Initial Molecular Weight Distribution Research Articles

Effect of initial molecular weight distribution on pattern formation of main-chain-scission-type resists

Recently, main-chain-scission-type resists have attracted considerable interest because of their highly resolving properties. In this study, the effect of initial molecular weight distribution on the pattern formation of main-chain-scission-type resists was investigated. The main-chain-scission-type resists with different molecular weight distributions were prepared by blending ZEP520A (M w, 56,000; M w/M n: 2.2) and ZEP7000 (M w, 412 000; M w/M n, 2.6) of Zeon. Independently of their initial molecular weight distribution, the molecular weight distributions of the resists become similar through the random main-chain scission. However, the initial molecular weight distribution affected the formation of boundaries between lines and spaces. When their weight ratio was 1:1, the bridges formed by pattern collapse or transient swelling were clearly observed at an irradiation dose lower than those in the case of the other weight ratios.

Fractal model of polymer electrolyte to investigate influence of high energy irradiation in molecular distribution and molar mass average

The present work is completely based on the theoretical investigation i.e. computer simulated study of the effect of gamma irradiation on the molecular weight distribution and the molar mass averages of solid polymer electrolytes which is relevant with the present trends of experimental works in this field. We propose a fractal model corresponding to polymer molecules by deterministic loop-less fractal (Vicsek). An initial un irradiated symmetrical molecular weight distribution has been considered. Application of high energy perturbation, for example gamma irradiation, affects the molecules mainly by two processes-scission and cross-linking of molecules which results morphological changes inside the system. A new parameter named as weight fraction, has been introduced to compare the structural modification of the sample with the experimental results. The four basic parameters representing the molar mass averages have been introduced in this context to analyze various structural properties such as intrinsic viscosity, number, weight and Z-average molecular weight etc. The results of our simulation work enables us an easy understanding about the nature of the response of solid polymer electrolyte to the external perturbation.

A general approach to determining the evolution of molecular weight distribution curves of linear polymers undergoing chain scission

A numerical method is developed to compute the development of molecular weight distribution (MWD) curves of linear polymers undergoing chain scission. The method can be applied to complex chain scission kinetics and for arbitrarily complex initial MWD curves. Our method is based on the method of lines (MoL). Different from the existing numerical scheme, we propose the use of logarithmically spaced points. This development ensures the accuracy of the computed MWD curves at low molecular weights, and it does not require a very fine discretization to produce an accurate result.

Simulation of thermal decomposition of a polymer at random scissions of C-C bonds

A mathematical formulation of the polymer thermal decomposition model at random scissions of C-C bonds in the backbone is presented. The model is based on ideas about a macrokinetic character of the observed process Polymer → Gaseous products, and the thermofluctuation nature of the bond scission. The suggested approach makes it possible to calculate the decomposition rate in a wide pressure range at any initial molecular weight distribution of the polymer. As an example, a comparison of the calculation results for temperature-time dependences of the conversion degree and decomposition rate with experimental data obtained in isothermal and non-isothermal regimes is performed for linear polyethylene.

Random Scission of Polymers: Numerical Simulations, and Experiments on Hyaluronan Hydrolosis

We present a study of the random scission process of polymers, in which numerical simulations are com- bined with experimental investigations into the acid hydrolysis ofthepolysaccharidehyaluronan(HA),inparticularatpH1.1and 50 � C. As input for the simulations, an initial molecular weight distribution (MD(0)) and the hydrolysis rate constant (kh) are needed.The firstwasobtainedusingagarosegelelectrophoresis followed by densitometric analyses, by which we determined the evolution of the full molar-mass distribution during hydro- lysis. The rate constant was experimentally obtained by two independent techniques. Kinetic plots were obtained from both the number- and the weight-average molar mass (Mn and Mw, respectively), converted to degrees of polymerization (Nn and Nw, respectively),andfromthese,khvaluesforHAhydrolysiswerederived.Forconfirmation,khwasalsodeterminedfromtheevolution oftheconcentrationofreducingchainends.Experimentallydeterminedkhvalueswereusedasinputforthemodel,andtheevolution of MD during hydrolysis was simulated for various hypothetical MD(0) functions as well as for an experimentally determined MD(0) curve.Agreementbetweenexperimentalandsimulatedresultsdemonstratedconsistencyofthemodelandindicatesthatacidhydrolysisof hyaluronan can indeed be considered a random scission process. We show that for cases where the initial molar mass distribution is notoftheKuhn-type—whichisoftenthecase—thevalueforthekhdeterminedfromtheevolutionofMnismoreaccuratethanthat obtained from Mw.

A gaussian model for substrates of entangled cross‐linked poly(ethylene glycol) in biomedical applications

Cells usually spread on a synthetic substrate through bonds between receptors and chemical groups on the substrate (ligands). Therefore, it is valuable to study the effects of the average number density of these chemical groups and the average distance between them to model and predict the cell behavior. Poly(ethylene glycol) [PEG] modified with peptide groups has been used widely in biomedical applications as a substrate material. In this study, a coarse-grained model is proposed for PEG to predict the average number density of ligands and the average distance between them. Molecular information such as initial molecular weight distribution, average molecular weight between cross-links, and average molecular weight between entanglements is used as input parameters. Based on simulation results, it is concluded that both entanglement and cross-link densities are required to create a network structure. The results suggest that an average initial molecular weight 2-3 times the average molecular weight between entanglements and a moderate cross-link density are sufficient to create a closed network structure with a high ligand density and a small average distance between them.

Factors affecting selectivity during dissolved organic matter removal by anion-exchange resins

Anion-exchange processes have received increased attention in recent years as efficient alternatives for removing disinfection byproduct precursors. In this research the preferential uptake of different dissolved organic matter (DOM) components, and hence the resulting reactivity after treatment, is shown to depend on the initial molecular weight (MW) distribution and the sulfate concentration. MW distribution is important because size-exclusion phenomena can occur in ion-exchange sorption, leading to the preferential uptake of low (ca. 1000 Da) MW species. Sulfate competition can reverse resin preference for low-MW species. DOM components that compete best with sulfate combine ionogenic group affinity and entropy-assisted adsorption. Entropy-assisted sorption, whereby sorption is promoted by the entropy gained from the desolvation of hydrophobic DOM moieties, is shown to be significant for two surface water sources. Entropic contributions are most significant when resin dosages are low and competition between DOM components and between DOM and sulfate are high. DOM components having MW near 1 kDa are sufficiently large to have significant hydrophobic moieties to promote entropy-assisted sorption and sufficiently small to enable access to exchange sites. Total uptake and preferential removal of specific UV absorbance (SUVA), an indicator of DOM reactivity, will thus depend on the initial MW distribution, how SUVA depends on MW, and the sulfate concentration.

Effect of Lubricant Degradation on Contact Fatigue

It is well known that contact fatigue is affected by contact pressure, frictional stress, residual stress, initial distribution of material flaws, and so on. The behavior of contact pressure and, primarily, the frictional stress is determined by the viscous properties of the lubricant used. It is also recognized that lubricants degrade while passing through lubricated contacts. Degradation of lubricants causes viscosity loss that, in turn, reduces the frictional stress and raises contact fatigue life. The objective of this study was to find out the extent to which lubricant degradation may change contact fatigue life of elastic surfaces completely separated by lubricant. The analysis was performed numerically based on the models of contact fatigue and lubricant degradation recently developed by the author. The results showed that contact fatigue life of solids completely separated by lubricants with the same ambient viscosity may vary significantly due to the specific way lubricants are formulated. In particular, contact fatigue life is strongly affected by the initial molecular weight distribution of the polymeric additive (viscosity improver) in the lubricant and contact operating conditions, which in some cases promote fast lubricant degradation caused by high lubricant shearing stresses.

The effect of polydispersity on structure of ultrasonically treated rubbers

Structure of ultrasonically treated rubbers, as recently shown by us, can be analyzed using the classical theory of rubber network statistics. This theory allows one to calculate gel fraction and crosslink density of a rubber network, provided, in particular, that molecular weight distribution (MWD) of the rubber chains is given. In previous studies, the initial MWD of ultrasonically treated rubbers was assumed to be of Flory's type in order to facilitate calculations. The present paper demonstrates that shape of the initial MWD insignificantly affects calculations of gel fraction and crosslink density if rubber network degradation proceeds through random scissions of main chains and crosslinks as in the case of continuous (with flow) ultrasonic treatment. MWD has been demonstrated to affect kinetics of rubber network degradation if a partial depolymerization of broken chains (thermal degradation) takes place during the ultrasonic treatment, which might happen under the static (no flow) conditions of treatment. The results of illustrative calculations are presented on structure of ultrasonically treated unfilled styrene-butadiene rubber.

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

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

Thermal pyrolysis of polypropylene: effect of reflux-condenser on the molecular weight distribution of products

When polypropylene is heated in an inert atmosphere and the volatile products are condensed, the molecular weight distribution (MWD) of the product obtained is very wide. In addition, this product is very waxy, has poor flow properties, and is unusable as a liquid fuel. To improve the product quality, ZSM-5 and other catalysts are usually used in the recycling process. However, these catalysts are costly. On the other hand, if the higher boiling fractions of the volatiles evolved due to degradation are not allowed to escape, then the MWD of the final product can be improved. This paper compares the effects of degradation with and without a reflux on the MWD of the product. Initial MWD of the polypropylene determined by GPC was used for all the simulations. In solving the governing population balance equation for the polymer degradation process, the rate constant for degradation has been fitted to the total weight loss of the polypropylene at a given temperature. The problems arising from the use of moment method with an assumed gamma-distribution are also discussed. A fixed-pivot discretization technique has been adopted for solving the governing equations.

Irreversible thermodynamics of reversible polymerization reactions

Based on the theory of irreversible thermodynamics explicit expressions are derived for the entropy production during reversible polymerization of bifunctional linear polymers whose initial molecular weight distribution can be chosen arbitrarily. The time-dependent course of the entropy production is explicitly calculated for two cases where the reaction starts (a) from monomer and (b) from monodisperse polymer molecules. In both cases we treat the system to be ideal and the time dependant change of the number of molecules is described by a kinetic approach using two kinetic constants for the forward and backward reactions, respectively. During reversible polymerization the entropy production σred is a monotonously decreasing function approaching zero when the system reaches the equilibrium molecular weight distribution with σred being positive in accordance with the second law of thermodynamics. In case of starting reaction from monodisperse polymer molecules under constraint that the number average chain length remains constant during reaction we calculate the entropy of mixing and discuss it with results obtained from statistical considerations.

Molecular weight distribution in random crosslinking of polymer–polyfunctional monomer systems

A Monte Carlo sampling algorithm for the simulation of molecular structural evolution in a random crosslinking process of polymer–polyfunctional monomer (PFM) systems is proposed. Combining a simple gel content experiment with this algorithm, various important property changes in a random crosslinking reaction, such as molecular weight distribution, location of gel points, crosslinking density within sol and gel fractions, PFM molecular density within sol and gel fractions, etc., can be fully explored. A virtual polymer–PFM system with a very narrow initial molecular weight distribution and a commercial low density polyethylene–triallyl cyanurate system have been used to demonstrate the application of this algorithm. The implications of the simulated results were also discussed.

Dynamic simulation and experimental evaluation of EPDM synthesis with ET(IND)2ZRCL2/MAO catalyst system

A mathematical model for the homogeneous terpolymerization of ethylene–propylene–diene (EPDM) in a semibatch reactor using Et(Ind)2ZrCl2/MAO as a catalyst system was developed and reported herein. In this study, we developed a kinetic model in order to explain the catalyst and EPDM properties such as catalyst activity, weight-average molecular weight, and terpolymer composition, which were experimentally and theoretically obtained. For this system, a lower E/P feed ratio leads to a lower molecular weight and a broader initial molecular weight distribution, while the increase in diene concentration leads to a decrease in the catalyst activity without broadening the MWD of the resulting polymers. The proposed model accounts for these experimental trends and for some data in the literature.

The ideality of polydisperse perfluoropolyether lubricants with application to physical vapor deposition

We have used thermogravimetric analysis (TGA) to measure the evaporation rate as a function of temperature and molecular weight for an alcohol-derivatized perfluoropolyether (PFPE), Fomblin Zdol. We show that the bulk evaporation rate of a polydisperse Zdol solution during temperature ramp TGA can be numerically simulated by combining molecular weight dependent Arrhenius parameters, the initial molecular weight distribution as measured by size exclusion chromatography, and Raoult’s law of vapor pressures. The simulation is shown to be in good agreement with experiment for both a low molecular weight polydisperse Zdol, and for a mixture of the low molecular weight Zdol with a heavier Zdol fraction. Mixtures of Zdol with non-functionalized Z lubricants are shown qualitatively to deviate substantially from ideality. In the disc drive industry, physical vapor deposition (PVD) is receiving renewed interest as an alternative method of applying the PFPE lubricants commonly employed as topical coatings on thin film magnetic media. In a process involving vaporization of a polydisperse liquid phase lubricant, quantitative prediction of deposition rates and vapor phase molecular weight distributions will in general only be possible with accurate knowledge of liquid phase distributions, component evaporation rates, and the ideality of the solution.

Oxidative degradation kinetics of polystyrene in solution

Polymer degradation is an example of fragmentation of macromolecules of distributed molecular weight (MW). We investigated polystyrene (PS) oxidative degradation kinetics by di-tert-butyl peroxide in solvent trichlorobenzene at 428 K. Peroxide was consumed by the PS decomposition reaction and also by an independent deactivation reaction involving the polymer. Gel permeation chromatography (GPC) showed that the initial PS molar molecular weight distribution (MWD) was exponential in MW. After the peroxide was depleted (in less than 15 min), GPC analysis of polymer samples showed that the final MWD was also exponential in MW for all experimental conditions. The initial peroxide concentration, 5–40 g/l, and initial polymer concentration, 12.5–50 g/l, affected the reaction rates and hence the final MWDs. A continuous-distribution model for polymer fragmentation (first-order in both peroxide concentration and polymer MWD) and simultaneous peroxide deactivation (first-order in polymer concentration) describes the temporal behavior of the MWD and its moments. To be consistent with the experimental data, the model incorporates random chain scission and rate coefficients that increase linearly with MW. Moment analysis provides the ratio of the rate parameters for the peroxide deactivation and polymer decomposition.

A way to gel-point determination

In order to linearize the representation of gel-formation kinetics, logarithmic coordinates for sol fraction and irradiation dose are proposed. Slopes have been obtained for initial molecular weight distributions (Schulz type) with polydispersities in the range 1.5–6. The high linearity of the approximation, together with the pre-known slope, can reduce the experimental inaccuracy of gel-point determination.

Random Degradation of Branched Polymers. 1. Star Polymers

A random sampling technique in which polymer molecules are sampled from an infinite number of polymer molecules in the reaction mixture is used to predict the molecular weight distribution (MWD) change during random scission reactions of star-shaped polymers. For simpler initial MWDs, the analytical solutions for the full MWD change, as well as the average molecular weights, can be derived in a straightforward manner. For any initial MWD, the concept of the random sampling technique provides a unique Monte Carlo simulation algorithm that enables one to estimate the change in the statistical properties during random degradation quite effectively. Compared with the random degradation of linear polymer molecules, the decrease in the weight-average molecular weight is slower; however, such differences are made smaller as the initial MWD becomes broader. In the course of random degradation, linear and branched polymer fractions are formed. As the degradation reaction proceeds, the polydispersity index of the l...

Random Degradation of Branched Polymers. 2. Multiple Branches

The random sampling technique discussed in part 1 of this series1 is used to investigate the molecular weight distribution (MWD) change during random scission reactions of the polymers with multiple branches. By application of the concept of the random sampling technique to the Monte Carlo method, one obtains a very powerful simulation method that can be applied to the random degradation of virtually any type of branched polymer. Suppose branched polymers are formed first by randomly combining linear polymer molecules, and then these branched polymer molecules are used for the random degradation reactions (branching → degradation). If the processes of branching and degradation are interchangeable, then the same MWD can be obtained from the sequence of processes, degradation → branching. In contrast with random cross-linking and degradation, the processes are not interchangeable except when all of the primary chains possess the most probable distribution with randomly distributed branch points. The MWDs given by the random branching of primary chains with the most probable distribution provide the limiting distributions to which polymers with multiple branches approach as the extent of the scission reaction increases, irrespective of the initial MWD including nonrandomly branched polymers. An analytical expression for such a limiting MWD is derived by the application of the random sampling technique.

Accurate description of intrinsic viscosity changes under polymer degradation: Narrow schulz distributions

AbstractFor the Shulz distributions with weight—polydispersity from 1.4 to 2.0, the following equation is correct: ln [η] = ln [η]0 − a{ln P0 + DD − ln[PF − P0) × exp(−1.2 × DD)]}. Here, P0 and PF are viscosity–polydispersities of the initial molecular weight distribution (MWD) and the Flory distribution, respectively; a is the Mark–Houwink exponent; and DD = ln(Mn0/Mn). For more narrow MWDs, the complicated equation is required: ln [η] = ln[η]0 − a{ln P0 + DD − ln[PF − (PF − P0 × exp(−0.9 × DD − 0.28 × DD2)]}. The inaccuracy of these equations is less than 1.5%. © 1995 John Wiley & Sons, Inc.