Polymers polydispersity

Polydisperse polymers do not yield sharp peaks in the detector output as indicated in Fig. 9.14. Instead, broad bands are produced which reflect the polydispersity of synthetic polymers. Assuming that suitable calibration data are available, we can construct molecular weight distributions from this kind of experimental data. An indication of how this is done is provided in the following example. 

In another study Milehev and Landau [27] investigated in detail the transition from a disordered state of a polydisperse polymer melt to an ordered (liquid erystalline) state, whieh oeeurs in systems of GM when the ehains are eonsidered as semiflexible. It turns out that in two dimensions this order-disorder transition is a eontinuous seeond-order transformation whereas in 3d the simulational results show a diseontinuous first-order transformation. Comprehensive finite-size analysis [27] has established... 

A. Milchev. Phase transitions in polydisperse polymer melts. Polymer 24 362, 1993. 

S. Livne. A polydisperse polymer solution as a critical system. Macromolecules 27 5318-5328, 1994. 

When applied to the SEC column, the calibrated polydisperse polymer solution provides a large number of data points in a single run. Use of a standard with a molecular size distribution that encompasses the full separation range for the column allows the entire separation range to be calibrated in a single run (Fig. 2.4). 

The resolving capability is the same over the full operating range of the column. This offers an ideal situation for the analysis of very polydisperse polymers that may also contain lower molecular weight additives. 

A criterion for selecting a right pore size to separate a given polydisperse polymer is provided here. To quantify how much the MW distribution narrows for the initial fraction, an exponent a is introduced (2). The exponent is defined by [PDI(0)] = PDI(l), where PDI(O) and PDI(l) are the polydispersity indices of the original sample and the initial fraction, respectively. A smaller a denotes a better resolution. If a = 0, the separation would produce a perfectly monodisperse fraction. Figure 23.7 shows a plot of a as a function of 2RJd (2). Results... 

In analytical SEC, the optimal pore size for a given polydisperse polymer is approximately 1/4 < IRJd — 1/2 when a single-pore size column is used (20). In contrast, the pore size needs to be much smaller in HOPC. Small pores are deliberately used in HOPC to exclude nearly all MW components at low concentrations but to allow the entry of low MW components only at high concentrations by the high osmotic pressure (2). Use of the same pore size as used in SEC results in a poor separation. The latter is essentially an overloading in SEC. 

FIGURE 23.8 Range of the original polydisperse polymer to be separated in high resolution by HOPC using CPG of a given diameter indicated adjacent to each bar. 

Data of Figs 8-10 give a simple pattern of yield stress being independent of the viscosity of monodisperse polymers, indicating that yield stress is determined only by the structure of a filler. However, it turned out that if we go over from mono- to poly-disperse polymers of one row, yield stress estimated by a flow curve, changes by tens of times [7]. This result is quite unexpected and can be explained only presumably by some qualitative considerations. Since in case of both mono- and polydisperse polymers yield stress is independent of viscosity, probably, the decisive role is played by more fine effects. Here, possibly, the same qualitative differences of relaxation properties of mono- and polydisperse polymers, which are known as regards their viscosity properties [1]. 

According to the concepts, given in the paper [7], a significant difference between the values of yield stress of equiconcentrated dispersions of mono- and polydisperse polymers and the effect of molecular weight of monodisperse polymers on the value of yield stress is connected with the specific adsorption on the surface of filler particles of shorter molecules, so that for polydisperse polymers (irrespective of their average molecular weight) this is the layer of the same molecules. At the same time, upon a transition to a number of monodisperse polymers, properties of the adsorption layer become different. 

The algorithm we used for solvent/polydisperse polymer equilibria calls for only one solvent/polymer interaction parameter. The interaction parameter (pto) i ed in the algorithm can be determined from essentially any type of ethylene/polyethylene phase equilibrium data. Cloud-point data have been used (18). while Cheng (16) and Harmony ( ) have done so from gas sorption data. 

First Steps to Simulate Polydisperse Polymer Melts. 128... 

In direct insertion techniques, reproducibility is the main obstacle in developing a reliable analytical technique. One of the many variables to take into account is sample shape. A compact sample with minimal surface area is ideal [64]. Direct mass-spectrometric characterisation in the direct insertion probe is not very quantitative, and, even under optimised conditions, mass discrimination in the analysis of polydisperse polymers and specific oligomer discrimination may occur. For nonvolatile additives that do not evaporate up to 350 °C, direct quantitative analysis by thermal desorption is not possible (e.g. Hostanox 03, MW 794). Good quantitation is also prevented by contamination of the ion source by pyrolysis products of the polymeric matrix. For polymer-based calibration standards, the homogeneity of the samples is of great importance. Hyphenated techniques such as LC-ESI-ToFMS and LC-MALDI-ToFMS have been developed for polymer analyses in which the reliable quantitative features of LC are combined with the identification power and structure analysis of MS. 

Ordered conformation. Figure 1. shows representative electron micrographs of samples A, B, C, and D vacuum dried from xanthan solutions under ordering conditions as specified in the legend. Xanthan samples A -D appear as unbranched, uniformly thick, convoluted chains. The contour length varies from molecule to molecule as expected for a polydisperse polymer. The electron micrographic... 

In the case of a polydisperse polymer it is still the total number n of solute molecules that is measured and the total mass m of solute molecules that is known from sample preparation, resulting in the number average molar mass M = ... 

V is the molar volume of the solvent and pp the density of the polymer. For polydisperse polymers A2 is a more complex average, which shall not be discussed here in detail [7]. For good solvents and high concentrations, the influence of the 3rd virial coefficient A3 cannot be ignored, and n/c versus c sometimes does not lead to a linear plot. In these cases, a linearization can frequently be obtained with the approximation A3 = A (M)n/A by plotting [12,13]... 

Method for the Atomistic Monte Carlo Simulation of Polydisperse Polymer Melts. 

The reader s attention is especially directed to the new terms uniform polymer and nonuniform polymer which denote polymers composed of molecules that are uniform or nonuniform, respectively, with respect to relative molecular mass and constitution. These terms replaced the widely used, but non-descriptive and self-contradictory terms monodisperse polymer and polydisperse polymer . 

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