Experimental Molecular Weight Distribution Research Articles

Scaling of the linear viscoelasticity of entangled poly(ethylene oxide) aqueous solutions

The dynamic modulus of polymer solutions and melts can be expressed as a universal function of reduced frequency when the modulus is scaled by a characteristic value according to the scaling theory of polymer physics. Although the plot of the scaled modulus as a function of the scaled frequency supports the theory, it suffers from considerable scattered distribution of data points around the hypothetical master curve. Compared with the master curve of the time–temperature superposition (TTS) of polymer melts, the master curve of polymer solutions has poor quality. Furthermore, the scale factors of polymer solutions may not show a clear dependency on molecular weight and concentrations. Experimental errors and molecular weight distribution appear to enhance the inaccuracy of the master curve. Therefore, we apply a global optimization for the superposition of the viscoelastic data of polymer solutions with various molecular weights and concentrations. The global optimization resulted in the superposition of data as accurate as that of TTS. Furthermore, the numerically determined shift factors, which were relative scale factors, showed clear dependences on molecular weight and concentrations. We compared our global optimization with previous scaling methodologies.

Characterization of Polyisobutylene Succinic Anhydride (PIBSA) and Its PIBSI Products from the Reaction of PIBSA with Hexamethylene Diamine.

The nature of the end-groups of a PIBSA sample, namely a polyisobutylene (PIB) sample, where each chain is supposedly terminated at one end with a single succinic anhydride group, was characterized through a combination of pyrene excimer fluorescence (PEF), gel permeation chromatography, and simulations. The PIBSA sample was reacted with different molar ratios of hexamethylene diamine to generate PIBSI molecules with succinimide (SI) groups in the corresponding reaction mixtures. The molecular weight distribution (MWD) of the different reaction mixtures was determined by fitting the gel permeation chromatography traces with sums of Gaussians. Comparison of the experimental MWD of the reaction mixtures with those simulated by assuming that the reaction between succinic anhydride and amine occurs through stochastic encounters led to the conclusion that 36 wt% of the PIBSA sample constituted unmaleated PIB chains. Based on this analysis, the PIBSA sample was found to be constituted of 0.50, 0.38, and 0.12 molar fractions of PIB chains that were singly maleated, unmaleated, and doubly maleated, respectively.

Modeling of the molecular weight distribution and short chain branching distribution of linear low-density polyethylene from a pilot scale gas phase polymerization process

Molecular weight distribution (MWD) and short chain branching distribution (SCBD) play a decisive role in the performance of linear low-density polyethylene (LLDPE). A model based on a non-standard polymerization reaction scheme is developed for ethylene/α-olefin gas phase copolymerization in a fluidized bed reactor. Experimental MWD and SCBD are simultaneously deconvoluted. The results obtained by this simultaneous deconvolution method are physically more relevant. Reduction of parameters and parameter estimability analysis are conducted to screen parameters to obtain a subset for reliable parameter estimation. The model based on the estimated parameters yields MWD and SCBD which are in good agreement with experimental ones for several LLDPE grades obtained from a pilot-scale gas phase polymerization process. The non-standard polymerization reaction scheme depicts well the “comonomer effect” - activation of dormant ethylene species.

Influence of N- and P-substituents in N-aryl-phosphinoglycine ligands on the selectivity of Ni-catalysed ethylene oligomerization

Quantum-chemical calculations were performed to rationalize the experimental molecular weight distribution of α-olefin products, revealing the main mechanistic models of the process.

All-atom molecular dynamics study of impact fracture of glassy polymers. I: Molecular mechanism of brittleness of PMMA and ductility of PC

Molecular mechanism of brittle and ductile impact fractures of glassy polymers has been investigated. We performed atomistic molecular dynamics (MD) calculations for two glassy polymers, brittle poly(methyl methacrylate) (PMMA) and ductile polycarbonate (PC) using the dissociative force fields. The systems were prepared as realistic as possible such that they reproduced the experimental molecular weight distribution, tacticity, radius of gyration, and entanglement density. The calculated system simulated a small portion of the macroscopic specimen near the notch. The simulations adopted a uniaxial extension condition with the lateral pressure maintained as 1 atm. Under this condition, our atomistic models reproduced the brittle fracture of PMMA via cavitation and ductile fracture of PC via shear yielding and strain hardening. The fracture pathways were determined only by the differences in the material. A conceptual bridge between microscopic simulations and macroscopic experimental observations was provided. The brittle fracture of PMMA is found to be caused by the less flexible backbones with fewer entanglements as well as the inhomogeneity of the material. This contrasts with the finding that more flexible backbones with denser entanglement network result in ductility for PC.

(Keynote) All-Atomistic Molecular Dynamics Calculation of Impact Fracture of Glassy Polymers

Impact-resistance has been one of the target properties of polymer technology from a view point of their mechanical applications. A huge number of investigations have been done for this very important property. One of the key to understand the impact resistance is to investigate the difference in microscopic behavior between brittle and ductile fractures by comparing two extrema of industrial polymers such as PMMA and PC, respectively. However, in spite of an abundance of information about macroscopic behavior of the impact fracture, little has been known about its microscopic picture. This is from difficulty in experiment for the very rapid phenomena.Molecular dynamics (MD) calculation has been one of the powerful tools for investigating microscopic behavior of molecular assemblies at an atomistic resolution. However, so far, poor performance of the supercomputers has prevented us from investigating polymers based on all-atomistic MD calculations since the systems are huge. Then, we have been obliged to depend upon coarse-grained models such as Kremer-Grest model and DPD model. But, they are not good at describing chemical character of polymers which is essential for the investigation of fracture. However, recent very rapid progress of supercomputer technology is going to enable us to investigate polymers based on all-atomistic MD calculations free from phenomenological parameters. The all-atomistic model can describe chemical details of the polymers, which is essential for the investigation of the diversity of polymers. Fracture of the polymers depends much on their chemical details such as main-chain bond breaking and side-chain motions.In particular, it is very important to include bond fracture in the simulation. Since most of the traditional MD calculations have not included bond breaking explicitly, the calculations couldn’t describe brittle fracture of polymers but always resulted in artificial ductile fracture. The bond fracture can be described using potential function such as Morse-type one. The function can be obtained by high quality quantum chemical calculations prior to the MD calculations. In the present study, brittle fracture has been investigated for PMMA including bond fracture explicitly. Systems constructed for the simulation mimicked the real system. There, experimental molecular weight distribution, density, radius of gyration, and entanglement molecular weight were reproduced well in the initial configuration prepared for the impact fracture test calculations. The calculations clearly show characteristics of the brittle fracture at a molecular level such as void formation, chain reactions of main-chain bond breaking, and small Poisson ratio.

Copolymerization of Ethylene with 1,9‐Decadiene: Part II—Prediction of Molecular Weight Distributions

In the present work, adaptive orthogonal collocation and a Monte Carlo method are used to compute the molecular weight distributions (MWD) of ethylene/1,9‐decadiene copolymers produced with a constrained geometry catalyst. Predictions from each model are compared to each other and to the experimental MWDs, allowing for the evaluation of relative strengths and weaknesses of each mathematical modeling method. Comparisons with experimental results indicate that the rate of macromonomer incorporation in the growing polymer chains decays with the macromonomer radius of gyration. In all cases, the proposed models are able to fit appropriately the available experimental MWDs.

Large-scale molecular dynamics simulation of crosslinked phenolic resins using pseudo-reaction model

Abstract We constructed and characterized a network structure of crosslinked phenolic resins using a large-scale atomistic molecular dynamics simulation with a pseudo-reaction algorithm. The atomic configuration of the reaction products was controlled by the reaction probabilities and initial molecular structures. The crosslinked structure obtained from phenols as initial molecules agreed well with experimental results in terms of the branching structure of the phenolic units and the methylene linkages, molecular weight distributions, densities, and scattering functions at various reaction conversions. The calculated structure factor for phenolic resins indicated inhomogeneous crosslinking, which expanded as the reaction proceeded after gelation. Voronoi tessellation analysis of the change in the occupation volume of the phenolic units after crosslinking indicated that the initial molecular configuration influenced the resulting crosslinked structure. The experimental molecular weight distribution before gelation and the scattering function were well reproduced by a large-scale simulation with 232,000 atoms.

Monte Carlo Simulation of Asphaltenes and Products from Thermal Cracking

Analytical data from the characterization of the liquid products from the thermal cracking of n-C7 Cold Lake asphaltenes were transformed to probability density functions (PDFs) that described the molecular weight distributions of the asphaltene building blocks. These distributions were used for Monte Carlo construction of populations of 10 000 asphaltene molecules, constrained by an experimental molecular weight distribution and the yield of products boiling below 538 °C from cracking in the presence of hydrogen and iron sulfide. The resulting distribution of asphaltene molecules contained between 1 and 15 building blocks, with a mode of 4. The mode of the distribution was insensitive to the fraction of the asphaltenes that consisted of large building blocks, boiling above 538 °C. Breakage of the bonds between the building blocks, to simulate cracking, gave yields of product fractions and boiling curves that were consistent with the experimental data. The relatively small number of building blocks in the majority of the asphaltene molecules suggests that molecular topology is not significant in the cracking reactions. Simulation of the cracking reactions linear versus dendritic molecular topology did not show significant differences in yield of product fractions.

Cyclic polystyrene topologies via RAFT and CuAAC

Cyclic polymer have attracted interest due to their different self-assembly behavior and physical properties compared to their linear counterparts with the same molecular weight. There are only a few examples of using polymer made by RAFT to create cyclic polymers, and no reports of coupling these cyclic polymers together to form stars. In this work, we have demonstrated a novel approach to produce cyclic polymers by RAFT with the required functionality for further coupling to form 2- and 3-arm stars. Cyclization of a chemically modified linear RAFT polystyrene (PSTY) using the copper-catalyzed azide–alkyne cycloaddition (CuAAC) gave cyclic polystyrene (cPSTY) with a purity of 95% as determined by simulating the experimental molecular weight distribution using the log-normal distribution method. The –OH group on cPSTY was converted to an azide via a two step procedure, allowing the cyclic polymers to be coupled together using propargyl ether or tripropargylamine via the CuAAC reaction to form the 2- and 3-arm stars, respectively. When the conventional ligand complex and solvent was used (i.e. CuBr–PMDETA in toluene), the linkage between the cyclic arms degraded fully after 24 h due to base cleavage. We overcame this by changing the ligand to a triazole or carrying out the reaction in ligand-free conditions (i.e. CuBr in DMF). These latter experimental conditions gave ‘click’ efficiencies of greater than 82%. Our methodology for producing cyclic polymers by RAFT will not only extend the range of cyclic polymer by the ring closure method but allow one to utilize these cyclic polymers as building blocks in the formation of more complex polymer architectures.

Ethylene polymerization over supported titanium‐magnesium catalysts: Effect of polymerization parameters on the molecular weight distribution of polyethylene

AbstractThe data on the effects of polymerization duration, cocatalyst, and monomer concentrations upon ethylene polymerization in the absence of hydrogen, and the effect of an additional chain transfer agent (hydrogen) on the molecular weight (MW), molecular weight distribution (MWD), and content of vinyl terminal groups for polyethylene (PE) produced over the supported titanium‐magnesium catalyst (TMC) are obtained. The effects of these parameters on nonuniformity of active sites for different chain transfer reactions are analyzed by deconvolution of the experimental MWD curves into Flory components. It has been shown that the polymer MW grows, the MWD becomes narrower and the content of vinyl terminal groups in PE increases with increasing polymerization duration. It is assumed to occur due to the reduction of the rate of chain transfer with AlEt3 with increasing polymerization duration. The polydispersity of PE is found to rise with increasing AlEt3 concentration and decreasing monomer concentration due to the emergence of additional low molecular weight Flory components. The ratios of the individual rate constants of chain transfer with AlEt3, monomer and hydrogen to the propagation rate constant have been calculated. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

Heterogeneity of active sites of Ziegler‐Natta catalysts: The effect of catalyst composition on the MWD of polyethylene

AbstractExperimental data on the molecular weight distribution (MWD) of polyethylene (PE) produced over a broad number of Ziegler‐Natta catalysts differing in composition and preparation procedure are presented. These catalysts include nonsupported TiCl3 catalyst, four types of supported titanium‐magnesium catalysts (TMC) differing in the content of titanium and the presence of various modifiers in the composition of the support, and a supported catalyst containing VCl4 as an active component instead of TiCl4. The studied catalysts produce PE with different molecular weights within a broad range of polydispersity (Mw/Mn = 2.8–16) under the same polymerization conditions. The heterogeneity of active sites of these catalysts was studied by deconvolution of experimental MWD curves into Flory components assuming a correlation between the number of Flory components and the number of active site types. Five Flory components were found for PE produced over nonsupported TiCl3 catalysts (Mw/Mn = 6.8), and three–four Flory components were found for PE produced over TMC of different composition. A minimal number of Flory components (three) was found for PE samples (Mw/Mn values from 2.8 to 3.3) produced over TMC with a very low titanium content (0.07 wt %) and TMC modified with dibutylphtalate. It was shown that five Flory components are sufficient to fit the experimental MWD curve for bimodal PE (Mw/Mn = 16) produced over VMC. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010

Study of Multi‐Site Nature of Supported Ziegler‐Natta Catalysts in Ethylene‐Hexene‐1 Copolymerization

AbstractSummary: Heterogeneity of active centers (AC) of titanium‐magnesium catalysts (TMC) and vanadium‐magnesium catalyst (VMC) in ethylene‐hexene‐1 copolymerization has been studied on the base of data of polymer molecular weight distribution (MWD) deconvolution technique and copolymer fractionation onto narrow fractions. It was found that 3 and 4 Flory components (groups of active centers) are required to describe experimental MWD curves of copolymers produced over TMC with different Ti content. In the case of VMC MWD of homopolymer and copolymer are characterized by set of 5 Flory components (5 groups of AC).Different character of inter‐relationship between MW and short chain branching (SCB) was found for ethylene‐hexene‐1 copolymers produced over different catalysts: heterogeneous type in the case of TMC and more uniform for copolymer prepared over VMC. The content of Ti affects on the slope of that profile in copolymers produced over TMC.The results indicated that TMC and VMC are different greatly on the heterogeneity of active centers to the formation of polymers with different molecular weights and to formation of copolymers with different inter‐relationship between MW and short chain branching. TMC produces polymers with more narrow MWD but it contains highly heterogeneous centers regarding comonomer reactivity ratios. VMC produces polymers with broad and bimodal MWD but it contains more homogeneous centers regarding comonomer reactivity ratios.

Synthesis of Poly(glycidyl Methacrylate-r-photochromic Monomer) by ATRP

The preparation of the random photochromic copolymer poly(glycidyl methacrylate-r-1′-(2-methacryloxyethyl)-6-nitro-3′,3′-dimethylspiro-[2H-1]-benzopyran-2,2′-indoline) by ATRP is reported, which can be used for the preparation of smart materials. Narrow homopolymers obtained from glycidyl methacrylate (GMA) are prepared when HMTETA-copper bromide and ethyl 2-methyl-2-bromo-propionate are used as the catalytic system with methyl-ethyl-ketone at 50°C. By using a molar ratio of 1:1 ligand:initiator, good correlations between experimental and theoretical molecular weights and narrow molecular weight distribution are obtained. These experimental conditions are also employed for the copolymerization of GMA with a photochromic monomer, where again good control of the polymerization reaction is obtained. The copolymer is fully characterized by spectroscopic techniques. The reactivity ratios are calculated according to the extended Kelen-Tüdos method, while the composition of the copolymer is calculated by NMR. Determination of r GMA and r PHM gives a value of 0.985 for GMA and 0.596 for the photochromic monomer.

Ethylene Polymerization over Supported Titanium‐Magnesium Catalysts: Heterogeneity of Active Centers and Effect of Catalyst Composition on the Molecular Mass Distribution of Polymer

AbstractNew experimental approach was used for analysis of molecular weight distribution (MWD) of polymers produced over titanium‐magnesium catalysts (TMC). Polymers were fractionated on to fractions with narrow MWD (polydispersity (PD) values Mw/Mn ≤ 2). Then some of these fractions were combined to get the minimal quantity of fractions with PD values close to 2 (Flory components). It was found that three fractions corresponding to three groups of active centers are sufficient for proper fitting experimental MWD curve for PE obtained over TMC with different Ti content and with different hydrogen concentration in polymerization.

Determination of Intramolecular Chain Transfer and Midchain Radical Propagation Rate Coefficients for Butyl Acrylate by Pulsed Laser Polymerization

A novel method to extract individual free-radical polymerization rate coefficients for butyl acrylate intramolecular chain transfer (backbiting), kbb, and for monomer addition to the resulting midchain radical, , is presented. The approach for measuring kbb does not require knowledge of any other rate coefficient. Only the dispersion parameter of SEC broadening has to be determined by fitting measured MWDs or should be available from separate experiments. The method is based upon analysis of the shift in the position of the inflection point of polymer molecular weight distributions produced by a series of pulsed-laser polymerization (PLP) experiments with varying laser pulse repetition rate. The coefficient kbb is determined from the onset of the sharp decrease of the apparent propagation rate coefficient ( ) with decreasing repetition rate, an approach verified by simulation. With experiments performed between −10 and +30 °C, the estimated values are fitted well by an Arrhenius relation with pre-exponential factor A(kbb) = (4.84 ± 0.29) × 107 s-1 and activation energy Ea(kbb) = (31.7 ± 2.5) kJ·mol-1. At low pulse repetition rates, the experimental values are related to an averaged propagation rate coefficient, , that is dependent on the relative population of chain-end and midchain radicals. Evaluated by comparing simulated and experimental molecular weight distributions, provides an estimate for . The Arrhenius parameters are: A( ) = (1.52 ± 0.14) × 106 L·mol-1·s-1 and Ea( ) = (28.9 ± 3.2) kJ·mol-1.

Determination of the Mode of Free Radical Termination from Pulsed Laser Polymerization Experiments

AbstractThe molecular‐weight distribution (MWD), obtained by pulsed laser polymerization (PLP) at the high termination rate limit has been considered for investigating termination kinetics. The proposed methodology takes into account both the composite model for termination and the chain‐length dependencies of propagation for short‐chain and long‐chain radicals. Power‐law expressions are used to represent propagation $[k_{\rm p}^L = k_{\rm p}^0 (L)^{ - \alpha } ]$ and termination $[k_{\rm t}^{L,L} = k_{\rm t}^0 (L)^{ - \beta } ]$ of long‐chain radicals (where k and k represent the maximum “virtual” rate coefficients for monomeric radicals, and α and β capture the chain‐length dependencies for propagation and termination), with the combined value of (β − α) evaluated from the MWD, after correcting for the influence of the kinetics of short‐chain radicals. A novel method is also developed for determining the mode of termination, δ, from MWDs produced by PLP at the high termination rate limit. Simulations for methyl methacrylate (MMA) polymerization at 25 °C confirm that the method can be applied robustly in the presence of complicating factors such as chain transfer to monomer and SEC broadening. The analysis of an experimental MWD obtained for MMA polymerization at 25 °C results in estimates of 0.14 ± 0.03 for (β − α) and 0.75 ± 0.04 for δ.magnified image

Synthesis, structure and catalytic properties of [Cp*Cr(C 6F 5)(Bn)(THF)] toward ethylene in the presence of AlEt 3

Treatment of [Cp*CrCl(C 6F 5)] 2 with BnMgCl (Bn = benzyl) in Et 2O/THF affords [Cp*Cr(C 6F 5)(Bn)(THF)] ( 1) which has been isolated in 72% yield. This compound whose magnetic moment is equal to of 4.037 μ B has been characterized by NMR and single crystal X-ray analysis. Compound 1 alone does not polymerize ethylene when dissolved in toluene. However, addition of excess AlEt 3 to a solution of 1 in toluene leads to a catalytically active system which readily oligomerizes ethylene under standard conditions. Oligomerization experiments carried out with [ 1] = 10 −3 M and [AlEt 3] = 9 × 10 −2 M for 15 min lead to the production of ethylene oligomers with an activity of 280 kg mol Cr −1 h −1. The experimental molecular weight distribution observed at intermediate times during the reaction is satisfactorily accounted for by the Poisson distribution formula, which is indicative of a living polymerization system. These observations are in agreement with a catalytic cycle in which the growing alkyl chain is transferred from chromium to aluminum via a bimetallic complex in which the chromium and aluminum centers are bridged by an alkyl group and the growing polymer chain.

Molecular Weight Distributions and Chain-Stopping Events in the Free-Radical Polymerization of Methyl Methacrylate

The chain-stopping and radical-loss events in the seeded emulsion polymerization of methyl methacrylate are determined using information from the complete molecular weight distributions (MWDs) and rate behavior with initiation by gamma radiolysis followed by removal from the radiation source (gamma relaxation). The system follows pseudo-bulk kinetics, implying that the chain-stopping and radical-loss events are kinetically the same as in corresponding bulk and solution free-radical polymerizations. It was essential to take SEC (size-exclusion chromatography) band broadening into account when interpreting the MWDs. The MWDs are interpreted by plotting the log(instantaneous number MWD), which is expected to be linear from theory, but it is shown that broadening leads to an upward curvature, consistent with experimental observation in this and many other systems. It is proven that the slope of the true (unbroadened) log(instantaneous number MWD) can be found from that of the experimental (broadened) one by taking the slope at the peak of the SEC distribution. The experimental MWDs are found to be dominated by transfer to monomer. The gamma-initiated rate data also show that radical loss is predominantly caused by the rapid diffusion of short radicals generated by transfer to monomer (i.e., the rate coefficient for termination is a function of those for transfer and primary radical termination). The transfer constant inferred from all these data (k(tr)/k(p) = 2.3 x 10(-5)) is in agreement with that obtained by alternative methods (Stickler, M.; Meyerhoff, G. Makromol. Chem. 1978, 179, 2729). All data can be acceptably modeled using diffusion theory to predict the rate coefficients of chain length dependent termination, with the few parameters adjusted to give the fit having values that are in good accord with the expected range.

Addition‐Fragmentation Chain Transfer to Polymer in the Free Radical Ring‐Opening Polymerization of an Eight‐membered Cyclic Allylic Sulfide Monomer

AbstractSummary: A detailed investigation of chain transfer to polymer during free radical ring‐opening polymerization of the eight‐membered disulfide monomer 2‐methyl‐7‐methylene‐1,5‐dithiacyclooctane (MDTO) is presented. It has been shown that extensive chain transfer to polymer occurs involving both poly(MDTO) radicals and cyanoisopropyl radicals. Significant decreases in molecular weight were observed when cyanoisopropyl radicals were generated in the presence of poly(MDTO) in the absence of monomer. The molecular weight distribution (MWD) obtained from polymerization of MDTO in the presence of pre‐added poly(MDTO) was markedly different from that obtained without pre‐added polymer. A kinetic model was constructed in an attempt to quantitatively describe the chain transfer to polymer process based on the addition fragmentation chain transfer mechanism. It was found however that the simulated MWDs were considerably broader than the experimental MWDs, which were similar to the Schulz‐Flory distribution.Mechanism for chain transfer to polymer.imageMechanism for chain transfer to polymer.