High-energy radiation forming chain scission and branching in polypropylene

The degradation of high molecular weight isotactic polypropylene (iPP) subjected to gamma rays irradiation up to 100 kGy in inert atmosphere was analyzed. The investigation relied upon complex viscosity, elastic modulus, gel fraction, morphology of the insoluble fraction and deconvoluted molecular weight distribution (MWD) curves. At low irradiation doses, already at 5 kGy, the MWD curve is strongly shifted to the low molecular weight side showing chain scission, which is confirmed using the calculated chain scission distribution function (CSDF). At high dose levels, the appearance of a shoulder in the high molecular weight side of the MWD curve indicates the formation of chain branching. The presence of a considerable insoluble fraction at these high dose levels indicates also the formation of cross-linking, which has different morphology then the insoluble fraction present in the original iPP. The rheological results show changes in the molecular structure of irradiated samples in agreement with the gel content data. The chromatographic and rheological data has shown that gamma irradiation of iPP produces chain scission, branching and cross-linking.     

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     

Mechanical degradation of polypropylene solutions under large pressure drops

The degradation of polypropylene (PP), dissolved in n‐alkanes at high temperatures and pressures, during the solution discharge to ambient conditions was experimentally studied. Molecular weight distributions (MWD) of the solubilized PP were measured by gel permeation chromatography. The MWD curves of PP obtained after discharge of the polymer solution shift to the low molecular weight side of the distribution and the polydispersity is reduced. In this work, a systematic study on the discharge products was performed to elucidate the degradation mechanism and the effects of temperature and concentration on this phenomenon. Initially, pure polymers, PP and polystyrene (PS) were studied varying the solution temperature. In a second stage, the effect of polymer concentration on chain scission was assessed using experiments on physical blends of PP/PS. In all cases, thermal and oxidative degradation were previously analyzed. Mechanical degradation was found to be the main chain scission mechanism. A negative linear functionality of the chain scission was found in both temperature and polymer concentration. To analyze the relationship between polymer degradation and molecular weight, the chain scission distribution function was calculated. On this basis, a critical molecular weight for the beginning of chain scission was obtained. This value is a function of temperature but remains constant with concentration. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 455–465, 2007     

Synthesis of Branched Polymer Architectures from Molecular Weight and Branching Distributions for Radical Polymerisation with Long‐Chain Branching,Accounting for Topology‐Controlled Random Scission

Branched polymers like LDPE are known to possess a wide range of architectures. In this paper a modelling approach is developed, describing the relation between architectures, chemistry and reactor conditions with the general objective of improving characterisation and controlling visco‐elastic properties. More specifically, the particular scission kinetics of branched molecules as strongly contrasting with linear scission is described. A new method to synthesise branched architectures is developed as an alternative to full Monte Carlo (MC) sampling. It employs MC sampling for coupling of primary polymers only. Graph theory is used as an efficient storage method containing all topological information of individual molecules. The algorithm synthesises molecules for any given combination of chain length (n) and number of branches (N). The explicit and detailed knowledge of branched architectures allows finding the correct topological scission kinetics. Distributions of fragment lengths and numbers of branches on fragments after scission are obtained, showing a preference for short and long fragments. Approximate functions describing this have been implemented in another model, predicting molecular weight (MWD) and degree of branching (DBD) distributions using a Galerkin finite element method. Topological scission is seen to give MWD broadening and a higher branching density for long chains. Distributions of longest end‐to‐end distances could be computed for all architectural alternatives for given n, N. In conclusion, it is demonstrated that this method yields distributions of architectures consistent with MWD/DBD for radical polymerisation with long‐chain branching and random scission.     

Mathematical Modelling and Computer Simulation of Linear Polymer Degradation: Simple Scissions

Summary: Degradation of a polymer in a reactor by the degrading agent(s) follows a distinct pattern, primarily influenced by structural integrity and reactor environment. This distinct pattern is recorded in the changes in the evolved molecular weight distribution (MWD) or polymer chain length distribution (PCLD) curve characteristics from the initial intact state. Modern size exclusion chromatography (SEC) is the best laboratory‐based method that can clearly provide these plots in the form of chromatogram; however, detailed molecular information is not available. The nature of molecular destruction can be well‐characterised if the distinct MWD shift patterns can be simulated to fingerprint the different chain scission dynamics. This is investigated by our current research using the power of computer simulation techniques to gain insight into the polymer ageing processes. One such technique for studying simple decay processes is presented here, and the results are compared with experimental findings. The concept of a binary tree scission model is introduced to show chain rupture as a sequence of probabilistic events and as a non‐linear function of time. Two new mathematical algorithms, an iterative Monte Carlo structured probability scheme and a semi‐iterative algebraic exact statistical formulation method, are investigated to implement this model and simulate the evolution of resultant temporal MW distribution. The latter, an innovative approach to mathematical modelling, has the potential to generate a statistically perfect instant MWD decay curve. A statistical comparison of the product yield is presented from the data obtained using a wide variety of simulated scission regimes to determine the sources of variability.

Simulated MWD lateral shift for percent cut scission model showing deviation from the initial MWD (red) over degradation time zones T_j(0 ≥ j ≤ 9) with bimodal and curve broadening effect due to accumulation of varied percent cut range 5–30%.     

MWD of i-Polypropylene Under Degradation by Selc Using a New Eluting Solvent

Abstract

A new eluting solvent, cyclohexane, for steric exclusion liquid chromatography (SELC) at 70°C of i-polypropylene (PP) has been applied to the study of molecular weight distribution (MWD) of samples of PP under repeated extrusion and under oxidative degradation in the presence of incorporated organic peroxide. Various parameters characterizing the changes in MW and MWD of the samples are listed in TABLE 1. M_z changed pronouncedly with increasing extent of degradation in both degradation processes, while M_n changed very slightly indicating the average number of chain scission per chain had been very small, much less than one. Difference in the mechanism of the mechanical as compared to the oxidative degradation has shown up in the way the low MW end of the MWD curves changed during the progress of the degradation process.     

Evaluation of Philips and Ziegler-Natta high-density polyethylene degradation during processing in an internal mixer using the chain scission and branching distribution function analysis

The oxidative and thermo-mechanical degradation of HDPE was studied during processing in an internal mixer under two conditions: totally and partially filled chambers, which provides lower and higher concentrations of oxygen, respectively. Two types of HDPEs, Phillips and Ziegler-Natta, having different levels of terminal vinyl unsaturations were analyzed. Materials were processed at 160, 200, and 240 °C. Standard rheograms using a partially filled chamber showed that the torque is much more unstable in comparison to a totally filled chamber which provides an environment depleted of oxygen. Carbonyl and transvinylene group concentrations increased, whereas vinyl group concentration decreased with temperature and oxygen availability. Average number of chain scission and branching (n_s) was calculated from MWD curves and its plotting versus functional groups' concentration showed that chain scission or branching takes place depending upon oxygen content and vinyl groups' consumption. Chain scission and branching distribution function (CSBDF) values showed that longer chains undergo chain scission easier than shorter ones due to their higher probability of entanglements. This yields macroradicals that react with the vinyl terminal unsaturations of other chains producing chain branching. Shorter chains are more mobile, not suffering scission but instead are used for grafting the macroradicals, increasing the molecular weight. Increase in the oxygen concentration, temperature, and vinyl end groups' content facilitates the thermo-mechanical degradation reducing the amount of both, longer chains via chain scission and shorter chains via chain branching, narrowing the polydispersity. Phillips HDPE produces a higher level of chain branching than the Ziegler-Natta's type at the same processing condition.     

Molecular weight distributions of linear polymers: Detailed analysis from GPC data

The GPC method is used widely to measure molecular weights of linear polymers. High-quality GPC data contains detailed information on many aspects of the polymer's molecular weight distribution (MWD). This information can be extracted from the data using computer analysis. Equations have been derived for the two simplest MWD functions in the GPC coordinates: the Flory function (one growing polymer chain produces one polymer molecule), and for the case when two polymer radicals combine into one polymer molecule. The equations were used to analyze MWD of two classes of polymers. The first class includes polymers with narrow MWD: polyethylene, ethylene-propylene and ethylene-hexene copolymers, syndiotactic polystyrene, and radical polystyrene. The second class includes polymers with broad MWD: ethylene copolymers and polypropylene produced with heterogeneous, Ti-based catalysts. The examples demonstrate that the resolution of complex GPC curves into their constitutents serve as an important source of information about kinetics of polymerization reactions. © 1995 John Wiley & Sons, Inc.     

Degradation of Polystyrene in Solution by Ultrasonation - A Molecular Weight Distribution Study

Ultrasonically induced degradation of polystyrene in tetrahydrofuran solutions has been studied. Four narrow molecular weight distribution (MWD) samples, a material with a wide MWD, and a bimodal MWD sample were degraded at various concentrations, temperatures, and ultrasonic intensities. The MWDs after a number of ultrasonation time periods were obtained from gel permeation chromatograms corrected for instrumental spreading. Degradation index DI, defined as the number of bonds broken per original number of molecules, has been used to describe the extent of degradation. The results of the experiments were used to determine the values of two parameters occurring in the degradation model developed previously. It was found that the course of the changes in MWDs predicted by the model are in good agreement with those observed experimentally when the following values of the model parameters are used. The probability of scission of a molecule with molecular weight M is proportional to the product of its number fraction and the 1.25 power of M. The probability density function of the location of scission along the chain is described by a Caussian curve centered at the midpoint of the chain with a standard deviation of 35% of the chain lengths and truncated 3I the chain ends.

The agreement between observed and calculated MWDs was good for degrees of degradation as high as DI = 15. The course of the changes in MWDs was independent of the initial MWD and of the experimental conditions of concentration, temperature, and sonation intensity and, therefore, independent of the rate of degradation which varied greatly.     

Monte Carlo simulation of size exclusion chromatography for branched polymers formed through free‐radical polymerization with chain transfer to polymer

The elution curves of size exclusion chromatography (SEC) for branched polymers formed through free‐radical polymerization that involves chain transfer to polymer were theoretically investigated by using a Monte Carlo method. We considered two types of measured molecular weight distribution (MWD), (1) the calibrated MWD relative to standard linear polymers, and (2) the MWD obtained by using a light scattering photometer (LS) in which the weight‐average molecular weight of polymers within the elution volume is determined directly. It was found that the calibrated MWD clearly underestimates the high molecular weight tail, and the measured distributions are narrower than the true MWD. On the other hand, the present simulation results showed that the LS method gives reasonable estimates of the true MWDs. The mean square radius of gyration of the polymer molecules having the same molecular weight was also investigated. The radii of gyration showed clear deviation from the Zimm‐Stockmayer equation^[1] because of the non‐random nature of branched structure and the difference in the primary chain length distribution.     

Molecular weight distribution in living polymerization proceeding with reshuffling of polymer segments due to chain transfer to polymer with chain scission, 1. Determination of kp/ktr ratio from DPw/DPn data. Ideal reproduction of polymer chain activities

The molecular weight distribution (MWD) curves for polymerization systems with chain transfer to polymer leading to reshuffling of polymer segments (and broadening of the MWD), but not changing chain functionalities, were simulated by the Monte Carlo method. The bimodality observed in some distributions was explained by different distribution functions of chains which did not undergo reshuffling and of those which underwent the chain transfer reaction. Using this observation, a numerical integration method for computing DP _w/DP _n (and the MWD curves) in the systems under consideration was devised. Plots relating DP _w/DP _n to monomer conversion and k_tr/k_p are presented and a method of determination of k_tr/k_p from the DP _w/DP _n data is proposed.     

Calculation of Molecular Weight Distributions in Non‐Linear Free‐Radical Polymerization Using the Numerical Fractionation Technique

Mathematical Modeling of non‐linear polymerization systems subject to gel formation is a challenging endeavor. At the gel point, the second and higher molecular weight moments diverge to infinity making it impossible to obtain the molecular weight distribution (MWD). The numerical fractionation (NF) technique utilizes a refinement of the method of moments to model non‐linear polymerization systems that form gel. Since the method of moments yields results in terms of average quantities, some information is lost when reconstructing the MWD using NF. As a consequence, a broad shoulder appears at the high chain length end of the MWD tail. This study demonstrates that the validity of the gamma distribution deteriorates for the broader branched polymer generations and evaluates the performance of various alternative model distributions. Proper selection of the model distribution enhances the NF‐reconstructed MWD.     

Simultaneous long‐chain branching and random scission: I. Monte Carlo simulation

In free‐radical olefin polymerizations, the polymer transfer reactions could lead to chain scission as well as forming long‐chain branches. For the random scission of branched polymers, it is virtually impossible to apply usual differential population balance equations because the number of possible scission points is dependent on the complex molecular architecture. On the other hand, the present problem can be solved on the basis of the probability theory by considering the history of each primary polymer molecule in a straightforward manner. The random sampling technique is used to solve this problem and a Monte Carlo simulation method is proposed. In this simulation method, one can observe the structure of each polymer molecule formed in this complex reaction system, and virtually any structural information can be obtained. In the illustrative calculations, the full molecular weight distribution development, the gel point determination, and examples of two‐ and three‐dimensional polymer structure are shown. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 391–403, 2001     

Influence of electron-beam irradiation on plasticity-controlled and crack-growth-controlled failure in high-density polyethylene

In the present study, the influence of electron-beam irradiation on plasticity-controlled and crack-growth-controlled failure in high-density polyethylene (HDPE) is investigated and the effect of both molecular weight distribution (MWD) and short chain branching (SCB) content are taken into account. Size exclusion chromatography (SEC) is used to study the evolution of the MWD of the sol fraction as a function of irradiation dose. Here, it is seen that chains shorter than the percolation threshold (5 kDa) are largely unaffected by electron beam radiation, while the fraction of longest chains (M > 300 kDa) is nearly entirely incorporated into the cross-linked network. Both yield stress and Young's modulus increased with irradiation dose, where the magnitude of the increase appears to be connected to the gel fraction. The (fatigue) crack growth kinetics of the grades changed relatively little with irradiation dose, which is unexpected. Furthermore, convergence of the crack growth kinetics parameter to a narrow range of values could be observed for the investigated grades at relatively high gel fractions. This would imply that the crack growth kinetics become increasingly independent of the MWD upon irradiation cross-linking, which could be attributed to a shift in the underlying crack growth mechanism from chain slip to chain scission.     

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

Summary: 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.     

Numerical Techniques for the Solution of the Molecular Weight Distribution in Polymerization Mechanisms,State of the Art

The molecular weight distribution (MWD) is possibly the most important characteristic of a polymer. Polymers derive many of their physical properties from their MWD. Therefore, since the origins of polymer science, the theory provides a link between the kinetic mechanism and the mathematical expression of the MWD, and there are analytical solutions for ideal cases. However, the MWD formed in real‐life polymerization processes is usually more complex; the solution of the mathematical models that describe them can be quite challenging and has been the focus of enormous research efforts. These models may consist of systems of very large dimension: thousands of differential equations, often stiff, which demand special numerical techniques for their solution. In this paper the numerical techniques that can be used to solve this challenging problem are reviewed and contrasted, including weighted residual methods, direct integration, numerical inversion of transformed equations, and lumping methods. Stochastic techniques are also surveyed.     

Evolution of molecular weight distributions in the catalytic chain transfer polymerization of methyl methacrylate up to high monomer conversions

The evolution of molecular weight distributions (MWDs) with monomer conversion in the catalytic chain transfer (CCT) polymerization of methyl methacrylate at 60 °C is investigated by simulation (via the program package PREDICI®) and experiment. A Co(III)‐based complex is used as the precursor for the CCT agent, which is formed in situ by initiator‐derived (2,2′‐azobisisobutyronitrile) radicals to yield the catalytically active Co(II) species. The small shifts seen in the MWD toward lower molecular weights with increasing monomer conversion are shown to be of the same order of magnitude as the associated changes in the MWD in non‐CCT controlled free‐radical polymerization, indicating that no significant change in the MWD with monomer conversion is associated with the CCT process. These results are compared to the evolution of MWDs in conventional chain transfer polymerizations with thiols as transfer agents. A clear shift toward higher molecular weights is seen with increasing monomer conversion, indicating disparate rates of thiol and monomer consumption. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3303–3312, 2000     

Enzymatic chain scission kinetics of poly(epsilon-caprolactone) monolayers

The hydrolytic and enzymatic degradation behavior of poly(epsilon-caprolactone) (PCL) is investigated using the Langmuir monolayer technique, and an improved data acquisition and data reduction procedure is presented. Hydrolytic and enzymatic monolayer degradation experiments of PCL with various molecular weights by Pseudomonas cepacia lipase have been carried out to analyze the influence of subphase pH, subphase temperature, enzyme concentration, and the packing density of polymer chains on the degradation kinetics. The enzymatic monolayer degradation results in an exponential increase in the number of dissolved degradation fragments with increasing degradation time, which confirms random chain scission to be the dominant scission mechanism. The increase in the enzymatic scission rate constant with decreasing initial average molecular weight of the polymers is assigned to the influence of the area density of polar terminal groups on the substrate-enzyme complex formation.     

Monte Carlo simulation of size exclusion chromatography for randomly branched and crosslinked polymers

The elution curves of size exclusion chromatography for nonlinear polymers formed through random branching and crosslinking of long polymer chains were simulated with a Monte Carlo method. We considered two types of measured molecular weight distributions (MWDs): (1) the MWD calibrated relative to standard linear polymers and (2) the MWD obtained with a light scattering (LS) photometer in which the weight‐average molecular weight of polymers within the elution volume is determined directly. The calibrated MWDs clearly underestimate the molecular weights for both randomly branched and crosslinked polymers, and this technique can be used to assess the degree of deviation from the true MWD. When the primary chains conform to the most probable distribution, the calibrated MWD can be estimated reasonably well with the Zimm–Stockmayer equation for the g factor with the help of the relationship between the average number of branch points per molecule and the degree of polymerization. However, the LS method gives good estimates of the true MWD for both randomly branched and crosslinked polymers, although the agreement is better for the branched ones. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2009–2018, 2000