End Scission Research Articles

Mechanistic insights into Ga-modified hollow ZSM-5 catalyzed fast pyrolysis of cassava residue

The preparation of valuable chemicals by catalytic fast pyrolysis (CFP) is a promising and environmentally-friendly approach for the selective upgrading of waste cassava residue (CR). This work systematically investigated the conversion mechanism and kinetic characteristics of CR pyrolysis over Ga-modified hollow ZSM-5, for the purpose of enhancing aromatics production. The hollow configuration significantly regulated the structural characteristics of ZSM-5, thus facilitating the diffusion, deoxygenation, and aromatization of pyrolysis intermediates. The incorporation of Ga species and generated Brønsted acid sites remarkably accelerated the reaction rate and suppressed the carbonization at high temperatures, through enhancing the end scission of starch and cellulose components. With the aid of 5Ga/ZSM-H, the relative content of aromatics achieved 95.4% at 700 °C, and still maintained over 92.5% even after 5 cycles. The ring-opening and retro-aldol degradation were identified as crucial steps for the production of ketones and aldehydes separately, which were further transformed into hydrocarbon pools by deoxygenation and subsequently converted into aromatics via Diels-Alder reaction. Kinetic analysis demonstrated that the use of 5Ga/ZSM-H lowered the average activation energy of CR pyrolysis by 14.8%, particularly for the initial pyrolysis stage. Moreover, the plausible mechanism for aromatics formation from Ga-modified hollow ZSM-5 catalyzed CR pyrolysis was proposed.

Cellular Automaton Simulation for Degradation of Poly Lactic Acid with Acceleratable Reaction-Diffusion Model.

Biodegradability is a fundamental property of poly lactic acid (PLA). Numerous simulation algorithms based on reaction-diffusion model have been utilized to analyze the degradation behaviors of PLA. In the present work, a cellular automaton (CA) algorithm combined with an acceleratable reaction-diffusion model and coarse-grained kinetic Monte Carlo method is applied to simulate the degradation behaviors of PLA, such as random or end scission and crystallization of PLA chains, diffusion of soluble oligomers. The CA algorithm can reveal the global changes of molecular weight, mass, reaction number and soluble oligomer number generated by hydrolysis as well as the local distributions of molecular weight, soluble oligomer number and cellular state. The calculation result of experiment demonstrates that such a CA model can accurately simulate the change of molecular weight and mass loss simultaneously. The effects of hydrolysis mode, reaction rate constant, diffusion coefficient, device size and pore structure on the degradation behaviors of PLA especially the change in the molecular weight and the famous autocatalysis effect are comprehensively investigated. A novel classification method of molecular weight change curve is presented and the effects of various factors are concluded. In general, big reaction rate constant, small diffusion coefficient, big device size, solid or low porosity, and no or few initial soluble oligomers can more easily generate a type I curve, which corresponds to a strong autocatalysis hydrolysis.

Oligo(lactic acid)n-Paclitaxel Prodrugs for Poly(ethylene glycol)-block-poly(lactic acid) Micelles: Loading, Release, and Backbiting Conversion for Anticancer Activity.

Poly(ethylene glycol)-block-poly(d,l-lactic acid) (PEG-b-PLA) micelles are nanocarriers for poorly water-soluble anticancer agents and have advanced paclitaxel (PTX) to humans due to drug solubilization, biocompatibility, and dose escalation. However, PEG-b-PLA micelles rapidly release PTX, resulting in widespread biodistribution and low tumor exposure. To improve delivery of PTX by PEG-b-PLA micelles, monodisperse oligo(l-lactic acid), o(LA)8 or o(LA)16, has been coupled onto PTX at the 7-OH position, forming ester prodrugs: o(LA)8-PTX and o(LA)16-PTX, respectively. As expected, o(LA)n-PTX was more compatible with PEG-b-PLA micelles than PTX, increasing drug loading from 11 to 54%. While in vitro release of PTX was rapid, resulting in precipitation, o(LA)n-PTX release was more gradual: t1/2 = 14 and 26 h for o(LA)8-PTX and o(LA)16-PTX, respectively. Notably, o(LA)8-PTX and o(LA)16-PTX in PEG-b-PLA micelles resisted backbiting chain end scission, based on reverse-phase HPLC analysis. By contrast, o(LA)8-PTX and o(LA)16-PTX degraded substantially in 1:1 acetonitrile:10 mM PBS, pH 7.4, at 37 °C, generating primarily o(LA)2-PTX. The IC50 value of o(LA)2-PTX was ∼2.3 nM for A549 human lung cancer cells, equipotent with PTX in vitro. After weekly IV injections at 20 mg/kg as PEG-b-PLA micelles, o(LA)8-PTX induced tumor regression in A549 tumor-bearing mice, whereas PTX delayed tumor growth. Surprisingly, o(LA)8-PTX caused less toxicity than PTX in terms of change in body weight. In conclusion, o(LA)n acts as a novel promoiety, undergoing backbiting conversion without a reliance on metabolizing enzymes, and o(LA)n-PTX improves PTX delivery by PEG-b-PLA micelles, providing a strong justification for clinical evaluation.

Study on the Thermal Degradation Kinetics of Biodegradable Poly(propylene carbonate) during Melt Processing by Population Balance Model and Rheology

The degradation behavior of poly(propylene carbonate) (PPC) was investigated during melt processing to infer the mechanism and kinetics of thermal degradation. First, the degradation experiments were carried out in a miniature conical twin-screw extruder at different temperatures, rotating speeds, and processing times. Gel permeation chromatography (GPC) was applied to analyze the molecular weight and molecular weight distributions (MWDs) of melt processed PPC samples. The degradation process at various processing conditions was described by the population balance equations (PBEs) with random chain scission and chain end scission. By comparing the prediction of PBE model with the experimental evolution of molecular weight, it is proposed that random chain scission and chain end scission occur simultaneously. At temperature higher than 160 °C, random chain scission dominates with the activation energy about 120 kJ/mol. Second, a method combining the PBE model and rheology was suggested to determine the kinetics of degradation directly from the torque of mixer during melt processing without further measurements on molecular weight. Such method was applied to melt mixing of PPC in a batch mixer, from which a higher kinetic parameter of thermal degradation and similar activation energy were successfully determined as compared to those obtained from extrusion experiments.

Degradation mechanisms of bioresorbable polyesters. Part 2. Effects of initial molecular weight and residual monomer

This paper presents an understanding of how initial molecular weight and initial monomer fraction affect the degradation of bioresorbable polymers in terms of the underlying hydrolysis mechanisms. A mathematical model was used to analyse the effects of initial molecular weight for various hydrolysis mechanisms including noncatalytic random scission, autocatalytic random scission, noncatalytic end scission or autocatalytic end scission. Different behaviours were identified to relate initial molecular weight to the molecular weight half-life and to the time until the onset of mass loss. The behaviours were validated by fitting the model to experimental data for molecular weight reduction and mass loss of samples with different initial molecular weights. Several publications that consider initial molecular weight were reviewed. The effect of residual monomer on degradation was also analysed, and shown to accelerate the reduction of molecular weight and mass loss. An inverse square root law relationship was found between molecular weight half-life and initial monomer fraction for autocatalytic hydrolysis. The relationship was tested by fitting the model to experimental data with various residual monomer contents.

Degradation mechanisms of bioresorbable polyesters. Part 1. Effects of random scission, end scission and autocatalysis

A mathematical model was developed to relate the degradation trend of bioresorbable polymers to different underlying hydrolysis mechanisms, including noncatalytic random scission, autocatalytic random scission, noncatalytic end scission or autocatalytic end scission. The effect of each mechanism on molecular weight degradation and potential mass loss was analysed. A simple scheme was developed to identify the most likely hydrolysis mechanism based on experimental data. The scheme was first demonstrated using case studies, then used to evaluate data collected from 31 publications in the literature to identify the dominant hydrolysis mechanisms for typical biodegradable polymers. The analysis showed that most of the experimental data indicates autocatalytic hydrolysis, as expected. However, the study shows that the existing understanding on whether random or end scission controls degradation is inappropriate. It was revealed that pure end scission cannot explain the observed trend in molecular weight reduction because end scission would be too slow to reduce the average molecular weight. On the other hand, pure random scission cannot explain the observed trend in mass loss because too few oligomers would be available to diffuse out of a device. It is concluded that the chain ends are more susceptible to cleavage, which produces most of the oligomers leading to mass loss. However, it is random scission that dominates the reduction in molecular weight.

Computer Simulation of Polymer Chain Scission in Biodegradable Polymers

Biodegradable polymers are used in medical devices such as fixation plates, sutures, or micro particles for the controlled release of drugs. Typical polymers are poly lactic acid (PLA), poly glycolic acid (PGA), and poly caprolactone (PCL). During degradation, the ester bonds within polymer chains are cleaved due to the hydrolysis reaction in the presence of water. It has been suggested that both chain end scission and random chain scission occur [1] and mathematical models have been able to fit experimental data with assumptions of random scission [2-4], end scission [5], or a combination of both [6]. In random scission, every bond in a polymer chain is assumed to be equally susceptible to hydrolysis. In chain end scission, the final bond in a chain is cleaved resulting in the production of a monomer.

Thermal degradation kinetics of poly(trimethylol propane triacrylate)/poly(hexane diol diacrylate) interpenetrating polymer network

Interpenetrating polymer networks (IPNs) of trimethylol propane triacrylate (TMPTA) and 1,6-hexane diol diacrylate (HDDA) at different weight ratios were synthesized. Temperature modulated differential scanning calorimetry (TMDSC) was used to determine whether the formation resulted in a copolymer or interpenetrating polymer network (IPN). These polymers are used as binders for microstereolithography (MSL) based ceramic microfabrication. The kinetics of thermal degradation of these polymers are important to optimize the debinding process for fabricating 3D shaped ceramic objects by MSL based rapid prototyping technique. Therefore, thermal and thermo-oxidative degradation of these IPNs have been studied by dynamic and isothermal thermogravimetry (TGA). Non-isothermal model-free kinetic methods have been adopted (isoconversional differential and KAS) to calculate the apparent activation energy (Ea) as a function of conversion (α) in N2 and air. The degradation of these polymers in N2 atmosphere occurs via two mechanisms. Chain end scission plays a dominant role at lower temperature while the kinetics is governed by random chain scission at higher temperature. Oxidative degradation shows multiple degradation steps having higher activation energy than in N2. Isothermal degradation was also carried out to predict the reaction model which is found to be decelerating. It was shown that the degradation of PTMPTA follows a contracting sphere reaction model in N2. However, as the HDDA content increases in the IPNs, the degradation reaction follows Avrami–Erofeev model and diffusion governed mechanisms. The intermediate IPN compositions show both type of mechanism. Based on the above study, debinding strategy for MSL based microfabricated ceramic structure has been proposed.

Kinetics of the hydrolytic degradation of poly(lactic acid)

The hydrolysis of water soluble PLA oligomers of different chain lengths and chirality was investigated at acidic pH and temperatures in the range from 40 to 120 °C. The time evolution of the concentrations of all oligomers was measured by HPLC and the corresponding degradation rates were evaluated for each specific chain length. In agreement with the preferential chain end scission mechanism suggested in the literature, the ester groups were classified as α (chain end esters) and β (backbone esters). A kinetic model was developed from the resulting kinetic scheme and it was found to well reproduce the concentration values of all different oligomers during degradation as a function of time. The corresponding rate constants kdα and kdβ were estimated over the whole temperature range, with activation energies of 73 and 58 kJ/mol and pre-exponential factors of 8.21·107 and 1.77·105 l/mol/h, respectively. It is seen that the faster hydrolysis of the ester groups close to the carboxylic and hydroxyl chain end groups (α) with respect to those inside the polymer chain (β) is mainly due to the largely different pre-exponential factors. This steric effect can be explained considering that the water approach is favoured by the hydrophilic nature of the chain end groups compared to the hydrophobic character of the polymer backbone. No dependence of kdα and kdβ on chiral composition was found, suggesting that the differences reported earlier in the literature are due to the effect of crystallinity on diffusion phenomena rather than to different reactivity of the two stereoisomers.

Enzymatic Degradation of Poly(soybean oil-g-methyl methacrylate)

This study discusses grafting of methyl methacrylate units from thepolymeric soybean oil peroxide to produce poly(soybean oil-graft-methyl methacrylate) (PSO-g-PMMA). The degradation of this copolymer in solution was evaluated in the presence of different lipases, viz Candida rugosa (CR), Lipolase 100T (LP), Novozym 435 (N435) and Porcine pancreas (PP), at different temperatures The copolymer degraded by specific chain end scission and the mass fraction of the specific product evolved was determined The degradation was modeled using continuous distribution kinetics to determine the rate coefficients ofmenzymatic chain end scission and deactivation of the enzyme The enzymes, CR. LP and N435 exhibited maximum activity for the degradation of PSO-g-PMMA at 60 degrees C, while PP was most active at 50 degrees C. The thermal degradability of the copolymer, assessed by thermo-gravimetry, indicated that the activation energy of degradation of the copolymer was 154 kJ mol(-1), which was lesser than that of the PMMA homopolymer.

Photooxidative and pyrolytic degradation of methyl methacrylate-alkyl acrylate copolymers

Different compositions of poly(methyl methacrylate-co-methyl acrylate) (PMMAMA), poly(methyl methacrylate-co-ethyl acrylate) (PMMAEA) and poly(methyl methacrylate-co-butyl acrylate) (PMMABA) copolymers were synthesized and characterized. The photocatalytic oxidative degradation of all these copolymers were studied in presence of two different catalysts namely Degussa P-25 and combustion synthesized titania using azobis-iso-butyronitrile and benzoyl peroxide as oxidizers. Gel permeation chromatography (GPC) was used to determine the molecular weight distribution of the samples as a function of time. The GPC chromatogram indicated that the photocatalytic oxidative degradation of all these copolymers proceeds by both random and chain end scission. Continuous distribution kinetics was used to develop a model for photocatalytic oxidative degradation considering both random and specific end scission. The degradation rate coefficients were determined by fitting the experimental data with the model. The degradation rate coefficients of the copolymers decreased with increase in the percentage of alkyl acrylate in the copolymer. This indicates that the photocatalytic oxidative stability of the copolymers increased with increasing percentage of alkyl acrylate. From the degradation rate coefficients, it was observed that the photocatalytic oxidative stability follows the order PMMABA > PMMAEA > PMMAMA. The thermal degradation of the copolymers was studied by using thermogravimetric analysis (TGA). The normalized weight loss and differential fractional weight loss profiles indicated that the thermal stability of the copolymer increases with an increase in the percentage of alkyl acrylate and the thermal stability of poly(methyl methacrylate-co-alkyl acrylate)s follows the order PMMAMA > PMMAEA > PMMABA. The observed contrast in the order of photostability and thermal stability of the copolymers was attributed to different mechanisms involved for the scission of polymer chain and formation of different products in both the processes.

Photocatalytic and Thermal Degradation of Poly(methyl methacrylate), Poly(butyl acrylate), and Their Copolymers

The photocatalytic and thermal degradations of poly(methyl methacrylate), poly(butyl acrylate), and their copolymers of different compositions were studied. The photocatalytic degradation was investigated in o-dichlorobenzene in the presence of two different catalysts, namely, Degussa P-25 and combustion synthesized nanotitania (CSN-TiO2). The samples were analyzed by using gel permeation chromatography (GPC) to obtain the molecular weight distributions (MWDs) as a function of reaction time. Experimental data indicated that the photodegradation of these polymers occurs by both random and chain end scission. A continuous distribution kinetic model was used to determine the degradation rate coefficients by fitting the experimental data with the model. Both the random and specific rate coefficients of the copolymers decreased with increasing percentage of butyl acrylate (BA). Thermal degradation of the copolymers was investigated by thermogravimetry. The normalized weight loss profiles for the copolymers showed that the thermal stability of the copolymers increased with mole percentage of BA in the copolymer (PMMABA). The Ozawa method was used to determine the activation energies at different conversions. At low acrylate content in the copolymer, the activation energy depends on conversion, indicating multiple degradation mechanisms. At high acrylate content in the copolymer, the activation energy is independent of conversion, indicating degradation by a one-step mechanism.

Thermal and Photocatalytic Degradation of Poly(methyl methacrylate), Poly(butyl methacrylate), and Their Copolymers

The photocatalytic degradation of the homopolymers, poly(methyl methacrylate) (PMMA), poly(butyl methacrylate) (PBMA), and their copolymers (PMMABMA) was studied in o-dichlorobenzene in the presence of commercial TiO2 (Degussa P-25) and TiO2 synthesized by combustion synthesis (CSN-TiO2). Gel permeation chromatography was used to determine the evolution of molecular weight distributions with reaction time. The experimental data indicated that the polymers PMMA and PBMA and their copolymers degrade by simultaneous random and chain end scission. A continuous distribution model was developed for the mechanism involved in degradation by both random and chain end scission and used to determine the degradation rate coefficients. The degradation rate coefficients of the polymers in the presence of CSN-TiO2 were higher than the degradation rate coefficients obtained with commercial TiO2 (Degussa P-25). The degradation rate coefficient of copolymers was in between that of the homopolymers and increased linearly with the increase of mol % of PMMA. The degradation of PMMA, PBMA, and their copolymers was also investigated by thermogravimetric analysis. The copolymers exhibited better thermal stability than the homopolymers in contrast to that observed for photocatalytic degradation.

Degradation of polycaprolactone in supercritical fluids

The degradation of polycaprolactone (PCL) was studied in subcritical and supercritical toluene from 250 to 375 °C at 50 bar. The degradation was also investigated in various solvents like ethylbenzene, o-xylene and benzene at 325 °C and 50 bar. The effect of pressure on degradation was also evaluated at 325 °C at various pressures (35, 50 and 80 bar). The variation of molecular weight with time was analyzed using gel permeation chromatography and modeled using continuous distribution kinetics to evaluate the degradation rate coefficients. PCL degrades by random chain scission in subcritical conditions (250–300 °C) and by chain end scission (325–375 °C) in supercritical conditions in toluene. The degradation of PCL in other solvents at 325 °C was by chain end scission under both subcritical and supercritical conditions indicating that the mode of scission depends on the temperature and not on the supercriticality of the solvent. The thermogravimetric analysis of PCL was investigated at various heating rates (2–24 °C/min) and the activation energy was determined using Friedman, Ozawa and Kissinger methods. It was shown that PCL degrades by random scission at lower temperatures and by chain end scission at higher temperatures again indicating that the mode of scission is dependent on the temperature.

Effect of the Alkyl Group Substituents on the Thermal and Enzymatic Degradation of Poly(n-alkyl acrylates)

The effect of alkyl group substituents on the thermal degradation kinetics of poly (n-alkyl acrylate) was investigated in pyrolysis and in solution. The activation energies for the pyrolytic degradation of poly (n-butyl acrylate) (PBA), poly (ethyl acrylate) (PEA), and poly (methyl acrylate) (PMA), determined by the Friedman's technique, were 150, 170 and 203 kJ/mol, respectively. For the thermal degradation of the polymers in solution, a continuous distribution kinetic model was used to determine the random chain degradation rate coefficients. The activation energies, determined from the temperature dependence of the rate coefficients, for PBA, PEA and PMA in solution were 109, 117, and 138 kJ/mol, respectively. This indicates that the variation of the activation energies with chain length of the substituent in the polymer is similar to degradation both by pyrolysis and in solution, though the values obtained are lower for degradation in solution. The enzymatic degradation of these polymers was also investigated at different temperatures with various enzymes (Novozym 435, Lipolase and Porcine Pancreas) in different solvents. A continuous distribution kinetic model was used to evaluate the polymer chain end scission rate coefficient. The degradation rates were highest when the acrylates were degraded in presence of Porcine Pancreas in toluene at $50\hspace{2mm}^oC$.

Enzymatic and Thermal Degradation of Poly(ε-caprolactone), Poly(d,l-lactide), and Their Blends

The enzymatic degradation of poly(d,l-lactide) (PLA), poly(\epsilon-caprolactone) (PCL), and their blends by Novozym 435 was studied in toluene at 60 C. Both of the polymers were found to degrade by specific chain end scission. A model based on the continuous distribution kinetics was developed to determine the rate coefficient. The degradation rate coefficient was determined from the time evolution of the specific product. The pyrolytic degradation of these polymers and their blends was also investigated. The presence of PLA did not affect either the thermal or enzymatic degradation of PCL. It was thus concluded that the degradations of the polymers were independent of each other

Hydrolytic degradation of oligo(lactic acid): a kinetic and mechanistic study

This study shows that the degradation mechanism and kinetics of monodisperse oligo(lactic acid)s esterified with N-(2-hydroxypropyl)methacrylamide (HPMAm) are strongly influenced by the nature of the chain end. Oligomers with free hydroxyl chain ends degraded predominantly by chain end scission via a backbiting mechanism with a pseudo first-order rate constant k bb=2.7 h −1 in aqueous buffer (37 °C, pH 7.2). Once the hydroxyl groups were protected by acetylation, random chain scission became the rate limiting step with k r=0.022 h −1 under the same conditions. Using these rate constants, the theoretical time-resolved degradation profile was calculated for every (intermediate) degradation product and corresponded very well with the experimental results. The rate of formation of HPMAm was independent of the chain length for the acetylated oligomers, while the hydroxyl terminated oligomers with an even number of lactic acid units formed HPMAm more rapidly than oligomers with an odd number of units. The possibility to fine-tune the degradation rate is relevant when applied as e.g. hydrogels for controlled release or tissue engineering materials.

Thermal degradation of binary physical mixtures and copolymers of poly(ε-caprolactone), poly( d, l-lactide), poly(glycolide)

The thermal degradation of various aliphatic polyesters such as poly(ε-caprolactone) (PCL), poly(glycolide) (PGA), and poly( d, l-lactide) (PLA), their physical blends and copolymers were investigated in a thermogravimetry analyzer under dynamic heating in an inert nitrogen atmosphere. The peak decomposition temperatures of the PCL, PGA, and PLA are 402, 360 and 295 °C, respectively. The Friedman plots showed a 2.5- to 3-fold increase in the activation energy from lower temperatures to higher temperatures during degradation. This suggested that the governing mechanism changes during degradation from random chain scission to specific chain end scission with increase in temperature. The activation energies for the random chain scission of PCL, PGA and PLA are 18.5, 16.5, and 10.2 kcal/mol, respectively and the corresponding activation energies for the specific chain scission are 55.5, 32.0, and 25.2 kcal/mol. Experiments were also conducted under isothermal holding to evaluate the activation energies for specific chain scission and are 47.5, 28.0, and 22.2 kcal/mol for PCL, PGA, and PLA, respectively. The degradation of the blends and copolymers was also investigated. The presence of PLA in the copolymer destabilized the other polymers (PCL and PGA). However, the presence of PLA in the mixture did not influence the degradation of PGA.

Tuning the Degradation Rate of Poly(2-hydroxypropyl methacrylamide)-graft-oligo(lactic acid) Stereocomplex Hydrogels

The degradation time of stereocomplex hydrogels based on poly(2-hydroxypropyl meth- acrylamide) (pHPMAm) with oligo(lactic acid) side chains of opposite chirality can be tailored from approximately 1 week to almost 3 months under physiological conditions by adjusting the grafting density and the side chain terminus. The polymers were prepared by free radical copolymerization of HPMAm- oligo(lactic acid) macromonomers and HPMAm. The viscoelasticity and degradation time of hydrogels formed by mixing aqueous solutions of two polymers containing side chains of opposite chirality increased with increasing grafting density. Gels based on polymers with side chains having acetyl chain ends degraded slower than those containing hydroxyl-terminating side chains, because of a change in the hydrolysis mechanism from slow random chain scission to more rapid chain end scission (backbiting), respectively. The ease of preparation and the possibility of tuning the degradation rate over a wide range make these pHPMAm-based hydrogels ideal materials for the controlled release of, e.g., therapeutic proteins.

Modeling of lipase catalyzed ring-opening polymerization of epsilon-caprolactone.

Enzymatic ring-opening polymerization of epsilon-caprolactone by various lipases was investigated in toluene at various temperatures. The determination of molecular weight and structural identification was carried out with gel permeation chromatography and proton NMR, respectively. Among the various lipases employed, an immobilized lipase from Candida antartica B (Novozym 435) showed the highest catalytic activity. The polymerization of epsilon-caprolactone by Novozym 435 showed an optimal temperature of 65 degrees C and an optimum toluene content of 50/50 v/v of toluene and epsilon-caprolactone. As lipases can degrade polyesters, a maximum in the molecular weight with time was obtained due to the competition of ring opening polymerization and degradation by specific chain end scission. The optimum temperature, toluene content, and the variation of molecular weight with time are consistent with earlier observations. A comprehensive model based on continuous distribution kinetics was developed to model these phenomena. The model accounts for simultaneous polymerization, degradation and enzyme deactivation and provides a technique to determine the rate coefficients for these processes. The dependence of these rate coefficients with temperature and monomer concentration is also discussed.