Entire Molecular Weight Distribution Research Articles

Transfer Learning of Full Molecular Weight Distributions via High-Throughput Computer-Controlled Polymerization.

The skew and shape of the molecular weight distribution (MWD) of polymers have a significant impact on polymer physical properties. Standard summary metrics statistically derived from the MWD only provide an incomplete picture of the polymer MWD. Machine learning (ML) methods coupled with high-throughput experimentation (HTE) could potentially allow for the prediction of the entire polymer MWD without information loss. In our work, we demonstrate a computer-controlled HTE platform that is able to run up to 8 unique variable conditions in parallel for the free radical polymerization of styrene. The segmented-flow HTE system was equipped with an inline Raman spectrometer and offline size exclusion chromatography (SEC) to obtain time-dependent conversion and MWD, respectively. Using ML forward models, we first predict monomer conversion, intrinsically learning varying polymerization kinetics that change for each experimental condition. In addition, we predict entire MWDs including the skew and shape as well as SHAP analysis to interpret the dependence on reagent concentrations and reaction time. We then used a transfer learning approach to use the data from our high-throughput flow reactor to predict batch polymerization MWDs with only three additional data points. Overall, we demonstrate that the combination of HTE and ML provides a high level of predictive accuracy in determining polymerization outcomes. Transfer learning can allow exploration outside existing parameter spaces efficiently, providing polymer chemists with the ability to target the synthesis of polymers with desired properties.

Elucidating pathways of polypropylene chain cleavage and stabilization for multiple loop mechanical recycling

AbstractMechanical recycling is a decisive contribution for a sustainable circular economy of polypropylene (PP) but faces the challenge of processing‐induced and use‐phase accumulated molecular damage, exacerbated by multiple loop recycling. In this contribution, the molecular origin of degradation of PP under up to 30 repetitive reprocessing loops is analyzed together with the influence of stabilization, and processability data linked to changes of the entire molecular weight distribution. By comparison of experiments with simple Monte Carlo simulations, a coupled mechanism of random scission and shear‐induced cleavage can be inferred, while stabilizing additives effectively protect the material from progressing along this combined degradation pathway.

Relationship between failure strain, molecular weight, and chain extensibility in biodegradable polymers

Prior to degradation, biocompatible polymers exhibit ductile behaviour and yield stress offers a suitable design approach. However, as degradation proceeds the material transitions to a brittle failure mode, suggesting a more conservative design approach is necessary. Here, we predict the evolving ductility of biodegrading polymers, concentrating on the relationship between molecular weight and failure strain, εf, in poly (lactic acid). Several datasets are chosen from literature to explore the relationship, with an overview of the experimental techniques provided. Failure criteria are proposed and examined alongside these datasets: the first assumes εf is related to the finite chain extensibility of an average chain; the second introduces an exponential empirical trend; the third proposes a modified extensibility criterion (based on the first criterion) that considers the entire molecular weight distribution; and the fourth offers an alternative to the third by considering the effect of chain scissions. Combining the failure criteria with a previously introduced time-dependent kinetic scission model provides results as a function of degradation duration. The predictions obtained can offer insight into material failure, particularly at advanced stages of degradation.

Lignin Stabilization and Carbohydrate Nature in H-transfer Reductive Catalytic Fractionation: The Role of Solvent Fractionation of Lignin Oil in Structural Profiling.

Reductive Catalytic Fractionation (RCF) of lignocellulosic materials produces lignin oil rich in monomer products and high-quality cellulosic pulps. RCF lignin oil also contains lignin oligomers/polymers and hemicellulose-derived carbohydrates. The variety of components makes lignin oil a complex matrix for analytical methods. As a result, the signals are often convoluted and overlapped, making detecting and quantifying key intermediates challenging. Therefore, to investigate the mechanisms underlining lignin stabilization and elucidate the structural features of carbohydrates occurring in the RCF lignin oil, fractionation methods reducing the RCF lignin oil complexity are required. This report examines the solvent fractionation of RCF lignin oil as a facile method for producing lignin oil fractions for advanced characterization. Solvent fractionation uses small volumes of environmentally benign solvents (methanol, acetone, and ethyl acetate) to produce multigram lignin fractions comprising products in different molecular weight ranges. This feature allows the determination of structural heterogeneity across the entire molecular weight distribution of the RCF lignin oil by high-resolution HSQC NMR spectroscopy. This study provides detailed insight into the role of the hydrogenation catalyst (Raney Ni) in stabilizing lignin fragments and defining the structural features of hemicellulose-derived carbohydrates in lignin oil obtained by the H-transfer RCF process.

Asymmetrical flow field-flow fractionation combined with liquid chromatography enables rapid, quantitative, and structurally informative detection of resistant starch

Resistant starch (RS) is one kind of biomacromolecules with prebiotic effects. Nowadays, it is still a challenge to characterize structure and content of RS over entire molecular weight (Mw) distribution. In this study, a combined technique of asymmetrical flow field-flow fractionation (AF4) and liquid chromatography (LC) for the accurate structure characterization and quantitative analysis of RS was developed. AF4 coupled online with multiangle light scatting (MALS) and differential refractive index (dRI) detectors (AF4-MALS-dRI) was used to characterize the structural information (radius of gyration and Mw) and content of RS with Mw larger than 5 kDa. Meanwhile, RS was characterized by scanning electron microscopy, X-ray diffraction, and Fourier transform infrared spectroscopy. The glucose content in the digested starch solution was quantitatively determined using LC. The results demonstrated that AF4-LC is a simple and rapid method for structurally informative detection and quantitative analysis of RS over entire Mw distribution.

A revised relationship between molecular weight and reduced angular frequency in δ-method applied to unmodified petroleum bitumens

The δ-method has been developed to estimate molecular weight distributions of bitumens from phase-angle master curves. The method uses a correlation between the cross-over frequency(ωC) and the molecular weight (MW) that was developed from average MW measured by vapour pressure osmometry. This study proposes a revised correlation whose parameters have been calculated from Gel Permeation Chromatography (GPC), which can be conducted at a low level of dilution preserving the interactions in the bitumen bulk. Furthermore, data from the GPC allow the optimisation of the parameters considering the entire MW distribution (MWD), thus improving the predictive capability of the method. Three unmodified petroleum bitumens at different levels of ageing and three rheological models were used in the optimisation. Two groups of parameters were identified; one for hard (e.g. Pen 35-50) and another one for soft-medium bitumens (e.g. Pen 50–70 or Pen 70-100). The apparent-MWDs (A-MWDs) calculated with the new parameters show improved correlation with the respective distributions and average molecular weight from GPC.

Detection of Surface Enrichment Driven by Molecular Weight Disparity in Virtually Monodisperse Polymers.

The preference for a shorter chain component at a polymer blend surface impacts surface properties key to application-specific performance. While such segregation is known for blends containing low molecular weight additives or systems with large polydispersity, it has not been reported for anionically polymerized polymers that are viewed, in practice, as monodisperse. Observations with surface layer matrix-assisted laser desorption ionization time-of-flight mass spectrometry (SL-MALDI-ToF-MS), which distinguishes surface species without labeling and provides the entire molecular weight distribution, demonstrate that entropically driven surface enrichment of shorter chains occurs even in low polydispersity materials. For 6 kDa polystyrene the number-average molecular weight (Mn) at the surface is ca. 300 Da (5%) lower than that in the bulk, and for 7 kDa poly(methyl methacryalate) the shift is ca. 500 Da. These observations are in qualitative agreement with results from a mean-field theory that considers a homopolymer melt with a molecular-weight distribution matched to the experiments.

A Thorough Study on the Molecular Weight Distribution in Natural Asphalts by Gel Permeation Chromatography (GPC): The Case of Trinidad Lake Asphalt and Asphalt Ridge Bitumen

The roadway performance is chiefly governed by the chemical composition of asphalt, which in turn depends on the molecular weight distribution in this product. Gel permeation chromatography is one of the most powerful and convenient analytical technique available for characterizing the entire molecular weight distribution of a bitumen. Molecular weight and polydispersity of two natural asphalts viz. Trinidad Lake asphalt (TLA) and Asphalt Ridge bitumen (ARB) have been determined. The number average molecular weight (Mn) of TLA was 893, whereas that of ARB was 993. It is predicted that TLA will deliver a smoother and higher-quality pavement than does ARB.

How good is CuAAC “click” chemistry for polymer coupling reactions?

ABSTRACT1H NMR and SEC analyses are used to investigate the overall efficiency of Copper Catalyzed Azide Alkyne Cycloaddition (CuAAC) “click” coupling reactions between alkyne‐ and azide‐terminated polymers using polystyrene as a model. Quantitative convolution modeling of the entire molecular weight distribution is applied to characterize the outcomes of the functional polymer synthesis reactions (i.e., by atom transfer radical polymerization), as well as the CuAAC coupling reaction. Incomplete functionality of the azide‐terminated polystyrene (∼92%) proves to be the largest factor compromising the efficacy of the CuAAC coupling reaction and is attributed primarily to the loss of terminal bromide functionality during its synthesis. The efficiency of the SN2 reaction converting bromide to azide was found to be about 99%. After taking into account the influence of non‐functional polymer, we find that, under the reaction conditions used, the efficiency of the CuAAC coupling reaction determined from both techniques is about 94%. These inefficiencies compromise the fidelity and potential utility of CuAAC coupling reactions for the synthesis of hierarchically structured polymers. While CuAAC efficiency is expected to depend on the specific reaction conditions used, the framework described for determining reaction efficiency does provide a means for ultimately optimizing the reaction conditions for CuAAC coupling reactions. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018, 56, 75–84

Tunable Large Pore Mesoporous Carbons for the Enhanced Adsorption of Humic Acid.

Tunable large pore soft templated mesoporous carbons (SMC) were obtained via the organic self-assembly of resorcinol/formaldehyde with the triblock copolymer F127 and by investigating the effect of carbon precursor to surfactant (p/s) ratio and carbonization temperature on the material characteristics. The p/s ratio and carbonization temperature were varied respectively from 0.83 to 0.25 and from 400 to 1200 °C. The resulting SMCs had various average pore sizes, tunable from 7 up to 50 nm. At lower p/s ratios, the pore size increased, pore size distributions broadened, and pore volumes increased. An increase of hydrophobicity was observed at elevated carbonization temperatures. A 2D hexagonal ordered SMC with a narrow pore size distribution was obtained at a ratio of 0.83. Lower ratios (0.5 and 0.25) transformed into disordered porous carbons containing micropores, mesopores, and even macropores. The SMCs were tested for adsorption of a large organic molecule, humic acid (HA), from water. The material characteristics that significantly affected HA adsorption capacity were pore size and mass % (wt %) carbon. The novel SMCs showed an unprecedented high adsorption of HA in the entire molecular weight distribution range. SMCs with large mesopores resulted in higher maximum adsorption capacities and improved HA adsorption kinetics compared to activated carbon.

The Role of Transesterification in SnOct2‐Catalyzed Polymerizations of Lactides

l‐lactide or meso‐lactide are polymerized either at 120 °C where the polymerization process of l‐lactide is accompanied by crystallization, or at 180 °C where poly(l‐lactide) remains in the molten state. Polymerizations at 120 °C initially yield even‐numbered chains (with respect to lactic acid units) having relatively low dispersity, but the fraction of odd‐numbered chains increases with time and the entire molecular weight distribution changes. Traces of cyclics are only formed after 7 d. Polymerizations at 180 °C yield equilibrium of even and odd‐numbered chains from the beginning, but at low monomer/initiator ratios and short reaction times (<4 h) cyclics are again not formed. They appear at longer reaction times and entail higher dispersities. The results are discussed in terms of five different transesterification mechanisms. image

High Temperature Semibatch Free Radical Copolymerization of Styrene and Butyl Acrylate

AbstractSummary: High temperature semibatch free radical solution copolymerizations of n‐butyl acrylate (BA) and styrene (ST) were carried out over a range of copolymer composition. The significant increase in experimental polymer weight‐average molecular weight with time, as well as the shift in the entire polymer molecular weight distribution, is explained by assuming fast β‐scission of BA midchain radicals with an adjacent styrene unit, followed by subsequent addition of the resultant macromonomer to growing radicals. A mechanistic model including backbiting and β‐scission, macronomer incorporation, long‐chain branching, and propagation and termination penultimate effects was constructed in Predici; the model provides a good representation of the experimental data using rate coefficients taken from literature.

Control of molecular weight distribution of polyethylene in gas-phase fluidized bed reactors

This paper presents a feasibility study of the broadening of polyethylene molecular weight distribution produced using a multisite Ziegler-Natta catalyst in a fluidized-bed reactor. A nonlinear model predictive control algorithm, applied to a validated model of the reactor, is used for the on-line control of the entire molecular weight distribution of the produced polymer. Control of a target chain-length distribution is achieved by selecting a collection of points in the distribution and using them as set points for the control algorithm. An on-line Kalman filter is used to incorporate infrequent and delayed off-line molecular weight measurements. Through simulation the control algorithm is evaluated, under tracking conditions as well as plant-model mismatch. The results demonstrate that the control algorithm can regulate the entire molecular weight distribution with minimum steady state error. However, the efficiency of this approach is highly dependent on the dynamics of hydrogen inside the reactor.

Control of Molecular Weight Distribution and Density of Polyethylene in Gas Phase Reactors

This paper addresses the polyethylene quality transition in gas phase fluidized bed reactors using feedback control. Specifically, a nonlinear model predictive controller is utilized to steer the polymer density and the entire molecular weight distribution to follow predefined targets. The hydrogen and co-monomer inflows are used as the manipulated variables. In this work, the molecular weight distribution is modeled as a function of the reaction kinetics and hydrogen to monomer ratio. The simulation results indicated successful implementation of the control algorithm to attain the desired molecular weight distribution and density, even with the existence of modeling errors. Economically undesirable operations such as excessive purge and/or reduced production rate are avoided by the limited use of monomer and catalyst inflows.

Broadening the polyethylene molecular weight distribution by controlling the hydrogen concentration and catalyst feed rates

This paper discusses the control of an industrial gas-phase polyethylene reactor to produce a desired molecular weight distribution (MWD) of the polymer. The controller objective is to regulate online the entire molecular weight distribution by either manipulating the hydrogen content inside the reactor or coordinating the feed rates of two different types of catalysts. In this work, the molecular weight distribution is modeled as a function of the reaction kinetics and hydrogen to monomer ratio. Nonlinear model predictive controller (NLMPC) algorithm is used to maintain the desired molecular weight distribution online. The closed-loop simulations indicated the effectiveness of NLMPC to achieve its goal even in the presence of modeling errors. Moreover, the results showed that, altering the hydrogen concentration solely can produce the required polymer quality provided that an efficient mechanism is available to readily alter the hydrogen composition. Alternatively, the desired MWD can also be guaranteed with proper manipulation of the catalyst feed rates while the other process inputs are kept constant.

Molecular Weight Distribution (Soluble and Insoluble Fraction) in Emulsion Polymerization of Acrylate Monomers by Monte Carlo Simulations

A Monte Carlo simulation model for the semibatch emulsion polymerization of acrylate monomers was developed. The model accounts for the complex kinetics of acrylate monomers (presence of chain-end and midchain radicals), the compartmentalization of emulsion polymerization systems and the development of the entire molecular weight distribution (MWD) as well as the branching density. It was found that the MWD produced in the semibatch process was bimodal (a sharp and extremely high Mw peak and a broad and lower Mw mode), the midchain radicals were predominant during the polymerization, and most of the branches were short and produced by the backbiting mechanism. Interestingly, the bimodality of the MWD could be avoided under certain experimental conditions (those who led to a decrease of particles with more than two radicals), but this did not prevent the formation of polymer chains of molecular weights above 107 g/mol (which are typically insoluble). The model also shows the importance of the presence of midchain radicals in the microstructure of the polymer formed. Thus, the fraction of termination by combination and disproportionation of the midchain radicals had a significant influence on the location of the high molecular weight peak. The predictions of the Monte Carlo model were in good agreement with experimental data and a previously developed deterministic mean-field theory model for the seeded semibatch emulsion polymerization of n-butyl acrylate.

Influence of molecular weight distribution on flow properties of commercial polyolefins

AbstractThe aim of this work is to investigate the effects of molecular weight distribution on some conventional flow properties of polyolefins like melt flow index, melt flow ratio, and power law index. The study is designed in two steps. First, the statistical correlation analysis was carried out for proper choice of input variables for each output property and to find the most relevant mathematical forms of the considered parameters for the modeling section. Then the considered property was correlated to the entire molecular weight distribution using spline functions. The best fit was achieved by variation of the number of spline nodes and their values. The proposed methodology is able to be coupled with a polymerization model to correlate the polymerization conditions to the final properties of the product and design a polymerization control loop. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

Effect of Rheological Strain Hardening on Extrusion Blown Film of Polyvinylidene Fluoride

In this work the effect of strain hardening on poly-vinylidene fluoride (PVDF) extrusion blown film is investigated. Controlled long chain branching is introduced via a multi-functional initiator to produce two PVDF samples with different molecular weight and chain architecture. The branched samples are compared to two reference resins having identical molecular weight and no chain branching. All samples are characterized by size exclusion chromatography (SEC) coupled with triple detection system comprising a Differential Refractive Index (DRI) detector, Intrinsic Viscosity (IV) detector, and Multi-Angle Laser Light Scattering (MALLS) detector, to determine their molecular weights and their distribution as well as to detect chain branching via measuring the coil size in dilute solution. The rheological properties are determined using oscillatory measurement and melt strength at 230°C while extensional viscosity measurements are conducted at 180°C to determine strain hardening at different extension rates. The resins are evaluated using a small scale extrusion blown film set-up to determine the blow-up ratio and the minimum thickness achievable. The characterization results show that the control samples are different in molecular weight and almost identical in the polydispersity index (Mw/Mn). The branched samples, however, have higher molecular weight and a slightly broader molecular weight distribution. Light scattering data together with inherent viscosity data show that the branched samples have a lower radius of gyration (RG) and inherent viscosity (IV) over the entire molecular weight distribution confirming chain branching. The rheological properties in oscillatory measurements show that the branched samples exhibit almost identical viscosities as the control samples. However, a broader transition from the Newtonian to the non-Newtonian region for the branched sample is observed confirming the SEC—MALLS results. This is corroborated using extensional viscosity and melt strength measurements, which show a significant strain hardening and an increase in melt strength, respectively. Blown film experiments show that the samples containing chain branching could be processed under similar process conditions as the control samples, and with a higher blow up ratio thereby achieving 5 μm film thickness with high clarity.

Correlating Polymer Parameters to the Entire Molecular Weight Distribution: Application to the Melt Index

AbstractSummary: A method that takes into account the entire molecular weight distribution (MWD) for the prediction of polymer point properties and/or indexes is presented. The method is based on the convolution of the polymer mass molecular weight distribution and an empirical kernel function. Thus, the problem of relating the polymers properties to the MWD is reduced to the estimation of this empirical function. The proposed methodology is able to successfully predict melt indexes (MI) of a set of poly(propylene) samples. magnified image

Development of a unified framework for calculating molecular weight distribution in diffusion controlled free radical bulk homo-polymerization

In the present work, two different approaches to model diffusion controlled free radical polymerization, namely the free volume model and the entanglement theory are compared. These approaches are applied to methyl methacrylate bulk polymerization in a batch reactor to calculate the conversion, total radical concentration, the number and weight average molecular weights as well as the entire molecular weight distribution as a function of the polymerization time and the process conditions. All the diffusion-controlled phenomena were taken into account, including gel, glass and cage effects as well as residual termination. The molecular weight distribution is calculated by direct numerical integration of a large system of non-linear ordinary differential equations describing the conservation of the mass of macromolecular species in the batch reactor. Model predictions are in good agreement with available experimental data for conversion, number and weight average molecular weights as well as the entire molecular weight distribution, thus justifying the ability of these models to describe the main issues of the diffusion-controlled free radical polymerization.