Statistical Theory of Stable and Meta-stable Transition for Crystallization and Fusion of Homopolymers V Statistical Dynamics of Polymeric Crystallization by Molecular Segregation—Dependence of Growth-Rate for Crystals on the Grown Mechanism and Initial S

First a short review on the dependence of growth-rate for crystals on the grown mechanism and initial structure of polymers was presented. Based on the structural model of micro-nucleus and crystal-constituent chains and the feature of statistical dynamics for polymeric crystallization by molecular segregation, a general method for characteristics of the number growth-rate for micro-crystal-constituent chains and the size growth-rate for crystals was proposed. According to the method, a set of quantitative expressions for the correlation of the number growth-rate and the size growth-rate to the four types of growth was obtained (folding, extending and combination of folding and extending). Their dependences of the crystalline temperature and the initial structure of polymers were also derived, then the exponential parameters of H for molecular weight were combined with the fraction of conformation on segments, a new correlation of the exponential parameter to the temperature of crystallization and the flexibility of polymeric chain was theoretically obtained, and the dependence of H on the different types of growth was also studied. Finally the relationship between the growth-rate for crystals and the molecular weight of polymers of solution was verified by a great number of experimental data, and an excellent agreement between the theoretical prediction and experimental data was obtained.     

Statistical Theory of Stable and Meta-stable Transition for Crystallization and Fusion of Homopolymers Ⅵ. Statistical Dynamics of Polymeric Crystallization by Molecular Segregation-Dependence of Crystal Growth Rate on the Grown Mechanism and Concentratio

First a short review on the dependence of crystal growth rate on the growth mechanism and concentration is present. Based on the structural model of micronucleus and crystal constituent chains, and the feature of statistical dynamics for polymeric crystallization by molecular segregation, a general method for characterizing number the growth rate and micro crystal constituent chains and the size growth rate for crystals was proposed. According to this method, a set of quantitative expressions for correlating the growth rate in number and size with the four types of growth (folding, extending and combination of folding and extending), the crystalline temperature and the crystalline concentration was derived. Then combined the concentration index is combined with the fraction of conformation for segments, a new correlation of the concentration index to the temperature of crystallization and the flexibility of polymeric chain is theoretically obtained. The dependences of the index on the different types of growth are also studied. Finally the relationships between the growth rate for crystals and the concentration of solution were verified by the experimental validating the predictions made by the theory.     

Statistical Theory of Stable and Meta stable Transition for Crystallization and Fusion of Homopolymers ⅣStatistical Dynamics of Polymeric Crystallization by Molecular Segregation-Division of Crystal Grow-rate Regimes and Their Temperature and Grown Mechan

First a short review on the crystal growth theories and the experimental data was presented. Then a set of quantitative expressions for the size growth-rate of crystals produced by four different micro-growth mechanisms (folding, extending and two types of combination for folding and extending) was derived by a general evaluating method. A set of quantitative expressions for the correlations between the crystal size growth-rate and the product of crystalline temperature and super-cooling temperature at four different micro-growth mechanisms was obtained. Three growth-rate regimes were divided, the variations of the morphology for the crystals in the three types of regimes with the crystalline and super-cooling temperatures were discussed. They showed that these theoretical correlations between the morphology of crystals and the crystalline and super-cooling temperatures are in agreement with the later important observation on the lateral shape of crystals.     

均聚物结晶与熔融化的稳态和亚稳态转变统计理论

基于多重微晶网络结构模型和分子分凝机制建立了高分子晶体的微晶核-和微晶粒-高分子链组模型,推导出了平衡态下高分子预结晶动力学方程,计算出了平衡态下不同尺寸微晶核-和微晶粒-高分子链组的几率分布函数.建立了非稳态下不同尺寸的微晶核-高分子链组的成核演化方程和微晶粒-高分子链组的增长演化方程,求解一般状态下的两个演化方程后,得到了不同时间和不同尺寸的微晶核-和微晶粒-高分子链组的一般密度分布函数.最后根据成核自由能和增长自由能对晶核和晶粒的尺寸大小的依赖性,提出了微晶核-高分子链组和微晶粒-高分子链组存在稳定性的热力学条件和动力学条件,成功地表征为三个特征区(稳态、亚稳态和非稳态).     

带有端烷烃链的超支化聚酯的受限结晶及动态黏弹行为

以三羟甲基丙烷(TMP)为核,二羟甲基丙酸(DMPA)为支化单体,通过熔融缩聚法合成了第3代端羟基脂肪族超支化聚酯,并用十八酸对其进行端基改性,采用广角X射线衍射(WAXD)、示差扫描量热分析(DSC)及红外光谱(FTIR)研究了不同端基改性程度的超支化聚酯的结晶熔融行为及端烷烃链的构象和堆积结构随温度的变化,采用旋转流变仪研究了端烷烃链对脂肪族超支化聚酯熔体动态黏弹行为的影响.结果表明,这类改性超支化聚酯的结晶归因于长链端烷烃的有序排列,改性程度越高,衍射峰强度越大.受限结晶的端烷烃链在升温后并不能完全转变为无序的结构状态,改性超支化聚酯在"熔点"以上仍有部分有序结构存在.超支化聚酯的线性黏弹区随着端基改性程度的增大而逐渐变短,超支化聚酯的弹性逐渐增大,剪切变稀越明显.动态流变测试中所出现的现象与改性超支化聚酯中端烷烃链的受限密切相关.     

Kinetics of Nonisothermal and Isothermal Crystallization of Metallocene Polyethylene

Thedevelopmentofmetallocenecatalystsundoubtedlyrepresentsarevolutioninthepolyolefinbusiness.MetallocenePE(MPE)coverspolyethyleneswhichareproducedbymetallocenecatalysttechnology.EXXONChemicalCo.developedanewmeta-llocenepolyethylene-EXCEED'"PEin1991.Nowmoreandmoreeffortsarespentonthisinterestingproject.Uniformmolecularstructureandnarrowmoleculardistribution,makeMPEbetterphysicalpropertiesthanthoseofconventionalPE,andalsomakeitlowmeltstrengthandbadprocessability.Sotherelationshipbetween…     

大柴旦富硼浓缩盐卤中硼酸镁盐稀释结晶动力学

采用动力学法研究了富硼浓缩盐卤稀释过程硼酸镁盐的结晶动力学,重点探讨了温度、稀释比和硼浓度对结晶过程的影响。利用单纯形优化法配合Runge-Kutta微分方程组数值解法对实验数据进行拟合,给出了结晶动力学方程和结晶速率。结果表明,低温、高硼浓度和中间稀释比有利于硼酸镁盐的结晶析出,最优条件下析硼率(以B_2O_3计)高达88%;结晶速率随硼浓度的增加和温度的降低快速增大;反应级数表明稀释结晶过程硼酸镁盐结晶主要受多核表面反应控制,同时提出了结晶相转化机理。     

草酸钙的结晶动力学及不同种类羧酸盐的影响

通过检测体系中游离Ca2+离子浓度及草酸钙(CaOxa)的粒径随时间的变化,研究了CaOxa的结晶动力学及3种羧酸盐对CaOxa结晶动力学的影响,这些羧酸盐为:一元羧酸盐甘氨酸钠(NaGlu)、二元羧酸盐酒石酸钠(Na2Tart)和三元羧酸盐柠檬酸三钠(Na3Cit)。在生理盐水中CaOxa的结晶动力学方程为r=kc3.3±0.3,平均反应速率常数(k)为(3.1±1.8)×109;3种抑制剂对k的影响程度从大到小为:Na3Cit>Na2Tart>NaGlu,但其平均反应级数(α)相差不大,α=3.2±0.1。Na3Cit、Na2Tart可抑制CaOxa晶体的生长和聚集过程,是潜在的肾结石抑制剂。     

Crystallization kinetics and morphology of binary phenolic/poly(ϵ-caprolactone) blends

For the first time, quantitative analyses of the crystallization kinetics, surface free energy of chain folding, and morphology in phenolic/poly(ϵ-caprolactone) (PCL) binary blends have been studied. The spherulite growth rate and the overall crystallization rate depend on the crystallization temperature and PCL content in the blend. In addition, the crystallization and melting temperatures of the PCL phase decrease with an increase in the phenolic content. An Avrami analysis shows that the addition of phenolic to PCL results in a decrease in the overall crystallization rate of the PCL phase. The presence of an amorphous phenolic phase results in a reduction in the rate of the spherulite growth of PCL. The surface free energy of folding increases with increasing phenolic content, and the crystal thickness of a phenolic/PCL blend, according to small-angle X-ray scattering (SAXS), is greater than that of pure PCL because of the increase in the surface free energy of chain folding and the decrease in the degree of supercooling. The observed domain size of the crystalline/amorphous phase (5.9 nm) from SAXS is also consistent with that from solid-state NMR (3–20 nm). All these results indicate that the crystallization ability of PCL decreases with increasing phenolic content in the blends. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 117–128, 2004     

Polypropylene-POSS Nanocomposites: Morphology and Crystallization Behaviour

Nanocomposites of isotactic polypropylene (PP) with polyhedral oligomeric silsesquioxanes (POSS) [RSiO_1,5]₈ having different alkyl substituents (R = methyl, isobutyl, isooctyl) were obtained by melt blending and analysed with electron microscopy, optical microscopy and DSC calorimetry. The influence of POSS structure on the morphological characteristics, the crystallization and melting behaviour of PP/POSS composites was investigated with varying the filler amount. The crystallization kinetics of the composites from the melt, examined both in isothermal and non-isothermal conditions, demonstrated that the nucleation activity of the examined POSS can be related to the length of alkyl substituents which, depending on the loading amount, affect the filler dispersion in the PP matrix and the growth of polymer crystals.     

Crystallization of markoffian copolymers

An equilibrium theory is proposed for crystallization of (A, B) binary copolymers whose comonomeric unit sequences are statistically described by conditional pair probabilities P_AA, P_AB, P_BA, and P_BB. These are linked to the product of the reactivity ratios by r = r_Ar_B = (P_AAP_BB)/(P_ABP_BA). Three cases are considered here, (i) B units are rejected from the crystals, (ii) cocrystallization of A and B comonomeric units is possible in the full range of compositions within a single crystal structure (copolymer isomorphism), (iii) cocrystallization takes place either in a poly(A)-type or in a poly(B)-type structure, depending on composition (copolymer isodimorphism). For case (i) crystallization the theory demonstrates, according to expectation, that alternating copolymers (r = 0) produce the largest melting point depression, whereas in case (ii) they give rise to the smallest composition difference between the crystals and the liquid. The theory developed here further illustrates that for binary copolymers which are isodimorphic (case iii), a phase diagram is obtained similar to that for a classical binary system of small molecules.     

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.     

Chitosan‐Assisted Crystallization and Film Forming of Perovskite Crystals through Biomineralization

Biomimetic mineralization is a powerful approach for the synthesis of advanced composite materials with hierarchical organization and controlled structure. Herein, chitosan was introduced into a perovskite precursor solution as a biopolymer additive to control the crystallization and to improve the morphology and film‐forming properties of a perovskite film by way of biomineralization. The biopolymer additive was able to control the size and morphology of the perovskite crystals and helped to form smooth films. The mechanism of chitosan‐mediated nucleation and growth of the perovskite crystals was explored. As a possible application, the chitosan–perovskite composite film was introduced into a planar heterojunction solar cell and increased power conversion efficiency relative to that observed for the pristine perovskite film was achieved. The biomimetic mineralization method proposed in this study provides an alternative way of preparing perovskite crystals with well‐controlled morphology and properties and extends the applications of perovskite crystals in photoelectronic fields, including planar‐heterojunction solar cells.     

Absolute Configuration of Small Molecules by Co‐Crystallization

The most reliable method to determine the absolute configuration of chiral molecules is X‐ray crystallography, but small molecules can be difficult to crystallize. We report rapid co‐crystallization of tetraaryladamantanes with small molecules as different as n‐decane to nicotine to produce crystals for X‐ray analysis and the assignment of absolute configuration when the molecules are chiral. A screen of 52 diverse compounds gave inclusion in co‐crystals for 88 % of all cases and a high‐resolution structure in 77 % of cases. Furthermore, starting from three milligrams of analyte, a combination of NMR spectroscopy and X‐ray crystallography produced a full structure in less than three days using an adamantane crystallization chaperone that encapsulates the analyte at room temperature.     

Crystallization kinetics and crystalline morphology of poly(ε-caprolactone) in blends with grafted rubber particles

The crystallization behavior of pure PCL and PCL in blends with crosslinked rubber particles was studied under (non)isothermal crystallization conditions, where the rubber particles were grafted with PCL chains via hydrogen abstraction of the aliphatic moieties in PCL. The crystal growth and the organization of crystals into spherulitic superstructures are significantly influenced by the presence of the grafted rubber particles, which act as an excellent nucleating agent for PCL. The nucleating efficiency shows an exponential dependency on the PCL grafting density and, according to an Avrami analysis, an increased PCL grafting density increases the overall crystallization rate of the PCL matrix. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1438–1448, 2010     

Crystallization of carboxylic acid salts in poly(ethylene oxide) oligomers at higher temperatures

Many alkali metal carboxylates when dissolved in poly(ethylene oxide) (PEO) oligomers, are phaseseparated by heating. These were revealed to be the crystals of the initially dissolved corresponding salts from the X-ray diffraction patterns. Some acetate salts achieve the lower limit of the lattice energy for phase separation of ordinary inorganic salts by heating in PEO oligomers. These carboxylate salts were therefore expected to show crystallization behavior in PEO oligomers by heating. The effects of cation size, alkyl chain length and molecular weight of PEO on the solubility are summarized. Negative temperature dependence of solubility of these acetate salts is seen in the PEO oligomers only when the salts have long alkyl chains. The salts containing larger cations needed a longer chain length of PEOs for crystallization by heating. These salts with longer alkyl chains showed positive temperautred dependence in lower molecular weight polyethers, but negative temperature dependence in solubility in PEO with molecular weights higher than 400. In PEO₄₀₀, all the carboxylates with longer alkyl chains were phase separated by heating.     

SAPO-5分子筛的可控合成及晶化过程探索

在非醋酸体系下分别通过动态和静态水热晶化方法合成了SAPO-5分子筛, 并考察了转速、 晶化时间及凝胶体系水硅比对SAPO-5分子筛晶相及形貌的影响, 采用X射线衍射(XRD)和扫描电子显微镜(SEM)技术研究了静态、 动态水热条件下SAPO-5分子筛的晶化过程. 结果表明, 静态水热条件下晶化6 h得到的SAPO-5分子筛为球状、 六边形柱状聚集晶体; 而在20 r/min转速下晶化2和6 h得到的SAPO-5分子筛分别为分散的凹面柱状晶体(凹面直径约6~8 μm)及均一分散的球状晶体(直径为16 μm); 在60 r/min转速下晶化3 h即可得到高度分散的六边形柱状晶体(六边形直径约5~8 μm); 提高转速至100和140 r/min时仅需晶化1 h即可得到六边形柱状晶体. 通过考察体系水硅比(H₂O/Si摩尔比)的影响, 确定最佳的水硅比为70, 此条件下所得晶相为纯相且分子筛的分散度最好. 综上可知, 相较于静态晶化, 动态晶化不仅从形貌上改善了晶体的分散度, 通过缩短晶化时间、 降低晶化转速也提高了SAPO-5分子筛的晶化效率. 本文采用较小的水硅比(H₂O/Si摩尔比为70)、 较低的模板剂用量在非醋酸体系下合成了SAPO-5分子筛, 为SAPO-5分子筛的合成提供了一条更简单、 经济的路线.     

等规聚丙烯自成核的等温结晶动力学

近年来 ,有关等规聚丙烯 (i PP)的自成核研究已引起了人们的关注 [1 ] ,但有关其结晶动力学的报道并不多见 .Carfagna等 [2 ]用膨胀计法研究了 i PP在未完全熔融重结晶情况下的等温结晶动力学 ,得到的 Avrami指数远远小于 3 .张新远等[3 ] 研究了 i PP未完全熔融情况下的非等温结晶动力学 .到目前为止 ,i PP自成核的熔体降温等温结晶动力学尚未见报道 .本文在 i PP自成核研究的基础上 [4] ,用 DSC方法研究了 i PP自成核在较高温度下的等温结晶动力学 ,讨论了结晶机理 .结果表明 ,在本实验的自成核条件下 ,i PP依然是三维球晶生长 ,…     

Crystallization of isotactic polystyrene from solution

Difficulties previously encountered in the growth of chain-folded single crystals of isotactic polystyrene suitable for study by electron microscopy and electron diffraction have been overcome using very poor solvents (including atactic polystyrene of low molecular weight). The hexagonal lamellar crystals produced are relatively stable under electron bombardment and, as a consequence, dark-field moiré patterns produced by double diffraction from overlapping layers are easy to study. These patterns show no evidence of differences in lattice spacing between fold and nonfold planes such as have been reported in single crystals of several other polymers. Such differences were attributed to congestion at fold surfaces and their absence in polystyrene, for which the surface energy of fold surfaces is small, supports this interpretation. A comparison of crystallization kinetics of polystyrene crystals grown from good and from poor solvents reveals differences in growth rates of three or more orders of magnitude at comparable supercoolings. This disparity cannot be accounted for by acceptable adjustments of thermodynamic parameters in current theories of crystallization with chain folding. The role of molecular conformation in solution appears to exert an unexpectedly large influence on crystallization rate.     

Crystallization of tethered polyethylene in confined geometries

Ordered poly(ethylene)‐poly(vinylcyclohexane) (PE‐PVCH) block copolymers are employed to study the crystallization of tethered PE in confined geometries. The high T_g of the PVCH component of these materials forces PE chains to crystallize in well‐defined geometries dictated by the mesophase structure of the block copolymer. Effects of chain tethering on crystallization are examined through comparison of singly‐tethered PE chains in PE‐PVCH (EV) diblocks and doubly‐tethered PE in PVCH‐PE‐PVCH (VEV) triblocks. Crystallinity is independent of the block copolymer mesophase structure in both the EV and VEV systems, although crystallinity in VEV depends on the molecular weight of the PE block of the copolymer. Melting temperature data indicate that spatial confinement reduces crystallite size in EV and VEV, and that the double tethering of PE chains in VEV reduces crystallite size further through topological constraints. Crystal nucleation and growth depend strongly on the type of microstructure in both EV and VEV block copolymers. Differences in the overall rate of crystallization are correlated with the dimensional continuity of the PE microdomains. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37:2053–2068, 1999