefficients to generate the distribution. Although we use oligomers synthesized under RAFT control to test and characterize our model, this approach could be easily applied to longer chain polymers, and could be extended to other living polymerization methods such as ATRP. We chose RAFT polymerization as, of all living radical polymerization methods, it is the most applicable to the synthesis of functional oligomers because it offers good control over molecular weight, even for short chains, and excellent tolerance to chemical functionalities.18,21 NMP does not offer the same degree of control over short polymeric chains, and is still limited to certain monomer classes, while requiring relatively high temperatures (>100 °C).30 ATRP is also limited by the functionality of monomers, as it cannot polymerize monomers with carboxylic acid groups, since the acid moiety deactivates the catalyst.31 On the other hand, RAFT provides access to an almost infinite number of functional oligomers, which find applications in many areas, including coating of small particles,32 as stabilizers in emulsion polymerization,6-8 and even in potential microphase separation studies.5,33 In this paper we synthesize oligomers by RAFT. These oligomers are used to test our model, and show its capabilities, although the model is not limited to such oligomers. We characterize each oligomer by electrospray ionization mass spectrometry (ESI-MS). Mass spectrometry has been widely used to characterize RAFTsynthesized polymers,34-44 and Barner-Kowollik et al.37 have reviewed the use of mass-spectrometric techniques in various systems such as free-radical and controlled polymerizations. In addition, Gruendling et al.43 have recently optimized a technique that combines size-exclusion chromatography and mass spectrometry. This technique gives the exact molecular weight with no band-broadening effects. In our work, we use ESI-MS, to illustrate our model’s capabilities and descriptive power. It could easily be extended to other techniques such as capillary electrophoresis or size-exclusion chromatorgraphy with bandbroadening correction. Over the past 7 years, many models and kinetic schemes have been developed to describe polymers formed under RAFT control. The current models are reviewed by Monteiro45 and
J. Phys. Chem. B, Vol. 113, No. 20, 2009 7087 Barner-Kowollik et al.46 These kinetic models have been refined to describe the polymerization well, but they tend to have many input parameters and rate coefficients, which can bury the descriptive power of the model. Recently, both our group47 and soon after Tobita48 independently developed models for the chain-length distribution of polymers under RAFT control. These models are based on the fact that a living radical polymerization progresses by multiple decapping-recapping events, and that chain growth only occurs between decapping and recapping. Tobita’s48 work was exclusively theoretical following from their earlier theoretical works.49,50 In contrast, our group47 fitted conversion and PDI data. We then input the fitted rate coefficients to compare against the distributions of long-chain styrene. In that earlier work, our model was shown to agree well with molecular weight distributions determined experimentally and distributions simulated by the PREDICI method.28,29 In this paper we have improved our earlier model by simplifying it, and only focusing on two parameters that describe the distribution and reaction kinetics. We consider the main features of RAFT and other living radical polymerizations, rather than describing all details of the reaction, which are not needed to capture the chain-length distribution. The first parameter we consider is the mean number of monomers added each time a dormant chain becomes an active radical. This is proportional to the probability of propagation versus deactivation. The second parameter is the mean number of times the average polymer decaps over the whole polymerization. Fitting our two-parameter model to an experimental chain-length distribution allows us to directly extract kinetic information. This is the first time that such an approach has been taken. The method is opposite to other studies in the literature, and to the approach adopted in our own earlier work, where we fitted conversion and PDI data and used the fitted rate coefficients to predict the full chainlength distribution. In order to demonstrate the versatility of this novel approach, we study here both hydrophilic and hydrophobic polymers synthesized by RAFT, based on the monomers acrylic acid, n-butyl acrylate, and styrene. We also study the effect of changing the RAFT agent from a trithiocarbonate to a dithiobenzoate. Our model agrees well with each experimental oligomer’s chain-length distribution, and the comparison gives information about the kinetics of the polymerization. The monomers chosen are important for applications as electrosteric stabilizers, since acrylic acid is a very common hydrophilic block, and both butyl acrylate and styrene are common hydrophobic blocks. Our work could easily be extended to any other monomer polymerized by RAFT, or indeed any other controlled radical method such as ATRP. In each case, our model gives information about the reaction process and the relative likelihood of the key chain growth steps. Furthermore, the model described here can be extended further to allow the optimization of synthetic strategies to obtain the narrowest distribution possible, and to describe more complex architectures. Experimental Section Materials. Acrylic acid (AA) and 1,4-dioxane (both Aldrich) were purified by distillation under reduced pressure. n-Butyl acrylate (BA) and styrene (St) were filtered through basic alumina (Aldrich) to remove the inhibitor. 4,4′-Azobis(4cyanovaleric acid) (V501; Fluka), was used as received. 2,2′Azobisisobutyronitrile (AIBN; Aldrich) was recrystallized from ethanol. 2-Propanoic acid dodecyltrithiocarbonate (PADTC), 2-propanoic acid butyltrithiocarbonate (PABTC), 2-propanoic
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TABLE 1: Polymerization of AA Using Different Types of RAFT Agents at 70 °C: PABTC for 3 h, PADB Overnight, and EOSSA for 5 h ingredient RAFT RAFT-capped monoblock PABTC
AA 5 AAPABTC10 AAPABTC15 AAPADB10 AAEOSSA5 AAEOSSA10 AAEOSSA20
mass (g) 1.5043 1.5043 0.7503 0.2148 0.2053 0.3074 0.2053
V501 mol
mass (g) -3
6.31 × 10 6.31 × 10-3 3.15 × 10-3 9.49 × 10-4 8.62 × 10-4 1.29 × 10-3 8.62 × 10-4
0.0883 0.0883 0.0439 0.0268 0 0 0
AIBN mol
mass (g) -4
3.20 × 10 3.20 × 10-4 1.60 × 10-4 9.56 × 10-5 0 0 0
AA mol
0 0 0 0 0.0345 0.0520 0.0342
mass (g)
0 0 0 0 2.10 × 10-4 3.17 × 10-4 2.08 × 10-4
2.2737 4.5462 3.4019 0.6905 0.3191 0.9330 1.2498
dioxane mol
mass (g) -2
3.16 × 10 6.31 × 10-2 4.72 × 10-2 9.58 × 10-3 4.43 × 10-3 1.29 × 10-2 1.73 × 10-2
5.8001 7.5106 6.3135 2.1822 1.2176 2.8540 3.2501
TABLE 2: Polymerization of PABTC and BA at 70 °C for 3 h ingredient PABTC
V501
BA
dioxane
RAFT-capped monoblock
mass (g)
mol
mass (g)
mol
mass (g)
mol
mass (g)
BAPABTC10 BAPABTC15 BAPABTC20
0.4003 0.3515 0.2007
1.68 × 10-3 1.47 × 10-3 8.40 × 10-4
0.0234 0.0410 0.0244
8.35 × 10-5 1.46 × 10-4 8.70 × 10-5
2.1512 2.8180 2.1468
1.68 × 10-2 2.20 × 10-2 1.68 × 10-2
3.8728 4.8530 3.5662
TABLE 3: Polymerization of PADTC and Styrene at 70 °C Overnight ingredient PADTC RAFT-capped monoblock PADTC
St 7 StPADTC9
mass (g) 0.33 0.33
AIBN mol
mass (g) -4
9.41 × 10 9.41 × 10-4
0.0308 0.0305
acid dithiobenzoate (PADB), and 2-(ethoxycarbonothioylthio)succinic acid (EOSSA) were supplied by Dulux, Australia. Electrospray Mass Spectrometric Analysis. Electrospray mass spectrometric analysis was done on a Finnigan LCQ MS Detector with Finnigan LCQ Data Processing using Instrument Control Software. Ten microliters of solution (10 µg of sample dissolved in 1 mL of HPLC-grade methanol) were fed into the electrospray ionization unit at 0.05 mL/min. The electrospray voltage was 4.5 kV, the shear flow rate was set to 50, and the temperature of the heated capillary was 300 °C. MALDI-ToF Mass Spectrometry. MALDI-ToF mass spectrometry was performed on Waters (Micromass) TOF SPEC 2E equipment using a 337 nm nitrogen laser and an accelerating potential of 17.5 kV. Samples were dissolved in HPLC methanol (∼1 mg/mL). Then, 1 µL of the dilute solution was deposited on a stainless plate and the solvent was evaporated at room temperature. Spectra were recorded in the reflectron mode. Size-Exclusion Chromatography (SEC). SEC was performed on a Shimadzu SEC system. For acrylic acid polymers a Waters HR1-HR2-HR3-HR4 Styragel column set was used. The eluent was THF with 5% w/w acetic acid with a flow rate of 1 mL min-1. For n-butyl acrylate polymers a Polymer Laboratories Mixed C column set was used. The eluent was THF with a flow rate of 1 mL min-1. Polystyrene standards from 160 to 6 × 106 were used for calibration; both UV (254 nm) and DRI detection were employed. Synthesis of Oligomers by RAFT Polymerization. RAFT agent, monomer, initiator, and dioxane were mixed in a roundbottom flask according to the amounts indicated in Tables 1, 2, and 3. The mixture was stirred at room temperature (until both RAFT agent and initiator were completely dissolved), deoxygenated with nitrogen gas (10 min), and then immersed in a heated oil bath at 70 °C. All oligomers were characterized by electrospray mass spectrometry. For RAFT polymerization of styrene, the target degrees of polymerization (DP) were 20 and
St mol
dioxane
mass (g) -4
1.90 × 10 1.90 × 10-4
mol
mass (g) -2
1.89 × 10 2.36 × 10-2
1.9680 2.4598
6.9589 8.4281
25 units. However, the reactions were stopped after reaching DP ) 7 and 9, respectively. Details of the reactions are given in Tables 1, 2, and 3. Theoretical Section Our model for the distribution of polymers made by RAFT has two input parameters:47 (i) the mean number of decappings of the RAFT agent (µdecap); (ii) the mean number of monomers added per decapping (µadd). These two parameters depend on the kinetic properties of the RAFT agent and the radical propagation kinetics. The parameter µdecap depends on how long the reaction runs, and how many times a polymer is activated by the RAFT mechanism: kRAFT
Pj• + X-Pk Pj-X + Pk•
(1)
where Pj and Pk are polymers of j and k monomers; X represents the center of the RAFT agent (the thiocarbonylthio group and the stabilizing group). µadd depends on the probability of a linear chain propagating, relative to the probability of transferring the radical to an active chain kp
Pj• + M 98 Pj+1•
(2)
where M is a monomer. In this work we focus especially on µadd, and obtain information about the rate coefficients of the processes it represents. For a given concentration of monomer [M] and RAFT agent [X-R], µadd is given by
µadd )
kp[M] kRAFT[X-R]
(3)
We assume that the probability of a polymer decapping j times over the whole reaction is given by the Poisson distribution.47
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The Poisson distribution gives the probability of observing some number of events, given that they are all independent of each other.47,51 Once a given polymer has decapped, the probability of the polymer propagating m units before transferring to another chain is given by the geometric distribution.47 The geometric distribution gives the probability of observing a number of successful events (propagations), before the first failure (transfer to a different chain). In this work we focus on the statistical properties of the polymeric radical, and the number of decappings, without explicit assumptions of the value of certain rate constants. We model our system by focusing only on three important events: the decapping of the radical, the addition of monomers, and the recapping of the radical. Although events such as termination, transfer to monomer, etc. can be significant, for simplicity we ignore these effects. A treatment which includes such effects may be found in our earlier work.47 We assume that there is a steady state in the concentration of the radicals and RAFT agents; thus µdecap is assumed constant throughout the reaction. This implies that the probability of a polymer undergoing j decappings over the whole synthesis is given by the Poisson distribution with mean µdecap:51
exp(-µdecap)(µdecap)j Pdecap(j|µdecap) ) j!
(4)
We assume that the mean number of monomers added per decapping is µadd; therefore, the probability of adding i monomers in a single decapping is given by the following geometric distribution:47
Padd(i|µadd) ) ui(1 - u)
(5)
where u ) µadd/(1 + µadd). It is important to incorporate the fact that as the polymerization progresses there is a decrease in the concentration of monomer, and a decrease in µadd. We use the properties of RAFT polymerization to write 47
DPj )
[M]0 - [M]j [X-R]
(6)
where DPj is the number-average chain length after j decappings and [M]0 is the initial monomer concentration. We write µadd after j decappings as follows:
[M]j kp [M]0 - DPj[X-R] µadd ) ) kRAFT [X-R] kRAFT [X-R] kp
(7)
We label k* ) kp/kRAFT, and it can be shown that
µadd,j ) k*
[M]0 (1 - k*)j-1 [X-R]
(8)
In this way we account for the consumption of monomer through the polymerization. We denote the distribution of chain lengths after j decappings as Plin(m|k*,j). We assume that the initial chain length is zero, which corresponds to all species being RAFT agents:
Plin(m|k*, 0) )
{
1 if m ) 0 0 otherwise
(9)
We evolve the chain-length distribution by the following method. We determine the probability of propagating i monomers (Padd) in one decapping from µadd,j and eq 5. We estimate the probability of finding a polymer with m monomers after j decappings as the probability of finding a polymer with m monomers in the previous decapping, times the probability of not propagating, plus the probability of finding a polymer with
m - 1 monomers in the previous decapping, times the probability of propagating 1 monomer in the jth decapping, plus the probability of finding a polymer of m - 2 monomers in the previous decapping, times the probability of propagating 2 monomers, etc. We write the chain-length distribution of a polymer that has decapped exactly j times as follows: m
Plin(m|k*, j) )
∑ Plin(m - i|k*, j - 1) Padd(i|µadd,j) i)0
(10) In general, different polymers undergo different numbers of decappings. To account for this, we average Plin(m|k*,j) for all possible numbers of decappings. This averaging gives ∞
PCLD(m|µdecap, k*) )
∑ Pdecap(j|µdecap) PMWD|j(m|k*, j) j)0
(11) The equation above states that the full chain-length distribution is the sum of the chain-length distribution after j decappings Plin(m|k*,j), times the probability of the polymer decapping j times Pdecap(j|µdecap). The full chain-length distribution is denoted as PCLD. The chain-length distribution is a function of two variables k* and µdecap. The parameter k* is the relative likelihood of propagation versus transfer of the radical to a different polymer. k* affects the breadth of the distribution, since a large value of k* implies a high probability of propagation versus transfer. This suggests poor control of the polymerization, and a broad distribution. The parameter µdecap affects the average chain length and the overall conversion of the reaction. A large value of µdecap implies that the average polymer has decapped many times, and the average chain length should be close to the target chain length [M]0/[R-X ]. We can fit the parameters µdecap and k* to an experimental chain-length distribution, to obtain an estimate of both these parameters. In the following section we fit the parameters µdecap and k* to experimental chain-length distributions. These fits both test the model and give information about the polymerization kinetics. Results and Discussion The polymerization of acrylic acid (AA) was mediated by PABTC, PABD, and EOSSA, the polymerization of n-butyl acrylate (BA) was mediated by PABTC, and the polymerization of styrene (St) was mediated by PADTC. Each polymerization yielded oligomers denoted as MMYx, where MM is the monomer (AA, BA, or St), Y is the RAFT agent used to mediate the polymerization, and x is the degree of polymerization. The molecular weight of the oligomer was determined by electrospray ionization mass spectroscopy (ESI-MS). Figure 1 shows a typical mass spectrum for the PABTC-mediated polymerization of acrylic acid targeting a degree of polymerization of 10 (AAPABTC10). In Figure 1 we labeled all peaks that we could identify as being an combination of RAFT agent and acrylic acid. In Figure 1 a label of P5 is a polymer with five acrylic acid units plus the RAFT agent PABTC. We were unable to identify the small peaks at very high molecular weight. We argue that these peaks are mostly noise, although it is possible that they are also terminated polymers. However, these peaks are sufficiently small that they make a negligible difference to the overall distribution and fitted parameters. For each polymer we considered, the raw ESI-MS spectrum is qualitatively similar to the one shown in Figure 1.
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Figure 1. Typical mass spectrum used in this work, in this case showing oligomers of acrylic acid, targeting a degree of polymerization of 10, with PABTC.
Figure 3. Chain-length distribution of oligomers of n-butyl acrylate polymerized by PABTC-mediated RAFT polymerization as measured by ESI-MS and fitted by our model.
Figure 2. Chain-length distribution of oligomers of acrylic acid polymerized by PABTC-mediated RAFT polymerization as measured by ESI-MS and fitted by our model.
Figure 4. Chain-length distribution of oligomers of styrene polymerized by PADTC-mediated RAFT polymerization as measured by ESIMS and fitted by our model.
TABLE 4: Table Showing Parameters Used for Fitting Acrylic Acid Data
TABLE 5: Table Showing Parameters Used for Fitting Butyl Acrylate Data
DPavg k* µdecap
AAPABTC5
AAPABTC10
AAPABTC15
5.1 0.051 72.1
9.2 0.048 43.7
13.6 0.072 25.5
Figure 2 shows the fit of our model for experimental chainlength distributions obtained from ESI-MS analyses of the oligomers AAPABTC5, AAPADTC10, and AAPABTC15. In all cases PCLD denotes the normalized probability of finding a polymer with a given chain length. The fitted values of k* and µdecap are given in Table 4. A value of k* ) 0.06 ( 0.01 is obtained for these oligomers, and the value does not vary drastically between the series. We would expect smaller deviations in k* between AAPABTC10 and AAPABTC15; however, this may be an experimental artifact arising from the ESI-MS data. The same model was also applied to BA oligomers BAPABTC10, BAPABTC15, and BAPABTC20. Figure 3 shows the experimental chain-length distribution and model fit. As for the acrylic acid, excellent agreement is seen between experimental data and the model. The details of the fit are shown in Table 5. We estimate k* ) 0.029 ( 0.009 from the fit. Our results are consistent with a priori expectations that BA propagates more slowly than acrylic acid and gives a lower value of k*.
DPavg k* µdecap
BAPABTC10
BAPABTC15
BAPABTC20
9.5 0.038 78.46
13.3 0.023 86.84
14.8 0.029 43.2
In order to test our model with a different type of monomer, we selected the polymerization of styrene. Styrene propagates much slower than acrylates; hence we expect k* to be lower for styrene compared to the acrylic monomers. The low rate of propagation of styrene prevents the polymerization going to completion, even after 16 h at 70 °C. However, our model compensated for this effect by predicting a lower value of µdecap compared to a system that has gone to completion. Figure 4 shows the experimentally determined chain-length distributions and the fit of the theory to the experimental data. We show this for the series StPADTC7 and StPADTC9 with the fitted values of k* and µdecap given in Table 6. As in previous cases, good agreement is observed between theory and experiment for both series, and a value of k* ) 0.007 ( 0.003 is estimated for styrene. The variations in k* values observed between each series is likely to be due to experimental error in the electrospray mass spectrometry. Nevertheless, and as expected, the value of k* is much smaller for both styrene series when compared to acrylate polymerizations. Although these styrene polymerization have not reached completion, we
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TABLE 6: Table Showing Parameters Used for Fitting Styrene Data DPavg k* µdecap
StPADTC7
StPADTC9
6.9 0.0049 86
8.8 0.0098 47
TABLE 7: Table Showing Parameters Used for Fitting Acrylic Acid Data with Two Different RAFT Agents, Trithiocarbonate and Dithiobenzoate DPavg k* µdecap
AAPABTC10 (trithiocarbonate)
AAPADB10 (dithiobenzoate)
9.2 0.048 43.7
8.6 0.12 11.7
assumed steady-state conditions in the concentration of propagating radicals and RAFT intermediate radicals. Due to the long reaction time of 16 h, we argue that a steady state would be achieved in the radical concentration within the first few hours and persist for much of the reaction. We argue for steady-state radical concentrations on the basis of the electron spin resonance experiments of Calitz et al.52 In their experiments Calitz et al. found that the concentration of dithiobenzoate RAFT intermediate radicals reached a steady state within about 2-3 h at 70 °C. It should be noted that there are models for RAFT kinetics that assume slow fragmentation, which implies that the steady state is not reached quickly for dithiobenzoates.53,54 However, we used a trithiocarbonate RAFT agent, which shows much weaker rate retardation than the dithiobenzoates studied by Barner-Kowollik et al. Therefore, even under the slow fragmentation model,53 a reaction time of 16 h is sufficient to invoke the steady-state assumption for trithiocarbonate RAFT agents. This allows us to illustrate our model for polymers such as the styrene oligomers in Figure 4. Having determined that our model gives reasonably good fits for the acrylic acid oligomers, we investigated the difference in control over molecular weights of acrylic acid oligomers by trithiocarbonate and dithiobenzoate RAFT agents. Experimental results show that dithiobenzoate RAFT agents give control over molecular weight similar to that of their trithiocarbonate counterparts, although the distribution is slightly narrower for the trithiocarbonate derivative. Figure 5 shows the experimental data fitted with our model for series AAPABTC10 and AAPADB10, and Table 7 gives the detail of the fit. An interesting outcome is that the dithiobenzoate-mediated polymerization of acrylic acid shows a larger value of k* than the trithiocarbonatemediated polymerization. The larger value of k* for the dithiobenzoate compared to the trithiocarbonate suggests that the trithiocarbonate-mediated polymerization of acrylic acid is better controlled than the dithiobenzaote-mediated polymerization. However, the factor of 2 difference in the value of k* is small, and is unlikely to affect the properties of the polymer significantly. In addition to the trithiocarbonate and dithiobenzoate RAFT agents, which provide very good control over the oligomer molecular weights, we attempted to test our model on xanthatebased RAFT agents, which do not provide good control over molecular weight distribution. Three polymerizations of acrylic acid mediated by the xanthate EOSSA were undertaken to yield oligomers AAEOSSA5, AAEOSSA10, and AAEOSSA20. Unfortunately, the lack of control of xanthate-mediated polymerization led to molecular weight distributions, which could not be resolved accurately by ESI-MS, thus making the fit by our model impossible (see Supporting Information).
Figure 5. Chain-length distribution of oligomers of acrylic acid polymerized by PABTC-mediated RAFT polymerization and PADBmediated RAFT polymerization, as measured by ESI-MS and fitted by our model.
Figure 6. Comparison between the chain-length distributions of BAPABTC20 determined by ESI-MS and SEC.
Despite the excellent performance of our model, some limitations remain in our study, the most important of which is the use of electrospray ionization mass spectrometry (ESI-MS) to characterize the polymers. Electrospray ionization may degrade the polymers, and it is possible that biases are introduced in the analysis of the polymers. However, ESI-MS is not the only characterization method that suffers from potential biases and processing errors. Size-exclusion chromatography (SEC) is a popular technique for characterizing both long-chain polymers and oligomers. However, SEC can also give biased results if baselines are poorly selected, and due to the band-broadening effect.43,55,56 Other techniques such as capillary electrophoresis are not sufficiently developed for application to a wide range of oligomers. Due to these issues, it is difficult to obtain unbiased chain-length distributions. Recently, Gruendling et al.43 developed a combined SEC-ESIMS technique that gives absolute molecular weight distributions with no band broadening. To address the potential issues and biases in our ESI-MS data, we calibrated our electrospray mass spectrometer by comparison to size-exclusion-chromatography data. Figure 6 shows the electrospray ionization mass spectrum (ESI-MS), the number distribution obtained by size-exclusion chromatography (SEC), and the fit of our model to the ESI-MS data. All three distributions in Figure 6 agree well with each other, which suggests that both SEC and ESI-MS can be used to
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Figure 7. Sensitivity of the chain-length distribution to variations in the parameter k*.
Figure 8. Sensitivity of the chain-length distribution to variations in the parameter µdecap.
characterize our oligomers. We attribute the additional breadth in the SEC distribution to band broadening,43,56 although the broadening is reasonably small for our polymers. The comparison in Figure 6 suggests that ESI-MS data are sufficiently accurate to test our model and describe its behavior. In the future, techniques such as the SEC-ESI-MS technique43 or capillary electrophoresis methods could be used to experimentally determine the distributions used to extract information from our model. One other important consideration is the sensitivity of our model’s parameters to small variations in the chain-length distribution. We determine the robustness of our model by performing a sensitivity analysis on our model on the best fit to the data series BAPABTC20. This series was fitted with the parameters k* ) 0.029 and µdecap ) 43.2. Figure 7 shows our model’s response to variations in the parameter k*. From the plot we see that even varying k* by a factor of 2 causes appreciable deviations from the original curve. Furthermore, and if we increase k* by a factor of 10, we see very significant broadening. Alternatively, if we decrease k* by a factor of 10, we see significant narrowing of the distribution and we notice that the distribution is strongly shifted to low molecular weight. Figure 8 show our model’s response to changes in the parameter µdecap. If we increase µdecap, we shift the distribution toward high chain lengths, and decreasing µdecap shifts the distribution toward short chain lengths. There seems to be minimal effect on the breadth of the distribution if we change µdecap. The final
Konkolewicz et al.
Figure 9. Sensitivity of the chain-length distribution to increases in the parameter k* with equivalent decreases in the parameter µdecap.
sensitivity analysis we perform is to increase k* and decrease µdecap. Figure 9 shows the effect on the distribution of increasing k* by 2, 5, or 10 and decreasing µdecap by an equivalent factor. When we increase k* and decrease µdecap by an equivalent amount, we notice the peak remains at the same chain length, but the distribution becomes significantly broader. When we increase k* by a factor of 2, the distribution is still relatively narrow, while increasing k* by a factor of 5 gives a significantly broader distribution, and increasing k* by a factor of 10 gives an extremely broad distribution. This demonstrates the robustness of our model. This is because our model gives similar parameter values when the distributions are similar, and it gives very different parameters for vastly different distributions. This implies that it should give parameters with errors much less than 1 order of magnitude. This analysis also suggests that, in order to have a well-controlled distribution, k* should be much less than 0.3, since k* ) 0.3 gave an unacceptably broad distribution in Figure 9. In addition to demonstrating the robustness of our model, Figure 7, Figure 8, and Figure 9 demonstrate the behavior of our model as the parameters are varied. These figures show how the model can give narrow or broad distributions by varying k*, and how the peak of the distribution can be shifted by varying µdecap. We have studied three different monomers, acrylic acid, n-butyl acrylate, and styrene, and we were able to quantify the trend in the parameter k*, which measures the ratio of the propagation rate coefficient kp to the RAFT transfer rate coefficient kRAFT. It is known that kpAA > kpBA > kpSt, and this trend is replicated in the values of k*, with the value for styrene being about an order of magnitude smaller than the value for acrylic acid. Similarly, k* is higher for the faster propagating acrylic monomers, with k* being twice as large for the acid compared to the butyl ester. In contrast, styrene propagates orders of magnitude slower than acrylic acid, and k* is lower by an order of magnitude. We use the values of k* to estimate the RAFT deactivation rate kRAFT. We estimate kRAFT by using k* and literature values57-59 of the propagation rate coefficient kp. There is some uncertainty in the literature over the propagation rate coefficient of acrylic acid, as it shows variation with solvent and composition. We estimate the propagation rate coefficient of acrylic acid by using the Arrhenius parameters outlined by Lacik et al.59 at 40% monomer. These results are shown in Table 8. We find that kRAFT is comparable for the two acrylic radicals,60 with both AA and BA giving a deactivation rate coefficient of (1-2) × 106 M-1 s-1. We also predict that the deactivation
Kinetics and Chain-Length Distribution of Polymers TABLE 8: Estimates of Deactivation Rate Coefficient Based on k* and kp AAPABTC BAPABTC StPADTC AAPABD
k*
kp (M-1 s-1) [ref]
kRAFT (M-1 s-1)
0.06 0.029 0.007 0.12
1.2 × 105 [59] 4.1 × 104 [57] 4.8 × 102 [58] 1.2 × 105 [59]
2 × 106 1.4 × 106 6.9 × 104 1.0 × 106
rate coefficient for styrene with the trithiocarbonate is 6.9 × 104 M-1 s-1. This deactivation rate is about 1.5 orders of magnitude smaller than the deactivation rate of the acrylic-based radicals. Coote et al.61 performed quantum calculations of the activation and deactivation rate coefficients, and they found that acrylic radicals have deactivation rates about 1-2 orders of magnitude higher than styrl radicals. The rate coefficients determined by this method are approximately 2 orders of magnitude lower than the quantum estimates.61 We also mention that this study finds a RAFT deactivation rate coefficient of ∼105 M-1 s-1 with the trithiocarbonate, while our earlier study47 found a value of 106-107 M-1 s-1 for the deactivation of a styrl radical with a dithiobenzoate. Although these two studies disagree by about 1-2 orders of magnitude, they are performed on different RAFT agents, which is likely to explain the difference in the rate coefficients. In our model, we have neglected chain-length dependence in both the propagation and also the termination. The parameter k* is an important part of our model, and it depends on the ratio of the propagation rate coefficient kp and kRAFT, the RAFT deactivation rate coefficient. Therefore, chain-length dependence in either rate coefficient could influence our model. Very short polymers, typically shorter than two to three monomers, can have propagation rates that are very different to their long chain propagation rates.62 Similar chain-length effects have been found in quantum calculations of the RAFT reaction; hence kRAFT is also likely to be chain-length-dependent.44,61 When we fit our model to a chain-length distribution, we determine the chainlength-averaged value of k*. This includes the possible variations in k* at very short chain lengths. In this paper, we outline the simplest model capable of describing the chain-length distribution of polymers formed by living radical techniques. Therefore, we ignore chain-length effects and calculate averaged parameters, although, in the future, chain-length-dependent effects could be included. Another important consideration is the possible introduction of biases in our chain-length distribution due to the increased termination rate of short oligomers.62,63 To minimize biases due to termination effects, we perform our reactions with a high ratio of RAFT agent to initiator. We argue that the vast majority of our polymers are living due to the very strong living chain signals in the mass spectra and the absence of any high molecular weight shoulders in the GPC traces. Termination effects are unavoidable in RAFT systems; however,
J. Phys. Chem. B, Vol. 113, No. 20, 2009 7093 we believe that our reactions are sufficiently well controlled by the RAFT mechanism to characterize our model. Although termination effects could cause small discrepancies in the distribution, our sensitivity analysis suggests that the parameters are likely to vary by less than a factor of 2. In summary, our results show that a simple model may be used to gain information about the relative reactivities of various monomer combinations, such as styrene versus acrylates. Our model successfully predicts the characteristics of the experimental chain-length distribution, and in doing so provides information about the polymerization kinetics. Our model gives the relative likelihood of a radical propagating to the likelihood of that radical transferring to a different polymer chain. This ratio, k*, determines the breadth of the distribution, and the broader the distribution, the larger the value of k*. A small value of k* implies a well-controlled reaction and a narrow molecular weight distribution. Our theoretical method may be applied to any polymerization where the reaction may be described as “living”, although the best results are obtained in systems that show good control over the polymerization. Our theoretical model can be readily applied to other monomers, and could become an excellent tool for predicting the chain-length distribution of other oligomers and long-chain polymers. Alternatively, our model can give kinetic information about a polymerization, providing the chain-length distribution is kept relatively narrow. Conclusions We describe a simple model that can give the chain-length distribution and kinetic information about polymers synthesized by living radical methods. The model is based on the assumption that, in a living radical polymerization, a given polymeric chain spends the majority of its time as a dormant chain, and the time spent as an active radical is short. The model uses this information to characterize the chain-length distribution by two parameters: µdecap and k*. µdecap is the average number of times a given chain decaps over the whole polymerization time, and k* is the mean number of monomers added per decapping. The second parameter is particularly useful from a kinetic point of view, as it characterizes the ratio of the probability of propagating to the probability of transferring. This describes the degree of control, since a well-controlled polymerization will only add a small number of monomers per decapping. Our study suggests that a controlled distribution is obtained if k* is kept well below 0.3, and a very narrow distribution is obtained if k* is below 0.1. The value of µdecap is not as important to the degree of control in the polymer as it shifts the center of the distribution, rather than broadening or contracting the distribution. However, µdecap must be large enough that the polymer decaps sufficiently many times that all RAFT agents are converted to oligomers or polymers, which is almost always the case in successful
SCHEME 2: RAFT Agents Used in This Worka
a
(a) 2-Propanoic acid dodecyltrithiocarbonate (PADTC), (b) 2-propanoic acid butyltrithiocarbonate (PABTC), (c) 2-propanoic acid dithiobenzoate (PADB), and (d) 2-(ethoxycarbonothioylthio)succinic acid (EOSSA).
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RAFT polymerizations. We have synthesized oligomers of acrylic acid, n-butyl acrylate, and styrene via the RAFT process. These oligomers are model systems used to test and benchmark the model. The chain-length distribution of these oligomers was determined by electrospray mass spectrometry and compared to the model’s predictions. In all cases our model agreed well with the experiments. We used our model to extract kinetic information from the chain-length distribution, with the results being consistent with a priori expectations and quantum calculations. The features of our model are its simplicity, its ability to optimize reaction conditions for certain properties, and the fact that it can be applied to any monomer and control agent that yield polymers with a relatively narrow chain-length distribution. These attributes make it an excellent tool for the synthetic polymer chemist who wants to design a polymerization system to obtain materials with predefined properties. Acknowledgment. The authors acknowledge the Australian Research Council for funding, an Australian Postdoctoral Fellowship (AGW), and an Australian Postgraduate Award (DK). Supporting Information Available: Electrospray, MALDIToF, and size exclusion analyses of EOSSA mediated RAFT polymerization of acrylic acid. This information is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Matyjaszewski, K.; Gaynor, S. G. Appl. Polym. Sci. 2000, 929– 977. (2) Boutevin, B. J. Polym. Sci., Part A: Polym. Chem. 2000, 38, 3235– 3243. (3) Imrie, C. T.; Henderson, P. A. Chem. Soc. ReV. 2007, 36, 2096– 2124. (4) Grimsdale, A. C.; Mullen, K. Macromol. Rapid Commun. 2007, 28, 1676–1702. (5) Lynd, N. A.; Meuler, A. J.; Hillmyer, M. A. Prog. Polym. Sci. 2008, 33, 875–893. (6) Thickett, S. C.; Gilbert, R. G. Polymer 2007, 48, 6965–6991. (7) Ferguson, C. J.; Hughes, R. J.; Nguyen, D.; Pham, B. T. T.; Gilbert, R. G.; Serelis, A. K.; Such, C. H.; Hawkett, B. S. Macromolecules 2005, 38, 2191–2204. (8) Ferguson, C. J.; Hughes, R. J.; Pham, B. T. T.; Hawkett, B. S.; Gilbert, R. G.; Serelis, A. K.; Such, C. H. Macromolecules 2002, 35, 9243– 9245. (9) Clay, P. A.; Gilbert, R. G. Macromolecules 1995, 28, 552–569. (10) Szwarc, M. Nature (London) 1956, 178, 1168–1169. (11) Matyjaszewski, K.; Spanswick, J. Mater. Today 2005, 8, 26–33. (12) Szwarc, M. J. Polym. Sci., Part A: Polym. Chem. 1998, 36, ix. (13) Moad, G.; Rizzardo, E.; Solomon, D. H. Macromolecules 1982, 15, 909–914. (14) Georges, M. K.; Veregin, R. P. N.; Kazmaier, P. M.; Hamer, G. K. Macromolecules 1993, 26, 2987–2988. (15) Kato, M.; Kamigaito, M.; Sawamoto, M.; Higashimura, T. Macromolecules 1995, 28, 1721–1723. (16) Wang, J.-S.; Matyjaszewski, K. J. Am. Chem. Soc. 1995, 117, 5614– 5615. (17) Chiefari, J.; Chong, Y. K.; Ercole, F.; Krstina, J.; Jeffery, J.; Le, T. P. T.; Mayadunne, R. T. A.; Meijs, G. F.; Moad, C. L.; Moad, G.; Rizzardo, E.; Thang, S. H. Macromolecules 1998, 31, 5559–5562. (18) Moad, G.; Rizzardo, E.; Thang, S. H. Aust. J. Chem. 2006, 59, 669–692. (19) Moad, G.; Rizzardo, E.; Thang, S. H. Aust. J. Chem. 2005, 58, 379–410. (20) Moad, G. Aust. J. Chem. 2006, 59, 661–662. (21) Perrier, S.; Takolpuckdee, P. J Polym. Sci., Part A: Polym. Chem. 2005, 43, 5347–5393. (22) Barner, L.; Barner-Kowollik, C.; Davis, T. P.; Stenzel, M. H. Aust. J. Chem. 2004, 57, 19–24. (23) Barner-Kowollik, C.; Davis, T. P.; Stenzel, M. H. Aust. J. Chem. 2006, 59, 719–727.
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