The study of banded spherulite patterns by coupled logistic map lattice model

Banded spherulite patterns are simulated in two dimensions by means of a coupled logistic map lattice model. Both target pattern and spiral pattern which have been proved to be existent experimentally in banded spherulite are obtained by choosing suitable parameters in the model. The simulation results also indicate that the band spacing is decreased with the increase of parameter mu in the logistic map and increased with the increase of the coupling parameter epsilon, which is quite similar to the results in some experiments. Moreover, the relationship between the parameters and the corresponding patterns is obtained, and the target patterns and spiral patterns are distinguished for a given group of initial values, which may guide the study of banded spherulite.

Simulation of Banded Spherulite Patterns by Coupled Logistic Map Lattice Model in Three Dimensions

Banded spherulite patterns are simulated in three dimensions by means of a Coupled Logistic map lattice model. The patterns obtained by numerical calculation are consistent with those in experiments. The simulation results also indicate that the hand spacing is decreased with the increase of parameter mu in the Logistic map and increased with the increase of the coupling parameter e for cube lattices, and increased with the increase of the thickness of the lattice for polymer film, which is quite similar to the results in some experiments. Spiral pattern in three dimensions is also shown in this paper, which helps us understand the form of banded spherulite in polymers.

Crystallization and ring-banded spherulite morphology of poly(ethylene oxide)-block-poly(epsilon-caprolactone) diblock copolymer

The crystallization behavior of crystalline-crystalline diblock copolymer containing poly(ethylene oxide) (PEO) and poly(epsilon-caprolactone) (PCL), in which the weight fraction of PCL is 0.815, has been studied via differential scanning calorimeter (DSC), wide-angle X-ray diffraction (WAXD), and polarized optical microscopy (POM). DSC and WAXD indicated that both PEO and PCL blocks crystallize in the block copolymer. POM revealed a ring-banded spherulite morphology or the PEO-b-PCL diblock copolymer.

Ring-banded spherulite surface structure of poly(epsilon-caprolactone) in its miscible mixtures with poly(styrene-co-acrylonitrile)

The surface structure of the ring-banded spherulites in polymer blends PCL/SAN (90/10) was studied by optical microscopy, SEM, and TEM, respectively. It is interesting to find that the surface structure of the ring-banded spherulites in polymer blends PCL/SAN (90/10) is made up of the convex bands. The landscape of the convex bands on the surface has been little emphasized before. Radial fibrils are arranged on the bands. Details of the radial fibrils on the bands can be observed by TEM. The landscape of the convex bands on the surface and twisting of lamellae in the convex bands for PCL/SAN blends may be useful to explain the formation mechanism of the ring banded spherulites in polymer blends or even in homopolymers. (C) 1999 John Wiley & Sons, Inc.

Application of digital image analysis to the study of banded spherulite during growing and melting process

A digital image analysis(DIA) technique can be applied directly to the image obtained by polarizing microscope. The time-resolved DIA apparatus including image collecting, showing and data analysis has been home-made. As an example, it has been used to study the banded spherulite in the blends of poly(epsilon-caprolactone) (PCL) and poly(styrene-ran-acrylonitrile) (SAN).

THE RING-BANDED SPHERULITE STRUCTURE OF POLY(EPSILON-CAPROLACTONE) IN ITS MISCIBLE MIXTURES WITH POLY(STYRENE-CO-ACRYLONITRILE)

The structure of the PCL spherulite in poly(epsilon-caprolactone)/poly(styrene-co-acrylonitrile) (PCL/SAN) blends was investigated by optical microscopy and small angle light scattering. The spherulite structure with a Maltese cross has been observed in pure PCL. Similar PCL/SAN blends exhibited not only spherulites with a Maltese cross, but also distinct extinction rings. The H(v) light scattering pattern especially caused diffraction rings in PCL/SAN blends but not in pure PCL. The spherical symmetry of spherulite PCL becomes more incomplete and the twist of the lamella becomes more irregular with increasing SAN content. It is found that the spherulite structure of PCL/SAN blends is dependent on the crystallization temperature and the concentration of SAN in PCL/SAN blends.

One-step macroscopic alignment of conjugated polymer systems by epitaxial crystallization during spin-coating

The one-step preparation of highly anisotropic polymer semiconductor thin films directly from solution is demonstrated. The conjugated polymer poly(3-hexylthiophene) (P3HT) as well as P3HT:fullerene bulk-heterojunction blends can be spin-coated from a mixture of the crystallizable solvent 1,3,5-trichlorobenzene (TCB) and a second carrier solvent such as chlorobenzene. Solidification is initiated by growth of macroscopic TCB spherulites followed by epitaxial crystallization of P3HT on TCB crystals. Subsequent sublimation of TCB leaves behind a replica of the original TCB spherulites. Thus, highly ordered thin films are obtained, which feature square-centimeter-sized domains that are composed of one spherulite-like structure each. A combination of optical microscopy and polarized photoluminescence spectroscopy reveals radial alignment of the polymer backbone in case of P3HT, whereas P3HT:fullerene blends display a tangential orientation with respect to the center of spherulite-like structures. Moreover, grazing-incidence wide-angle X-ray scattering reveals an increased relative degree of crystallinity and predominantly flat-on conformation of P3HT crystallites in the blend. The use of other processing methods such as dip-coating is also feasible and offers uniaxial orientation of the macromolecule. Finally, the applicability of this method to a variety of other semi-crystalline conjugated polymer systems is established. Those include other poly(3-alkylthiophene)s, two polyfluorenes, the low band-gap polymer PCPDTBT, a diketopyrrolopyrrole (DPP) small molecule as well as a number of polymer:fullerene and polymer:polymer blends. Macroscopic spherulite-like structures of the conjugated polymer poly(3-hexylthiophene) (P3HT) grow directly during spin-coating. This is achieved by processing P3HT or P3HT:fullerene bulk heterojunction blends from a mixture of the crystallizable solvent 1,3,5-trichlorobenzene and a second carrier solvent such as chlorobenzene. Epitaxial growth of the polymer on solidified solvent crystals gives rise to circular-symmetric, spherulite-like structures that feature a high degree of anisotropy.

Size dependent structural relaxations and dielectric properties induced by surface functionalized MWNTs in poly(vinylidene fluoride)/poly(methyl methacrylate) blends

Structural dynamics, dielectric permittivity and ferroelectric properties in poly(vinylidene fluoride) (PVDF)/poly(methyl methacrylate) (PMMA) (PVDF/PMMA) blends with respect to crystalline morphology was systematically investigated in presence of amine functionalized MWNTs (NH2-MWNTs) using dielectric spectroscopy. The crystalline morphology and the crystallization driven demixing in the blends was assessed by light microscopy (LM), wide angle X-ray diffraction (WXRD) and, in situ, by shear rheology. The crystal nucleation activity of PVDF was greatly induced by NH2-MWNTs, which also showed two distinct structural relaxations in dielectric loss owing to mobility confinement of PVDF chains and smaller cooperative lengths. The presence of crystal-amorphous interphase was supported by the presence of interfacial polarization at lower frequencies in the dielectric loss spectra. On contrary, the control blends showed a single broad relaxation at higher frequency due to defective crystal nuclei. This was further supported by monitoring the dielectric relaxations during isothermal crystallization of PVDF in the blends. These observations were addressed with respect to the spherulite sizes which were observed to be larger in case of blends with NH2-MWNTs. Higher dielectric permittivity with minimal losses was also observed in blends with NH2-MWNTs as compared to neat PVDF. Polarization obtained using P-E (polarization-electric field) hysteresis loops was higher in case of blends with NH2-MWNTs in contrast to control blends and PVDF. These observations were corroborated with the charge trapped at the crystal-amorphous interphase and larger crystal sizes in the blends with NH2-MWNTs. The microstructure and localization of MWNTs were assessed using SEM.

Cooperativity and Structural Relaxations in PVDF/PMMA Blends in the Presence of MWNTs: An Assessment through SAXS and Dielectric Spectroscopy

Intermolecular cooperativity and structural relaxations in PVDF/PMMA blends were studied in this work with respect to different surface modified (amine, similar to NH2; carboxyl acid, similar to COOH and pristine) multiwalled nanotubes (MWNTs) at 1 wt % near blend's T-g and in the vicinity of demixing using dielectric spectroscopy, SAXS, DSC, and WAXD. Intermolecular cooperativity at T-g and configurational entropy was addressed in the framework of cooperative rearranging region (CRR) at T-g. Because of specific interactions between PVDF and NH2-MWNTs, the local composition fluctuates at its average value resulting in a broad T-g. The scale of cooperativity (xi(CRR)) and the number of segments in the cooperative volume (N-CRR) is comparatively smaller in the blends with NH2-MWNTs. This clearly suggests that the number of segments cooperatively relaxing is reduced in the blends due to specific interactions leading to more heterogeneity. The configurational entropy at T-g, as derived from Vogel-Fulcher and Adam-Gibbs analysis, was reduced in the blends in presence of MWNTs manifesting in entropic penalty of the chains. The crystallite size and the amorphous miscibility was evaluated using SAXS and was observed to be strongly contingent on the surface functional groups on MWNTs. Three distinct relaxations-alpha(c) due to relaxations in the crystalline phase of PVDF, alpha(m) indicating the amorphous miscibility in PVDF/PMMA blends, and alpha beta concerning the segmental dynamics of PMMA-were observed in the blends in the temperature range T-g < T < T-c. The dynamics as well as the nature of relaxations were observed to be dependent the surface functionality on the MWNTs. The dielectric permittivity was also enhanced in presence of MWNTs, especially with NH2-MWNTs, with minimal losses. The influence of the MWNTs on the spherulite size and crystalline morphology of the blends was also confirmed by POM and SEM.

Logistic Map耦合格子模型模拟环带

本论文采用Logistic Map耦合格子模型对高聚物中特有的环带球晶进行了模拟，所得到的模拟结果与实验结果吻合较好。同时，研究结果能够对实验制备环带球晶样品提供可靠的理论指导。 首先，我们对Logistic Map耦合格子模型及模型中的两个模拟参量μ和ε进行分析，同时结合实验中各种实验条件对聚合物结晶行为的影响，认为Logistic Map的动力学特征与聚合物结晶行为非常相似，并且参量μ与实验中的结晶温度相关，即随温度的升高而减小，而参量ε与实验中影响扩散的因素有关，即随温度的升高而增大、随分子量的增大而减小，并且随样品厚度的增大而增大。我们对模型的整个参数空间进行计算，得到了可以形成环带球晶形貌的参数范围，通过进一步研究发现环带图案的带宽随参量μ的增大而变窄，随参量ε的增大而变宽。上述研究结果与实验中带宽随实验条件的变化规律是一致的。 在得到环带图案的基础上，我们又进一步计算得到了靶状和螺旋状形貌的参量μ和ε的具体取值范围。通过改变μ和ε的参数取值，模拟了环带球晶形貌由靶状过渡到螺旋状的过程，即靶状图案的环带由外层向内层逐渐断裂成较短的条带结构，所有的条带结构呈现出以空间某处为中心团聚在一起的形貌；随后，这种“团聚”的形貌逐渐消失了，空间中小的条带结构的排列呈无序状态。随着参数的进一步变化，短的条带结构变成较长的带状结构，并且这些带状结构的边缘逐渐发生卷曲，最终形成了螺旋状图案。我们还考察了系统初值和耦合方式对上述图案的影响，结果发现，形成环带球晶的参数范围对系统初值没有明显的依赖性，然而靶状和螺旋状图案的分布受初值的影响较大。此外，发现只有采用交替耦合、并考虑长程耦合作用的Logistic Map耦合格子模型才可以得到环带球晶图案。 为了更好地与实验结果进行对比，我们利用Logistic Map耦合格子模型对二维空间中的几种受限体系进行了模拟。（一）对温度梯度场中的环带球晶进行模拟，发现环带球晶在低温处较易成核，向高温处生长，并且，高温处环带的带宽比低温处宽。（二）对格子宽度受限情况进行了模拟，发现随着受限方向的宽度越来越窄，球晶尺寸逐渐变小，相邻两个环带球晶碰撞产生的界线变短，三个相邻环带球晶所形成的界线的交汇点减少。（三）研究了受限边界上的成核作用对狭长格子中环带球晶的影响，结果发现，随着受限边界上成核点密度的不断增加，其形貌转变分为三个不同阶段：①当成核密度稍有增大时，环带球晶数量增加，直径变小；②继续增大边界成核密度，使得大量晶层从受限边界向格子内生长，导致环带球晶的数量减少，直径也减小；③当成核点增加到一定程度时，整个空间中只有极少数由格子内部成核生长且直径非常小的环带球晶，而占主导地位的是由成核点垂直于受限边界生长出的穿透晶层。这些模拟结果均与实验结果相符合。 我们将Logistic Map耦合映象格子模型发展到三维空间格子中，得到了与环带球晶形貌一致的图案，并且其带宽随模拟参量μ的增大而变窄，随ε的增大而变宽。这一规律性结果与二维正方格子的模拟结果是一致的。这一部分的研究结果还表明，边界条件和格子尺寸对模拟结果有显著的影响，周期性边界条件导致在小体积立方格子中只能得到靶状图案；而当格子尺寸很大时，可以得到螺旋状环带球晶的图案。最后，通过调节垂直于薄膜平面方向上的格子数来研究薄膜厚度对环带图案带宽的影响，发现环带的带宽随厚度的增加而变宽，这与实验中环带球晶的带宽随样品厚度的增加而变大的结论是一致的。

Crystallization and morphology of poly(ethylene oxide-b-lactide) crystalline-crystalline diblock copolymers

The crystallization behaviors and morphology of asymmetric crystalline-crystalline diblock copolymers poly(ethylene oxide-lactide) (PEO-b-PLLA) were investigated using differential scanning calorimetry (DSC), wide angle X-ray diffraction (WAXD), and microscopic techniques (polarized optical microscopy (POM) and atomic force microscopy (AFM)). Both blocks of PEO5-b-PLLA(16) can be crystallized, which was confirmed by WAXD, while PEO block in PEO5-b-PLLA(30) is difficult to crystallize because of the confinement induced by the high glass transition temperature and crystallization of PLLA block with the microphase separation of the block copolymer.

Crystallization Kinetics of Syndiotactic Polypropylene Studied by Time-Dependent Light Attenuation

Crystallization kinetics of syndiotactic polypropylene ( sPP) was observed by light attenuation measurements. The initial stages of temperature dependent sPP crystallization fall in the range of Rayleigh scattering and Rayleigh-Debye-Gans scattering. Initial time and growth time of crystallization were obtained, and the trend of crystallization temperature dependent linear attenuation coefficient on the radius and the index of the refraction of the spherulite were evaluated.

Rhythmic growth of ring-banded spherulites in blends of liquid crystalline methoxy-poly(aryl ether ketone) and poly(aryl ether ether ketone)

Rhythmic growth of ring-banded spherulites in blends of liquid crystalline methoxy-poly(aryl ether ketone) (M-PAEK) and poly(aryl ether ether ketone) (PEEK) has been investigated by means of differential scanning calorimetry (DSC), polarized light microscopy (PLM), and scanning electron microscopy (SEM) techniques. The measurements reveal that the formation of the rhythmically grown ring-banded spherulites in the M-PAEK/PEEK blends is strongly dependent on the blend composition. In the M.-PAEK-rich blends, upon cooling, an unusual ring-banded spherulite is formed, which is ascribed to structural discontinuity caused by a rhythmic radial growth. For the 50:50 M-PAEK/PEEK blend, ring-banded spherulites and individual PEEK spherulites coexist in the system. In the blends with PEEK as the predominant component, M-PAEK is rejected into the boundary of PEEK spherulites. The cooling rate and crystallization temperature have great effect on the phase behavior, especially the ring-banded spherulite formation in the blends. In addition, the effects of M-PAEK phase transition rate and phase separation rate on banded spherulite formation is discussed.

Thermal stability, crystallization, structure and morphology of syndiotactic 1,2-polybutadiene/organoclay nanocomposite

Syndiotactic 1,2-polybutadiene/organoclay nanocomposites were prepared and characterized by thermogravimetry analysis (TGA), X-ray diffraction (XRD), polarized optical microscopy (POM), and differential scanning calorimetry (DSC), respectively. The XRD shows that exfoliated nanocomposites are formed dominantly at lower clay concentrations (less than 2%), at higher clay contents intercalated nanocomposites dominate. At the same time, the XRD indicates that the crystal structures of sPB formed in the sPB/organoclay nanocomposites do not vary, only the relative intensity of the peaks corresponding to (0 1 0) and (2 0 0)/(1 1 0) crystal planes, respectively, varies. The DSC and POM indicate that organoclay layers can improve cooling crystallization temperature, crystallization rate and reducing the spherulite sizes of sPB. TGA shows that under argon flow the nanocomposites exhibit slight decrease of thermal stability, while under oxygen flow the resistance of oxidation and thermal stability of sPB/organoclay nanocomposites were significantly improved relative to pristine sPB. The primary and secondary crystallization for pristine sPB and sPB/organoclay (2%) nanocomposites were analyzed and compared based on different approaches.

Synthesis and crystallization behaviors of poly(styrene-b-isoprene-b-epsilon-caprolactone) triblock copolymers

The triblock copolymers, poly(styrene-b-isoprene-b-epsilon-caprolactone)s (PS-b-PI-b-PCL) have been synthesized successfully by combination of anionic polymerization and ring-opening polymerization. Diblock copolymer capped with hydroxyl group, PS-b-PI-OH was synthesized by sequential- anionic polymerization of styrene and isoprene and following end-capping reaction of EO, and then it was used as macro initiator in the ring-opening polymerization of CL. The results of DSC and WAXD show big effect of amorphous PS-b-PI on the thermal behaviors of PCL block in the triblock copolymers and the lower degree of crystalline in the triblock copolymer with higher molecular weight of PS-b-PI was observed. The real-time observation on the polarized optical microscopy shows the spherulite growth rates of PCL27, PCL328 and PS-b-PI-b-PCL344 are 0.71, 0.46 and 0.07 mu m s(-1), respectively. The atomic force microscopy (AFM) images of the PS90-b-PI66-b-PCL-(28) show the columns morphology formed by it's self-assembling.