Nucleation-controlled growth. Observations on (110) twinned polyethylene crystals

The growth of (110) twinned crystals of a sharp fraction of linear polyethylene (M_w/M_n = 1.10) of moderate molecular weight (M_w = 17,000) is followed during crystallization by the isochronous decoration method. New morphological features are observed. The fast-growing tip of our laths presents, in addition to the two (100) facets usually observed, a possibly stable small reentrant (110) corner. This is a situation intermediate between the facies described by Dawson and Keller. Moreover, the slow tip of our laths presents various degrees of asymmetry with respect to the junction plane. A new characteristic length L_n = j/i is introduced to explain our morphological observations on (110) twinned crystals: j is the nucleation rate at a reentrant corner and i the nucleation rate on a smooth facet. Three linear growth rates G_hkl are calculated as a function of the length L of the face (hkl): G_hkl and G_?kl or G′_hkl are respectively the growth rates of a face bordered by two salient corners and by a reentrant corner. A distinction between G_?kl and G′_hkl is introduced to take into account the relative sizes of the two faces of the reentrant dihedral angle. The major points of the discussion concern (i) the stability of the (110) reentrant corner of the fast tip of the lath, (ii) the nearly constant shape of the twinned crystals, (iii) the effects of dislocations incorporated in the fast edge of the laths, and (iv) the various asymmetries observed in the slow tip of our laths. Theories of surface nucleation-controlled growth explain our various morphological observations on (110) twinned PE crystals, and growth usually proceeds in regime II.     

Preparation of urea-poly(tetrahydrofuran) complexes and their application for fractionation of oligomers

The synthesis of the urea channel inclusion complexes of poly(tetrahydrofuran)) (PTHF) is described. These complexes could be obtained in the form of single crystals forM _n 1700 g/mol of PTHF as the guest, and they exhibit a hexagonal unit cell (a=8.20(2) Å,c=11.05(3) Å) very similar to the wellknown urea-n-alkane complexes. X-ray investigations, elemental analysis and density measurements suggest an all trans zig-zag conformation of the polymer chain.The formation of the complexes was exploited for the purpose of fractionation of PTHF, making use of the correlation between temperature of crystallization andM _n of the included polyether chain.The distribution and the molecular weights of the fractions, obtained by extractive crystallization, were determined by reversed phase HPLC analysis and vapour pressure osmometry (VPO). Narrow fractions with M_w/M_n=1.02 were obtained from commercial PTHF samples.Successive fractionation was applied also on product mixtures from oligomer synthesis, as demonstrated for the separation of the dodecamer H-(o-(CH₂)₄-)₁₂OH.Herrn Prof. Dr. R. Bonart mit den besten Wünschen zum 60. Geburtstag gewidment     

Fast growth rates of polyethylene single crystals grown at high temperatures and their relevance to crystallization theories

The rates of growth of polyethylene single crystals grown from dilute solution in hexadecane and tetradecanol have been measured over the temperature range T_c = 98–120°C by following the change in turbidity during crystallization of a suspension of crystals of known shape and final size. The rates decrease similarly with T_c in each solvent, but for a given supercooling crystals grow much faster in tetradecanol where the corresponding crystallization temperature is higher. Similarly, the rates are much higher in hexadecane than those previously reported from xylene at equivalent supercoolings but lower T_c. Changes in the corresponding crystal morphologies as T_c is raised are quantified in terms of the axial ratio and the degree of curvature of the nominally {100} faces, both of which increase with T_c. The results can be interpreted as showing a transition from regime I to regime II growth in both solvents, which agrees both qualitatively and quantitatively with the predictions of the nucleation-based kinetic theories. Such a transition has never before been reported for solution crystallization. Using this analysis, reasonable values are obtained for the crystal side-surface energy σ of 7.4–7.5 erg cm^?2 and for the regime I substrate length L of 0.14 μm. No correlation is found between crystal morphology and growth rate and there are no discontinuous changes in morphology at the proposed transition points. The occurrence of curved crystal edges raises the fundamental issue of how to reconcile noncrystallographic growth surfaces with nucleation-controlled growth. A new approach to polymer crystal growth based on equilibrium surface roughening, which does not require nucleation, is therefore very pertinent in this respect and this is discussed.     

Degradation on freezing dilute polystyrene solutions in p-xylene

Chain scission was observed during the crystallization of p-xylene in dilute polystyrene solutions. Degradation yields were determined by gel permeation chromatography, as a function of the number of freeze-and-thaw cycles, polymer concentration, and initial polymer molecular weight (M). The rate constant for chain scission K_c increases with the polymer chain length, from 0.021%/cycle at M = 110·10³ to 4.7%/cycle at M = 8.5·10⁶. Over the two decades range of investigated molecular weights, K_c follows an empirical scaling law of the form K_c ～ (M ? M_lim)^1.17578, where M_lim is a limiting molecular weight ? 29,000 g. mol^?1 below which no degradation could be induced. Some propensity for midchain scission was detected, although this tendency was much weaker in comparison to flow-induced degradation. A chain scission model based on crack propagation failed to reproduce the experimental results. To explain the observed dependence of K_c with the square of the radius of gyration, an interfacial stress transmission mechanism between the crystallization fronts and the polymer coil has been proposed. © 1994 John Wiley & Sons, Inc.     

An isochronous decoration method for measuring linear growth rates in polymer crystals

The long spacing l of lamellar crystals of linear polyethylene increases with the crystallization temperature T_c. For low degrees of supercooling, the ratio Δl/ΔT is around 0.5 nm K^?1 for PE single crystals obtained from solution in xylene. In the restricted situation where only conduction in the crystallization vessel is involved, a heat transfer analysis shows that about 20 s is needed to change by 5 K the crystallization temperature T_c in a cylindrical vessel of 1.5 mm radius. Such rapid change of the crystallization temperature induces a sharp increase or decrease of the thickness of the single crystals. After conventional shadowing with palladium–gold alloy, the steps on the crystals are observed by conventional bright-field electron microscopy. A pioneering work was performed in this way by Bassett and Keller in 1962. Our technique allows one to determine both the shape and the dimensions of single crystals or twinned crystals of polyethylene as a function of the time of crystallization, and therefore give the quasi-instantaneous growth rates at various times.     

Fractionation of linear polyethylene during bulk crystallization under high pressure

Two linear polyethylene fractions (M_η, 11,260 and 100,000) and mixtures of these fractions have been isothermally crystallized from the melt under pressures up to 3000 atm. Characterization of individually crystallized fractions with transmission electron microscopy indicates that pressure can be used to produce a crystallite whose thickness is a measure of the chain length within it. Although the high molecular weight fraction yields spherulites containing individually varying lamellae thicknesses, the maximum thickness of each lamella is a measure of the chain length within it. Both electron micrographs and differential thermal analysis results show that crystallization of homogeneous mixtures of the high and low molecular weight fractions under high pressure results in a distinct fractionation and segregation according to molecular weight.     

Melt crystallization and morphology of poly(ε‐caprolactone)‐poly(ethylene glycol) diblock copolymers with different compositions and molecular weights

Ring opening polymerization of ε‐caprolactone was realized in the presence of monomethoxy poly(ethylene glycol) with M_n = 1000 and 2000, using Zn(La)₂ as catalyst. The resulting PCL‐PEG diblock copolymers with CL/EO repeat unit molar ratios from 0.2 to 3.0 were characterized by using DSC, WAXD, SEC, and ¹H NMR. The crystal phase of PCL blocks exist in all polymers, and the crystallization ability of PCL blocks increases with CL/EO ratio. PEG blocks are able to crystallize for copolymers with CL/EO below 1.0 only. Melt crystallization results were analyzed with Avrami equation. The Averami exponent n is around 3.0 in most cases, in agreement with heterogeneous nucleation with three dimensional growth. The morphology of the crystals was observed by using POM. Rod‐like crystals were found to grow in 1, 3 or 2, 4 quadrants for samples with low molecular weights. In the case of a copolymer with M_n,PEG = 2000 and M_n,PCL = 800, PEG blocks could crystallize and grow on PCL crystals after PCL finished to form rod‐like crystals, leading to formation of poorly or well structured spherulites. The spherulite growth rate (G) was determined at different crystallization temperatures (T_c) ranging from 9 to 49 °C. All the copolymers present a steady G decrease with increasing crystallization temperature due to lower undercooling. On the other hand, increase of CL/EO ratio leads to increase of G in the same T_c range. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 286–293, 2010     

Crystallization kinetics of the monoclinic modification of poly(3,3-dimethyl oxetane)

Poly(3,3-dimethyl oxetane) fractions ranging in number average molecular weights from 18500 to 130000 have been isothermally crystallized from the relaxed melt state in the temperature range from 12 to 44 °C, where only the monoclinic modification is formed. The influence of molecular weight and undercooling in crystallization kinetics has been analyzed. The level of crystallinity is very slightly dependent on molecular weight but the influence of this parameter on the time scale of the crystallization is relatively pronounced. The crystallization temperature coefficient was determined and it was found a constant value of the product of the interfacial energies in the range of molecular weights which has been analyzed. Growth rate measurements were carried out for fraction ¯M _n=130000 and it was found that the temperature coefficients for overall and growth rates are equal. Finally, the comparison of the experimental results for this polymer with those reported for poly(oxetane) shows two main differences: first, the crystallization rate is slower for poly(3,3-dimethyl oxetane) and second, the temperature coefficient is smaller for this polymer.     

Isotactic poly(butene‐1) trigonal crystal growth in the melt

Crystal growth of the trigonal form of isotactic poly(butene‐1) (it‐PB1) was successfully observed in the melt at atmospheric pressure. The growth rate of trigonal crystals was obtained by in situ optical microscopy. It is one hundredth that of it‐PB1 tetragonal crystals. The growth rate of trigonal crystals, as well as that of tetragonal crystals, shows supercooling dependence derived from the nucleation theory. The value of the kinetic constant K of trigonal crystals is about 3.3 times larger than that of tetragonal crystals. The value of the pre‐exponential factor G₀ of trigonal crystals was found to be 41 times as large as that of tetragonal crystals. The difference between these K values can be attributed to the conformational entropy of the ethyl side groups in a nucleating stem. The discrepancy found in the values of G₀ could be explained by introducing pinning and nucleation barriers, which originate from the crystal thickness δl_c, which does not depend on the crystallization temperature. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 684–697, 2007     

Determination of nucleation rate in polymers using isothermal crystallization experiments and computer simulation

Within the frame of overall kinetics of crystallization, polymer crystallization is characterized by only three parameters: the initial density of potential nucleiN ₀, their activation frequencyq and the growth rateG. The growth rateG is rather easy to measure, whereas the nucleation parameters are generally unknown. Our purpose is to determine bothN ₀ andq using experimental isothermal two-dimensional crystallizations and computer simulation. Both these parameters are deduced from the rate of appearance of spherulites expressed as a function of the transformed surface fraction. The activation times of the spherulites are deduced from the shape of the boundaries between spherulites at the end of the transformation. When the growth rateG is known, the evolution of the transformed surface fraction is rebuilt using a computer simulation, so that only one observation of the final stage of the crystallization is needed.     

Non-isothermal crystallization behaviors of poly(4-methyl-pentene-1)

Non-isothermal crystallization of isotactic poly(4-methyl-pentene-1) (P4MP1) is studied by differential scanning calorimeter (DSC), and kinetic parameters such as the Avrami exponent and the kinetic crystallization rate (Z _c) are determined. From the cooling and melting curves of P4MP1 at different cooling rates, the crystalline enthalpy increases with the increasing cooling rate, but the degree of crystalline by DSC measurement shows not much variation. Degree of crystalline of P4MP1 calculated by wide angle X-ray diffraction pattern shows the same tendency with crystalline enthalpy, indicating that re-crystallization occurs when samples heated above the second glass transition temperature of P4MP1. By Jeziorny analysis, n ₁ value suggests that mainly spherulites’ growth at 2.5 K min⁻¹ transforms into a mixture mode of three-dimensional and two-dimensional space extensions with further increasing cooling rate. In the secondary crystallization process, n ₂ values indicate that the secondary crystallization is mainly the two-dimensional extension of the lamellar crystals formed during the primary crystallization process. The rates of the crystallization, Z _c and t _1/2 both increase obviously with the increase of cooling rate, especially at the primary crystallization stage. By Mo’s method, higher cooling rate should be required in order to obtain a higher degree of crystallinity at unit crystallization time.     

Crystal growth of polyethylene from dilute solution: Growth kinetics of {110} twins and diffusion-limited growth of single crystals

We have studied the growth kinetics of {110} twins and single crystals of polyethylene in dilute solution of tetrachlorethylene. In terms of {110} twins, we succeeded in obtaining twins without {100} sectors, using a relatively high molecular weight fraction M_w > 10⁴. It is confirmed that the growth is enhanced at the reentrant corner of the twins, and the enhanced growth face inclines to the {110} face because of consecutive generation of steps at the corner. These facts are strong evidence for nucleation-controlled growth of single crystals. The growth rates and obliquity are measured at various supercoolings and concentrations. From consideration of kinetics of steps on the growth face, the following rates and velocity are independently determined from the experimental data: nucleation rate on a flat face, velocity of step propagation, and generation rate of steps at the reentrant corner. The supercooling dependence strongly supports regime II growth. The results on concentration dependence show that the velocity of steps is proportional to concentration over the whole range examined, and the nucleation rate is independent of it in the usual range and becomes proportional to it in the lower range. This concentration dependence of nucleation rate is attributed to the density of adsorbed polymer on the growth face. From this evidence, it is suggested that the rate of travel of steps is limited by volume diffusion of solute polymer, whereas the growth face is saturated with adsorbed polymer at ordinary concentrations. This contradictory situation could be explained by the hypotheses that the saturation density is rather low and that surface diffusion of adsorbed polymer is much slower than volume diffusion of solute polymer. The lower limit of the rate of folding is also determined for the first time from the velocity of step propagation. As regards the single crystals, it is found that the habit maintains a lozenge shape with sharpened points, even at very high supercooling (δT < 50°C) if the concentration is very dilute. Diffusion-limited growth is verified for the first time at the higher supercoolings, where the growth rate is almost independent of supercooling. The growth rate becomes almost equivalent to the velocity of steps determined in the experiments with twins, and this fact will support the accuracy of the evaluation of the step velocity. The order of magnitude of the growth rate obtained agrees with the value which is calculated from the balance between the flux of solute polymer to the growth face and the rate of growth of single crystals.     

Morphology of polypropylene crystals. I. Dilute solution-grown lamellar crystals

The dependence of crystalline morphology of isotactic polypropylene crystallized from dilute solutions on its molecular weight and growing conditions and the mechanism of crystal growth were studied by electron microscopy and electron diffraction. Lathshaped lamellar crystals 150–300 A. in thickness are obtained from fractionated polypropylene powders of M _w (average molecular weight) = 600,000 and 240,000, but not from the samples of M _w = 82,000 and 44,000, by means of isothermal crystallization at 130°C. for 20 hr. in dilute α-chloronaphthalene solution (0.005 wt.-%). Precipitation of the fractionated polypropylene sample of M _w = 82,000 from a dilute solution of carbitol gives typical dendritic crystals under the same isothermal crystallizing conditions as mentioned above. The mode of chain folding in these crystals based on the orientation and the crystal structure of the lamellar crystals agrees with that proposed by Sauer, Morrow, and Richardson. From the morphological observations, the mechanism of growth pertinent to polypropylene lamellar crystals is presumed to be as follows: fibrils at first aggregate, then the molecular chains are folded to form small lamellae, and then these small lamellae accumulate compactly to grow to large, lath-shaped, lamellar crystals.     

Inclusion of Poly(ethylene glycol)s by Crystalline (R)-(1-Naphthyl)glycyl-(R)-phenylglycine

Abstract

Crystallization of (R)-(1-naphthyl)glycyl-(R)-phenyl-glycine [(R,R)-1] in the presence of oligo(ethylene glycol) dimethyl ethers 2(n) or poly(ethylene glycol)s (PEGs, 3(M_n )) afforded inclusion compounds. The ratio of (R,R)-1/the guest polymer (2 or 3) was proportional to the length of the polymer chain. The crystal structure of a hepta(ethylene glycol) dimethyl ether-included compound was disclosed by X-ray crystallography which showed that (R,R)-1 molecules form a sheet and the guest molecule penetrates the crystal lattice of (R,R)-1 through a one-dimensional channel on the sheet. Powder X-ray analysis revealed that, regardless of the length of the guest polymer, the distance between the neighboring sheets remains unchanged (12.0–12.3 Å) in these inclusion crystals. By thermal analysis, it was shown that the decomposition points of these inclusion compounds became higher with the longer PEG included. The inclusion phenomenon enabled the fractionation of PEGs with various molecular weights, among which longer PEG was preferably included.     

Dendritic growth of poly(ε-caprolactone) crystals from compatible blends with poly(t-butyl acrylate) at the air/water interface

Thermodynamic analyses of surface pressure-area (Π-A) isotherms and Brewster angle microscopy (BAM) reveal that poly(ε-caprolactone) (PCL) with a weight average molar mass of M_w = 10 kg mol⁻¹ and polydispersity index of M_w/M_n = 1.25 and poly(t-butyl acrylate) (PtBA, M_w = 25.7 kg mol⁻¹; M_w/M_n = 1.07) form compatible blends as Langmuir films below the dynamic collapse transition for PCL at Π = 11 mN m⁻¹. For PCL-rich blends, in situ BAM studies reveal growth of PCL crystals for compression past the PCL collapse transition. PCL crystals grown in the plateau regime of the Π-A isotherm exhibit a dendritic morphology presumably resulting from the rejection of PtBA from the growing PCL crystals and hindered diffusion of PCL from the surrounding monolayer to the crystal growth fronts. The ability to transfer the PCL dendrites as Langmuir–Schaefer films onto silicon substrates spincoated with a polystyrene layer facilitates detailed morphological characterization by optical and atomic force microscopy (AFM). AFM reveals that the dendritic branching occurs along the {100} and {110} sector boundaries and is essentially independent of composition. AFM also reveals that the average thickness of PCL dendrites formed at room temperature (22.5 °C), ∼7–8 nm, is comparable with that of PCL crystals grown from single-component PCL Langmuir films and spincoated thin films. In contrast, for PtBA-rich blend films PCL crystallization is suppressed. These findings establish PCL blends as an ideal system for exploring the interplay between chain diffusion and crystal growth in a two-dimensional confined geometry. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3300–3318, 2007     

Crystallization studies of isotactic polypropylene containing nanostructured polyhedral oligomeric silsesquioxane molecules under quiescent and shear conditions

Crystallization studies at quiescent and shear states in isotactic polypropylene (iPP) containing nanostructured polyhedral oligomeric silsesquioxane (POSS) molecules were performed with in situ small‐angle X‐ray scattering (SAXS) and differential scanning calorimetry (DSC). DSC was used to characterize the quiescent crystallization behavior. It was observed that the addition of POSS molecules increased the crystallization rate of iPP under both isothermal and nonisothermal conditions, which suggests that POSS crystals act as nucleating agents. Furthermore, the crystallization rate was significantly reduced at a POSS concentration of 30 wt %, which suggests a retarded growth mechanism due to the molecular dispersion of POSS in the matrix. In situ SAXS was used to study the behavior of shear‐induced crystallization at temperatures of 140, 145, and 150 °C in samples with POSS concentrations of 10, 20, and 30 wt %. The SAXS patterns showed scattering maxima along the shear direction, which corresponded to a lamellar structure developed perpendicularly to the flow direction. The crystallization half‐time was calculated from the total scattered intensity of the SAXS image. The oriented fraction, defined as the fraction of scattered intensity from the oriented component to the total scattered intensity, was also calculated. The addition of POSS significantly increased the crystallization rate during shear compared with the rate for the neat polymer without POSS. We postulate that although POSS crystals have a limited role in shear‐induced crystallization, molecularly dispersed POSS molecules behave as weak crosslinkers in polymer melts and increase the relaxation time of iPP chains after shear. Therefore, the overall orientation of the polymer chains is improved and a faster crystallization rate is obtained with the addition of POSS. Moreover, higher POSS concentrations resulted in faster crystallization rates during shear. The addition of POSS decreased the average long‐period value of crystallized iPP after shear, which indicates that iPP nuclei are probably initiated in large numbers near molecularly dispersed POSS molecules. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2727–2739, 2001     

Solution grown isotactic polystyrene crystals. I. Degree and distribution of crystallinity; thermal stability

The subject of this paper is the degree of crystallinity and annealing behavior of solution grown single crystals of isotactic polystyrene (IPS) in relation to the fold length, an enquiry which acquires special significance in view of the fact that previously the fold length had been found to be identical over a wide range of crystallization temperatures (T_c). It was found that both crystallinity and thermal stability increase with T_c even over the range of constant fold length thus invalidating the usual assumption that the fold length and crystal properties are uniquely correlated. Further, the crystallinity figures as measured by conventional calorimetry are very low (<50% throughout) which by conventional ideas would require an unrealistically thick amorphous surface layer. However, the “linear crystallinity” (crystal core thickness as determined from x-ray linewidths) is much larger, commensurate with crystallinities in single crystals from other materials. It is suggested that this is the more relevant figure for the subdivision of the lamellas into crystal core and surface layer. The additional amorphous content being otherwise accommodated. Further, this “linear crystallinity” is broadly unaffected by fold length changes induced by heat annealing. The thermal stability (including annealing ability) of the crystals differs markedly whether T_c is above or below ～60°C, a T_c value which is in the range where the fold length is constant, but corresponds to a maximum in the crystallization rate. Possible connections between crystallization conditions and the stability of the resulting crystals (fold length considerations apart) are pointed out.     

A STUDY OF LOW-TEMPERATURE CRYSTALLIZATION BEHAVIOR THE cis-1,4 POLYBUTADIENE PREPARED WITH RARE-EARTH CATALYST SYSTEM

The effects of molecular weight and temperature on crystallization processes at low tempera-ture for cis-1,4 polybutadiene prepared with rare-earth catalyst (Ln-PB) have been studied by WAXDmethod. In the range of molecular weight from     

A distribution kinetics approach for crystallization of polymer blends

The cluster distribution approach is extended to investigate the crystallization kinetics of miscible polymer blends. Mixture effects of polymer-polymer interactions are incorporated into the diffusion coefficient. The melting temperature, activation energy of diffusion, and phase transition enthalpy also depend on the blending fraction and lead to characteristic kinetic behavior of crystallization. The influence of different blending fractions is presented through the time dependence of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots). Computational results indicate how overall crystallization kinetics can be expressed approximately by the Avrami equation. The nucleation rate decreases as the blending fraction of the second polymer component increases. The investigation suggests that blending influences crystal growth rate mainly through the deposition-rate driving force and growth-rate coefficient. The model is further validated by simulating the experimental data for the crystallization of a blend of poly(vinylidenefluoride)[PVDF] and poly(vinyl acetate)[PVAc] at various blending fractions.     

乌梅提取液对草酸钙晶体生长的抑制作用研究

本文研究了水体系中加入乌梅提取液对草酸钙晶体生长的抑制作用,通过FTIR、SEM及XRD等测试方法对所得晶体进行表征。结果表明,不加乌梅提取液的体系中形成的晶体为一水合草酸钙(COM)晶体,加入乌梅提取液后,形成的是二水合草酸钙(COD)晶体,而且COD晶体的尺寸随着乌梅提取液浓度的增大而减小,直至消失,这说明乌梅提取液具有抑制草酸钙晶体生长的作用,且这种抑制作用随乌梅浓度的增大而增大。本文还通过电导率法研究了草酸钙晶体生长的动力学过程,发现乌梅提取液主要能抑制草酸钙晶体的成核过程。