Synthesis and solution behavior of poly(ε-caprolactone) grafted hydroxyethyl cellulose copolymers

Trimethylsilylated hydroxyethyl cellulose (TMSHEC) was synthesized by using hexamethyldisilazane (HMDS) as silylated agent. With the partial protection of hydroxyl groups of HEC by silylation, the novel poly(?-polycaprolactone) (PCL) grafted HEC (HEC-g-PCL) copolymers were successfully prepared by homogenous ring-opening graft polymerization and deprotection procedure. The structure of HEC-g-PCL copolymers was characterized by FTIR and 1H NMR. Fluorescence spectrum of HEC-g-PCL copolymer dilute solution indicated that copolymers could associate and form hydrophobic microdomains in aqueous solution. With the increasing of grafted PCL content, the critical association concentration (cac) of HEC-g-PCL copolymers decreased. The surface tension of HEC-g-PCL copolymers decreased dramatically with the increasing of the concentration and then approached to a plateau value when concentration was above the cac of HEC-g-PCL copolymers. The hydrodynamic radius of the aggregate of copolymer in dilute solution was found to increase with the increasing of the grafted PCL content. When the concentration of copolymer was above the cac, the zero-shear viscosity of the copolymer increased sharply and became much higher than that of HEC at the same concentration.     

Synthesis of geranyl propionate in a solvent-free medium using Rhizomucor miehei lipase covalently immobilized on chitosan–graphene oxide beads

The chemical route of producing geranyl propionate involves the use of toxic chemicals, liberation of unwanted by-products as well as problematic separation process. In view of such problems, the use of Rhizomucor miehei lipase (RML) covalently bound onto activated chitosan–graphene oxide (RML-CS/GO) support is suggested. Following analyses using Fourier transform infrared spectroscopy, field emission scanning electron microscopy, transmission electron microscopy, and thermogravimetry, properties of the RML-CS/GO were characterized. A response surface methodological approach using a 3-level-four-factor (incubation time, temperature, substrate molar ratio, and stirring rate) Box–Behnken design was used to optimize the experimental conditions to maximize the yield of geranyl propionate. Results revealed that 76?±?0.02% of recovered protein had yielded 7.2?±?0.04?mg?g^?1 and 211?±?0.3%?U?g^?1 of the maximum protein loading and esterification activity, respectively. The actual yield of geranyl propionate (49.46%) closely agreed with the predicted value (49.97%) under optimum reaction conditions (temperature: 37.67°C, incubation time: 10.20?hr, molar ratio (propionic acid:geraniol): 1:3.28, and stirring rate: 100.70?rpm) and hence, verifying the suitability of this approach. Since the method is performed under mild conditions, the RML-CS/GO biocatalyst may prove to be an environmentally benign alternative for producing satisfactory yield of geranyl propionate.     

Synthesis of poly(lactide-co-glycolide-co-ε-caprolactone)-graft-mannosylated poly(ethylene oxide) copolymers by combination of "clip" and "click" chemistries

Poly(lactide-co-glycolide) (PLGA) is extensively used in pharmaceutical applications, for example, in targeted drug delivery, because of biocompatibility and degradation rate, which is easily tuned by the copolymer composition. Nevertheless, synthesis of sugar-labeled amphiphilic copolymers with a PLGA backbone is quite a challenge because of high sensitivity to hydrolytic degradation. This Article reports on the synthesis of a new amphiphilic copolymer of PLGA grafted by mannosylated poly(ethylene oxide) (PEO). A novel building block, that is, α-methoxy-ω-alkyne PEO-clip-N-hydroxysuccinimide (NHS) ester, was prepared on purpose by photoreaction of a diazirine containing molecular clip. This PEO block was mannosylated by reaction of the NHS ester groups with an aminated sugar, that is, 2-aminoethyl-α-d-mannopyroside. Then, the alkyne ω-end-group of PEO was involved in a copper alkyne- azide coupling (CuAAC) with the pendent azides of the aliphatic copolyester. The targeted mannose-labeled poly(lactide-co-glycolide-co-ε-caprolactone)-graft-poly(ethylene oxide) copolymer was accordingly formed. Copolymerization of d,l-lactide and glycolide with α-chloro-ε-caprolactone, followed by substitution of chlorides by azides provided the azido-functional PLGA backbone. Finally, micelles of the amphiphilic mannosylated graft copolymer were prepared in water, and their interaction with Concanavalin A (ConA), a glyco-receptor protein, was studied by quartz crystal microbalance. This study concluded to the prospect of using this novel bioconjugate in targeted drug delivery.     

Biodegradation of poly(ε-caprolactone) (PCL) by a new Penicillium oxalicum strain DSYD05-1

In this study, fungi isolated from soil were screened for their ability to form clear zones on agar plates with emulsified poly(ε-caprolactone) (PCL). The most active strain, designated as DSYD05, was identified as Penicillium oxalicum on the basis of morphological characteristics and phylogenetic analysis. Mutant DSYD05-1, obtained by ultraviolet-light mutagenesis from strain DSYD05, was more effective in PCL degradation. In liquid cultures of the mutant strain with PCL emulsion, DSYD05-1 showed the highest PCL-degrading activity after 4?days of cultivation. The products of PCL degradation were analysed by mass spectrometry; the results indicated that 6-hydroxyhexanoic acid was produced and assimilated during cultivation. The degradation of PCL film by DSYD05-1 was observed by scanning electron microscopy, and was indicative of a three-stage degradation process. The degradation of amorphous parts of the film preceded that of the crystalline center and then the peripheral crystalline regions. In addition, DSYD05-1 showed a wide range of substrate specificity, with capability to degrade PCL, poly(β-hydroxybutyrate), and poly(butylene succinate), but not poly(lactic acid), indicating that the strain could have potential for application in the treatment or recycling of bio-plastic wastes.     

Lipase-catalyzed synthesis of poly(ε-caprolactone) and characterization of its solid-state properties

Abstract

Ring-opening polymerization of ε-caprolactone has been successfully conducted using an immobilized form of Candida antarctica lipase B as catalyst. The effects of enzyme concentration, reaction medium, reaction temperature and time on monomer conversion and product molecular weight were investigated. Through optimization of reaction conditions, poly(ε-caprolactone) (PCL) was obtained with 99% monomer conversion and a number-average molecular weight (M_n) of 18870 g/mol. The reaction system was then scaled up, and PCL was synthesized in 78% isolated yield, with M_n and polydispersity index of 41540 g/mol and 1.69, respectively. The solid-state properties of this sample were systematically evaluated using thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), wide-angle X-ray diffraction (WAXD) and polarized optical microscopy (POM). The product PCL showed excellent thermal stability, with degradation of the main chain in the temperature range of 280–450°C. Remarkably, this high molecular weight PCL was a typical crystalline polymer with a high degree of crystallinity observed by DSC, WAXD and POM.     

Biodegradable molecularly imprinted polymers based on poly(ε-caprolactone)

Novel biodegradable molecularly imprinted polymers (MIPs) based on poly(ε-caprolactone) (PCL) were prepared by combining two important properties required of ideal biomaterials, biodegradability (with biocompatibility) and molecular recognition properties. Acrylate or methacrylate end-capped PCL macromers were synthesized through the reaction of PCL diol or triol with acryloyl or methacryloyl chloride. The synthesis of acrylate or methacrylate end-capped macromers was confirmed using FT-IR and H NMR spectroscopic techniques. These macromers were used to prepare biodegradable crosslinked networks by photopolymerization with functional monomer (acrylic acid) and a model template (theophylline). The theophylline-imprinted polymer showed higher binding capacity for theophylline compared with non-imprinted polymer (NIP), and also showed selectivity for theophylline over caffeine (similar structure molecules). PCL-based MIP degraded 8% of the initial weight in 30 days in phosphate-buffered saline (PBS) solution (pH 7.4) and over 90% of the initial weight within 24 h in 1 N NaOH at 37°C.     

Dye adsorption characteristics of magnetite nanoparticles coated with a biopolymer poly(γ-glutamic acid)

Magnetite nanoparticles coated with an anionic biopolymer poly(γ-glutamic acid) (PGA-MNPs) were synthesized and characterized for their methylene blue dye adsorption capability. Both bare- and dye-loaded PGA-MNPs were characterized by FTIR, TEM and VSM measurements, revealing the PGA-MNPs to be superparamagnetic with average particle diameter being 12.4 nm and magnetization value 59.2 emu/g. The synthesized PGA-MNPs were stable in deionized, tap and river waters as well as in acidic and basic media. Redlich-Peterson and Langmuir models precisely described the isotherm and the maximum adsorption capacity was 78.67 mg/g. A pseudo-second-order equation best predicted the kinetics with a maximum adsorption attained within 5 min. Incorporation of sodium or calcium ions reduced the dye adsorption, while a raise in pH enhanced adsorption and a complete desorption occurred at pH 1.0. Dye removal mechanism by PGA-MNPs was probably due to electrostatic interaction through exchange of protons from side-chain α-carboxyl groups on PGA-MNPs surface.     

Synthesis of poly-(ε)-caprolactone grafted starch co-polymers by ring-opening polymerisation using silylated starch precursors

Poly-(ε)-caprolactone grafted corn starch co-polymers were synthesized using a hydrophobised silylated starch precursor. The silylation reaction was performed using hexamethyl disilazane (HMDS) as the reagent in DMSO at 70 °C. Silylated starch with a degree of substitution (DS) between 0.45 and 0.7 was obtained. ε-Caprolactone is grafted to silylated starch by a ring-opening polymerisation catalysed by Al(OiPr)₃ in THF at 50 °C. The grafting efficiency varies between 28% and 58%, the remainder being homopolymers of ε-caprolactone. The DS of the polycaprolactone graft is between 0.21 and 0.72. The poly-(ε)-caprolactone side chains consist of 40–55 monomer units and is a function of the reagent intakes. Experiments with native starch under similar conditions do not result in the desired poly-(ε)-caprolactone grafted corn starch co-polymers and unreacted starch was recovered after work-up. Removal of the silyl groups of the poly-(ε)-caprolactone grafted starch co-polymers is possible using a mild acid treatment with diluted hydrochloric acid in THF at room temperature.     

Investigation of polymer and nanoparticle properties with nicotinic acid and p-aminobenzoic acid grafted on poly(ε-caprolactone)-poly(ethylene glycol)-poly(ε-caprolactone) via click chemistry

In this study, the grafting of nicotinic acid and p-aminobenzoic acid (PABA) onto poly(ε-caprolactone)-poly(ethylene glycol)-poly(ε-caprolactone) was performed by Huisgen's 1,3-dipolar cycloaddition, also known as click chemistry. Concentrations used for grafting were 0.10, 0.20, and 0.30 molar ratios with respect to caproyl units. The grafted copolymers were successfully obtained at all ratios as confirmed by NMR, GPC, and FT-IR. According to the DSC results, the polymorphisms of these grafted copolymers were mostly changed from semicrystalline to amorphous depending on the type and the amount of grafting compounds. TGA thermograms showed different thermal stabilities of the grafted copolymers compared to the original copolymers. Cytotoxicity results from HUVEC models suggested that the toxicity of grafted nanoparticles increased with the molar ratios of grafting units. Due to differences in molecular structure between nicotinic acid and PABA, physicochemical properties (particle size and surface charge) of grafted copolymer nanoparticles were substantially different. With increasing molar ratio of the grafting units, the particle size of blank nanoparticles tended to increase, resulting from an increase in the hydrophobic fragments of the grafted copolymer. Ibuprofen was chosen as a model drug to evaluate the interaction between grafted copolymers and loaded drug. After ibuprofen loading, the particle size of the loaded nanoparticles of both grafted copolymers increased compared to that of the blank nanoparticles. Significant differences in loading capacity between nicotinic acid and PABA grafted copolymer nanoparticles were clearly shown. This is most likely a result of different compatibility between each grafting compound and ibuprofen, including hydrogen bond interaction, π-π stacking interaction, and steric hindrance.     

Photo-cross-linked biodegradable poly(ester anhydride) networks prepared from alkenylsuccinic anhydride functionalized poly(ε-caprolactone) precursors

Biodegradable poly(ester anhydride) networks based on linear and star-shaped poly(ε-caprolactone)-based precursors were synthesized with the aim of obtaining matrixes suitable for release of macromolecular active agents. The ring-opening polymerization yielded hydroxyl telechelic oligomers, which were end-functionalized with succinic anhydride or with alkenylsuccinic anhydrides containing 8, 12, or 18 carbons in their alkenyl chains. Before cross-linking, the acid-terminated oligomers were reacted with methacrylic anhydride to obtain methacrylated precursors containing labile anhydride bonds. The degrees of substitution for the acid functionalization and methacrylation were >93%. Cross-linking of the precursors was carried out with visible light at room temperature. Gel contents and cross-linking densities were higher for networks cross-linked from the star-shaped precursors than for networks prepared from the linear precursors. In in vitro erosion tests, the presence of the alkenyl chain slowed down the erosion rate. The networks exhibited characteristic surface erosion: the mass loss was linear, whereas the dimensions of the specimens decreased steadily. A macromolecular release study showed the release of the model compound to be linear and in proportion to the mass loss.     

Functionalized hydrophobic poly(glycerol-co-ε-caprolactone) depots for controlled drug release

A limitation to many polymer-based drug delivery systems is the lack of ability to customize a particular polymer composition for tailoring drug release kinetics to a specific clinical application. In this study, we investigated the structure-property effects of conjugating various hydrophobic biocompatible side chains to poly(glycerol-co-caprolactone) copolymers with the goal of achieving prolonged and controlled release of a chemotherapeutic agent. The choice of side chain significantly affected the resulting polymer properties including thermal transitions, relative crystallinity (ΔH(f)), and hydrophobicity. Drug-loaded films cast from solutions of polymer and 10-hydroxycamptothecin demonstrated prolonged release from four to over seven weeks depending upon side chain structure without initial burst release behavior. Use of the stearic acid-conjugated poly(glycerol-co-caprolactone) films afforded substantial anticancer activity in vitro for at least 50 days when exposed to fresh cultures of A549 human lung cancer cells over 24 h intervals, correlating well with the measured drug release kinetics.     

Cortisol Δ1-dehydrogenation by cells of Arthrobacter simplex immobilized by capture on the surface of unwoven cloth coated with a pyridinium-type polymer

Cells of Arthrobacter simplex having 3-ketosteroid-Δ¹-dehydromonogenase activity were immobilized by capture on the surface of unwoven cloth, which was coated with a copolymer of N-benzyl-4-vinylpyridinium chloride and styrene (soluble BVPS), a pyridinium-type polymer. The captured bacterial cells catalyzed the dehydrogenation of cortisol to prednisolone in solvents containing methanol. A fixed-bed column reactor 15 mm in diameter and 12 cm long was continuously operated. The reactor contained about 200 mg of A. simplex cells, captured on an unwoven cloth 12 cm wide, 20 cm long, and 0.5 mm thick coated with 6.5 g/m² of the soluble BVPS, and yielded approximately 90% prednisolone during 6 d when the influent cortisol concentration was 1.0 mmol/l and the space velocity was 0.57 h⁻¹ at 20°C and pH 8.2.     

Chemosynthesis of poly(ε-lysine)-analogous polymers by microwave-assisted click polymerization

Poly(ε-lysine) (ε-PL)-analogous click polypeptides with not only similar α-amino side groups but also similar main chain to ε-PL were chemically synthesized for the first time through click polymerization from aspartic (or glutamic)-acid-based dialkyne and diazide monomers. With microwave-assisting, the reaction time of click polymerization was compressed into 30 min. The polymers were fully characterized by NMR, ATR-FTIR, and SEC-MALLS analysis. The deprotected click polypeptides had similar pK(a) value (7.5) and relatively low cytotoxicity as ε-PL and could be used as substitutes of ε-PL in biomedical applications, especially in endotoxin selective removal. Poly(ethylene glycol) (PEG)-containing alternating copolymers with α-amino groups were also synthesized and characterized. After deprotection, the polymers could be used as functional gene vector with PEG shadowing system and NCA initiator to get amphiphilic graft polymers.     

Fabrication of highly porous scaffolds for tissue engineering based on star-shaped functional poly(ε-caprolactone)

The potential of novel functional star‐shaped poly(ε‐caprolactone)s of controlled molecular weight and low molecular weight distribution bearing acrylate end groups as material for biomedical applications was demonstrated in this study. The polymers were functionalized via Michael‐type addition of amino acid esters containing amino or thiol groups showing the potential for immobilization of biomolecules. Furthermore, scaffolds of different geometries were prepared by uniaxial freezing of polymer solutions followed by freeze drying. Different solvents and polymer concentrations were investigated, resulting in scaffolds with porosities between 76 and 96%. Mechanical properties of the scaffolds were investigated and the morphology was determined via scanning electron microscopy. Scaffolds with interconnected channels were prepared using benzene, 1,2‐dichloroethane or dioxane as solvent. The tubular longitudinal pores in honeycomb arrangement extend throughout the full extent of the scaffolds (typical pore sizes: 20–100 µm). Biotechnol. Bioeng. 2011; 108:694–703. © 2010 Wiley Periodicals, Inc.     

Thermally controlled release of anticancer drug from self-assembled γ-substituted amphiphilic poly(ε-caprolactone) micellar nanoparticles

A thermo-responsive poly{γ-2-[2-(2-methoxyethoxy)ethoxy]ethoxy-ε-caprolactone}-b-poly(γ-octyloxy-ε-caprolactone) (PMEEECL-b-POCTCL) diblock copolymer was synthesized by ring-opening polymerization using tin octanoate (Sn(Oct)(2)) catalyst and a fluorescent dansyl initiator. The PMEEECL-b-POCTCL had a lower critical solution temperature (LCST) of 38 °C, and it was employed to prepare thermally responsive micelles. Nile Red and Doxorubicin (DOX) were loaded into the micelles, and the micellar stability and drug carrying ability were investigated. The size and the morphology of the cargo-loaded micelles were determined by DLS, AFM, and TEM. The Nile-Red-loaded polymeric micelles were found to be stable in the presence of both fetal bovine serum and bovine serum albumin over a 72 h period and displayed thermo-responsive in vitro drug release. The blank micelles showed a low cytotoxicity. As comparison, the micelles loaded with DOX showed a much higher in vitro cytotoxicity against MCF-7 human breast cancer cell line when the incubation temperature was elevated above the LCST. Confocal laser scanning microscopy was used to study the cellular uptake and showed that the DOX-loaded micelles were internalized into the cells via an endocytosis pathway.     

Ring-opening polymerization of ɛ-caprolactone catalyzed by a novel lipase Candida sp. 99-125

The ring-opening polymerization of ?-caprolactone catalyzed by a novel lipase Candida sp. 99-125 was achieved in organic solvents. ?-Caprolactone was found to be polymerized in quantitative yield in toluene at 80?°C for 5 days. The poly (?-caprolactone) obtained had a number-average molecular weight of 14,120 (polydispersity index?=?1.161). The effect of enzyme concentration, temperature, reaction time, reaction medium, and water content on monomer conversion and product molecular weight were investigated. Kinetic analysis showed that the enzyme displayed Michaelis–Menten kinetics and showed stronger affinity for ?-caprolactone (with a K_m value of 6.1?mmol/L) than other reported lipases.     

Electrospun chitosan-graft-poly (ε -caprolactone)/poly (ε-caprolactone) cationic nanofibrous mats as potential scaffolds for skin tissue engineering

This research is aimed to develop cationic nanofibrous mats with improved cellular adhesion profiles and stability of three-dimensional fibrous structure as potential scaffolds for skin tissue engineering. Firstly, amino-remained chitosan-graft-poly (?-caprolactone) (CS-g-PCL) was synthesized with a facile one-step manner by grafting ?-caprolactone oligomers onto the hydroxyl groups of CS via ring-opening polymerization by using methanesulfonic acid as solvent and catalyst. And then, CS-g-PCL/PCL nanofibrous mats were obtained by electrospinning of CS-g-PCL/PCL mixed solution. Scanning electron microscopy (SEM) images showed that the morphologies and diameters of the nanofibers were mainly affected by the weight ratio of CS-g-PCL to PCL. The enrichment of amino groups on the nanofiber surface was confirmed by X-ray photoelectron spectroscopy (XPS). With the increase of CS-g-PCL in CS-g-PCL/PCL nanofiber, the content of amino groups on the nanofiber surface increased, which resulted in the increase of zeta-potential of nanofibers. Studies on cell-scaffold interaction were carried out by culturing mouse fibroblast cells (L929) on CS-g-PCL/PCL nanofibrous mats with various contents of CS-g-PCL by assessing the growth, proliferation and morphologies of cells. The results of MTS assay and SEM observation showed that CS-g-PCL/PCL (2/8) mats with a moderate surface zeta-potential (ζ=3mV) were the best in promoting the cell attachment and proliferation. Toluidine blue staining further confirmed that L929 cells grew well and exhibited a normal morphology on the CS-g-PCL/PCL (2/8) mats. These results suggested the potential utilization of CS-g-PCL/PCL (2/8) nanofibrous mats for skin tissue engineering.     

Synthesis of the penicillin precursor, δ-(l-α-aminoadipyl)-l-cysteinyl-d-valine (ACV), by an immobilized enzyme preparation

Summary -(l--Aminoadipyl)-l-cysteinyl-d-valine (ACV) synthetase activity has been partially-purified from cell-free extracts of Streptomyces clavuligerus by ammonium sulfate precipitation. The salt precipitated enzyme was immobilized on an anion exchange resin and synthesis of ACV was observed by exposing the immobilized enzyme preparation to a reaction mixture containing l--aminoadipic acid, l-valine and l-cysteine in the presence of appropriate cofactors. Reaction mixtures containing l--aminobutyric acid(aB) in place of l-valine synthesized the ACV analog ACaB. Immobilized ACV synthetase can be reused, and after six cycles of reaction, 28.9% of original activity remains.     

Galactose-decorated cross-linked biodegradable poly(ethylene glycol)-b-poly(ε-caprolactone) block copolymer micelles for enhanced hepatoma-targeting delivery of paclitaxel

The inferior in vivo stability of micellar drugs has been a prime challenge for their application in targeted drug delivery. Here we report on novel galactose-decorated covalently cross-linked biodegradable micelles based on photo-cross-linkable poly(ethylene glycol)-b-poly(acryloyl carbonate)-b-poly(ε-caprolactone) (PEG-PAC-PCL) and galactose-conjugated PEG-PCL (Gal-PEG-PCL) copolymers for enhanced hepatoma-targeting delivery of paclitaxel (PTX). The molecular weight of PEG in Gal-PEG-PCL was higher than that in PEG-PAC-PCL, thereby fully exposing Gal ligands at the micellar surface. These micelles, either with or without loading of PTX, were readily cross-linked by UV irradiation to afford micelles with small sizes (ca. 79-94 nm) and enhanced stability. The in vitro release studies confirmed that drug release from cross-linked micelles was significantly inhibited. Interestingly, MTT assays showed that Gal-decorated PTX-loaded cross-linked micelles retained a high antitumor activity in HepG2 cells, which was much more effective than PTX-loaded cross-linked micelles without Gal ligands and comparable to Gal-decorated PTX-loaded non-cross-linked micelles. Remarkably, the preliminary in vivo antitumor efficacy studies in SMMC-7721 tumor (human hepatoma)-bearing nude mice revealed that Gal-decorated PTX-loaded cross-linked micelles inhibited the growth of the human hepatoma more effectively than PTX-loaded cross-linked micelles as well as Gal-decorated PTX-loaded non-cross-linked micelles. These results indicate that Gal-decorated cross-linked PEG-PCL micelles have great potential in liver tumor-targeted chemotherapy.     

Inversion of sucrose in a continuous process with β-d-fructofuranosidase (invertase) immobilized on bead DEAHP-cellulose

Inversion of sucrose with β-d-fructofuranosidase (EC 3.2.1.26) immobilized by the ionic bond on bead DEAHP-cellulose has been studied under flow conditions. Under these conditions, the inversion of sucrose is affected by the concentration and flow rate of the substrate and by the reaction temperature. The effect of substrate concentration on the reaction was investigated in the range 19.5–64.2 wt %; the effect of flow rate was examined in the range 0.25–5.57 g solution per min, and the temperature range used was 25–50°C. It was found that the activities of immobilized β-d-fructofuranosidase in stirred and flow reactors were the same. The lower activities of β-d-fructofuranosidase in the case of concentrated solutions, and of immobilized β-d-fructofuranosidase compared with the native enzyme are attributed to more difficult diffusion through the beads of the ion exchanger, especially of the strongly viscous substrate. A long-term investigation of the enzyme activity over a period of three months demonstrated the stability of the β-d-fructofuranosidase immobilized by the ionic bond on bead DEAHP-cellulose; the half-life of the enzyme was 215 days. It was also found that the immobilization of the enzyme on a carrier was more effective under flow conditions, i.e. through an ion exchanger in the column, than under the equilibrium conditions of a stirred reactor.