Coil entanglement

Fig. 15. Expected stress distribution at the die exit both in the no-slip and slip states corresponding to the coil (entangled) and stretch (disentangled) states (a) and (b) of the adsorbed chains on the exit wall (see Fig. 16)...

Turner et al. [41-43] do not consider reduced coil mobility with increasing polymer concentration as decisive. Under these conditions, macromolecules behave as rigid balls, mutually hardly penetrable the probability of radical encounter decreases. The onset of autoacceleration is also ascribed to mutual coil entanglement which only occurs at and above the critical polymer concentration Cc and a certain minimum mean molecular mass A (0.5 < a < 1). The product of these critical quantities is constant... 

The objectives of this study were to determine the influence of increasing concentration of the random coil polysaccharide guar gum on odor (perceived orthonasally by smelling), thickness, taste, and aroma (perceived retronasally when sample is placed in the mouth) perception and to study the effect of onset of random coil entanglement above c on odor, thickness, taste, and aroma perception, with particular emphasis on aroma release and perception. Guar gum was chosen for this study because it is used extensively for thickening products by the food industry and because it is a neutral polymer. 

Perceived thickness increased with increasing coil overlap, increasing abruptly with the onset of coil entanglement at c. Sucrose concentration had little influence on perceived thickness in the presence of the guar gum (Fig. 1). Perceived sweetness was independent of coil overlap at concentrations of guar below c and increased somewhat as thickness increased. However, the intensity of perceived sweetness decreased rapidly with the onset of coil entanglement above c (Fig. 2). The three different concentrations of sucrose were clearly distinguished by perceived sweetness... 

The electrospinning of HA nanofibers is challenging. The HA chains take the form of expanded, random coils entangling with each other at very low concentration. The resultant high viscosity and siuface tension at relatively low concentration hinder electrospinning. Additionally, the insufficient evaporation of water is likely to refuse the nanofibers on the collector [205]. 

It has already been mentioned that polymer melts are non-Newtonian and are in fact under normal circumstances pseudoplastic. This appears to arise from the elastic nature of the melt which will be touched on only briefly here. In essence, under shear, polymers tend to be oriented. At low shear rates Brownian motion of the segments occurs so polymers can coil up at a faster rate than they are oriented and to some extent disentangled. At high shear rates such re-entangling rates are slower than the orientation rates and the polymer is hence apparently less viscous. 

When polymer melts are deformed, polymer molecules not only slide past each other, but they also tend to uncoil—or at least they are deformed from their random coiled-up configuration. On release of the deforming stresses these molecules tend to revert to random coiled-up forms. Since molecular entanglements cause the molecules to act in a co-operative manner some recovery of shape corresponding to the re-coiling occurs. In phenomenological terms we say that the melt shows elasticity. 

How do highly interpenetrated random coil chains disentangle to cause fracture Disentanglement is considered to occur as shown in Fig. 14, where we depict the response of an entangled chain to a constant (step function) draw ratio X as follows ... 

How does the polymer chain sneak out from the entangled random coil state and how does it order into a crystalline state ... 

Under quiescent conditions, polymer solutions are divided into four categories depending on the average distance separating the centers of mass of the molecular coils the dilute, the semi-dilute (or semi-concentrated), the concentrated and the entangled state. 

In elongational flow, the entanglement regime was observed at much lower concentrations, even below [r ] c = 0.1 [169], The effect was initially thought to be the result of coil expansion in flow, but was later discarded in favor of the lifetime for entanglement formation, under dynamic conditions of flow. 

It is expected, however, that the Gaussian representation is inadequate in transient elongational flow, even if the chain is only weakly deformed. During a fast deformation, the presence of non-equilibrium effects, like internal viscosity , noncrossability and self-entanglements will stiffen the molecular coil which is now capable of storing a much larger amount of elastic energy than that predicted from Eq. (113). 

Polymerizations Above Tg. Let the polymerization begin in pure monomer. As the concentration of polymer chains increases initially one observes a relatively small increase in the termination rate constant. This is related to the effect of polymer concentration on coil size. A reduction in coil size increases the probability of finding a chain end near the surface and hence causes an increase in k-. Soon thereafter at conversions 15-20 polymer chains begin to entangle causing a dramatic reduction in radical chain translational mobility giving a rapid drop in k-j. ... 

For polymer melts or solutions, Graessley [40-42] has shown that for a random coil molecule with a Gaussian segment distribution and a uniform number of segments per unit volume, a shear rate dependent viscosity arises. This effect is attributed to shear-induced entanglement scission. 

The range of semi-dilute network solutions is characterised by (1) polymer-polymer interactions which lead to a coil shrinkage (2) each blob acts as individual unit with both hydrodynamic and excluded volume effects and (3) for blobs in the same chain all interactions are screened out (the word blob denotes the portion of chain between two entanglements points). In this concentration range the flow characteristics and therefore also the relaxation time behaviour are not solely governed by the molar mass of the sample and its concentration, but also by the thermodynamic quality of the solvent. This leads to a shift factor, hm°d, is a function of the molar mass, concentration and solvent power. 

The crystallization process of flexible long-chain molecules is rarely if ever complete. The transition from the entangled liquid-like state where individual chains adopt the random coil conformation, to the crystalline or ordered state, is mainly driven by kinetic rather than thermodynamic factors. During the course of this transition the molecules are unable to fully disentangle, and in the final state liquid-like regions coexist with well-ordered crystalline ones. The fact that solid- (crystalline) and liquid-like (amorphous) regions coexist at temperatures below equilibrium is a violation of Gibb s phase rule. Consequently, a metastable polycrystalline, partially ordered system is the one that actually develops. Semicrystalline polymers are crystalline systems well removed from equilibrium. 

Fig. 33 Schematic illustration of the model of two-stage melt relaxation. When ECSCs are melted, the chains within ECSCs are rapidly changed to a random coiled conformation. Then, chains are gradually entangled with each other. Cross-mark denotes the entanglement. rconf and tent are the conformational and topological relaxation time, respectively. At is the melt annealing time (see text)...

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