Isothermal Flow-Induced Crystallization of Polyamide 66 Melts

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

Isothermal Flow-Induced Crystallization of Polyamide 66 Melts Jiho Seo,† Hideaki Takahashi,‡ Behzad Nazari,† Alicyn M. Rhoades,§ Richard P. Schaake,∥ and Ralph H. Colby*,† †

Department of Materials Science and Engineering, Penn State University, University Park, Pennsylvania 16802, United States Toray Research Center Inc., Otsu, Shiga 520-8567, Japan § School of Engineering, Penn State Behrend, Erie, Pennsylvania 16563, United States ∥ SKF Research & Technology Development, 3439 MT Nieuwegein, The Netherlands ‡

S Supporting Information *

ABSTRACT: When the molten state of a semicrystalline polymer is subjected to sufficiently intense flow before crystallization, the crystallization kinetics are accelerated and the crystalline superstructure is transformed from spherulites to smaller anisotropic structures. In this study, flow-induced crystallization (FIC) of polyamide 66 (PA 66) was investigated using rheology and polarized optical microscopy. After an interval of shear flow at 270 °C, above the melting temperature (Tm = 264 °C) and below the equilibrium melting temperature, small-amplitude oscillatory shear time sweeps at 245 °C were used to monitor FIC kinetics. As specific work was imposed on a PA 66 melt at 270 °C from 10 Pa to 40 kPa, the onset of crystallization at 245 °C did not change. Above the critical work of 40 kPa up to 100 MPa, the onset of crystallization at 245 °C was progressively shifted from 628 to 26 s, as the applied specific work was increased. For quantitative analysis of the acceleration, the Avrami equation was used with Pogodina’s storage modulus normalization method, revealing the transition of Avrami exponent from ∼3 to ∼2 at the critical specific work of ∼40 kPa. Strong FIC acceleration was observed after the transition. After applying very low shear rates, large spherulites were observed without cylindrites, while a mixture of small spherulites and large anisotropic cylindrites was seen after applying a shear rate of 10 s−1.

1. INTRODUCTION Polyamide 66 (PA 66) is an engineering thermoplastic which has amide groups in the polymer chain, separated by methylene sequences.1,2 Because of the amide groups, PA 66 generally forms multiple hydrogen bonds with adjacent chains, resulting in a higher melting temperature (Tm = 264 °C) and a higher heat deflection temperature (200 °C for 0.45 MPa) than those of polyolefins.3,4 Moreover, the regular and symmetric chemical structure along the PA 66 macromolecular chain can provide relatively high degree of crystallinity with superior mechanical strength.5 Thus, PA 66 has been widely used in many industries such as fiber, aerospace, automotive, power management, and electronics.4 In polymer processing techniques such as injection molding and fiber spinning, a molten polymer undergoes strong elongational or shear flow during the operation.6 When a semicrystalline polymer melt, such as PA 66, is subjected to sufficiently intense flow prior to crystallization, the crystallization kinetics are accelerated, and the crystalline superstructure is transformed from spherulites into anisotropic structures, referred to as flow-induced crystallization (FIC).7 The accelerating influence of FIC is observed in PA 66 at low and moderate levels of supercooling encountered during polymer processing, specifically influencing the heterogeneous nucleation regime.8 © XXXX American Chemical Society

From the thermodynamic point of view, the entropyreduction model (ERM), initially proposed by Flory, has been most widely accepted to account for FIC kinetics.9−11 According to the ERM, chain stretching caused by flow can lower the number of polymer chain configurations, resulting in a decrease of entropy relative to the quiescent melt. Using the classical two-phase polymer nucleation model, the nucleation rate of FIC (Ṅ f) can be expressed by12,13 ⎛ ΔGf ⎞ ⎛ ΔG ⎞ Nḟ = C exp⎜ − d ⎟ exp⎜ − ⎟ ⎝ kTc ⎠ ⎝ kTc ⎠

(1)

where ΔGd and ΔGf are the diffusion activation energy and nucleation energy barrier under the flow to form stable nuclei, and C, k, and Tc are a constant prefactor, Boltzmann constant, and crystallization temperature, respectively. The diffusion term is nearly constant at high temperatures, so the nucleation barrier is generally of interest to determine the nucleation rate during crystallization. Based on ERM, the nucleation energy barrier of FIC (ΔGf) can be expressed in terms of the quiescent Received: January 14, 2018 Revised: May 16, 2018

A

DOI: 10.1021/acs.macromol.8b00082 Macromolecules XXXX, XXX, XXX−XXX

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was 60 °C, and the melting temperature of dry Vydyne 21SPC was 264 °C (Figure S1 in the Supporting Information). The reported equilibrium melting temperature of PA 66 is 275 °C.4 According to the technical data sheet, the density of Vydyne 21SPC is 1.14 g/cm3 at room temperature. Kapton tape used for the fabrication of thin PA 66 discs for microscopy was purchased from Makerbot (Brooklyn, NY). 2.2. Rheology. All rheological measurements were performed using an ARES-G2 rheometer (TA Instruments, New Castle, DE) with a heated nitrogen stream for temperature control. 25 mm cone and plate fixtures were used for oscillatory and steady shear to observe the linear viscoelastic (LVE) response and the shear rate dependence of viscosity at 270 °C, between the melting temperature of 264 °C and the equilibrium melting temperature of 275 °C. To avoid transducer compliance issues when samples are fully crystallized with ∼30 MPa modulus, 8 mm parallel plates were used for oscillatory shear experiments and to monitor crystallization kinetics of PA 66. The 8 mm parallel plates used to monitor the crystallization kinetics of course have nonuniform shear rate. The stress growth during crystallization can be expressed as σ = ηγ̇ where σ is stress, η is viscosity, and γ̇ is shear rate. The plate edge has higher shear rates (γ̇) than the center because the shear rate in parallel plates is linearly proportional to the radius. Moreover, the viscosity (η) near the plate edge increases faster during crystallization than that of the center due to FIC effects. Hence, the stress evolution (σ) is strongly dominated by the perimeter of the parallel plates, so shear rate and shear stress reported are mostly from the perimeter. For the preparation of rheological measurements, dry PA 66 pellets were melted on a plate fixture at 280 °C for 1 min. A shear rate of 0.5 s−1 was then applied for 5 min with a gap of ∼1 mm to aggregate pellets without air bubbles. After squeezing to form the correct geometry gap of ∼ 0.5 mm, the molten PA 66 was annealed at 300 °C for 1 min (∼6 min above Tm° = 275 °C) to erase any remaining thermal memory.20 It has been observed that the molecular weight and the molecular weight distribution of PA 66 increased with time at 270 °C under N2 (Figure S2) as well as higher dynamic moduli (Figures S3 and S4). Hence, in order to minimize the thermal cross-linking reaction known to occur in PA 66 at high temperatures,21 all preparation above the melting temperature (>264 °C) was completed in ∼20 min. Such a protocol precludes many useful experiments that have been done on polyolefins but still allows a limited study of FIC effects for PA melts. 2.2.1. Oscillatory and Steady Shear. Shear thinning and the Cox− Merz rule failure are strongly related to the onset of chain deformation, such as orientation and stretching, and FIC in isotactic polypropylene18 and poly(ether ether ketone).22 To determine the onset of chain deformation, the complex viscosity and the steady shear viscosity of PA 66 were compared at 270 °C using 25 mm cone and plate fixtures. Figure 1 shows that mild shear thinning of steady shear viscosity started around 0.1 s−1 with the onset of Cox−Merz rule

nucleation energy barrier (ΔGq) and the degree of entropy reduction by shear (ΔSf):13 ΔGf = ΔGq + TsΔSf

(ΔSf < 0)

(2)

where Ts is the shearing temperature. Such simple considerations allow an estimation of the entropy reduction relative to the quiescent nucleation rate (Ṅ q) by combining eqs 1 and 2: ⎛ −TsΔSf ⎞ Nḟ = exp⎜ ⎟ Nq̇ ⎝ kTc ⎠

(3)

The strength of FIC, which is related to the degree of entropy reduction, is strongly governed by molecular-based polymer chain deformations induced by shear rate (γ̇) and shearing time (ts). According to the rheological classification of FIC, two major regimes are generally identified depending on the chain deformation: the equilibrium chain configuration (no FIC) and the polymer chain stretching by strong flow (FIC).14,15 The transition between the regimes is usually defined by the Weissenberg number (Wi) of the longest chains which is a product of imposed shear rate and characteristic relaxation time of the longest chain; WiR = γ̇τR where γ̇ and τR are imposed shear rate and stretching relaxation time (Rouse time) of the longest chains, respectively. Since the transition onset is determined by the slowest relaxation, the relaxation time of the longest chains is usually considered as the critical relaxation time.16 Thus, characteristic relaxation times depend on the polymer’s molecular weight distribution and the Rouse time of an entanglement strand.17 In most cases, shearing time is investigated as a form of cumulative shear strain (γ) or specific work (W) to study FIC effects using eqs 4 and 5: γ=

∫0

W=

ts

∫0

γ ̇ dt ts

γσ̇ dt

(4)

(5)

where σ is the shear stress. For isotactic polypropylene, there is a critical specific work (Wc), below which there is no acceleration of the crystallization kinetics. For W > Wc , the crystallization kinetics are accelerated up to a saturation work (Wsat) beyond which the crystallization kinetics nearly hold constant.18 Over the past decades, vast experimental and theoretical efforts have been conducted to investigate FIC, but primarily for polyolefins. Thus, there is still a lack of FIC studies on semicrystalline engineering thermoplastics, such as PA 66. In this study, FIC of PA 66 was rheologically investigated in terms of shear rate and shearing time (60 or 120 s) above the melting temperature (Ts = 270 °C and Tm = 264 °C) followed by quenching to the crystallization temperature (Tc = 245 and 250 °C). Then, the morphological transformations induced by shear flow were observed using polarized optical microscopy. From the experimental observations, the isothermal FIC mechanism was speculated in different flow strengths.

2. EXPERIMENTAL SECTION 2.1. Materials. PA 66 (Vydyne 21SPC) was kindly provided by Ascend Performance Materials (Houston, TX). Vydyne 21SPC, which is a general-purpose grade designed for injection molding, was investigated after drying at 80 °C in a vacuum oven for at least 1 week following a previously reported method.19 The glass transition temperature of dry Vydyne 21SPC at the heating rate of 10 °C/min

Figure 1. Steady shear viscosity and complex viscosity of PA 66 at 270 °C as functions of shear rate and angular frequency, respectively. Mild shear thinning and the Cox−Merz rule failure were observed above 0.1 s−1. B


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Macromolecules failure. Such mild shear thinning has been previously reported for PA 66.23 2.2.2. Flow-Induced Crystallization Kinetics. FIC of PA 66 was investigated at two crystallization temperatures: 245 and 250 °C. The high crystallization temperature (Tc = 250 °C) provided a good resolution to determine the onset of crystallization, but the crystallization kinetics were too slow to efficiently study the completion of crystallization. Thus, our more thorough study of crystallization kinetics was at a lower temperature (Tc = 245 °C). Figure 2 shows the overall sample preparation protocol to monitor the

Figure 2. Time−temperature preparation protocol of the PA 66 sample to monitor the crystallization kinetics at Tc = 245 and 250 °C after any interval of shear at Ts = 270 °C. Figure 3. Photographs of (a) Kapton tape attached to two 16 mm parallel plates before loading the PA 66 sample and (b) Kapton tape after fabricating a sheared PA 66 disc.

crystallization kinetics using two 8 mm parallel plate fixtures with a gap of 0.5 mm. The molten PA 66 sample annealed for 1 min at 300 °C was cooled down to the 270 °C shearing temperature and maintained at 270 °C for 5 min to reach thermal equilibrium, and then the designated shear rate (0.01−10 s−1) and shearing time (60 or 120 s) were imposed on the PA 66 melt. After the designated shear, the molten PA 66 was cooled to Tc = 245 or 250 °C without undershooting and allowed to crystallize. The viscoelastic response was monitored during the crystallization by using a small-amplitude oscillatory shear time sweep following the previously reported method18,22,24 using a constant frequency of 1 rad/s with a small strain amplitude of 0.05. During the measurement at the crystallization temperature, both storage modulus and loss modulus increased with the crystallization time due to the space-filling with crystal and the growing physical network of connected crystallites within the polymer melt.18 The measurement was stopped when the storage modulus maintained a steady plateau state for ∼10 min at the end of crystallization for the crystallization at 245 °C and when the phase angle reached 40° for the crystallization at 250 °C. The heating and cooling rates between each step were ∼10 °C/min. No noticeable sign of crystallization was observed during the cooling to the crystallization temperatures of 245 and 250 °C. 2.3. Polarized Optical Microscopy. A sheared PA 66 disc for polarized optical microscopy was fabricated using an ARES-LS rheometer (Rheometric Scientific) with two 16 mm parallel plate fixtures. The sample preparation protocol was identical to that of the crystallization kinetics measurement in Figure 2, but the sample was sheared at 10 s−1 for 1 min at 270 °C and solidified for 60 min at 245 °C instead of undergoing the oscillatory shear time sweep. In order to peel off a sheared PA 66 disc from the parallel plates after the solidification, a Kapton tape was attached on the plate fixtures before loading PA 66 pellets as shown in Figure 3a. The Kapton tape was easily removed after cooling the sheared disc down to room temperature as shown in Figure 3b. The average thickness of the prepared PA 66 disc was 154 ± 7 μm, which was measured at four points around the sample. The disc was sheared using parallel plates so that it had a range of shear rates from ∼0 s−1 (at the center) to ∼10 s−1 (at the edge). The crystal morphology of the sheared disc was

observed using a polarized optical microscope BX51 (Olympus, Tokyo) installed with 20× and 40× objective lenses, for which the thinner sample is vital. 2.4. Size Exclusion Chromatography. Size exclusion chromatography (LC-20AD, Shimadzu, Japan) was used to measure the molecular weight and molecular weight distribution of PA 66 following a previously reported method.25 Two analysis columns (HFIP-606M, Shodex, Japan), one guard column (HFIP-G, Shodex, Japan), and a differential refractive index detector (RI-104, Shodex, Japan) were used with a mobile phase of 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP, CAS# 920-66-1) containing 5 mM sodium trifluoroacetate (NaTFA, CAS# 2923-18-4). The injection volume was 20 μL, and the flow rate was 0.2 mL/min at 40 °C. For the sample preparation, 100 mg of PA 66 was dissolved in 1 mL of HFIP/NaTFA solution, stirred overnight, and diluted to the concentration of 0.05 wt %. The prepared solution was filtered prior to the injection using a Millex syringe filter (EMD Millipore, Billerica, MA) with 0.45 μm pore size. The molecular weight and molecular weight distribution curve were determined relative to poly(methyl methacrylate) (PMMA) standards, and then the molar mass of PA 66 was calculated using the following Mark−Houwink parameters: KPMMA = 0.115 × 10−3 cm3/g, aPMMA = 0.746, KPA66 = 1.236 × 10−3 cm3/g, and aPA66 = 0.673.26 Figure 4 shows the molecular weight distribution of PA 66. The number-average molecular weight (Mn), the weight-average molecular weight (Mw), and the polydispersity index (Mw/Mn) of PA 66 (Vydyne 21SPC) were 11 100 g/mol, 22 300 g/mol, and 2.0, respectively.

3. RESULTS AND DISCUSSION 3.1. Flow-Induced Crystallization Kinetics. The rise of the dynamic modulus during crystallization is correlated to the increase of the crystallinity.24 For semicrystalline polymer melts, the crystallization kinetics are accelerated if a sufficiently intense flow is imposed to the melt prior to the crystallization.27 C


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(0.5 s−1), the storage modulus evolution curves showed steeper initial slopes. Since the FIC precursor formed at γ̇ > 0.5 s−1, which is presumably a bundle of stretched chains, could act as a stable active nucleus that does not require the same nucleation induction time, the steeper initial slope may indicate the existence of FIC precursors at the very early stage of crystallization. Thus, the crystallization may start before the experimental temperature reduction reaches the isothermal condition at Tc = 250 °C for the FIC kinetics measurement.30 Crystallization at 250 °C showed a good demonstration of FIC acceleration, but the crystallization was too slow to investigate the whole crystallization kinetics. Thus, the crystallization of PA 66 at Tc = 245 °C was more fully investigated, as shown in Figure 6.

Figure 4. Molecular weight distribution of PA 66 (21SPC). Mn = 11 100 g/mol, Mw = 22 300 g/mol, and Mw/Mn = 2.0.

In this study, the degree of acceleration was investigated in a range of imposed shear rates from no shear to 10 s−1 with the shearing time of 120 s. For the investigation of crystallization onset, the designated shear was imposed on the PA 66 melt at 270 °C, and the crystallization kinetics were monitored at 250 °C through small-amplitude oscillatory shear time sweeps as shown in Figure 5.

Figure 5. (a) Storage (blue) and loss (red) modulus evolution and (b) the complex viscosity (black) of PA 66 during crystallization at Tc = 250 °C. The samples were prepared using 8 mm parallel plates by shearing at Ts = 270 °C for 120 s. The range of applied shear rates was from no shear to 10 s−1. The constant frequency of 1 rad/s was applied during crystallization with the constant strain amplitude of 0.05.

Figure 6. Storage modulus evolution of PA 66 at Tc = 245 °C as a function of crystallization time. The samples were prepared by shearing at Ts = 270 °C for (a) 60 s and (b) 120 s using 8 mm parallel plates. The constant frequency of 1 rad/s was applied during crystallization with the constant strain amplitude of 0.05.

The shape of storage modulus evolution reflects both the type and the rate of crystallization.28,29 It has been reported that the shift of storage modulus evolution with a similar initial slope indicates an increase in the number density of point-like nuclei, while the shift of storage modulus evolution with a slope change implies a morphological transition from isotropic spherulites to smaller oriented structures.16 At low shear rates

The storage modulus evolution shows a single sigmoidal ′ = 3 × 103 Pa and the behavior with the initial modulus of Gmin final modulus of G′max = 3 × 107 Pa. Thus, the actual storage modulus grew by 4 decades during the crystallization. Because of slightly different sample positions between parallel plate fixtures and mild edge fractures, the initially measured storage D


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Macromolecules modulus showed variations less than a factor of 2.30 The samples sheared at 5 s−1 in Figure 6 have a higher initial G′ value, presumably because they crystallized somewhat during cooling from Ts = 270 °C to Tc = 245 °C. For further analysis, the measured storage modulus evolution curve was normalized using the previously developed method of Pogodina et al.:24 ϕ(t ) ≡

′ ) log G′(t ) − log(Gmin ′ ) − log(Gmin ′ ) log(Gmax

(6)

where G′min, G′(t), and G′max are the storage moduli before crystallization, at intermediate time, and at the final stage of crystallization, respectively. This logarithmic mixing rule has been investigated to relate the mechanical properties of crystallinity with time for semicrystalline polymers, such as isotactic polypropylene,24 polylactide,31 and polycaprolactone.32 From the rheological point of view, the degree of space-filling (ϕ) is considered to be the fraction of the crystallizing portion that has transformed from amorphous phase to crystalline phase during the crystallization.24 Figure 7

Figure 8. Avrami exponents as a function of (a) shear rate and (b) specific work at Ts = 270 °C followed by crystallization at Tc = 245 °C. All samples were prepared by shearing at Ts = 270 °C for 60 s (open symbols) or 120 s (filled symbols) using 8 mm parallel plates. The range of applied shear rates was from 0.01 to 5 s−1 with the symbol shapes defined in Figure 6.

Figure 8 shows the Avrami exponents (n) as functions of shear rate and imposed specific work. The transition of Avrami exponent from ∼3 to ∼2 was observed at the specific work of ∼40 kPa with the shear rate of ∼0.3 s−1. This result may quantitatively imply that the morphological transformation from three-dimensional growth to two-dimensional growth takes place at the critical specific work of ∼40 kPa. Using X-ray scattering, Balzano et al. have reported that the Avrani exponents of highly sheared isotactic polypropylene (i-PP) at 60 s−1 for 3 s; at 90 s−1 for 2 s; and at 180 s−1 for 1 s were n = 1.36 ± 0.02 in the early stage of crystallization showing FIC formation.33 The observation reasonably agreed with the PA 66 Avrami exponents of n = 1.45 ± 0.42 at ϕ = 0.15, which were sheared at 1, 3, and 5 s−1 for 60 and 120 s. The Avrami plot is presented in Figure S5 (Supporting Information). Another common way to characterize the effectiveness of shear flow on FIC is to define the induction time of crystallization. It has been reported that the onset of FIC is consistent with the shear rate for the failure of the Cox−Merz empirical rule,22 possibly caused by structural deformation of the polymer chains reducing their entropy by having fewer possible conformations in the stretched state. The Cox−Merz empirical rule can be expressed as34

Figure 7. Comparison of the normalized G′ evolution obtained by rheology (open symbols) to the relative crystallinity with time monitored by DSC (solid line) for not sheared PA 66 (black) and sheared PA 66 at 5 s−1 for 2 min at 270 °C (red). All samples were crystallized at 245 °C.

shows the comparison of the normalized G′ evolution of PA 66 obtained by rheology to the relative crystallinity with time monitored by DSC. Because of the relatively good agreement of the normalized G′ evolution with the relative crystallinity, the degree of space-filling was assumed to be determined well by the normalized storage modulus in this study.24 To quantitatively characterize the crystalline superstructure induced by the imposed shear, Avrami exponents were computed by fitting the space-filling evolution data of Figure 6 to the Avrami equation: ϕ(t ) = 1 − exp( −Kt n)

(7)

where ϕ(t) is the degree of space-filling at time t during crystallization, K is the space-filling rate constant, and n is the Avrami exponent related to the growing crystal dimension. Combining eqs 6 and 7, the Avrami exponent (n) can be obtained as a function of storage modulus evolution ⎛ ⎛ ′ ) ⎞⎞ log(G′(t )/Gmin log⎜⎜ −ln⎜1 − ⎟⎟ = log K + n log t ′ /Gmin ′ ) ⎠⎟⎠ log(Gmax ⎝ ⎝

η(γ )̇ = |η*(ω)|

(ω = γ )̇

(9)

where η is the shear viscosity, γ̇ is the steady shear rate, η* is the complex viscosity, and ω is the angular frequency. Figure 9 shows the onset of crystallization as a function of imposed shear

(8)

by plotting the left side of eq 8 against logt. E


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Figure 9. Onset time of FIC (ϕ = 0.1) as a function of shear rate (black; left axis) for PA 66 at Tc = 245 °C plotted with the test of the Cox−Merz rule (blue; right axis) at Ts = 270 °C. A critical shear rate of ∼0.3 s−1 above which FIC effects are observed coincides with the failure of the Cox−Merz rule.

Figure 10. Onset of FIC (ϕ = 0.1) of PA 66 at Tc = 245 °C as a function of imposed specific work. All samples were prepared by shearing at Ts = 270 °C for 60 s (open symbols) or 120 s (filled symbols) with the different symbol shapes defined in Figure 6. Dashed lines represent fitted values. The onset time is independent of specific work below the critical work Wc = 40 kPa and onset time scales as W−0.54 for W > Wc.

rate with the Cox−Merz plot. For quantitative clarification, the onset time of crystallization was determined when the storage modulus reaches the space-filling ϕ = 0.1 (G′ ∼ 7000 Pa) during the crystallization. Below the applied shear rate of 0.1 s−1, crystallization was not noticeably accelerated. Beyond the shear rate of 0.3 s−1, the onset of the Cox−Merz rule failure is observed as well as the coincident onset of crystallization acceleration. For shear rates 0.1 < γ̇ < 5 s−1, when the shearing time was doubled from 60 to 120 s, the degree of acceleration became stronger, with the onset time decreased by a factor of 2. This result addresses the importance of shearing time on FIC.16 Using the quiescent crystallization onset time tq = 628 s at Tc = 245 °C and the fastest FIC onset time tf = 26 s at Tc = 245 °C after applying a shear rate of 5 s−1 for 120 s at Ts = 270 °C, the entropy reduction by that shear can be estimated using eq 3 as ΔSf = −

Wc > 3 MPa, but that is not reflected in the onset of crystallization (ϕ = 0.1) in Figures 9 and 10. The saturation work (Wsat) reported for isotactic polypropylene18 was not observed for PA 66 at Tc = 245 °C perhaps because crystallization became too rapid for our methods. 3.2. Kinetic Modeling of Flow-Induced Crystallization. To build an isothermal FIC kinetic model, a modified Avrami equation was obtained by combining eqs 6 and 7: ′ − log Gmin ′ )[1 − exp( − Kt n)] + log Gmin ′ log G′(t ) = (log Gmax (11)

⎛ ⎞ kTc ⎛ 1/t f ⎞ ⎟ = − 518 K ln⎜ 1/26 s ⎟k = − 3.04k ln⎜ Ts ⎜⎝ 1/tq ⎟⎠ 543 K ⎝ 1/628 s ⎠

where G′min, G′(t), and G′max are the storage moduli before crystallization, at intermediate time, and at the final stage of crystallization, respectively. K is the space-filling rate constant, t is the crystallization time, and n is the Avrami exponent. Based on Figure 8, an Avrami exponent n = 3 was used for no FIC (W < Wc), while n = 2 was used for FIC (W > Wc). Figure 11a shows the fittings of eq 11 to the storage modulus evolution data of PA 66 at Tc = 245 °C. The Avrami model is seen to be reasonable for low values of the storage modulus, but the simplistic model consistently overpredicts the measured data in the range of high storage moduli. The Avrami model typically displays overprediction toward the end of crystallization due to the secondary crystallization which often has a lower crystal growth dimension.37 In this study, the space-filling evolution curves obtained from the Avrami model were relatively well correlated to the measured data up to the space-filling of 0.75 as shown in Figure 11b. Beyond ϕ = 0.75, the measured normalized storage modulus started to be overpredicted by the Avrami model. To better model the secondary crystallization behavior for ϕ > 0.75, the data in Figure 11b just beyond ϕ = 0.75 were fit again to the Avrami model (eq 8), and the Avrami exponents are shown in Figure 12. The Avrami exponent for the last stage of crystallization was nearly constant (n ≅ 2) for no FIC, while the Avrami exponent became less than 2 for FIC. Compared to Figure 8b, it was identified that almost one dimension was reduced above ϕ = 0.75. Hence, the Avrami exponent beyond

(10)

where k is the Boltzmann constant. In order to evaluate the effect of both shear rate and shearing time on FIC, the onsets of crystallization were plotted as a function of imposed specific work using eq 5 in Figure 10. With hydrogenated polybutadienes, Mykhaylyk et al. reported that the critical shear rate decreased with longer shear times, suggesting that the specific work applied on a polymer melt controlled the resulting FIC.35 Comparison of Figures 9 and 10 reveals the importance of specific work, which reduces the onset times resulting from two different shearing times to a common curve. The main observation was that there was a significant FIC acceleration after the critical applied specific work of Wc ∼ 40 kPa at Ts = 270 °C and Tc = 245 °C with a critical shear rate of ∼0.3 s−1. The critical specific work of Wc ∼ 40 kPa agrees with the transition point of Avrami exponents from ∼3 to ∼2 in Figure 8b. Van Puyvelde et al. reported that critical specific work was required for poly-1-butene to form highly oriented morphology.36 Thus, the result implies that the stretched polymer chains induced much faster FIC kinetics accompanied by morphological transformation from large spherulites to smaller cylindrites. At even higher shear rates, Figure 8b shows another transition from ∼2 to ∼1 for the Avrami exponents for F


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Figure 13. Fitting of the Avrami model with rheologically measured data after lowering the Avrami exponent by 1 for ϕ > 0.75. The sample was sheared at Ts = 270 °C for 60 s and crystallized at Tc = 245 °C. This figure uses the notation defined in Figure 6.

3.3. Polarized Optical Microscopy. A PA 66 melt crystallizes upon cooling below the melting temperature by aligning and folding the molecular chains into lamellae.38−40 For quiescent crystallization, in general, the lamellae grow radially from a point-like nucleation site forming a spherulitic structure. However, when a strong flow is imposed on the polymer melt before crystallization, the crystalline superstructure can change to an anisotropic structure.36 The coil− stretch transition (CST) model, initially proposed by de Gennes, has been commonly employed to explain the morphological transformation from spherulite to anisotropic structure.41,42 According to the CST model, the longest polymer chains undergo a sharp transition under strong flow from a randomly coiled state to an extended chain conformation. Keller et al. provided the experimental evidence of the CST model for polyethylene by using birefringence.42,43 They demonstrated that polymer chains were extended under strong elongational flow, forming a chain bundle called shish and showed that lamellae grew perpendicular to the shish structure called kebab. In this study, such morphological transformation of FIC was observed through polarized optical microscopy. The sheared disc used for polarized optical microscopy was fabricated to be ∼154 μm thick with two 16 mm parallel plate fixtures so that the disc sample had a range of shear rates from ∼0 s−1 (at the center) to ∼10 s−1 (at the edge) as shown in Figure 14. Figure 15 shows the crystal morphologies of a sheared PA 66 disc at the center (a) and at the edge (b) obtained using a polarized optical microscope with a 40× objective lens. At the center where the shear rate approaches zero, large spherulites (∼50 μm) were developed without anisotropy, while a mixture of smaller spherulites and cylindrites was found at the edge where the shear rate approaches ∼10 s−1. The reason for the mixed formation at the edge may be because the PA 66 melt used in this study had a broad polydispersity of molecular weight (Mw/Mn = 2.0) so that only the longest polymer chains, which were long enough to be stretched at the imposed shear rate, were able to form FIC precursors. For a linear polymer, the Rouse time (τR) of a specific molecular weight (M) is given by

Figure 11. (a) Fitting of the Avrami model (eq 11 with either n = 3 for no FIC with W < Wc and n = 2 for FIC with W > Wc) to G′ evolution. (b) Fitting of the Avrami model to normalized G′ evolution data eq 6. Each sample was sheared at Ts = 270 °C for 60 s and crystallized at Tc = 245 °C. These figures use the notation defined in Figure 6.

Figure 12. Avrami exponents just beyond ϕ = 0.75 as a function of specific work. All samples were prepared by shearing at Ts = 270 °C for 60 and 120 s and crystallized at Tc = 245 °C. The different symbol shapes are defined in Figure 6.

the divergence point was defined as n − 1 to establish a better FIC kinetic model, as shown in Figure 13 (n = 2 for no FIC and n = 1 for FIC beyond ϕ = 0.75). The result agrees relatively well with the measured rheological data except for a sample sheared at 1 s−1 for 60 s near the FIC transition (no FIC → FIC). G


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Macromolecules ⎛ M ⎞2 τR = ⎜ ⎟ τe ⎝ Me ⎠

(12)

where Me is the entanglement molecular weight and τe is the Rouse time of an entanglement strand. Because of the fact that the Me and τe are constants, if shear rate 0.3 s−1 is taken as the reciprocal of the Rouse time of the longest chains with M ∼ 1.5 × 105 g/mol shown in Figure 4, 10 s−1 is then the reciprocal of the Rouse time for chains with M ∼ 3.4 × 104 g/mol using (M2/M1)2 = (τR2/τR1). This suggests that roughly at least 80% of the molecular weight distribution is not being stretched at 10 s−1. Thus, the shorter chains are likely developed into small spherulitic structure or became epitaxial parts of the anisotropic cylindrite44 (i.e., kebab). Additionally, the sheared PA 66 melt was quenched from Ts = 270 °C using liquid N2 to observe the beginning stage of FIC. The glass transition temperature of PA 66 obtained from DSC analysis was 60 °C so that the polymer chain mobility was halted rapidly after immersing the sheared PA 66 melt in liquid nitrogen. Figure 16 shows the polarized optical image of the

Figure 14. Prepared 16 mm diameter PA 66 disc for polarized optical microscopy. The fabricated disc had a range of shear rates from ∼0 s−1 at the center to ∼10 s−1 at the edge (W ∼ 15 MPa) with some evidence of edge fracture near the perimeter.

Figure 16. Polarized optical microscopic images (20×) of a quenched 16 mm PA 66 disc at the edge (∼10 s−1). A PA 66 disc was fabricated by shearing at 10 s−1 for 1 min at Ts = 270 °C and cooled down to 245 °C at ∼10 °C/min. A Kapton tape sandwiched molten PA 66 disc was removed at 245 °C from an ARES-G2 rheometer using tweezers and swiftly quenched in liquid N2. The disc thickness was ∼150 μm. An anisotropic structure was developed in the early stage of crystallization with small spherulitic structures. The scale bar is 200 μm.

quenched PA 66 observed through a 20× objective lens. It was found that the anisotropic structure was developed in the very early crystallization stage along with small spherulitic structures. The spherulite diameter was similar to the width of the cylindrite. This observation implies that the kebab grew at a similar rate as the surrounding spherulites. 3.4. Flow-Induced Crystallization Mechanism. Based on experimental data obtained from rheological and optical measurements, a FIC mechanism was speculated as shown in Figure 17. For no FIC, the polymer chains maintain their equilibrium chain configurations. The imposed shear rate is slower than stretching relaxation rates so that the crystallization rate is almost the same as quiescent condition without FIC effects. For FIC, the longest polymer chains are stretched at a higher shear rate than their stretching relaxation rate.35 As a consequence, the polymer melt has fewer possible chain configurations

Figure 15. Polarized optical microscopic images (40×) of (a) large spherulites observed at the center (∼0 s−1) and (b) a mixture of small spherulites and cylindrites observed at the edge (∼10 s−1). A PA 66 disc was fabricated by shearing at 10 s−1 for 1 min using two 16 mm parallel plates at Ts = 270 °C, cooled down to 245 °C at ∼10 °C/min, and crystallized at Tc = 245 °C for 60 min. The disc thickness is ∼150 μm. The scale bar is 100 μm. H


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Macromolecules

10 Pa to Wc = 40 kPa, the crystallization onset was unaffected by shear. For W > Wc up to 107 Pa at Ts = 270 °C before the crystallization, the onset of crystallization time was progressively accelerated from 628 to 26 s, suggesting a roughly 3kT entropy reduction of the free energy from the strongest flow applied (2 min of shear at 5 s−1). For further quantitative analysis, the Avrami equation was used with Pogodina’s storage modulus normalization method. The FIC acceleration was started after the transition of Avrami exponent from ∼3 to ∼2 at the critical specific work of Wc ∼ 40 kPa. This observation may imply that the flow-induced morphological transformation is related to the acceleration of FIC. The Avrami model was in relatively good agreement with the measured data up to a space-filling fraction ϕ = 0.75 but overpredicted the space-filling at the end of crystallization due to secondary crystallization. For ϕ > 0.75, the Avrami exponent decreases by 1; n = 3 → 2 for no FIC and n = 2 → 1 for FIC. Such quantitative phenomenological models are a first step toward including FIC effects in injection molding flow simulation software.45,46 The shear-induced morphological transformation was also observed using a polarized optical microscope. At nearly zero shear rate, large spherulites were observed without anisotropic structures, while a mixture of small spherulites and large anisotropic cylindrites was shown at a shear rate of ∼10 s−1. Based on the measured experimental data, a FIC mechanism in different flow strengths was suggested.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b00082. DSC first cooling and second heating trace of PA 66; Molecular weight distributions of PA 66 pristine, annealed for 1 h, and annealed 2 h at 270 °C under N2; Oscillatory time sweep of polyamide 66 at 270 °C under N2; linear viscoelasticity of PA 66 (Vydyne 21SPC) pristine, annealed for 1 h, and annealed for 2 h at 270 °C under N2; Avrami plot constructed with storage modulus evolution of PA 66 at Tc = 245 °C as a function of crystallization time (PDF)

Figure 17. Two dimensional scheme of crystal growth in terms of flow strengths. White and blue indicate amorphous and semicrystalline regions, respectively.

(lower entropy) than that of the quiescent condition. Such entropy reduction decreases the nucleation barrier, accelerates the nucleation rate, and increases the number density of nuclei during the crystallization. Moreover, the stretched polymer chains develop into a FIC precursor, presumably composed of a bundle of stretched chains. The FIC precursor may act as an active nucleus so that the crystallization takes place immediately after cessation of shear flow and quench to Tc. In general, semicrystalline polymer melts have a broad molecular weight distribution. Thus, the chains that are long enough to be stretched at the shear rate (γ̇ > 1/τR(M)) can form FIC precursors, while shorter chains grow in spherulites or epitaxial parts of cylindrites as shown in Figure 15b.44

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AUTHOR INFORMATION

Corresponding Author

*(R.H.C.) E-mail [email protected]; Tel +1-814-863-3457. ORCID

Behzad Nazari: 0000-0002-9106-5445 Alicyn M. Rhoades: 0000-0003-4678-419X Ralph H. Colby: 0000-0002-5492-6189 Notes

The authors declare no competing financial interest.

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4. CONCLUSION In this study, isothermal flow-induced crystallization of PA 66 was investigated in terms of shear rate and shearing time at Ts = 270 °C using rheology and polarized optical microcopy. For the rheological measurement, a small-amplitude oscillatory shear time sweep was performed during crystallization at Tc = 245 or 250 °C. As a specific work was imposed on a PA 66 melt from

ACKNOWLEDGMENTS This research was funded by SKF. The authors thank Hirokazu Hasegawa of Toray Research Center Inc. for help with the SEC measurements. The authors also thank René Androsch at Martin Luther University Halle-Wittenberg for great comments on this paper. I


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Isothermal Flow-Induced Crystallization of Polyamide 66 Melts

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