Power law of molecular weight dependence of lateral growth rate of isotactic polypropylene

Molecular weight (M) dependence of the lateral growth rate (V) of α form crystal of isotactic polypropylene (iPP) was studied. Reliable equilibrium melting temperature determined in our previous study was used for the analysis of supercooling dependence of V. A power law of M of V, , was obtained, where H is a small constant (H = 0.7). The small H, which is similar to that of the hexagonal phase of polyethylene (H = 0.7) in comparison with the value of H = 1.7 for the orthorhombic phase of polyethylene, confirmed our prediction of smaller H for “rod like” chain polymers because of easier chain sliding within the interface between the crystalline phase and the melt. Thus, the universality of the important role of topological nature in polymer crystallization was confirmed. Lateral surface free energy (σ) of the α form of iPP was obtained as σ ≅ 1.59 × 10⁻⁶ J/cm².     

Master curve of crystal growth rate and its corresponding state in polymeric materials

The temperature dependence of linear crystal growth rate (G) for various polymers shows a bell shape with the maximum growth rate (G_max). The G_max shows remarkable molecular weight dependence. The G_max was formulated on the basis of a crystallization theory, both for Arrhenius and WLF expressions in the molecular transport term. The plots of the reduced growth rate (G/G_max) against the reduced temperature (T/T_cmax) for a given polymer showed a single master curve without molecular weight dependence. The ratio of G₀/G_max gave a constant value for each polymer, indicating a material constant. On the basis of G_max for many polymers, a universal master curve was observed when the ratio of ln(G/G_max)/ln(G₀/G_max) was plotted against the reduced temperature (T/T_cmax).     

Molecular weight scaling of the spherulite growth rate in isothermally melt crystallized polyethylene nanocomposites

The spherulite growth rate, G_II, was measured for three monodisperse linear polyethylenes filled with up to 4 vol. % of SiO₂ nanoparticles in the crystallization regime II of small undercooling, ΔT. The fumed SiO₂ used did not exhibit any measurable nucleation activity. The G_II scaled with the number average molecular weight, M_n, as M_n^ν with the scaling exponent, ν, equal to (2.2 ± 0.1). This corresponds to the reptation controlled surface self-diffusion of loop-train adsorbed chains with the contour length fluctuation (CLF) and the chain constraint release (CR) contributions. In order to verify the hypothesis of the chain reptation as the molecular mechanism responsible for the chain transport, logG_II was plotted against the logarithm of the number of effective entanglements per chain, logN_eff. The N_eff was the sum of the number of “true” entanglements in the neat resin of a given M_n and the number of apparent “temporary” entanglements due to adsorption/desorption of segments of PE chains onto SiO₂ nanoparticles with their inter-particle distance equal or shorter than the average entanglement length. Adding 2 vol % and 4 vol. % SiO₂, respectively, resulted in an increase of the N_eff by 40% and 80% of apparent “temporary” entanglements, respectively. When plotted against logN_eff, all the experimental logG_II data for a given undercooling, ΔT, collapsed to a single line. The slope of the logG_II vs. logN_eff dependence was independent of ΔT and varied from −2.13 to −2.24, similarly to the slope of the logG_II vs. logM_n dependence. This supported the conclusion that the effects of increasing the M_n and/or adding the non-nucleating nanometer sized SiO₂ on the spherulite growth rate were additive in nature and their effect can be superimposed. The retarded reptation of the chains to the growing crystal front was identified as the primary molecular mechanism of chain transport controlling the reduction of the spherulite growth rate in the model PE/SiO₂ nanocomposites investigated.     

Rheological studies of hyaluronan solutions based on the scaling law and constitutive models

We have investigated the scaling relationship between rheological behavior and concentration for both salt-free and saline solutions of hyaluronan (HA), and adopted three viscoelastic constitutive models to predict the linear/non-linear viscoelastic behavior of these aqueous solutions of HA with different molecular weights at different concentrations up to 20 mg/ml. A series of concentration equations are obtained to describe the influence of HA concentration on solution viscosity. Corresponding to dilute and semi-dilute concentration region, salt-free HA solutions have scaling relationship between specific viscosity and HA concentration as η_sp ∼ c^1.0 and η_sp ∼ c^3.5, respectively, while for 0.15 M NaCl HA solutions, the scaling exponents are 1.5 and 4.2, respectively. Simulation results indicate that these constitutive models have good applicability to describe quantitatively the rheological properties of HA entangled solutions under either dynamic or steady shear flow. In addition, the plateau modulus scaling of HA solutions can be well described by the concentration-dependent length scale.     

Solution of the growth equation for asymmetric crystal faces

Most melt-grown and many solution-grown lamellar polymer crystals have curved lateral faces. Mathematical treatments by Mansfield, Point and Villers, and Toda, have provided a satisfactory interpretation of the shape of such crystal faces in terms of nucleation and relatively slow propagation rates of layers of attaching stems. The treatments by these authors, which start with the Frank-Seto growth model, assume that the propagation rates of growth steps to the right (v_r) and to the left of the secondary nucleus (v_l) are equal. However, for many crystal growth faces this is not the case; faces which lack a mirror plane perpendicular to the lamella have v_r≠v_l, resulting in asymmetric curvature. Here, we set up and solve the differential equations and reconstruct the shape of the growth front for the case of asymmetric spreading of steps. The solution is presented for the simple square lattice model. The asymmetric growth front is still described as part of an ellipse, as in the symmetric case, except that the centre of the ellipse is translated parallel to the underlying crystallographic plane in the direction of fast v. In forthcoming publications we will adapt the solution to other 2D Bravais lattices, appropriate to the crystal structures of specific polymers. Thus we will analyze complete habits of polymers such as polyethylene, poly(ethylene oxide), and poly(vinylidene fluoride), whose {110}, {120} and {110} growth faces, respectively, are asymmetric. The results of the present work allow a detail kinetic analysis of any well-developed polymer growth face in terms of the step initiation rate i and the propagation rates v_r and v_l. The present work also quantifies explicitly the deviations from elliptic shape and the substrate edge effects, and discusses when these can be ignored.     

鸟粪石晶体生长速率关键影响因素的定量分析

鸟粪石（MAP）结晶法处理氨氮废水具有去除效果好、反应速度快等特点,但MAP生长过程缓慢,晶粒细小,限制了MAP副产品的回收率,经济价值降低。利用基于黏附型生长机制建立的化学势梯度模型结合德拜-休克尔极限公式计算活度系数,研究了不同因素（温度、搅拌速度、pH、离子摩尔比）对MAP晶体生长速率的影响。结果表明,温度、搅拌速度和摩尔比的提升导致动力学生长速率常数k_t提高,从而导致鸟粪石生长速率上升,pH的升高使得反应初期的生长速率常数k_t和热力学推动力?\mu都得到了增强,到了反应后期,主要影响生长速率常数k_t,最终导致整个反应过程中MAP生长速率上升。对MAP晶体的平均生长速率计算发现,其生长速率分布在10^-9～10^-8 m/s之间;在pH=9.5时,生长速率提高至1.02×10^-8 m/s;离子摩尔比[Mg²⁺]∶[\mathrm{P}{\mathrm{O}}_{\mathrm{4}}^{\mathrm{3}-}]∶[\mathrm{N}{\mathrm{H}}_{\mathrm{4}}^{+}]=1∶1∶1提高至1.2∶1.2∶1时,MAP生长速率最高达到了1.29×10^-8 m/s。综上分析表明,温度、搅拌速度、pH和离子摩尔比提升,MAP晶体的生长速率均有不同程度的提高,其中,离子摩尔比影响最大,pH次之,温度和搅拌速度影响较小。因此,在实际工业中,pH和离子摩尔比的改变有望调控MAP的结晶过程。     

Surface characterization of aspirin crystal planes using molecular dynamics simulations

Molecular dynamics simulations have been implemented to study the effect of polar and non-polar solvents on the different faces of the aspirin crystal and the possible mechanisms of surface growth. We focus on the role of the H-bond in stabilizing the crystal faces and do a systematic study on the effect of the solvents at intermediate stages of the process of growth. Our results show that for both polar and non-polar solvents, the (0 1 0) surface of aspirin maintains its robustness and lattice order after equilibration, which allows for the fast deposition of additional aspirin molecules onto the existing surface. We find that the growth on this face can be mostly accomplished in a molecule-by-molecule manner, which is favored both thermodynamically and kinetically. The (0 0 1) surface shows that the molecules lose their lattice structure completely if they are not paired with other aspirin molecules before they are in contact with any solvent. For this reason, growth in this direction can only be in a layer-by-layer manner if there is any at all. Our results also show that as the unpaired (1 0 0) surface of aspirin is populated with-OH groups, their hydrophilic nature favors the interaction with a polar solvent and thus growth along this face is enhanced when contacting with ethanol. The methyl and carboxyl groups covering the unpaired (0 0 1) plane cause unfavorable interaction with the polar solvent. On the (0 1 0) plane, the interlaced arrangement of hydrophilic hydroxyl groups and hydrophobic phenyl groups stabilizes the surface structure in both polar and non-polar solvents.     

Crystallization of polyformals: 2. Influence of molecular weight and temperature on the morphology and growth rate in poly(1,3-dioxolane)

The morphology and growth rates of crystallized molecular weight fractions of poly(1,3-dioxolane) covering the range M_n = 8 800 to 120 000 have been studied by polarized light microscopy. Two different supermolecular structures, dependent on molecular weight and crystallization temperature have been found. Spherulites are formed after rapid crystallization and a more disordered morphology is formed at the lowest undercoolings but there is a temperature region where both forms are observed. The disordered form appears first and a consecutive spherulitic growth takes place. The crystallization kinetics were analysed over the temperature range 10°C to 36°C. At crystallization temperatures lower than 15°–18°C, the growth rate is linear and only spherulites are found. In the temperature range from 18°C to 36°C a well defined break is observed in the growth rate but the spherulitic growth rate is always higher than that of the irregular form. The growth rate temperature coefficient was studied and the usual plots are not linear in the whole range of crystallization temperatures. For the high crystallization temperature region, the slope is about twice as great as the low crystallization temperature slope. This is the region where regular spherulites are formed. The comparison between dilatometric and growth rate data has shown that the overall rate and growth rate temperature coefficients are the same.     

Studies on the crystal growth of rice bran wax in a hexane medium

Rice bran oil (RBO) is well known for its high wax content (2–4%). A good separation of waxes must be ensured through the formation of crystals that can be removed with a minimal retention of oil to maintain high yields of refined oil. In the present study, the form and size distribution of RBO wax crystals were investigated using a laser diffraction technique. An attempt was made to study the effect of cooling on growth and size distribution of RBO wax crystals in hexane medium, and it showed that high cooling rate and low temperature induces the formation of a great number of small nuclei. In addition, experiments were performed to evaluate the effect on the growth of wax crystals of successive additions of gum and pure TG to the medium. The entire experiment was designed to optimize the temperature and incubation time of wax crystallization to facilitate the efficient separation of wax from crude RBO-hexane miscella using membrane technology.     

Polymorphism of D-mannitol: Crystal structure and the crystal growth mechanism

The polymorphism of D-Mannitol(mannitol) is reviewed in this paper. It was found that the structure of the stable form is consistent in most literatures, but different authors have given different information about the two metastable forms. Therefore the commonly used nomenclature of mannitol was summarized based on the crystal unit cell parameters with the help of X-ray powder diffraction. Moreover, the crystal growth mechanism of mannitol polymorphs was summarized. Considering the lack of kinetic data for the metastable form especially, a reported method was attempted to apply to δ mannitol in an aqueous cooling crystallization process based on the induction time previously measured, and it was identified that the growth of the δ form follows the two-dimensional(2D) nucleationmediated mechanism. The results also indicate that the method based on induction time and supersaturation should have the potential to be expanded to the metastable polymorphs for the growth property study in a bulk system.     

Molecular weight dependence of melt crystallization behavior and crystal morphology of low molecular weight linear polyethylene fractions

Melt crystallization behavior and corresponding crystal morphology of five low molecular weight (3,900 ≤ MW ≤ 20,800) linear polyethylene (PE) fractions have been investigated. The overall crystallization data indicate that the lower molecular weight (MW) fraction possesses a higher crystallization rate at the same undercooling (ΔT). On the contrary, at the same crystallization temperature (T_c) the rate increases with MW. The Avrami exponent (n) varies from ca. 3 to 4 with decreasing ΔT for the fractions studied, which implies the nucleation process changes from athermal type to thermal type as T_c increases. For the low MW PE’s, the different crystal growth regimes (regime I and II) have been first time identified via linear crystal growth rate (G) measurements. The regime I/II transition temperatures are close to previously reported data, which were obtained through a different method. As reported for intermediate MW PE’s, the transitions occur at an almost constant ΔT of 17.5±1 °C for each fraction studied. Morphological study shows that single crystals could be formed isothermally at low ΔT’s. Typical banded spherulites and axialites, which are MW and ΔT dependent, are also observed. Orthorhombic structure is ascertained to be the dominant crystal structure that exists irrespective of MW and crystal growth regime.     

Recent progress of crystal growth modeling and growth control

With the rapid growth of electronic and optoelectronic industry, the demand for crystal materials increased dramatically for the past two decades. The requirement for better, cheaper, and larger single crystals has driven extensive research and development in crystal growth. To understand the interplay of associated transport processes and phase transformation, as well as to provide a design basis, crystal growth modeling is becoming more important in both fundamentals and practice. In this article, we review some recent progress of numerical modeling in crystal growth through three subjects: (1) hot-zone design, (2) active growth control, and (3) morphological simulation. Examples are given through our research results in recent years. For better illustration and process understanding some visualization results using transparent materials are given. The needs and the challenges ahead for crystal growth modeling are also discussed.     

Crystal growth pattern changes in low molecular weight poly(ethylene oxide) ultrathin films

A low molecular weight (MW) poly(ethylene oxide) (PEO) crystallized in ultrathin films displays various crystal growth patterns in a crystallization temperature (T_x) range from 20.0 °C to 50.0 °C. In succession, the following patterns are found: nearly one-dimensional (1D) dendrite-like crystal patterns at T_x ≤ 38.0 °C, two-dimensional (2D) seaweed-like patterns between 39.0 °C ≤ T_x ≤ 42.0 °C and again, nearly 1D dendrite-like patterns at T_x ≥ 43.0 °C. These transitions result from a complex interplay of varying growth rates along different growth directions and preservation of growth planes. Structural analysis carried out via electron diffraction indicates that the dendrite-like crystals formed at the low and high T_x values differ by their fast growth directions: along the {120} normal at the low T_x values and along the (100) and (010) normal at the high T_x values. In the later case however, the major growth faces are still the {120}, this time tilted at 45° and indicating the a∗ and b axes growth tips. In the intermediate T_x range (39.0 °C-42.0 °C), three growth directions coexist giving rise to the seaweed morphology. The crystal growth rates at the low and high T_x values are constant versus time. For the seaweed, a square-root dependence is obtained. These differences are probably due to 1D and 2D growth in the ultrathin films and are associated with different growth patterns of the dendrites and the seaweed, respectively.     

果糖在高黏度水溶液中的生长模型及机理

果糖是一种高附加值的甜味剂,其水溶液的黏度很高,导致晶体生长速率非常缓慢。利用常规的在线和离线测量方法会因为黏度大和成核而造成测量不准确。这导致果糖晶体在纯水中的生长速率目前尚无可靠数据,难以精确实现果糖工业生产过程的设计及优化。本文通过考察黏度、密度与扩散作用研究了高黏度果糖水溶液中的晶体生长速率。首先,利用旋转黏度计测定了果糖水溶液的黏度,考察了温度、浓度对其黏度的影响,使用经验模型对黏度数据进行了关联。随后利用比重瓶法测定了果糖水溶液的密度,考察了温度、浓度对溶液密度的影响。基于黏度和密度的测定结果,利用自由体积模型预测了果糖饱和水溶液的扩散系数,探究了在高黏度果糖水溶液中影响溶质分子传递过程的关键因素。最后,使用扩散控制的生长模型预测了果糖晶体的理论生长速率。采用单晶生长实验测定了果糖晶体的实际生长速率,将理论生长速率与之进行比较,结果吻合良好。此外,基于扩散控制和实际生长形貌,判断果糖晶体的生长机理属于螺旋错位生长。     

The viscosity dependence on concentration,molecular weight and shear rate of xanthan solutions

Summary This paper concerns the viscosity dependence of Xanthan as a function of polymer concentration, shear rate and molecular weight in the ordered conformation. The different samples with various molecular weights are obtained by ultrasonication. A unique curve is obtained for the reduced specific viscosity ( ) as a function of γ · γ _r ⁻¹ for the different molecular weight samples and polymer concentrations below an overlap concentration C [η]₀⩽ 1.5. The master curve giving the relation as a function of C [η]₀ is drawn and compared with that of polystyrene in good solvent. The largest increase of in semidilute solution may be due to larger interchain interactions and to larger stiffness of the Xanthan molecule.     

Electrocrystallisation of zinc from acidic sulphate baths; A nucleation and crystal growth process

The electrochemical nucleation and growth of zinc on low-carbon steel from acidic (pH 2.0-4.5) baths containing ZnSO₄, NaCl, and H₃BO₃, was studied by means of chronoamperometry at various cathodic potentials under a charge-transfer controlled regime. It is shown that at overpotentials in the range 0.30-0.55 V (negative to the Zn²⁺/Zn redox value) the electrodeposition proceeds by instantaneous three-dimensional nucleation, which turns to progressive at higher overpotentials and/or very acidic baths. At low cathodic overpotentials (<0.30 V), a two-dimensional contribution limited by the incorporation of Zn ad-atoms in the developing lattice becomes significant at the early stages of deposition, and is more progressive in type the more acidic is the bath pH. Nucleation rate constants were calculated and correlated analytically with the respective potentials, using the classical theory of heterogeneous nucleation, which though fails to lead to reasonable values for the critical nucleus size.     

Modelling of crystal growth of KDP in a 100 dm suspension crystallizer using combination of CFD and multiblock model

In this study a combination of computational fluid dynamics (CFD) and multiblock model is used for modelling crystal growth in a 100 dm³ suspension crystallizer equipped with two turbine impellers. Local hydrodynamics and crystal suspension densities were modelled using CFD. Simulation results were compared with experimental results to verify flow profile and slip velocities (Hatakka et al., 2008, 2009), and classification of crystals. Results from CFD simulations were then translated to a proper form and used as input data for the multiblock model.     

Self-catalytic crystal growth,formation mechanism,and optical properties of indium tin oxide nanostructures

In-Sn-O nanostructures with rectangular cross-sectional rod-like, sword-like, and bowling pin-like morphologies were successfully synthesized through self-catalytic growth. Mixed metallic In and Sn powders were used as source materials, and no catalyst layer was pre-coated on the substrates. The distance between the substrate and the source materials affected the size of the Sn-rich alloy particles during crystal growth in a quartz tube. This caused In-Sn-O nanostructures with various morphologies to form. An X-ray photoelectron spectroscope and a transmittance electron microscope with an energy-dispersive X-ray spectrometer were used to investigate the elemental binding states and compositions of the as-synthesized nanostructures. The Sn doping and oxygen vacancies in the In₂O₃ crystals corresponded to the blue-green and yellow-orange emission bands of the nanostructures, respectively.     

A study of phase evolution and crystal growth for nano-sized monoclinic Y4Al2O9 as a novel thermal barrier coatings

Nano-sized monoclinic Y₄Al₂O₉ was produced by sol-gel process as a novel potential candidate material for thermal barrier coatings. The thermal behavior, structural evolution of the products and the morphological characteristics of the compacted bodies were investigated by Thermogravimetric analysis and differential scanning calorimeter (TG-DSC), X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR), and Field emission scanning electron microscopy (FESEM). Qualitative analyses indicate that monoclinic Y₄Al₂O₉ was formed at about 1000 °C, and exhibited good phase stability throughout the annealing temperature ranging from 1000 °C to 1400 °C. The thermophysical properties of Y₄Al₂O₉ ceramics were also evaluated compared with 8YSZ and La₂Zr₂O₇. The determined activation energy of crystal growth is about 72.71 ± 0.31 kJ mol⁻¹. Meanwhile, Y₄Al₂O₉ represents low thermal conductivity (1.71 W m⁻¹ K⁻¹), moderate thermal expansion coefficient (8.73 × 10⁻⁶ K⁻¹), and high sintering-resistance ability. Such results reveal that nano-sized Y₄Al₂O₉ is favorable for the application of TBCs.