Crystallization behavior and hydrophilicity of poly(vinylidene fluoride) (PVDF)/poly(methylmethacrylate) (PMMA)/poly(styrene-<Emphasis Type="Italic">co</Emphasis>-acrylonitrile) (SAN) ternary blends

Compatibilization of the partially miscible poly(vinylidene fluoride) (PVDF)/poly(styrene-co-acrylonitrile) (SAN) pair by a third homopolymer, i.e., poly(methyl methacrylate) (PMMA), was investigated in relation to cross section morphology, crystallization behaviors and hydrophilicity of the polyblends. Scanning electron microscopy showed a more regular and homogeneous morphology when more than 15 wt.% PMMA was incorporated. The samples presented only α phase regardless of PMMA content in the blend. As the PMMA content increased in the blends, the interactions between each component were enhanced, and the crystallization of PVDF was limited, leading to a decreasing of the crystallinity and the crystallite thickness. Besides, the hydrophilicity of PVDF was further improved by PMMA addition. The sample containing 15 wt.% PMMA showed a more hydrophilic property due to the more polar part of surface tension induced by PMMA addition. Observed from the cross section of the blends, the miscibility of partially miscible PVDF/SAN blends were efficiently improved by PMMA incorporation.     

Non-Isothermal Crystallization of Poly(vinylidene Fluoride)/Multiwalled Carbon Nanotube Composites

Poly(vinylidene fluoride)/multiwalled carbon nanotube (PVDF/MWCNT) composites were prepared by the method of solution blending. The non-isothermal crystallization of PVDF and its composites was investigated by differential scanning calorimetry (DSC). The results showed that the crystallization peaks shifted to lower temperature and the exothermic trace became wider when cooling rate increased for PVDF and its composites. The MWCNTs caused an increase in crystallization temperature and initial crystallization temperature. In addition, the Jeziorny and Mo methods were used to analyze the non-isothermal crystallization kinetics. The results showed that the crystallization rate rose with an increase in cooling rate, however, the MWCNTs decreased the crystallization rates of PVDF.     

Investigation on LCST behavior of a new amorphous/crystalline polymer blend: Poly(n‐methyl methacrylimide)/poly(vinylidene fluoride)

The liquid–liquid phase‐separation (LLPS) behavior of poly(n‐methyl methacrylimide)/poly(vinylidene fluoride) (PMMI/PVDF) blend was studied by using small‐angle laser light scattering (SALLS) and phase contrast microscopy (PCM). The cloud point (T_c) of PMMI/PVDF blend was obtained using SALLS at the heating rate of 1 °C min^?1 and it was found that PMMI/PVDF exhibited a low critical solution temperature (LCST) behavior similar to that of PMMA/PVDF. Moreover, T_c of PMMI/PVDF is higher than its melting temperature (T_m) and a large temperature gap between T_c and T_m exists. At the early phase‐separation stage, the apparent diffusion coefficient (D_app) and the product (2Mk) of the molecules mobility coefficient (M) and the energy gradient coefficient (k) arising from contributions of composition gradient to the energy for PMMI/PVDF (50/50 wt) blend were calculated on the basis of linearized Cahn‐Hilliard‐Cook theory. The kinetic results showed that LLPS of PMMI/PVDF blends followed the spinodal decomposition (SD) mechanism. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1923–1931, 2008     

Influence of size reduction of crosslinked rubber particles on phase interface in dynamically vulcanized poly (vinylidene fluoride)/silicone rubber blends

In this paper, the influence of rubber particle size on the phase interface in dynamically vulcanized poly(vinylidene fluoride)/silicone rubber (PVDF/SR) blends without any modifier is discussed through the studies of specific surface of crosslinked SR particles, crystallization behavior and crystal morphology of the PVDF phase, interfacial crystallization, melt rheological behavior and mechanical properties of blends. A series of decreased average particle size was successfully obtained by control of rotor rate. It was found that properly high rotor rate helped to achieve a reduced particle size and a narrowing size distribution. The reduced SR particle size enlarged the PVDF/SR interface which has a positive effect on the interfacial crystallization and the melt rheological behavior. At high SR content, the negative effect of the poor interface interactions played the dominate role on determining the mechanical properties. However, the blend exhibited a unique stiffness-toughness balance at the PVDF/SR = 90/10. We hope that the present study could help to lay a scientific foundation for further design of a useful PVDF/SR blend with promoted properties to partly replace the high-cost synthetic fluorosilicone materials.     

Miscibility and crystallization behavior in blends of poly(methyl methacrylate) and poly(vinylidene fluoride): Effect of star‐like topology of poly(methyl methacrylate) chain

A tetraarmed star‐shaped poly(methyl methacrylate) (s‐PMMA) was synthesized via atom transfer radical polymerization with 2‐bromoisobutyryl pentaerythritol as the initiator. For comparison, a linear PMMA with the identical molecular weight (l‐PMMA) was also prepared. The blends of the two PMMA samples with poly (vinylidene fluoride) (PVDF) were prepared to investigate the effect of macromolecular topological structure on miscibility and crystallization behavior of the binary blends. The behavior of single and composition‐dependent glass transition temperatures was found for the blends of s‐PMMA with PVDF, indicating that the s‐PMMA is miscible with PVDF in the amorphous state just like l‐PMMA. The miscibility was further evidenced by the depression of equilibrium melting points. It is found that the blends of s‐PMMA and PVDF displayed the larger k value of Gordon–Taylor equation than the blends of l‐PMMA and PVDF blends. According to the depression of equilibrium melting points, the intermolecular parameters for the two blends were estimated. It is noted that the s‐PMMA/PVDF blends displayed the lower interaction parameter than l‐PMMA/PVDF blends. The isothermal crystallization kinetics shows that the crystallization of PVDF in the blends containing s‐PMMA is faster than that in the blends containing the linear PMMA. The surface‐folding free energy of PVDF chains in the blends containing s‐PMMA is significantly lower than those in the blends containing l‐PMMA. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2580–2593, 2007     

Poly(vinylidene fluoride)/polycarbonate blend-based nanocomposites with enhanced rigidity — Selective localization of carbon nanofillers and organoclay

Carbon nanotube (CNT), graphene nanoplatelet (GnP) and organo-montmorillonite (15 A) individually and simultaneously served as reinforcing fillers to prepare poly (vinylidene fluoride) (PVDF)/polycarbonate (PC) blend-based multicomponent nanocomposites. Scanning electron microscopy and transmission electron microscopy results confirmed the selective localization of individual and hybrid fillers within the PC domains. Some 15 A was located at the interface of PVDF/PC phases to modify the blend morphology. Addition of CNT led to the development of a quasi co-continuous PVDF-PC morphology. Differential scanning calorimetry results showed that 15 A, not CNT/GnP, facilitated PVDF crystallization in the composites. Among the fillers, 15 A alone induced β-form PVDF crystals, as revealed by the X-ray diffraction results, and consequently caused the complex crystallization and melting of PVDF. The rigidity (Young's and flexural moduli) of the PVDF/PC blend increased after the formation of various blend-based nanocomposites. The hybrid filler of CNT/15 A increased the Young's modulus by approximately 90% compared with that of the blend. Rheological property measurements confirmed the formation of a pseudo-network structure in the composites. Adding CNT increased the complex viscosity of the samples to a higher extent than did adding GnP, and the viscosity further increased with the co-existence of carbon nanofiller(s) and 15 A.     

STUDIES OF THE CRYSTALLIZATION BEHAVIOR IN THE CRYSTALLINE/AMORPHOUS POLYMER BLENDS: POLY(ETHYLENE OXIDE)/POLY(METHYL METHACRYLATE) AND POLY(ETHYLENE OXIDE)/POLY(VINYL ACETATE)

The crystallization process of poly(ethylene oxide) (PEO)/poly(methyl methacrylate) (PMMA)and PEO/poly(vinyl acetate) (PVAc) blends has been characterized by Fourier Transform Infrared(FTIR) spectra in conjunction with Differential Scanning Calorimeter (DSC) measurements. Thecrystallinity of PEO varies consistently with PEO content in PEO/PVAc blends and the PEO/PMMAblends containing 50 wt% or less PMMA. For the PEO/PMMA blends containing 60 wt% ormore PMMA, the crystallinity of PEO decreases more than PEO content but develops with crystal-lization time. These results can be explained in terms of difference between the crystallization tem-perature (T_c) and glass transition temperature (T_g) of the blends as a function of content of amorphouscomponent.     

Crystallization behavior and hydrophilicity of poly (vinylidene fluoride) (PVDF)/poly (styrene-<Emphasis Type="Italic">co</Emphasis>-acrylonitrile) (SAN) blends

Poly (styrene-co-acrylonitrile) (SAN) is a hydrophilic non-crystalline copolymer, which is initially used in this paper to improve the hydrophilicity of poly (vinylidene fluoride) (PVDF). Investigation of the crystallization behavior of PVDF/SAN blends showed that the samples presented only α phase regardless of SAN content as cooling from the melt. A double-melting phenomenon was related to the perfection or crystal size of PVDF crystals. As the SAN content is increasing, crystallization of PVDF was limited, leading to a decreased crystallinity and lamellar growth. Besides, the hydrophilicity of PVDF was improved by blending with SAN. The sample containing 70 wt.% SAN performed a similar surface property of the neat SAN owing to the besieging of the PVDF phase by SAN. Observed from the cross section of the blends, PVDF/SAN blends were partially miscible with less than 50 wt.% SAN addition. As the SAN content was more than 50 wt.%, the crystalline PVDF particles clearly dispersed in the amorphous matrix.     

Preparation and characterization of poly(methyl methacrylate)/titanium oxide composite particles

Before polymerization, the introduction of double bonds onto the surface of the TiO₂ particles was achieved by the treatment of the TiO₂ particles with the silane-coupling agent. Via in-situ emulsion polymerization, the poly(methyl methacrylate) (PMMA)/titanium oxide (TiO₂) composite particles were prepared by graft polymerization of MMA from the surface of the modified TiO₂ particles. The structure of the obtained PMMA/TiO₂ composite particles was characterized using fourier transform infrared spectra (FT-IR), thermo-gravimetric analysis (TGA), differential scanning calorimetry (DSC) and size excluding chromatography (SEC). The morphology of the obtained PMMA/TiO₂ composite particles was observed by transmission electron microscope (TEM). The results of FT-IR and TGA measurements show that PMMA is successfully grafted from the surface of the TiO₂ particles and that the percentage of grafting and the grafting efficiency can reach 208.3% and 96.6%, respectively. At the same time, the TGA and DSC measurements indicate an enhancement of thermal stability. TEM images demonstrate a better dispersion of the TiO₂ particles in the composite latex. In addition, UV-visible absorption measurements show that the PMMA/TiO₂ composite particles can absorb over 95% UV light at 210–400 nm wavelength.     

具有纳米结构的聚偏氟乙烯/1-乙烯基-3-丁基咪唑氯盐离子液体复合材料的结晶行为

用示差扫描量热(DSC)、偏光显微镜(POM)及X射线衍射(XRD)分析考察了具有纳米结构的聚偏氟乙烯(PVDF)/1-乙烯基-3-丁基咪唑氯盐离子液体([VBIM][Cl])复合材料(PVDF/[VBIM][Cl])中经[VBIM][Cl]接枝的PVDF(PVDF-g-[VBIM][Cl])纳米微区对PVDF结晶行为的影响.研究结果表明,[VBIM][Cl]化学接枝在PVDF的分子链上,在PVDF/[VBIM][Cl]复合材料中,PVDF-g-[VBIM][Cl]嵌段形成大量纳米微区,分散在PVDF基体中.PVDF-g-[VBIM][Cl]纳米微区能够显著提高PVDF熔体结晶温度(Tc)并显著降低PVDF晶体的等温结晶时间.与纯PVDF相比,在纳米结构的PVDF/[VBIM][Cl]复合材料中,PVDF-g-[VBIM][Cl]纳米微区大大提高了PVDF晶体的成核速率,PVDF的球晶尺寸明显减小.由于[VBIM][Cl]完全"受限"于PVDF-g-[VBIM][Cl]纳米微区中,无法与PVDF分子链发生相互作用,因此纳米结构的PVDF/[VBIM][Cl]复合材料最终以非极性的α晶体为主.由于PVDF-g-[VBIM][Cl]纳米微区与PVDF基体具有热力学不相容性,因此其界面处的PVDF分子链处于部分有序的状态,有助于PVDF晶体的成核,加速了PVDF晶体的结晶速率.     

Crystal Orientation Behavior of a Poly(vinylidene fluoride)/Nylon 11 Blend

The oriented crystallization of poly(vinylidene fluoride) (PVDF) in stretched films of a PVDF/nylon 11 blend was investigated. At low crystallization temperature the c‐axis of the PVDF α‐form was oriented to the orientation axis of the nylon 11 matrix, but c‐axis orientation gradually changed to a‐axis orientation upon increasing the crystallization temperature. Under all crystallization conditions studied, considerable amounts of PVDF in its β‐form with c‐axis orientation were produced as well.

Phase morphology of a stretched film of PVDF/nylon 11 blend observed with confocal laser scanning microscopy.     

Pyrolysis mass spectrometry analysis of polycarbonate/poly(methyl methacrylate)/poly(vinyl acetate) ternary blends

Direct insertion probe pyrolysis mass spectrometry (DIP-MS) analyses of polycarbonate/poly(methyl methacrylate)/poly(vinyl acetate), (PC/PMMA/PVAc), ternary blends have been performed. The PC/PMMA/PVAc ternary blends were obtained by coalescing from their common γ-cyclodextrin-inclusion compounds (CD-ICs), through the removal of the γ-CD host (coalesced blend), and by a co-precipitation method (physical blend). The coalesced ternary blend showed different thermal behaviors compared to the co-precipitated physical blend. The stability of PC chains decreased due to the reactions of CH₃COOH formed by deacetylation of PVAc above 300 °C, for both coalesced and physical blends. This process was more effective for the physical blend most likely due to the enhanced diffusion of CH₃COOH into the amorphous PC domains, where it can further react producing low molecular weight PC fragments bearing methyl carbonate chain ends. The decrease in thermal stability of PC chains was less significant for the coalesced ternary blend indicating that the diffusion of CH₃COOH was either somewhat limited or competed with intermolecular reactions between PMMA and PC and between PMMA and PVAc, which were detected and were associated with their close proximity in the intimately mixed coalesced PC/PMMA/PVAc ternary blend.     

Dual-phase polymer electrolyte with enhanced phase compatibility based on Poly(MMA-g-PVC)/PMMA

A new plasticized dual-phase polymer electrolyte (DPE) with enhanced phase compatibility based on Poly(MMA-g-PVC)/PMMA blends has been studied. For the DPE, PMMA is selectively impregnated with the lithium salt solution forming an ion-conducting network, while Poly(MMA-g-PVC) produces good mechanical strength. Their chemical characters, thermal behavior, morphology, ionic conductivity and interfacial compatibility with lithium metal electrode were characterized by using of infrared spectroscopy (IR), differential scanning calorimetry (DSC), scanning electron microscopy (SEM), optical microscopic images, alternating current impedance (AC impedance) and linear sweep voltammetry (LSV), respectively. The ionic conductivity of DPE increases with the ratio of PMMA/Poly(MMA-g-PVC) (by weight), and the absorbed liquid electrolyte in the polymer blends plays the first important way in this behavior. Room-temperature ionic conductivity of the order of 10⁻³ S cm⁻¹ has been achieved for DPE, in addition, the DPE also shows good compatibility with Li electrodes and sufficient electrochemical stability for safe operation in Li batteries.     

Poly(vinylidene fluoride)/clay nanocomposites prepared by melt intercalation: Crystallization and dynamic mechanical behavior studies

The preparation and properties of poly(vinylidene fluoride) (PVDF)/clay nanocomposites are reported for the first time. PVDF/clay nanocomposites were prepared by melt intercalation with organophilic clay. The composites were characterized with X‐ray diffraction, differential scanning calorimetry, and dynamic mechanical analysis. X‐ray diffraction results indicated intercalation of the polymer into the interlayer spacing. PVDF in the nanocomposites crystallized in the β form. Differential scanning calorimetry nonisothermal curves showed an increase in the melting and crystallization temperatures along with a decrease in crystallinity, as evidenced by the melting and crystallization peaks. Isothermal crystallization studies showed an enhanced rate of crystallization with the addition of clay, as evidenced by a reduction in the crystallization time. Dynamic mechanical analysis indicated significant improvements in the storage modulus over a temperature range of ?100 to 150 °C. The tan δ peak signifying the glass‐transition temperature of PVDF shifted to higher temperatures. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1682–1689, 2002     

Poly(methyl methacrylate)-induced Microstructure and Hydrolysis Behavior Changes of Poly(L-lactic acid)/Carbon Nanotubes Composites

Poly(L-lactic acid)(PLLA)-based composites exhibit wide applications in many fields.However,most of hydrophilic fillers usually accelerate the hydrolytic degradation of PLLA,which is unfavorable for the prolonging of the service life of the articles.In this work,a small quantity of poly(methyl methacrylate)(PMMA)(2 wt%-10 wt%)was incorporated into the PLLA/carbon nanotubes(CNTs)composites.The effects of PMMA content on the dispersion of CNTs as well as the microstructure and hydrolytic degradation behaviors of the composites were systematically investigated.The results showed that PMMA promoted the dispersion of CNTs in the composites.Amorphous PLLA was obtained in all the composites.Largely enhanced hydrolytic degradation resistance was achieved by incorporating PMMA,especially at relatively high PMMA content.Incorporating 10 wt%PMMA led to a dramatic decrease in the hydrolytic degradation rate from 0.19%/h of the PLLA/CNT composite sample to 0.059%/h of the PLLA/PMMA-10/CNT composite sample.The microstructure evolution of the composites was also detected,and the results showed that no crystallization occurred in the PLLA matrix.Further results based on the interfacial tension calculation showed that the enhanced hydrolytic degradation resistance of the PLLA matrix was mainly attributed to the relatively strong interfacial affinity between PMMA and CNTs,which prevented the occurrence of hydrolytic degradation at the interface between PLLA and CNTs.This work provides an alternative method for tailoring the hydrolytic degradation ability of the PLLA-based composites.     

聚甲基丙烯酸甲酯/聚(异戊二烯-co-苯乙烯)核壳纳米乳液的合成与直接氢化方法的研究

利用可控微乳液法合成粒径19~200 nm,且呈球状分布均匀的聚甲基丙烯酸甲酯/聚(异戊二烯-co-苯乙烯)(PMMA/PIS)核壳纳米粒子,通过水合肼产生原位氢的技术,对合成的PMMA/PIS乳液体系进行直接常压氢化,对影响氢化度的因素、聚合物氢化前后结构、热性能进行了研究.结果显示,聚合物粒径、水合肼及双氧水用量等都是影响聚合物的氢化度的因素.研究发现,氢化以PMMA为核,PIS为壳的核壳结构乳液可以显著提高PIS氢化程度,减少氢化过程中凝胶产生.利用FTIR、~1H-NMR、Na_2S_2O_3滴定法测定了乳液的氢化度.结果表明,当聚合物粒径小于200 nm时,乳液氢化度可达到95%以上,且无凝胶现象产生.GPC结果证明了反应是氢化而非凝胶过程.利用TEM、DLS测试了氢化后乳液的核壳结构和粒径.实验结果显示,PMMA/HPIS为核壳纳米结构.TGA结果显示,当氢化度为98%时,聚合物耐热性提高41°C.     

Thermal Properties of Poly(L-lactide)/Calcium Carbonate Nanocomposites

Summary: Thermal properties of nanocomposites prepared of poly(L-lactide) (PLLA) and CaCO₃ applying differential scanning (DSC) calorimetry and thermogravimetry (TG) were studied. Nanocomposites were prepared by extrusion process at 170 °C. DSC measurements show that CaCO₃ has no influence on glass transition and melting point of PLLA but lowers its cold crystallization temperature. There is no difference in glass transition temperature of PLLA before and after extrusion. High temperature thermal stability of the PLLA in the composites is poorer than neat PLLA. Kinetic parameters also indicate greater reactivity of the system upon CaCO₃ addition.     

Comparison of PVDF/MWNT,PMMA/MWNT,and PVDF/PMMA/MWNT nanocomposites: MWNT dispersibility and thermal and rheological properties

Pristine multi-walled carbon nanotubes (MWNTs) were incorporated into poly(vinylidene fluoride) (PVDF), poly(methyl methacrylate) (PMMA), and PVDF/PMMA blends to achieve binary and ternary nanocomposites. MWNTs were more compatible with the PVDF matrix than with the PMMA-containing matrices. MWNT addition did not alter the development of α-form PVDF crystals in the binary/ternary composites. Nucleation and overall isothermal crystallization of PVDF were enhanced by the presence of MWNTs, and enhancements were optimal in the PVDF/MWNT binary composites. Avrami analysis revealed that addition of MWNTs led to more extensive athermal-type nucleation of PVDF, and that PMMA slightly decreased the crystal growth dimension of PVDF. The equilibrium melting temperature (T_m°) of PVDF increased in the binary composites but remained nearly constant in the ternary system. Thermal stability was enhanced in the binary/ternary composites, and enhancements were more evident in the air environment than in nitrogen. Rheological property measurements revealed that the intensely entangled chains of high-molecular weight PVDF dominated the rheological response of PVDF-included samples in the melt state. A (pseudo)network structure was developed in each of the PVDF-included samples as well as in the 1 phr MWNT-added PMMA/MWNT composite. The storage moduli of the PVDF, PMMA, and PVDF/PMMA:1/1 blend increased to 37%, 22% and 34%, respectively, at 40 °C after addition of 1 phr MWNT.     

Thermally induced phase separation of poly(vinylidene fluoride)/diluent systems: Optical microscope and infrared spectroscopy studies

Thermally induced phase separation (TIPS) has been developed to prepare porous membranes. The porous structures are mainly dependent on diluents adopted in the TIPS process. We obtained two typical morphologies of poly(vinylidene fluoride) (PVDF) membranes using cyclohexanone (CO) and propylene carbonate (PC) as diluents, respectively. SEM observation displays that porous spherulites are formed from PVDF/CO system, whereas smooth particles result from PVDF/PC system. The TIPS processes of these two systems have been investigated in detail by optical microscope observation and temperature‐dependent FTIR combined with two‐dimensional infrared correlation analysis. Rapid crystallization of PVDF can be seen around 110 °C in the PVDF/CO system, which is consistent with the results of temperature‐dependent FTIR spectra. The spectral evolution indicates a transform of PVDF from amorphous to α‐phase after 110 °C. The ν_s(C?O) band at 1712 cm^?1 narrows and the ν_s(C? F) band at 1188 cm^?1 shifts to 1192 cm^?1 before crystallization, which implies the destruction of interaction between PVDF and CO. In contrast, the PVDF/PC system shows slow crystallization with all‐trans conformation assigned to β‐phase and γ‐phase below 60 °C but no obvious change of polymer?diluent interaction. We propose two mechanisms for the different phase behaviors of PVDF/CO and PVDF/PC systems: a solid?liquid phase separation after destruction of polymer?diluent interaction in the former, and a liquid?liquid phase separation process coupled with rich‐phase crystallization in the later. This work may provide new insight into the relationship among morphologies, crystal forms, and phase separation processes, which will be helpful to adjust membrane structure. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 1438–1447     

Non-isothermal crystallization kinetics of poly(trimethylene terephthalate)/poly(ethylene 2,6-naphthalate) blends

The glass-transition temperature and non-isothermal crystallization of poly(trimethylene terephthalate)/poly(ethylene 2,6-naphthalate) (PTT/PEN) blends were investigated by using differential scanning calorimeter (DSC). The results suggested that the binary blends showed different crystallization and melting behaviors due to their different component of PTT and PEN. All of the samples exhibited a single glass-transition temperature, indicating that the component PTT and PEN were miscible in amorphous phase. The value of T_g predicted well by Gordon-Taylor equation decreased gradually with increasing of PTT content. The commonly used Avrami equation modified by Jeziorny, Ozawa theory and the method developed by Mo were used, respectively, to fit the primary stage of non-isothermal crystallization. The kinetic parameters suggested that the PTT content improved the crystallization of PEN in the binary blend. The crystallization growth dimension, crystallization rate and the degree of crystallinity of the blends were increased with the increasing content of PTT. The effective activation energy calculated by the advanced iso-conversional method developed by Vyazovkin also concluded that the value of E_a depended not only on the system but also on temperature, that is, the binary blend with more PTT component had higher crystallization ability and the crystallization ability is increased with increasing temperature. The kinetic parameters U^* and K_g were also determined, respectively, by the Hoffman-Lauritzen theory.