Molecular Weight Distribution Information Research Articles

Hybrid deterministic and stochastic approach for dynamic simulation of photoinduced atom-transfer radical polymerization processes with microscopic resolution

Among the various polymerization mechanisms available for producing polymers, photoinduced atom-transfer radical polymerization (photoATRP) stands out as a promising technique. By utilizing light as an external stimulus, photoATRP facilitates the production of well-defined polymers with precise distributions. The demand for advanced polymeric materials synthesis necessitates a deep understanding of polymer chains at the molecular level. As molecular weight distribution (MWD) is a key quality index of polymers, developing models with embedded MWD information holds significance for process design and optimization tasks. In this work, an accelerated hybrid deterministic and stochastic approach is proposed for simulating dynamic photoATRP processes. The proposed approach demonstrates computational efficiency and flexibility, enabling precise predictions for the evolution of both macroscopic and microscopic properties of polymers. An application to a batch photoATRP system model is presented to illustrate the validity and performance of the proposed hybrid approach.

Cascaded encryption/decryption using digital polymer toward high-level information security

Encoding information in digital polymers has become a promising approach for data storage in recent years. High-level information security is crucial for practical application, which is still challenging in digital polymers due to the lack of efficient techniques. Herein, we proposed a cascaded encryption/decryption approach that uses Morse-coded digital polymers to encipher sequence information as well as molecular weight distribution (MWD) information. The MWD information could be deconvoluted in size exclusion chromatography (1st decryption), whereas the 2nd decryption was performed in tandem mass spectrometry. The correct information could only be accessed after two successive decryption processes, thus providing high-level information security. Furthermore, this cascaded strategy was applied to a printing ink formulation for multidimensional anti-counterfeiting applications toward high-value artwork.

A novel method for the direct detection of light stabilizer Tinuvin 622 in polymer additives by gel permeation chromatography combined with multi-angle laser light scattering

Tinuvin 622, an oligomeric light stabilizer, is widely used in plastics to reduce light and heat induced degradation and extend their service life, therefore its detection is of great importance for quality control of plastic products. However, the classical analytical methods of Tinuvin 622, such as chromatography and mass spectrometry, are difficult to achieve direct qualitative and quantitative analysis, and simultaneously to obtain the molecular weight and molecular weight distribution information. Herein, we propose for the first time the combination of gel permeation chromatography with multi-angle laser light scattering as a simple and direct method to detect Tinuvin 622 in polymers and simultaneously to obtain its molecular weight distribution information. The linearity of the method was good in the concentration range of 0.1–5.0 mg/mL Tinuvin 622 with correlation coefficient (R2 = 0.9999), and the recoveries of Tinuvin 622 at three addition levels ranged from 94.0% to 98.7%, with relative standard deviations of no more than 1.73%. The proposed method has been successfully used to detect Tinuvin 622 in actual samples of polymer additives. Compared with existing analytical methods, Tinuvin 622 has a single peak shape in our method, which is easy to identify and quantify accurately; more importantly, our method can simultaneously characterize the molecular weight and molecular weight distribution of Tinuvin 622, which makes up for the shortcomings of other approaches and provides a new tool for quality monitoring of polymer additives.

Evaluation of the Degree of Polymerization of the Proanthocyanidins in Cranberry by Molecular Sieving and Characterization of the Low Molecular Weight Fractions by UHPLC-Orbitrap Mass Spectrometry.

4-dimethylammino-cinnamaldehyde (DMAC) assays quantify total proanthocyanidins (PACs) but do not provide qualitative PAC molecular weight distribution information and cannot discriminate between A- and B-type PACs. We developed an efficient method for assessing PAC molecular weight distributions. The PACs from three commercial cranberry extracts (A1–A3) were fractionated by molecular sieves with cut-offs of 3, 10, 30, 50, and 100 kDa, and each fraction was analyzed by DMAC assays. A1, A2, and A3 contained 27%, 33%, and 15% PACs, respectively. Approximately 28 PACs, 20 flavonols, and 15 phenolic acids were identified by UHPLC-DAD-Orbitrap MS in A1 and A3, while A2 contained only flavan-3-ols. Epicatechin was the main monomer in A1 and A3, and catechin was the main in A2. Procyanidin A2 was the main dimer in A1 and A3, representing more than 85% of the total dimers, while it constituted approximately only 24% of A2. A1 and A3 contained quercetin, isorhamnetin, myricetin, and their glycosides, which were totally absent in A2. In A1 and A3 the PACs were mainly distributed in the fractions 30–3 and <3 kDa, while in A2 more than 70% were present in the fraction less than 3 kDa. Overall, obtained data strongly suggests that A2 is not cranberry-derived, or is adulterated with another source of PACs.

Thermal polymerization of styrene in the presence of TEMPO

To investigate aspects of the contribution of (thermal) self-initiation in nitroxide-mediated radical polymerization (NMRP) of styrene, selective styrene polymerizations with 2,2,6,6-tetramethyl-1-piperidinyloxy (TEMPO) in the absence of initiator were carried out at 120 and 130 °C. The results of these experiments (including conversion data, molecular weight averages, polydispersity and molecular weight distribution information) were compared with regular thermal polymerization of styrene and NMRP of styrene in the presence of a bimolecular initiator (benzoyl peroxide; BPO). It was observed that although the thermal polymerization of styrene can be controlled to some extent in the presence of TEMPO to provide polystyrene with low polydispersity, the polymerization was never as controlled as that obtained by a BPO-initiated NMRP.

Comprehensive Two-Dimensional Liquid Chromatography Analysis of a Block Copolymer

A two-dimensional liquid chromatography (2D-LC) method, normal phase liquid chromatography (NPLC) for one dimension and reversed phase liquid chromatography (RPLC) for the other dimension, was employed to map the molecular weight distribution (MWD) of the individual blocks of a polystyrene-block-polyisoprene (PS-b-PI) diblock copolymer. The first-dimension (1st-D) NPLC separates PS-b-PI according to the PS block length while the second-dimension (2nd-D) RPLC separates PS-b-PI according to the PI block length. For the first-dimension NPLC separation, the column temperature was controlled to improve the resolution while the 2nd-D RPLC was run isothermally to reduce the separation time. The MWD information of individual blocks provides equivalent information to MWD and chemical composition distribution of a block copolymer. In this analysis, the effluent from the 1st-D LC separation is concentrated before the injection to the 2nd-D LC by use of a trap column, which allows an efficient interface between the two LC separations. Over 200 different block copolymer species could be identified from the 2D-LC chromatogram.

Polydispersity index from linear viscoelastic data: unimodal and bimodal linear polymer melts

This article describes a method for determining the polydispersity index Ip2=Mz/Mw of the molecular weight distribution (MWD) of linear polymeric materials from linear viscoelastic data. The method uses the Mellin transform of the relaxation modulus of a simple molecular rheological model. One of the main features of this technique is that it enables interesting MWD information to be obtained directly from dynamic shear experiments. It is not necessary to achieve the relaxation spectrum, so the ill-posed problem is avoided. Furthermore, a determinate shape of the continuous MWD does not have to be assumed in order to obtain the polydispersity index. The technique has been developed to deal with entangled linear polymers, whatever the form of the MWD is. The rheological information required to obtain the polydispersity index is the storage G′(ω) and loss G″(ω) moduli, extending from the terminal zone to the plateau region. The method provides a good agreement between the proposed theoretical approach and the experimental polydispersity indices of several linear polymers for a wide range of average molecular weights and polydispersity indices. It is also applicable to binary blends.

Letter to the Editor: Comment on “Obtaining molecular-weight distribution information from the viscosity data of linear polymer melts” [J. Rheol. 42, 453–476(1998)

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Response to “Comment on ‘Obtaining molecular-weight distribution information from the viscosity data of linear polymer melts’ ” [J. Rheol. 42, 1555–1562 (1998)

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Obtaining molecular-weight distribution information from the viscosity data of linear polymer melts

Based on the model of Bersted and Slee, and later Malkin and Teishev, both differential and integral methods were developed to determine the molecular-weight distribution (MWD) from viscosity data. The more sensitive differential method can detect small inflections in the viscosity data and convert these into MWD information. The integral method is, however, capable of handling moderately incomplete viscosity data. Combining self-consistent differential and integral approaches, we are able to resolve details of a MWD and quantify reasonably broad MWDs from many sets of limited viscosity data. These methods both have very short computation times. A reported overemphasis of the high-molecular-weight end of distribution is due to the excitation of Rouse modes during the rheological measurements at high frequencies, which masks the diffusive contributions of the low-molecular-weight components to the relaxation process.

Analysis of the Accuracy of Determining Average Molecular Weights of Narrow Polydispersity Polymers by Matrix-Assisted Laser Desorption Ionization Time-of-Flight Mass Spectrometry

Matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOFMS) can be used to determine number- and weight-average molecular weights of narrow polydispersity polymers. In this work, several possible sources of error in determining molecular weights of polymers with narrow polydispersity by MALDI-TOFMS are rigorously examined. These include the change in polymer distribution function, broadening or narrowing of the overall distribution, and the truncation of selected oligomer peaks within a distribution (i.e., the oligomer peaks at the high- and low-mass tails expected to be observed are not detected). These variations could be brought about by a limited detection sensitivity, background interference, and/or mass discrimination of oligomer analysis in MALDI-TOFMS. For narrow polydispersity polystyrenes, it is shown that by using an appropriate MALDI matrix and sample preparation protocol and a sensitive ion detection instrument, no systematic errors from these possible variations were detected within the experimental precision (0.5% relative standard deviation) of the MALDI method. It is concluded that MALDI mass spectrometry can provide accurate molecular weight and molecular weight distribution information for narrow polydispersity polymers, at least for polystyrenes examined in this work. The implications of this finding for polymer analysis are discussed.

On‐line molecular weight distribution estimation and control in batch polymerization

AbstractA molecular weight distribution (MWD) estimator for batch methyl methacrylate solution polymerization is implemented experimentally for on‐line control and estimation of the MWD. The estimator is based on an extended Kalman filter and provides current estimates of the entire MWD, reaction temperature, monomer conversion, and initiator conversion. It uses a detailed polymerization model, on‐line monomer conversion measurements, temperature measurements, and periodic, time‐delayed measurements of the MWD from an on‐line size‐exclusion chromatograph. The estimator is shown to perform well with several on‐line MWD estimation experiments. Real‐time feedback control of the molecular weight is presented by utilizing the on‐line MWD information. Temperature, monomer‐addition, and simultaneous temperature and monomer‐addition control are investigated experimentally to achieve a specific constant weight‐average molecular weight. The on‐line feedback control is effective in rejecting realistic disturbances which deteriorate molecular weight control.

The novolak calibration method applied to the GPC analysis of the UV photoresists

This paper first summarizes the influence of the molecular weight of the novolak-based photoresists on the different microlithographic steps: film deposition, soft bake, exposure, and hard bake. The second part deals with the use of gel permeation chromatography (GPC) for characterizing the photoresists. In order to convert elution curves into molecular weight distribution information, a calibration method is needed. The usual calibration techniques are poorly adapted to the analysis of photoresists. The proposed calibration method uses the first observable low molecular weight oligomers on the chromatogram as a standard. It is shown that experimental results are not dependent on the column set.

Rheology of polyphosphazene melts and solutions—some surprises

AbstractRheological tests are reported for two types of polyorganophosphazenes, one being a fluorinated alkoxy terpolymer (PNFT) and the other an aryloxy copolymer (PAP). Non‐Newtonian viscosity η(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) and complex viscosity components η′(ω) and η″(ω) were measured as functions of shear rate \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document} and oscillatory frequency ω, using a Weissenberg rheogoniometer, and a limited amount of normal stress data was also obtained. Solutions of both polymers in tetrahydrofuran were tested, over a concentration range 0‐22 percent for PNFT and 0‐35 percent for PAP. Melts of PNFT were examined for temperatures 50‐178°C, and melts of PAP at 210°C even though they were not truly fluid at this temperature. Solution and melt data are shown to obey conventional superposition principles to give master curves. For solutions, superposition is achieved by using the Bueche relaxation time as a concentration reducing factor with no adjustable parameters, and the Spriggs model also proves useful in predicting normal stress and shear stress results. For PNFT melts, master curves are fitted by the new WS2H2 model which incorporates detailed molecular weight distribution (MWD) information and extracts the entanglement length Me from the data. Temperature shift factors aT show Arrhenius behavior and the corresponding activation energies Ere are reported. Results for PNFT melts were complicated by lack of agreement between two samples of nominally the same composition; η′(ω) shapes and levels and Ere values differed widely. This is interpreted in terms of detailed MWD information and the possibility of mesomorphic phase transitions occurring in these nominally amorphous materials.

Multiple detectors for molecular weight and composition analysis of copolymers by gel permeation chromatography

AbstractThe use of a single detector in gel permeation chromatography (GPC) for samples of varying composition leads to erroneous conclusions. With certain simplifying assumptions, a gel permeation chromatograph equipped with properly selected dual detectors yields composition and molecular weight distribution information that is meaningful. Examples discussed are a mixture of homopolymers and a sample supposed to have been a styrene–butadiene block copolymer. The ultraviolet absorption is used in conjunction with the refractive index trace to give qualitative information that is much more informative than could be obtained with one detector. Calibration of the relative responses of the detectors to each of the components of the mixture is described, and these calibrations are used to calculate point‐by‐point composition, molecular weights, and molecular weight averages.