Extended-chain Single Crystals Research Articles

Fracture and Deformation of Extended-Chain Crystals in Poly(ethylene Terephthalate)/Bisphenol-A Polycarbonate Blends Crystallized at High Pressure

With a combination of three-dimensional crystal ordering and long-chain molecular orientational ordering, the extended-chain crystals of polymers are ideal system for the studies on low-dimensional physics, and have potential applications as functional components. In this study, poly (ethylene terephthalate) / bisphenol-A polycarbonate (PET/BAPC) blend samples were prepared with solid phase forming technique under high pressure, and extended-chain single crystals with large c-axis thickness were formed within a relative short time. The fracture and deformation behaviors of the grownup crystals were investigated using scanning electron microscopy (SEM) and atomic force microscopy (AFM). Morphological observation showed that most of the extended-chain crystals were endowed with perfect appearance after the sample fracture. However, there were still a few crystals fractured apart, along or perpendicularly to their c-axis direction, or with cohesive fracture surfaces. Fractured spherulites with extended-chain lamellae as substructures were also disclosed in extended-chain crystals with AFM. Furthermore, the parallel lamellae deformed and changed their striation direction during the crystal growth, as was observed on a kind of extended-chain crystals grown in a PET oligomer and BAPC blend (PETO/BAPC). This study may be instructive to the improvement of the separation technique of such single crystals, so as to hasten their real applications.

Morphology of High-Pressure Crystallized Poly (Ethylene Terephthalate)/Bisphenol-A Polycarbonate Blends

The high-pressure crystallized poly (ethylene terephthalate) / bisphenol-A polycarbonate (PET/BAPC) blend samples were investigated using scanning electron microscopy (SEM) and atomic force microscopy (AFM). Besides the extended-chain single crystals with high quality and large c-axis thickness, the results showed that some novel crystal morphologies were formed in the multi-phase system within a relative short time. Spherulitic structures with different characteristics were observed, in and out the cultured polyester extended-chain crystals, respectively, and their substructures were found to be extended-chain lamellae. Furthermore, bud-like nano-crystals with zero- or one-dimensional structures, some of which aggregated and then evolved into three-dimensional nano-dendrites, were grown during the cooling process of the polyester blends at high pressure. The disclosed entities during this study may promote the understanding of formation process and mechanism for both spherulite and extended-chain crystals of polyesters, so as to instruct the processing of such alloyed engineering plastics with high performance.

Extended-Chain Crystals of High-Pressure Crystallized Poly (Ethylene Terephthalate) Oligomer/Bisphenol-A Polycarbonate Blends

In this study, the crystallization behaviors of the poly (ethylene terephthalate) oligomer/bisphenol-A polycarbonate (PETO/BAPC) blends were investigated under high pressure, and the recovered PETO/BAPC samples were characterized using XRD, DSC, SEM and AFM. The results showed that high-quality extended-chain single crystals with large c-axis thickness were formed in the multi-phase system within a relative short time, and the inner defects of the disclosed crystals could be removed by a self-healing process through high-temperature and high-pressure annealing. Morphologies of extended-chain crystals with different characteristics were also revealed with SEM and AFM. Wedge-shaped and bent extended-chain morphologies suggested that sliding diffusion and transesterification occurred simultaneously in the system, and the crystallization of the large crystals was a self-assembling process induced by chemical reactions at high pressure. This process provides a new route to grow large polymer extended-chain crystals and suggests self-assembly under high pressure is a promising method to create materials with new structures and properties.

Role of entanglement in nucleation and ‘melt relaxation’ of polyethylene

An experimental formula of the nucleation rate I of polyethylene as a function of number density of entanglement ν e within the melt was obtained as I( ν e)∝exp(− γν e), where γ is a constant. In order to obtain a functional form of I( ν e), I is determined by changing ν e within the melt. The ν e within the melt can be changed when crystals with different lamellar thickness l are melted. It is shown that the ν e within the melt just after melting is related to l before melting. The ν e of folded chain crystals (FCCs) is large, while that of extended chain single crystals (ECSCs) is very small. Therefore, strictly speaking, the experimental formula is a kind of ‘semi-experimental’ one. Because it is obtained by combining an experimental formula of I as a function of l before melting I( l) and a formula between l and ν e based on the most probable model. It was found that the ν e dependence of I is mainly controlled by the topological diffusion process within the interface between the melt and a nucleus and/or within the nucleus not by the forming process of a critical nucleus. The slope of the plots of log I against Δ T −2 was constant, irrespective of morphologies, FCCs and ECSCs, where Δ T is the degree of supercooling. From this fact, it was concluded that the fold type nucleus are formed from the melt of ECSCs as well as from the melt of FCCs. In our previous study, we found that I decreases exponentially with increase of annealing time Δ t at a temperature above the melting temperature. From these results, we proposed a ‘two-stage melt relaxation’, i.e. fast conformational and slow topological relaxations. When the ECSCs are melted, extended chains within ECSCs are rapidly changed to random coiled chain conformation and then chains gradually entangle each other. We also proposed a formula, ν e ( Δt)∝− ln{ const.+A exp(− Δt/τ m )}, where A is a constant and τ m is the ‘melt relaxation’ time.

Power Law of Molecular Weight of the Nucleation Rate of Folded Chain Crystals of Polyethylene

The molecular weight (Mn) dependence of the primary nucleation rate (I) of folded chain single crystals (FCSCs) of polyethylene (PE) was studied. A power law for the nucleation rate, I ∝ Mn-2.4, was found. The FCSCs were formed by isothermal crystallization from the melt into an ordered phase (=orthorhombic phase). A new experimental method was established to obtain reliable I, which has been difficult in the case of heterogeneous nucleation for long years. The degree of supercooling (ΔT) dependence of I fits well with the theoretical I given by classical nucleation theory, I = I0 exp(−ΔG*/kT) ∝ D exp(−C/ΔT2), where I0 is proportional to the topological diffusion coefficient of polymer chains (D), ΔG* is the free energy for forming a critical nucleus, k is the Boltzmann constant, T is temperature, and C is a constant. It is found that ΔG* (∝C) does not depend on Mn, while I0 decreases with increase of Mn, from which it is concluded that formation of a critical nucleus is not controlled by Mn, while only topological diffusion of polymers is controlled by Mn, i.e., I ∝ D(Mn). Similar power laws of PE were already found by the present authors on I of extended chain single crystals (ECSCs), i.e., I ∝ Mn-1.0, and on the lateral growth rates (V) of ECSCs and FCSCs, V ∝ Mn-0.7 and V ∝ Mn-1.7, respectively. ECSCs were formed by isothermal crystallization from the melt into a disordered phase (=hexagonal phase). Therefore, it is concluded that a common power law, I, V ∝ D(Mn) ∝ Mn-H of PE is confirmed, irrespective of nucleation or growth and irrespective of crystalline phases, ordered or disordered phases. It is to be noted that the power H depends on the degree of order of the crystalline phase, from which it is concluded that both nucleation and growth are controlled by the “topological” diffusion of polymer chains within interface between a nucleus (or crystal) and the melt and/or within the nucleus. The “topological” diffusion is related to chain sliding diffusion and disentanglements.

Effect of Entanglement on Nucleation Rate of Polyethylene

Recently, present authors found a power law of nucleation rate (I) of single crystals of polyethylene (PE), I ∝ M−H, where M is molecular weight and H is a constant.1, 2 This indicates that the topological nature of polymer chain plays an important role on nucleation of polymers. Topological nature is related to the chain entanglement and chain sliding diffusion.3, 4 Polymer chains should be disentangled within interface between the melt and a nucleus during nucleation. Therefore, if number density of entanglement (νe) is small, it is expected that I becomes large. This expectation was confirmed in our preliminary study5 that I decreases with increase of keeping time at a temperature above melting temperature (∆t). This result was speculated that when the melt is kept above melting temperature, νe gradually increases with increase of ∆t and approaches to thermal equilibrium νe (νe = 1), which can be regarded as “melt relaxation”. However, any experimental evidence of the expectation has not been reported yet, therefore it is important to show the evidence. Purpose of this work is to show an experimental evidence that I increases with decrease of νe within the melt. It is reasonable that a giant extended chain single crystals (ECSCs) includes little entanglement (νe ∼ 0), while thin lamellae of folded chain crystals (FCCs) do a lot of entanglements. Therefore, when the giant ECSC and thin FCCs are melted, the melt should have small νe and large νe, respectively for small ∆t, because the above “melt relaxation” process takes long time, i.e., we showed that it takes about several hours or a few days depending on the conditions and molecular weight.5 This suggests that νe should decrease with increase of lamellar thickness (l). In the case of polyethylene, l can be changed easily from several nm to several μm by changing crystallization conditions, such as degree of supercooling (∆T ) and pressure. According to classical nucleation theory by Becker and Doring and Turnbull and Fisher, I is expressed by two competing factors as

Lamellar thickening growth of an extended chain single crystal of polyethylene (II) : ΔT dependence of lamellar thickening growth rate and comparison with lamellar thickening

The degree of supercooling (ΔT0) dependence of lamellar thickening growth rate (U) of an isolated extended chain single crystal (ECSC) of polyethylene is studied. The experimental formula,U = C exp(−D/ΔT0), where C = 130 nm/s and D = 20.0 K is obtained for the first time. The formula is the same as that of lateral growth rate (V). The reason why U and V obey the same formula is well explained by a model named “sliding diffusion model of the lamellar thickening growth”. The model proposed that the lamellar thickening growth is controlled by both chain sliding diffusion within the ECSC and the nucleation on the side surface. The observed fact that the U increases with increase of ΔT0 is opposite to the well known fact that lamellar thickening rate W decreases with increase of ΔT0. This siginificant difference was well explained by the difference between the “primary crystallization” and the “secondary crystallization”, which is a kind of “Ostwald's ripening process”. The origin of the “tapered shape” is well explained by coupling of lamellar thickening and lateral growths.

Molecular Weight Dependence of Primary Nucleation Rate of Polyethylene I. An Extended Chain Single Crystal

Molecular weight (M) dependence of the primary nucleation rate (I) of an extended chain single crystal of polyethylene crystallized at high pressure (P=0.4 GPa) was studied. We obtained for the first time an experimental formula that I∝M−1 which we named “power law of primary nucleation”. We showed a well-known experimental formula that I=I0exp(−κ/ΔT2), where I0 is a constant proportional to the diffusion constant of molecules (D), κ is related to the activation free energy for forming a critical nucleus (ΔG*) and ΔT is the degree of supercooling. We showed that only I0∝D decreases with increase in M and κ does not depend on M. From this results we concluded that M dependence of I is mainly controlled by the “chain sliding diffusion” process not by the formation process of a critical nucleus, that is, I(M)∝D(M)∝Ps(M) and ΔG*=const. Here D can be regarded as an “expanded diffusion constant” and Ps is a survival probability defined in “chain sliding diffusion” theory presented before by one of authors (MH). Based on these results we proposed a “chain sliding diffusion theory of primary nucleation” that the primary nucleation is a process of “chain sliding diffusion” within the nucleus which requires disentanglement of molecular chains within the interface between the nucleus and the melt. The theory explained well the observed power law.

Molecular weight dependence of the lateral growth rate of polyethylene 2. Folded-chain crystals

Molecular weight ( M) dependence of the lateral growth rate ( V) of folded chain crystals (FCCs) of polyethylenes (PE) was investigated. This study was carried out on single (or single crystal-like) crystals using the equilibrium melting temperature ( T m 0) determined by applying Gibbs-Thomson's equation. The well-known relation V= V 0 exp(− B/Δ T) was obtained where V 0 and B are constants and Δ T is a degree of supercooling. V 0 strongly decreased with increase of M, whereas B did not, which indicates that the self-diffusion process of polymer chains mainly controls the M dependence of V, whereas the nucleation one does not. Experimental formula that V∝ V 0∝D∝ M − H where D is self-diffusion constant and H is a constant; H=1.7 was obtained. These results are similar to Hoffman et al.'s results but their H was rather smaller, H=1–1.5. A similar study on extended-chain single crystals (ECSCs) reported in our previous paper gave the same experimental formula but H was much smaller, H=0.7. From the difference in H between FCCs and ECSCs, a new proposal that M dependence of V may be mainly controlled by the surface diffusion process of chain polymers on the growing crystal surface, is discussed briefly.

Crystal structures and morphology of thin-film, melt-crystallized, and polymerized poly(ethylene naphthalate)

Application of electron diffraction (ED) to poly(ethylene naphthalate) (PEN) crystallized isothermally from the melt at 260°C has permitted determination of the α-and β-form unit cells. While the α-form lattice parameters and cell agree well with those proposed in the literature, a different cell is proposed for the β-form (monoclinic, P21/n11 space group; 4 chains, with a = 1.304 nm, b = 0.926 nm, c = 1.300 nm, α = 131.47°, β = γ = 90°, ρ = 1.368 g/cm3). The β-form crystals were large, resembling hedrites (axialites). A number of different, single-zone ED patterns from at least one additional two-chain unit cell (γ) were found, indicating a large degree of PEN polymorphism. The γ unit cell has not yet been determined. Nascent melt-polymerized samples were also examined, giving rise to both β-and γ-type patterns. The γ-patterns arise from extended-chain single crystals of variable thickness.

Molecular weight dependence of lateral growth rate of polyethylene (I) — an extended chain single crystal

Molecular weight ( M) dependence of lateral growth rate ( V) of an extended chain single crystal (ECSC) of polyethylene (PE) crystallized at high pressure ( P = 0.4 GPa) was studied. We obtained a well-known relation that V=V 0 exp(− B ΔT ), where V 0 and B are constants related to a self-diffusion constant of molecules and free energy of forming a critical nucleus and ΔT is degree of supercooling. We showed that V 0 decreases with increasing M and B does not depend on M, which are similar to results reported by Hoffman et al. for a folded chain crystal (FCC) of PE. This indicates that M dependence of V is controlled by the self-diffusion process of molecules, while that is not done by the nucleation process. We obtained an experimental formula, V( M) ∝ D( M) ∝ M − H , where D is a self-diffusion constant and H is a constant, H=0.7. A similar relation has been shown, reported by Hoffman et al. and by us in a separate paper. But the H given by us was larger. H=1.8. It should be noted that the H of a FCC is much larger than that of an ECSC. We will propose a new mechanism from this significant difference on H in a separate paper, that M dependence of V is mainly controlled by the surface diffusion process of chain molecules on a surface of a crystal not by the self-diffusion process within the melt.

Lamellar Thickening Growth of an Extended Chain Single Crystal of Polyethylene. 1. Pointers to a New Crystallization Mechanism of Polymers

Crystallization and growth of an isolated extended chain single crystal (ECSC) of polyethylene (PE) under high pressure from the melt into the mobile phase, such as hexagonal phase, was studied by in-situ optical microscopy and transmission electron microscopy. Direct evidence is obtained that an isolated ECSC was formed from a folded chain single crystal through the combination of newly recognized “lamellar thickening growth” and the long familiar lateral growth. This confirmed the prediction of chain sliding diffusion theory that the lamellar thickening growth takes place the important role in the origin of folded chain and extended chain crystals (FCCs and ECCs) presented by one of authors (M.H.) previously. The lamellar thickness (l) inceased linearly with time (t), indicating that the lamellar thickening growth rate is constant as long as the crystal is in isolation, i.e., it does not impinge on others, directly reflected also by the straightened taper of the cross-sectional shape. This is quite different from the well-known lamellar thickening of stacked-lamellar system where l increases linearly with logarithm of time (log t). It is shown that the difference is due to the difference between the primary and the secondary crystallization processes. The lamellar thickening growth rate (U), defined by (dl/dt)/2, was measured for the first time by developing two methods, “direct method” and “mapping method”.

Dependence of the lamellar thickness of an extended-chain single crystal of polyethylene on the degree of supercooling and the pressure

The dependence of the lamellar thickness (I) of an extended-chain single crystal (ECSC) of polyethylene (PE) crystallized at various pressures below or at the triple-point pressure (Ptri= 0.5 GPa) on the degree of super-cooling (ΔT) and the pressure have been studied. The value of I increased with the decrease in ΔT[i.e. increase in the crystallization temperature (Tc)] at a fixed pressure, similar to the well known ΔT dependence of I for a folded-chain single crystal (FCC). The observed maximum value of I, obtained at the lowest ΔT(Imax) increased with increasing pressure and the crystal changed from FCC to an extended-chain crystal (ECC) at ca. 0.25 GPa. Application of the chain-sliding diffusion theory, previously proposed by one of the authors (M.H.) was found to explain well observed significant ΔT dependence of I and the pressure dependence of Imax. It was proposed that the value of I is determined by the cessation of lamellar thickening growth at the phase transition from metastable hexagonal to stable orthorhombic. The phase transition was also studied and it is suggested to be a nucleation-controlled process of the primary nucleus.

Role of Transient Metastable Hexagonal Phase in the Formation of Extended Chain Single Crystals of Vinylidene Fluoride and Trifluoroethylene Copolymers

Crystallization of vinylidene fluoride and trifluoro-ethylene copolymer, P(VDF/TrFE), with higher VDF molar content (x) than the triple point x (x tri=0.82) was studied. When the copolymer is crystallized at atmospheric pressure below the melting temperature from the melt, thick extended-chain crystals (ECCs) are formed. It is suggested that the ECCs were formed in the metastable hexagonal phase which appears transiently and then transforms into the stable orthorhombic phase, as has been shown on polyethylene (PE) previously by Rastogi et al.. [Macromolecules 24 (1991) 6384] This suggests the important role of the metastable hexagonal phase in the formation of ECCs, which is discussed by the the chain sliding diffusion theory presented by one of us (M. H.).

Lateral Growth of Extended-Chain Single Crystals of Vinylidene Fluoride and Trifluoroethylene Copolymers

Lateral growth of extended chain single crystals (ECSCs) of vinylidene fluoride and trifluoroethylene copolymers, P(VDF/TrFE), within the mobile hexagonal phase at high temperature and at atmospheric and high pressures was investigated directly by polarized optical microscopy. The VDF molar contents (x) studied were 0.75 and 0.78, which were less than x at the triple point (x=0.82) at atmospheric pressure. The lateral growth was steady growth. The plot of logarithmic lateral growth rate (log V) against the inverse of the degree of supercooling (ΔT-1) gave a straight line, i.e., V=V0 exp (-C/ΔT), where V0 and C are constants, and does not show any breaking. These results confirmed that the lateral growth is mainly controlled by a two-dimensional nucleation process and shows only one “regime”. The number of ECSCs increased linearly with time, which indicates homogeneous nucleation.

Morphology of Extended Chain Single Crystals of Vinylidene Fluoride and Trifluoroethylene Copolymers

The morphology of extended chain crystals (ECCs) or extended chain single crystals (ECSCs) of vinylidene fluoride and trifluoroethylene copolymers, P(VDF/TrFE), with VDF molar content x\\lesssim0.82 was observed by polarized optical microscopy and transmission electron microscopy. It was found that a thick isolated ECSC and thick stacked ECCs, about 0.3-0.8 µm thick, were formed when P(VDF/TrFE) was crystallized from the melt into the mobile hexagonal phase at atmospheric pressure or under high pressure, 80 MPa or 170 MPa. The isolated ECSCs were found for the first time on the copolymer. This confirmed the prediction of chain sliding diffusion theory proposed by Hikosaka that ECSCs or ECCs will be formed when polymers are crystallized from the melt into the mobile hexagonal phase.

Extended chain crystal growth of low molecular mass poly(ethylene oxide) and α,ω-methoxy poly (ethylene oxide) fractions near their melting temperatures

For low molecular mass poly(ethylene oxide) (PEO) and α,ω-methoxy poly(ethylene oxide) (MPEO) fractions, extended chain crystals can grow when isothermal crystallization temperatures are near their melting temperatures (supercooling ΔT = T m − T e is in the range of a few degrees). Experimentally, observed lamellar thicknesses of the extended chain crystals are constants in this supercooling region. Linear relationships between crystal growth rate ( G) and supercooling ( ΔT) can be observed. Absolute values of the slopes of these relationships decrease with increasing molecular length. Additionally, MPEO fractions generally have higher slope values when compared with their PEO counterparts. Nevertheless, this difference between PEO and MPEO fractions gradually vanishes with increasing molecular length. Extended chain single lamellar crystals are highly faceted in these temperature regions, and their aspect ratios vary with supercooling as well as molecular length. Nucleation theory for the growth of extended chain crystals is applied. The transient chain-end surface free energy, σ, for the PEO and MPEO fractions possess entropic origins. The rough surface growth model is also discussed.

Equilibrium triple point pressure and pressure-temperature phase diagram of polyethylene

The equilibrium triple point and pressure and temperature phase diagram of polyethylene were obtained by in situ optical microscopic and X-ray observations of the melting temperature of hexagonal and orthorhombic isolated extended chain single crystals at high pressure. The melting temperatures of extended chain crystals still showed a ΔT dependence at high pressure, which has been neglected in previous studies. The triple point pressure and temperature were 0.5 × 10 8 − 1.5 × 10 8 Pa and 20–30°C higher than those previously obtained by the d.t.a. method. These results suggest that lamellar thickness dependence is important even in extended chain crystals to obtain equilibrium thermodynamic physical quantities of polymers.

Growth Rate of Polyethylene Single Crystals at High Pressure

The growth kinetics of extended-chain single crystals (ECSC) of polyethylene are studied. The results of an expertment on the growth rate and the structure of the high-pressure form suggest that the segments in the crystal slide along their own axes very easily and that the ends of the segments form uneven contour surfaces so as to minimize the boundary free energy. On such a secondary nucleus model, we assume that the elementary step of the growth is the “creeping in” of a repeating unit linked directly to a crystalline segment through the boundary surface of the nucleus. We have the normal growth rate V∝=Texp (-G*/3 kT), where ΔT is the degree of supercooling and G* is the least free energy of formation of a critical nucleus. By fitting this relation with the experimental one, we obtain G*=134/ΔT (kJ/mol) at 300 MPa, a value 1/14 of that at 0.1 MPa.

Growth of Bulky Extended Chain Single Crystals of Polyethylene

Crystallization process of fractionated polyethylene (PE) about 10 µm thick from liquid at high pressure was observed by optical microscope and X-ray method. The needle-like crystal obtained was unchanged in the shape except for appearing of striation through the hexagonal-orthorhombic transition and it gave spotty X-ray pattern corresponding to the a * -b * plane of reciprocal lattice of hexagonal and orthorhombic form. The direction of its long axis coincided to that of [010] in the hexagonal form and to that of [010], [110] or [\=110] in the orthorhombic form. These results suggests that the needle-like crystal was composed of rather bulky single crystals of µm dimension as compared with the usual polymer single crystals of 100 A thick and that the formation of the hexagonal needle-like crystal corresponds to that of extended chain crystal of PE.