Molar Mass Distribution Of Polymers Research Articles

Free radical copolymerization kinetics of bio-based dibutyl itaconate and n-butyl acrylate

The free radical copolymerization of dibutyl itaconate (DBI), a monomer derived from renewable resources, and n-butyl acrylate (BA) is investigated to explore the potential of incorporating itaconate monomers into commercial acrylic resins to enhance the sustainability of coating materials. Batch experiments were conducted at 50 °C and 80 °C, varying initial monomer and initiator concentrations as well as monomer compositions, with proton NMR and size exclusion chromatography used to analyze monomer conversion profiles and polymer molar mass distributions (MMDs). The data were analyzed using a kinetic model developed to guide the experimental studies and estimate key kinetic parameters controlling copolymer composition, polymerization rate and polymer MMDs. The use of the more reactive BA as comonomer significantly increases the conversion and molar mass of the resulting copolymer. Furthermore, semi-batch operating conditions similar to current industrial practice can incorporate a substantial fraction of DBI into acrylic copolymer resins, thus enhancing their sustainability profile.

Evolution of Molar Mass Distributions Using a Method of Partial Moments: Initiation of RAFT Polymerization.

We describe a method of partial moments devised for accurate simulation of the time/conversion evolution of polymer composition and molar mass. Expressions were derived that enable rigorous evaluation of the complete molar mass and composition distribution for shorter chain lengths (e.g., degree of polymerization, Xn = N < 200 units) while longer chains (Xn ≥ 200 units) are not neglected, rather they are explicitly considered in terms of partial moments of the molar mass distribution, μxN(P)=∑n=N+1∞nx[Pn] (where P is a polymeric species and n is its' chain length). The methodology provides the exact molar mass distribution for chains Xn < N, allows accurate calculation of the overall molar mass averages, the molar mass dispersity and standard deviations of the distributions, provides closure to what would otherwise be an infinite series of differential equations, and reduces the stiffness of the system. The method also allows for the inclusion of the chain length dependence of the rate coefficients associated with the various reaction steps (in particular, termination and propagation) and the various side reactions that may complicate initiation or initialization. The method is particularly suited for the detailed analysis of the low molar mass portion of molar mass distributions of polymers formed by radical polymerization with reversible addition-fragmentation chain transfer (RAFT) and is relevant to designing the RAFT-synthesis of sequence-defined polymers. In this paper, we successfully apply the method to compare the behavior of thermally initiated (with an added dialkyldiazene initiator) and photo-initiated (with a RAFT agent as a direct photo-iniferter) RAFT-single-unit monomer insertion (RAFT-SUMI) and oligomerization of N,N-dimethylacrylamide (DMAm).

Asymmetric-Flow Field-Flow Fractionation of complex waterborne polymer dispersions: Effect of the concentration of water in the measurement of molar mass distributions

Asymmetric-Flow Field-Flow Fractionation is a very powerful technique for measuring the molar mass distribution of polymers with complex microstructures. The analysis of some samples such as self-crosslinkable latexes requires to directly dissolve the polymer dispersion in the eluent (THF) without drying it, and this work studies the effect of the presence of this water in those analysis. Taking a polystyrene latex as model system, it was observed that the measured molar mass and radius of gyration increased as the concentration of water in the sample increased. This was an effect of a decrease in the compatibility between the solvent mixture (THF and water) and the polymer, which formed aggregates, and could be predicted calculating the polymer-solvent interaction parameter. When the study was extended to poly(methyl methacrylate), poly(n-butyl acrylate) and poly(vinyl acetate) the same general trend was observed, however, the impact of the water was less significant as the hydrophilicity of the polymer increased. Most importantly, if the samples with the highest water content were first dissolved in THF and afterwards dried using MgSO4 the measured molar mass and radius of gyration values were the same as for the reference sample (dried in the oven), providing a method to analyze samples that cannot be dried into a film and remove the negative effect of the water at the same time.

Experimental and Modeling Investigation of Radical Homopolymerization of 2‐(Methacryloyloxyethyl) Trimethylammonium Chloride in Aqueous Solution

AbstractThe radical homopolymerization kinetics of 2‐(methacryloyloxyethyl) trimethylammonium chloride (TMAEMC) in aqueous solution is investigated across a wide range of initial monomer contents (5–35 wt%), ionic strengths, and pH levels using an in‐situ NMR technique to track monomer consumption over the complete conversion range. Molar mass distributions (MMD) of the final homopolymers are also examined, with additional batch and semi‐batch experiments conducted in a stirred vessel. The rates of monomer conversion and polymer MMDs are dependent on initial monomer content but almost entirely independent of pH and the presence of salts, with some acceleration of rate observed for low monomer levels at very high salt concentration. To aid with the interpretation of these results, the conductivity and counterion activity of monomer and polymer mixtures are measured to determine the extent of electrostatic interactions at various levels of conversion. These results are combined with recently reported measurements of TMAEMC homopropagation kinetics to develop a TMAEMC homopolymerization model that captures the systematic decrease in rates of monomer conversion observed with increased initial monomer content during batch polymerization as well as provides a good representation of semi‐batch polymerization.

The Hafnium-Pyridyl Amido-Catalyzed Copolymerization of Ethene and 1-Octene: How Small Amounts of Ethene Impact Catalysis

Copolymerization of ethene and 1-octene is catalyzed by the Hf-pyridyl amido complex used in chain-shuttling polymerization. Active site counts and the molar mass distribution of catalyst-bound polymeryls are determined by chromophore quench-labeling. Catalytic data for copolymerization (1-octene consumption, active site counts, molar mass distributions of polymers, and I2-labeling of Zn-polymeryls) are compared with similar data for the homopolymerization of 1-octene. Such comparisons reveal that small amounts of ethene have a significant impact on catalysis. The rate of 1-octene consumption increases in a copolymerization ∼3-fold compared to a homopolymerization; this likely results from in situ ligand modification. The first insertion of alkene occurs into the Hf–naphthyl bond of the Hf-pyridyl amido catalyst; in copolymerization, competition between ethene and 1-octene for this insertion creates multiple active species. We propose that ethene insertion into the Hf–naphthyl bond leads to a faster polym...

Physicochemical characterization and study of molar mass of industrial gelatins by AsFlFFF-UV/MALS and chemometric approach.

Industrial gelatins have different physicochemical properties that mainly depend of the raw materials origin and the extraction conditions. These properties are closely related to the molar mass distribution of these gelatins. Several methods exist to characterize molar mass distribution of polymer, including the Asymmetrical Flow Field Flow Fractionation method. The goal of this study is to analyze the relationship between physicochemical properties and the gelatins molar mass distribution obtained by Asymmetrical Flow Field Flow Fractionation. In this study, 49 gelatins samples extracted from pig skin are characterized in terms of gel strength and viscosity and their molar mass distribution are analyzed by Asymmetrical Flow Field Flow Fractionation coupled to an Ultraviolet and Multi Angle Light Scattering detector. This analytical method is an interesting tool for studying, simultaneously, the primary chains and the high-molar-mass fraction corresponding to the polymer chains. Correlation analysis between molar mass distribution data from the different fractions highlights the importance of high molar mass polymer chains to explain the gel strength and viscosity of gelatins. These results are confirmed by an additional chemometric approach based on the UV absorbance of gelatin fractograms to predict gel strength (r2Cal = 0.85) and viscosity (r2Cal = 0.79).

Analysis using size exclusion chromatography of poly(N-isopropyl acrylamide) using methanol as an eluent

Size Exclusion Chromatography is traditionally carried out in either aqueous or non-polar solvents. A system to present molar mass distributions of polymers using methanol as a mobile phase is presented. This is shown to be a suitable system for determining the molar mass distributions poly(N-isopropylacrylamide)s (PNIPAM); a polymer class that is often difficult to analyze by size exclusion chromatography. DOSY NMR was used to provide intrinsic viscosity data that was used in conjunction with a viscometric detector to provide absolute calibration. Then the utility of the system was shown by providing the absolute molar mass distributions of dispersed highly branched PNIPAM with biologically functional end groups.

Modeling the Radical Batch Homopolymerization of Acrylamide in Aqueous Solution

A kinetic model for the radical homopolymerization of acrylamide in aqueous solution is developed, incorporating propagation and termination rate coefficients as functions of monomer concentration and including the formation and reaction of midchain radicals based on the insights and measured rate coefficients from recent pulsed‐laser studies. The model successfully represents the batch conversion profiles measured using an in situ NMR technique between 40 and 70 °C with initial monomer concentrations of 5 to 40 wt%, as well as the associated polymer molar mass distributions. In particular, the model captures the decreased rate that occurs at lowered monomer concentrations as a result of the formation of less‐active midchain radicals by backbiting. Previous literature data are also well represented by the model. image

Modeling Acrylic Acid Radical Polymerization in Aqueous Solution

AbstractBatch radical polymerization of 5–40 wt% non‐ionized acrylic acid (AA) in aqueous solution has been studied between 35 and 90 °C under variation of initiator concentration and type as well as upon addition of different levels of 2‐mercaptoethanol as chain‐transfer agent (CTA). Chain‐length‐dependent termination was taken into account in a model developed to describe the system, as high amounts of CTA have an impact on polymerization kinetics due to reduced chain length. The model also considers the 1,5‐hydrogen shift (backbiting) reaction that transforms the secondary propagating radical into a tertiary midchain radical, with the backbiting reaction quantified via 13C NMR. The model developed is the most comprehensive treatment to date of this complex polymerization system and is able to represent monomer conversion profiles and polymer molar mass distributions over a wide range of conditions.

Effect of Head-To-Head Addition on Vinyl Acetate Propagation Kinetics in Radical Polymerization

The radical propagation kinetics of vinyl acetate (VAc) has been studied by pulsed-laser polymerization coupled with analysis of the resulting polymer molar mass distributions. The significant increase in the apparent propagation rate coefficient observed with increasing pulse repetition rate is explained by the influence of the head-to-head defects formed during chain growth. Simulations that include head-to-head monomer addition are combined with an analysis of the experimental results to estimate the subsequent rate coefficients for reaction of the resultant radical as well as the propagation rate coefficient of normal head-to-tail addition. An analytical expression is derived for an averaged rate coefficient, kpav, for the system, with the best-fit Arrhenius parameters of ln(A/L mol–1 s–1) = 16.56 ± 0.35 and E/R= 2508 ± 108 K.

The Molar Mass Distribution of Polymers in Step‐Growth Polymerization is Influenced by Cyclization Reactions. The Simplified Case of Irreversible Reactions with Cyclizations is Independent of the Ring Size

There were derived equations describing kinetics of the step‐growth polymerization (SGP) proceeding in parallel with cyclization. Only a simplified case of irreversible reactions and cyclization involving terminal functional groups of linear polymer, with the rate independent of ring‐size was analyzed. The analytical solutions for all main features of the SGP were obtained. The linear polymer exhibits the most probable distribution and attains its limited maximum degree of polymerization before vanishing at complete conversion due to cyclization. The eventual cyclic polymer has lower degree of polymerization than linear one and much broader distribution.

The effect of the oxidant used during polymerization on the solid-state decomposition kinetics of poly(4-methyl catechol)

Herein, the oxidative polymerization of 4-methyl catechol using different oxidants including NaOCl, H2O2, and air were reported. Potassium hydroxide solution was used as the reaction solvent and polymerization studies were carried out between 323 and 363 K. Optimum reaction conditions of the polymerization were established and NaOCl was found as the most active oxidant. The structure and characterization of the polymer using FT-IR, ultraviolet–visible (UV–Vis), 1H-NMR, 13C-NMR, thermogravimetry and size exclusion chromatography were confirmed. In addition, the relationship between molar mass distribution of polymer and kinetics parameters such as activation energy, pre-exponential factor of decomposition process was investigated. For this purpose, methods based on multiple heating rates such as Flynn–Wall–Ozawa, Friedman, Tang, Kissinger–Akahira–Sunose, and Kissinger were used. The results obtained show that activation energy increased with an increase of molar mass.

Aqueous‐Phase Copolymerization of N‐Vinylpyrrolidone and N‐Vinylformamide

AbstractAqueous‐phase batch free‐radical copolymerization of NVP and NVF is studied at 60 and 85 °C with varying initial monomer mixture compositions and monomer to water ratios. The rate of monomer conversion is found to increase with increasing NVP molar fraction and with decreasing total monomer concentration, in accordance with the expected behavior based on homopolymerization kinetics. The copolymer composition is equal to the initial comonomer composition, indicating monomer reactivity ratios to be unity. A terminal copolymerization model provides a good description of polymerization rate, copolymer composition, and polymer molar mass distributions using the same kinetic rate coefficients as used to previously describe the homopolymerization of the two monomers.

Predictive control and verification of conversion kinetics and polymer molecular weight in semi-batch free radical homopolymer reactions

Polymer molar mass distributions critically affect macroscopic characteristics and performance of polymeric materials. While multi-detector methods coupled to size exclusion chromatography (SEC) are widely used to measure endproduct mass distributions, less progress has been made in simultaneously controlling and verifying the evolution of these distributions during synthesis. This work focuses on quantitative predictions and online verification of conversion kinetics and of molecular weight during free radical homopolymerization of acrylamide, where reagents were fed into the reactor during the reaction. The central task is to establish and experimentally test a formalism combining free radical polymerization kinetics with time dependent processes related to flows of material into and out of the reactor. Monomer feed experiments were performed that alternately hold molecular weight constant and ramp the weight up, in contrast to batch reactions, where molecular weight decreases. Three types of initiator feed ‘tapers’ were also used to produce predictable conversion kinetics and mass distributions: (i) constant initiator feed, (ii) linearly stepped feed to produce Gaussian conversion kinetics, and (iii) booster shots to produce multi-modal masses. Automatic Continuous Online Monitoring of Polymerization reactions (ACOMP) was used to follow the conversion and evolution of the average mass distribution, and multi-detector SEC was used to cross-check results and measure full distributions of endproducts. In general, there was good agreement between the predictions and results. In future work this approach can be used as an Ansatz for reaction trajectory prediction, and the online monitoring signals exploited to make feedback controlled corrections to the reagent flows and other reaction conditions.

Taylor Dispersion Analysis of Mixtures

Taylor dispersion analysis (TDA) is a fast and simple method for determining hydrodynamic radii. In the case of sample mixtures, TDA, as the other nonseparative methods, leads to an average diffusion coefficient on the different molecules constituting the mixture. We set in this work the equations giving, on a consistent basis, the average values obtained by TDA with detectors with linear response functions. These equations confronted TDA experiments of sample mixtures containing different proportions of a small molecule and a polymer standard. Very good agreement between theory and experiment was obtained. In a second part of this work, on the basis of monomodal or bimodal molar mass distributions of polymers, the different average diffusion coefficients corresponding to TDA were compared to the z-average diffusion coefficient (D(z)) obtained from dynamic light scattering (DLS) experiments and to the weight average diffusion coefficient (D(w)). This latter value is sometimes considered as the most representative of the sample mixture. From these results, it appears that, for monomodal distribution and relatively low polydispersity (I = 1.15), the average diffusion coefficient generally derived from TDA is very close to Dw. However, for highly polydisperse samples (e.g., bimodal polydisperse distributions), important differences could be obtained (up to 35% between TDA and D(w)). In all the cases, the average diffusion coefficient obtained by TDA for a mass concentration detector was closer to the Dw value than the z-average obtained by DLS.

Molar mass distributions of polymers from size exclusion chromatography and matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry: Methods for comparison

AbstractEquations are presented for calculating molar mass averages and molar mass distributions from matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry (MALDI‐TOF MS) data and from size exclusion chromatography (SEC) data. The utility of polydispersity is examined as an indicator of the expectation of MALDI‐TOF MS mass discrimination effects. Cumulative distributions are found to be rich in information for comparing the two techniques and are easily obtained from both SEC and MALDI‐TOF MS data. Analyses of a series of narrow molar mass distribution poly(methyl methacrylate) (PMMA) standards and one polydisperse sample have been performed with both methods. MALDI‐TOF MS did not detect dimer and trimer in the PMMA samples, and it often indicated lower amounts of high‐molar‐mass polymers than did SEC. The results showed that the distribution breadth, as evidenced by the standard deviation of the distribution (calculated from the polydispersity and number‐average molar mass), correlated well with the molar mass range observed in the MALDI‐TOF MS spectra, whereas the polydispersity alone did not. Ratioing the extremes in the molar mass concentrations measured with the SEC differential refractometer, which were necessary to adequately define molar mass distributions, showed that detector dynamic range values as high as approximately 370,000 were required for the polydisperse samples. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 627–639, 2005

Inertial Effects on Polymer Chain Scission in Planar Elongational Cross-Slot Flow

The molar mass and molar mass distribution of polymers subjected to chain scission in planar elongational flow are profoundly affected by the inertial character of the flow, as quantified by the Reynolds number. The degradation of dilute poly(ethylene oxide) (PEO) chains in aqueous-based solvents of varying viscosity was quantified in the planar elongational flow of a cross-slot flow device by gel permeation chromatography with multiangle laser light scattering detection. At low Reynolds number (Re ∼1000), the observed scaling was e ∝ Mw,f-1.04±0.07. Differences of this kind, first quantified by comparing results from stagnation point elongation flows and contraction flows, have previously been attributed to different molecular me...

Simultaneous determination of polymer average molar mass and molar mass distribution, and concentration of additives by GPC-GC

In this paper, the gel permeation chromatography–gas chromatography (GPC–GC) method was proposed to carry out determination of average molar masses and molar mass distribution of polymers and concentration of additives simultaneously. In this method, after the determination of average molar masses and molar mass distribution by ordinary GPC, a part of the effluent that contains additives was transferred to GC, and the analysis was done successively. As an apparatus, Shimadzu LC-10A system and GC-17AAFver.3 were applied. Tetrahydrofuran was used as the mobile phase of GPC, and a mixed gel-type column was applied. Repeatability of the analysis was examined using polyvinyl chloride in which plasticizers of phthalic acid esters were added. The R.S.D. for each peak area of plasticizers were within 0.5–2.0%. This GPC–GC method was also available for the analysis of samples that contain additives, such as antioxidants. © 2000 John Wiley & Sons, Inc. J Micro Sep 12: 501–507, 2000

Analytical ultracentrifugation with the new Optima XL-A and its digital u.v./vis. detector: determination of molar mass distribution of polymers from sedimentation velocity

The determination of average molar masses and molar mass distributions (MMDs) of polymers and polyelectrolytes is demonstrated with the new analytical ultracentrifuge Optima XL-A and its very sensitive digital u.v./vis. detector (180–800 nm continuously) from Beckman Instruments, Inc. The machine was tested with the narrow distribution polystyrenes PS 106 000 and 300 000 (and a 50:50 mixture), sodium poly(styrene sulfonate) NaPSS 100 000 and the broad distribution polystyrene NBS 706. Full details of the calculation of average molar masses and MMDs of the polymers from the experimental values are given. The results show that the new absorption optics enable the above-mentioned quantities to be determined as the absorption optics are able to measure at very low concentrations, which allows either a precise extrapolation to zero concentration or averaging of the data. Owing to the fact that a sedimentation run is a real fractionation process (with a higher resolution than size exclusion chromatography) one measures the real MMD. There is no need to presume a special model MMD to analyse the measurement data. The data from the Optima XL-A are accessible as ASCII-files. As the original Beckman computer programs are not suitable for our purposes, we have developed own programs, which are available on request.

Modern methods for determining the molar mass distribution of polymers. General considerations and application to sedimentation equilibrium

A new procedure for the determination of the molar mass means Mn, Mw and Mz and of the molar mass distribution W(M) = f(M) of polymers is proposed and applied on measurements of the sedimentation equilibrium. The procedure includes the extrapolation of the experimentally determined polydisperse measurable quantity at different concentrations to zero concentration. From these values the molar mass distribution is calculated by nonlinear least squares routines of the integral equation. This method of calculation is, contrary to the inverse transformation of the integral equation, which has been used up to now, well conditioned and stable. The proposed method has been applied to sedimentation equilibrium. In this case the reduced concentration profiles (interference optic, absorption optic) or reduced concentration gradient profiles (schlieren optic) measured at different concentrations must be extrapolated to zero concentration and followed by nonlinear regression of the integral equation Uw(X) = ∫ W(M) U(X,M) dM. Measurements on polystyrenes with different polydispersities and modalities (e.g. bimodal molar mass distributions), and on the polyelectrolytes sodium polystyrene sulfonate and polyethylene imine exhibit resonable results. The result of the investigation is, that the proposed procedure is a suitable and reasonable possibility for the determination of molar mass distribution of polymers by sedimentation equilibrium. For polyelectrolytes in particular this method is better than gel permeation or size exclusion chromatography.