Connection between Polymer Molecular Weight, Density, Chain Dimensions, and Melt Viscoelastic Properties

Abstract

One of the main goals of polymer science has been to relate the structure of macromolecular chains to their macroscopic properties. In particular, it has been hoped that one could relate the sizes of polymer coils to the degree to which they entangle with one another and thus to their viscoelasticity in the melt. In recent years, the availability of model polymers with nearly monodisperse molecular weight distributions and precisely controlled chemical structures has allowed for improved data both on rheology and on the dimensions of the chains. This has now allowed us to determine the correlations between such properties as chain dimensions, density, and plateau modulus and to show that some quite simple relations exist between them. The main body of these data is on polymers that can be considered to be models for polyolefins. These have been made by the hydrogenation of polydienes synthesized by anionic polymerization techniques. In this way the molecular weight distribution can be made to be nearly monodisperse (Afw/M" < 1.1) and the chemical structure is well controlled. For example, models of a wide range of ethylene-butene copolymers have been made by the saturation of polybutadienes with a range of vinyl content. Such polymers can be made at many molecular weights as well. The viscoelastic properties of these polymers have been measured very precisely, and their chain dimensions have been determined by small-angle neutron scattering. To a high degree of correlation, we find that the mean-square unperturbed end-to-end distance, <R2)o, the density, p, and molecular weight, M, are related to the plateau modulus, G^, G^{{R2)op/M}3 a finding in accord with that of Ronca. This simple relationship gives us a deep understanding of what controls the rheology of these polyolefins and of how we might be able to predict the properties of as yet unsynthesized polymers.

Molecular Dynamics Simulation of Polymer–Metal Bonds

“…It is a measure of how "fat" a chain is in relation to how stiff it is. The sizes of the chain segments used in the atomistic models are in accordance with those proposed by other authors for similar polymers [16]. In this way, it is possible to use models involving thousands of atoms, but with a size that is still treatable using Molecular Dynamics calculations, and is meaningful to the length and time scales related to the adhesion phenomena.…”

A stick-slip/Rouse hybrid model for viscoelasticity in polymers

“…The value of M 0 was given above as M 0 = 68.114. For the polymer density we use the value given by Abdel-Goad, et al, [1], as ρ = 0.90 × 10 −24 g/Å 3 at T = 298 K (values range from 0.9 × 10 −24 to 1 × 10 −24 g/Å 3 , [14], [16], [17], [18], but most commonly 0.9 × 10 −24 g/Å 3 ). The segment density is then…”

Polymer dynamics: long time simulations and topological constraints

“…The available experimental data for dense melts are the result of a long term substantial experimental effort [33,34]. Rheological measurements were performed on these samples and in many cases the R 2 values were determined using small angle neutron scattering.…”

“…Refs. [33,34] provide the values for the plateau modulus, G 0 N , the mass density, ρ m , the ratio of the mean-square end-to-end distance to the molecular weight of the polymer, R 2 /M, and the packing length, p = M/( R 2 ρ m N A ), where N A is the Avagadro number. All the melt data points obey the empirical relation G 0 N = 0.00226k B T /p 3 , indicated as the dashed line in Fig.…”