Article pubs.acs.org/Macromolecules
Propagation Rate Coefficients for Vinylidene Fluoride Homopolymerizations Rebekka Siegmann, Marco Drache, and Sabine Beuermann* Institute of Technical Chemistry, Clausthal University of Technology, Arnold-Sommerfeld-Straße 4, 38678 Clausthal-Zellerfeld, Germany ABSTRACT: For the first time individual propagation rate coefficients, kp, for the homopolymerization of vinylidene fluoride (VDF) have been determined in homogeneous phase reactions with supercritical carbon dioxide. Experiments combining pulsed laser initiation and polymer analysis by size-exclusion chromatography were carried out for temperatures up to 90 °C and pressures up to 1100 bar. Absolute polymer molar masses required for the determination of kp were calculated on the basis of experimentally derived Mark−Houwink constants. A general equation kp(VDF) = f(p,T) was derived by applying multiple regression analysis of kp data. All data may be expressed by ln[kp/(L·mol−1·s−1)] = 19.96 − 3633 K/T + 0.27 p/bar × T−1/K−1. Due to the fluorine atoms in the monomer the kinetic data is significantly different from the nonfluorinated structural analogue ethene. For example, at 60 °C and 1000 bar VDF kp is 19400 L·mol−1·s−1, while kp for ethene is by a factor of 200 lower.
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INTRODUCTION Optimization of polymerization processes and resulting polymer properties requires modeling of the polymerization on the basis of a robust detailed kinetic model. Despite the technical importance of poly(vinylidene fluoride) (PVDF), reliable individual rate coefficients are not yet available for vinylidene fluoride (VDF) homopolymerizations. VDF homoand copolymers exhibit outstanding properties, such as excellent thermal, chemical, and mechanical stability, excellent weatherability, low surface energy, low water absorptivity, and low flammability.1,2 Thus, fluoropolymers are present in many technical applications, e.g., in architecture, petrochemical, and automotive industries, aerospace and aeronautics, optics, and textile treatment.3 Furthermore, due to their biocompatibility they are attractive materials for medical devices like in reconstructive surgery.4,5 In addition, PVDF showing β phase crystallinity possesses piezoelectric and pyroelectric properties leading to applications in, e.g., transducers, sensors, and switches.3,6−8 Generally, in industry heterogeneous phase processes like emulsion polymerizations employing stabilizers are carried out. However, common experimental methods for the determination of individual rate coefficients applying IR and UV spectroscopy or UV irradiation are mostly not feasible for heterogeneous systems. These experimental methods are more straightforward in homogeneous phase, because light scattering or phase transfer processes do not need to be considered. In the case of VDF the use of supercritical carbon dioxide (scCO2) as solvent allows for stabilizer-free homogeneous phase polymerizations.9,10 scCO2 has the outstanding ability to dissolve fluorinated polymers11 while being environmentally benign and easy to separate from the polymer, which can lower the postproduction costs significantly. Therefore, the use of scCO2 as reaction medium establishes an alternate route for PVDF © 2013 American Chemical Society
synthesis and at the same time permits the use of common experimental methods to derive rate coefficients. The lack of individual rate coefficients for VDF polymerizations may be due to the need for laborious experiments at elevated pressure and the occurrence of highly reactive primary radicals. However, reliable modeling and process optimization require information on individual rate coefficients. Experimental access to propagation rate coefficients, kp, is provided by the so-called PLP-SEC technique, which combines a pulsed laser initiated polymerization (PLP) with subsequent polymer analysis by size-exclusion chromatography (SEC). The IUPAC Working Party Modeling of Polymerization Kinetics and Processes recommended the PLP-SEC technique as the most direct and robust method for the determination of kp.12 In PLP experiments chain starting and stopping events are controlled by the pulse-wise formation of photoinitiator-derived radicals. Therefore, the molar mass distribution (MMD) shows a socalled typical PLP-structure with at least two inflection points, which may be identified by the maxima, M1 and M2, in its derivative curve as depicted in Figure 1 (b). Equation 1 allows for the determination of kp L i = i·k p·c M·t0 with i = 1, 2, 3, ...
(1)
where cM is the monomer concentration, t0 is the time between two successive laser pulses, and L1 is the number of propagation steps between two subsequent pulses. L1 is calculated according to L1 = M1/MM, where MM is the molar mass of the monomer, and M1 the first inflection point of the MMD.12,13 The existence of a second or even a third inflection point at degrees Received: September 2, 2013 Revised: November 20, 2013 Published: December 11, 2013 9507
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description of the HPC is given in ref 22. The HPC was filled through a side boring with 0.1 mL of a stock solution of DMPA in acetone, sealed and connected with the high pressure setup. Vacuum (10−3 mbar) was applied to the HPC for 15 min to ensure complete evaporation of acetone of the DMPA stock solution. Afterward, the VDF-CO2 mixture was transferred from the autoclave to the syringe pump of the setup and subsequently from the setup to the HPC, which was equipped with a pressure gauche from HBM (P3MB). To avoid heterogeneity during the filling procedure the pressure was kept constant by the HPLC pump at 350 bar. The final pressure in the HPC was adjusted by the syringe pump. Then, the HPC was heated to the reaction temperature using an Eurotherm 3200 PID temperature controller. Finally, the HPC was disconnected from the high pressure setup and located inside the laser beam pathway. The polymerization was initiated using a Quanta−Ray Nd:YAG laser (Spectra Physics) and an excimer laser ExiStar XS 500 (Coherent) operating at 355 and 351 nm, with laser pulse repetition rates, νrep, of 100 and 500 Hz, and pulse energies of 6 and 4 mJ, respectively. The concentration of the photoinitiator DMPA, cDMPA, ranges from 0.004 to 0.04 mmol·L−1. The polymer was analyzed via SEC. PLP Experiments for Establishing SEC Calibration. PVDF from several low conversion PLP experiments with 0.04 mol·L−1 DMPA at 60 °C and 1050 bar were combined to get a sufficient amount of material for SEC analysis to determine Mark−Houwink (MH) constants. Purification by washing the PVDF samples twice with pentane and drying in high vacuum should remove the remaining nondecomposed photoinitiator, which is the requirement for precise polymer concentration in SEC analysis. Size-Exclusion Chromatography. Molar mass distributions were obtained by size-exclusion chromatography using an Agilent 1200 isocratic pump, an Agilent 1200 differential refractive index detector, a WEG Dr. Bures ETA 2010 online viscosity detector, and three PSS analytical GRAM columns (8 × 300 mm, particle size 10 μm, pore sizes 100 Å and 2 × 3000 Å). N,N-Dimethyl acetamide containing 0.1% LiBr at 45 °C at a flow rate of 1 mL·min−1 was used as eluent. The SEC setup was calibrated against polystyrene (PS) standards of narrow dispersity (molar masses between 500 and 1 × 106 g·mol−1, PSS). Absolute molar masses were calculated via the principle of universal calibration. FT/NIR Spectroscopy. To monitor VDF and CO2 concentrations, NIR spectra were recorded on a Bruker Vertex 70 spectrometer equipped with a halogen lamp, a Si-coated CaF2 beam splitter, and a liquid nitrogen cooled InSb detector. The spectra were recorded with a resolution of 2 cm−1, coaddition of 30 scans, and a zero filling factor of 2. The spectrometer is operated by OPUS 6.5 software. A HPC with an optical path length of 0.38 cm was used to record the characteristic near-infrared peaks of VDF and CO2 of a reaction mixture simultaneously. Determination of concentrations via FT/NIR spectroscopy is detailed in the supplemental data of ref 23. Computational Methods. A complex data analysis method was developed leading to an optimal set of Mark−Houwink constants. The applied optimization method with constraints is based on a genetic algorithm.24 The optimization program was implemented using the programming language C++. In addition, the program library PGAPack was integrated. PGAPack is a parallel genetic algorithm library being developed at Argonne National Laboratory.25 The optimization has been processed on the following system: 2 AMD Opteron 6134 Magny Cours CPU (16 cores, 2.2 GHz), 128 GB RAM, operating system: Open SuSE Linux 11.4, compiler: gcc 4.5.1.
Figure 1. MMDs and their first derivatives of PVDF obtained from PLP experiments in the presence of 60 wt % CO2 at 1050 bar and temperatures as indicated (valid for all graphs): (a,b) cDMPA = 0.004− 0.010 mol·L−1, Ep = 6.0 mJ, νrep = 100 Hz and (c,d) cDMPA = 0.040 mol·L−1, Ep = 4.0 mJ, νrep = 500 Hz. The distributions refer to calibration as polystyrene.
of polymerization around L2 = 2·L1 and L3 = 3·L1 indicates that the shape of the MMD is controlled by the pulse-wise initiation of the polymerization and serves as a consistency criterion (M1/ M2 ∼ 0.5) for kp determination via PLP-SEC.14−16 Since the first publication on the application of PLP-SEC by the group of Olaj13 a large number of monomers was studied,17 resulting in benchmark value data sets for various methacrylates, styrene, and two acrylates.14,16,18−20 The determination of acrylate kp was largely improved by using high laser pulse repetition rates of up to 500 Hz. Due to the occurrence of chain transfer events, at low repetition rates the correlation between L1 and t0 was destroyed and prohibited the derivation of kp. Similarly, first experiments with vinylidene fluoride at laser pulse repetition rates of at most 10 Hz were not successful,21 because the highly reactive primary radical may readily undergo hydrogen transfer. Consequently, the linear propagating radical is transformed into a relatively stable midchain radical (MCR). As reported for acrylates the propagation of MCRs is associated with lower rate coefficients than the linear propagating radical and leads to branched polymer chains. Since for acrylate PLP experiments an increase in pulse repetition rate up to 500 Hz overcomes the problems associated with the formation of MCRs it seemed very promising to investigate VDF homopolymerizations with the PLP-SEC technique applying high pulse repetition rates.
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EXPERIMENTAL SECTION
Materials. The monomer vinylidene fluoride (VDF, 99%, provided by Dyneon GmbH), the photoinitiator 2,2-dimethoxy-2-phenylacetophenon (DMPA, 99%, Acros), the solvents carbon dioxide (CO2, grade 4.5, Westfalengas), pentane (99%, VWR), and N,Ndimethyl acetamide (DMAc, 99% pure, Acros), and the salt LiBr (99%, Riedel-de Haën) were used as received. Experimental Setup and Pulsed Laser Initiated Polymerization. The experimental high pressure setup and the procedure to prepare the mixture consisting of VDF and CO2 are detailed in ref 9. In contrast, here no initiator is added to the mixing autoclave. The optical high pressure cell (HPC) is equipped with two sapphire windows, which results in an optical path length of 1.4 cm and allows for the application of UV laser light to the reaction system. A detailed
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RESULTS AND DISCUSSION Pulsed Laser Initiated Polymerization. In first VDF PLP experiments in bulk, in solution with organic solvents, or in scCO2 well-structured MMDs were not obtained for a wide range of experimental conditions with pulse repetition rates of at most 10 Hz.21 It was suggested, that termination was not controlled via the pulse-wise formation of photoinitiator radicals due to too long dark times between two successive
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the supposed transfer to polymer events occurring in VDF homopolymerizations. In Figure 1 (b) resulting MMDs and their first derivatives are displayed. The MMDs possess a PLPstructured shape, and their first derivatives show two resolved maxima, which are shifted to higher molar masses with increasing reaction temperature. In addition, the consistency criterion of M1/M2 being around 0.5 is fulfilled. The second maximum is less pronounced with enhanced temperature. This is in accordance with the enhanced probability of transfer to polymer due to the significantly higher activation energy of backbiting compared to the activation energy of propagation observed for acrylate polymerizations.38 The strong reduction of the dark time between subsequent laser pulses leads to a control of bimolecular termination events by the pulse-wise formation of photoinitiator radicals. This finding is supported by the fact that PLP experiments of VDF−hexafluoropropene (HFP) copolymerizations with 65 mol % VDF are already successful at lower pulse repetition rates of 100 Hz due to the absence of hydrogen atoms in the HFP molecule.23 Moreover, a lowering of photoinitiator concentration by 1 order of magnitude did not lead to a shift of the position of M1 or M2 to higher molar masses in ref 23 as observed for PLP experiments with vinyl acetate.39 Thus, the high termination limit phenomenon40 may not be responsible for the required high pulse repetition rate in PLP experiments with VDF. Reliable calculation of kp according to eq 1 requires the knowledge of the precise monomer concentration and absolute polymer molar masses. The determination of the monomer concentration on the basis of quantitative IR spectroscopy was detailed before.21,23 The evaluation of absolute molar masses is considered below. Determination of Mark−Houwink Constants. Since no commercial PVDF standards are available, a conventional calibration curve for the determination of absolute molar masses of PVDF samples cannot be established. Therefore, the principle of universal calibration is applied to calculate absolute MMDs derived from SEC with conventional calibration using for example polystyrene (PS) standards.41 Until now absolute molar masses of various homo- and copolymers were determined by adopting this principle.17,18,42 The product of molar mass M and intrinsic viscosity [η] at a certain retention volume is equal for two chemically different polymers according to eq 2:
laser pulses. Therefore, it appeared rewarding to investigate VDF homopolymerizations with the PLP-SEC technique using higher pulse repetition rates. First, PLP experiments with scCO2 as reaction medium and 0.004 to 0.01 mol·L −1 photoinitiator were carried out at pulse repetition rates of 100 Hz at various temperatures. To establish homogeneous phase behavior during the PLP experiment a pressure of 1050 bar and a CO2-content of 60 wt % were applied. A minor increase in temperature of 0.1 °C and a slight decrease in pressure of 3 bar due to higher PVDF density compared to its monomer density were noticed during pulsing. The resulting MMDs and their first derivatives are depicted in Figure 1 (a). All MMDs shown refer to calibration as PS. Figure 1 (a) shows monomodal molar mass distributions for all reaction temperatures and only one resolved maximum in each corresponding derivative. Since the maximum does not shift to higher molar masses with increasing reaction temperature and no second inflection points in the MMDs are obtained, the shape of the MMDs appears to be not controlled via the pulse-wise initiation. The maxima in the derivative curves in Figure 1 at 60 and 90 °C show almost identical molar masses of log M = 4.95 and log M = 4.97, respectively, although propagation and thus polymer chain lengths obtained at identical repetition rate should be strongly enhanced due to the 30 °C higher temperature. The finding may be explained by uncontrolled chain stopping events occurring in the dark time between the laser pulses. Several reasons like bimolecular termination rate of the macroradicals being too high26 or transfer events to monomer, polymer, or solvent may be put forward. First, the influence of transfer is discussed. CO2 as reaction medium prevents any transfer to solvent.27,28 Furthermore, transfer to monomer is excluded since signals characteristic for terminal double bonds are not observed in 19 F-NMR spectra of PVDF. 29 In contrast, intra- and intermolecular transfer to polymer resulting in short chain branches (SCB) and long chain branches (LCB), respectively, can occur due to the presence of hydrogen atoms in the polymer backbone. However, the formation of LCBs via intermolecular transfer to polymer is strongly favored only at high polymer content in the reaction mixture.17 PLP experiments were always stopped at conversion below 5% to ensure a relatively constant monomer concentration. Thus, it is safe to assume that LCBs are not formed to a significant degree under these PLP conditions. In contrast, intramolecular transfer to polymer cannot be avoided by low polymer content. Pianca et al. proposed a mechanism for transfer to polymer in VDF homopolymerizations:30 The hydrogen atom of a VDF macroradical is transferred from the δ to the α position, and afterward the radical function is located in the δ position, which is then called a midchain radical. In comparison to linear propagating radicals MCRs are more stable and grow with a lower propagation rate coefficient.31 As a consequence, SCBs are formed, whose corresponding signals in 19F-NMR spectra were reported.30,32−34 In addition, signals of the tertiary CH group were observed in 13C NMR spectra of PVDF.30 The phenomenon of MCR formation is well-known from acrylate and ethene polymerizations.19,20,35,36 An enhancement of the pulse repetition rate up to 500 Hz minimized the transfer to polymer events in bulk PLP experiments of butyl and methyl acrylate to such a degree that PLP-structured MMDs were obtained.20,37 Thus, VDF PLP experiments were repeated with a significantly higher pulse repetition rate of 500 Hz to minimize
M1·[η1] = M 2 ·[η2]
(2)
The correlation between intrinsic viscosity of a polymer sample with its molar mass is quantified by the Mark-Houwink (MH) constants a and K, which is given by the following relationship: [η] = K ·M a
(3)
By combining eqs 2 and 3 the absolute molar mass of polymer 2 can be calculated using eq 4 and the measured relative molar mass M1, derived from SEC with conventional calibration based on narrow polymer standards 1: log(M 2) =
K 1 + a1 1 ·log 1 + ·log(M1) 1 + a2 K2 1 + a2
(4)
a and K must be known for the polymer under investigation (index 2) and the polymer standards (index 1) at a given temperature in a given eluent. MMDs from PLP experiments with VDF were derived using a conventional calibration curve based on narrow dispersity PS 9509
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standards. The MH constants of PS in DMAc at 45 °C are reported in the literature: aPS = 0.69; KPS = 0.013 mL·g−1,43 which were confirmed by analysis of PS standards in the SECsetup used.44 MH constants for high MW PVDF were published, too.45 However, due to the high molar masses ranging from 105 to 106 g·mol−1 these values may not be appropriate to convert the relative of PLP-structured MMDs, which range from 7000 to 50000 g·mol−1. If MH constants are used for polymers outside the molar mass range, in which they were determined, an error in molar mass determination of up to 40% may occur.46 Moreover, the degree of branching of the high MW PVDF used in the literature is not known and may cause additional errors. Thus, MH constants for PVDF were determined in the range of molar masses covering the MMDs derived from VDF PLP experiments. For this purpose an SEC setup, which consists of a concentration sensitive differential refractive index detector and an online viscosity detector, is used. The general procedure is described in detail in ref 44. Three samples were analyzed by this method. Several injections were performed for each sample to check for reproducibility of the MH constants. The resulting double logarithmic MH plots derived from all injections are depicted in Figure 2 (a). The agreement of the curves is good.
applying objective criteria was developed. The degrees of freedom of the optimization are the starting and end point of the linearization as well as the number of MH plots selected. The latter is the number of MH plots accounted for in the final optimization. As objective function the minimization of variation coefficients of the kp values derived from all PLP experiments listed in Table 1 was applied. Each selected MH plot and the corresponding limits for linearization lead to a kp value for every single PLP experiment. The objective function minimizes the sum of variation coefficients of all derived kp values. This optimization problem may be solved ideally with a genetic algorithm, where each individual is represented by a binary chromosome.24 The MH plots included are labeled with 1 and the plots excluded with 0. In addition, a boundary condition was incorporated: at least five MH plots have to be included in the solution of the optimization. The starting and end points of the linearization were determined between log Mstart and log Mend (see Figure 2 (b)). The molar mass ranges are indicated by dashed and dotted lines, respectively. The values derived for log Mstart and log Mend are valid for all selected MH plots. Each of these two molar mass ranges was represented by 8 bits in the chromosome. Since 16 MH plots are used in the optimization, this results in a chromosome with 32 bits. The optimization was performed with a population size of 500 individuals over 5000 generations. After about 500 generations the optimization converged with an average variation coefficient of approximately 0.7%. The resulting five relevant MH plots and associated limits for linearization (full line) are depicted in Figure 2 (b). Finally, one pair of a and K was determined. For this purpose, for each PLP experiment in Table 1 five kp values were calculated using the MH constants derived from the optimal five linearizations between log Mstart = 3.95 and log Mend = 5.31. Subsequently, for each PLP experiment an arithmetic mean value k p was calculated from the aforementioned five individual kp,j values, with j referring to one of the five a and K pairs. For each pair of a and K the sum of all |kp,j − k p| was calculated. The set of a and K leading to the lowest value for Σi|kp,j − k p| is selected as the optimal data set. The resulting data is as follows: a = 0.683, K = 0.0180 mL·g−1, which were derived for molar masses ranging from 8900 to 204 000 g·mol−1. Calculation of kp and Activation Parameters. Propagation rate coefficients, kp, for VDF homopolymerizations in 60 wt % CO2 are derived according to eq 1 in a wide range of temperatures and pressures. The absolute molar masses of first and second inflection points, M1 and M2, are calculated using the MH constants determined for PVDF (a = 0.683, K = 0.0180 mL·g−1) and MH constants for PS (a = 0.69, K = 0.013 mL·g−1).44 Table 1 summarizes reaction conditions, absolute molar mass at the first and second point of inflection, M1(abs) and M2(abs), and kp values for all successful PLP experiments. In almost all cases excellent reproducibility of repeat experiments is found. For future modeling purposes a general equation is desirable, which provides kp as a function of temperature and pressure. Therefore, a multiple regression analysis according to eq 5 was carried out. Equation 5 correlates the experimentally derived kp values with the pre-exponentional factor, A, activation energy, Ea, and the activation volume, ΔV‡. Previously, this equation was successfully applied to describe the temperature and pressure dependence of kp in ethene homopolymerizations.47
Figure 2. Experimentally derived MH plots for PVDF prepared via PLP experiments (a) and results of the optimization: Residual MH plots for PVDF and limits for linearization (b).
According to eq 3 a set of a and K values may be calculated for each MH plot. The resulting a and K values may differ for the different injections, partly due to the choice of limits for linearization, log Mstart and log Mend. Moreover, a and K are strongly correlated and may only be determined as a pair. Thus, although a and K values may look very different for various injections, calculation of M2 according to eq 4 may result in very similar values, differing only by a few percent. Due to the coupling of a and K calculation of an arithmetic mean of all determined values for each MH constant is not feasible. Therefore, for data analysis purposes an optimization program 9510
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Table 1. Absolute Molar Masses of Inflection Points, M1(abs) and M2(abs), and Associated M1(abs)/M2(abs) of PVDF Obtained from PLP Experiments in 60 wt % CO2, with cDMPA Ranging from 0.02 to 0.04 mol·L−1, a Pulse Repetition Rate of 500 Hz, and a Pulse Energy of 4 mJa
a
T/°C
p/bar
[M]/mol·L−1
M1(abs)/g·mol−1
45 45 45 45 45 45 45 60 60 60 60 60 60 60 60 60 60 60 75 75 75 75 75 75 75 75 75 90 90 90 90 90 90
410 610 610 810 810 1050 1060 410 410 420 610 610 620 810 820 1060 1080 1100 410 420 610 630 810 810 1070 1070 1070 610 630 820 1060 1080 1090
6.4 6.9 6.9 7.5 7.5 7.9 7.9 6.1 6.1 6.1 6.6 6.6 6.6 7.2 7.2 7.7 7.7 7.7 6.0 6.0 6.5 6.5 7.0 7.0 7.5 7.5 7.5 6.3 6.3 6.9 7.3 7.3 7.3
6134 7675 7720 10 309 9154 13 421 12 845 8763 9909 11 732 14 135 12 142 11 153 14 329 14 235 19 290 20 671 23 501 13 588 13 716 21 000 21 528 24 616 24 883 38 208 29 535 29 434 26 752 28 879 34 214 41 364 41 344 45 340
M2(abs)/g·mol−1 13 17 16 24 22 30 29 17 20 21 26 22 23 31 30 36 39 41 21 23 33 35 41 41 63 52 51 − − 55 71 68 82
595 113 923 815 095 184 185 321 032 189 629 939 718 951 679 073 782 498 459 528 834 592 369 663 743 191 799
191 052 675 028
M1(abs)/M2(abs)
kp/L·mol−1·s−1
0.45 0.45 0.46 0.42 0.41 0.44 0.44 0.51 0.49 0.55 0.53 0.53 0.47 0.45 0.46 0.53 0.52 0.57 0.63 0.58 0.62 0.60 0.60 0.60 0.60 0.57 0.57 − − 0.62 0.58 0.60 0.55
7488 8690 8741 10 738 9535 13 272 12 703 11 223 12 691 12 020b 13 386b 14 373 13 202 15 548 15 446 19 572 20 973 23 845 17 693 17 859 25 241 25 876 27 473 27 771 31 840 30 766 30 661 33 174 35 812 38 739 44 268 44 247 48 523
Propagation rate coefficients kp were calculated with M1(abs) values. bνrep = 400 Hz.
ln k p = ln A −
Ea ΔV ‡·p − R·T R·T
−1.03)·108 L·mol−1·s−1 and an activation volume of (−22.7 ± 1.3) cm3·mol−1 were determined, which are valid for temperatures ranging from 45 to 90 °C and pressures between 400 and 1100 bar. The resulting general expression for kp(VDF) = f(p,T) is given in eq 9
(5)
Fitting of eq 5 to experimentally derived kp data was performed using the R Project for Statistical Computing.48 33 kp values listed in Table 1 (represented by yi in eq 6) are provided as vector of dimension 33, the number of experimental data points. yi = a0 − a1·t1,i − a 2 ·t 2,i with 1 ≤ i ≤ 33
ln k p = 19.96 −
The corresponding information on temperature and pressure are considered with the two terms t1 and t2 according to eqs 7 and 8: 1 R·T
(7)
t 2,i =
p R·T
(8)
(9)
with 318.15 K ≤ T ≤ 363.15 K and 400 bar ≤ p ≤ 1100 bar. In Figure 3 experimentally derived kp values and kp data calculated according to eq 9, given by the grid lines, are shown. It is easily seen that the experimental kp values agree very well with the surface calculated according to eq 9. Figure 4 shows the correlation between experimentally derived values, ln kpexp, and ln kpcal calculated according to eq 9. The straight line in Figure 4 corresponds to equal values for ln kpexp and ln kpcal pairs. All data points deviate only slightly from the straight line. A systematic drift is not seen. Thus, eq 9 provides an excellent representation of the temperature and pressure dependence of VDF homopolymerization kp in 60 wt % CO2. Discussion of kp and Activation Parameters. Activation parameters of VDF homopolymerizations in scCO2 from
(6)
t1,i =
0.27·p /bar 3633 + T /K T /K
The model coefficients a0, a1, and a2 represent the activation parameters A, Ea, and ΔV‡, respectively. For VDF homopolymerizations in 60 wt % CO2 an activation energy of (30.2 ± 0.7) kJ·mol−1, a pre-exponential factor of (4.66 +1.34/ 9511
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the original work.47,51 As an approximation it is assumed that Φ equals unity. For comparison the kp value for ethene was calculated for 60 °C and 1000 bar. The data in Table 2 indicates that VDF kp is 2 orders of magnitude higher than for ethene. The presence of fluorine atoms in VDF molecules seems to have a strong influence on the reactivity of the macroradicals and of the monomer. The double bond in an ethene molecule is nonactivated, which may lower the rate of propagation and causes a low kp value. This reasoning is in line with findings by Fischer et al.: electron rich olefins react much faster with electron poor than with electron rich radicals. In analogy, this is valid for electron poor olefins.52 In ethene homopolymerizations both reactants, the macroradical and the monomer, are rather electron rich, since a pulling inductive effect does not occur. The propagation step is not favored. In contrast, the VDF molecule possesses an electron rich and an electron poor carbon atom: The carbon atom carrying two fluorine atoms exhibits a low electron density due to the electron withdrawing effect caused by the very high electronegativity of fluorine. As a consequence, the electron density is much higher at the carbon atom carrying two hydrogen atoms. Therefore, VDF has a much more reactive double bond than ethene, the propagation is favored, and a high kp value becomes comprehensible. This explanation is supported by the occurrence of only 3 to 5% head to head and tail to tail sequences in PVDF.30 The preferred link of monomer molecules in PVDF is formed between a CH2 and a CF2 group. However, kp values for VDF are significantly lower than for acrylates. The double bond in acrylates is partially positively charged, because it forms a conjugated system with the carbonyl group. Thus, acrylate polymerizations are associated with very high propagation rate coefficients. The activation energy of VDF homopolymerizations (Ea = 30.2 kJ·mol−1) is significantly higher than for acrylates but lower than for ethene. Since in VDF macroradicals the radical function is particularly located at the CF2 group, the electron withdrawing effect of fluorine atoms contributes to a better stabilization of the propagating radical compared to an ethene macroradical. The extraordinary high value of 34.3 kJ·mol−1 for ethene is explained by the nonactivated double bond. Ea for VDF is in agreement with the activation energy of methacrylonitrile. This appears to be reasonable, since the cyano group of methacrylonitrile has a strong electron withdrawing effect, too. The pre-exponential factor A = 4.7 · 108 L·mol−1·s−1 determined for VDF homopolymerizations is significantly higher than for its nonfluorinated structural analogue ethene (1.9 · 107 L·mol−1·s−1) and all other monomers listed in Table 2. Such a difference was also found for 1H,1H,2H,2Htridecafluorooctyl methacrylate and nonfluorinated methacrylates.53 In general, A is associated with steric hindrance in the transition state structure.54,55 Therefore, an increase in A values
Figure 3. kp data calculated according to eq 9 (grid lines) and experimental kp data for VDF homopolymerization in 60 wt % CO2.
Figure 4. Correlation between predicted, ln kpcal (according to eq 9), and experimentally derived, ln kpexp, propagation rate coefficients.
multiple regression analysis and kp at 60 °C and 1000 bar are given in Table 2. In addition, literature values for bulk polymerizations of ethene, methacrylonitrile (MAN), and butyl acrylate (BA) are listed. The data for MAN and BA was derived from PLP-SEC experiments; ethene data originates from a different PLP technique (see below). So far propagation rate coefficients were not yet reported for VDF homopolymerizations in the literature, and direct comparison of our experimental data with literature data is not possible. To evaluate our kp values they are compared to kinetic data of other monomers. First, the nonfluorinated structural analogue ethene is considered. kp data is available for temperatures between 190 and 230 °C and in a pressure range from 1950 to 2900 bar.47 These values were determined using a technique which combines PLP and subsequent time-resolved NIR spectroscopy to determine changes in monomer concentration with a time resolution of microseconds.51 The so-called SP-PLP-NIR method yields the coupled parameters kp/kt, with the termination rate coefficient kt and kp · Φ. Φ accounts for the quantum efficiency of the UV-induced initiator decomposition and the initiator efficiency. Details are given in
Table 2. Activation Energies Ea, Pre-Exponential Factors A, Activation Volumes ΔV‡, and Propagation Rate Coefficients kp for Polymerizations of Different Monomers in the Given Temperature and Pressure Rangea
a
system
T/°C
p/bar
Ea/kJ·mol−1
A × 10−8/L·mol−1·s−1
ΔV‡/cm3·mol−1
kp/L·mol−1·s−1 (60 °C, 1000 bar)
VDF in CO2 ethene47 MAN49 BA in CO250
45−90 190−230 10−60 −9−20
400−1100 1950−2900 200−2000
30.2 34.3 29.7 17.0
4.66 0.19 0.03 0.17
−22.7 −27.0 −12.2
19414 208 55985
Ethene data derived via SP-PLP-NIR.47 9512
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Table 3. Activation Volume of kp (ΔV‡(kp)), Monomer and Polymer Densities at Given Temperature and Pressure, and Decrease in Density during a Polymerization Process monomer/polymer
ΔV‡(kp)/cm3·mol−1
styrene/PS MMA/PMMA VDF/PVDF ethene/PE
−11.7 −16.717 −22.7 −27.047 17
T/°C 25 25 60 200
ρ/g·cm−3 (polymer)
Δρ/%
1.057 1.259 1.860 1.060
10 25 40 50
56
1 1 1000 2000
0.9 0.958 1.121 0.561
implemented in modeling software for polymerization processes. It is stressed that kp refers to the propagation reaction of a macroradical that carries the radical functionality at the chain end. The master equation must not be used to account for the propagation of midchain radicals that were formed in transfer reactions. To account for contributions from MCR propagation currently PLP experiments with varying pulse repetition rate are carried out. It is tested whether the method suggested by Nikitin et al.36 to derive chain transfer rate coefficients and propagation rate coefficients of the MCR may be applied to VDF. The kinetic data indicate that kp for VDF is by more than 2 orders of magnitude higher than the corresponding values for ethene. The finding may be explained by the strong electronwithdrawing effect of the fluorine atoms. The difference in Arrhenius parameters and the activation volume of kp for VDF and ethene may as well be explained by the fluorination. In addition to changes in reactivity, the lower inter- and intramolecular interactions between polymer segments leads to a comparably high pre-exponential factor. The rather high absolute value of the activation volume may be explained by the strong volume contraction upon polymerization in a system where the monomer is gaseous.
observed for VDF and 1H,1H,2H,2H-tridecafluorooctyl methacrylate may indicate that the chain end possesses a higher rotational mobility in the transition state compared to nonfluorinated macroradicals, which may be caused by less intra- and intermolecular interactions between the polymeric species in the reaction system due to their partial fluorination. Activation volumes are assigned to the pressure influence on rate coefficients. The absolute value for ΔV‡ of VDF (−22.7 cm3·mol−1) is lower than for ethene but significantly higher than for acrylates, methacrylates, and styrene. ΔV‡ values for the above-mentioned monomers are given in Tables 2 and 3. In the literature the relatively slight differences in activation volume of methacrylates, acrylates, and styrene were explained by the different substitution pattern at the α position in the macroradicals. However, this reasoning cannot explain the very high ΔV‡ value for ethene, which exhibits the least steric hindrance of all monomers listed in Tables 2 and 3, and thus, should be associated with the lowest activation volume. It is suggested that the differences in densities of monomer and the resulting polymer have a substantial influence on the pressure dependence of kp. In homopolymerizations of VDF or ethene under high pressure always a significant continuous pressure drop with reaction time is observed. In general, polymers exhibit higher densities than their corresponding monomers, and therefore, in polymerizations a volume reduction occurs. However, the volume contraction is more or less pronounced depending on the monomer/polymer pair. Table 3 lists densities of styrene, methyl methacrylate (MMA), VDF, and ethene at given temperatures and pressures and their corresponding polymer densities. In addition, the decrease in density for each monomer/polymer pair is given. In homopolymerizations of styrene and MMA the density is decreased by 10 and 25%, respectively. The highest density drop with 50% is obtained for ethene polymerizations, which leads to a strong pressure dependence of the propagation rate coefficient and thus, the highest activation volume in Table 3. The difference in densities of VDF and PVDF is less pronounced than for ethene/PE but still significantly higher than for MMA/PMMA and styrene/PS. This reasoning may explain the intermediate value of ΔV‡ for VDF homopolymerizations. Costa et al. reported on the modeling of heterogeneous phase copolymerizations of VDF and HFP in the presence of scCO2.62 Despite the very different reaction conditions (50 °C, ∼400 bar, heterogeneous process) the agreement of kp = 4300 L·mol−1 s−1 calculated according to eq 9 with the value of 3000 L·mol−1 s−1 introduced for VDF homopolymerizations in the model is quite impressive.
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ρ/g·cm−3 (monomer)
p/bar
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors gratefully acknowledge financial support by Dyneon GmbH and Deutsche Forschungsgemeinschaf t. We thank the EU and the state of Brandenburg for financial support within the Hochschulinvestitionsprogramm. Furthermore the authors are very thankful to Dr. Eléonore Möller, who started the work on PLP of VDF.
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REFERENCES
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CONCLUSIONS
For the first time, VDF homopolymerization propagation rate coefficients kp were successfully determined using the PLP-SEC technique. A master equation relating kp to pressure and temperature is provided, which may conveniently be 9513
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