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1 School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332. 2 Department of Industrial and Manufacturing Engineering, High-Performance Materials Institute, Florida State. University, Tallahassee ...
Investigation of Polyacrylonitrile Solution Inhomogeneity by Dynamic Light Scattering Vijay Raghavan,1 Murari Gupta,2 Zhiwei Xiao,2 Han Gi Chae,1 Tao Liu,2 Satish Kumar1 School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332 2 Department of Industrial and Manufacturing Engineering, High-Performance Materials Institute, Florida State University, Tallahassee, Florida 32310

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Dynamic light scattering (DLS) has been used to quantify nanoscale heterogeneity in the industrially significant polyacrylonitrile (PAN) polymer solution. The heterogeneity in polymer solution, traced by the ratio of amplitudes of the slow to fast mode, is observed to be related to various parameters, such as molecular weight of the polymer, the type of co-monomer, processing time, concentration of the solution, and the choice of the solvents. It has been identified that low molecular weight PAN homopolymer have the least heterogeneity issues. Amongst the chosen co-polymers for this study, similar degree of heterogeneity was observed at concentration slightly above the critical concentration at which the polymer chains begin to overlap. Whereas, at higher concentration, PANmethacrylic acid (4 wt%) copolymer showed the least heterogeneity issue. The aggregate diffusion coefficient of PAN-methacrylic acid (4 wt%) copolymer solution in dimethylformamide (DMF) and N,N-dimethylacetamide (DMAc) are respectively determined to be 1.6 3 10212 cm2/s and 1.6 3 10213 cm2/s, which results in an estimated aggregate size of 9 nm and 90 nm. POLYM. ENG. SCI., 55:1403– C 2015 Society of Plastics Engineers 1407, 2015. V

INTRODUCTION

Dynamic light scattering (DLS) has been extensively used to study the dynamics and relaxation behavior of polymer chains [1–9] and to measure the particle size of various colloids [10]. Unlike simple colloidal particles, the decay rate distribution functions of most polymer solutions in semidilute regime often shows two relaxation modes, namely fast and slow modes. The interpretation of fast mode is straight forward. The fast mode originates from the cooperative diffusion of polymer chains. It is related to the density/concentration fluctuation of polymer segments within the correlation blobs of a given correlation length n. The correlation length n is defined as [11, 12]: n5kT=ð6pgDÞ;

(1)

where g is the viscosity of the solvent, and D is the cooperative diffusion coefficient that can be determined by dynamic light scattering measurement and is given by D5C=q2

(2)

where C is the delay rate of the fast relaxation mode at a scattering vector q. q is related to the length scale that can be

probed [13] and is inversely proportional to the wavelength of the laser and directly proportional to the sine of the one half of the scattering angle. The origin of the slow mode has been attributed to a variety of reasons such as long range density/concentration fluctuation of polymer segments in the transient network [14], temporal or permanent aggregates [15], dust particles and artifacts in solution preparation [2, 16, 17]. Sedla’k ruled out the ascription of slow mode to dust particles by demonstrating that in polyelectrloyte solution, the absolute scattering intensity associated with the slow mode increases upon decreasing ionic strength [18]. Li et al. recently ascribed the origin of the slow mode to heterogeneity in the polymer solution [19, 20]. To elaborate, when the polymer concentration (C) is lower than the entanglement concentration (Ce), the slow mode is attributed to the large or temporal polymer chain clusters or aggregates which have the same microenvironment, but different sizes. At polymer concentration C > Ce, the manifestation of slow mode is due to the overlap and entanglement of chains with each other leading to the restricted interaction of polymer chains near the entanglement points. The versatility of DLS over other techniques for quality control of colloidal materials in the industrial application is well known. However, in view of confusion over the interpretation of the slow mode, the application of DLS as a tool for the quality control of the polymer solution in industries, especially to assess the heterogeneity of the polymer solution has been limited. Polyacrylonitrile (PAN) polymers are of great interest because they are currently the predominant precursor for producing carbon fiber [21–25]. In the due course, PAN polymer solution homogeneity is an important parameter to process high quality precursor fiber. Therefore, the assessment of heterogeneity in the PAN polymer solution is very critical to achieve consistent and enhanced quality in precursor fiber. It will help fine tune the processing parameters to make better fibers. Herein, a variety of parameters in the solution preparation, such as, concentration of polymer solution, choice of the solvent, copolymer composition, molecular weight of the polymer, and stirring time to make solutions, have been studied for their effect on the heterogeneity of PAN solutions. Beyond quality control, the results reported in this study can also be beneficial to establish the processingstructure-property relationship of PAN-based carbon fibers. EXPERIMENTAL

Correspondence to: Satish Kumar; e-mail: [email protected] or Tao Liu; e-mail: [email protected] Contract grant sponsor: DARPA and ARO; contract grant number: W911NF-10-1-0098. DOI 10.1002/pen.24084 Published online in Wiley Online Library (wileyonlinelibrary.com). C 2015 Society of Plastics Engineers V

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Polyacrylonitrile (PAN) homo- and co-polymers were supplied by the Japan Exlan Company (Okayama, Japan). The details of the polymers used in this study are listed in Table 1. Anhydrous N,N-dimethylacetamide (DMAc) and N,N-dimethylformamide (DMF) was purchased from Sigma Aldrich, Co. and used as received. The as-received PAN polymer was vacuum

RESULTS AND DISCUSSION

TABLE 1. Polymers used in this study.

Sample designation PAN PAN PAN PAN

1 2 3 4

PAN 5 PAN 6

Chemical structure and copolymer composition

Molecular weighta (kg/mol)

Polyacrylonitrile (PAN) homopolymer PAN homopolymer PAN-methacrylic acid (4 wt%) copolymer PAN-methacrylic acid (4 wt%)–itaconic acid (1 wt%) copolymer PAN-itaconic acid (2 wt%) copolymer PAN-methacrylic acid (4 wt%) copolymer

250 900 250 230 250 470

a Molecular weight of each polymer was provided by manufacturer and it is viscosity average molecular weight.

dried at 60 C for 24 h and at 100 C for another 24 h. The dried polymer was pulverized using mortar and pestle into fine powder. The polymer solutions for each PAN polymer were prepared by dissolving predetermined amount of dried polymer powder in DMAc or DMF at around 110 C using magnetic stirrer. The DLS measurements for PAN polymer solutions were carried out at 25 C with Delsa Nano C (Beckman Coulter, Inc.) with a laser of 658 nm wavelength. A multiangle DLS instrument (BI-200SM/TruboCorr scattering system with excitation laser of wavelength 514 nm, Brookhaven Instruments) was also used for DLS measurements in some cases. In DLS measurements, the time fluctuation of the scattered light intensity, Is(t), of a dynamic system is recorded, from which the time correlation functions, g1(s), of the scattered electric field is accordingly determined [26, 27] and used for extracting the diffusion coefficients of the fast and the slow relaxation modes of PAN solutions using the well-known CONTIN method [28, 29].

The concentrations of the PAN polymer solutions used in this study is such that C/C* 1.5, 10, and 45. C* is the critical concentration at which the polymer chains begin to overlap and the solution enters semidilute regime. C* is defined as 3M/ (4pNARg3) or M/(23/2NARg3) or [g]21, where M, Rg, NA, and [g] are molar mass, radius of gyration, Avogadro constant, and intrinsic viscosity, respectively [12, 16]. The representative correlation function of PAN 1–4 solutions in DMAc measured at C/C* 1.5 and 10 are shown in Fig. 1. The correlation functions in Fig. 1, show the presence of two decay modes, which are well separated over the time scales. The two decay modes are recognized as fast and slow modes in view of the polymer concentration being higher than Ce [20]. The manifestation of slow mode is due to the overlap and entanglement of polymer chains with each other leading to the restricted interaction of polymer chains near the entanglement points. The presence of two decay modes in the correlation function of PAN polymer solutions shown in Fig. 1, is further confirmed by the decay rate (C) distribution functions G(C), obtained by CONTIN analysis [28, 29]. In line with the literature [14], the characteristic relaxation time of the slow mode shifts toward longer delay time with increase in concentration from C/C* 1.5 to 10. Further, slow mode becomes more prominent with increase in concentration. The increase in the prominence of the slow mode with concentration can be interpreted as increase in the heterogeneity of the solution due to (a) increase in the chain entanglement with concentration and (b) increased aggregation of polymer chains due to the presence of highly polar side groups of polymer (acrylonitrile unit) and hydrophobic backbone. Henceforth, herein, polymeric entanglement, clustering, or aggregates will be referred as aggregates. Note that in some situations, it is difficult to differentiate the degree of heterogeneity of the solution by mere observation

FIG. 1. Correlation function g1(s) of PAN 1–4 at C/C* 1.5 and 10. (a) PAN-1; (b) PAN-2; (c) PAN-3; and (d) PAN-4. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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FIG. 2. Histogram showing (A) the ratio of the amplitudes of the slow to fast mode of polymers PAN 1–5 at concentration C/C* 1.5, 10, (B) the increase in the heterogeneity of the PAN 1–5 at C/C* 10 with respect to respective concentration at C/C* 1.5.

of the correlation function and decay rate distribution functions, for example, in the case when the solution concentration is close to one another. Therefore, alternative method for quantification of heterogeneity is necessary. Sedla’k [30] used the ratio of the amplitudes of the slow to fast mode (As/Af) in the decay rate distribution function G(C) to assess the formation of “domains” (aggregates) in the solution. It is noted that the systematic work by Sedla’k [18, 30] has been focusing on aqueous polyelectrolyte system, where the slow mode is attributed to the formation of multichain domains/aggregates caused by electrostatic interactions among charged species. In PAN solution being studied here, there is no or negligible charged species. We presume the polar/hydrogen bonding/hydrophobic interactions might be responsible for the aggregate formation in PAN solutions. The As/Af derived from the G(C) function for PAN 1–5 solutions at concentrations C/C* 1.5 and 10 is plotted as a histogram (Fig. 2A). Note that PAN 3, 4, and 5 are co-polymers of PAN and have molecular weight similar to the homopolymer PAN 1. At C/C* 1.5, the As/Af of PAN 1, 3, 4, and 5 is at 0.10, 0.12, 0.09, and 0.07, respectively. At, C/C* 10, the As/Af of PAN 1, 3, 4, and 5 is at 0.12, 0.34, 0.75, and 0.71, respectively. Interestingly, at both concentrations of C/C* 1.5 and 10, the PAN 1 solution has lower As/Af in comparison to PAN 3, 4, and 5 solutions. Since the As/Af is a measure of heterogeneity in the solution and that PAN 1, 3, 4, and 5 have similar molecular weight, it is inferred that homo-polymers (PAN 1) have least heterogeneity issues in comparison to co-polymers (PAN 3, 4, and 5) . Amongst the copolymer chosen for this study, PAN 5 has the least heterogeneity issues at low concentration and PAN 3 has least heterogeneity issues at high concentration. The contribution of the co-polymer segment toward the manifestation of heterogeneity in the solution is interesting. The manifestation of heterogeneity due to the copolymer segments is probably a result of the presence of ionizable and capable of hydrogen-bonding formation co-monomers in the polymer. These co-monomers can cause stronger inter-molecular chain interaction. As a result, polymer clustering becomes more prominent for co-polymers.

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Note that PAN 2 is a hompolymer and has molecular weight of 900 kg/mol, which is much higher than PAN 1 (250 kg/mol). At concentrations C/C* 1.5 and 10, the As/Af of PAN 2 with respect to the As/Af of PAN 1 increases by 3.4 and 7.3 times, respectively. Since the only difference between PAN 1 and PAN 2 is in molecular weight, it is inferred that the molecular weight of the polymer contributes significantly to the solution heterogeneity. The results further demonstrate that the molecular weight contribution towards increase in the heterogeneity of the polymer solution is more prominent at higher concentrations. The histogram in Fig. 2B depicts increase in the heterogeneity of PAN 1–5 solutions at C/C* 10 in comparison with that at C/C* 1.5. The increase in the heterogeneity of various PAN solutions at high concentration (C/C* 10) in comparison with respective PAN solutions at low concentration (C/C* 1.5) is obtained by dividing the respective As/Af. It is inferred from Fig. 2B that the increase in the concentration of PAN solution increases the respective heterogeneity in the solution by 1.2,

FIG. 3. Histogram showing ratio of the amplitudes of the slow to fast mode of PAN 6 solutions prepared at different stirring time.

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FIG. 4. The normalized correlation function of the PAN 6 in (A) DMAc and (B) DMF at different scattering angles.

2.5, 2.8, 7.8, and 10.3 times. The results from above-mentioned experiments are important towards making the right choice of PAN solution with least heterogeneity issues to produce good quality fibers. Further experiments were conducted to study the effect of processing time and type of solvent on the solution heterogeneity. These studies were performed using PAN 6 co-polymer at very high concentration C/C* 45, where the spinning solution is typically prepared. The histogram in Fig. 3 depicts the As/Af of PAN 6 solution as a function of stirring time. The amplitude ratio of slow to fast mode exhibites decreasing trend with increasing stirring time, suggesting that the PAN 6 solution became more homogeneous with longer stirring time. To make this conclusion statistically significant, the uncertainty/variation of As/Af with respect to stirring time should be established through performing DLS measurements on the replicated PAN solutions prepared at different stirring time, which has not been done in this study. For this reason, we consider the conclusion regarding the effect of stirring time a tentative one. Figure 4 shows the normalized correlation functions of PAN 6 solution in DMF and DMAc measured at different angles. The time scale at which the slow decay mode occurs in PAN 6 solution with DMF as solvent is about 1 order of magnitude faster than in DMAc as solvent, suggesting that in comparison to DMAc, DMF is a better solvent for PAN to avoid larger polymer aggregation. The slow-mode diffusion coefficients of the polymer aggregates in DMF and DMAc are about 1.6 3 10212 cm2/s and 1.6 3 10213 cm2/s, respectively. Based on Stokes-Einstein relation, the estimated size of polymer clustering in DMF and DMAc are at 9 nm and 90 nm, respectively. These results indicate that DMF is a better solvent than DMAc to prepare PAN solutions with least heterogeneity issues.

CONCLUSIONS

DLS has been used to quantify nanoscale heterogeneity in the industrially significant PAN polymer solutions. The interpretations of the results reported herein are in the light of the recent developments, wherein the slow mode is considered to be a manifestation of solution heterogeneity. The heterogeneity in polymer solution is studied based on various materials and

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processing parameters such as the molecular weight of the sample, the type of copolymer segments, stirring time, concentration of the solution, and the choice of the solvents. It has been found that the degree of heterogeneity is high if the PAN solution is prepared at high concentration, with high molecular weight polymers, with a co-polymer that has a comonomer being ionizable/capable of hydrogen-bonding formation, and with less string time. Low molecular weight homopolymers are expected to have least heterogeneity issues. Amongst the chosen co-polymers for this study, all the co-polymer solutions (PAN 3, 4, and 5) exhibited similar degree of heterogeneity at low concentrations (C/C* 1.5). Whereas, at high concentrations (C/C* 10), PAN 3 (methacrylic acid co-polymer) has the least heterogeneity issues. For an increase in the concentration of PAN 1–5 solutions by 6.7 times, the respective heterogeneity increases by 1.2, 2.5, 2.8, 7.8, and 10.3 respectively. Amongst the solvents generally used to dissolve PAN (DMF vs DMAc), DMF proves to be a better solvent that significantly lower heterogeneity issues. The diffusion coefficient of the PAN 6 aggregates in DMF and DMAc vary by an order at 1.6 3 10212 cm2/s and 1.6 3 10213 cm2/s respectively. The size of polymer aggregates in DMF and DMAc, estimated by applying Stokes-Einstein relation, is 9 nm and 90 nm respectively. REFERENCES 1. A. Ritzl, L. Belkoura, and D. Woermann, Phys. Chem. Chem. Phys., 1, 1947 (1999). 2. E.J. Amisand and C.C. Han, Polymer, 23, 1403 (1982). 3. W. Brown and P. Stepanek, Macromolecules, 25, 4359 (1992). 4. C.H. Wang, J. Chem. Phys., 95, 3788 (1991). 5. T. Nicolai, W. Brown, R.M. Johnsen, and P. Stepanek, Macromolecules, 23, 1165 (1990). 6. T. Nicolai and W. Brown, Macromolecules, 23, 3150 (1990). 7. M. Sedla’k, C. Konak, P. Stepanekand, and J. Jakes, Polymer, 28, 873 (1987). 8. R. Borsali, E.W. Fischer, and M. Benmouna, Phys. Rev. A., 43, 5732 (1991). 9. V.A.V. de Oliveira, W.A. de Morais, M.R. Pereira, and J.L.C. Fonseca, Eur. Polym. J., 48, 1932 (2012). 10. R. Pecora, J. Nanoparticle Res., 2, 123 (2000).

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