Coil Stretch under Flow

When a polymer chain is subjected to a shear or an extensional flow field, polymer conformations undergo deformation, resulting in many technologically relevant rheological properties such as shear thinning. In the context of polymer translocation through a pore with strong suction forces, substantial 

In dilute solutions of uncharged macromolecules, experiments show that the diffusion coefficient of a chain obeys the Stokes-Einstein law. 

This law can only be understood by considering long-ranged hydrodynamic interactions among polymer segments. 

The longest relaxation time of the chain with hydrodynamic interactions, called the Zimm time, is proportional to the volume of the macromolecule, 

In the presence of an externally imposed flow, a flexible polymer molecule can undergo the coil-stretch transition at a critical value of shear rate (for shear flows) or strain rate (for elongational flows), which is proportional to the reciprocal of the Zimm time. 

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Fig.4.a A perfectly flat wall in presence of sufficient polymer adsorption and interfacial chain entanglements, b An entangling melt under high stresses (o>oc) in contact with a molecularly smooth wall, where the adsorbed (thick) chains undergo a coil-stretch transition and the unbound chains are no longer in entanglement with the tethered chains. Here the first layer of adsorbed chains is stagnant, as the unbound chains flow by. 

Chilcott and Rallison (1988) simulated the zero Reynolds number flow of a dumbbell model with finite extensibility across a cylinder. In particular, they performed time-dependent calculations and reported the regions of high deformations near stagnation points, especially downstream from stagnation points. Likewise, Ambari et al. (1984) have considered the underlying phenomena of coil-stretch transition of macromolecules in laminar flow about cylindrical obstacles. 

Thermoplastics are composed of flexible macromolecules, which adopt a random-coil conformation at rest, and can be easily deformed by flow. Under flow, they also tend to be oriented along the flow direction. Stretching and orientation of macromolecules in the melt have consequences on crystallization thermodynamics and kinetics, as well as on the subsequent morphologies. 

Finally, we will briefly discuss the properties of polymer blends under shear flow. In small molecule mixtures, shear flow is known to produce an anisotropy of critical fluctuations and anisotropic spinodal decomposition [244, 245], In polymer mixtures, the shear has the additional effect of orienting and stretching the coils, thus making the single-chain structure factor anisotropic. In the framework of the Rouse model these effects have been incorporated into the RPA description of polymer blends [246, 247]. Assuming a velocity field v = yyex, where x, y, z are cartesian coordinates, y the shear rate, and ex is a unit vector in x direction, the single chain structure factor becomes [246, 247]... 

De Gennes provided a scaling analysis on the deformation transition of polymer coils under elongational flows (De Gennes 1979). Under one-dimensional stretching, the strain rate of polymer chain... 

Fig. 8.10. Schematic representation of the entanglement network of HMVIT E chains (A) under uniaxial deformation (LMVIT E chains are not shown here). E pon shearing, some chain segments between entanglements (shown as round dots) are stretched along the flow direction, but most segments remained in the coiled state (B). The stretched segments form the precursors for the shish formation, and the coiled segments can grow into kebabs (reprinted with permission from [27])...

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