Molecular weight distribution, simulation

Generally, the models used for simulation of living polymers can be divided roughly into two classes, focused on static or dynamic properties of the LP or GM. The static models are mainly designed to study equilibrium conformational properties of the polymer chains, critical behavior at the polymerization transition, and molecular weight distribution... 

IV. SIMULATIONAL RESULTS—STATIC PROPERTIES A. Molecular Weight Distribution... 

The influence of selectivity in the initiation, termination or chain transfer steps on the distribution of monomer units within the copolymer chain is usually neglected. Galbraith et a .u provided the first detailed analysis of these factors. They applied Monte Carlo simulation to examine the influence of the initiation and termination steps on the compositional heterogeneity and molecular weight distribution of binary and ternary copolymers. Spurting et a/.250 extended this... 

Jackson, C. and Yau, W. W., Computer simulation study of multidetector size-exclusion chromatography. Flory-Schulz molecular weight distribution, in Chromatographic Characterization of Polymers, Hyphenated and Multidimensional Techniques, Provder, T., Barth, H. G., and Urban, M. W., Eds., American Chemical Society, Washington, D.C., 1995, chap. 6. 

A number of interesting and non-obvious insights into molecular weight distributions can be gained from these simulations. For example, Fig. 3 demonstrates the effect of X on M IM as a function of C0 for irreversible chain transfer where C = 0. 

Equations suitable for simulation of molecular weight distributions for any initial distribution and chosen values of G(scission) and G(crosslinking) have been developed and demonstrated. The molecular weight distributions may be obtained by GPC (with the limitation of changes in relative hydrodynamic volumes) and by sedimentation velocity in the ultracentrifuge. 

For a theoretical description of crosslinking and network structure, network formation theories can be applied. The results of simulation of the functionality and molecular weight distribution obtained by TBP, or by off-space or in-space simulations are taken as input information. Formulation of the basic pgf characteristic of TBP for crosslinking of a distribution of a hyperbranched polymer is shown as an illustration. The simplest case of a BAf monomer corresponding to equation (4) is considered ... 

Table I indicates good agreement between the molecular weight distribution statistics obtained by coupled GPC/Viscometer method and the nominal values for t BS 706. The discrepancy between the Mark-Houwink parameters obtained here and the reported values for polystyrene standard ( ) in THF at 25°C (i.e., a = 0,706 and k = 1.60 x 10 ) may in part be due to the uncertainty involved in the determination of the dead volume between DRI and viscometer detectors. Our simulation studies over a range of dead volume values (0 to 120u)l) showed that a and k are quite sensitive to the dead volume between the detectors. Larger dead volume results in smaller o and larger k values. This is a direct result of a clockwise rotation of log [q] vs. log M(v) curve (Figure 12) which occurs when the dead volume correction is applied in quantitative analysis. The effect on the molecular weight statistics, however, appeared to...

This is done in simulating complex reactions such as polymerization. The zeroth, first, and second moments of the molecular weight distribution are used to characterize the kinetics of the reaction. 

In order to compare the results of an analysis technique with the true solution it is essential that the MWD be known before the analysis is started. Consequently, computer simulated data generated by assuming a molecular weight distribution and subsequently using Equation 3 to generate g(x) for a series of t values, was used for analysis. Five different MWDs were used, four of which were generated using GEX functions as models (two GEX functions for bimodal peaks), and Table I shows the GEX parameters used for each of these MWDs. 

The utilization properties of PVC are intimately linked to the molecular-weight distribution (MWD) of macromolecules. The MWD may be measured by appropriate techniques, such as gel-permeation chromatography, but also predicted by computation. Comparing experimental and calculated MWD allows the validation of a kinetic model as well as the tuning of parameters. On this basis, the operation procedure necessary to get a target MWD may be simulated. 

Table 13.3 presents the expressions for the rate constants applied in this work. The parameters are taken mostly from the work of Xie et al. [6], A distinctive feature of the numerical simulation of the influence of gel effect on the termination in the polymer-phase is described by a relation proposed by Kipparisides et al. [5], This combination of parameters gives realistic results on modeling both the reaction dynamics and the development of the molecular-weight distribution, reproducing closely experimental data (see Figure 13.6). The subscript 1 refers to the monomer phase, 2 to the polymer phase, and 22 to the polymer-phase after the critical conversion Xf. In addition, Table 13.4 presents first-order constants for usual initiators. 

Polymerization rate represents the instantaneous status of reaction locus, but the whole history of polymerization is engraved within the molecular weight distribution (MWD). Recently, a new simulation tool that uses the Monte Carlo (MC) method to estimate the whole reaction history, for both hnear [263-265] and nonlinear polymerization [266-273], has been proposed. So far, this technique has been applied to investigate the kinetic behavior after the nucleation period, where the overall picture of the kinetics is well imderstood. However, the versatility of the MC method could be used to solve the complex problems of nucleation kinetics. 

A computer simulation of size-exclusion chromatography-viscom-etry-light scattering is described. Data for polymers with a Flory-Schulz molecular weight distribution (MWD) are simulated, and the features of the different detector signals are related to the molecular weight and polydispersity of the distribution. The results are compared with previously reported simulated results using a Wesslau MWD. 

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