Computer modeling of the crystallization process of single‐chain ethylene/1‐hexene copolymers from dilute solutions

Langevin molecular dynamics (LMD) simulations have been performed to understand the role of the short chain branches (SCB) on the formation of ordered domains by cooling dilute solutions of ethylene/α‐olefins copolymer models. Three different long single‐chain models (C₂₀₀₀) with 0, 5, and 10 branches each 1000 carbons were selected. These models were equilibrated at high reduced temperature (T* = 13.3) and cooling in steps of 0.45 until the final temperature (T* = 6.2) by running a total of 35 × 10⁶ LMD steps. During the cooling process, global order parameter, torsion distribution, position of the branches, and local‐bond order parameter were calculated and monitored. The peaks of crystallization for each model were calculated by differentiating the global order parameter with temperature. The T_c (crystallization temperature) decreases as the number of branches increases as has been experimentally reported. The formation of order in the copolymers is affected by the amount of the SCB in the backbone of the polymer chain. Initially, the SCB move to the folding surface. Once the SCB are located near the folding surface the order starts to grow. In all cases here shown, the C₄ branches are excluded from the ordered domains. To take into account, the influence of the branch distribution, a different branch distribution model has been considered for the two‐branched systems. The crystallization fraction (α) and the density of the amorphous and ordered fractions was defined using the local‐bond order parameter. Both magnitudes decrease as the number of branches increases. These facts fairly agree with experimental literature data. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

A study of ADMET polyethylene with 21-carbon branches on every 15th compared to every 19th carbon: What a difference four extra backbone methylenes make

Precision polyethylenes with 21-carbon alkyl branches precisely spaced on every either 15th or 19th carbon along the polymer backbone lead to the formation of two kinds of lamellae, yielding different thicknesses during the crystallization process. Thinner lamellae originate from side-chain crystallization, whereas thicker lamellae are formed by cocrystallization of the branch and the main chain. Side-chain crystallization (separate from main chain crystallization) is favored when the branch is placed on every 15th carbon. Cocrystallization (side chain with main chain) is favored with the branch on every 19th carbon. Both form stable hexagonal crystal units. A branch spacing separation of just four carbons along the main chain makes a remarkable difference in crystallization behavior. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 3090–3096     

Side Reactions in Aqueous Phase Polymerization of N‐Vinyl‐Pyrrolidone as Possible Source for Fouling

An improved kinetic model for the radical polymerization of N‐vinyl‐pyrrolidone (NVP) in aqueous medium is developed. Quantum chemical simulations reveal that the transfer to polymer is of minor importance whereas the transfer to monomer by hydrogen abstraction in 3‐position of the pyrrolidone ring leads to a radical with a double bond which initiates a new chain bearing a terminal double bond (TDB). The resulting dead chains with one, two, or more TDB are the main source for a strong increase of molar mass in batch reactors at high conversion due to long chain branching and crosslinking. This can be a source for gel formation and fouling in continuous reactors.     

Stochastic simulations of polymer growth and isomerization in the polymerization of propylene catalyzed by Pd-based diimine catalysts

A model is presented that employs a stochastic approach to the simulation of polyolefin chain growth and isomerization. The model is applied to propylene polymerization catalyzed by Pd-based diimine catalysts. The stochastic approach links the microscopic (quantum chemical) approach with modeling of the macroscopic systems. The DFT calculated energies of the elementary reactions and their barriers have been used as input parameters for the simulations. The influence of the catalyst's steric bulk, as well as polymerization temperature and olefin pressure on the polymer branching and its microstructure, is discussed. The results are in good agreement with available experimental data. In the propylene polymerization catalyzed by Pd(II) complexes with methyl backbone- and -Ph-(i)Pr(2) imine substituents a number of branches of 238 branches/1000 C have been obtained. An increase in polymerization temperature leads to a decrease in the number of branches. Change in olefin pressure does not affect the global number of branches, while it strongly affects the polymer microstructure, leading to hyperbranched structures at low pressures. Further, the simulations confirm the experimental interpretation of the mechanistic details for this process: (1) both 1,2- and 2,1-insertion happen with the ratio of ca. 7:3; (2) there are no insertions at the secondary carbons; and (3) most of the 2,1-insertions are followed by a chain straightening isomerization. Thus, for this catalyst the total number of branches is controlled exclusively by the 1,2-/2,1-insertion ratio. For the catalysts with different substituents the branching can be controlled by a 1,2-/2,1-insertion ratio as well as the fraction of the insertions at the secondary carbons. The results of the present studies demonstrate that a stochastic approach can be successfully used to model the polyolefin microstructures and their catalyst, temperature, and pressure dependence. Further, it can also facilitate interpretation of the experimental results, and can be used to draw general conclusions about the influence of the specific elementary reaction barriers on the polymer structures; this can be helpful for a rational design of the catalysts producing a desired microstructure.     

Multiscale Modeling of Branch Length in Butyl Acrylate Solution Polymerization

Branch lengths resulting from both backbiting and intermolecular chain transfer to polymer are examined for the solution polymerization of butyl acrylate, using a rate‐equation model and ordinary differential equations. Backbiting is allowed to generate branches of varying length, according to a cumulative distribution function obtained from a lattice kinetic Monte Carlo simulation. About 8% of the branches produced by backbiting are 10 mers or longer. In contrast to common assumptions about the origins of short‐chain and long‐chain branches, the model indicates that nearly all of the long‐chain branches may be produced by backbiting, rather than intermolecular chain transfer to polymer.

     

End‐group fidelity of copper(0)‐meditated radical polymerization at high monomer conversion: an ESI‐MS investigation

Copper(0)‐mediated radical polymerization (single electron transfer‐living radical polymerization) is an efficient polymerization technique that allows control over the polymerization of acrylates, vinyl chloride and other monomers, yielding bromide terminated polymer. In this contribution, we investigate the evolution of the end‐group fidelity at very high conversion both in the presence and in the absence of initially added copper (II) bromide (CuBr₂). High resolution electrospray‐ionization mass spectroscopy (ESI‐MS) allows determination of the precise chemical structure of the dead polymers formed during the polymerization to very high monomer conversion, including post polymerization conditions. Two different regimes can be identified via ESI‐MS analysis. During the polymerization, dead polymer results mainly from termination via disproportionation, whereas at very high conversion (or in the absence of monomer, that is, post‐polymerization), dead polymers are predominantly generated by chain transfer reactions (presumably to ligand). The addition of CuBr₂ significantly reduces the extent of termination by both chain transfer and disproportionation, at very high monomer conversion and under post‐polymerization conditions, offering a convenient approach to maintaining high end‐group fidelity in Cu(0)‐mediated radical polymerization. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Following the Crystallization Process of Polyethylene Single Chain by Molecular Dynamics: The Role of Lateral Chain Defects

Summary: Langevin molecular dynamics (LMD) simulations have been performed in order to understand the role of the short chain branches (SCB) on the formation of ordered domains by cooling ethylene/α-olefins single chain models. Different long single-chain models (C₂₀₀₀) with 0, 5 and 10 branches each 1000 carbons were selected. The branches were randomly distributed along the backbone chain. Furthermore, C₁ (methyl) and C₄ (butyl) branches were taken into account. These models mimic the molecular architecture of ethylene/1-butene and ethylene/1-hexene random copolymers. The simulations are performed according to the following protocol: 20 random chain conformations for each model were equilibrated at high temperature (T* = 13.3) and then they were cooled in steps of 0.45 until the final temperature (T* = 6.2) by running a total of 35 × 10⁶ LMD steps. The distribution peaks of crystallization for each model were calculated by differentiating the global order parameter with respect to the temperature. The Tc* (crystallization temperature) decrease as the number of branches increases as it is experimentally observed. The formation of order in the copolymers is affected by the type and amount of the SCB in the backbone of the polymer chain. The stem lenght and crystallization fraction (α) were defined using the local-bond order parameter. Both parameters decrease as the number of branches increase. In all cases here shown, the C₄ branches are excluded from the ordered domains. However, we have observed that the methyl branch can be incorporated into the ordered regions. These facts satisfactorily agree with experimental data available in the literature.     

The Stability of the Micelle Formed by Chain Branch Surfactants and Polymer Under Salt and Shear Force: Insight from Dissipative Particle Dynamics Simulation

The influence of salt and shear force on the stability of the micelle formed by surfactants and polymer are studied using dissipative particle dynamics (DPD) simulation method. The research system mainly includes four types of surfactants with different hydrophilic/hydrophobic chain branches and two kinds of polymers with hydrophilic/hydrophobic properties, respectively. The stability of the micelle is studied based on the analyses of the density peak and root mean square (RMS) of polymer chain under different salt and shear force. The calculated results show that the density peak reduced and RMS increased for all surfactants with the salt concentration and shear force increasing, and then indicate that the micelle has a certain degree of deformation. Whereas, the surfactant chain branch has important influence on the deformation extent of the micelle. For hydrophobic polymer, surfactants containing hydrophobic chain branch (T2H2T2) are beneficial to the stability of the micelle. On the contrary, for hydrophilic polymer, the micelle formed by surfactants with stronger hydrophilic nature such as the hydrophilic groups located in the both ends of the molecule (H1T4H1) have the best salt and shear resistance. The results have certain theoretical significance and can provide theoretical support for the selection of surfactants and polymers in practical application.     

Computing the Trivariate Chain Length/Degree of Branching/Number of Combination Points Distribution for Radical Polymerization with Transfer to Polymer and Recombination Termination

Summary: Polymer molecules made by radical polymerization with transfer to polymer and recombination termination contain branch points (connecting branch arms to backbones) and combination points (connecting various molecular structures). The trivariate chain length/degree of branching/number of combination points distribution (CLD/DBD/CPD) was calculated using a two‐dimensional version of a previously used pseudo‐distribution approach. This yielded the CPD moments for given chain length n and number of branches i. Both DBD and CPD at given chain length resemble a binomial distribution. For the construction of the full DBD and CPD a set of orthogonal polynomials, the Krawtchouk polynomials, in combination with the binomial distribution was employed. A first‐order Krawtchouk approximation enabled to compute the full CLD/DBD/CPD from the three CPD moments as a function of n and i. Results agree well with those from a Monte Carlo (MC) simulation method. However, the large scatter due to the small numbers of molecules collected in the MC method at longer chain lengths prevents comparison in this range.

Solutions of 3D CLD/DBD/CPD: CPD at constant chain length (20 000) and number of branch points (20).     

Graft copolymers having hydrophobic backbone and hydrophilic branches. III. Synthesis of graft copolymers having oligovinylpyrrolidone as hydrophilic branch

Graft copolymers were synthesized by the esterification reaction between acrylic copolymers and carboxyl group terminated vinylpyrrolidone oligomer using phase transfer catalysts. Acrylic copolymers were obtained by the radical copolymerization of β-bromoethyl methacrylate, chloromethylstyrene or glycidyl methacrylate with methyl methacrylate. Hydrophilic oligomers were prepared by the radical oligomerization of vinylpyrrolidone using β-mercaptopropionic acid as chain transfer agent. The degree of esterification increased with decreasing the molecular weight of oligomer and with increasing the number of potential grafting sites on polymer backbones. The water dispersibility of graft copolymers increased with increasing the nitrogen content and was therefore dependent on the branch oligomer content.     

Influence of branch length asymmetry on the electrophoretic mobility of rigid rod-like DNA

The electrophoretic mobility of three-arm asymmetric star DNA molecules, produced by incorporating a short DNA branch at the midpoint of rigid-rod linear DNA fragments, is investigated in polyacrylamide gels. We determine how long the added branch must be to separate asymmetric star DNA from linear DNA with the same total molecular weight. This work focuses on two different geometric progressions of small DNA molecules. First, branches of increasing length were introduced at the center of a linear DNA fragment of constant length. At a given gel concentration, we find that relatively small branch lengths are enough to cause a detectable reduction in electrophoretic mobility. The second geometric progression starts with a small branch on a linear DNA fragment. As the length of this branch is increased, the DNA backbone length is decreased such that the total molar mass of the molecule remains constant. The branch length was then increased until the asymmetric branched molecule becomes a symmetric three-arm star polymer, allowing the effect of molecular topology on mobility to be studied independent of size effects. DNA molecules with very short branches have a mobility smaller than linear DNA of identical molar mass. The reason for this change in mobility when branching is introduced is not known, however, we explore two possible explanations in this article. (i) The branched DNA could have a greater interaction with the gel than linear DNA, causing it to move slower; (ii) the linear DNA could have modes of motion or access to pores that are unavailable to the branched DNA.     

Pursuit of reinitiation efficiency of resonance‐stabilized monomeric allyl radical generated via “degradative monomer chain transfer” in allyl polymerization

For a deeper understanding of allyl polymerization mechanism, the reinitiation efficiency of resonance‐stabilized monomeric allyl radical was pursued because in allyl polymerization it is commonly conceived that the monomeric allyl radical generated via the allylic hydrogen abstraction of growing polymer radical from monomer, i.e., “degradative monomer chain transfer,” has much less tendency to initiate a new polymer chain and, therefore, this monomer chain transfer is essentially a termination reaction. Based on the renewed allyl polymerization mechanism in our preceding article, the monomer chain transfer constant in the polymerization of allyl benzoate was estimated to be 2.7 × 10^?2 at 80 °C under the polymerization condition, where the coupling termination reaction of growing polymer radical with allyl radical was negligible and, concurrently, the reinitiation reaction of allyl radical was enhanced significantly. The reinitiation efficiencies of monomeric allyl radical were pursued by the dead‐end polymerizations of allyl benzoate at 80, 105, and 130 °C using a small amount of initiators; they increased remarkably with raised temperature. Thus, the enhanced reinitiation reactivity of allyl radical at an elevated temperature could bias the well‐known degradative monomer chain transfer characteristic of allyl polymerization toward the chain transfer in common vinyl polymerization. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Reduced‐order model for monitoring spectroscopic and chromatographic polymer properties

A reduced‐order mechanistic polymerization model and its application in the design of a low‐dimension multi‐rate state estimator (soft sensor) for monitoring spectroscopic and chromatographic polymer properties are presented. A model reduction approach is used to simplify a method‐of‐moments mechanistic model. Using this approach, the order (number of the state variables) of the model is reduced from 20 to 7. The soft sensor estimates spectroscopic and chromatographic polymer properties from (a) frequent measurements of the reactor temperature and the flow rates of monomer (n‐butyl acrylate), initiator (t‐butyl peroxy acetate) solution and solvent (xylene) feed streams, and (b) infrequent and delayed measurements of polymer number‐ and weight‐average molecular weights and the concentrations of terminal solvent groups, terminal double bonds and short chain branches. The benefits of using the infrequent measurements in the estimation are shown. The soft sensor is implemented in real‐time, and the calculated continuous estimates of polymer number‐ and weight‐average molecular weights and the concentrations of solvent, terminal double bonds and short chain branches are compared to the corresponding chromatographic and spectroscopic measurements. Copyright © 2007 John Wiley & Sons, Ltd.     

Crystallization and melting of narrow composition distribution polyethylenes: Investigation and implications of crystal thickening

The crystal structure produced during the isothermal crystallization of polyethylene (PE) copolymers with a broad range of comonomer concentrations was determined by the measurement of the melting endotherms directly after crystallization. PE copolymers with higher concentrations of short‐chain branches (≥10 branches per 1000 total carbon atoms) exhibited strong resistance to crystal thickening during isothermal crystallization. Negligible thickening, estimated to be only about 0.1 nm in 10 min of isothermal crystallization, was observed. The side‐chain branches apparently acted as limiting points of chain incorporation into the crystals, which exhibited great resistance to the modification of their position, that is, crystal thickening. Even with long periods (up to 8 h) of isothermal storage, crystal thickening was very small or negligible, about 0.3 nm. The crystal thickness was calculated from differential scanning calorimetry data. The behavior of copolymers with lower branching concentrations and the unbranched PE homopolymer was quite different from that of the copolymers with higher branching. Polymers with low or no branching exhibited the initial crystallization of a thinner crystal population, which thickened substantially with increasing time. The thickening observed for these lower or unbranched polymers was an order of magnitude larger, that is, 1.6–2.0 nm in 10 min of isothermal crystallization. Copolymers with higher concentrations of branching had relatively short sequence lengths of ethylene units between branch points, and this resulted in strong control over the crystal thickness by the branch points and great resistance to crystal thickening, even with long times of isothermal crystallization. Copolymers with low concentrations of branching had relatively long sequence lengths of ethylene units between branch points, and this resulted in little control over the crystal thickness by the branch points and rapid crystal thickening upon isothermal crystallization. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 235–246, 2003     

Dimensions of branched polymers formed in simultaneous long‐chain branching and random scission

In free‐radical olefin polymerizations, the polymer‐transfer reactions could lead to chain scission as well as the formation of long‐chain branches. The Monte Carlo simulation for free‐radical polymerization that involves simultaneous long‐chain branching and random scission is used to investigate detailed branched structure. The relationship between the mean‐square radius of gyration 〈s²〉 and degree of polymerization P as well as that between the branching density and P is the same for both with and without random scission reactions—at least for smaller frequencies of scission reactions. The 〈s²〉 values were larger than those calculated from the Zimm–Stockmayer (Z‐S) equation in which random distribution of branch points is assumed, and therefore, the Z‐S equation may not be applied for low‐density polyethylenes. The elution curves of size exclusion chromatography were also simulated. The molecular weight distribution (MWD) calibrated relative to standard linear polymers is much narrower than the true MWD, and high molecular weight tails are clearly underestimated. A simplified method to estimate the true MWD from the calibrated MWD data is proposed. The MWD obtained with a light scattering photometer in which the absolute weight‐average molecular weight of polymers at each retention volume is determined directly is considered a reasonable estimate of the true MWD. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2960–2968, 2001     

凝胶点前氯乙烯－邻苯二甲酸二烯丙基酯共聚物表征，支化度模型及悬挂双键活性

根据单烯－二烯自由基共聚合反应特点，提出一种新的支化点对分子量的分布模型，讨论了用凝胶色谱－特性粘数法表征文化聚合物时，文化点对分子量分布和式［η］０，ｂ／［η］０．１＝ｇ０中的指数ｃ对结果的影响．建立了氯乙烯－二烯类单体悬浮聚合凝胶点前的平均支化度模型．用凝胶点前平均文化度和平均分子量模型拟合实验结果发现：ａ．新的支化分布模型更合理，且ｃ＝０．７２；ｂ．悬挂双键活性下降一个数量级；ｃ．对本文样品，特性粘数和分了量仍符合Ｍａｒｋ－Ｈｏｕｗｉｎｋ方程，［η］＝０．２３５７Ｍ￣０．５２７．     

Mathematical Modeling of the Long‐Chain Branch Structure of Polyolefins Made with Two Metallocene Catalysts: An Algebraic Solution

A mathematical model was developed to describe the populations of polymer chains containing different numbers of long‐chain branches (LCBs) made with a combination of two single‐site catalysts. One of the catalysts produces only linear chains (linear‐catalyst) and the other produces linear and long‐branched chains (LCB‐catalyst). The model shows that when the selectivity for macromer formation of the linear‐catalyst is the same as that of the LCB‐catalyst, it is not possible to maximize the number of LCB per chain, even though the number of LCB per 1 000 carbon atoms (C) can be maximized. On the other hand, if the selectivity for macromer formation of the linear‐catalyst is higher than that of the LCB‐catalyst, both LCB/1 000 C and LCB/chain pass through maxima when varying the fraction of the linear‐catalyst in the reactor. More importantly, polymer populations with different numbers of LCB per chain will reach their maximum values at different ratios of linear‐catalyst to LCB‐catalyst, thus permitting the maximization of individual polymer populations in the mixture.     

Stress relaxation under large step equibiaxial elongation for low‐density polyethylene

The stress relaxation under large step equibiaxial elongation for low‐density polyethylene with long‐chain branches revealed that the time‐strain separability holds in relaxation modulus G_B(t, ε_B), and damping function h_B(ε_B) exhibits weaker equibiaxial elongational strain ε_B dependence than that predicted by the Doi–Edwards theory without the independent alignment approximation. Dependencies of damping function h(γ) for step shear deformation and h_B(ε_B) on stretch ratio α of polymer contour length and orientation of a polymer chain in direction of the maximum orientation were evaluated, and it was found that the α dependencies of h(γ) and h_B(ε_B) are different, whereas dependencies of h(γ) and h_B(ε_B) on the orientation coincide fairly well. These results indicate that the damping is dominated by the chain orientation rather than α. This implies that withdrawal of long‐chain branches into tube of a backbone chain occurs when the orientation of the long‐chain branches is large and friction force against the branch point withdrawal is small. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1275–1284, 2009     

Dependence of slow crack growth in polyethylene on butyl branch density: Morphology and theory

A theoretical equation has been developed to described the rate of slow crack growth in an ethylene-hexene copolymer in terms of the basic morphological parameters. These parameters are spacing of the butyl branches, number of tie molecules, and the thickness of the lamellar crystal. Experimentally, the thickness of the lamellae and the long period were determined as functions of the branch density. The calculation of the number of tie molecules is based on the values of the molecular weight and the long period. The model of slow crack growth is based on the rate of disentanglement of the tie molecules. The rate of disentanglement varies inversely with the number of tie molecules and directly with the number of tie molecules that are not pinned by the branches.     

Multiconstituent identification in root,branch, and leaf extracts of Juglans mandshurica using ultra high performance liquid chromatography with quadrupole time‐of‐flight mass spectrometry

As a traditional medicinal plant, Juglans mandshurica has been used for the treatment of cancer. Different organs of this plant showed anti‐tumor activity in clinic and laboratory. Comparative identification of constituents in different plant organs is essential for investigation of the relationship between chemical constituents and pharmacological activities. For this aim, the roots, branches, and leaves of J. mandshurica were extracted with 50% v/v methanol and then subjected to ultra‐high performance liquid chromatography with quadrupole time‐of‐flight mass spectrometry analysis conducted under low and high energy. As a result, we have to date identified 111 compounds consisting of 56 tannins, 29 flavonoids, 13 organic acids, 8 naphthalene derivatives, and 5 anthracenes. Five compounds, namely, diquercetin trihydroxy‐truxinoyl‐glucoside, two quercetin kaempferol dihydroxy‐truxinoyl‐glucosides, syringoyl‐tri‐galloyl‐O‐glucose, and dihydroxy‐naphthalene syringoyl‐glucoside, were tentatively identified as new compounds. Of the compounds identified, 76 were found in the root extract, 67 in the branch extract, and 37 in the leaf extract. Only six compounds including four organic acids and two tannins were found in all three extracts. We developed a rapid and sensitive ultra high performance liquid chromatography with quadrupole time‐of‐flight mass spectrometry approach to identify multiple constituents of complex extracts without separation and ion selection. The results presented provide useful information on further research of the bioactive compounds of J. mandshurica .