Intrinsic Entanglement molecular weight

On the other hand, the mechanical properties also depend on the materials molecular composition and structure, i.e., intrinsic parameters. Intrinsic parameters are, for instance, chemical composition or constitution, configuration, conformation, chain cross section, entanglement molecular weight, free volume, chain stiffness, macromolecular mobility, crystallinity, and others [4, 16, 17]. Chain length and chain length distribution (or molecular weight M ) have a basic influence on mechanical properties, which is illustrated in Fig. 1.17. Three regions can be identified ... 

The packing length concept can also be used to develop an equation for estimating the entanglement molecular weight Mf from intrinsic viscosity data [53]. We start with Eq. 2.86 for the intrinsic viscosity of a polymer in its theta state ... 

As the craze microstructure is intrinsically discrete rather than continuous, the connection between the variables in the cohesive surface model and molecular characteristics, such as molecular weight, entanglement density or, in more general terms, molecular mobility, is expected to emerge from discrete analyses like the spring network model in [52,53] or from molecular dynamics as in [49,50]. Such a connection is currently under development between the critical craze thickness and the characteristics of the fibril structure, and similar developments are expected for the description of the craze kinetics on the basis of molecular dynamics calculations. 

It is interesting to observe that cholesteric copolyesters synthesized from i+,U -dihydroxyazoxybenzene and mixtures of (+) -3-methyl-adipic acid and dodecanedioic acid do not orient. Systematic variations with molecular weight and careful analysis in certain homologous series should give information on the influence of the intrinsic flexibility of the chains, the apparent viscosity of the melt and certain basic microscopic processes such as entanglement effects on the tendency for macromole cular chains to become aligned when placed in a magnetic field. 

The essential concept involved in the statistical theory of rubber elasticity is that a macroscopic deformation of the whole sample leads to a microscopic deformation of individual polymer chains. The microscopic model of an ideal rubber consists of a three-dimensional network with junction points of known functionality greater than 2. An ideal rubber consists of fully covalent junctions between polymer chains. At short times, high-molecular-weight polymer liquids behave like rubber, but the length of the chains needed to describe the observed elastic behavior is independent of molecular weight and is much shorter than the whole chain. The concept of intrinsic entanglements in uncrosslinked polymer liquids is now well established, but the nature of these restrictions to flow is still unresolved. The following discussion focuses on ideal covalent networks. 

Eq. (131) shows the viscosity is proportional to the 0.67 power of the concentration and 0.47 power of the molecular weight when there is no entanglement in the solution. Experimental data shows the relative viscosity should be proportional to the 0.5 power of concentration [87, 88]. The viscosity (not the intrinsic viscosity) only shows the 0.5 power of the molecular weight when the polymer concentration is low, which is in agreement with the experimental results [89J. 

Equation 14.13a quantitatively holds for just about all polymer melts. The addition of a low molecular weight solvent, of course, cuts down the entanglements and raises M c-Equation 7.15 suggests that entanglements set in when the dimensionless product of intrinsic viscosity and concentration (the Berry number) exceeds one, [tj]c >1. Thus, if you know [rj] for your polymer in the solvent, you can get an idea of the concentration above which Equation XAA ib should be used (and the viscosity rises much more sharply ). In practice, even moderately concentrated (say 25% or more) polymer solutions have viscosities proportional to provided that M , is in the range of commercial... 

Polyethylene crystallizes from the molten state or solution when prevailing conditions make the crystalline state more stable than the disordered one. The processes by which polyethylene crystallizes reflect the properties of the disordered state from which the ordered phase condenses. Thus, for instance, levels of chain entanglement, molecular dimensions, and viscosity all play important roles. The factors affecting the structure of the disordered state are both intrinsic to the molecules and extrinsic to the surrounding conditions. The principal molecular factors are the molecular weight, molecular weight distribution, and concentration, type, and distribution of branches. External factors include temperature, pressure, shear, concentration of solution, and polymer-solvent interactions. 

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