Monomer Reactivity Ratios for Acrylonitrile–Methyl Acrylate Free-Radical Copolymerization K. B. WILES, V. A. BHANU, A. J. PASQUALE, T. E. LONG, J. E. MCGRATH Department of Chemistry and Materials Research Institute, College of Science, 2109 Hahn Building, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061

Received 9 September 2002; accepted 10 February 2004 DOI: 10.1002/pola.20149 Published online in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: Nonlinear monomer reactivity ratios for the homogeneous free-radical copolymerization of acrylonitrile and methyl acrylate were determined from 1H NMR and real-time Fourier transform infrared (FTIR) analyses. All 1H NMR data were obtained on polymers isolated at low conversions (⬍10%), whereas the FTIR data were collected in situ. The copolymerizations were conducted in N,N-dimethylformamide at 62 °C and were initiated with azobisisobutyronitrile. The real-time FTIR technique allowed for many data points to be collected for each feed composition, which enabled the calculation of copolymer compositions (dM1/dM2) with better accuracy. Monomer reactivity ratios were estimated with the Mayo–Lewis method and then were reﬁned via a nonlinear least-squares analysis ﬁrst suggested by Mortimer and Tidwell. Thus, monomer reactivity ratios at the 95% conﬁdence level were determined to be 1.29 ⫾ 0.2 and 0.96 ⫾ 0.2 for acrylonitrile and methyl acrylate, respectively, which were valid under the speciﬁc system conditions (i.e., solvent and temperature) studied. The results are useful for the development of acrylonitrile (⬍90%) and methyl acrylate, melt-processable copolymer ﬁbers and ﬁlms, including precursors for carbon ﬁbers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2994 –3001, 2004

Keywords: reactivity ratios; acrylonitrile; methyl acrylate; in situ FT-IR; nonlinear analysis

INTRODUCTION Copolymers of acrylonitrile (AN) and minor molar concentrations of alkyl acrylates form the base materials for acrylic textile ﬁbers and for currentgeneration carbon ﬁber precursors.1 Polyacrylonitrile (PAN) is important for ﬁber science and technology because of its combination of economics, physical properties, and aesthetic qualities. It is desirable to introduce comonomers into these materials to enhance solution processability and ﬁber characteristics such as dyability.2 The copolCorrespondence to: J. E. McGrath (E-mail: [email protected] vt.edu) Journal of Polymer Science: Part A: Polymer Chemistry, Vol. 42, 2994 –3001 (2004) © 2004 Wiley Periodicals, Inc.

2994

ymers are prepared by statistical free-radical copolymerizations. At the usual molar concentrations of comonomer (i.e., 3– 6%), semicrystalline transitions approaching 300 °C are still observed, which are well above the PAN degradation temperatures. One motivation for this study was to precisely generate monomer reactivity ratios to better deﬁne concentrations of comonomers that would be required to eliminate minor high-temperature transitions that restrict melt processability. These copolymers are now processed with solvent-based spinning because long-range order causes them to decompose/cyclize below the crystalline melting point (Tm) of about 300 °C (Fig. 1).3–7 The long-range order8 –14 has been very dif-

REACTIVITY RATIOS

2995

Figure 1. Initial intramolecular degradative cyclization of PAN.

ﬁcult to quantify, but it can be disrupted by the efﬁcient utilization of comonomers. The use of a second monomer, like methyl acrylate (MA), interrupts the AN sequences and can reduce and eventually eliminate semicrystallinity. The amorphous copolymer would allow economical and environmentally attractive melt processing at perhaps 200 °C, which is approximately 100 °C above the glass-transition temperature (Tg).15–17 Monomer reactivity ratios for the AN/MA system were ﬁrst reported by Okamura and coworkers.18,19 The Mayo–Lewis method20 for determining reactivity ratios was used where a linear form of the copolymerization equation was used: r 1 ⫽ r 2 共m 1 M22 /m2 M12兲 ⫹ 共M2 /M1 兲关共m1 /m2 兲 ⫺ 1兴 With the equations m1M22/m2M12 and (M2/ M1)[(m1/m2) ⫺ 1] for the slope and intercept, respectively, a plot was produced for a set of experiments, after the copolymer compositions had been determined. The linear lines that were produced on the plot for each experiment, where r1 represented the ordinate and r2 represented the abscissa, intersected at a point on the r1 versus r2 plot. The point where these lines intersected was taken to be r1 and r2 for the system under study. Unfortunately, this method only gave a qualitative observation of the validity of the intersection area. Over the entire range of possible copolymer compositions that were examined, a more compact intersection would have better deﬁned the system. This article describes a kinetic study of the homogeneous copolymerization of AN and MA. The descriptive approach, not mechanistic, of this research was intended to probe the parameters that deﬁne the composition, not the mechanism of propagation that considers penultimate unit effects.21 One objective was to produce precursors of carbon ﬁbers that could be melt-spun. Further objectives of this research were to determine precise statistically signiﬁcant reactivity ratios22–25 for the homogeneous free-radical azobisisobuty-

ronitrile (AIBN) initiated AN/MA copolymer formed in N,N-dimethylformamide (DMF) at a polymerization temperature of 62 °C (Fig. 2). New, real-time Fourier transform infrared (RTFTIR) techniques for determining comonomer disappearance as the reaction proceeds has been discussed by Pasquale and Long,26 which permits quantitative comonomer values to be determined throughout the entire reaction. Moreover, datareduction programs have furthered the precise calculations of rate-constant ratios.27 1H NMR was performed on the isolated copolymers to determine the copolymer compositions. Furthermore, modern, real-time FTIR spectroscopy was used to provide the copolymer information as a function of the disappearance of the comonomers. Both of these data sets were obtained at low conversions of the comonomers. The investigation of existing linear and nonlinear methodologies to calculate monomer reactivity ratios was examined with particular focus on the nonlinear, computer program, data-reduction method of van Herk and coworkers.28,29

Figure 2. Statistical copolymerization of acrylonitrile with methyl acrylate.

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EXPERIMENTAL Materials A ﬂame-dried, 500-mL, three-necked, round-bottom ﬂask with a magnetic stirring bar was ﬁtted with a submerged nitrogen purge, thermocouple, condenser, and rubber septum. The solvent, DMF, obtained from Aldrich (99.9⫹ %, high-pressure liquid chromatography grade), was dried over calcium hydride and was then vacuum-distilled. The free-radical initiator, AIBN, was obtained from Aldrich (mp: 104 °C). The two monomers, AN and MA, were puriﬁed by passing them through an activated alumina column to remove the inhibitor. Reactions For each batch experiment, the monomers and DMF were charged to a ﬂask that had been purged with nitrogen for 20 min at room temperature. The reaction mixture was deoxygenated for 20 min to remove oxygen. The reaction was then submerged in a 62 °C oil bath and was stirred. The AIBN was dissolved in 5 mL of DMF and added to the reaction ﬂask once the solution reached 62 °C. The reactions were investigated with systematically varied concentrations of AN and MA. The concentration of DMF was held constant at 80 wt % relative to the monomers. The concentration of initiator, AIBN, was 0.5 mol % relative to the monomers throughout the study. Each reaction was polymerized until less than 10% monomer conversion was reached, where the reactions were quenched by cooling in an ice bath. The polymers were precipitated into an excess of water and then were vacuum-ﬁltered onto preweighed ﬁlter paper. The copolymer cake was washed three times with methanol to remove any remaining monomer. The ﬁlter paper and polymer were then dried in vacuo at 70 °C. The percentage of conversion of the polymer was calculated by weighing the dried polymer and ﬁlter paper. Characterization 1

H NMR samples were dissolved in deuterated dimethyl sulfoxide and analyses were performed at room temperature. 1H NMR experiments were conducted with a JEOL Eclipse ⫹500 NMR operating at 500.159 MHz. This produced well-resolved peaks corresponding to the methyl group

Figure 3. Real-time FTIR spectra of AN, MA, and DMF.

on the MA and the methylene groups on both the AN and MA monomers in the copolymer. The integrals of these peaks were used to calculate the copolymer composition. RT-FTIR experiments were performed in situ. The RT-FTIR experiments were performed with an Applied Systems, Inc. ReactIR 1000. The apparatus used for these experiments was identical to that described previously in the Experimental, but instead of the rubber septum on the threenecked ﬂask, an RT-FTIR probe was placed into the reaction vessel. The probe was submerged in the solution, and data were collected beginning at the time the AIBN was added until 10% conversion. The disappearance of AN was monitored quantitatively by measuring the absorbance at 690 cm⫺1, and a two-point baseline was used from 680 to 715 cm⫺1 to determine the decrease in the area under the peak. The disappearance of MA was monitored by noting the absorption at 814 cm⫺1, and a two-point baseline was used from 790 to 832 cm⫺1. The MA and AN absorbencies were well resolved from each other and also resolved from DMF (Fig. 3).

RESULTS AND DISCUSSION The monomer reactivity ratios for the AN/MA system were determined with two different analytical techniques: (1) in situ, real-time FTIR analyses and (2) 1H NMR of copolymers isolated at early conversions. The in situ FTIR technique is a recent development for monitoring polymerizations that allows rapid accumulation of differential copolymerization data. This enables one to

REACTIVITY RATIOS

Figure 4.

2997

1

H NMR spectrum of an AN/MA (85/15 mol %) copolymer.

record many copolymer composition points at the required low conversions (e.g., up to ca. 10% conversion), and hence, accurate kinetic constants can be obtained with a minimum of experiments. The disappearance of the comonomers can quantitatively be measured with respect to the initial absorption intensities for the two monomers in solution. The decrease in the normalized areas under the peaks for the two comonomers can be directly related to the copolymer compositions.29 This in situ analytical methodology afforded a procedure for recording compositional data at a consistent extent of conversion (10%). For this technique, isolation of the copolymer was not required, and the process of following the reaction was quick and accurate. The alternative, and classical, approach for acquiring copolymer data was to isolate the copolymers from each of 17 feed compositions at early conversions and analyze the copolymer compositions by 1H NMR. This technique included the isolation and drying of each copolymer. The 1H NMR spectrum of an 85/15 mol % AN/MA copolymer (Fig. 4) identiﬁed the methyl protons on the MA monomer and the methylene protons on both the MA and AN monomers. The 17 different charge ratios that were investigated and the results of the 1H NMR copolymer composition measurements provided the database for the kinetic monomer reactivity ratio calculations (Fig. 5). Various statistical treatments of the feed and copolymer compositions can be used to determine monomer reactivity ratios. The nonlinear methodology used selected values of r1 and r2, where

the sum of the squares of the differences between the observed and the computed polymer compositions was minimized. With this criterion for the nonlinear least-squares method of analysis, the values for the monomer reactivity ratios were unique for a given set of data. The program produces monomer reactivity ratios for the monomers in the system with a 95% joint conﬁdence limit determination. The joint conﬁdence limit is a quantitative estimation of the validity of the results of the experiments and the calculations performed. This method of data analysis consists of obtaining initial estimates of the monomer reactivity ratios for the system and experimental data of comonomer charge amounts and comonomer amounts that have been incorporated into the copolymer, both in molar fractions. Many repeated sets of calculations were performed by the processor, which rapidly determines a pair of monomer reactivity ratios that ﬁt the criterion where the value of the sum of the squares of the differences between the observed polymer composition and the computed polymer composition was minimized. The terminal model30,31 for free-radical copolymerization is based on the steady-state approximation.32,33 This approximation assumes a steadystate concentration of free radicals because the rate of initiation (Ri) is equivalent to the rate of termination (Rt). The monomers in the reaction vessel disappeared in four different ways during copolymerization of two different monomer species. The required four equations to deﬁne the system are the following:

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Figure 5. Molar fraction of AN in the feed versus molar fraction of AN in the copolymer calculated from data at less than 10% monomer conversion.

k11

M1䡠 ⫹ M1 O ¡ k12

M1䡠 ⫹ M2 O ¡ k22

M2䡠 ⫹ M2 O ¡ k21

M2䡠 ⫹ M1 O ¡

M 1䡠

(1)

M 2䡠

(2)

M 2䡠

(3)

M 1䡠

(4)

tration of monomer 2 relative to an instantaneous time: ⫺d[M1]/dt ⫽ k11[

Equation 1 shows the disappearance of monomer 1 adding to the growing radical chain that ends with monomer one. This reaction produces a new growing radical chain that ends with monomer 1. Equation 2 shows monomer 2 adding to a growing radical chain that ends in monomer 1. The new growing radical chain that is produced ends in monomer 2. The third and fourth equations show the disappearance of monomer 2 and monomer 1 as they add to a growing radical chain that ends with monomer 2. The rate constants for each equation are deﬁned as the rate of addition for each monomer to add to a growing radical chain that ends in either monomer 1 or monomer 2. Differential equations, which are based on an instantaneous time, can be drawn from these reaction equations and determined to be the change in the concentration of monomer 1 relative to an instantaneous time and the change in the concen-

M*1][M1] ⫹ k21[

⫺d[M2]/dt ⫽ k12 关

M*2][M1]

(5)

M*2][M2]

(6)

M*1][M2] ⫹ k22[

Dividing eq 5 by 6 gives a form of the copolymer equation d[M1] [M1](r1[M1] ⫹ [M2]) ⫽ d[M2] [M2]([M1] ⫹ r2[M2])

(7)

Manipulation of eq 7 and transforming the concentrations into the molar fractions then express the copolymer equation in a more usable form:34 F1 ⫽

共r 1 f 12 ⫹ f 1 f 2 兲 共r 1 f 12 ⫹ 2f 1 f 2 ⫹ r 2 f 22 兲

(8)

The monomer reactivity ratio coefﬁcients are deﬁned with the rate constants from eqs 1– 4:22 r 1 ⫽ k 11 /k 12

and r2 ⫽ k22 /k21

(9)

Several different subsets can be deﬁned for the monomer reactivity ratio coefﬁcients. For a perfectly random copolymerization to occur, the re-

REACTIVITY RATIOS

2999

Figure 6. Mortimer–Tidwell monomer reactivity ratios of AN and MA showing a 95% joint conﬁdence limit determined from limited 1H NMR data.

activity ratios of both monomers need to be equal to a value of one (r1 ⬃ r2 ⬃ 1). For this type of reaction, the propagating radical has the same preference for both of the monomers and therefore produces a perfectly random incorporation of both types of monomers. Furthermore, an alternating copolymerization is produced when both monomer reactivity ratios are equal to zero (r1 ⬃ r2 ⬃ 0). Nonrandom equal molar amounts of the two monomers enter into the copolymer thereby producing an alternating structure. When both monomer reactivity ratios are greater than a value of one, both monomers add to themselves. This, in theory, produces block copolymers but in actuality produces larger sequences of similar monomers throughout the entire polymer chain. The literature values of the monomer reactivity ratios for AN and MA are 1.54 for AN and 0.844 for MA.18,19,35 In general, many different methods have been used to calculate monomer reactivity ratios,36,20,37,38 which include the approximation method, intersection method, linearization method, and the curve-ﬁtting method. Tidwell and Mortimer32 produced a nonlinear least-squares method that allowed rigorous applications of statistical analysis for reactivity ratios r1 and r2. This method is a modiﬁcation or extension of the curve-ﬁtting model and allows the calculations to be quantitatively analyzed. Extensive calculations are needed, but a computer pro-

gram by van Herk permits rapid data analysis of the nonlinear calculations.27,28 The data obtained from the isolation of the copolymer and subsequent 1H NMR experiments were converted into the molar fraction of the comonomer for AN in the feed and the molar fraction of the comonomer AN that was incorporated into the copolymer. Then, theoretical values of the molar fraction of the incorporated monomer (F1) were determined, and the difference of this value and the actual value was calculated. The molar fraction of the comonomer AN, the molar fraction of the incorporated comonomer AN, and the difference of the experimental F1 and theoretical F1 were entered into the computer program, and nonlinear monomer reactivity ratio calculations were conducted. A monomer reactivity ratio plot with a 95% joint conﬁdence limit was produced for the 17 copolymers that were isolated. The reactivity ratios were 1.29 for AN and 0.96 for MA (Fig. 6). The scale shown on the plot indicates that, unfortunately, on the basis of the experimental data, at 95% conﬁdence, the monomer reactivity ratios should fall within the relatively large ellipse. Therefore, the values could be ⫹1.0 and ⫺0.2. The RT-FTIR monitoring of AN and MA conversion determined 171 copolymer composition data points. The disappearance of the MA monomer relative to time at 814 cm⫺1 is observed in Figure 7. The raw data generated from the in situ

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Figure 7. Decrease of the MA double bond at 814 cm⫺1 during copolymerization via real-time FTIR.

FTIR probe were normalized and then converted into moles of the incorporated comonomers.39 From these data, the molar fractions of the comonomers incorporated into the copolymer were calculated. These values were then entered into the computer program, and a monomer reactivity ratio plot with 95% joint conﬁdence limit was produced with 171 copolymer composition data points. The monomer reactivity ratios were determined to be 1.29 for AN and 0.96 for MA (Fig. 8), which are the same values as determined by the isolated copolymers. The dif-

ference in this plot was a more highly reﬁned 95% joint conﬁdence limit. Thus, the values were determined to be ⫾0.2 for both AN and MA, which indicated improved accuracy in the monomer reactivity ratio calculations.

CONCLUSIONS Monomer reactivity ratios for the copolymerization of AN and MA at 62 °C in DMF were deter-

Figure 8. Mortimer–Tidwell monomer reactivity ratios for AN and MA copolymerization determined from real-time FTIR.

REACTIVITY RATIOS

mined by a nonlinear least-squares method. Two complimentary methods, 1H NMR and RT-FTIR, were used to establish copolymer compositions for the nonlinear least-squares analyses. The RTFTIR method allowed for improved accuracy because of a 10-fold increase in data points. The AN and MA monomer reactivity ratios were 1.29 ⫾ 0.2 and 0.96 ⫾ 0.2, respectively, which are valid under the speciﬁc system examined. By contrast, the 1H NMR approach with isolated copolymer composition data was less accurate (rAN ⫽ 1.29 ⫹1.0/⫺0.2; rMA ⫽ 0.96 ⫹1.0/⫺0.2). The authors are grateful for the ﬁnancial support of the Department of Energy under contract Subc. 4500011036. The authors also thank the Omnova Foundation for their generous fellowship support.

REFERENCES AND NOTES 1. Bajaj, P. Manufactured Fibre Technology; Chapman & Hall: London, 1997. 2. Dalin, A.; Kolchin, I. K.; Serebryakov, B. R. Acrylonitrile; Technomic: Westport, CT, 1971; Vol. VI. 3. Edie, D. D. Carbon 1998, 36, 345–362. 4. Gupta, A. K.; Paliwal, D. K.; Bajaj, P. J Appl Polym Sci 1998, 70, 2703–2709. 5. Frushour, B. G. Polym Bull 1984, 11, 375. 6. Grove, D.; Desai, P.; Abhiraman, A. S. Carbon 1988, 26, 403. 7. Dalton, S.; Heatley, F.; Budd, P. M. Polymer 1999, 40, 5531–5543. 8. Bajaj, P. Polymer 2001, 42, 1707–1718. 9. Gupta, A. K.; Chand, N. Eur Polym J 1979, 15. 10. Grassie, N.; McGuchan, R. Eur Polym J 1972, 8, 257. 11. Gupta, A. K.; Singhal, R. P. J Appl Polym Sci 1983, 21, 2243. 12. Gupta, A. K.; Singhal, R. P.; Bajaj, P. J Appl Polym Sci 1983, 28, 1167. 13. Bajaj, P.; Padmanabhan, M. Eur Polym J 1984, 20. 14. Gupta, A. K.; Paliwal, D. K.; Bajaj, P. J Appl Polym Sci 1995, 58, 1161. 15. Yang, J.; Banthia, A. K.; Godshall, D.; Rangarayan, P.; Wilkes, G. L.; Baird, D. G.; McGrath, J. E. Polym Prepr (Am Chem Soc Div Polym Chem) 2000, 41. 16. Bhanu, V. A.; Rangarayan, P.; Wiles, K. B.; Bortner, M.; Sankarpandian, M.; Godshall, D.; Glass,

17.

18. 19. 20. 21. 22. 23. 24. 25.

26. 27. 28. 29.

30. 31. 32. 33. 34. 35. 36. 37. 38. 39.

3001

T. E.; Banthia, A. K.; Yang, J.; Wilkes, G. L.; Baird, D. G.; McGrath, J. E. Polymer 2002, 43, 2699 – 2709. Rangarayan, P.; Yang, J.; Bhanu, V. A.; Godshall, D.; Wilkes, G. L.; McGrath, J. E.; Baird, D. G. J Appl Polym Sci 2002, 85, 69 – 83. Okamura, S.; Yamashita, T. J. Soc Textile Cellulose Ind Jpn 1953, 9, 444. Marvel, C. S.; Schwen, R. J Am Chem Soc 1957, 79, 6003. Mayo, F. R.; Lewis, F. M. J Am Chem Soc 1944, 66, 1594. Coote, M. L.; Davis, T. P.; Radom, L. Macromolecules 1999, 32, 2935–2940. Davis, T. P. J Polym Sci Part A: Polym Chem 2001, 39, 597. Polic, A. L.; Duever, T. A.; Penlidis, A. J Polym Sci Part A: Polym Chem 1998, 36, 813– 822. Hill, D. J. T.; Lang, A. P.; O’Donnell, J. H. Eur Polym J 1991, 27, 765–772. Jenkins, A. D.; Ledwith, A. Reactivity, Mechanism and Structure in Polymer Chemistry; Wiley-Interscience: New York, 1974; Vol. 117–170. Pasquale, A. J.; Long, T. E. Macromolecules 1999, 32, 7954 –7957. van Herk, A. M.; Manders, B. G.; Smulders, W.; Aerdts, A. Macromolecules 1997, 30, 322–323. van Herk, A. M. J Chem Educ 1995, 72, 138. Wiles, K. B.; Bhanu, V. A.; Pasquale, A. J.; Long, T. E.; McGrath, J. E. Polym Prepr (Am Chem Soc Div Polym Chem) 2001, 41, 608. Bauduin, G.; Boutevin, B.; Meghabar, R.; Belbachir, M. Makromol Chem 1990, 191, 2767. Hill, D. J. T.; Lang, A. P.; O’Donnell, J. H.; O’Sullivan, P. W. Eur Polym J 1989, 25, 911. Tidwell, P. W.; Mortimer, G. A. J Polym Sci Part A: Gen Pap 1965, 3, 369. Hagiopol, C.; Frangu, O.; Dumitru. J Macromol Sci Chem 1989, 26, 1363. Odian, G. Principles of Polymerization; Wiley: New York, 1991. Greenley, R. Z. Polymer Handbook Part II, 3rd ed.; Wiley: New York, 1989. Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953. Finemann, M.; Ross, S. D. J Polym Sci 1950, 5, 259. Alfrey, T.; Bohrer, J. J.; Mark, H. Copolymerization; Interscience: New York, 1952. Wiles, K. B. MS Thesis, Chemistry, Virginia Polytechnic Institute and State University, Blacksburg, 2002.

Received 9 September 2002; accepted 10 February 2004 DOI: 10.1002/pola.20149 Published online in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: Nonlinear monomer reactivity ratios for the homogeneous free-radical copolymerization of acrylonitrile and methyl acrylate were determined from 1H NMR and real-time Fourier transform infrared (FTIR) analyses. All 1H NMR data were obtained on polymers isolated at low conversions (⬍10%), whereas the FTIR data were collected in situ. The copolymerizations were conducted in N,N-dimethylformamide at 62 °C and were initiated with azobisisobutyronitrile. The real-time FTIR technique allowed for many data points to be collected for each feed composition, which enabled the calculation of copolymer compositions (dM1/dM2) with better accuracy. Monomer reactivity ratios were estimated with the Mayo–Lewis method and then were reﬁned via a nonlinear least-squares analysis ﬁrst suggested by Mortimer and Tidwell. Thus, monomer reactivity ratios at the 95% conﬁdence level were determined to be 1.29 ⫾ 0.2 and 0.96 ⫾ 0.2 for acrylonitrile and methyl acrylate, respectively, which were valid under the speciﬁc system conditions (i.e., solvent and temperature) studied. The results are useful for the development of acrylonitrile (⬍90%) and methyl acrylate, melt-processable copolymer ﬁbers and ﬁlms, including precursors for carbon ﬁbers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2994 –3001, 2004

Keywords: reactivity ratios; acrylonitrile; methyl acrylate; in situ FT-IR; nonlinear analysis

INTRODUCTION Copolymers of acrylonitrile (AN) and minor molar concentrations of alkyl acrylates form the base materials for acrylic textile ﬁbers and for currentgeneration carbon ﬁber precursors.1 Polyacrylonitrile (PAN) is important for ﬁber science and technology because of its combination of economics, physical properties, and aesthetic qualities. It is desirable to introduce comonomers into these materials to enhance solution processability and ﬁber characteristics such as dyability.2 The copolCorrespondence to: J. E. McGrath (E-mail: [email protected] vt.edu) Journal of Polymer Science: Part A: Polymer Chemistry, Vol. 42, 2994 –3001 (2004) © 2004 Wiley Periodicals, Inc.

2994

ymers are prepared by statistical free-radical copolymerizations. At the usual molar concentrations of comonomer (i.e., 3– 6%), semicrystalline transitions approaching 300 °C are still observed, which are well above the PAN degradation temperatures. One motivation for this study was to precisely generate monomer reactivity ratios to better deﬁne concentrations of comonomers that would be required to eliminate minor high-temperature transitions that restrict melt processability. These copolymers are now processed with solvent-based spinning because long-range order causes them to decompose/cyclize below the crystalline melting point (Tm) of about 300 °C (Fig. 1).3–7 The long-range order8 –14 has been very dif-

REACTIVITY RATIOS

2995

Figure 1. Initial intramolecular degradative cyclization of PAN.

ﬁcult to quantify, but it can be disrupted by the efﬁcient utilization of comonomers. The use of a second monomer, like methyl acrylate (MA), interrupts the AN sequences and can reduce and eventually eliminate semicrystallinity. The amorphous copolymer would allow economical and environmentally attractive melt processing at perhaps 200 °C, which is approximately 100 °C above the glass-transition temperature (Tg).15–17 Monomer reactivity ratios for the AN/MA system were ﬁrst reported by Okamura and coworkers.18,19 The Mayo–Lewis method20 for determining reactivity ratios was used where a linear form of the copolymerization equation was used: r 1 ⫽ r 2 共m 1 M22 /m2 M12兲 ⫹ 共M2 /M1 兲关共m1 /m2 兲 ⫺ 1兴 With the equations m1M22/m2M12 and (M2/ M1)[(m1/m2) ⫺ 1] for the slope and intercept, respectively, a plot was produced for a set of experiments, after the copolymer compositions had been determined. The linear lines that were produced on the plot for each experiment, where r1 represented the ordinate and r2 represented the abscissa, intersected at a point on the r1 versus r2 plot. The point where these lines intersected was taken to be r1 and r2 for the system under study. Unfortunately, this method only gave a qualitative observation of the validity of the intersection area. Over the entire range of possible copolymer compositions that were examined, a more compact intersection would have better deﬁned the system. This article describes a kinetic study of the homogeneous copolymerization of AN and MA. The descriptive approach, not mechanistic, of this research was intended to probe the parameters that deﬁne the composition, not the mechanism of propagation that considers penultimate unit effects.21 One objective was to produce precursors of carbon ﬁbers that could be melt-spun. Further objectives of this research were to determine precise statistically signiﬁcant reactivity ratios22–25 for the homogeneous free-radical azobisisobuty-

ronitrile (AIBN) initiated AN/MA copolymer formed in N,N-dimethylformamide (DMF) at a polymerization temperature of 62 °C (Fig. 2). New, real-time Fourier transform infrared (RTFTIR) techniques for determining comonomer disappearance as the reaction proceeds has been discussed by Pasquale and Long,26 which permits quantitative comonomer values to be determined throughout the entire reaction. Moreover, datareduction programs have furthered the precise calculations of rate-constant ratios.27 1H NMR was performed on the isolated copolymers to determine the copolymer compositions. Furthermore, modern, real-time FTIR spectroscopy was used to provide the copolymer information as a function of the disappearance of the comonomers. Both of these data sets were obtained at low conversions of the comonomers. The investigation of existing linear and nonlinear methodologies to calculate monomer reactivity ratios was examined with particular focus on the nonlinear, computer program, data-reduction method of van Herk and coworkers.28,29

Figure 2. Statistical copolymerization of acrylonitrile with methyl acrylate.

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EXPERIMENTAL Materials A ﬂame-dried, 500-mL, three-necked, round-bottom ﬂask with a magnetic stirring bar was ﬁtted with a submerged nitrogen purge, thermocouple, condenser, and rubber septum. The solvent, DMF, obtained from Aldrich (99.9⫹ %, high-pressure liquid chromatography grade), was dried over calcium hydride and was then vacuum-distilled. The free-radical initiator, AIBN, was obtained from Aldrich (mp: 104 °C). The two monomers, AN and MA, were puriﬁed by passing them through an activated alumina column to remove the inhibitor. Reactions For each batch experiment, the monomers and DMF were charged to a ﬂask that had been purged with nitrogen for 20 min at room temperature. The reaction mixture was deoxygenated for 20 min to remove oxygen. The reaction was then submerged in a 62 °C oil bath and was stirred. The AIBN was dissolved in 5 mL of DMF and added to the reaction ﬂask once the solution reached 62 °C. The reactions were investigated with systematically varied concentrations of AN and MA. The concentration of DMF was held constant at 80 wt % relative to the monomers. The concentration of initiator, AIBN, was 0.5 mol % relative to the monomers throughout the study. Each reaction was polymerized until less than 10% monomer conversion was reached, where the reactions were quenched by cooling in an ice bath. The polymers were precipitated into an excess of water and then were vacuum-ﬁltered onto preweighed ﬁlter paper. The copolymer cake was washed three times with methanol to remove any remaining monomer. The ﬁlter paper and polymer were then dried in vacuo at 70 °C. The percentage of conversion of the polymer was calculated by weighing the dried polymer and ﬁlter paper. Characterization 1

H NMR samples were dissolved in deuterated dimethyl sulfoxide and analyses were performed at room temperature. 1H NMR experiments were conducted with a JEOL Eclipse ⫹500 NMR operating at 500.159 MHz. This produced well-resolved peaks corresponding to the methyl group

Figure 3. Real-time FTIR spectra of AN, MA, and DMF.

on the MA and the methylene groups on both the AN and MA monomers in the copolymer. The integrals of these peaks were used to calculate the copolymer composition. RT-FTIR experiments were performed in situ. The RT-FTIR experiments were performed with an Applied Systems, Inc. ReactIR 1000. The apparatus used for these experiments was identical to that described previously in the Experimental, but instead of the rubber septum on the threenecked ﬂask, an RT-FTIR probe was placed into the reaction vessel. The probe was submerged in the solution, and data were collected beginning at the time the AIBN was added until 10% conversion. The disappearance of AN was monitored quantitatively by measuring the absorbance at 690 cm⫺1, and a two-point baseline was used from 680 to 715 cm⫺1 to determine the decrease in the area under the peak. The disappearance of MA was monitored by noting the absorption at 814 cm⫺1, and a two-point baseline was used from 790 to 832 cm⫺1. The MA and AN absorbencies were well resolved from each other and also resolved from DMF (Fig. 3).

RESULTS AND DISCUSSION The monomer reactivity ratios for the AN/MA system were determined with two different analytical techniques: (1) in situ, real-time FTIR analyses and (2) 1H NMR of copolymers isolated at early conversions. The in situ FTIR technique is a recent development for monitoring polymerizations that allows rapid accumulation of differential copolymerization data. This enables one to

REACTIVITY RATIOS

Figure 4.

2997

1

H NMR spectrum of an AN/MA (85/15 mol %) copolymer.

record many copolymer composition points at the required low conversions (e.g., up to ca. 10% conversion), and hence, accurate kinetic constants can be obtained with a minimum of experiments. The disappearance of the comonomers can quantitatively be measured with respect to the initial absorption intensities for the two monomers in solution. The decrease in the normalized areas under the peaks for the two comonomers can be directly related to the copolymer compositions.29 This in situ analytical methodology afforded a procedure for recording compositional data at a consistent extent of conversion (10%). For this technique, isolation of the copolymer was not required, and the process of following the reaction was quick and accurate. The alternative, and classical, approach for acquiring copolymer data was to isolate the copolymers from each of 17 feed compositions at early conversions and analyze the copolymer compositions by 1H NMR. This technique included the isolation and drying of each copolymer. The 1H NMR spectrum of an 85/15 mol % AN/MA copolymer (Fig. 4) identiﬁed the methyl protons on the MA monomer and the methylene protons on both the MA and AN monomers. The 17 different charge ratios that were investigated and the results of the 1H NMR copolymer composition measurements provided the database for the kinetic monomer reactivity ratio calculations (Fig. 5). Various statistical treatments of the feed and copolymer compositions can be used to determine monomer reactivity ratios. The nonlinear methodology used selected values of r1 and r2, where

the sum of the squares of the differences between the observed and the computed polymer compositions was minimized. With this criterion for the nonlinear least-squares method of analysis, the values for the monomer reactivity ratios were unique for a given set of data. The program produces monomer reactivity ratios for the monomers in the system with a 95% joint conﬁdence limit determination. The joint conﬁdence limit is a quantitative estimation of the validity of the results of the experiments and the calculations performed. This method of data analysis consists of obtaining initial estimates of the monomer reactivity ratios for the system and experimental data of comonomer charge amounts and comonomer amounts that have been incorporated into the copolymer, both in molar fractions. Many repeated sets of calculations were performed by the processor, which rapidly determines a pair of monomer reactivity ratios that ﬁt the criterion where the value of the sum of the squares of the differences between the observed polymer composition and the computed polymer composition was minimized. The terminal model30,31 for free-radical copolymerization is based on the steady-state approximation.32,33 This approximation assumes a steadystate concentration of free radicals because the rate of initiation (Ri) is equivalent to the rate of termination (Rt). The monomers in the reaction vessel disappeared in four different ways during copolymerization of two different monomer species. The required four equations to deﬁne the system are the following:

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Figure 5. Molar fraction of AN in the feed versus molar fraction of AN in the copolymer calculated from data at less than 10% monomer conversion.

k11

M1䡠 ⫹ M1 O ¡ k12

M1䡠 ⫹ M2 O ¡ k22

M2䡠 ⫹ M2 O ¡ k21

M2䡠 ⫹ M1 O ¡

M 1䡠

(1)

M 2䡠

(2)

M 2䡠

(3)

M 1䡠

(4)

tration of monomer 2 relative to an instantaneous time: ⫺d[M1]/dt ⫽ k11[

Equation 1 shows the disappearance of monomer 1 adding to the growing radical chain that ends with monomer one. This reaction produces a new growing radical chain that ends with monomer 1. Equation 2 shows monomer 2 adding to a growing radical chain that ends in monomer 1. The new growing radical chain that is produced ends in monomer 2. The third and fourth equations show the disappearance of monomer 2 and monomer 1 as they add to a growing radical chain that ends with monomer 2. The rate constants for each equation are deﬁned as the rate of addition for each monomer to add to a growing radical chain that ends in either monomer 1 or monomer 2. Differential equations, which are based on an instantaneous time, can be drawn from these reaction equations and determined to be the change in the concentration of monomer 1 relative to an instantaneous time and the change in the concen-

M*1][M1] ⫹ k21[

⫺d[M2]/dt ⫽ k12 关

M*2][M1]

(5)

M*2][M2]

(6)

M*1][M2] ⫹ k22[

Dividing eq 5 by 6 gives a form of the copolymer equation d[M1] [M1](r1[M1] ⫹ [M2]) ⫽ d[M2] [M2]([M1] ⫹ r2[M2])

(7)

Manipulation of eq 7 and transforming the concentrations into the molar fractions then express the copolymer equation in a more usable form:34 F1 ⫽

共r 1 f 12 ⫹ f 1 f 2 兲 共r 1 f 12 ⫹ 2f 1 f 2 ⫹ r 2 f 22 兲

(8)

The monomer reactivity ratio coefﬁcients are deﬁned with the rate constants from eqs 1– 4:22 r 1 ⫽ k 11 /k 12

and r2 ⫽ k22 /k21

(9)

Several different subsets can be deﬁned for the monomer reactivity ratio coefﬁcients. For a perfectly random copolymerization to occur, the re-

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2999

Figure 6. Mortimer–Tidwell monomer reactivity ratios of AN and MA showing a 95% joint conﬁdence limit determined from limited 1H NMR data.

activity ratios of both monomers need to be equal to a value of one (r1 ⬃ r2 ⬃ 1). For this type of reaction, the propagating radical has the same preference for both of the monomers and therefore produces a perfectly random incorporation of both types of monomers. Furthermore, an alternating copolymerization is produced when both monomer reactivity ratios are equal to zero (r1 ⬃ r2 ⬃ 0). Nonrandom equal molar amounts of the two monomers enter into the copolymer thereby producing an alternating structure. When both monomer reactivity ratios are greater than a value of one, both monomers add to themselves. This, in theory, produces block copolymers but in actuality produces larger sequences of similar monomers throughout the entire polymer chain. The literature values of the monomer reactivity ratios for AN and MA are 1.54 for AN and 0.844 for MA.18,19,35 In general, many different methods have been used to calculate monomer reactivity ratios,36,20,37,38 which include the approximation method, intersection method, linearization method, and the curve-ﬁtting method. Tidwell and Mortimer32 produced a nonlinear least-squares method that allowed rigorous applications of statistical analysis for reactivity ratios r1 and r2. This method is a modiﬁcation or extension of the curve-ﬁtting model and allows the calculations to be quantitatively analyzed. Extensive calculations are needed, but a computer pro-

gram by van Herk permits rapid data analysis of the nonlinear calculations.27,28 The data obtained from the isolation of the copolymer and subsequent 1H NMR experiments were converted into the molar fraction of the comonomer for AN in the feed and the molar fraction of the comonomer AN that was incorporated into the copolymer. Then, theoretical values of the molar fraction of the incorporated monomer (F1) were determined, and the difference of this value and the actual value was calculated. The molar fraction of the comonomer AN, the molar fraction of the incorporated comonomer AN, and the difference of the experimental F1 and theoretical F1 were entered into the computer program, and nonlinear monomer reactivity ratio calculations were conducted. A monomer reactivity ratio plot with a 95% joint conﬁdence limit was produced for the 17 copolymers that were isolated. The reactivity ratios were 1.29 for AN and 0.96 for MA (Fig. 6). The scale shown on the plot indicates that, unfortunately, on the basis of the experimental data, at 95% conﬁdence, the monomer reactivity ratios should fall within the relatively large ellipse. Therefore, the values could be ⫹1.0 and ⫺0.2. The RT-FTIR monitoring of AN and MA conversion determined 171 copolymer composition data points. The disappearance of the MA monomer relative to time at 814 cm⫺1 is observed in Figure 7. The raw data generated from the in situ

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Figure 7. Decrease of the MA double bond at 814 cm⫺1 during copolymerization via real-time FTIR.

FTIR probe were normalized and then converted into moles of the incorporated comonomers.39 From these data, the molar fractions of the comonomers incorporated into the copolymer were calculated. These values were then entered into the computer program, and a monomer reactivity ratio plot with 95% joint conﬁdence limit was produced with 171 copolymer composition data points. The monomer reactivity ratios were determined to be 1.29 for AN and 0.96 for MA (Fig. 8), which are the same values as determined by the isolated copolymers. The dif-

ference in this plot was a more highly reﬁned 95% joint conﬁdence limit. Thus, the values were determined to be ⫾0.2 for both AN and MA, which indicated improved accuracy in the monomer reactivity ratio calculations.

CONCLUSIONS Monomer reactivity ratios for the copolymerization of AN and MA at 62 °C in DMF were deter-

Figure 8. Mortimer–Tidwell monomer reactivity ratios for AN and MA copolymerization determined from real-time FTIR.

REACTIVITY RATIOS

mined by a nonlinear least-squares method. Two complimentary methods, 1H NMR and RT-FTIR, were used to establish copolymer compositions for the nonlinear least-squares analyses. The RTFTIR method allowed for improved accuracy because of a 10-fold increase in data points. The AN and MA monomer reactivity ratios were 1.29 ⫾ 0.2 and 0.96 ⫾ 0.2, respectively, which are valid under the speciﬁc system examined. By contrast, the 1H NMR approach with isolated copolymer composition data was less accurate (rAN ⫽ 1.29 ⫹1.0/⫺0.2; rMA ⫽ 0.96 ⫹1.0/⫺0.2). The authors are grateful for the ﬁnancial support of the Department of Energy under contract Subc. 4500011036. The authors also thank the Omnova Foundation for their generous fellowship support.

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