Effect of the blend ratio of cyclic and linear polyethylene blends on isothermal crystallization in the quiescent state

The role of entanglements that form between cyclic and linear polymers in crystallization is of particular interest, but it is not fully understood. We investigated the crystallization behaviors of blends of cyclic polyethylene (C-PE) and linear polyethylene (L-PE) in a quiescent state to elucidate the role of this novel entanglement in crystallization. The samples were prepared by mixing the prepared C-PE and L-PE specimens at L-PE weight fraction (ΦL-PE) values of 0–100 wt%, with the weight average molecular weights of C-PE and L-PE being 175 × 103 and 154 × 103, respectively. The isothermal crystallization behaviors were analyzed through polarizing optical microscopy (POM) and differential scanning calorimetry (DSC). The morphology observed through POM was similar to that of ΦL-PE. From the time evolution of the heat flow measured via DSC, we obtained the half-crystallization time (t1/2) values as functions of ΦL-PE at different degrees of supercooling (ΔT). The 1/t1/2 values of the C-PE and L-PE homopolymers were approximately the same at ΔT = 25.5 and 26.5 K. At a larger ΔT value, the 1/t1/2 value of C-PE was significantly larger than that of L-PE. In contrast, 1/t1/2 reached a minimum value at ΦL-PE = 30–40 wt%, irrespective of ΔT. As the entanglement density increased with increasing ΦL-PE, the crystallization rate was expected to decrease monotonically. By considering the experimental relationship between 1/t1/2 and ΦL-PE, we speculated that the suppression of crystallization in the blended system was caused by a novel entanglement formed by the penetration of the L-PE chain into the C-PE chain. The isothermal crystallization behaviors of blends of cyclic polyethylene (C-PE) and linear polyethylene (L-PE) in a quiescent state were investigated. This figure shows the inverse of the half-crystallization time (1/t1/2) as a function of the weight fraction of L-PE (ΦL-PE) at different degrees of supercooling (ΔT). The 1/t1/2 showed a minimum at ΦL-PE = 30–40 wt%, irrespective of ΔT. By considering the experimental relationship between 1/t1/2 and ΦL-PE, we speculated that the suppression of crystallization in the blended system was caused by a novel entanglement formed by the penetration of the L-PE chain into the C-PE chain.


Introduction
The crystallization mechanisms of linear polymers in quiescent states have been studied for several decades.Numerous studies have been devoted to clarifying the effect of molecular weight on crystallization, such as studies on the crystallization characteristics of polyolefins and polyesters from isotropic melts; these investigations are conducted because it is known that the topological nature of chain molecules is explicitly dependent on their molecular weight.For example, Hoffman et al. [1] conducted a series of studies on the crystal growth of polyethylene.Okui et al. [2] reported the primary nucleation and crystal growth attributes of several polymers in the melt.The role of chain entanglements in polymer crystallization is one of the most challenging problems of this process.Psarski et al. [3] and Hikosaka et al. [4] independently reported that entanglements suppress the nucleation and growth of polymers.However, it remains unclear which type of entanglement (knots, twists, or threads) most strongly affects polymer crystallization.
Cyclic polymers have long been of interest because, unlike linear polymers, they have the unique topological feature of no chain ends.Many studies on the viscoelastic properties of cyclic polymers have been conducted.These results indicate that cyclic polymers have fewer entanglements than linear polymers because of their lack of knot entanglements [5].In the last few decades, the number of studies on the crystallization of cyclic polymers has markedly increased [6][7][8][9][10].The reported results are controversial, and discussions are still ongoing [10].Therefore, with this study, we do not intend to reach a universal conclusion about whether cyclic or linear polymers crystallize faster than the other.
Recently, López et al. [11] and Ruiz et al. [12] analyzed the crystallization characteristics of blends of cyclic and linear polyesters.In these cases, it is expected that the novel entanglements formed between the cyclic and linear polymers, known as the threading effect [11,12], are important.Scholars have noted several times that the influences of linear contaminants are apparent in the rheological behaviors of tested specimens.For example, Kapnistos et al. found that the entanglements formed by blending cyclic and linear polystyrene are more difficult to disentangle than those formed with cyclic polystyrene through stress relaxation only [13].
In this work, we investigate the crystallization behaviors of blended cyclic polyethylene (C-PE) and linear polyethylene (L-PE) samples in a quiescent state.The M w values of C-PE and L-PE are fixed for all specimens, and the blend ratios of C-PE and L-PE are changed.The halfcrystallization time (t 1/2 ) is measured for a fixed degree of supercooling (ΔT), not for a fixed crystallization temperature (T c ).The effects of the entanglement species formed by C-PE and L-PE and their blends on crystallization are discussed.

Sample preparation
C-PE and L-PE were prepared using previously reported procedures [14].Cyclic and linear polyoctenamers, which are PE precursors, were synthesized by the ring-opening metathesis polymerization of cis-cyclooctene after catalysis by a cyclic Ru-alkylidene complex and a secondgeneration Grubbs catalyst, respectively.Both PE precursors were hydrogenated with p-toluenesulfonyl hydrazide and converted to the corresponding PE.The chemical structures of the samples were confirmed through FT-IR spectroscopy (JASCO FT/IR-410 spectrometer) and 1 H-and 13 C-NMR spectroscopy (JEOL AL300 SC-NMR).The weight average molecular weights, M w , of C-PE and L-PE were determined by measuring the intrinsic viscosities [η] of the PE precursors in tetrahydrofuran at 30 °C [14].The M w values of the C-PE and L-PE precursors were converted to those of C-PE and L-PE, respectively, by assuming 100% hydrogenation.The M w values of C-PE and L-PE were 175 × 10 3 and 154 × 10 3 g/mol, respectively.The equilibrium melting temperatures (T m 0 ) of C-PE and L-PE [15,16] were calculated by assuming that the T m 0 of C-PE was equal to that of the perfect extended chain crystals of an L-PE specimen with half the M w of the C-PE specimen.The T m 0 values of C-PE and L-PE were 140.9 and 146.1 °C, respectively.For the T m 0 of blended samples (T m 0 (C/L)), we assumed an additive property given by the following equation: where T m 0 (C-PE) and T m 0 (L-PE) are the T m 0 values of the C-PE and L-PE homopolymers, respectively.Since the blend of C-PE and L-PE could be regarded as a perfectly miscible system, this treatment was accepted as a first-order approximation.
A blend of C-PE and L-PE was prepared as follows: C-PE and L-PE homopolymers were mixed with hot o-xylene.The solution was poured into excess methanol, and the precipitate was recovered.The powder blended samples were dried in vacuo.The weight fraction of L-PE (Φ L-PE ) in the blended samples was varied from 0 to 100 wt%.

Instruments and measurements
The isothermal crystallization behavior in the quiescent state was observed through polarizing optical microscopy (POM; Olympus, BX-53) using a hot stage (Linkam 10002L) and differential scanning calorimetry (DSC; Per-kinElmer, DSC 8000) in a nitrogen stream (20 mL/min) to avoid sample degradation.The samples were sandwiched between two cover glasses for POM analysis and placed in an Al pan for DSC analysis.Each sample was heated at a rate of 30 °C/min and annealed at a temperature above T m 0 (melt annealing temperature T max = 160 °C) for 1 min to erase the previous thermal history.The samples were then cooled to T c at a rate of 30 °C/min.The range of ΔT was 25.5-28.5K.The isothermal crystallization behavior was recorded through POM using a video camera (Victor KY-F1030).During isothermal crystallization, we measured the heat flow as a function of crystallization time t using DSC.The experimental conditions of isothermal crystallization are summarized in Table 1.

Kinetic analysis with the Avrami equation
In this study, the isothermal crystallization kinetics of the C-PE and L-PE blends were analyzed using the classical Avrami equation [17,18].The Avrami equation could be expressed as follows: 1 where Χ t is the relative degree of crystallinity at time t, k is the overall crystallization rate constant, and n is the Avrami index.Χ t could be defined as follows: where ΔH t is the heat generated at t and ΔH ∞ is the total heat generated until the end of crystallization.Equation ( 2) could be transformed into a double logarithmic form as follows: The Avrami index n could be determined from the slope of the log Àln 1 À X t ð Þ ½ vs. log t curve.Fitting between experimental data and Eq. ( 4) was performed with the data under the condition of X t < 0.2, as recommended by Lorenzo et al. [18].The fitting parameters are summarized in Supplementary Table S1.The Avrami index n is related to the nucleation and geometry types of the growing crystal, and its value usually ranges from 0.5 to 4 [17].By substituting Χ t = 0.5 into Eq.( 4), we could obtain t 1/2 ; that is, we could obtain the time necessary for the completion of 50% crystallization as follows: In this study, we calculated the t 1/2 values using the n and k values determined from the Avrami plot based on Eq. ( 4).Notably, the half-crystallization time included the contributions of both primary nucleation and crystal growth.In this study, we did not intend to prove the validity of the Avrami analysis, and we only used it for the quantitative estimation of t 1/2 .For reference, the t 1/2 values obtained from the curve of the relative degree of crystallinity (t 1/2 exp ) and calculated by Eq. ( 5) using k and n values determined from the Avrami plot (t 1/2 fit ) are summarized in Supplementary Table S2.

Results and discussion
Morphologies of the blends of C-PE and L-PE observed by POM ΔT and t are fixed at 25.5 K and 210 s, respectively.This crystallization period observed by POM corresponds to the early stages of crystallization, which is mainly the nucleation stage.Nucleation at Φ L-PE = 0 wt%, that is, the C-PE homopolymer, occurs with the highest density, although each nucleus remains small.The nucleation density at Φ L-PE = 100 wt%, that is, the L-PE homopolymer, is slightly more diluted than that of the C-PE homopolymer; however, each nucleus grows to a relatively large size.Eventually, the nucleation at Φ L-PE = 50 wt% becomes the slowest among the samples.The overall crystallization rate includes the contributions of both the primary nucleation rate and the crystal growth rate.Because the M w values of C-PE and L-PE are different, it is difficult to conclude which homopolymer has a faster crystallization rate.The morphology of the formed crystal does not seem to be significantly different according to the blend ratio, as reported for the cyclic and linear blends of poly(ε-caprolactone) [11] and poly(L-lactide) [12].[20].As the ΔT values used in this study are relatively large, it is natural to consider that general polyethylene crystallizes via three-dimensional spherulitic growth.In this situation, the Avrami index n is expected to be close to 3 for heterogeneous nucleation and 4 for homogeneous nucleation.The morphology observed in Fig. 1 resembles a twodimensional distorted shape but not a three-dimensional one.This phenomenon may be caused by the sample prepared by the hydrogenation of polyoctenamers, which have certain imperfect chemical structures with spectroscopically undetectable levels.Figure 3 shows plots of the inverse of the half-crystallization time (1/t 1/2 ) against Φ L-PE for different ΔT values.The 1/t 1/2 for C-PE is approximately the same as that for L-PE at ΔT = 25.5 and 26.5 K.At a larger ΔT, the former is significantly larger than the latter.As mentioned before, t 1/2 involves contributions from both primary nucleation and crystal growth.It is well known that the primary nucleation density easily fluctuates depending on the density of heterogeneity within the system [4].

Crystallization kinetics of the blends of C-PE and L-PE
According to the data obtained at a large ΔT value where the contribution of nucleation is relatively low, C-PE seemingly crystallizes faster than L-PE.Conversely, the Φ L-PE dependence of 1/t 1/2 roughly shows a downward convex curve, and a minimum of 1/t 1/2 is observed at approximately Φ L-PE = 30-40 wt%, irrespective of ΔT.López et al. [11] and Ruiz et al. [12] reported the plots of the inverse of the half-crystallization (1/t 1/2 ) against the weight fraction Φ of the cyclic polymer at a fixed T c .The scholars have demonstrated a complicated dependence of 1/t 1/2 on Φ.
The difference between their results and this study may arise from the difference between plotting against T c or ΔT.Since crystallization is suppressed by the entanglements, the suppression effect of crystallization by the entanglements is

Conclusion
To clarify the effects of entanglement species on crystallization in a quiescent state, we studied the t 1/2 values of blends of C-PE and L-PE from the melt as functions of Φ L-PE and ΔT through POM and DSC.We prepared C-PE and L-PE specimens with M w values of 175 × 10 3 and 154 × 10 3 , respectively.The 1/t 1/2 values of the C-PE and L-PE homopolymers were approximately the same at ΔT = 25.5 and 26.5 K.In contrast, the 1/t 1/2 values of the blends of C-PE and L-PE were significantly lower than those of the C-PE and L-PE homopolymers, and a minimum value of 1/t 1/2 was observed at Φ L-PE ≈ 30-40 wt%.This finding suggested that the suppression of crystallization in the blended system was caused by the novel entanglement formed by the penetration of the L-PE chain into the C-PE chain.

Figure 1
Figure 1 shows typical examples of POM images of the crystals formed in the blends of C-PE and L-PE at (a) Φ L-PE = 0 wt%, (b) Φ L-PE = 50 wt%, and (c) Φ L-PE = 100 wt%.ΔT and t are fixed at 25.5 K and 210 s, respectively.This crystallization period observed by POM corresponds to the early stages of crystallization, which is mainly the nucleation stage.Nucleation at Φ L-PE = 0 wt%, that is, the C-PE homopolymer, occurs with the highest density, although each nucleus remains small.The nucleation density at Φ L-PE = 100 wt%, that is, the L-PE homopolymer, is slightly more diluted than that of the C-PE homopolymer; however, each nucleus grows to a relatively large size.Eventually, the nucleation at Φ L-PE = 50 wt% becomes the slowest among the samples.The overall crystallization rate includes the contributions of both the primary nucleation rate and the crystal growth rate.Because the M w values of C-PE and L-PE are different, it is difficult to conclude which homopolymer has a faster crystallization rate.The morphology of the formed crystal does not seem to be significantly different according to the blend ratio, as reported for the cyclic and linear blends of poly(ε-caprolactone)[11] and poly(L-lactide)[12].

FigureFig. 1
Figure 2a shows a typical example of the time evolution of heat flow for the blends of C-PE and L-PE at ΔT = 27.5 K.All samples show uniform exothermic peaks, although the half-widths of the peaks differ depending on the blend ratio.The peak positions of the C-PE and L-PE homopolymers,

Fig. 2 Fig. 3
Fig. 2 Typical examples of the time evolution of a heat flows of the blends of C-PE and L-PE at ΔT = 27.5 K and b relative degrees of crystallinity Χ t of the blends of C-PE and L-PE at ΔT = 27.5 K.