Molecular Weight Distribution Data Research Articles

Correlations of single‐point parameters of linear rheology and molecular weight distribution of polypropylene homo‐ and copolymers

AbstractFor various purposes, it is required to compress the shape of the molecular weight distribution (MWD) of polymers into a limited set of parameters. With increasing molecular weight and polydispersity, the MWD data obtained from chromatography become increasingly unreliable due to deficiencies in the high molecular weight region, making estimation via melt rheology more preferable. A number of empirical parameters obtained from melt rheology can be related back to MWD parameters. The target of this study is to establish the reliability of such relations for polypropylene homo‐ and copolymers. It is found that correlations between polydispersity from rheological crossover modulus and polydispersity via chromatography are not always valid. Therefore, the range of applicability must be kept in mind when attempting predictions based on these correlations because rheological measurements are sensitive to molecular characteristics in ways different from chromatography. The use of a modified polydispersity index is shown to be more reliable.

Modeling and Parameter Estimation for Gas‐Phase Polyethylene Product Properties Using Dynamic and Steady‐State Data

AbstractModels are developed for gas‐phase ethylene/1‐hexene copolymerization using a 3‐site hafnocene catalyst. The models accurately predict joint molecular weight distribution and copolymer composition data for 15 semibatch lab‐scale copolymerization runs and 6 steady‐state pilot‐plant copolymerization runs, respectively. Kinetic rate constants and activation energies, which are common to both models, are estimated for the three types of active sites for each reaction in the kinetic scheme. Using parameter subset selection and estimation techniques, it is found that 34 of the 61 parameters should be estimated from the data. Incorporating the pilot‐plant data allow for estimation of two parameters, a deactivation rate constant and a β‐hydride elimination activation energy, that are not estimable using the lab‐scale data alone. At the 95% confidence level, 25 of the 34 parameters are significantly different than zero, which is more than the 19 significant parameter estimates obtained from the lab‐scale data alone. Good fits to the data are obtained, as are reliable predictions for a validation run not used in parameter estimation.

Combining 13C‐NMR Triad Sequence Data with Joint Molecular Weight and Composition Data to Estimate Parameters in a Gas‐Phase Polyethylene Reactor Model

AbstractA three‐site metallocene catalyst is used in a gas‐phase semi‐batch reactor to produce ethylene/hexene copolymers. At the end of each batch, polyethylene (PE) is collected and analyzed to determine the carbon‐13 nuclear magnetic resonance (13C‐NMR) triad sequence distribution. Joint molecular weight (MW) and composition distribution data are obtained using gel permeation chromatography with an infrared detector (GPC‐IR). Data from ten experimental runs are used for kinetic parameter estimation. Using a mean‐squared error (MSE) selection methodology, 23 of the 36 model parameters are selected for estimation using the available polymerization rate and PE characterization data. The remaining parameters are held at initial guesses to avoid overfitting. Addition of the triad data to the parameter estimation problem allows for one additional parameter to be estimated and results in improved parameter estimates. Standard deviations of all but one of the estimated parameters decreased due to inclusion of triad data. The updated parameter estimates result in good fits for the triad data and for joint MW and composition data. The model accurately predicts four validation data sets not used for parameter estimation. The new model and its updated parameter estimates will be valuable for scaling up new polymer grades from laboratory‐scale to commercial‐scale.

Effect of drying method and process conditions on physicochemical and rheological properties of arabinoxylans extracted from corn-lime-cooking-liquor on a pilot plant scale

Corn-lime-cooking-liquor (nejayote), which is a pollutant wastewater from the corn-tortilla-industry, contains valuable products, such as arabinoxylans (AXs) and phenolics. Recently, an innovative process that employs enzymatic and ultrafiltration processes for recovering and purifying AXs from nejayote was described, although neither the drying methods nor the physicochemical and rheological properties of the recovered AXs by this method at the pilot plant scale have been studied. Nejayote from a batch artisanal process (NBAP) and from a continuous industrial process (NCIP) were compared with a corn-bran-hydrolysate (CBH) as sources for AXs obtention. Freeze drying (FD), spray drying (SD) and solvent drying (SoD) were assessed as processes for drying purified and concentrated AXs solutions. Regardless of the process, AXs obtained from nejayote contain 3 times less (0.30 mg/g) esterified ferulic acid (EFA) than did AXs from corn bran (1.01 mg/g) and thus fail to yield elastic gels upon oxidative cross-linking. Molecular weight distribution (MwD) and dynamic viscosity data show that AXs from nejayote are shorter than AXs from corn bran. In general, the drying method had no effect on the physicochemical and rheological properties of AXs, although additional purification using ethanol precipitation and SoD, eliminated low molecular weight oligosaccharides and residual salts resulting from the neutralization of the corn-lime-cooking-liquor. Spray drying seems to be the most cost-effective unit operation for the industrial production of AXs from nejayote without affecting their physicochemical characteristics.

When Mayo falls short (Ctr ≫ 1): the use of cumulative chain length distribution data in the determination of chain transfer constants (Ctr) for radical polymerizations

A method to determine chain transfer constants in free radical polymerizations that are >1 using molecular weight distribution data.

Molecular weight distribution of asphalt binders from Laser Desorption Mass Spectroscopy (LDMS) technique and its relationship to linear viscoelastic relaxation spectra

Asphalt binder is a complex viscoelastic hydrocarbon, whose performance depends upon interaction between its physical and chemical properties, both of which are equally important to the successful understanding of the material. In this research effort, a physico-chemical relationship is developed by utilizing the technique of Laser Desorption Mass Spectroscopy (LDMS) to relate the molecular structure of asphalt binders to its viscoelastic properties. The molecular weight distribution (MWD) data obtained from the LDMS technique is used to develop a relationship between number average molecular weight and width of relaxation spectrum of asphalt binders obtained from linear viscoelastic characterization using dynamic shear rheometer. The relationship shows that as the molecular weight of asphalt binders increase, they require more time to relax the developed stresses. Also, the shape descriptors of the molecular weight distribution suggest that asphalt binders possessing greater asymmetry and kurtosis require more time to relax the developed stresses.

Molecular Weight Distributions and Average Molecular Weights of Pyrolysis Oils from Oil Shales: Literature Data and Measurements by Size Exclusion Chromatography (SEC) and Atmospheric Solids Analysis Probe Mass Spectroscopy (ASAP MS) for Oils from Four Different Deposits

Molecular weight (MW) data for shale oils, including molecular weight distributions (MWDs) as well as average MWs, is difficult to find. A thorough literature review of MW data for shale oils from different pyrolysis processes, found scattered across a wide range of topics (or papers on various topics) and analyzed here, was carried out as part of the study. However, because the data are for oils produced under different conditions, and the exact pyrolysis conditions are sometimes not fully described, then the MW values generally are not directly comparable. Therefore, in the experimental part of the current study, average MWs and MWDs were measured for shale oils from four different oil shales (Green River in the western United States, Attarat Umm Ghudran in Jordan, Kukersite in Estonia, and Dictyonema in Estonia) obtained by retorting under identical pyrolysis conditions, using a standardized Fischer assay method. The main goal of the study, to measure the MWDs of the Fischer assay oils, was accomplished using size exclusion chromatography (SEC). The MWD data obtained was also compared to that from atmospheric solids analysis probe mass spectroscopy (ASAP MS). In addition, MWDs of industrial Kukersite shale oil from Kiviter and Galoter processes were evaluated for comparison. The MWDs of Fischer assay shale oils obtained in the current study ranged from 100 g mol–1 to 600 g mol–1. While the oils show comparable average MW values, the parameters describing the width and shape of MWDs were more dependent on the parent oil shale.

Chromophore Quench-Labeling: An Approach to Quantifying Catalyst Speciation As Demonstrated for (EBI)ZrMe2/B(C6F5)3-Catalyzed Polymerization of 1-Hexene

Chromophore-containing quench agents 2 and 3 enable quantitative active site counting and determination of the mass distribution of active catalyst polymeryls by refractive index (RI) and UV detected gel permeation chromatography (GPC) for the polymerization of 1-hexene catalyzed by (EBI)ZrMe2/B(C6F5)3. Time evolution of catalyst speciation data and the time profiles of monomer consumption, end-group generation, and bulk molecular weight distribution data have been analyzed by kinetic modeling to determine rate constants for initiation by insertion of hexene into a Zr–Me bond (ki), propagation (kp), chain transfer to form vinylidene (k1,2) and vinylene (k2,1) end groups, and reinitiation from a Zr–H bond (kr). Unlike previous models that assumed fast catalyst reinitiation, this analysis reveals that kr is considerably slower than kp; catalyst speciation data are critical to making this distinction. This study demonstrates that chromophore quench-labeling with 2 and 3 enables rapid, quantitative analysis o...

A Straightforward Estimation of Activation and Deactivation Parameters for ATRP Systems from Actual Polymerization Rate and Molecular Weight Distribution Data

The accuracy of a model prediction relies heavily on the quality of the parameters used. Some of the available methods to estimate the activation and deactivation rate constants in atom transfer radical polymerization (ATRP) are done in the absence of monomer, hence they may not be representative of the polymerization conditions. Others offer great accuracy but requires data that are not commonly measured in experiments. In this study, a simple method is proposed to estimate activation and deactivation rate constants through correlating the recently reported theoretical equations with experimental data of monomer conversion and polymer molecular weight dispersity. The kinetics and dispersity equations used are straightforward and explicit, thus can be easily calculated. Only two parameters (activation and deactivation rate constant) are involved in the correlation of two data sets without any other adjustable parameters. In addition, the experimental data required are some of the most often measured quantities in polymerization, thus no additional experiments or measurements are required. Since the conversion and dispersity are obtained from actual polymerization, the reaction rate constants estimated are representative of the real reaction conditions. The applicability of this method is demonstrated by estimating parameters using reported experimental data of ATRP of methyl methacrylate conducted at various conditions. image

Direct Mapping of RAFT Controlled Macromolecular Growth on Surfaces via Single Molecule Force Spectroscopy.

Single molecule force spectroscopy (SMFS) is employed to gain insight into reversible addition-fragmentation chain transfer (RAFT) polymerization processes with living characteristics on glass surfaces. Surface-initiated (SI)-RAFT was selected to grow poly(hydroxyethyl methacrylate) (PHEMA). After aminolysis of the RAFT chain termini, thiol moieties serve as anchoring points for the gold tip of an atomic force microscope. The results allow to directly monitor the macromolecular growth of the surface-initiated polymerization. The obtained SMFS-based molecular weight distribution data of the polymers present on the surface indicate that the RAFT chain extension proceeds linearly with time up to high conversions. The current study thus adds SMFS as a valuable tool for the investigation of SI-RAFT polymerizations.

Real-Time Correction of Molecular Weight Distribution Model Based on the Field-Measurable Moments

Polymer molecular weight distribution (MWD) lacks the on-line measurement instrument. Soft sensing technology is the main method to establish its data model and give prediction on-line. The soft sensing model will be inevitably unmatched to the real process during being used in the practical industrial process. In order to improve the precision of soft sensing model, the MWD model needs to be corrected in real time or periodically. Here, the orthogonal polynomials combined neural network, i.e. soft sensing model, is used to simulate the real-time changes of MWD. Since molecular weight distribution is online un-measurable, the measurable variables, such as average molecular weight and low-order moment statistics, are used to adjust the MWD model in real time. Furthermore, these historical collected MWD data also can be used to correct this model periodically.

Advanced bamboo industry wastewater treatment through nanofiltration membrane technology

The present study reports the results of nanofiltration (NF) for treating COD, ammonium, color, and conductivity of bamboo industry wastewater (BIWW). The influence of operational parameters such as trans-membrane pressure (TMP), influent concentration, pH, permeate flux and operating temperature on the membrane rejection efficiencies were investigated. Molecular weight distribution (MWD) and gas chromatography–mass spectrometer (GC–MS) analyses were also performed in the study. Results demonstrated that the color obtained during rejection was higher than 99% regardless of any operating parameter. However, permeate flux, COD, ammonium, and conductivity rejections were affected by operational parameters’ discrepancies. The operational changes along with the polarization concentration and accumulative mass had mainly influenced the effluent water quality. The permeate flux was recorded higher than 40 L/m2 h, while the TMP was around 7 bar. Moreover, during the experiment, 90, 84, and 83% rejection of COD, ammonium, and conductivity, respectively, were observed. MWD data indicated that the NF module effectively removed most of the macromolecular organics and GC–MS analysis revealed the majority of organic compounds in BIWW were rejected by NF membrane.

Design and optimization of an efficient enzymatic extrusion pretreatment for Chinese rice wine fermentation

Chinese rice wine, produced by simultaneous saccharification and fermentation (SSF), has an uneconomic, time-consuming and environment-unfriendly pretreatment. In this study, an enzymatic extrusion pretreatment was applied to manufacture Chinese rice wine. Response surface methodology (RSM) was used to investigate the effect of process parameters namely barrel temperature (BT), moisture content (MC), and α-amylase concentration (AC) on the alcoholic degree of rice wine. Statistical analyses revealed that the experimental data were adequately fitted into the second-order polynomial model with a high coefficient of determination (R2) of 0.97. It also showed that MC had the most significant effect on the alcoholic degree among the three parameters. Starch molecular weight distribution data indicated that the alcoholic degree was closely related to the oligosaccharides forming during enzymatic extrusion. Total of amino acids (AA) in the extrusion-processed wine was 41% higher than that in the traditional one. These results suggest that the enzymatic extrusion pretreatment, instead of the traditional one, is feasible for Chinese rice wine production.

Obtaining the kinetic function of depolymerization from evolving molecular weight distribution data–an inverse problem

Depolymerization of macromolecules is generally regarded as a first order process with a kinetic function that depends on the molecular weights of the fragmenting molecule and fragmentation products. This article describes a computation scheme for obtaining the kinetic function from observed molecular weight distribution (MWD) data. The integro‐differential equation used by most investigators to compute MWD with some assumed kinetic function is reformulated as an inverse problem in which the kinetic function is treated as the unknown to be extracted from evolving MWD data. A numerical procedure based on two consecutive applications of Tikhonov regularization is developed to solve this inverse problem. It gives the kinetic function as the solution of a set of linear algebraic equations. Implementation of this procedure is described in full and its performance is assessed by applying it to simulated MWD data. A number of issues associated with discretization and regularization are discussed. © 2012 American Institute of Chemical Engineers AIChE J, 59: 912–922, 2013

“True” Concentration Determination Using a Concentration and Composition Sensitive Infrared Detector for Molecular Weight Characterization of Polyolefins

AbstractSummary: The infrared detector with a composition channel provides the ability to construct “true” concentration of the polyethylene‐polypropylene copolymer and polymer blends to compensate the different infrared responses to each component. Using this “true” concentration constructed by the infrared detector, triple detector gel permeation chromatography (GPC) could generate conventional (by column calibration) and absolute (by laser light scattering) molecular weight and molecular weight distribution data comparable to data obtained by using the concentration obtained by a differential reflex index concentration detector. In addition to its unique feature of in‐situ composition detection, the infrared detector in its mass detection mode possesses the advantages of faster equilibrium time, more stable baseline, less effect from temperature variation, and low sensitivity to moisture or air in the solvent.

Cu(0) mediated polymerization in toluene using online rapid GPC monitoring

AbstractPolymerization of methyl acrylate (MA) catalyzed by Cu(0) is carried out in toluene using a range of alcohols and phenol as additives to facilitate the reaction. The polar/coordinating additives promote disproportionation of Cu(I) to Cu(0), the proposed active species in single electron transfer living radical polymerization (SET‐LRP), and Cu(II) whilst toluene maintains solubility of the reagents and products. In this work, the use of alcohols as additives is optimized. Polymerizations are monitored in real time using rapid chromatography to obtain conversion and molecular weight distribution data without the necessity of manual sampling. Rapid gel permeation chromatography with low angle laser light scattering detection is shown to be a viable method of obtaining molecular weight distribution data in real time compared with conventional analytical techniques. Moreover, the changes in CuBr2 concentration during SET‐LRP reactions are monitored online using a photodiode array detector. Finally, the kinetics of SET‐LRP of MA using an ultra pure highly porous Cu(0) is performed and a detailed discussion on the role of Cu(II) is provided. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011

Synthesis of poly(methyl methacrylate) via reverse atom transfer radical polymerization catalyzed by FeCl3/lactic acid

AbstractReverse atom transfer radical polymerization (RATRP) of methyl methacrylate (MMA) with azobisisobutyronitrile (AIBN)/FeCl3/lactic acid as initiating system was successfully carried out in N,N‐dimethylformamide (DMF) for the first time. Kinetics as well as molecular weight distribution data indicated towards the controlled nature of polymerization. The polymerization not only showed the best control of molecular weight and its distribution but also provided a rather rapid reaction rate with the molar ratio of [MMA]:[AIBN]:[FeCl3]:[lactic acid] = 300 : 1 : 1 : 2. The polymerization rate increased with increasing the polymerization temperature. The apparent activation energy was calculated to be 47.90 kJ/mol. The rate of polymerization in DMF was faster than that in acetonitrile, cyclohexanone, toluene, and xylene. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Biodegradation of oxo‐biodegradable polyethylene

AbstractBiodegradation of polyethylene and oxo‐biodegradable polyethylene films was studied in this work. Abiotic oxidation, which is the first stage of oxo‐biodegradation, was carried out for a period corresponding to 4 years of thermo‐oxidation at composting temperatures. The oxidation was followed by biodegradation, which was achieved by inoculating the microorganism Pseudomonas aeruginosa on polyethylene film in mineral medium and monitoring its degradation. The changes in the molecular weight of polyethylene and the concentration of oxidation products were monitored by size exclusion chromatography and Fourier transform infrared (FTIR) spectroscopy, respectively. It has been found that the initial abiotic oxidation helps to reduce the molecular weight of oxo‐biodegradable polyethylene and form easily biodegradable product fractions. In the microbial degradation stage, P. aeruginosa is found to form biofilm on polymer film indicating its growth. Molecular weight distribution data for biodegraded oxo‐biodegradable polyethylene have shown that P. aeruginosa is able to utilize the low‐molecular weight fractions produced during oxidation. However, it is not able to perturb the whole of the polymer volume as indicated by the narrowing of the polymer molecular weight distribution curve toward higher molecular fractions. The decrease in the carbonyl index, which indicates the concentration of carbonyl compounds, with time also indicates the progress of biodegradation. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Polymerization of methyl methacrylate with Nickel(II)α‐benzoinoxime complex

AbstractPolymerizations of methyl methacrylate (MMA) monomer initiated by a novel Ni(II)α‐benzoinoxime complex have been achieved under homogeneous conditions in the 25–60°C temperature range. The activity for polymerization increases with reaction temperature and by carrying out the polymerization in solution of low‐polarity solvents without any induction time. The obtained polymers have weight‐average molecular weights about 105 and slight broad polydispersity indexes (2.2 ≤ Mw/Mn ≤ 3.3). Dependence of rate constants polymerization and decomposition of initiator (kapp and kd, respectively) on temperature was investigated and activation parameters were computed from Arrhenius plot. 1H‐NMR analysis of PMMA revealed a syndio‐rich atactic microstructure in agreement with conventional radical process. Radical scavenger TEMPO effect together with microstructure and molecular weight distributions data supported that the polymerization proceed via free radical mechanism. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

Abiotic Oxidation Studies of Oxo-biodegradable Polyethylene

The best approach to induce oxo-biodegradation in polyethylene is the use of special additives known as pro-oxidants. Pro-oxidants accelerate abiotic oxidation and subsequent polymer chain cleavage rendering the product apparently more susceptible to biodegradation. In this work, the abiotic oxidation is studied to understand how the addition of nanoclay affects the oxidation rate and the degradation mechanism of oxo-biodegradable polyethylene. In order to achieve this, the following materials were used in this study: (1) polyethylene (PE), (2) oxo-biodegradable polyethylene (OPE), (3) polyethylene nanocomposite (PENac), and (4) oxo-biodegradable polyethylene nanocomposite (OPENac). Wide-Angle X-ray scattering (WAXS) and Transmission Electron Microscopy (TEM) studies reveal that grafting in the preparation of composites helps to achieve mixed intercalated/exfoliated morphology in PENac and OPENac. Abiotic oxidation was carried out in an oven for a period of 14 days at 70 °C with air supply. The effect of abiotic oxidation was evaluated by measuring the changes in tensile strength, elongation at break, carbonyl index and molecular weight. Results show that OPE and OPENac are more susceptible to oxidation than PENac. The molecular weight distribution data obtained from GPC reveal that the addition of nanoclay does not alter the oxidation mechanism in OPE significantly.