A growing 2D spherulite and calculus of variations Part I: A 2D spherulite in a linear field of growth rate

We propose to take the calculus of variations in order to compute the shape of a growing 2D spherulite in an uniaxial field of growth rate. We are concerned with the growth line (a path that is traveled in the shortest possible time from nucleus to a point (x₁, y₁), where a molecule just crystallizes) and the growth front (the times between spherulite and supercooled material). The Euler differential equation—a result of the calculus of variations—is derived for all uniaxial growth ratesv (x). Here we especially investigatev(x)=px+q.     

Computer simulation of two-dimensional spherulite growth

The two-dimensional growth of spherulites with impingement was simulated by a computer for athermal, thermal, and combined primary nucleation mechanisms. The simulation provided data on the spherulite size distributions and spherulite shapes. The results of the computer simulation were compared with experimental data on poly(methylene oxide) films.     

Computer simulation of three-dimensional spherulite growth

A computer program for modeling three-dimensional spherulite nucleation, growth, and impingement was elaborated. The Monte Carlo method was used to determine the degree of conversion and calculate the volume of the spherulites. Athermal, thermal, and mixed types of nucleation were tested. The experimental Avrami exponent agrees with the predictions for athermal and thermal nucleation while for mixed nucleation a nonintegral exponent is characteristic. The spherulite size distributions are very different from athermal and thermal nucleations. An intermediate pattern of distribution is proper for the mixed type of nucleation. The boundaries of the largest spherulites from thermal and mixed nucleation are concave while those of the smallest spherulites are convex.     

Non-isothermal model for nematic spherulite growth

A computational study of the growth of two-dimensional nematic spherulites in an isotropic phase was performed using a Landau-de Gennes-type quadrupolar tensor order parameter model for the first-order isotropic/nematic transition of 5CB (pentylcyanobiphenyl). An energy balance, taking anisotropy into account, was derived and incorporated into the time-dependent model. Growth laws were determined for two different spherulite morphologies of the form t(n), with and without the inclusion of thermal effects. Results show that incorporation of the thermal energy balance correctly predicts the transition of the growth law exponent from the volume driven regime (n=1) to the thermally limited regime (approaching n = 1/2), agreeing well with experimental observations. An interfacial nematodynamic model is used to gain insight into the interactions that result in the progression of different spherulite growth regimes.     

Measurement of spherulite growth rates using tailored temperature programs

A method recently proposed for measuring spherulite growth rates (G) using temperature programs, tailored for each polymer, is reviewed. This method, compared to the conventional isothermal procedure, permits to expand the temperature range where spherulite growth rates can be measured. Examples of application of this method are reported, in particular, the spherulite growth rates of isotactic polypropylene (iPP) and poly(l-lactic acid) (PLLA) are analyzed. For iPP, growth rates were obtained from 112 to 148 °C using different cooling rates and a self-nucleation procedure. For PLLA, measurements in both isothermal and non-isothermal conditions allowed to overcome the difficulties due to the very high nucleation density that prevent determination of growth rates at low crystallization temperatures. For this polymer the entire curve of G vs. T was obtained.     

Anomalous two-stage spherulite growth in poly(aryl ether ketones) during isothermal crystallization

Anomalous two-stage spherulite growth has been observed in poly(aryl ether ketones) during isothermal crystallization. The first stage consists of a conventional growth with Maltesecross pattern at a lower growth rate. The morphology shows a smooth interface, dense structure and negative birefringence. The second stage grows in the form of “aggregate” at a higher rate. The morphology shows an open dendrite structure without preferred optical orientation. The second morphology is also termed the “overgrowth.” The occurrence of overgrowth is favored only near the maximum growth rate region and diminishes in the slow growth region. The transition of the two-stage growth is attributed to the change of growth direction of the constituent lamellae. We have confirmed this by microbeam small-angle light-scattering measurements. The lamellar structures in both growth stages were followed by time-resolved small-angle synchrotron x-ray scattering. It was found that the lamellar structures of the crystals formed at both stages are the same. A possible explanation for the two-stage growth is the interface breakdown caused by large perturbations of local composition and/or stress fields. © 1996 John Wiley & Sons, Inc.     

Nonisothermal crystallization kinetics and spherulite morphology of poly(trimethylene terephthalate)

The nonisothermal melt crystallization behavior of poly(trimethylene terephthalate) (PTT) was investigated using the DSC technique. PTT peak exothermic crystallization temperature was found to move to lower temperatures as the cooling rate was increased. The modified Avrami equation exponent, n, was 4 when the cooling rates were between 5 and 15 °C/min, indicating a thermal nucleation and a three-dimensional spherical growth mechanism. When the cooling rate was increased to 25 °C/min, n gradually decreased to near 3, implying the nucleation mechanism changed to an athermal mode. PTT nonisothermal crystallization behavior could also be analyzed using the Ozawa equation and the combined equations of Ozawa and Avrami with very good fit of the data.PTT spherulite morphologies and the sign of the birefringence depended strongly on the spherulite's growth temperature. When the growth temperature was decreased from 222 to 170 °C, the spherulite changed from a saturation-type dendritic morphology to one with a colorful banded texture; the sign of the birefringence also changed in the following order: from a weakly positive spherulite → mixed spherulite → weakly negative spherulite → negative spherulite → positive spherulite → negative spherulite → positive spherulite.     

Isothermal-crystallization kinetics and spherulite growth of aliphatic polyketone/polyamide-6 blends

In this research,the morphologies,isothermal-crystallization kinetics,and spherulite growth of aliphatic polyketone/polyamide-6 blends were studied.A single glass-transition temperature (Tg) was determined,and the composition dependence of Tg for these blends was well described by the Kwei equation.The strong intermolecular interaction between the two polymer components was confirmed by melting-point depression.The isothermal-crystallization kinetics were analyzed on the basis of the Avrami approach.A linear increase in the radii of the spherulites with time was observed for all compositions.All the spherulites continued to grow at nearly identical growth rates.With increasing polyamide-6 content,the size of the spherulites in the polyketone/polyamide-6 blends gradually decreased,and the number of spherulites in the blends increased.     

Heat conduction in a two-dimensional spherulite

The anisotropy of thermal conduction in a spherulite is calculated for a two-phase model. The problem of the temperature distribution due to cooling of a spherulite suddenly heated at one point is solved. An analytical result is given and isothermal contours are calculated for wide ranges of thermal conduction anisotropy and cooling time. Experiments with spot-heated isotactic polypropylene (i-PP) and isotactic polystyrene (i-PS) spherulites were conducted using a laser pulse and a needle as heat sources. The isotherms were recorded using a thin coating of a heat-sensitive indicator substance, and then by comparison with theoretical isotherm patterns the heat conduction anisotropy of a PP spherulite was estimated. Additional measurements of heat conduction coefficients of at least two polymer films characterized by different crystallinity permit calculation of the thermal conductivity of the amorphous phase, and the conductivities of single crystals along chains and perpendicular to the chains. The results show that the heat is transferred mainly along the primary bonds of polymer chains. However, the morphology of sperulites and lamellas plays an important role.     

A 1D/2D Helical CdS/ZnIn2S4 Nano‐Heterostructure

Multidimensional nano‐heterostructures (NHSs) that have unique dimensionality‐dependent integrative and synergic effects are intriguing but still underdeveloped. Here, we report the first helical 1D/2D epitaxial NHS between CdS and ZnIn₂S₄. Experimental and theoretical studies reveal that the mismatches in lattice and dangling bonds between 1D and 2D units govern the growth procedure. The resulting well‐defined interface induces the delocalized interface states, thus facilitate the charge transfer and enhance the performance in the photoelectrochemical cells. We foresee that the mechanistic insights gained and the electronic structures revealed would inspire the design of more complex 1D/2D NHSs with outstanding functionalities.     

Localized volume deficiencies as an effect of spherulite growth. II. The three-dimensional case

As in the two-dimensional case, the density change due to crystallization leads to a buildup of internal strain in some regions of a polymer melt occluded by growing spherulites. The occluded parts of the sample are called “weak spots.” Computer simulation of spherulite growth in bulk samples shows that the largest weak spots have the size of an average spherulite. The total volumes of weak spots are 0.47, 0.094, and 0.119% of the sample for athermal, thermal, and mixed primary nucleation, respectively. The weak spots in the bulk material exhibit distance correlation. Within weak spots, internal strain is released (Raman spectroscopy), and holes develop. Polypropylene bulk spherulite samples contain holes distinctly visible under a microscope with infrared optics and illumination. The number of visible holes is in agreement with the computer prediction. The increase of impact strength with decreasing spherulite size is explained in terms of changes in the number and size of weak spots.     

Hydrothermal synthesis of 2D ordered macroporous ZnO films

The ZnO films with two-dimensional ordered macroporous structure were successfully fabricated through hydrothermal crystal growth of ZnO on the ZnO substrate covered with a monolayer of polystyrene (PS) spheres as template. The precursor solution of hydrothermal crystal growth of ZnO were prepared by equimolar solution of Zn(NO₃)₂·6H₂O and hexamethylenetramine (HMT). The confinement effect of the PS spheres template on the growth of ZnO nanorods and the influence of sodium citrate on the crystal growth of ZnO had been studied. The film surface morphology and the preferential growth of ZnO crystal were investigated by scanning electron microscopy (SEM) and X-ray diffraction (XRD), respectively. Also, the photoluminescence spectrum of ZnO films had been measured, and the corresponding mechanism was discussed. __________ Translated from Chemistry, 2007, 70 (8): 587–592 [译自: 化学通报]     

Polypropylene spherulite morphology and growth rate changes in blends with low-density polyethylene

Morphological studies of isotactic polypropylene/low-density polyethlene blends revealed that the shape, size, and orientation of LDPE occlusions remain undisturbed during the crystallization of IPP spherulites. On the other hand, LDPE occlusions introduce large changes in the internal structure of IPP spherulites. It was found that many new boundaries similar to those between spherulites are fromed when the crystallizing front passes the LDPE occlusion. Dead-ended boundaries with soft LDPE occlusions at the ends give rise to an improvement of the impact properties. It was shown that LDPE obstacles do not influence significantly the IPP spherulite growth rate in thin films or in the bulk.     

Localized volume deficiencies as an effect of spherulite growth. I. The two-dimensional case

Two-dimensional spherulite growth leads to the encirclement of regions of molten polymer in a polymer film. On further crystallization localized volume defects arise, resulting in thin spots in the film. Since this effect lowers the mechanical strength of films, we call these volume defects “weak spots.” A computer program is developed to evaluate the number, size, and shape of such volume defects for athermal, thermal, and mixed modes of primary nucleation of spherulites. It is shown that the total area of weak spots exceeds 10% of the sample area for all types of nucleation studied. The largest weak spots arise in samples crystallized via athermal and mixed nucleation; their size is of the same order as that of an average spherulite. Formation of weak spots is observed in thin films of poly(ethylene oxide) and poly(methylene oxide). The disadvantageous role of weak spots is confirmed by observation of electric breakdown occurring preferentially in weak spots in polypropylene films.     

一维碳纳米管/二维二硫化钼混合维度异质结的原位制备及其电荷转移性能

一维(1D)材料与二维(2D)材料的结合可形成独特的混合维度异质结,其在继承2D/2D范德瓦尔斯异质结的独特物性之外,还具有丰富的堆叠构型,为进一步调控异质结的结构及性能提供了新的可操控自由度。p型1D单壁碳纳米管(SWCNT)与n型2D二硫化钼(MoS₂)的结合,为调控异质结的能带结构及器件性能提供了丰富的选择。本文直接在高密度、手性窄分布的SWCNT定向阵列及无序薄膜表面原位生长MoS₂,制备出高质量1D SWCNT/2D MoS₂混合维度异质结。深入分析形核点的表面形貌与结构,提出了“吸附-扩散-吸附”生长机制,用于解释混合维度异质结的生长。利用拉曼光谱分析,证实SWCNT与MoS₂间存在显著的电荷转移作用,载流子可在界面处快速传输,为后续基于此类1D/2D异质结的新型电子及光电器件的设计与制备提供了新思路。     

Determination of the temperature dependence of spherulite growth rate in low-density polyethylene using the small-angle light scattering technique

Small-angle light scattering technique has been used to record changes in spherulite size during non-isothermal crystallization of low-density polyethylene under different cooling conditions. From these changes, the spherulite growth rates at various temperatures in the range 72–91° have been determined. The results are discussed on the basis of the Hoffman Lauritzen theory.     

Theoretical aspects of 2D electrochemical phase formation

Journal of Solid State Electrochemistry - Two-dimensional electrochemical phase formation as a result of nucleation, growth, and overlap of disk-shaped nuclei of a new phase on the electrode...     

Small-angle light scattering from a distribution of spherulite sizes

Depolarized small-angle light scattering from spherulites in semicrystalline polymers gives rise to a characteristic cloverleaf pattern. For scattering from a single spherulite, the position of the maximum in scattered intensity is readily related to the spherulite radius. For a distribution of spherulites, the maximum should be related to some characteristic measure of the distribution. It is shown for a wide variety of distributions that this characteristic radius is a ratio of high moments of the size distribution, specifically R* ≈ 〈R⁷〉/〈R⁶〉. The shape of the light-scattering profile should in principal be related to the nature of the spherulite distribution. Calculations of scattering profiles from a variety of distributions fail to demonstrate this, owing to the strong dependence of scattering power on spherulite size. Exceptions are noted for the case of certain bimodal distributions.