Theoretical study of temperature induced phase transitions in poly(β-benzyl-l-aspartate) and it's copolymer

In polypeptides and proteins, the phenomenon of conformational transitions has been successfully explained on the basis of Zimm and Bragg model, as a function of temperature, pressure, solvent concentration and pH etc. The Zimm and Bragg theory of helix↔coil transition has been modified to explain the temperature induced helix→helix transitions in solid films of poly(β-benzyl-l-aspartate) and in its copolymer copoly(β-stearyl-l-aspartate-β-benzyl-l-aspartate) with varying degrees of stearylation. An expression for the degree of order is obtained from the grand partition function for the entire chain in terms of nucleation parameter, which controls the transition width. At low degree of stearylation, an α→ω transition occurs with the increase in temperature, whereas, at degree higher than 40%, the reversal of α helix sense from right-handed to left-handed takes place. The theoretical transition curves are found to be in good agreement with the experimental data.     

Shear effects on thermoplastic foam nucleation

Polyethylene foam experiments were conducted on a twin screw foam extruder to study the process effects upon foam nucleation. The results indicate that, other than quantity of nucleators, throughput rate and die opening are important process parameters, underscoring the importance of shear in the die on nucleation. It is also found that shear effects increase as nucleator level increases. A modified cavity model shows at least qualitative agreement with experimental results. Dimensionless Capillary number, ratio of shear force to surface tension force, provides evidence that shear force rather than shear rate alone is the principal parameter affecting foam nucleation.     

High‐pressure induced formation of isotactic polypropylene mesophase: Synergistic effect of pressure and pressurization rate

The crystallization induced by high pressures up to 2 GPa was studied for isotactic polypropylene (iPP) using wide angle X‐ray diffraction, small angle X‐ray scattering, and atomic force microscopy methods. The iPP mesophase can be induced at 200°C by high pressures with fast pressurization rate. A pressure–pressurization rate kinetic phase diagram of mesophase and γ‐phase was established to systematically analyze the influences of pressure and pressurization rate on crystallization polymorphism. Under pressure not higher than 0.75 GPa, only γ‐phase is formed, even the pressurization rate reaches 5 × 10³ MPa/s. With increasing pressure to 1.0 GPa, the mesophase is possible to be generated. As pressure further increases to 1.5 GPa and higher, the pure mesophase system can be obtained for pressurization rate above the critical values (about 10 MPa/s). Moreover, the structure of iPP mesophase obtained by rapid pressurization was analyzed and compared with that prepared by temperature quenching. Also interestingly, the pressure‐induced mesophase can transform into γ‐phase by annealing under pressure at 200°C, and the rate of this phase transition is slowed down with increasing annealing pressure. POLYM. ENG. SCI., 59:439–446, 2019. © 2018 Society of Plastics Engineers     

Foaming of polymers with supercritical CO2: An experimental and theoretical study

Microcellular polystyrene (PS) foams and porous structures of the biodegradable poly(d,l-lactic acid) (P_d,lLA) were prepared with the batch foaming technique (pressure quench) using supercritical CO₂ as blowing agent. The effect of pressure, temperature and depressurization rate on the final porous structure was investigated. The results revealed that the size of the pores decreases and their population density increases with pressure increase, or decrease of temperature, and/or increase of the depressurization rate. The results were correlated by combining nucleation theory with NRHB model in order to account for and emphasize the physical mechanism related to nucleation of bubbles inside the supersaturated polymer matrix. A satisfactory agreement between correlations and experimental data was obtained indicating that the nucleation theory yields quantitative correlations when variables such as sorption, degree of plasticization, and surface tension of the system polymer-supercritical fluid are accurately described.     

Theoretical study of temperature induced transition and hyper stability of collagen mimics

Collagen a polymer, is the nature's most abundant protein. It has an immense tensile strength and is the main constituent of ligaments, tendons, etc. The present communication interprets the experimental data of thermally induced transition in collagen mimics as reported by Steven K. Holmgren and co-workers. The theoretical transition curves as obtained by the modified Zimm and Bragg model are found to be in good agreement with the experimental data. The order of the values of nucleation parameter and enthalpy changes obtained theoretically, attributes the increase in the degree of the stability of collagen mimics [(Pro-Pro-Gly)₁₀〈(Pro-Hyp-Gly)₁₀〈(Pro-Flp-Gly)₁₀].     

Orientational order and thermodynamic properties of mainchain trimer liquid crystals: a combined use of H NMR, PVT and high-pressure differential thermal analysis

The trimer compounds (4,4′-bis[ω-(4-cyanobiphenyl-4′-yloxy)alkoxy]biphenyls) (CBA-Tn, n=9, 10) with n indicating the number of carbon atoms in the spacer exhibit a nematic order on cooling from the melt. The orientational characteristics of the central and terminal mesogenic cores were separately investigated in the liquid-crystalline (LC) state for CBA-T10 by the ²H NMR method. The ratio of the quadrupolar splittings was found to remain nearly constant over the entire range of the nematic state, suggesting that the conformation of the intervening spacer is also stable. The pressure-dependence of the phase boundary curves has been studied for transitions such as crystal↔nematic LC↔isotropic melt by the high-pressure differential thermal analysis. The transition entropies have been obtained according to the Clapeyron relation. A combined use of the PVT data led to an estimate of the constant-volume transition entropies, which is in reasonable agreement with the conformational transition entropies estimated previously by the rotational isomeric state analysis of the spectroscopic data.     

湿蒸汽非平衡凝结流动的热力学特性

水蒸气凝结两相流动呈现高度的非平衡特性。目前,凝结参数都是利用半经验公式得出,很少考虑两相间传热温差以及耦合问题。在湿蒸汽两相流输运方程的基础上,建立了一种准确简单的凝结成核和水滴生长模型,采用具有较好激波捕获效果的高精度二阶TVD格式进行离散,计算了湿蒸汽非平衡凝结流动参数及凝结冲波分布。着重研究了湿蒸汽非平衡凝结流动的热力学特性,讨论了进口压力对凝结特性的影响,归纳了进口过冷度对成核率、水滴数、凝结冲波形态的变化规律。研究表明:进口压力增加,凝结位置逐渐向上游移动;进口过冷度降低,凝结位置向下游移动,达到较高的Mach数后,才会出现凝结成核;进口过冷度越高,非平衡凝结相变产生的湿度越高。凝结冲波出现后,湿蒸汽沿喷管继续高速流动,其流动规律与等熵流动相似。     

Molecular dynamics simulation of orientation and crystallization of polyethylene during uniaxial extension

Molecular dynamics simulations of realistic, united atom models of polyethylene undergoing uniaxial extension are described. Systems composed of chains ranging from 25 to 400 carbons have been studied, under a variety of processing histories, including isothermal deformation at constant applied stress below the melt temperature T_m, isothermal deformation below T_m followed by annealing, isothermal deformation above T_m followed by crystallization at a quench temperature below T_m, and non-isothermal crystallization during simultaneous deformation and cooling through T_m. Extension and orientation of large segments of flexible chains by uniaxial deformation accelerates the primary nucleation rate to a time scale accessible by molecular dynamics simulation. Entanglements operative during active deformation promote extension and orientation without nucleation of a crystal phase, while relaxation of stress at constant strain is sufficient to allow slippage of chains past pinning points and rapid nucleation and growth of crystallites as neighboring oriented chains come into registry. Isothermal crystallization of pre-oriented systems shows an apparent increase in nucleation density at lower temperatures; the resulting ordered regions are smaller and more closely aligned in the direction of orientation. During non-isothermal deformation, where stretching and cooling occur simultaneously, a first order transition is observed, with discontinuities in the volume and global order parameter, when the system crystallizes.     

Underpotential—overpotential transition phenomena in metal deposition processes

The transition phenomena in metal deposition processes have been studied in the system Ag(hkl)/Pb²⁺ by potentiostatic pulse experiments from the underpotential to the overpotential range. The analysis of the current-time transients indicates a model of progressive nucleation and hemispherical diffusion to the growing 3-D crystallites. An important influence of the initial state in the underpotential range on the nucleation rate has been found. Furthermore, the nucleation rate strongly depends on the overvoltage and on the substrate nature. All experimental results are explained by a stepwise bulk phase formation process including rearrangement of adatoms in the 2-D adsorbed layer, formation of critical clusters and further rearrangement and growth forming epitaxially orientated 3-D crystallites. The nucleation process must be treated by an atomistic model due to the derived low number of atoms in the critical cluster.     

青霉素亚砜结晶生长与成核动力学

利用Mydlarz 和 Jones 模型（MJ2）,对乙酸丁酯中青霉素亚砜的成核与生长动力学进行研究。通过矩量法对MJ2模型进行处理后,利用晶体产品的粒度分布计算得到青霉素亚砜的生长速率与成核速率,然后利用最小二乘法拟合回归求解出成核与生长动力学方程参数。通过实验设计考察了过饱和度、温度与搅拌速度对青霉素亚砜晶体成核和生长过程的影响。研究表明青霉素亚砜晶体生长速率随过饱和度比的增加呈现指数型增长,确定青霉素亚砜晶体生长属于晶体表面生长控制过程。由于高速搅拌会增加青霉素亚砜晶体的破碎,促进了二次成核过程,随着搅拌速度的增加,晶体生长速率出现小幅下滑,而成核速率则明显升高。青霉素亚砜成核与生长动力学研究将有助于工业生产过程优化。     

Kinetic analysis on spherulite growth rate of polypropylene catalloys

The kinetic analysis on melt-crystallization of polypropylene catalloys (PP-cats) was conducted through measuring their spherulite growth rates. A multiple melting behavior of PP-cats was found through differential scanning calorimetry (DSC) and the corresponding crystalline microstructures of PP-cats were studied by wide-angle X-ray diffraction (WAXD). The calculated T_m^o value of propylene homopolymer (PP) suggests an obvious melting point depression of PP-cats. Moreover, it is found that the existence of ethylene-propylene copolymer could result in the changes of crystalline microstructure of PP and the PP crystal is in favor of growing along (040) lattice plane of α-monoclinic crystal. The crystal growth rate of PP-cats decreases with the increase of ethylene-propylene copolymer content in PP-cats. A comparison of crystallization kinetics between PP-cats and virgin iPP through a modified Lauritzen-Hoffman model indicates that there appears a transition from regimes II to III in iPP and PP-cats containing low ethylene-propylene copolymer content. However, for the PP-cats containing high ethylene-propylene copolymer content, crystallization always processes in regime II. In addition, both calculated nucleation parameter (K_g) and the fold surface free energy (σ_e) for PP-cats increase with the increase of ethylene-propylene copolymer content, implying that the existence of ethylene-propylene copolymer is unfavorable for the surface nucleation of PP and regular folding of the molecule chain. It is believed that an increase in viscosity of the melts induced by different compositions could remarkably slow crystallization growth down, because under this condition surface nucleation dominates as compared with crystal growth.     

螺旋内槽管内天然气-水-表面活性剂体系的水合物生成动力学计算

针对多组分气体（天然气）-水-表面活性剂体系在螺旋内槽管内的水合物生成过程,首先采用CFD方法结合群体平衡模型（PBM）,基于溶质渗透模型和Kolmogorov各向同性湍流理论对螺旋内槽管内气液传质系数进行了模拟;其次基于Kashchiev和Firoozabadi的经典水合物成核和生长理论,将其体系从单组分-水系统扩展到多组分气体（天然气-水-十二烷基硫酸钠）系统,同时结合经典结晶理论利用传质系数对水合物生长模型进行了修正,建立了适用于螺旋内槽管流动体系内天然气水合物生成动力学模型。通过模拟计算,获得不同水合物生产条件下天然气在水中的平均传质系数;进而利用Microsoft Visual C++编程计算得到不同条件下水合物生成动力学数据,在考察范围内,天然气水合物的成核速率随着反应体系有效表面能的增大而锐减,而水合物生成驱动力和生长速率未受影响,同时水合物生长速率随着流速和反应压力的增大及温度的降低而增大,成核速率随着压力的增大和温度的降低而增大。     

An experimental and theoretical investigation of rarefied gas flow through circular tube of finite length

The conductance of nitrogen gas through circular tube of finite length was measured in the continuum and transition regimes for length to diameter ratios L/D ranging from 0.045 to 33.4 and pressure ratios across the tubes P₁/P₂ from 1.1 to 23. A numerical analysis was carried out to estimate the conductance using the continuum approach in the continuum regime and transition regime at low Knudsen number, and using direct simulation Monte Carlo (DSMC) method in the transition regime at high Knudsen number. The observed conductances were compared with the simulation and an empirical equation derived by Hanks-Weissberg. Both the experimental and simulation results show that the conductances at a constant gas flow rate increases linearly with increasing arithmetic mean pressure across the tube P_av=(P₁+P₂)/2, irrespective of the P₁/P₂ ratio. The observed conductances were smaller than those predicted by the Hanks-Weissberg's equation. The deviation increases with increasing gas flow rate, and with decreasing L/D ratio. It was confirmed that the deviation occurs due to the increase in the effects of inertia and expansion in the flowing gas with increasing flow rate and decreasing L/D. A semi-empirical equation was derived by substituting the Poiseuille term in the Bernoulli formula with Hank-Weissberg's equation under the condition of isothermal expansion. The proposed equation was found to be valid in the range of the continuum regime to the transition regime at low Knudsen number.     

Dye distribution in supercritical dyeing with carbon dioxide

The measurement of equilibrium dye uptake in PET fiber is carried out using a flow-type cylindrical vessel. Using the expanded liquid model in which both phases are supposed to be liquid mixtures, the equilibrium uptake of C.I. disperse red 60 may be calculated from each binary interaction parameter of carbon dioxide–dye, carbon dioxide–PET and dye–PET binary systems. The calculated uptake is compared with the observed one with the same order of magnitude, even though the former is overestimated. The binary interaction parameter of dye–PET system that is obtained from the equilibrium dye uptake in PET is smaller by about 1.5 than that obtained by the binary system. Nevertheless, it is found that the predicted uptake of dye with using the interaction parameter regressed from the ternary data is in excellent agreement with the experimental one. The distribution of C. I. disperse red 60 into supercritical fluid and PET phase at equilibrium can be predicted and compared with the experimental one. The estimated distribution coefficient increases with the pressure increase, because the sorption of dye in PET fiber increases slowly with the pressure than the dye solubility in carbon dioxide does. This tendency is weakened with increase of temperature.     

Effect of temperature on particle size for vapor-phase synthesis of ultrafine iron particles

For the vapor-phase synthesis of iron particles from FeCl₂ at temperatures ranging from 800 to 950‡C the reason is sought why the model based on the classical nucleation theory brought an increase of particle size with temperature increase, in reverse to experimental observation. The nucleation rate according to the classical theory should decrease with a temperature increase, due to the decrease of super-saturation ratio resulting from the increase of vapor pressure. The decrease of nucleation rate ultimately leads to an increase of particle size. Yang and Qiu’s nucleation theory was applied in place of the classical theory. However, the same result as with the classical theory was obtained : the nucleation rate decreased with the temperature increase. Finally, an Arrhenius-type nucleation rate equation was introduced. The preexponential factor and the activation energy for nucleation were determined to be 1348.2 sec_-1 and 159.1 KJ/mol, respectively. With these values put into Park et al.’s model, good agreement was obtained in temperature dependence of particle size between model prediction and experimental data.     

Study of reaction injection molding of polyurethane microcellular foam

Processing of microcellular foam was investigated for the feasibility of production of tough and lightweight polyurethanes. To increase the nucleation rate in a gas-supersaturated resin, ultrasonic excitation was applied to the mixture of polyol(polyether-based polyol) and isocyanate(diphenyl methane diisocyanate). A microcellular structure was produced by two sequential steps, i.e., supersaturationof the polyol resin with nitrogen gas at elevated pressure and ultrasonic bubble nucleation right after the impingement mixing of two components of the polyurethane system. Theoretical analyses based on nucleation theories were employed to predict the rate of nucleation in the gas-supersaturated polyurethane. The rate of nucleatio in the resin was predicted by classical nucleation and cluster theories. In the experimental investigation, ultrasonic excitation was applied to increase the nucleation rate in the resin that had been saturated by nitrogen at a saturation pressure < 2.0 MPa.     

The roles of the Trommsdorff–Norrish effect in phase separation of binary polymer mixtures induced by photopolymerization

Influence of the Trommsdorff–Norrish (T–N) effect on the phase separation of methyl methacrylate (MMA)/poly(ethyl acrylate) (PEA) mixtures undergoing photo-polymerization was examined by a combination of several experimental techniques. By FT-IR spectroscopy, it was found that the polymerization conversion explosively increases at the onset of this T–N effect. The characteristic irradiation time τ at which this effect occurs, strongly depends on the light intensity and gradually shifts to early time as the irradiation intensity increases. The shrinkage of the mixture observed in situ by laser-scanning confocal microscopy exhibits a transition at a particular irradiation time which is slightly longer than the characteristic time τ. By gel permeation chromatography (GPC), it was found that the molecular weight of the resulting PMMA was almost unchanged before τ and suddenly increases about an order of magnitude after the onset of the auto-acceleration effect. Finally, the characteristic length scales of the morphology also quickly increase with irradiation time and are eventually frozen by this T–N effect. These experimental results indicate that the Trommsdorff–Norrish effect plays an important role in the kinetic processes of polymerization-induced phase separation, suggesting an efficient tool to control the morphology of the polymerizing mixture.     

Time-resolved SAXS studies on ordering kinetics of block copolymers: Further investigation of two-step ordering from disorder-sphere to hex-cylinder

We have conducted the systematical investigations for the ordering process and kinetics of both hexagonally packed cylindrical microdomains (hex-cylinder) and spheres in a body-centered cubic lattice (bcc-sphere) from spherical microdomains with a short-range liquid-like order (disorder-sphere) over a wide range of quench depth for a polystyrene-block-polyisoprene-block-polystyrene triblock copolymer, having order-order transition (OOT) temperature, T_OOT, at 190 °C between hex-cylinder and bcc-sphere, by using time-resolved small-angle X-ray scattering. As a result, we clearly assessed a range of temperature over which the two-step ordering from disorder-sphere to hex-cylinder occurs. A possible interpretation for the two-step ordering process was proposed in the text. The following three kinds of ordering processes are observed. (i) The single-step ordering of hex-cylinder: when the system is quenched into the temperature below 183.2 °C, hex-cylinder is directly transformed from disorder-sphere via the nucleation and growth process. The incubation time for the nucleation and the transition rate largely depend on the quench depth. (ii) The ordering of bcc-sphere: when the system is quenched into the temperature above 190 °C in the bcc-sphere phase, bcc-sphere is formed from disorder-sphere via the nucleation and growth process. The quench-depth dependence of the incubation time is very small, compared with that for hex-cylinder, and the transition rate is independent of the quench depth. (iii) The two-step ordering of hex-cylinder: when the system is quenched into the temperature range from 183.2 to 190 °C, the volume-filling metastable bcc-sphere is first developed by nucleation and growth, followed by the OOT from metastable bcc-sphere to hex-cylinder via the nucleation and growth process. The incubation time for the formation of metastable bcc-sphere is very close to that for the formation of equilibrium bcc-sphere, and the transition rate for the formation of metastable bcc-sphere is independent of the quench depth. Thus, the ordering pathways for the volume-filling of metastable bcc-sphere are almost identical to that for the volume-filling equilibrium bcc-sphere. The incubation time for the OOT from metastable bcc-sphere to hex-cylinder is longer than that for the formation of metastable bcc-sphere, and the transition rate for the former is also slower than that for the latter. Moreover, the incubation time for the OOT from metastable bcc-sphere to hex-cylinder is longer than that for that from equilibrium bcc-sphere to hex-cylinder, and the transition rate for the former is also slower than that for the latter, because metastable bcc-sphere is considered to be more distorted than the equilibrium bcc-sphere, which suppress the epitaxial growth of hex-cylinder along a [111] direction of bcc-sphere.     

Effects of die geometry on cell nucleation of PS foams blown with CO2

This paper investigates the effect of varying the geometry of the die on the cell nucleation behavior of extruded PS foams blown with CO₂. Three interchangeable groups of carefully calibrated filamentary dies have been used in the experimental study. The dies were deliberately designed to have either different pressure drop rates while having identical die pressures and flow rates, or different die pressures while having identical pressure drop rates and flow rates. The experimental results revealed that the geometry of the die governs the cell density of extruded PS foams, especially because of its significant effect on the pressure drop rate across the die. However, the effect of the die back pressure on the cell density was found to be marginal, whereas its effect on the cell morphology was found to be predominant. In addition, regardless of die geometry, the CO₂ content proved to be a very sensitive parameter with respect to the cell nucleation behavior of extruded PS foams. On the other hand, the cell density was slightly improved by an increase of the tale content, especially at reduced concentrations of CO₂.     

Experimental and numerical studies on the effects of pressure release rate on number density of bubbles and bubble growth in a polymeric foaming process

A simulation of simultaneous bubble nucleation and growth was performed for a batch physical foaming process of polypropylene (PP)/CO₂ system under finite pressure release rate. In the batch physical foaming process, CO₂ gas is dissolved in a polymer matrix under pressure. Then, the dissolved CO₂ in the polymer matrix becomes supersaturated when the pressure is released. A certain degree of supersaturation produces CO₂ bubbles in the polymer matrix. Bubbles are expanded by diffusion of the dissolved CO₂ into the bubbles. The pressure release rate is one of the control factors determining number density of bubbles and bubble growth rate.To study the effect of pressure release rate on foaming, this paper developed a simple kinetic model for the creation and expansion of bubbles based on the model of Flumerfelt's group, established in 1996 [Shafi, M.A., Lee, J.G., Flumerfelt, R.W., 1996. Prediction of cellular structure in free expansion polymer foam processing. Polymer Engineering and Science 36, 1950-1959]. It was revised according to the kinetic experimental data on the creation and expansion of bubbles under a finite pressure release rate. The model involved a bubble nucleation rate equation for bubble creation and a set of bubble growth rate equations for bubble expansion. The calculated results of the number density of bubbles and bubble growth rate agreed well with experimental results. The number density of bubbles increased with an increase in the pressure release rate. Simulation results indicated that the maximum bubble nucleation rate is determined by the balance between the pressure release rate and the consumption rate of the physical foaming agent by the growing bubbles. The bubble growth rate also increased with an increase in the pressure release rate. Viscosity-controlled and diffusion-controlled periods exist between the bubble nucleation and coalescence periods.