Article Cite This: Macromolecules XXXX, XXX, XXX−XXX
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Agglomeration of Crystals during Crystallization of Semicrystalline Polymers: A Suspension-Based Rheological Study Peng He, Wei Yu,* and Chixing Zhou
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Advanced Rheology Institute, State Key Laboratory for Metal Matrix Composite Materials, Shanghai Key Laboratory of Electrical Insulation and Thermal Ageing, Department of Polymer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China ABSTRACT: The agglomeration of spherulites during isothermal crystallization of olefin multiblock copolymers and the role of mesophase separation on the agglomeration behavior were investigated by a new rheological method, which is based on the analogy between crystal morphology and particle suspension in polymeric matrix. The new suspension-based rheological method solved the problem of frequency dependency, which was encountered in the traditional rheological study in determination of the fraction of transformation. It was achieved by decomposing the time-resolved dynamic moduli during crystallization into the hydrodynamic part and the agglomerates’ part using a two-step shifting procedure. The relative crystallinity determined from the product of two shifting factors, the strain rate amplification factor and the stress amplification factor, was consistent with the DSC measurements. Moreover, the dependence of the agglomerates’ contribution to the storage modulus of the crystal (GAgg ′ ) on its volume fraction (ϕrheo) was found to be independent of the crystallization temperature, resulting in a master curve G′Agg vs ϕrheo that could be used as a unique parameter to characterize the agglomeration of spherulites. For olefin block copolymers with similar hard-block content (or crystallinity), it was found that mesophase separation not only delayed the agglomeration of spherulites but also changed its packing behavior. Comparisons with polymer nanocomposites further illustrated the differences in the spatial distribution and agglomeration of “fillers” in polymer nanocomposites, homogeneous semicrystalline polymers, and heterogeneous semicrystalline polymers.
1. INTRODUCTION In the processing of semicrystalline polymers, solidification due to crystallization is a fundamental issue and of great importance for the modeling of the process and optimizing the properties of products. It is well known that the crystal of polymers has a hierarchical character, and the structures at a specific length scale may directly affect the properties at a larger scale. Different techniques have been adopted to study the crystallization behavior under different length scales. For example, wide-angle X-ray diffraction (WAXD) can be used to understand the crystal structure, i.e., the ordering of molecules in a unit cell. Small angle X-ray scattering (SAXS) can be used to understand the packing of lamellae. At a larger length scale, polarized optical microscopy (POM) or small angle light scattering (SALS) helps to quantify the size of spherulite. However, it is still a challenge to understand how aggregates of lamellae (or spherulites) pack or agglomerate in the space and also its effect on mechanical properties. In the past decades, considerable works1−8 have been devoted to understanding the crystallization behavior of semicrystalline polymers by exploiting the rheological response during solidification due to its high sensitivity especially at the early stage of crystallization. Different attempts have been made to quantify the crystallinity from rheological functions. For example, Khanna et al.9 proposed a relation to transform © XXXX American Chemical Society
the dynamic storage modulus into the crystallization fraction (χRheo) to investigate the crystallization kinetics of nylon. However, Boutahar et al.3 found that the crystallinity curve (χRheo) determined from such relation is frequency dependent and shows obvious deviations from that measured by calorimetry (χDSC). Moreover, the difference between χDSC and χRheo is material dependent, which drove them to suggest different definitions of rheological crystallinity for different materials.3 These findings imply that the rheological responses of crystallizing polymers are sensitive to the morphology of crystals. On the other hand, characteristic time of crystallization was defined from the evolution of rheological functions during crystallization to infer the kinetics of crystallization under both quiescent and shear conditions. Usually the time were adopted at which the viscosity or storage modulus doubles (hardening criterion),10 or the crossover time of G′ and G″,11,12 or the gelation time13,14 according to the Winter− Chambon criterion. However, in a summary made by Lamberti et al.6 of a normalized hardening curve linking viscosity and crystallinity of the former studies1−5,15 on different crystallizing polymers, they noted that the crystallinity from the hardening Received: November 15, 2018 Revised: January 11, 2019
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DOI: 10.1021/acs.macromol.8b02452 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules Table 1. Molecular Parameters and Transition Temperatures of OBCs sample code
Mw (kg/mol)
total C8 (mol %)
Tma (°C)
Tcb (°C)
Xc,ΔHc (wt %)
TMSTd (°C)
mesophase separation
L01 L02 M01 M02 M03 H01
79.8 126.5 61.7 82.6 156.6 77.6
13.7 14.0 11.7 12.0 11.5 9.6
122.8 120.7 122.9 122.8 119.7 123.7
94.6 89.9 101.0 95.9 96.3 102.3
7.4 7.0 14.0 14.8 14.3 22.7
163.5 >200 153.8 160.4 >200 154.0
extremely weak strong extremely weak medium very strong medium
a The melting peak from DSC with heating rate 10 °C/min. bThe crystallization peak from DSC with cooling rate 10 °C/min. cCrystallinity from heat of melting. dMesophase separation temperatures determined from rheology.34
model system for the rheological study of crystallization, both at the early stage and at the intermediate/late stage. For semicrystalline OBCs, crystallization starts from the domains enriched in crystallizable ethylene segments. Both the confined crystallization and the breakout crystallization had been found in OBCs,28−35 i.e., crystallization will be confined in the ethylene-rich domains in the strong segregation limit because of the low content of the ethylene segment in the other domains; otherwise, in the weak segregation limit the crystals can breakout the ethylene-rich domains and further grow in domains containing less crystallizable segments. Therefore, it is also a good choice to understand the interplay between mesophase separation and crystallization because of the competition between the mesophase separation in the melt and crystallization. In preceding works34,36,37 we explored the phase behaviors of a series of multiblock OBCs with varying block structures in melt by linear and nonlinear rheology. On the basis of the understanding of the mesophase separation in OBCs melts, the rheological properties of the crystallizing melts could be different in OBCs with different block structure. Thus, the aim of this study is to suggest a new rheological method to understand the crystallization behavior of polymers which solves the problem of frequency dependency in determination of the crystallization fraction from the dynamic moduli. Moreover, additional information on the agglomeration of spherulites can be readily obtained, which helps to elucidate the interplay between phase separation and crystallization of block copolymers.
criterion could vary from 2% to about 50% and is also strongly frequency dependent. Therefore, direct comparison of the crystallization times from the rheological hardening criterion between different samples becomes meaningless because the same extent of hardening may not correspond to the same degree of crystallization. The problems encountered in the study of polymer crystallization by rheological measurements may be ascribed to the unclear relation between the crystalline structure, the crystallization fraction, and the viscoelastic properties. Generally, two main approaches have been applied to model the crystallizing polymer melts: the empirical formulas and the suspension models. A large number of empirical or phenomenological models1−3,9,16−19 have been developed in the literature to correlate the crystallinity and stress, but these models are all limited for a particular crystallizing systems. By contrast, the suspension models were found to fit the rheological properties of polymers during crystallization well mostly at high frequencies but fail for the low-frequency responses.20−22 The basic idea of the suspension model is that crystalline and amorphous melt phases are analogous to a hard or soft solid phase dispersed in a liquid matrix. During crystallization, a crystalline solid phase appears and smoothly grows in the continuous medium until the maximum percent of crystallinity is achieved. Therefore, a continuous variation of volume fraction is obtained. The failure of suspension at low frequency22 reflects the importance of the connected or agglomerated structure of the crystals in amorphous melt, which had been ignored in previous models. Recently, Roozemond et al.23 suggested using two time-hardening factors to reconstruct the dynamic moduli of semicrystalline polymer from those of the melt, which partially solved the failure of model prediction at low frequency range. However, the relaxation modes in semicrystalline polymer in their model are similar to those of polymer melt because they are just horizontally or vertically shifted.23 There are no additional relaxation modes included in their model, which have been experimentally observed at lower frequency.14 In the present work, a suspension model recently suggested that understanding the dispersion of nanoparticles24−26 will be adopted to investigate the isothermal crystallization of olefin multiblock copolymers (OBCs). The OBCs are statistically coupled linear multiblock copolymers of alternating soft segments (high octene content) and hard segments (low octene content). The soft segment is amorphous blocks having a low glass temperature similar to ultralow-density polyethylene, while the hard segment is semicrystalline blocks having a high melting point close to that of high-density polyethylene. Spherulite morphology had been observed in OBCs even when the crystallinity is as low as 7 wt %.27 Low crystallinity and spherulite morphology make OBCs a good
2. EXPERIMENTAL SECTION 2.1. Materials. The OBCs were provided as pellets by The Dow Chemical Co. Six different OBCs were selected in this work. The detailed information on molecular structure are given in Table 1. The total octene content is quite similar in all samples. The main difference among them is the molecular weight and the hard-block content. The former is the cause of mesophase separation, and the latter leads to different crystallinity.34 More detailed characterization and discussion on the block structures and mesophase separation behavior can be found in previous works.34,36 2.2. Measurements. Differential scanning calorimetry (DSC) measurements were carried out on a TA Instruments Q2000 for thermal analysis using sealed aluminum pans and specimens with the weight of 5−8 mg cut from pellets. The DSC was calibrated using indium and tin. All experiments were performed in nitrogen atmosphere with a flow rate of 50 mL/min. All rheological properties were obtained from small amplitude oscillatory shear (SAOS) measurements with 25 mm parallel plate geometry and a gap of 0.9 mm. The disc samples were made by compressing molding into films of 1 mm at 200 °C under a pressure of 10 MPa. All experiments were performed in the linear viscoelastic region determined by the strain sweeps. A strain-controlled rheometer (ARES-G2, TA Instruments) was used to monitor the isothermal crystallization processes for OBCs B
DOI: 10.1021/acs.macromol.8b02452 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules under quiescent conditions. In isothermal crystallization experiments, the samples were cooled rapidly from melt to the final crystallization temperatures, Tc, at a rate of 20 °C/min. Then the multiwave dynamic tests were applied to track the isothermal crystallization processes, as shown in Figure 1.
influence of the high moduli and possible wall slip in polymers with high crystallinity.3 It can be found that the growth of moduli at different frequencies follows different kinetic processes, suggesting the appearance of a kind of structure with a relaxation spectrum different from the melt. As the low hard-block content (low crystallinity), the final plateau modulus at different frequencies cannot superimpose in the late-stage crystallization, which is different from that in highdensity polyethylene with high crystallinity.3 The time evolution of dynamic moduli during crystallization can be transformed into the frequency spectrum at different crystallization times (Figure 3). For M01, it has been found that time−temperature superposition (TTS) worked well in the molten state,34,36 suggesting that it is homogeneous or very weakly segregated. The curves of the dynamic moduli with frequency at the beginning of crystallization (tc = 0 s or melt) are obtained by shifting the master curves to the crystallization temperature of 116 °C. The terminal slope for G′ and G″ at tc = 0 s in the log−log plot are found to be close 2 and 1 in Figure 3a and 3b, respectively, which are in accordance with the terminal flow of typical viscoelastic fluids. In the early stage of crystallization (tc = 14 s), the dynamic moduli over the frequency range of multiwave experiment are quite close to those in the melt state. As the crystallization proceeds, the filler effect of the increasing crystallization fraction drastically changes the low-frequency responses (∼1 rad/s) of the dynamic moduli, which is very similar to the filled polymer systems with different filler contents.24,25 The slopes at low frequency tend to decrease with time and can approach a constant in the late stage of crystallization. Meanwhile, the dynamic moduli at the high-frequency regime also show an obvious increase but with less extent than those at low frequency. The difference in the increment of dynamic moduli at different frequencies implies that there are contributions from structures with different length scales. Therefore, it is not unexpected that the crystallization fraction defined directly from dynamic moduli (or viscosity) would be frequency dependent. For example, Khanna9 proposed defining the relative crystallinity χrheo(t) by
Figure 1. Schematic indication of quiescent crystallization processes of olefin block copolymers. In the case of the multiwave test, several frequencies, which are higher order harmonics of the fundamental frequency (1 rad/s), are simultaneously applied. The strain amplitude of each harmonic is chosen to keep the overall strain amplitude in linear viscoelastic regime. The storage and loss moduli at each discrete frequency are obtained by means of Fourier transform of the stress response to the compound strain. Using this technique the experimental time needed for a frequency sweep is considerably shortened. It is then possible to cover a range of at least two decades of frequencies in a fraction of the time required for a normal dynamic frequency sweep.
3. RESULTS AND DISCUSSION 3.1. Evolution of Dynamic Moduli during Isothermal Crystallization. Figure 2 shows the evolution of dynamic moduli with time for sample M01 at seven oscillatory frequencies from 1 to 100 rad/s during the isothermal crystallization at 116 °C. It is clear that G′ and G″ increase with time at different frequencies and exhibit S-shaped growth. The initial growth of dynamic moduli can be correlated to the crystallization induction period and nucleation period, and then the sharp increases in moduli correspond to crystal growth stage. In the end of the crystallization, the moduli tend to increase gradually and can approach a plateau, which depends on the crystallinity and the crystal structure. Actually, the relatively low crystallinity of OBC makes the moduli still in the measurable range of the rheometer without a severe
χrheo (t ) =
G′(t ) − G′0 G′∞ − G′0
(1)
Figure 2. Evolution of storage modulus (a) and loss modulus (b) with time during the isothermal crystallization at 116 °C for M01. C
DOI: 10.1021/acs.macromol.8b02452 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules
Figure 3. Storage modulus (a) and loss modulus (b) with angular frequency at various crystallization times for M01 at 116 °C.
Figure 4. Transformed crystallization fraction χrheo(t) (a) and characteristic crystallization time (b) determined from rheological measurements for M01 at 116 °C.
where G′0, G′(t), and G′∞ are the storage moduli at the initial, intermediate, and final stage of crystallization. Figure 4a shows the relative crystallinity χrheo(t) with time at various frequencies for M01 at 116 °C, where the frequency dependency is obvious. More quantitatively, characteristic crystallization times, such as half-crystallization time t0.5 (when χrheo = 0.5) and the onset time tonset (when Gt′ = 2G0′),38 exhibit a decreasing trend with increasing frequency (Figure 4b). Thus, an important question arises as to how to eliminate the influence of frequency on the crystallinity curve determined from rheology. 3.2. Suspension Concept and Crystallization. 3.2.1. Stress Decomposition and Amplification Factors. We treat the crystallizing polymers as a composite, where crystals are suspended in the amorphous melt. Crystals are regarded as the solid particles, while the structures of the particle and the particle−matrix interaction are much more complex than those of the classical hard-sphere suspension. The analogy between particle suspensions in polymeric matrix and semicrystalline polymers lies in two aspects. The analogy can be made from a structural point of view (Figure 5), where both systems have two-level hierarchical structures. Primary particle and crystal lamella are the smallest structural unit in the two systems, respectively. The surface of primary particles is often attached by grafted or adsorbed chains. Similarly, the crystal lamellae are
Figure 5. Analogy between polymer nanocomposite and polymer crystal.
attached by unfolded chains. The interactions between fillers (particles or crystal lamellae) and polymer matrix are both reflected through the attached chains on the surface of fillers. These structural units can self-assemble into small aggregates or spherulites in suspensions and semicrystalline polymers. With the increase of particle content or crystallinity, small aggregates and spherulites can form large agglomerates in both D
DOI: 10.1021/acs.macromol.8b02452 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules
factors. This method has been found to be effective to quantify the dispersion of different nanoparticles.25,26 Under small amplitude oscillatory shear, the decomposition of stress leads to the decomposition of dynamic moduli
systems. A network of large agglomerates appears above a certain percolation concentration of particles or crystallinity. Therefore, in the early stage of crystallization, crystallization is mainly dominated by the growth of crystal aggregates, which can be regarded as adding more well-dispersed particles in the amorphous matrix. Later, some neighboring crystal aggregates can get in touch as they grow, which resembles the agglomeration of nanoparticles. After that growth of small agglomerates (spherulites) results in a percolated network of agglomerates, which is the critical point of the liquid−solid transition during crystallization. It is also similar to the gelation of nanoparticles in polymer matrix. The analogy can also be made from the viewpoint of linear viscoelasticity, where both the particle suspensions and the semicrystalline polymers exhibit an increment in the storage modulus (G′) at low frequency at a small amount of “filler” (particles or crystals). G′ at the low-frequency regime increases monotonically in both systems with the filler content and exhibits liquid-to-solid transition when the agglomerates percolate both in the particle suspension24,25 and in the semicrystalline polymers.13 In addition to the increment of G′ at low frequency, an increase of G′ can also be observed at the high-frequency regime, where the extent depends on the state of dispersion of particles in the matrix in suspension.26 Such phenomenon has also been observed in semicrystalline polymers;13 however, little is known about the underlying physics. Such similarities between particle suspension in polymeric matrix and semicrystalline polymer indicate the understanding of the relationship between the structures and the rheology of the suspension may be transferred to semicrystalline polymer to infer the kinetics of crystallization and the morphology of crystals as well. In suspension, the apparent stress σ can be generally decomposed into three parts.25,26 One comes from the matrix (σm), the second from the disturbance of flow field due to the particles, and the third from the particle−particle interactions between particles and particle agglomerates (σAgg). The sum of the first two contributions is also denoted as the hydrodynamic contribution (σH). If the particles are well dispersed in the matrix, the contribution from particle aggregates/agglomerates can be ignored. In this case, the hydrodynamic contribution to the stress (σH) should be directly correlated to the measured stress σ. For agglomerated particles, the mechanical contribution is more significant at low frequency (σAgg ≫ σH) due to the slow relaxation of agglomerated particles and is strongly related to the size of the agglomerates and the interactions among them. The high-frequency response, on the other hand, is assumed to be dominated by the hydrodynamic effect (σAgg ≪ σH), which mainly depends on the effective volume of particles. However, it is not easy to decouple the hydrodynamic effect from the overall mechanical properties, and it becomes extremely difficult when the matrix is viscoelastic. It means that the theoretical approach39 based on the micromechanical analysis of the particle pair would be not applicable for suspensions with a viscoelastic matrix. In contrast, we suggested another approach to evaluate the hydrodynamic effect by separating it into the strain rate amplification and stress amplification, whose correlation with classical models (such as Einstein model and Batchelor model) can be fulfilled by equating the apparent energy loss dissipation and the local energy dissipation.24,40 Such method has been extended to suspension with viscoelastic matrix, and the effect of particle dispersion and interactions are all ascribed to the amplification
G′c = G′H + G′Agg , G″c = G″H + G″Agg
(2)
where the subscript C denotes the crystallizing melt and Agg denotes the contribution from crystal agglomerates. The hydrodynamic contribution to the storage modulus and the loss modulus can be determined as24 G′H (ω) = asarG′m (arω), G″H(ω) = asarG″m(ar ω)
(3)
where ar and as in eq 3 are the rate amplification factor and the stress amplification factor, respectively. Under the ideal condition where there is no slip on the particle surfaces and the nondeformed particles are perfectly dispersed, the rate amplification factor can be evaluated as ar,ideal = 1/(1 − ϕ) with ϕ being the volume fraction of particles. The relation implies that the volume fraction of the nondeformable part in the total system is ϕ. For aggregated and agglomerated particles, ar would be larger than ar,ideal,25,26 indicating that the effective volume fraction of the nondeformable region is larger than the particle volume fraction. Such character has been utilized to determine the dispersion index of nanoparticles in polymer matrix for a relatively well-dispersed system (before particle separation or severe particle agglomeration).26 For agglomerated system, it is found that the combined amplification factor X = asa2r is related to the effective volume fraction of aggregates.22 The combined amplification factor can be described by the Bachelor model41,42 XB = 1 + 2.5ϕ + 6.2ϕ2
(4)
or the Krieger−Dougherty (KD) model XKD = (1 − ϕ/ϕm)−2.5ϕm
43
(5)
The Bachelor model and the Krieger--Dougherty model are originally suggested to describe the zero shear viscosity of suspension. The Bachelor model usually works well at low filler concentration (smaller than 0.1), while the KD model works well at much higher filler content, up to the maximum packing fraction (ϕm). In fact, when eq 5 is expanded to the second order of volume fraction, it becomes XKD = 1 + 2.5ϕ + 5.1ϕ2 + O(ϕ3), which is very close to the Batchelor model. The difference in the volume fraction of the crystal from the Batchelor model and the KD model is below 1% when the volume fraction of the crystal is smaller than 0.1. Thus, eq 5 is used to define the effective volume fraction of crystals ϕrheo = ϕm[1 − (asar2)−0.4/ ϕm ]
(6)
The maximum random packing volume fraction ϕm depends on the size distribution and compressibility of particles. The value for monodispersed hard sphere (ϕm = 0.637) is taken here. 3.2.2. Fraction of Crystal Aggregates. To obtain the effective volume fraction of crystals from rheology (eq 5), both the rate amplification factor ar and the stress amplification factor as need to be determined experimentally. It is critical to find that a two-step shifting procedure (horizontal shift with factor ar and vertical shift with factor asar) is necessary to obtain the hydrodynamic contribution from the dynamic moduli of matrix polymer.24 In fact, the loss tangent can be obtained from eq 3 as E
DOI: 10.1021/acs.macromol.8b02452 Macromolecules XXXX, XXX, XXX−XXX
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Figure 6. Shifted curves for the phase angle (a) and dynamic moduli (b) with crystallization time during isothermal crystallization of M01 at 116 °C. G″/(aras) in b are shifted vertically to avoid overlapping.
tan δ H(ω) = tan δm(arω)
frequency regime depends on the crystallinity. As seen from the example in Figure 6a, the high-frequency regime starts above ∼10 rad/s at an early stage of crystallization (
