Tube Dilation and Reptation in Binary Blends of Monodisperse Linear Polymers

Abstract

We extend the Milner-McLeish theory for monodisperse linear polymers to binary blends, where the reptation time of the long chain is set to either the reptation time in the undilated tube or the reptation time in the dilated tube depending on the value of the "Graessley parameter" Gr ≡ M2Me 2 /M1 3 , where M1 is the short chain molecular weight, M2 is the long chain molecular weight, and Me is the entanglement molecular weight. We find experimentally that, in blends in which Gr is much smaller than the critical value Grc ≈ 0.064 established by an observed crossover in diffusivity measurements [Green et al. Phys. Rev. Lett. 1984, 26, 2145, the long-chain motion in the binary blend is well predicted by the Milner-McLeish model using reptation in the undilated tube. However, for Gr larger than Grc, reptation must to be assumed to occur in a dilated tube to obtain agreement with the experimental data. These results confirm that the crossover behavior observed in diffusivity also occurs in rheology and show that existing tube models can accurately predict linear rheology in both regimes where reptation occurs in a dilated or an undilated tube.

Stress relaxation of bi-disperse polystyrene melts

“…In the frame of the Struglinsky-Graessley criterion we are consequently in 4.06 · 10 5 4.50 · 10 −2 10 1.15 · 10 6 8.27 · 10 −3 11 3.23 · 10 6 1.52 · 10 −3 12 5.14 · 10 7 2.80 · 10 −4 the limit of Gr >> Gr c . Our system (Gr = 0.112) therefore seems to agree with the value of 0.064 reported by Park and Larson (2004) rather than the value Gr c = 1 reported by Struglinski and Graessley (1985), Struglinski and Graessley (1986).…”

“…The original one proposed by Struglinski and Graessley was 1, whereas in a later work of Park and Larson (2004), was empirically fixed at 0.064, which gave a better estimate to delimit the two regimes of the skinny and dilated tube. The authors proposed an extended version of the Milner-McLeish model (Milner and McLeish (1998)) from linear monodisperse polymers to linear bi-disperse melts incorporating dynamic tube dilation (DTD) and Rouse constraint release mechanism (CRR).…”

i-Rheo: Measuring the materials' linear viscoelastic properties “in a step”!

“…The LVE properties of monodisperse amorphous linear polymer melts and their blends [14][15][16] represent a validation tool for a number of constitutive models (e.g., [17][18][19][20][21][22]) aimed at predicting the rheological behavior of complex polymer systems (e.g., [23][24][25]). This is because of their "simple" topological structure (i.e., entangled polymer chains), which has allowed, over the past 40 years, the establishment of a solid theoretical framework built on the pioneering tube model developed by de Gennes [26] and Doi and Edwards [27].…”

Prediction of linear viscoelastic properties for polydisperse mixtures of entangled star and linear polymers: Modified tube-based model and comparison with experimental results

“…The prediction of linear viscoelasticity (LVE) based on molecular "tube" or "slip-link" models and, very recently, atomistic simulations has received tremendous attention in recent years [1][2][3][4][5]. Major progress has been made, to the point that quite accurate quantitative predictions can now be made for linear polymers [6][7][8][9], including inverse predictions of molecular weight (M w ) distributions from knowledge of rheological response [10,11].…”

“…This is new in comparison with published models [21][22][23], which consider the reptation solvent as a step function. We analyze the influence of the polymer solvent on the fluctuations and reptation processes by using a similar approach to the one proposed by Graessley for bidisperse mixtures of linear chains [4,28], and compare our theory with a large set of experimental data taken from the literature.…”