2D-NMR Characterization of Sequence Distributions in the Backbone

Dec 11, 2012 - contribution using this method for polymer component analysis. This method ...... the conditional probabilities of monomer addition (Ma...
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2D-NMR Characterization of Sequence Distributions in the Backbone of Poly(vinylidene fluoride-co-tetrafluoroethylene) Linlin Li,† Eric B. Twum,† Xiaohong Li,†,§ Elizabeth F. McCord,‡ Peter A. Fox,‡ Donald F. Lyons,‡ and Peter L. Rinaldi†,* †

Department of Chemistry, University of Akron, Akron, Ohio 44325-3601, United States Experimental Station, E. I. du Pont de Nemours and Co., Wilmington, Delaware 19880-0402, United States

‡

S Supporting Information *

ABSTRACT: NMR is a powerful tool to study the microstructures of poly(vinylidene fluoride-co-tetrafluoroethylene), poly(VDF-co-TFE). This study shows that the microstructures in this copolymer can be established completely on the basis of 2D-NMR, in which improved dispersion is achieved by the second dimension (19F or 13C chemical shifts). 2D-NMR has been proven to be extremely effective for identifying the carbon sequence distributions in the polymer main chain. For lower level sequences (3- or 5-carbon sequences), resonance assignments on the basis of one- and two-bond 19F{13C} gradient heteronuclear single quantum coherence (gHSQC) experiments are in good agreement with assignments obtained by traditional methods. Higher level sequences (7- or 9-carbon sequences), which can not be assigned unambiguously by traditional methods, were determined by 19F−19F gradient double quantum correlation spectroscopy (gdqCOSY), which provides 19F−19F correlations over 3−5 bonds. A quantitative study was also conducted on the composition of this copolymer. Three different approaches were used to calculate the fraction of TFE and the inversion ratio of VDF units.

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more effective methods are needed to study the microstructures of these copolymers. Fortunately, multidimensional NMR is a powerful tool to elucidate the detailed structures of fluoropolymers by providing much better signal dispersion and atomic connectivity information.14−17 19F 1DNMR has long been recognized for its important features: high sensitivity and large chemical shift dispersion. Most importantly, unlike 13 C 1D-NMR spectra, which also have large spectral dispersion, the 19F NMR chemical shifts of 19F nuclei are very sensitive to changes in their surrounding chemical environments. Therefore, it is possible to resolve resonances of high level sequences in the 19F NMR spectra. In this study, improved resolution is also achieved by the dispersion of resonances into a second dimension in 2D-NMR spectra. Combined use of several 2D-NMR experiments can provide atomic connectivity information, which yields unequivocal evidence for the resonance assignments of structures because of variations in monomer sequences. Using these experiments, it is not only possible to validate previous resonance assignments of lower level sequences, but it is also possible to provide unequivocal resonance assignments for higher level sequences. To study the CF2-centered carbon sequences in this copolymer, first, one- and two-bond 19F{13C} gHSQC spectra were used to assign the resonances of 3-carbon sequences in both the 19F and 13C spectra. Second, in each region, resonances of 5-carbon sequences were identified with the help of two bond 19F{13C} gHSQC or 1H{19F}/19F{1H} heteronuclear correlation (HETCOR) spectra (provid-

INTRODUCTION

Fluorinated copolymers containing vinylidene fluoride exhibit many desirable properties, especially their extraordinary chemical and thermal resistance.1,2 Their applications can be found in diverse areas, such as coatings, corrosion/chemically resistant seals, chemical storage, automotive parts, and aircraft parts. In addition, it is also reported that poly(VDF-co-TFE) possess piezoelectric and pyroelectric properties.3,4 Many of the useful properties of these copolymers are influenced by their compositions and microstructures, such as sequence distribution, chain end units, etc. To further improve performance, it is useful to know the detailed structures of these copolymers.5−7 Much work has been done to study the sequence distribution of poly(VDF-co-TFE) copolymers; however, most of this work involves chemical shift prediction on the basis of empirical additivity schemes,8−10 or examination of spectra from polymers with varying comonomer compositions.11−13 Chemical shift prediction can be made on the basis of the γ-effect9,10 of fluorine atoms. A 19F atom is shielded when its γ fluorine substituent is in a gauche arrangement. The larger the numbers of γ fluorine substituents, the stronger the γeffect. In this way, the resonances of different sequences can be identified by their relative chemical shifts. Alternatively, the resonances of sequences can also be assigned by monitoring the peak intensities in the 1D-NMR spectra from polymers with varying monomer compositions.11 Although these methods can provide valuable information about the polymer’s microstructure, they are not very effective for studying higher level sequences and chain end units. In some circumstances it is impossible to get polymers with the variety of compositions needed for sequence determination. Additionally, solvent effects are ignored in these traditional methods. Therefore, © XXXX American Chemical Society

Received: September 26, 2012 Revised: November 17, 2012

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ing 3-bond 1H−19F correlations). Third, resonances of higher level sequences, (7- or 9-carbons), were assigned on the basis of 5-carbon sequence assignments with the help of 19F−19F gradient assisted double quantum filtered correlation spectroscopy (gdqCOSY) spectra, which can provide 3−5 bond 19F−19F correlations. Since 3-, 4- and 5bond correlations can not be distinguished from one another in gdqCOSY spectra, different structure possibilities were considered and impossible structures were excluded. In addition, the application of 2 JCF 19F{13C} gHSQC was also found to be useful for distinguishing between 3-, 4- and 5-bond 19F−19F correlations. Similarly, the CH2− centered sequences were studied by the combined use of 2D-NMR experiments. Once the resonances were assigned explicitly, a quantitative study was conducted to determine the compositions of two poly(VDF-coTFE) copolymers using three different methods. The first method involves adding an internal standard to the NMR tube to quantitatively relate the intensities of the resonances from CF2-centered sequences and the intensities of the resonances from CH2−centered sequences. The principle of the second method, proposed by R. E. Cais et al,11 is to convert the probabilities of CH2−centered sequences to those of CF2-centered sequences, so that the compositions can be calculated based on the 19F{1H} spectrum. The third method is based on statistical analysis. H. N. Cheng18−20 has made a significant contribution using this method for polymer component analysis. This method also allows studying the kinetics of copolymerization. All of these methods are discussed and evaluated for analyzing poly(VDFco-TFE) copolymers.

monomer feed was commenced. The resulting polymer suspension was withdrawn from the top of the reactor through a pressure reducing valve and degassed to remove residual monomers. Effluent from the first 15 min of the polymerization (approximately 1 residence time) was discarded. The polymer was coagulated with potassium aluminum sulfate, filtered, washed with water, and dried in a hot air oven. The compositions of the polymers and the overall conversions of the reactions (Table 1) were estimated by comparison of the off-gas collected at the degasser and analyzed by gas chromatography. Thermal Analysis Measurements. Tg/Tm were measured at DuPont. Samples for thermal analysis were prepared by pressing films at 150 °C between two pieces of Kapton in a laboratory press to obtain a flat surface for good thermal contact with the sample pan. Differential Scanning Calorimetry [DSC] was conducted using a TA Model 2820 Modulated DSC by sealing ca. 5 mg of polymer in a flat aluminum sample pan. The sample was annealed at 200 °C for 5 min, cooled to −60 °C, then the temperature was ramped from −60 to 200 °C at a rate of 10 °C/min. Sample Preparation for NMR Experiments. For poly(VDF-co-TFE)-B (ca. 82:18 mol %), two samples were prepared for NMR analysis, one containing 35 mg poly(VDFco-TFE) and the other containing 101 mg poly(VDF-co-TFE). The less concentrated sample was used for quantitative 1H{19F} and 19F{1H} 1D-NMR experiments and their T1 experiments, while the more concentrated sample was used for all the other experiments. Each sample was dissolved in about 700 μL of the acetone-d6, whose resonances were also used as a reference in 1 H (2.05 ppm) and 13C (29.92 ppm) NMR spectra. A drop of trichlorofluoromethane was added and used as an internal reference in the 19F (0.0 ppm) NMR spectra. A drop of 1,4dichloro-2-(trifluoromethyl)benzene was added to the less concentrated poly(VDF-co-TFE)-B sample and used as an internal signal intensity reference in quantitative comparison of the signal intensities in the 19F{1H} and 1H{19F} NMR spectra. The samples were flame-sealed in a 5 mm NMR tube and then heated in water at 45 °C for 2 h to get a homogeneous solution. The solution remained homogeneous for the NMR analysis. For comparison, another sample containing 35 mg poly(VDFco-TFE)-A (ca. 60:40 mol %) was prepared in a similar way. The majority of the NMR data were collected on poly(VDF-coTFE)-B (ca. 82:18 mol %) unless otherwise specified. Instrumentation. All the NMR spectra were collected on a Varian Direct-Drive 500 MHz spectrometer equipped with five broad-band rf channels and a 5 mm 1H/19F/13C triple resonance pulse field gradient (PFG) probe at 30 °C.21 Unless otherwise noted, all 1D-NMR spectral data were acquired while decoupling the undetected nuclei (i.e., 1H{19F}, 19F{1H}, 13 C{1H,19F}). In general, during the acquisition periods of both 1D- and 2D-NMR experiments 1H, 13C and 19F were decoupled with Waltz-16 (γHBH/2π = 2.7 kHz), WURST (γCBC/2π = 12.8 kHz) and CHIRP (γFBF/2π = 17.9 kHz) decoupler modulation, respectively. Similarly, in X{Y} HSQCtype 2D-NMR experiments triple resonance was employed. In standard X{Y} HSQC-type experiments the X nucleus is decoupled via an inversion pulse in the middle of the t1 evolution period (the sequence was modified to use a composite inversion pulse for 19F); when the third nucleus was 1H (i.e., for 19F{13C} HSQC-type experiments); continuous Waltz-16 decoupler modulation was employed throughout the experiment. When the third nucleus was 19F

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EXPERIMENTAL SECTION Materials. Trichlorofluoromethane (CFCl3, 99.5%) and 1,4dichloro-2-(trifluoromethyl)benzene (98%) were purchased from Aldrich Chemical Co, and used as internal standards for 19 F NMR. Acetone-d6 (d, 99.9%) was purchased from Cambridge Isotope Laboratories, Inc. and used as received. Synthesis of poly(VDF-co-TFE). These copolymers were prepared in a 2-L liquid-full stainless steel reactor equipped with an agitator. The reactor temperature was maintained at 101 °C and the reactor pressure was maintained at 4.14 MPa. The monomer feed compositions and rates are shown in Table 1. All other polymerization ingredients were combined in an aqueous feed stream whose compositions are also given in Table 1. The surfactant was ammonium perfluorooctanoate. The reactor was allowed to equilibrate for 1 h at the reaction temperature and pressure with just the aqueous feed components in the recipe. After the equilibration period, Table 1. Conditions under Which the PVDF and Poly( VDFco-TFE) Polymers Were Prepared polymer VDF feed, g/h TFE feed, g/h (NH4)2S2O8 feed, g/h NaOH feed, g/h APFOa feed, g/h total aqueous solution feed, L/h overall monomer conversion, % polymer composition, mol % VDF polymer composition, mol % TFE Tg/Tm, °C a

poly(VDF-coTFE)-A 790 810 12.8 2.4 24.0 8.0

poly(VDF-coTFE)-B 1220 380 12.8 2.4 16.0 8.0

PVDF 1600 12.8 1.6 16.0 8.0

96

94

97

60

82

100

40

18

−

7/171

−40/122

−

APFO: ammonium perfluorooctanoate. B

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(i.e., for 1H{13C} HSQC-type experiments) a modified version of the standard pulse program was used to apply a composite 180o 19F inversion pulse in the middle of t1 to accomplish 19F decoupling in the f1 dimension. In 1H/19F HETCOR experiments, the standard inversion pulse was used in the middle of t1 to decouple the second nucleus; 13C decoupling was not necessary because of its low natural abundance. 19 F, 1H, and 13C 1D-NMR. A 19F T1 NMR experiment was performed with the standard inversion recovery (relaxation delay−180°−τ−90°−acquire) experiment. The spectra were collected with the following parameters: 90°/180° pulse widths of 8.95/17.90 μs, 23.58 kHz spectral width, acquisition time of 1 s, and relaxation delay 32 s; 8 transients were averaged for each τ delay; 20 values of τ, arrayed from 0.00006 to 32 s, were used to measure the relaxation of different fluorine atoms in the polymer. Data were analyzed using the standard 3-parameter exponential fitting program in Varian’s VnmrJ 2.2D software. The 19F 1D-NMR spectrum of poly(VDF-co-TFE) was collected at 470 MHz with 1 s acquisition time, 20 s relaxation delay, 20.8 kHz spectral window, 128 transients, and 3.3 μs 30° pulse width using gated 1H decoupling with Waltz-16 modulation22,23 to suppress the nuclear Overhauser enhancement from 1H. The data were zero-filled to 256 k, exponentially weighted with a line broadening of 0.5 Hz and Fourier transformed. A 1H T1 NMR experiment was performed with the same sequence as that used for the 19F T1 experiment. The spectra were collected with the following parameters: 90°/180° pulse widths of 12.40/24.80 μs, 5.02 kHz spectral width, acquisition time of 2 s, and relaxation delay 10 s; 32 transients were averaged for each τ delay; 17 values of τ, arrayed from 0.005 to 20 s, were used to measure the relaxation of different protons in the polymer. Data were analyzed using the same program as above. The 1H NMR spectrum was collected on the same instrument with a 4.68 s acquisition time, 30 s relaxation delay, 3.2 kHz spectral window, 128 transients, 12.4 μs 90° pulse width, and gated 19F decoupling, for which CHIRP24,25 decoupler modulation was used. The data were zero-filled to 64 k, exponentially weighted with a line broadening of 0.5 Hz, and Fourier transformed. A 13C T1 NMR experiment was performed with the same sequence as that used for the 19F T1 experiment. The spectra were collected with the following parameters: 90°/180° pulse widths of 12.70/25.40 μs, 17.61 kHz spectral width, acquisition time of 1 s, and relaxation delay 4 s; 1152 transients were averaged for each τ delay; 10 values of τ, arrayed from 0.005 to 5 s, were used to measure the relaxation of different carbon atoms in the polymer. Data were analyzed using the same program as above. The 13C NMR spectrum was collected on the same instrument with 2 s acquisition time, 20 s relaxation delay, 17.6 kHz spectral window, 4224 transients, 12.7 μs 90° pulse width and simultaneous 1H and 19F decoupling, for which Waltz-16 and CHIRP decoupler modulation, respectively, were used. The data were zero-filled to 256 k, exponentially weighted with a line broadening of 3 Hz, and Fourier transformed. 19 13 F{ C} gHSQC 2D-NMR. 19F{13C} gHSQC experiments were performed with a pulse sequence previously reported,21 but with continuous 1H decoupling using Waltz-16 modulation and 13C decoupling during acquisition period using WURST25 modulation. Experiments were performed with 90° pulse widths of 10.4 and 12.9 μs for 19F and 13C, respectively. The

19

F dimension had a spectral width of 20.8 kHz, and the 13C dimension had a spectral width of 17.6 kHz, acquisition time of 0.123 s, 1 s relaxation delay; 16 transients were averaged for each 2 × 512 increments using the States26 method of phase sensitive detection in f1. Delays were optimized depending on the couplings of interest. The delay Δ = 1/4JCF was set to 0.9 ms (1JCF = 275 Hz) for one-bond 19F−13C correlations, and to 8.3 ms (2JCF = 30 Hz) for two-bond 19F−13C couplings. The data were zero-filled to 4096 × 4096 and weighted with sinebell and shifted sinebell functions prior to Fourier transformation. 1 13 H{ C} gHSQC 2D-NMR. The standard 1H{13C} gHSQC sequence was modified. Because of the large 19F spectral window, a more efficient decoupling method was used to remove 19F couplings. Instead of using continuous 19F decoupling, a composite 180° pulse was employed on the second decoupling channel in the middle of the 13C evolution period (This is essential as decoupler modulation using long sequences such as WURST is ineffective at removing large couplings during short evolution periods.); the 19F decoupler was only turned on during the acquisition period. WURST25 modulation was used for 13C decoupling. Experiments were performed with 90° pulse widths of 12.3 and 13.2 μs for 1H and 13 C, respectively. The 1H dimension had a spectral width of 4.0 kHz, and the 13C dimension had a spectral width of 10.1 kHz, acquisition time of 0.15 s, 1 s relaxation delay; 8 transients were averaged for each 2 × 1424 increments using the States26 method of phase sensitive detection in f1. The data were zerofilled to 4096 × 4096 and weighted with sinebell and shifted sinebell functions prior to Fourier transformation. 1 13 H{ C} gH2BC 2D-NMR. 1H{13C} gH2BC experiments were performed with a standard Varian pulse sequence, but with continuous 19F decoupling using CHIRP modulation and 13 C decoupling during the acquisition period using WURST25 modulation. Experiments were performed with 90° pulse widths of 8.8 and 13.2 μs for 1H and 13C, respectively. The 1 H dimension had a spectral width of 3.2 kHz, the 13C dimension had a spectral width of 12.9 kHz, acquisition time of 0.1 s, 1.2 s relaxation delay; 8 transients were averaged for each 2 × 116 increments using the States26 method of phase sensitive detection in f1. The data were zero-filled to 2048 × 4096 and weighted with sinebell and shifted sinebell functions prior to Fourier transformation. 19 1 F{ H} and 1H{19F} gHETCOR 2D-NMR. The 19F{1H} gHETCOR experiments were performed with the standard Varian sequence. This experiment can be set to detect 19F or 1 H based on different needs. Experiments were performed with 90° pulse widths of 10.6 and 14 μs for 19F and 1H, respectively. For the 19F detected experiment, the spectrum was collected with a 19F window of 20.8 kHz, 0.128 s acquisition time, and 1 s relaxation delay. The 1H detected experiment was performed with a 1H window of 3.7 kHz, 0.160 s acquisition time, 1 s relaxation delay, and 90° pulse widths of 12.6 and 11 μs for 1H and 19F, respectively. Eight transients were averaged for each 2 × 512 increments using the States method of phase sensitive detection in f1. Processing was done with sinebell and shifted sinebell weighting functions and zero-filling to a 4096 × 4096 data matrix prior to Fourier transformation. 19 F−19F gdqCOSY 2D-NMR. The 19F−19F gdqCOSY experiment was performed with the standard Varian sequence, but with continuous 1H decoupling using Waltz-16 modulation. This was done with a 20.8 kHz spectral width, 0.2556 s acquisition time, 1 s relaxation delay and 10.3 μs 90° pulse C

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width. Eight transients were averaged for each 2 × 512 increments using the States method of phase sensitive detection in f1. Processing was done with shifted sinebell weighting functions in both dimensions and zero-filling to a 4096 × 4096 data matrix prior to Fourier transformation.

(Scheme 1). On the basis of this system, there are 2-centered sequences and 0-centered sequences, which can be studied by 19 13 F/ C and 1H/13C experiments, respectively. As for 2centered 3-carbon sequences, there are three possibilities: 020, 022/220 and 222, in which the bold numbers represent the carbons whose resonances are assigned. Similarly, in 0centered carbon sequences, such as 002/200 and 202, the bold numbers indicate the assigned resonances in odd-numbered sequences. In this copolymer, it is impossible to have three consecutive 0 units, so the 000 sequence is not listed in Scheme 1. Those sequences can exist in higher level sequences (e.g., 5-, 7- or 9-carbon sequences), which will result in multiple peaks in each region of the fluorine spectra (Figure 1). In each region of the 19F NMR spectrum of poly(VDF-co-TFE) (84:16 mol %), the peaks are labeled alphabetically from An to Zn with increasing magnetic field, where n indicates the number of consecutive 2 units in the 3-carbon sequence. For example, in region 1, the resonances are attributed to sequences with only a single isolated 2 unit in 020 sequences. These 020 centered peaks are labeled from A1 to M1. Peaks in regions 2 and 3, derived from 022/220 and 222 sequences, respectively, are labeled in similar way. In the 13C 1D-NMR spectrum, for CH2 carbons, the peaks in the 20−50 ppm region are numbered from 1 to 12 with decreasing magnetic field (vide inf ra). For CF2 carbons, the resonances in the 110−125 ppm region are numbered from 13 to 28 (Supporting Information, Figure S1). Assignment of Resonances from CF2-Centered 3Carbon Sequences. The 19F 1D-NMR spectra of poly(VDF-co-TFE) with different compositions are shown in Figure 1. In Figure 1a, three regions can be clearly observed, which correspond to the 3-carbon sequences. Expansions of each of these regions are shown in the Supporting Information, Figure S2.

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RESULTS AND DISCUSSION Nomenclature and Structures. The copolymer used in this study was composed of two monomer units, vinylidene fluoride and tetrafluoroethylene. Vinylidene fluoride units can have two different orientations along the copolymer chain; these are units from normal (02, V) or reverse (20, B) addition. Tetrafluoroethylene contributes (22, T) segments to the polymer. In Scheme 1, 2 indicates CF2 groups, while 0 Scheme 1. Possible Odd-Numbered Carbon Sequences in Poly(VDF-co-TFE)

represents CH2 groups, where the number indicates the number of fluorines bound to carbon. In this study, to make the assignment systematic, only the resonances of the central atoms in odd-numbered carbon sequences were assigned

Figure 1. 470 MHz 19F 1D-NMR spectra with gated 1H Waltz-16 modulated decoupling (a) poly(VDF-co-TFE) (84:16 mol %) and (b) poly(VDFco-TFE) (56:44 mol %). D

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The 19F{13C} gHSQC spectra in Figure 2 can easily be used to determine both the 19F and 13C resonance assignments of

majority of resonances span a range of 15 ppm, compared with F NMR spectrum where the CF2 resonances span a range of 40 ppm. The 13C NMR spectrum gives much lower dispersion of the resonances for CF2-centered sequences. Only the resonances of the 3-carbon sequences can be resolved from each other and the assignments are indicated in 13C dimension in Figure 2a. For methylene carbons (CH2 region), resonance assignments of CH2−centered 3-carbon sequences can also be identified easily. Carbon resonances of 202 sequences are less shielded since these methylene carbons are flanked by two CF2 groups, which contain four strongly electron withdrawing fluorine atoms. The 002 carbon resonances are more shielded as these methylene carbons only have one neighboring CF2. These assignments were also confirmed by the 1H{13C} gH2BC 2DNMR spectrum (vide inf ra). The assignment of resonances from these 3-carbon sequences provides strong and necessary evidence for determining the assignments of resonances from 5-carbon sequences. Assignment of Resonances from CF2-Centered 5Carbon Sequences. The resonances of 3-carbon sequences were assigned in the last section. In this section, the correlations between the resonances of these 3-carbon sequences are used as the basis to assign resonances of 5-carbon sequences. The 020 sequence should exist in two different 5-carbon sequences, 20202 (structure 4) and 20200 (structure 5). The 00200 sequence is not possible since the copolymer is composed of only three types of units 20, 02, and 22. The 19F{1H} HETCOR spectrum can be used to distinguish between them. From Figure 3, it can be seen that the central fluorine in the 19

Figure 2. 19F{13C} gHSQC 2D-NMR spectra of poly(VDF-co-TFE) (84:16 mol %) with the corresponding regions from the 19F and 13C 1D-NMR spectra aligned along their respective axes from: (a) one bond (1JCF) experiment, and (b) two bond (2JCF) experiment.

these 3-carbon sequences. Figure 2a shows correlations between the resonances of directly attached carbons and fluorines, while Figure 2b shows correlations between the resonances of fluorines and carbons separated by two-bonds. Region 1 corresponds to 020 sequences (structure 1) because the resonances of the central fluorine atoms in 020 sequences are only correlated via 2JFC couplings with the resonances of CH2 carbons, which fall in the 23−45 ppm 13C chemical shift range (Figure 2b). Region 2 is assigned to 19F resonances of 022/220 sequences (structure 2), since the resonances of the central fluorine atoms are correlated via 2JFC with the resonances of both CH2 and CF2 carbons two bonds away. Likewise, the region containing cross-peaks from 222 sequences (structure 3) is determined because of the fact that the resonances of the central fluorine are only correlated with the resonances of CF2 carbons two bonds away, and no correlations with the resonances in the CH2 region are observed (Figure 2b). Therefore, in 19F NMR spectrum, the three regions with the increasing magnetic field correspond to the resonances of 020, 022/220 and 222 sequences.

Figure 3. 020 region from the 19F{1H} HETCOR 2D-NMR spectrum of poly(VDF-co-TFE) (84:16 mol %).

symmetric sequence 20202 is correlated with methylene protons that are both in 202 sequences. In comparison, since the 20200 sequence is unsymmetrical, the central fluorines in 20200 sequences are correlated with the proton resonances of two different types of methylene groups. One of these is from the methylene protons belonging to 202 sequences, while the other type of methylene proton resonance belongs to 200 sequences. The chemical shifts of methylene protons in 200 sequences are shielded (2.2−2.6 ppm) compared to those of 202 sequences (2.8−3.3 ppm) because of the lower number of α-fluorine atoms in the former (200) compared to the latter (202) sequences.

In the carbon chemical shift dimension there are two groups of resonances from different types of methylene carbons-those from CH2 carbons (23−45 ppm), and those from CF2 carbons (110−125 ppm). On close examination of the CF2 region in the carbon chemical shift dimension, it can be seen that the E

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The resonances for 5-carbon sequences in the 022/220 region are difficult to assign due to the complicated splitting patterns and signal overlap in the 19F 1D-NMR spectrum. Different resonance assignments were reported for the resonance at −113.3 ppm. This resonance was assigned to the central fluorine in 02200 sequences in Isbester’s work,27 however, it was assigned to 20220 sequences in Cais’ and Wormald’s work.11,28 This work shows that these resonances can be determined explicitly by 19F{13C} HSQC 2D-NMR. Since 022/220 sequences are not symmetrical, they can exist in four different 5-carbon sequences: 20222 (structure 6), 00222 (structure 7), 20220 (structure 8), and 00220 (structure 9). Among these sequences, 20222 and 00222 can be distinguished from the other two because the resonances of the central fluorines in these two sequences are correlated via 2JCF coupling with the resonances of the 222 carbons (highlighted in box with dotted lines (···) in Figure 4). The resonances of 20222 and

Figure 5. 470 MHz 19F 1D-NMR spectra with gated 1H Waltz-16 modulated decoupling: (a) PVDF, (b) poly(VDF:TFE) = 84:16, and (c) poly(VDF:TFE) = 58:42 (mol %).

can be seen that the peaks in the box with solid line () increase with increasing TFE content, so they are assigned to 20222 sequences, which contain at least one TFE (22) unit. In the same way, the resonances of 00220 sequences, which contain three VDF (02 or 20) units, can be determined since they increase with the increasing VDF content. As for the other two sequences, 00222 sequences do not exist in the PVDF homopolymer, so the peaks highlighted in box with dashed lines (---) are attributed to 00222 sequences. The other peaks in box with dotted lines (···) are attributed to 20220 sequences. Since the polymer with VDF:TFE mole ratio of 58:42 is largely composed of alternating VDF and TFE units, the probability adjoining VDF units and, a fortiori, head-to-head and tail-to-tail VDF units is low. Hence, the spectrum of this polymer contains weaker signals from 0202 sequences in the −90 ppm region (Figure 1b) compared to those from the polymer with VDF:TFE ratio of 84:16 (Figure 1a). Additionally, the polymer with VDF:TFE ratio of 58:42 has barely detectable signals from head-to-head and tail-to-tail sequences near −113 and −116 ppm (Figure 5c). These assignments are also in agreement with the results from 2D-NMR. Symmetrical 222 3-carbon sequences exist in three different 5-carbon sequences. In 02220 sequences, the resonances of the central fluorines are only correlated with the resonances of the 220 carbons, and therefore they can be distinguished from other resonances. In comparison, the central fluorine

Figure 4. Selected regions from the 19F{13C} 2JFC gHSQC 2D-NMR spectrum of poly(VDF-co-TFE) (84:16 mol %).

00222 can be distinguished from each other because the resonances of central fluorines in 20222 sequences are correlated via 2JCF coupling with 202 carbon resonances, which are less shielded (highlighted in the boxes with dashed lines (---) in Figure 4). By comparison, the resonances of the central fluorines in 00222 sequences are correlated via 2JCF coupling with 002 methylene carbon resonances, which are more shielded and highlighted in the boxes with solid lines, (). These assignments are supported by 19F 1D-NMR spectra of polymers with different monomer compositions. In Figure 5, it F

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same way on the basis of the spectra in the Supporting Information, Figures S4−S7. (Note that a number of weak resonances from polymer defect and chain-end structures are not addressed here. These will be the subject of research to be described in a second manuscript being prepared.) From this table, by the compositional analysis method, it can be seen that peak I2 can only be assigned to a 7-carbon sequence. From Table 3 in ref 8, it is noticed that additivity schemes can not provide good predictions for high level sequences if their resonances are very close to each other. In comparison, 2DNMR allows assignment of resonances from high level sequences unambiguously without having to make polymers of different compositions. Extra attention is needed to assign peak A3 in structure 11. In the previous section, A3 was assigned to the 5-carbon sequence 22222. In this 5-carbon sequence, the resonance of the central fluorine is correlated with two peaks in region 3 via 3 JFF. In the gdqCOSY spectrum, peak A3 is only correlated with the peak C3 (02222) in region 3 (Figure 7). This means that A3 exists in a symmetrical environment and that it must be attributed to 0222220 sequences. On the basis of this assignment, A3 should also be correlated with peaks in region 2 by four bond couplings. It can be seen that A3 is only correlated with H2 in Figure 7. Therefore, it can be concluded that the assignment of peak A3 is to a symmetric 9-carbon sequence 202222202 (structure 11).

resonances of 22220 sequences are correlated with both 222 and 220 carbon resonances. The rest of the signals will come from 22222 sequences. The 2D-NMR spectra and the resonance assignments of 5-carbon sequence are shown in the Supporting Information (Figure S3). Assignment of Resonances from CF2-Centered 7- and 9-Carbon Sequences. The assignments of resonances from higher level sequences (7- and 9-carbons) are based on the assigned resonances of 5-carbon sequences and identification of 2D-NMR correlations between pairs of resonances. In this section, the assignment of the resonance of the 9-carbon sequence 220022202 will be discussed. In addition, this 2DNMR based assignment methodology will be compared with that based on other methods. Taking 19F−19F gdqCOSY 2DNMR spectrum (Figure 6) as an example, in the above section,

Figure 6. Selected region from the 19F−19F gdqCOSY 2D-NMR spectrum of poly(VDF-co-TFE) (84:16 mol %) obtained with continuous 1H decoupling.

the peaks labeled as E2, I2 and M2 have been assigned to 02200, 00222 and 22202 sequences, respectively. In Figure 6, peak I2 is correlated with E2 in one direction and with M2 in the other direction. Therefore, sequence 00222 attributed to resonance I2 must occur between 02200 and 22202 sequences. The 9-carbon sequence 220022202 is the only possibility (structure 10). Therefore, peak I2 can be assigned to the 220022202 sequence.

The assignment of the H2 peak of structure 12 is a little more complicated. From the gdqCOSY spectrum, it can be seen that the H2 resonance (20222/22202) is correlated with the resonances belonging to the 20202 sequences in one direction (Supporting Information, Figure S4). In the other direction, it is correlated with both C3 and A3 resonances (Figure 7). Since it is not possible to distinguish between 3bond and 4-bond correlations, it is only possible to discuss all the permutations of arrangements and exclude the impossible ones. The central 19F resonance from peak H2 (belonging to 20222) must be as least four bond away from the central 19F atom attributed to peak A3 (22222). If the fluorines attributed to peaks H2 and A3 were 3 bonds away from each other, A3 would have to belong to the 0222X sequence, which is not consistent with the rest of the assignments above. If the fluorines attributed to peaks H2 and A3 were 5 bonds away, the sequence 2020222222 would result. Since A3 is assigned to 202222202 sequences, this possibility is precluded. Therefore, the fluorines attributed to peaks H2 and A3 must be separated by four bonds, and the 9-carbon sequence 202022222 (structure 12) is assigned to peak H2. In this sequence, the fluorine attributed to peak H2 can be either 3-, or 5-bonds away from the fluorines assigned to peak C3, and the same result is

Table 2 summarizes the 19F resonance assignments on the basis of 2D-NMR, statistical probabilities and chemical shift additivity schemes. Only a few high level sequences are discussed in detail in this paper. The others are assigned in the G

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Table 2. Summary of 19F Resonance Assignments from the Backbone Structures of poly(VDF-co-TFE) (84:16 mol %) assignments 19

peak

2D-NMR this work

−91.22 −91.40 −91.78 −91.97 −92.60 −95.07 −95.23 −95.38 −95.93 −110.56 −110.74 −111.27 −111.57 −111.69 −111.89 −113.07 −113.26 −113.48/−113.55 −115.84 −120.75 −122.57 −123.73 −124.64 −125.25 −125.52 −125.82

B1/C1 D1/E1/F1 G1 H1 I1 J1 K1 L1 M1 D2 E2 F2 G2 H2 H2′ I2 J2 K2 and K2′ N2 A3 B3 C3 D3 E3 F3 G3 a

F chemical shift (δ, ppm)

composition11

additivity8

a

0202020/02020220 02020222

0202020 2202020

2202020a 2202020

2202022 0202002

2202022 0202002

2202022

2202002 22202220X 222022200 202022202 202022200 202022222

2202002 2202220a 2202222b 0202220 0202222b 0202222a

202220022 2002220 202022002/2022022 (20)2022002 202222202 x20222220 020222220 220222022 020222022 020222002 020222020

2002220a/2002222a 2002220/2002222a 0202200a/2202202b 2022002a 0222220a 2022222a 2022220b 2022202a 2022202a 2022200a 2022202a

0202220b 0222022b

2022022b 2022022b 2022022b 2022002 202222202 220222220a 020222220 220222022 020222022 020222020

Matching resonance assignment but at different carbon sequence level. bDifferent resonance assignment.

Table 3. Summary of 13C and 1H Resonance Assignments of Poly(VDF-co-TFE) (84:16 mol %) 13

C peak

1, 2, 3 4 5′ 5 6 7 8, 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 a

13

C chemical shift (δ, ppm) 22.58/23.70 24.40 29.58/29.63 30.66 32.53 33.57 37.10/37.57 38.45 43.69 44.44 111.28 111.42 111.56 111.87 112.00 112.59 117.49 117.67 117.89 119.03 119.40 120.33 120.51 120.76 120.94 122.61

1

H chemical shift (δ, ppm)

assignment

2.33−2.52 2.46−2.54 2.34−2.45 3.10, 3.17 3.18−3.26 3.28−3.41 3.01−3.18 3.08−3.27 2.91−3.01 2.92−3.11 NAa NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

X200220 X200222 X200202 X220220 X22022X 2220222 2020220 X020222 X020200 X020202 220222022 020222022 020222020 020222220 020222002 202222202 22202220X/202022002 0202220/202022200/202022222/202220022 2002220/(20)2022002 222020222 02020222 0202020/02020220 0202002

NA: Not applicable to 2-centered sequences.

H

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Figure 7. Selected region from the 19F−19F gdqCOSY NMR spectrum of poly(VDF-co-TFE) (84:16 mol %) with continuous 1H decoupling.

Figure 8. Selected region from the 1H{19F} HETCOR 2D-NMR spectrum of poly(VDF-co-TFE) (84:16 mol %).

obtained. Similarly, most of the peaks in regions 2 and 3 can be assigned by 2D-NMR; the 19F resonance assignments are summarized in Table 2.

surrounded by the dashed lines (---) in Figure 8). Theoretically, the 19F resonances of B1 and C1 should correlate with some 19 F resonances in the same region of 20202 via four bond couplings. The missing correlations are probably because of the difficulty in detecting weak signals near the diagonal of COSYtype spectra. The D1/E1/F1 19F resonances of 20202 sequences are all correlated with the 19F resonance of 20222 sequences in one direction (Supporting Information, Figure S4). In the other direction, they are correlated with the central 13C resonance of 02020 sequences (vida inf ra). Therefore, D1/E1/F1 resonances are assigned to X02020222 sequences. Additional splittings of peaks in this region result from different chemical shifts because of different structures of the higher level sequences in which they reside. These higher level sequences are not identified because of the limited resolution in the current 2D-NMR spectra. From the gdqCOSY NMR spectrum, peak I1 is only correlated with one 19F resonance (Supporting Information, Figure S4), which belongs to the 20222 sequence. Furthermore, in the 1H{19F} HETCOR spectrum (Figure 8), I1 is also only correlated with resonances of one type of methylene CH2 group. This evidence suggests that I1 is the symmetric sequence 222020222. Confirmations of Previous Assignments by One- and Two-Bond 19F{13C} HSQC 2D-NMR. From 1JFC and 2JFC gHSQC 2D-NMR spectra, most of the previous assignments can be confirmed. In addition, the CH2−centered carbon sequences can be assigned on the basis of the two-bond 19 13 F{ C} gHSQC spectrum, which will be discussed in the next section. It has already been mentioned that 3-, 4- and 5-bond 19 F−19F correlations can not be distinguished from each other in COSY-type spectra. As a result, the method of exclusion was utilized to confirm some of the resonance assignments of the 9carbon sequences. Here, the approach of using gHSQC to tell the difference between 3JFF, 4JFF, and 5JFF will be discussed, and some examples will be presented. In structure 13, the direct attachments of Fa−Ca, Fb−Cb and Fc−Cc can be established from the 1JFC 19F{13C} gHSQC spectrum. The 2JFC gHSQC experiment can be utilized to identify multibond 19F−19F correlations. To prove that fluorine atom Fa is three bonds away from Fb, it is necessary to observe the correlation between the 19F resonance of Fa and the 13C

For the peaks in region 1, the assignments become more difficult because of severe signal overlap, especially in the 5carbon sequence 20202 region of the 19F 1D-NMR spectrum, ranging from −90 ppm to −95 ppm. Peaks B1 and C1 are not resolved very well in the 19F 1D-NMR spectrum; they are found to be correlated with resonances attributed to 20220 sequences (Supporting Information, Figure S4). Additionally, in the 1H{19F} HETCOR spectrum, the 19F resonances B1 and C1 are correlated with 1H resonances of both 02020 and 22020 sequences, but with very different intensities (Figure 8). This indicates that there are two different sequences contributing to B1 and C1: 0202020 and 0202022. In symmetric 0202020 sequences, the resonances of the central fluorines are correlated with the chemically equivalent proton resonances of 02020 sequences via 3JHF (highlighted by circle within the solid lines () in Figure 8). In comparison, the central fluorine resonances in unsymmetrical sequences 0202022 are correlated with two different proton resonances. In one direction, the resonance of the central fluorine in 0202022 is correlated with the central proton resonance of 02020 sequences, and the cross-peak is buried in the large circle within the solid lines shown in the 1H{19F} HETCOR spectrum. In the other direction, the central fluorine resonance in the 0202022 sequences is correlated with the resonance of the central protons in the 02022 sequences (the cross-peak in the circle I

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two bond 1H−13C correlations can be observed in gH2BC spectrum only when vicinal 1H−1H couplings are present in −CHn-CHm (n≠0, m≠0) structure fragments. Thus, the gH2BC experiment will provide unequivocal evidence for structure fragments like −CH2CH2−, >CH−CH2− and −CH2CH3. From Figure 10, it can be seen that only 1H

resonance of Cb, as well as the correlation between the Fb resonance and the Ca resonance in the 2JFC gHSQC spectrum.

To identify a four-bond 19F−19F COSY correlation, such as Fa−Fc in structure 13, it is necessary to see that both the 19F resonances of Fa and Fc are correlated with the same 13C resonance of Cb. As an example, in the previous discussion related to the 9-carbon sequence 202222202 (12), it was determined that the central fluorine atom A3 is three bonds away from C3 by the exclusion method. In Figure 9, it can be

Figure 10. 500 MHz 1H{13C} gH2BC 2D-NMR spectrum of poly(VDF-co-TFE) (84:16 mol %).

resonances between 2.3 and 2.6 ppm are correlated with carbon resonances at 22−29 ppm via 2JHC. This proves that peaks in this area contain resonances of the −CH2CH2− structure fragments. Therefore, the resonances between 2.3 and 2.6 ppm in 1H dimension, and the resonances in the range of 22−29 ppm in 13C dimension are assigned to the 002 3-carbon sequences. Since the 19F resonances have been reliably assigned, the assignment of resonances from CH2 centered 5-carbon sequences are easily established on the basis of the 2JFC gHSQC spectrum. For example, in 2002020 sequences (structure 14), the resonances of the central fluorine atoms are correlated with two different methylene carbon resonances, which are highlighted in the box within the solid lines () in Figure 11. Therefore, the less shielded carbon resonances near 44 ppm are assigned to the 02020 5-carbon sequences. The

Figure 9. Selected regions from the (a) one-bond and (b) two-bond 19 13 F{ C} gHSQC NMR spectrum of poly(VDF-co-TFE) (84:16 mol %).

seen that the fluorine atom A3 is directly attached to carbon atom 18 (structure 11). Furthermore, the 19F resonance C3 is correlated with the 13C resonance 18 in 2JFC gHSQC spectrum. This confirms that the fluorine atoms attributed to resonances A3 and C3 are three bonds away from each other. The other resonances can be confirmed in the same way. Additionally, the carbon resonances of CF2’s can be assigned on the basis of the 1 JFC gHSQC spectrum; the results are summarized in Table 3 (vide inf ra). Assignment of CH2-Centered Sequences. The assignment of CH2 centered carbon sequences starts at the 3-carbon level, with 202 and 002 sequences. Since there are two continuous CH2 groups in the 002 3-carbon sequences, the 1 H{13C} gH2BC experiment is effective to identify such structures. Unlike gHMBC, the coherence transfer in the gH2BC sequence is on the basis of 1JHC and 3JHH. Therefore,

Figure 11. Selected region from the two bond 19F{13C} gHSQC 2DNMR spectrum of poly(VDF-co-TFE) (84:16 mol %). J

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more shielded carbon resonances near 29 ppm, which are buried under the solvent peak in the 13C 1D-NMR spectrum, are assigned to the 20020 5-carbon sequences. Similarly, in the 020-centered 7-carbon sequence 2202020, the resonance of the central fluorine atom is correlated with two different carbon resonances near 39 and 45 ppm. These methylene carbon resonances correspond to 22020 and 02020 sequences, respectively.

Figure 13. Selected region from 1H{13C} gHSQC 2D-NMR spectrum of poly(VDF-co-TFE) (84:16 mol %).

In comparison, the resonances of the central fluorines in the 0202020 sequence are only correlated with one type of methylene carbon resonance (02020) near 45 ppm. On the basis of the above discussion, it can be seen that all of the methylene carbon resonances attributed to 02020 fall in a region between 43 and 46 ppm. The remaining CH2−centered methylene carbon resonances are assigned in a similar way; the details of these assignments are not elaborated here. The assignments of resonances for CH2 centered 5-carbon sequences are summarized in Figure 12

of the 1H resonances. The corresponding 1H chemical shifts for peaks in Figure 13 are summarized in Table 3. Composition Analysis. In addition to the detailed structure information, once resonance assignments are confirmed it is also possible to obtain quantitative information from 1D-NMR spectra, so that the composition of the polymers can be calculated. In this study, three different methods were used to calculate the mole percentages of normal VDF (PV), reverse VDF (PB), and TFE (PT) units in the three VDF-based polymers, and the results were compared. Method 1. In the first method, an internal standard, 1,4dichloro-2-(trifluoromethyl)benzene (DCTFB), was used to quantitatively relate the 1H and 19F signal intensities to each other, and ultimately to obtain the mole % of TFE in poly(VDF-co-TFE). This method is based on one first described by Brame and Yeager.29 First, the relative number of CF2’s and CH2’s were calculated. Then, the PT was calculated based on ratios of the number of CH2 and CF2 groups. In the quantitative 19F{1H} NMR spectrum (Supporting Information, Figure S8), the peak at −62 ppm is attributed to the fluorine atoms of the internal standard, DCTFB. The peaks between −90 and −126 ppm are attributed to the CF2’s in poly(VDF-coTFE). The integral areas of the peaks contributed by the internal standard and the CF2’s are divided by the numbers of fluorine atoms contained (3 and 2, respectively). Therefore, the relative number of CF2’s in the polymer (NCF2) compared to the number of molecules of standard (Nstd) can be obtained by eq 1, where ACF2 and AFstd are the total of the integral areas of the polymer’s CF 2 resonances, and the standard’s CF 3 resonance, respectively.

Figure 12. Expansion of the CH2 region from 13C 1D-NMR spectrum of poly(VDF-co-TFE) (84:16 mol %) with simultaneous 1H and 19F decoupling.

and higher level sequences are summarized in Table 3. It can be seen from this figure that the resonances from these 5-carbon sequences are well resolved from each other in the 13C NMR spectrum. On the basis of 1JHC 1H{13C} gHSQC 2D-NMR spectrum, the 1H resonances for CH2−centered 5-carbon sequences can also be easily found. This data is shown in Figure 13, where the horizontal axis corresponds to the 13C chemical shift dimension, and the vertical axis is the 1H chemical shift dimension. It can be seen that there is extensive overlap of the resonances from 5carbon sequences in the 1H chemical shift dimension. However, these signals are well resolved in the 13C chemical shift dimension. This dispersion permits resolution and assignment

NCF2 Nstd

=

A CF2 /2 AF std /3

(1)

Similarly, the relative number of CH2’s in the polymer (NCH2) compared to the number of molecules of standard can also be calculated on the basis of the quantitative 1H{19F} NMR spectrum (Supporting Information, Figure S9). The results are summarized in Table 4 and in the Suporting Information. Within experimental error, the ratio NCF2/NCH2 is near unity (0.99) for PVDF homopolymer, as expected. K

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Table 4. Quantitative Results for VDF-Containing Polymers monomer composition (%) PVDF normal VDF(PV)

method 1. internal STD 2. ref 11 3. Bernoullian model error 3. Markovian model error

95.1 95.1 94.9a 2.1 × 10−3 95.1b 1.7 × 10−3

poly(VDF-co-TFE) (84:16 mol %)

reverse VDF(PB)

TFE(PT)

4.9 4.9 5.1a

NA NA NA

4.9b

NA

normal VDF(PV) 80.9 80.2 77.8 3.8 × 10−2 80.9b 9.6 × 10−3

reverse VDF(PB)

TFE(PT)

3.2 3.6 3.1

15.9 16.2 19.2

3.2b

15.9b

poly(VDF-co-TFE) (56:44 mol %) normal VDF(PV) 55.5 58.3 60.7 1.5 × 10−1 55.5b 6.4 × 10−3

reverse VDF(PB)

TFE(PT)

0.8 1.5 −0.5

43.7 40.2 39.7

0.8b

43.7b

a Reference16 bThese numbers, obtained by the Internal standard method, were used as known values in the first order Markovian model to predict the conditional probabilities of monomer addition.

NCH2 Nstd

=

A CH2 /2 H

A

PV = 2P(0) − PB

std /3

(2)

= [(2a + b + c + d + e + f )/A total ] × 100% − PB (6)

Since the VDF monomer is composed of one CH2 unit and one CF2 unit, while the TFE monomer is composed of two CF2 units, PT can be calculated based on eq 3. PT =

(NCF2 − NCH2)/2 NCH2 + (NCF2 − NCH2)/2

PT = 100% − PV − PB

Method 3. Statistical analysis is another option to do the component analysis for polymers. The details of the method used here were described by Qiu et al.30 in their analysis of poly(ethylene-co-1-octene) 13C NMR spectra. The Solver function in Microsoft Excel was activated to conduct these compositional analyses. As applied here, the first step is to predict the probabilities of the triads with a model. Three of the most popular models are the Bernoullian model, the first order Markovian model, and the second order Markovian model. In the Bernoullian model, it is assumed that monomers add randomly to a growing polymer chain. In the first order and second order Markovian models, the addition of monomer depends on last one or two monomer units in the polymer chain, respectively. In this study, the Bernoullian model and the first order Markovian model were used for statistical analysis. With the Bernoullian model, the probability of each triad was calculated from the percentage of each monomer PV, PB, and PT, for example, P(VVT) = PVPVPT. On the other hand, in the first order Markovian model, P(VVT) = PVP(V|V)P(V|T), where P(V|V) and P(V|T) are the probabilities of adding V and T, respectively, to a growing chain terminated by a V radical. On the basis of the types of monomers and the orientations of VDF along the polymer chain, there are three possible monomer units that can add to a chain terminated with a V radical: V, B, and T, and therefore P(V|V) + P(V|B) + P(V|T) = 1. The probabilities of triads allow calculation of the integral values of spectral regions from 5-carbon sequences. In each spreadsheet in the Supporting Information, the matrix contains columns and rows that correspond to the integral regions of 5carbon sequences from the 19F NMR spectrum, and the probabilities of triads, respectively. If a triad contributes signals to a 5-carbon sequence, the probability of this triad will be entered into the cell of that column. The probabilities of all triads contributing to a 5-carbon sequence were added, and the sum is the calculated integral value for this sequence, which is compared with the measured integral value. The measured integral value of a 5-carbon sequence (AXX2XX/Atotal, where AXX2XX is the integral of the resonance from an XX2XX 2-centered 5-carbon sequence and Atotal is the total of the resonance integrals from all carbon sequences) is the normalized integral area of this sequence obtained from 19 1 F{ H} 1D-NMR spectrum. These measured integral values

× 100% (3)

Quantitative 1H{19F} 1D-NMR was used to calculate the percentage of reverse VDF units (PB). The occurrence of a VDF monomer inversion produces two consecutive methylene groups (00), which can be easily observed and identified in the 1 H{13C} gH2BC 2D-NMR spectrum. From the gH2BC spectrum shown in Figure 10, the 1H resonances between 2.3 and 2.6 ppm are attributed to 200 3-carbon sequences. Since these two methylene groups are from two different VDF units (one normal unit and one reverse unit), PB can be calculated using eq 4, where NReverse and NNormal are the number of reverse and normal VDF units, respectively, and A200 and A202 are the total integrated areas of the 200 and 202 methylene proton resonances, respectively. The results obtained when this calculation is applied to the three polymers studied here are summarized in Table 4. NReverse × (1 − PT) × 100% NNormal + NReverse A 200 /2 = × (1 − PT) × 100% (A 202 + A 200 /2) + A 200 /2

PB =

(4)

Method 2. The second method is based on one reported in a study of poly(VDF-co-TFE) by Cais,11 in which the probabilities of 0-centered sequences were expressed in terms of the probabilities of 2-centered sequences. Ultimately, the percentage of each component was obtained based on the 19F NMR spectrum using eqs 5, 6 and 7. In these two equations, the letters a-f, as defined in Cais’ paper, are the integral areas of 020, 022/220, 222, 00202/20200, 00222/22200, and 00220/ 02200 regions in the 19F NMR spectrum, respectively. ATotal is the total integrated intensity of all 0- and 2-centered sequences. PB = [P(200) + P(002)] = [(d + e + f )/A total ] × 100%

(7)

(5) L

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With the first order Markovian model, the peak intensities of all 5-carbon sequences were predicted with reasonable errors. Larger relative errors were seen for the calculation of integrals from weak resonances, such as those of 20200 and 00220 sequences. In comparison, the relative errors calculated from the first order Markovian model are significantly reduced compared to those obtained from the Bernoullian model, especially the relative errors of 5-carbon sequences in the copolymer with higher TFE content. The results of this study are in good agreement with those of G. Lutringer,12 showing that the copolymerization kinetics can be described by the first order Markovian model. Extra attention is needed to calculate the percentages of reverse VDF units in poly(VDF-co-TFE) copolymers. The integrals of the resonances from CH2-centered 3-carbon sequences in 1H spectrum are used in method 1, while the integrals of the resonances from CF2-centered 5-carbon sequence in 19F spectrum are used in methods 2 and 3. Therefore, it is necessary to check the resolution of resonances in the 1H and 19F spectra before calculating the percentages of reverse VDF units. For poly(VDF-co-TFE) (56:44 mol %), the resonances of 00222 sequences are not well resolved from that of 20220 sequences (Supporting Information, Figure S16). As a result, a larger error could be introduced in the calculation of their compositions. In this case, method 1 would be a better choice to calculate the percentages of reverse VDF units. The first order Markovian model also provides the conditional probabilities of monomer addition (Supporting Information, spreadsheets D, E, and F). Their values are summarized in Table 5. This model takes into account that the

are treated as knowns. For the homopolymer, there are four CF2-centered sequences, so there are four experimentally measurable parameters. For poly(VDF-co-TFE) copolymers, there are nine experimentally measurable integral values. The next step is to obtain the difference between calculated and measured integral values for each 5-carbon sequence. The square root of the sum of the squares of the differences between experimental and calculated integrals is determined. Solver is allowed to vary the monomer percentages and/or the probabilities of monomer addition in order to minimize the square root of the total of the differences squared between calculated integrals and measured integrals of 5-carbon sequences. It provides calculated values of the desired variables including: the monomer compositions (Bernoullian model), the conditional probabilities of monomer addition (Markovian model), compositions of n-ads, and the 19F NMR integral values. In the Bernoullian model for VDF homopolymerization, there are four measurable integrals that can be used to determine one unknown variable, PV (PV + PB = 100%). In VDF-TFE copolymerization, PV and PB were treated as unknown variables, as PV + PB + PT = 100%, and their values were varied to predict the nine calculated integral values. With the first order Markovian model, PV, PB, and PT were treated as knowns, as their values were obtained by the internal standard method (method 1 above). Therefore, for PVDF homopolymer, there are four measured integral values and two polymer compositions (PV and PB) to predict two unknowns P(V|V) and P(B|V) (since P(V|V) + P(V|B) = 1 and P(B|V) + P(B|B) = 1). In the copolymerization of VDF and TFE, it is possible to use the 12 known integral values to calculate six unknowns: P(V|V), P(V|B), P(B|V), P(B|B), P(T|V), and P(T| B). All of the above methods were used to calculate the compositions of the three polymers, and the results are summarized in Table 4. All these methods produced consistent and reliable results for PVDF homopolymer. From the Supporting Information, Table S4, it can be seen that both models gave similar relative percentage errors for the calculated integral values of 5-carbon sequences. For poly(VDF-co-TFE) with low TFE content, similar results were obtained with method 1 and method 2. From the Supporting Information, Table S4, it can be seen that there are large errors associated Method 3 using the Bernoullian model. In particular, the integral values of very weak resonances are poorly predicted. In 5-carbon sequence regions of 22220 and 22222 resonances, the relative errors are 406% and 608%, respectively. In comparison, method 3 using the first order Markovian model provides much better prediction for these weak resonances, and the relative errors were reduced to 53% and 20% respectively. These errors are reasonable considering the low signal noise ratio, which results in large errors for the measurement of these weak integrals. For the poly(VDF-co-TFE) sample with high TFE content, there is a significant difference between the percentages of reverse VDF (PB) obtained by the different methods. The method using Bernoullian statistics produced poor prediction of PB, −0.5%. It is not surprising to get such result. First, the relative errors are large for all of the three of the most important regions involving the reverse VDF units (20200, 00222, and 00220), 111−182%. In addition, in this copolymer, the resonances of 00222 sequences are not well resolved from that of 20220 sequences (Supporting Information, Figure S16).

Table 5. Conditional Probabilities of Monomer Addition in VDF-Containing Polymers Obtained with the First Order Markovian Model polymer conditional probability

PVDF

poly(VDF-co-TFE) (84:16 mol %)

poly(VDF-co-TFE) (56:44 mol %)

P(V|V) P(V|B) P(V|T) P(B|V) P(B|B) P(B|T) P(T|V) P(T|B) P(T|T)

0.948 0.052 − 0.978 0.022 − − − −

0.756 0.043 0.201 0.824 0.175 0.001 0.935 0.036 0.028

0.400 0.018 0.583 1.000 0.000 0.000 0.821 0.026 0.153

probabilities of the dyads will be influenced by the stabilities of the three types of radicals at the ends of growing polymer chains. The stabilities of fluorinated radicals, according to studies by Dolbier and Sawada,31,32 are, in order, CF3CH2• < CF3CF2• < CH3CF2•. This work indicated that quantitative NMR results might provide a correlation with the relative stabilities of the radical chain-ends. The more stable the radical, the more selective it will be toward reaction with monomers, and the larger the tendency of forming the thermodynamically more stable products. As a result, the conditional probabilities for this type of radical to add to another monomer vary significantly. The number of reactive monomer sites producing V and B units is always equal regardless of the VDF content in the monomer feed. Therefore, M

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the ratio of V/B units adding to T, V, and B units might be a good indication of the selectivity of these three reactive radical chain-ends. From Table 5, it can be seen that for poly(VDF-coTFE) (84:16), P(T|V)/P(T|B) (26) ≈ P(V|V)/P(V|B) (18) > P(B|V)/P(B|B) (5). These results indicate that the stabilities of radicals are in order of −CF2CF2• ≈ −CH2CF2• > −CF2CH2•. Similar results were obtained for poly(VDF-co-TFE) (56:44), where P(T|V)/P(T|B) (31) > P(V|V)/P(V|B) (23). Because of the extremely low content of B units in the polymer with this composition, the conditional probability P(B|B) could not be accurately calculated. Unlike the copolymers, for PVDF homopolymer the ratio of P(V|V)/P(V|B)=18 is less than that of P(B|V)/P(B|B) = 44. It is likely that there are larger probabilities of termination between B and V radicals, which could increase the ratio of P(B|V)/P(B|B). There are many factors that could influence the probabilities of monomer addition, including radical stabilities, kinetic vs thermodynamic control of the polymerization, etc., therefore, extra attention is needed to use this method for determining the stabilities of radicals.

§

College of Chemistry, Chemical Engineering and Material Science, Soochow University, Suzhou, China, 215123. Notes

The authors declare the following competing financial interest(s): The work was supported in part by E. I. duPont de Nemours and Co., which produces commercial materials based on the fluoropolymer research samples studied in this paper.

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ACKNOWLEDGMENTS We thank The National Science Foundation (DMR-0905120) and E. I. DuPont de Nemours and Co. for research support; and the NSF (CHE-0341701 and DMR-0414599) for funds used to purchase the NMR instrument used. We thank the staff of University of Akron Magnetic Resonance Center who maintain the equipment used, and made it possible do the experiments.

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CONCLUSIONS In summary, 2D-NMR is an effective method to study the microstructure of poly(VDF-co-TFE), and is especially useful to detect unique signals and assign them to high level sequences. The ability to continuously apply 1H decoupling throughout 19 F detected experiments (and vice versa) provides a great deal of spectral simplification and provides signal enhancement through collapse of multiplets from couplings between 1H and 19 F. 2D-NMR methods involving 19F detection provide enormous spectral dispersion and many valuable J-correlated peaks that help in making new resonance assignments. Triple resonance experiments, 2D-NMR involving decoupling of a third nucleus or 1D-NMR involving decoupling of the other two nuclei, provide a great deal of the spectral simplification needed to unravel the complex spectra of these polymers. Using these methods, most of the peaks in the 19F{1H} spectrum in regions containing resonances of 022/220 sequences and 222 sequences are well resolved from each other and can be assigned to up to 9-carbon sequences. In contrast, difficulties are encountered in resolving and assigning the overlapping signals in the region containing resonances of 020 sequences, therefore these 19F resonances are assigned at a lower sequence level. A variety of methods are available to calculate the composition of poly(VDF-co-TFE) copolymers. Proper selection of these methods is important to obtain accurate results. This study suggests that the internal standard method is preferred to calculate the percentage of reverse VDF units. Statistical methods also make it possible to obtain the conditional probabilities of monomer addition and shed light on the polymerization mechanism.

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ASSOCIATED CONTENT

S Supporting Information *

Figures showing 2D-NMR assignments and tables summarizing 13 C chemical shift assignments are provided. This material is available free of charge via the Internet at http://pubs.acs.org.

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