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1.
We have designed a new mucoadhesive drug delivery formulation based on H-bonded complexes of poly(acrylic acid) (PAA) or poly(methacrylic acid) (PMAA) with the poly(ethylene glycol) (PEG), of a (PEG)-drug conjugate. The PEGylated prodrugs are synthesized with degradable PEG-anhydride-drug bonds for eventual delivery of free drug from the formulation. In this work we have used indomethacin as the model drug which is PEGylated via anhydride bonds to the PEG. The complexes are designed first to dissociate as the formulation swells in contact with mucosal surfaces at pH 7.4, releasing PEG-indomethacin, which then hydrolyses to release free drug and free PEG. We found that as MW of PAA increases, the dissociation rate of the complex decreases, which results in decreased rate of release of the drug. On the other hand, the drug release from PEG-indomethacin alone and from solid mixture of PEG-indomethacin+PAA was much faster than that from the H-bonded complexes. Due to the differences in the thermal stability, PMAA complex exhibited slightly faster drug release than that of the PAA complex of comparable MW. These H-bonded complexes of degradable PEGylated drugs with bioadhesive polymers should be useful for mucosal drug delivery.  相似文献   

2.
The aim of the study was to develop a mucoadhesive ocular insert for the controlled delivery of ophthalmic drugs and to evaluate its efficacy in vivo. The inserts tested were based either on unmodified or thiolated poly(acrylic acid). Water uptake and swelling behavior of the inserts as well as the drug release rates of the model drugs fluorescein and two diclofenac salts with different solubility properties were evaluated in vitro. Fluorescein was used as fluorescent tracer to study the drug release from the insert in humans. The mean fluorescein concentration in the cornea/tearfilm compartment as a function of time was determined after application of aqueous eye drops and inserts composed of unmodified and of thiolated poly(acrylic acid). The acceptability of the inserts by the volunteers was also evaluated. Inserts based on thiolated poly(acrylic acid) were not soluble and had good cohesive properties. A controlled release was achieved for the incorporated model drugs. The in vivo study showed that inserts based on thiolated poly(acrylic acid) provide a fluorescein concentration on the eye surface for more than 8 h, whereas the fluorescein concentration rapidly decreased after application of aqueous eye drops or inserts based on unmodified poly(acrylic acid). Moreover, these inserts were well accepted by the volunteers. The present study indicates that ocular inserts based on thiolated poly(acrylic acid) are promising new solid devices for ocular drug delivery.  相似文献   

3.
Polyethylenimine (PEI) has been used for the gene delivery system in vitro and in vivo since it has high transfection efficiency owing to proton buffer capacity. However, the use of PEI for gene delivery is limited due to cytotoxicity, non-specificity and unnecessary interaction with serum components. To overcome cytotoxicity and non-specificity, PEI was coupled with poly(vinyl pyrrolidone) (PVP) as the hydrophilic group to reduce cytotoxicity and lactose bearing galactose group for hepatocyte targeting. The galactosylated-PEI-graft-PVP (GPP) was complexed with DNA, and GPP/DNA complexes were characterized. GPP showed good DNA binding ability, high protection of DNA from nuclease attack. The sizes of DNA complexes show tendency to decrease with an increase of charge ratio and had a minimum value around 59 nm at the charge ratio of 40 for the GPP-1/DNA complex (PVP content: 4.1 mol%). The GPP showed low cytotoxicity. And GPP/DNA complexes were mediated by asialoglycoprotein receptors (ASGP-R)-mediated endocytosis. Also, the transfection efficiency of GPP-1/DNA complex at charge ratio of 40 in the HepG2 was higher than that of PEI/DNA one.  相似文献   

4.
5.
Polymeric drug delivery systems are used not only to improve aqueous solubility of drug molecules but also to achieve desirable pharmacokinetics and an enhanced therapeutic index. New biodegradable polymers are needed to improve the biodistribution and targeting-ability of polymeric carriers. In this study, the synthesis and characterization of branched poly(L-glutamic acid) (PG) containing multiple PG chains centered on a poly(amidoamine) (PAMAM) dendrimer or polyethyleneimine (PEI) cores were described. The branched PG polymers were obtained by ring-opening polymerization of benzyl ester of L-glutamic acid N-carboxyanhydride using PAMAM or PEI as the initiator. These polymers were degradable in the presence of the lysosomal enzyme cathepsin B, albeit more slowly than linear PG. Unlike conventional linear PG, each branched PG possessed multiple terminal amino groups. This made it possible to attach multiple targeting moieties selectively to the termini of branched PG. Conjugation of monofunctional or heterodifunctional polyethylene glycol to the chain ends of branched PG was demonstrated in the presence of side chain carboxyl groups. Furthermore, folic acid, a model targeting moiety, and the near-infrared dye indocyanine green, a model diagnostic agent, were successfully conjugated to the terminal amino groups and the side chain carboxyl groups of branched PG, respectively. The resulting conjugate had reduced nonspecific interaction and bound selectively to tumor cells expressing folate receptors. Thus, branched PG may be useful as a polymeric carrier for targeted drug delivery.  相似文献   

6.
Galactosylated chitosan was conjugated with poly(vinyl pyrrolidone) (PVP) as a hydrophilic group. The complex formation of GC-graft-PVP (GCPVP)/DNA complexes was confirmed by agarose gel electrophoresis. The morphology of the complex observed by atomic force microscopy had a compact and spherical shape, around 40 nm particle sizes at a charge ratio of 3. The binding strength of GCPVP 10K/DNA complex measured by ethidium bromide binding assay was superior to that of the GCPVP 50K/DNA one, probably attributable to its higher flexibility due to the smaller size, whereas the DNase I protection of GCPVP 10K/DNA complex was inferior to that of the GCPVP 50K/DNA one. This indicated that effective complex formation required both higher binding strength and minimal molecular weight of polycation enough to induce the condensation of DNA. The DNA-binding property of GCPVP mainly depended on the molecular weight of chitosan and composition of PVP.  相似文献   

7.
Articular cartilage damage is a persistent challenge in biomaterials and tissue engineering. Poly(vinyl alcohol) (PVA) hydrogels have shown promise as implants, but their lack of integration with surrounding cartilage prevents their utility. We sought to combine the advantages of PVA hydrogels with poly(lactic-co-glycolic acid) (PLGA) scaffolds, which have been successful in facilitating the integration of neocartilage with surrounding tissue. Through a novel double-emulsion technique, PLGA microparticles and a high level of porosity were simultaneously incorporated into PVA hydrogels. The porosity, average pore size and swelling properties of the hydrogels were controlled by varying initial processing parameters, such as the relative amounts of PLGA and solvent. Average pore sizes were in the ranged 50-100 μm. The PLGA microparticles degraded within the hydrogels over time in aqueous conditions, resulting in increases in porosity and pore size. After 4 weeks in cell culture, immature cartilage tissue filled many of the pores of the hydrogels that initially contained PLGA, and proteoglycan production was proportional to the amount of PLGA. In contrast, there was little cell attachment and no proteoglycan production in control hydrogels without PLGA. The compressive moduli of the hydrogels were similar to that of healthy cartilage and increased over time from 0.05-0.1 to 0.3-0.7 MPa. The generation of a hybrid cartilage-hydrogel construct using this technique may finally allow the integration of PVA hydrogels with surrounding cartilage.  相似文献   

8.
Newly synthesised starch-g-poly(acrylic acid) copolymers and starch/poly(acrylic acid) mixtures were evaluated for their in vitro inhibition potency towards the proteolytic enzyme trypsin. Their Ca2+ and Zn2+ binding capacity was measured. Carbopol 934P was used as reference polymer. Starch-g-poly(acrylic acid) copolymers were prepared by chemical grafting and 60Co irradiation, the starch/poly(acrylic acid) mixtures by freeze-drying. The influence of preparation method, the ratio starch:acrylic acid, the neutralisation degree and for the freeze-dried polymers the influence of heat treatment after freeze-drying was investigated. All freeze-dried polymers showed a higher inhibition factor (IF) than the chemically grafted and 60Co irradiated starches, which all showed significantly lower IF than Carbopol 934P. The heat treated freeze-dried polymer Amioca/poly(acrylic acid) (1:1) showed a significantly higher IF than the reference polymer (Mann-Whitney test, p<0.05). The Ca2+ and Zn2+ binding capacity of all chemically grafted starches was much lower than for Carbopol 934P. Only the 60Co irradiated starches and freeze-dried polymers with ratio 1:3 approached the binding capacity of the reference polymer. The freeze-dried polymers showed the highest proteolytic enzyme inhibition potency. Freeze-drying and 60Co irradiation could result in the highest ion binding capacity. This combination of proteolytic enzyme inhibition activity and ion binding capacity makes these polymers hopeful excipients for successful oral peptide delivery.  相似文献   

9.
Starch-g-poly(acrylic acid) copolymers or grafted starches synthesized by 60Co irradiation or chemical modification and co-freeze-dried starch/poly(acrylic acid) mixtures were evaluated on their ex vivo bioadhesion capacity. The buccal absorption of testosterone from a bioadhesive tablet formulated with the grafted starches or starch/poly(acrylic acid) mixtures was investigated. The results were compared to a reference formulation (physical mixture of 5% Carbopol 974P and 95% Drum Dried Waxy Maize). Rice starch-based irradiated grafted starches showed the best bioadhesion results. Partial neutralization of the acrylic acid with Ca(2+) ions resulted in significantly higher bioadhesion values compared to the reference. Ca(2+) and Mg(2+) partially neutralized maltodextrin-based irradiated grafted starches showed significantly higher bioadhesion values compared to the reference formulation. The chemically modified grafted starches showed significantly higher adhesion force values than for the reference tablet. None of the co-freeze-dried starch/poly(acrylic acid) mixtures showed significantly higher bioadhesion results than the reference (Bonferroni test, P<0.05). A chemically modified grafted starch could sustain the 3 ng/ml plasma testosterone target concentration during +/- 8 h (T(>3 ng/ml)). By lyophilization of a partially neutralized irradiated grafted starch, the in vivo adhesion time (22.0 +/- 7.2 h) and the T(>3 ng/ml) (13.5 +/- 1.3 h) could be increased. The absolute bioavailability of the lyophilized formulation approached the reference formulation. Some of the grafted starches showed to be promising buccal bioadhesive drug carriers for systemic delivery.  相似文献   

10.
The purpose of the present study was to prepare and characterize a novel mucoadhesive microparticulate drug delivery system. Microparticles were prepared by the solvent evaporation emulsion technique using a poly(acrylic acid)-cysteine conjugate of an average molecular mass of 450 kDa with an amount of 308 micromol thiol groups per gram polymer. The cross-linking of thiol groups via the formation of disulfide bonds during this preparation process was pH-controlled. The resulting microparticles were characterized with regard to the degree of cross-linking and the amount of remaining free thiol groups, shape, size distribution and stability. Furthermore, the drug release behaviour using bromelain as model drug and the mucoadhesive properties were evaluated.Results demonstrated that the higher the pH of the aqueous phase was during the preparation process, the higher was the degree of cross-linking within the particles. However, even at pH 9, 8.9+/-2.2% of free thiol groups remained on the microparticles. Particles were of spherical and partially porous structure and had a main size in the range of 20-60 microm with a center at 35 microm. Because of the formation of disulfide bonds within the particles, they did not disintegrate under physiological conditions within 48 h. In addition, a controlled drug release of bromelain was achieved. Due to the immobilization of thiol groups on poly(acrylic acid), the mucoadhesive properties of the corresponding microparticles were improved threefold.These features should render poly(acrylic acid)-cysteine conjugate microparticles useful as drug delivery system providing a prolonged residence time on mucosal epithelia.  相似文献   

11.
Sequential interpenetrating network (IPN) of poly(vinyl alcohol) (PVA) and poly(acrylic acid) (PAA) were prepared and crosslinked with glutaraldehyde (GA) to form pH-sensitive microspheres by the water-in-oil (w/o) emulsification method. Microspheres were used to deliver a model anti-inflammatory drug, diclofenac sodium (DS), to the intestine. The formed IPN was analyzed by Fourier transform infrared spectroscopy (FTIR). Differential scanning calorimetry (DSC) and X-ray diffraction (XRD) analyses were done on the drug-loaded microspheres to confirm the polymorphism of DS. Results indicated a molecular level dispersion of DS in the IPN. Microspheres formed were spherical with the smooth surfaces as evidenced by scanning electron microscopy (SEM). Particle size and size distribution was studied using laser light diffraction particle size analyzer. Particle size analysis was also done by optical microscope for the selected microspheres; the change in diameter of the microspheres when soaked in different media at different time intervals was measured by optical microscope. Microspheres showed a pulsatile swelling behavior when the pH of the swelling media was changed. The swelling data were fitted to an empirical equation to understand the phenomenon of water transport as well as to calculate the diffusion coefficient (D). Values of D in acidic media were lower than those found in basic media. The values of D decrease with increasing crosslinking of the matrix. In-vitro release studies have been performed in 1.2 and 7.4 pH media to simulate gastric and intestinal conditions. The results indicated a dependence on the pH of the release media, extent of crosslinking and the amount of drug loading.  相似文献   

12.
The objective of the present study was to prepare nanoparticles composed of poly(gamma-glutamic acid) (gamma-PGA) and l-phenylalanine ethylester (l-PAE) in order to evaluate the possibility of using these nanoparticles as protein carriers. Novel amphiphilic graft copolymers composed of gamma-PGA as the hydrophilic backbone and l-PAE as the hydrophobic segment were successfully synthesized by grafting l-PAE to gamma-PGA using water-soluble carbodiimide (WSC). Due to their amphiphilic properties, the gamma-PGA-graft-l-PAE copolymers were able to form nanoparticles. The size of the gamma-PGA nanoparticles was measured by photon correlation spectroscopy (PCS) and showed a monodispersed size distribution with a mean diameter ranging from 150 to 200 nm. The solvents selected to prepare the gamma-PGA nanoparticles by a precipitation and dialysis method affected the particle size distribution. To evaluate the feasibility of vehicles for these proteins, we prepared protein-loaded gamma-PGA nanoparticles by surface immobilization and encapsulation methods. Ovalbumin (OVA) was used as a model protein and was immobilized onto the gamma-PGA nanoparticles or encapsulated into the inner core of these nanoparticles. Moreover, these OVA-encapsulated gamma-PGA nanoparticles could be preserved by freeze-drying process. The results of cytotoxicity tests showed that the gamma-PGA and gamma-PGA nanoparticles did not cause any relevant cell damage. It is expected that biodegradable gamma-PGA nanoparticles can immobilize proteins, peptides, plasmid DNA and drugs onto their surfaces and/or into the nanoparticles. These nanoparticles are potentially useful in pharmaceutical and biomedical applications.  相似文献   

13.
This paper outlines research which aimed to develop a new type of Glass-ionomer cement, the glass polyphosphonate cement. The glass polyalkenoate cement, a form of Glass-ionomer cement, is now widely used in dentistry and is based on the reaction between an ion-leachable aluminosilicate glass and an aqueous solution of poly(acrylic acid) or its copolymers. The new cements described in this paper employ a novel polymer, poly(vinyl phosphonic acid), PVPA, as the acidic component. This is a much stronger acid than those used in the glass polyalkenoate cement, and various means must be employed to moderate the reaction in order to obtain a viable cement. These cements show a number of important differences in performance in comparison with PAA-based systems and these differences are discussed in the paper.  相似文献   

14.
Resveratrol/tannic acid-poly(vinyl alcohol) (RETA-PVA) blends have been prepared by compression molding using poly(vinyl alcohol), tannic acid and resveratrol as raw materials. The effects of different resveratrol/tannic acid ratios on the flammability of RETA-PVA blends have been studied. The flammability of the RETA-PVA blends was assessed using cone calorimetry, thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). Results indicate that RETA-PVA molecules occur through hydrogen bonding and RETA-PVA blends are amorphous. The glass transition temperature for RETA-PVA-2 is the highest among all blends and the peak of heat release rate and smoke production rate for RETA-PVA is 38.4% and 43.9% lower than that for PVA, respectively. With the addition of resveratrol, the residual amount of RETA-PVA after complete combustion is greatly increased, to 30 times that for PVA, indicating that RETA-PVA blends display excellent flame retardant properties.

The rigid molecular structure of biobased resveratrol/tannic acid (RETA) complex increases the residual amount of RETA-poly(vinyl alcohol) after complete combustion.  相似文献   

15.
背景:聚乙烯醇和海藻酸钠均为亲水性的聚合物,互溶性好,但其单独使用在材料的弹性和含水率等性能方面不理想。 目的:制备聚乙烯醇-海藻酸钠-透明质酸组织工程支架,分析不同重均分子质量和醇解度的聚乙烯醇、不同质量分数的海藻酸钠、不同用量的透明质酸对材料含水率和膨胀率的影响。 设计、时间及地点:对比观察实验,于2006—10/2008—03在广州暨南大学生物材料省重点实验室,教育部再生医学研究中心重点实验室完成。 材料:聚乙烯醇,Mw14500,61500,为BS Chemical Technology产品,聚乙烯醇,Mw 88000,95000,为ACROS ORGANICS产品,聚乙烯醇-124,Mw24000,为广州市医药公司产品,透明质酸为美国Sigma公司产品,NaOH、CaCl2、海藻酸钠为国产分析纯。 方法:将不同重均分子质量和醇解度的聚乙烯醇与不同质量分数的海藻酸钠、不同用量的透明质酸复合。 主要观察指标:测定其复合材料的含水率和膨胀率,用扫描电镜观察材料内部的组织形态。 结果:制备的聚乙烯醇-海藻酸钙-透明质酸复合材料平滑、柔韧,具有弹性。含水率为62.66%~86.64%,膨胀率为145.74%~324.45%。含水率和膨胀率随着聚乙烯醇重均分子质量和醇解度的增加而减小,随着海藻酸钠增加而增加,随着透明质酸的增加变化不太明显。扫描电镜结果提示材料随聚乙烯醇重均分子质量增加,材料中孔数减少。随醇解度增加,材料中孔数增多,分布均匀。随海藻酸钠增加,材料由片状结构变为蓬松的层状结构,孔洞逐渐增多。随透明质酸增加,材料孔洞数量增加,且孔径大小更均一,孔分布更均匀,材料由蓬松多孔结构转变为网状交织多孔结构。 结论:聚乙烯醇Mw14500,醇解度98%形成的孔形态结构最好,含水率高,随海藻酸钠和透明质酸的加入,材料具有丰富的网状孔洞结构。  相似文献   

16.
Solid dispersion composed of the poly(ethylene oxide) (PEO)-carboxyvinylpolymer (CP) interpolymer complex containing phenacetin (PHE) was prepared by using nine grades of PEO having different molecular weights from 2000 to 4500000. We attempted to control the medicine release from the PEO-CP solid dispersion by varying the molecular weight of PEO. The physicochemical properties of the solid dispersion were analyzed by powder X-ray diffractometry and thermal analysis. The interaction between PEO and CP was analyzed by IR spectroscopy. Transmittance of the polymer solution was measured to study the complexation between PEO and CP. The release profile of PHE varied depending on the molecular weight of PEO. The minimum release rate was observed at the PEO molecular weight of 35000. It was found that the amount of the PEO-CP complex formation by hydrogen bonding changed depending on the molecular weight of PEO. These results indicate that it is feasible to control the medicine release from the PEO-CP solid dispersion by varying the molecular weight of PEO.  相似文献   

17.
Solid dispersion composed of the poly(ethylene oxide) (PEO)-Carbopol((R)) (CP) interpolymer complex containing phenacetin (PHE) was prepared by using six grades of CP having various cross-linking degrees. We attempted to control the medicine release from the PEO-CP solid dispersion by varying the CP grade. The powder X-ray diffraction pattern and differential scanning calorimetry curves suggested that PHE existed in the amorphous state, and PEO in the crystalline state disappeared in the solid dispersions. The release profile of PHE varied depending on the CP grade. A small release rate was observed at CP910 and CP971P that are cross-linked at low and middle degrees, respectively. The Fourier transform-infrared (FT-IR) spectra showed that the amount of the PEO-CP complex formed by hydrogen bonding changed depending on the CP grade. With the cross-linked CP, a good correlation was observed between the hydrogen bonding percent and the percent released of the PHE after 60 min (D(60 min)), indicating that PHE release was controlled by the amount of PEO-CP complex formation in the solid dispersion. These results show that it is feasible to control the medicine release from PEO-CP solid dispersion by varying the CP grade.  相似文献   

18.
This work describes how the control of grafting density and grafted chain length of a thermo-responsive polymer in membrane pores can be utilized to tune the pore size and the switchability of size-based selectivity in the ultrafiltration range. Using a previously established methodology for controlled synthesis, surface-initiated atom transfer polymerization (ATRP) of poly(N-isopropylacrylamide) (PNIPAAm) to the pore walls of poly(ethylene terephthalate) track-etched membranes with experimentally determined pore diameters of 35 nm (PET30) and 110 nm (PET80) is performed. Characterization in this study is mainly done with filtration experiments, making use of the well-defined pore structure of the base membranes. It is demonstrated that both the gravimetrically determined degree of functionalization and the effective pore size determined from water permeability are a linear function of ATRP time. For the grafted PET30 membranes, it is shown that the rejection of lysozyme (diameter ∼ 4 nm) can be switched between 99% at 23 °C and 65% at 45 °C for the membrane with the highest degree of functionalization. For the grafted PET80 membranes, it is found that two different types of membranes can be obtained. Membranes with long grafted chains at low grafting density show very large changes of water permeability as a function of temperature (effective pore size switching ratio of up to 10) and, for example, rejection for 20 nm silica particles of 95% and 23% at 23 °C and 45 °C, respectively. Membranes with PNIPAAm at high grafting density show much lower switching ratios (as low as 1.4, for long enough grafted chains). Effective pore size and thermo-responsive change of pore size can therefore be tuned by the combination of both synthesis parameters, initiator density and ATRP time. The switchable thermo-responsive separation of two colloids with a tailored membrane is demonstrated for mixtures of bovine serum albumin (BSA; ∼7 nm) and silica nanoparticles (20 nm); at 23 °C silica is completely rejected and only BSA is in the permeate; at 40 °C both colloids permeate through the membrane.

This work describes how the control of grafting density and grafted chain length of a thermo-responsive polymer in membrane pores can be utilized to tune the pore size and the switchability of size-based selectivity in the ultrafiltration range.  相似文献   

19.
The mechanical performances of hydrogels are greatly influenced by the functionality of cross-linkers and their covalent and non-covalent interactions with the polymer chains. Conventional chemical cross-linkers fail to meet the demand of large toughness and high extensibility for their immediate applications as artificial tissues like ligaments, blood vessels, and cardiac muscles in human or animal bodies. Herein, we synthesized a new graphene oxide-based two-dimensional (2D) cross-linker (GOBC) and exploited the functionality of the cross-linker for the enhancement of toughness and stretchability of a poly(acrylic acid) (PAA) hydrogel. The 2D nanosheets of GO were modified in such a way that they could provide multifunctional sites for both physical and chemical bonding with the polymer chains. Carboxylic acid groups at the surfaces of the GO sheets were coupled with the acrylate functional groups for covalent cross-linking, while the other oxygen-containing functional groups are responsible for physical cross-linking with polymers. The GOBC had been successfully incorporated into the PAA hydrogel and the mechanical properties of the GOBC cross-linked PAA hydrogel (PAA-GOBC) were investigated at various compositions of cross-linker. Seven times enhancement in both toughness and elongation at break has been achieved without compromising on the modulus for the as-synthesized PAA-GOBC compared to the conventional N,N′-methylenebis(acrylamide) (MBA) cross-linked PAA hydrogel. This facile and efficient way of GO modification is expected to lead the development of a high-performance nanocomposite for cutting-edge applications in biomedical engineering.

Incorporation of a novel GO based cross-linker into the conventional poly(acrylic acid) hydrogel remarkably enhances the toughness and stretchability.  相似文献   

20.
The paper introduced an improved fabrication technique, by which the hydrophobic polymer monofilament fiber loading hydrophilic drug was obtained. The micronized 5-Fu (5-fluorouracil) powders were homogeneously dispersed in PLLA (poly(l-lactic acid))–chloroform solution to form the suspension, and then the suspension was solidified in the nonsolvent to prepare the fibers by wet-spinning method under mild condition. The diameter of drug-loaded fiber was in the range of 50–250 μm. The hydrophilic drug powders were successfully encapsulated into the monofilament fiber with good stability, high drug loading content and efficacy. The MTT cytotoxicity assay in vitro revealed the satisfactory anticancer activity of the drug-loaded fibers. The long-term release characteristics of these fibers were also achieved. Furthermore, the drug release rate of the fibers could be regulated by the formulation and fabricating parameters, such as drug loading content, polymer concentration in suspension, nonsolvent composition and flow rate in wet-spinning. The release mechanism of the fibers was investigated and described by Fickian diffusion equation.  相似文献   

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