The theory of stimulated echo (SE) without magnetic field gradient is proposed. The theory made it possible for the first time to establish a relationship between the stimulated echo signal and correlation function of molecular mobility. Signals of free induction decay (FID) and SE in polymer networks and branched polymers were modeled. The type of the correlation function at different average chain lengths N0 between knots and different distribution functions of the knots was determined. A strong influence of the molecular weight distribution (MWD) on the type of the correlation function in polymer melts was shown. Two methods were proposed for the numerical determination of the correlation function from the observed FID and SE signals. These methods gave an information about the molecular mobility and topological structure in the samples of branched polymethyl methacrylates of different structures and various molecular weights.
In this paper, a statistical model is developed to determine the number‐average and weight‐average molecular weights of a branched polymer system formed through random branching of polymer chains. The average properties of the branched structures formed by T‐shaped junctions and by H‐shaped junctions through random branching of polymer chains are compared in detail. The model indicates that the H‐shaped chain connections can form a gel molecule while the T‐shaped chain connections alone can not cause gelation. Because only the randomly branched polymers for an equilibrium system are considered (under Flory's simplifying assumptions), the present results would not be a rigorous proof that the H‐shaped junctions are required to form a gel molecule in any type of reaction system. However, the present paper shows that the Macosko‐Miller model can be applied to this type of problem in a straightforward manner. The gel point for the branched structures formed by H‐shaped junctions can also be determined by the model. 相似文献
The technique for determining branching in polymers by using a combination of GPC and intrinsic viscosity data has been extended beyond current methods. Equations used in these analyses are presented. The derivations are based upon the assumption that branching is present only when there is a measurable reduction in the intrinsic viscosity. Techniques for calculating the functionality of the star branch point in starbranched polymers are given. Three random-branching parameters are calculated from a knowledge of the average branching density, \documentclass{article}\pagestyle{empty}\begin{document}$ \bar \lambda $\end{document}: (a) the lowest molecular weight branched polymer that can be measured, M?*; (b) the average molecular weight between branch points, M?bp; (c) the weight percentage of polymer that is branched. The applicability of this technique is demonstrated by using an analysis of published data on characterized fractions of a randomly branched polystyrene. 相似文献
Monte Carlo simulations were conducted to estimate the elution curve of size exclusion chromatography (SEC). The present simulation can be applied to various types of branched polymers, as long as the kinetic mechanism of nonlinear polymer formation is given. We considered two types of detector systems, (1) a detector that measures the polymer concentration in the elution volume to determine the calibrated molecular weights, such as by using the differential refractive index detector (RI), and (2) a detector that determines the weight‐average molecular weight of polymers within the elution volume directly, such as a light scattering photometer (LS). For polydisperse star polymers, both detector systems tend to give a reasonable estimate of the true molecular weight distribution (MWD). On the other hand, for comb‐branched polymers, the RI detector underestimates the molecular weight of branched polymers significantly. The LS detector system improves the measured MWD, but still is not exact. The present simulation technique promises to establish various types of complicated reaction mechanisms for nonlinear polymer formation by using the SEC data quantitatively. In addition, the present technique could be used to reinvestigate a large amount of SEC data obtained up to the present to estimate the true MWD. 相似文献
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. 相似文献
This work deals with the kinetics of the living polymerization initiated by a bifunctional initiator with different rate constants of the first and the second step of initiation. The expressions of the molecular weight distribution (MWD) function, the number- and weight-average degrees of polymerization and the polydispersity index were derived rigorously. Numerical results show that the nonequal initiation rate constants often lead to a bimodal MWD except the ratio of ki to ki′ being very large (>500, for instance) or relatively small (<1, for example). The MWD of the resultant polymer is rather narrow even in the presence of double peaks. With decreasing initiator concentration, the MWD at full conversion becomes narrower, and the shoulder peak of the MWD curve declines. 相似文献
The distribution of molecular weights in realistic free-radical polymerizations with branching was analyzed theoretically. Series solutions were obtained for the fraction of molecules with r repeating units and the number of branch points contained in molecules with r repeating units. Branching by transfer processes was found to increase the proportion of both high and low molecular weight components in the system. The apportioning of branch points among r-mer molecules was shown to be somewhat narrower than a Poisson distribution. The major difference between the calculated distributions and previous model distributions for branched systems was the absence of discontinuities in the moments at all levels of branching. 相似文献
Ambient temperature-initiated anionic polymerization has generated branched polystyrenes of varying molecular weights and architectures by inclusion of a distyryl branching comonomer into a conventional sec-Butylithium-initiated polymerization of styrene. Primary chain length control within the branched polymers, and restriction of the branching points to varying segments of the primary chains, led to variations of glass transition temperature with no direct correlation to the branched polymer molecular weight but a strong relationship to the length of individual chains comprising the branched macromolecules. 相似文献
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 ktr/kp are presented and a method of determination of ktr/kp from the DP w/DP n data is proposed. 相似文献
Two polymer molecules of the same length (n) and the same number of branch points (N) can have different properties, since they may possess distinct architectures. In this paper we present a conditional Monte Carlo algorithm for the virtual synthesis of metallocene‐catalyzed polyethylene (PE) in a continuous stirred tank reactor (CSTR). The condition for the Monte Carlo method consists of a fixed chain length distribution (CLD) and a degree of branching distribution (DBD). These distributions are calculated with a Galerkin finite element method. The synthesis method is a recursive algorithm that subsequently creates insertions of sub‐structures containing numbers of branch points according to a certain probability density function. This provides an adjacency matrix describing the connectivity between the branch points, while separately a vector containing the length of segments between branch points and terminal segments is generated. Characterization of the architectures proceeds by rheological features, seniorities and priorities, and molecular properties like the radius of gyration. Comparing the radii of gyration of metallocene polyethylene and low density PE (ldPE) shows the former to possess a more comb‐like structure on average. This is confirmed by the rheological characterization. The found bivariate seniority/priority distribution agrees well to the results of an analytical study of the same chemical system.