Evolution Of Molecular Weight Distribution Research Articles

Size exclusion chromatography to evaluate in vitro proteolysis: A case study on the impact of microstructure in pulse powders.

Cellular pulse ingredients are increasingly being studied but little knowledge on their proteolysis patterns upon digestion is available. This study investigated a size exclusion chromatography (SEC) approach to study in vitro protein digestion in chickpea and lentil powders, providing novel insights into proteolysis kinetics and the evolution of molecular weight distributions in the (solubilized) supernatant and (non-solubilized) pellet fractions. For the quantification of proteolysis, SEC-based analysis was compared to the commonly used OPA (o-phthaldialdehyde) approach and nitrogen solubilized upon digestion, leading to highly correlated proteolysis kinetics. Generally, all approaches confirmed that microstructure dictated proteolysis kinetics. However, SEC analysis delivered an additional level of molecular insight. For the first time, SEC revealed that while bioaccessible fractions reached a plateau in the small intestinal phase (around 45-60min), proteolysis continued in the pellet, forming smaller but mostly insoluble peptides. SEC elutograms showed pulse-specific proteolysis patterns, unidentified using other current state-of-the-art methods.

A Novel Method for Dynamic Molecular Weight Distribution Determination in Organometallic Catalyzed Olefin Polymerizations

In this study, a mathematical model for the time evolution of molecular weight distribution (MWD) was developed. This temporal model is based on the well-known Ziegler–Natta polymerization mechanism and reaction kinetics by the parametric solving of related differential equations. However, due to the generality of the reactions involved, the model can be extended to the other type of catalysts, such as metallocenes, Phillips, etc. The superiority of this model lies in providing the possibility of a more precise prediction over the active sites and kinetic parameters using a simple mathematical equation, which leads to improved reactor design in large-scale production. The model uses a function to develop a methodology for MWD calculations. In this way, the transient response is limited to the first few minutes of the reaction; however, it is important as it demonstrates the establishment of the final MWD. According to the results, almost for practical conditions with negligible transfer resistances, the time dependency of the MWD has a transient interval, depending on the kinetic constants of polymerization reactions. Increasing the time to infinity results in an increase in MW and a widening in MWD, which confirms the experimental plots well. In short, the main advantage of our proposed model over the previous ones is its ability to predict the MWD even before the completion of the polymerization reaction. The results of the present model match well with those of the well-known Schulz–Flory distribution, which only predicts the final molecular weight distribution, thus confirming that the model is reliable and generalizable.

Molecular weight development in the superacid-catalyzed polyhydroxyalkylation of 1-propylisatin and biphenyl at stoichiometric conditions

An experimental study on the importance of cyclization on molecular weight development in superacid catalyzed polyhydroxyalkylation of 1-propylisatin (B2) and biphenyl (A2) at stoichiometric conditions, is presented. Evolution of molecular weight distributions measured by gel permeation chromatography (GPC) and matrix-assisted laser-desorption/ionization-time-of-flight (MALDI-TOF) show that although linear polymer formation dominates the polymerization, there is significant cyclization taking place, and that the polymerization is kinetically controlled. They also show that there are two polymer populations in the reaction system. The polymer population in the low molecular region is richer in cyclic polymer molecules. Diffusion coefficients were measured by GPC and 2D NMR DOSY. The values obtained confirm that cyclization is more important in low molecular weight polymer molecules. A polymerization at non-stoichiometric conditions (excess of A2) is compared with the stoichiometric case. Unlike other superacid catalyzed polyhydroxyalkylations studied in the past, lower molecular weights were obtained in the non-stoichiometric situation.

Prediction of Viscoelastic Properties of Enzymatically Crosslinkable Tyramine-Modified Hyaluronic Acid Solutions Using a Dynamic Monte Carlo Kinetic Approach.

The present study deals with the mathematical modeling of crosslinking kinetics of polymer–phenol conjugates mediated by the Horseradish Peroxidase (HRP)-hydrogen peroxide (H2O2) initiation system. More specifically, a dynamic Monte Carlo (MC) kinetic model is developed to quantify the effects of crosslinking conditions (i.e., polymer concentration, degree of phenol substitution and HRP and H2O2 concentrations) on the gelation onset time; evolution of molecular weight distribution and number and weight average molecular weights of the crosslinkable polymer chains and gel fraction. It is shown that the MC kinetic model can faithfully describe the crosslinking kinetics of a finite sample of crosslinkable polymer chains with time, providing detailed molecular information for the crosslinkable system before and after the gelation point. The MC model is validated using experimental measurements on the crosslinking of a tyramine modified Hyaluronic Acid (HA-Tyr) polymer solution reported in the literature. Based on the rubber elasticity theory and the MC results, the dynamic evolution of hydrogel viscoelastic and molecular properties (i.e., number average molecular weight between crosslinks, Mc, and hydrogel mesh size, ξ) are calculated.

A modified collocation modeling framework for dynamic evolution of molecular weight distributions in general polymer kinetic systems

General modeling and optimization with molecular weight distributions (MWDs) are essential to determine optimal designs and operations for polymerization processes. Orthogonal collocation methods in two dimensions can capture the dynamic feature of MWD in time and the distributive feature in chain length. However, there are still computational challenges for complex reactions using this method. This study proposes a general framework based on the collocation methods. For different mathematical operations caused by different types of polymeric reactions, we propose corresponding model reformulation methods with specific coefficient matrices, including moment operations caused by chain propagation and disproportionate termination, moment operation without closure caused by scission, and convolution operation caused by coupling termination. The chain-length dependent rate can also be handled well through this general framework. Case studies show the effectiveness, accuracy, and generality of our approach.

Unravelling Electrochemical Lignin Depolymerization

Lignin valorisation via electrochemical depolymerization is a promising approach for commercial application due to its moderate reaction conditions. However, there is no available kinetics model for this reaction. Conventional reaction kinetics equations are inadequate when used for lignin degradation because of the limited kinetics information with respect the reaction mechanism. We suggest to use population balance equations to predict the evolution of molecular weight distribution of lignin with time. Solving the low molecular weight (MW) population balance equations is carried out discretely whereas a continuous solution was implemented for the high MW. Additionally, the model accounts for a recombination reaction for the depolymerized species. The model is capable of predicting the molecular weight distribution of lignin as a function of electrochemical processing time. New experimental results are used to extract kinetics constants for different kraft lignin samples.

Monte Carlo simulation of molecular weight distribution and copolymer composition in transamidation reaction of polyamides

AbstractMelt mixing of polyamides results in exchange reaction and generation of copolymers. In this work, Monte Carlo method is used to simulate the time evolution of molecular weight distribution (MWD) and copolymer composition during the exchange reaction process between polyamides with AA and BC structure. The influences of initial composition and molecular weight have been investigated. Decrease in the difference between the average molecular weight of two kinds of polyamides results in faster approach of the MWD toward Flory's distribution and higher probability of producing copolymers. When the ratio between the numbers of initial molecules of two homopolymers is increased, the number of generated copolymers is reduced and the wider MWD is obtained. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

Ultrasonic degradation of butadiene, styrene and their copolymers

Ultrasonic degradation of commercially important polymers, styrene–butadiene (SBR) rubber, acrylonitrile–butadiene (NBR) rubber, styrene–acrylonitrile (SAN), polybutadiene rubber and polystyrene were investigated. The molecular weight distributions were measured using gel permeation chromatography (GPC). A model based on continuous distribution kinetics approach was used to study the time evolution of molecular weight distribution for these polymers during degradation. The effect of solvent properties and ultrasound intensity on the degradation of SBR rubber was investigated using different pure solvents and mixed solvents of varying volatility and different ultrasonic intensities.

Oxidative and photooxidative degradation of poly(acrylic acid)

The oxidative degradation of poly(acrylic acid) (PAA), a water soluble polymer, was studied at various temperatures with different concentrations of persulfates, potassium persulfate (KPS), ammonium persulfate (APS) and sodium persulfate (SPS). The photodegradation of PAA was also examined with APS as oxidizer. The degraded samples were analyzed for the time evolution of molecular weight distribution by gel permeation chromatography. A theoretical model based on the continuous distribution kinetics was developed that accounted for the polymer degradation and the dissociation of persulfate. The rate coefficients for the oxidative and photooxidative degradation of PAA were determined from the parametric fit of the model with experimental data. The rate of degradation increased with increasing amount of persulfate in both oxidative and photooxidative degradation. The rate of degradation also increased with increasing temperature in the case of oxidative degradation.

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.

Photocatalytic Degradation of Poly(Acrylamide-co-acrylic Acid)

Poly(acrylamide-co-acrylic acid) copolymers of different compositions were synthesized and characterized. The copolymers were statistical with a relatively high percentage of acrylamide units, as determined by (13)C NMR. Reactivity ratios calculated by the Finemann-Ross and Kelen-Tudos methods showed that the copolymers were random with a reactivity ratio of r AM = 3.76 and r AA = 0.28. The photolytic and photocatalytic degradation of the copolymers and the homopolymers was conducted in the presence of combustion-synthesized nano anatase titania. The degradation of the copolymer in the presence of combustion-synthesized titania was significantly higher than that observed in the presence of commercial titania, Degussa P-25. The degradation was modeled by using continuous distribution kinetics by following the time evolution of molecular weight distribution. The degradation follows a two step mechanism, wherein the rapid first step comprises the scission of weak acrylic acid units along the chain which is followed by the breakage of relatively strong acrylamide units. The rate constants for the weak and strong links follow a linear trend with the percentage of acrylic acid and acrylamide in the copolymer, respectively. This linear variation can be correlated with a similar trend observed for the activation energies obtained for the pyrolytic degradation of the polymers.

Kinetic Modeling of the Thermal Degradation of Methacrylate Copolymers by Thermogravimetric Methods

The thermal degradation kinetics of a random copolymer of isobutyl methacrylate / lauryl methacrylate, produced by free-radical solution polymerization is investigated over a temperature range of 350 to 750 K, using dynamic thermogravimetric experiments. Heat treatment of the copolymer affects the main polymer backbone and side chains. The thermal degradation of the copolymer proceeds in three distinct steps of weight loss: the first and easiest step is initiated by scissions of head-to-head linkages representing one type of defect in the polymer backbone; the second and more difficult step is initiated by scissions at the vinylidene chain ends; the third and most energetic step is initiated by random scissions within the polymer chain.The time evolution of molecular weight distribution (MWD) is measured by gel permeation chromatography (GPC). The most pronounced changes in the trend of the average molecular weight are observed during the transition from each degradation step to the subsequent one. A continuous distribution kinetic model based on a population balance is developed to describe the observed degradation behaviour of the copolymer. This comprehensive model conforms to the special mechanisms for random chain-scission and chain-end depolymerization. The pseudo-kinetic rate parameters for each degradation step are estimated to be respectively equal to 1.1 10-8, 5.6 10-8 and 1.08 10-7 mol g-1 min-1. The average calculated activation energies are respectively 89.2, 116.4 and 134.8 kJ/mol.Global kinetic parameters of degradation are also determined using dynamic thermogravimetric (TGA/DTGA) data. The model-fitting and model-free isoconversional methods are used to retrieve the kinetic parameters of the degradation process. The model-free isoconversional method can satisfactorily describe the dependence of the activation energy on the conversion and is recommended over the model-fitting methods for obtaining the reliable and consistent kinetic parameters of polymer degradation.

Thermal Degradation of Starch in Production of Environmentally Benign Flocculants. 2. Experiments and Process Identification

Experiments were carried out to produce biodegradable flocculants by phophorylation and heat treatment of corn starch at elevated temperatures in the dry state. The temporal change of molecular weight distribution was measured by HPSEC/MALLS/RI. To elucidate the mechanism and kinetics of degradation during this treatment a Markov-chain stochastic model was used. For this, five molecular weight intervals were defined between >32 10 6 and 2 10 6 Da with exponentially decreasing spans. The probabilities of mass fraction transitions among these intervals at different processing temperatures were determined by fitting the calculated molecular weight distributions to the experimental data. Examining the transition probabilities between various MW intervals, it was concluded that degradation took place gradually by multiple splits of molecules, resulting in stepwise transition of fragments from higher intervals to lower ones. From the values of the transition probabilities between different molecular weight intervals, and considering the evolution of molecular weight distributions during the process, it was concluded that an end-scission mechanism did not play a role in the studied system under the applied conditions. The degradation probability of starch molecules diminished with decreasing molecular weight and increased with the temperature of treatment. These dependences were described by an exponential relationship.

Xanthate‐Mediated Living Radical Polymerization of Vinyl Acetate in Miniemulsion

AbstractSummary: The MADIX/RAFT mechanism, employing a xanthate as the reversible chain‐transfer agent, has been shown to facilitate the living radical polymerization of vinyl acetate in miniemulsion. Methyl (ethoxycarbonothioyl)sulfanyl acetate (MESA) successfully mediated the polymerization which was initiated with either of the water‐soluble initiators 2,2′‐azobis{2‐[1‐(2‐hydroxyethyl)‐2‐imidazolin‐2‐yl]propane} dihydrochloride (VA‐060) or 2,2′‐azobis[2‐(2‐dimidazolin‐2‐yl)propane] dihydrochloride (VA‐044). The polymerizations exhibit living characteristics, demonstrated by the evolution of molecular weight distributions. The formulation of the miniemulsion produced stable latexes with no coagulum.The number‐average molecular weight and PDI as a function of monomer conversion for the RAFT miniemulsion polymerization of vinyl acetate.magnified imageThe number‐average molecular weight and PDI as a function of monomer conversion for the RAFT miniemulsion polymerization of vinyl acetate.

Ultrasonic degradation of polybutadiene and isotactic polypropylene

The ultrasonic degradation of polybutadiene and isotactic polypropylene in solution was studied at different temperatures and in different solvents. The time evolution of molecular weight distribution was determined experimentally through gel permeation chromatography. Degradation rate coefficients were determined from a model based on continuous distribution kinetics and assuming mid-point chain scission. The variation of rate coefficients with vapour pressure and kinematic viscosity was also investigated.

Influence of temperature on the ultrasonic degradation of poly(vinyl acetate) and poly(vinyl chloride)

AbstractThis study investigates the effect of temperature on the ultrasonic degradation of polyvinyl acetate and polyvinyl chloride in chlorobenzene. The time evolution of molecular weight distribution was determined using gel permeation chromatography. Continuous distribution kinetics was used to obtain the degradation rate coefficients. The rate coefficients decrease with increasing temperature, and this is attributed to the increase of vapor pressure and the decrease of kinematic viscosity. The degradation rate coefficient also changes sharply near the glass transition temperature, indicating that this factor may play a role in the degradation process. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 12: 2818–2822, 2003

Thermal degradation of poly (ε-caprolactone)

The thermal degradation kinetics of poly (ε-caprolactone) (PCL) in solution was investigated at various temperatures (170–245 °C). The degradation was also investigated by pyrolysis at various temperatures (280–330 °C). The time evolution of molecular weight distribution (MWD) was obtained using gel permeation chromatography. It was observed that in pyrolysis, PCL degrades by specific chain end scission by unzipping of monomers from the hydroxyl end of the polymer chains. In contrast, the degradation of PCL in solution is by random chain scission. A continuous distribution kinetics model is proposed to explain the observed behaviour under both conditions. The activation energy, determined from the temperature dependence of rate coefficients, was 61 kJ/mol and 201 kJ/mol for the degradation in solution and by pyrolysis, respectively.

Kinetics of Degradation of Polycarbonate in Supercritical and Subcritical Benzene

The degradation kinetics of polycarbonate (Poly (bisphenol A carbonate)) in supercritical and subcritical benzene was studied at various temperatures (523-618 K) at 50 atm. The degradation was also investigated in other solvents at 573 K and 50 atm. The time evolution of molecular weight distribution (MWD) was obtained by gel permeation chromatography and modeled with continuous distribution kinetics to obtain the degradation rate coefficients. The activation energy, determined from the temperature dependence of the rate coefficient, increased from 16.7 kcal/mol to 20.4 kcal/mol from the sub-critical to supercritical region of solvent. The degradation rate coefficients at the supercritical conditions were an order higher than the rate coefficients at subcritical conditions, indicating enhanced degradation at supercritical conditions. The Arrhenius plot showed a break at the supercritical transition point whereas the semi-logarithmic plot of rate coefficients with density of the reaction mixture showed a continuous linear variation.

Thermal degradation kinetics of para‐substituted poly (styrene peroxide)s in solution

AbstractThe thermal degradation of three polymeric peroxides of styrene monomers with substituents in the para position was studied at various temperatures (65, 75, 85, and 95°C). A continuous distribution model was used to evaluate the rate coefficients for the random‐chain and chain‐end scission degradation from the evolution of molecular weight distributions with time. The activation energy determined from the temperature dependence of the rate coefficients was in the range 18–22 kcal mol−1. This result suggests that the thermal degradation of polyperoxide is controlled by the dissociation of the O—O bonds in the polymer backbone. The thermal stability for poly(p‐methylstyrene peroxide) lies in between that of poly(p‐tert‐butylstyrene peroxide) (highest) and poly(p‐bromostyrene peroxide) (lowest). © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 957–961, 2002

Measurement of Initial Degree of Polymerization without Reactivation as a New Method To Estimate Rate Constants of Deactivation in ATRP

A new simple method has been developed for the estimation of deactivation rate constants in atom transfer radical polymerization using copper catalysts. This method is based on the principle of reverse ATRP and is conducted under an air atmosphere, using molecular oxygen as an oxidant for Cu(I) species. The deactivation rate constants for several different reactive copper complexes were estimated by this procedure, and the results are correlated with those obtained from the analysis of the evolution of molecular weight distribution with conversion and with competitive trapping reactions using nitroxides. The effect of temperature on these rate constants was also studied.