Abstract
We combine a slip-spring model with an ‘entangled kink dynamics’ (EKD) model for strong uniaxial extensional flows (with Rouse Weissenberg number ) of long ( for polystyrene) entangled polymers in solutions and melts. The slip-spring model captures the dynamics up to the formation of a ‘kinked’ or folded state, while the kink dynamics simulation tracks the dynamics from that point forward to complete extension. We show that a single-chain slip-spring model using affine motion of the slip-spring anchor points produces unrealistically high tension near the center of the chain once the Hencky strain exceeds around unity or so, exceeding the maximum tension that a chain entangled with a second chain is able to support. This unrealistic tension is alleviated by pairing the slip links on one chain with those on a second chain, and allowing some of the large tension on one of the two to be transferred to the second chain, producing non-affine motion of each. This explicit pairing of entanglements mimics the entanglement pairing also used in the EKD model, and allows the slip spring simulations to be carried out to strains high enough for the EKD model to become valid. We show that results nearly equivalent to those from paired chains are obtained in a single-chain slip-spring simulation by simply specifying that the tension in a slip spring cannot exceed the theoretical maximum value of where , and are the friction per unit length, strain rate and contour length of the chain, respectively. The effects of constraint release (CR) and regeneration of entanglements is also studied and found to have little effect on the chain statistics up to the formation of the kinked state. The resulting hybrid model provides a fast, simple, simulation method to study the response of high molecular weight () polymers in fast flows (), where conventional simulation techniques are less applicable due to computational cost.
Highlights
The ability to predict the flow behavior of polymeric fluids in strong flows has been highly sought over the past decades because of its relevance to applications in consumer products, pharmaceutical industries, electronics, etc
We recently presented a new simulation technique for arbitrarily long polymer chains in entangled systems that we call the ‘entangled kink dynamics’ (EKD) method [18] that predicts the final unraveling of a chain after it has been collapsed into a quasi-1D folded, or ‘kinked’ state by fast extensional flow
Affine motion (AM) results are shown with black lines and maximum entanglement force (MEF) results with red lines
Summary
The ability to predict the flow behavior of polymeric fluids in strong flows has been highly sought over the past decades because of its relevance to applications in consumer products, pharmaceutical industries, electronics, etc. Single-chain slip-spring models have been developed in which the effect of neighboring chains is replaced by virtual springs (or slip-springs) along the backbone of a single chain that confine the motion of the chain, and exert force on the chain [40,41] Despite their simplicity compared to multi-chain simulations, single-chain results match very well with linear viscoelastic data and nonlinear data in shearing flow, and can provide an intermediate level of detail between multiple-chain simulations and the tube theory [33,41,42,43,44,45,46]. We recently presented a new simulation technique for arbitrarily long polymer chains in entangled systems that we call the ‘entangled kink dynamics’ (EKD) method [18] that predicts the final unraveling of a chain after it has been collapsed into a quasi-1D folded, or ‘kinked’ state by fast extensional flow. Our modified slip-spring model should with modifications, be useful for predicting other flows, such as shear
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