Moments Of Molecular Weight Distribution Research Articles

Enhanced spin capturing polymerization: Numerical investigation of mechanism

ABSTRACTSimulation on the kinetic scheme of enhanced spin capturing polymerizations (ESCP) were performed to reveal the influence of different parameters, e.g., initiation rate, spin capturing and side reactions on the properties (the monomer conversion, degree of polymerization, polydispersity index, and the fraction of “living” chains) of polymer obtained. The kinetic scheme of ESCP was solved numerically as well as the method of statistical moments of molecular weight distribution was applied to get some numerical expressions for analysis. The simulations showed that fast initiation rate can lead to decrease of living fraction and broadening of molecular weight distribution. Whereas high rate of spin capturing makes the polymer chains shorter but increases living character. And side reactions always decrease livingness of the polymer obtained. Finally in the case of absence of side reaction we were able to formulate criteria for formation of polymer with target molecular weight and quota of living chains via ESCP process. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015, 53, 2546–2556

Gray-box modeling and control of polymer molecular weight distribution using orthogonal polynomial neural networks

A method of modeling and control on polymer molecular weight distribution (MWD) is presented in this paper. An orthogonal polynomial feedforward neural network (OPFNN) and a recurrent neural network (RNN) are combined to model the shape of MWD. In this combined neural networks, the weights of OPFNN are equivalent to moments of MWD through a linear transformation, when the polynomial used as the basis function of OPFNN satisfies some requirements. So the weights are given practical feature, and terms the neural network model a gray-box model. Then the requirements of polynomial are deduced. After modeling, an optimal control scheme is discussed on tracking the desired MWD during the polymerization process. The modeling error is added into the performance function to improve the control effect. The modeling and control method is tested on styrene polymerization reacted in CSTR, and simulation results proved the effectiveness of the method.

High pressure polymerization of ethylene and rheological behavior of polyethylene product

AbstractA mathematical model of the high pressure polymerization of ethylene in tubular reactors was tested with experimental data obtained from an industrial size tubular reactor. Series of experiments involving changes in operating conditions were carried out, and process data and polyethylene samples were collected. The collected samples were characterized for their molecular weight distributions and various rheological material functions involving shear and extensional flows. The findings of the model were compared against the generated process data and the molecular weight distributions of the samples. The determined rheological behavior exhibited strong dependence on the primary characteristics of the resins. Overall, this study should introduce a better understanding of the interactions between high pressure reaction conditions and the primary properties of polyethylene, including moments of molecular weight distribution and extent of branching on one hand and the interrelationships between primary properties and the rheological behavior of the high pressure polyethylene product on the other hand.

Influence of molecular weight distribution of polymer melts on transition from Newtonian to non-Newtonian behaviour in shear flow

Dynamic moduli of high molecular weight monodisperse polystyrene melts and their binary blends have been measured as a function of frequency. The critical frequency ω c and loss modulus G″( ω c) corresponding to departure from Newtonian behaviour have been determined and related to the moments of molecular weight distribution. The experimental result that the product τ w ω c is independent of molecular weight distribution ( τ w is the weight-average relaxation time, defined as τ w = η o J o e ) has been interpreted by assuming: (1) the validity of the empirical Cox-Merz rule; and (2) that the transition from Newtonian to non-Newtonian behaviour in a steady shear flow occurs for a characteristic recoverable strain.

Relative and Absolute Measures of Heterogeneity of Polymer Sizes

Abstract The common measure of relative heterogeneity of a polymer sample is the ratio Mw/Mn, where Mw is the weight-average molecular weight and Mn is the number-average molecular weight [1]. A convenient measure of the absolute heterogeneity of polymer sizes is the variance of the molecular weight distribution. The variance [Var(M)] is formulated in terms of Mw and Mn as follows: where E(M) and E(M2) are, respectively, the first and second moments of the polymer molecular weight distribution taken about the origin. The rth moment of the molecular weight distribution about the origin is defined as where Mi represents the molecular weight of polymer containing i units and P(Mi) represents the fraction of polymer molecules with molecular weight Mi. It is easy to show that Mw and Mn can be represented in terms of moments as follows [1,2]: Substitution of E(M2) and E(M) in terms of Mw and Mn into Eq. (1)yields The positive square root of the variance is defined as the standard deviation, δ The relative utili...

On the Calculation of Moments of Molecular Weight Distribution from Sedimentation Equilibrium Data.

In this paper we discuss a technique for calculating moments of polydisperse materials in terms of concentration readings along the cell. The proposed method minimizes dependence on data from the end points where they may be unreliable. An analysis is given of the errors involved in the use of the proposed method when the underlying molecular weight distribution is the Schulz distribution or the lognormal.