Entanglements /Reptation
"Entanglement means the topological restriction of molecular motion by other chains."
"Entangled polymers are characterized with effective internal scale, commonly known as ‘the length of macromolecule between adjacent entanglements’ Me."
"Effective cross-links from entanglements with other polymer chains restrict polymer chain motion to a 'tube' within these restrictions. Since polymer chains would have to be broken to allow the restricted chain to pass through them, the mechanism for movement (flow) of this restricted chain is reptation. In the 'blob' model, the polymer chain is made up of n Kuhn lengths of individual length l. The chain is assumed to form tangled 'blobs' between each effective cross-link, containing ne Kuhn length segments in each."
"Reptation is the snake-like thermal motion of very long linear, entangled macromolecules in polymer melts or concentrated polymer solutions."
"The concept of reptation was introduced into polymer physics in 1971 by Pierre-Gilles de Gennes to explain the dependence of the mobility of a macromolecule on its length. It is used as a mechanism to explain the viscous flow in an amorphous polymer."
"The linear macromolecules reptate, if the length of macromolecule M is bigger than ten times ‘the length of macromolecule between adjacent entanglements’ Me . There is no reptation motion for polymers with M<10 Me, so that the point 10 Me is a point of dynamic phase transition. Due to the reptation motion the coefficient of self-diffusion and conformational relaxation times of macromolecules depend on the length of macromolecule as M−2 and M3, correspondingly.[2][3]The conditions of existence of reptation in the thermal motion of macromolecules of complex architecture (macromolecules in the form of branch, star, comb and others) have not been established yet."
"The dynamics of shorter chains or of long chains at short times is usually described by the Rouse model."
Recent Journal Articles
A simple scaling derivation of the shear thinning power-law exponent in entangled polymer melts
(3522-3525) Polymer 52 #16 (2011)
Fatkullin, Mattea and Stapf of Kazan Federal University, Russia and Technische Universität Ilmenau, Germany, based on that the polymer dynamics in entangled polymer melts possesses the property of dynamical self-similarity, propoase that the power-law exponent of the Carreau-Yasuda law, which empirically describes the shear thinning effect of the polymer melt viscosity, is inversely proportional to the exponent of the molecular mass dependence of the terminal relaxation time. This finding is obtained in cases where the shear rate dependence of the segmental relaxation time is negligible. If such dependence is essential, the Carreau-Yasuda law is slightly modified at high shear rates: instead of a power-law dependence with a small shear rate independent exponent, a weaker logarithmic dependence is found both for shear rate and molecular mass dependence, which resembles the approach to zero of an effective shear rate and molecular mass dependent power-law exponents at sufficiently high shear rates. (RDC 7/15/2011)
Translation and Rotation of Spherulites during the Crystallization of Isotactic Polypropylene with Reduced Chain Entanglements
(2844–2851) Macromolecules 44 #8 (2011)
|Wang et al of the University of Science and Technology of China and the Chinese Academy of Sciences, China, studied the isothermal crystallization of isotactic polypropylene (iPP) spherulites under chain entanglements, reduced chain entanglements, and unconfined thick film conditions using polarized optical microscopy (POM). While spherulite translations and rotations were not observed in entangled iPP samples, the growing spherulites crystallizing the melt with reduced entanglements conspicuously translated and/or rotated, even when their sizes exceeded the sample film thicknesses. Our entanglements-reduced samples were prepared by first slowly crystallizing a commercial entangled iPP in mineral oil (and then extracting the mineral oil with hexane) and by a direct polymerization