Strain recovery of model immiscible blends: effects of added compatibilizer

Abstract

The effect of added compatibilizer on the strain recovery of model immiscible blends after cessation of shear was studied. Blends were composed of polyisobutylene drops (up to 30% by weight) in a polydimethylsiloxane matrix, with viscosity ratio (viscosity of the drops relative to the matrix viscosity) ranging from 0.3 to 1.7. Up to 1% by weight of a PIB-PDMS diblock copolymer was added as compatibilizer. The ultimate recovery recorded after reaching steady-shear conditions increased significantly due to added compatibilizer. Furthermore, the compatibilizer also slowed down the kinetics of the recovery; however, unlike uncompatibilized blends, the recovery could no longer be captured by a single retardation time. The largest increase in ultimate recovery due to compatibilizer occurred at the lowest viscosity ratio. In contrast, the greatest slowing down of the recovery due to compatibilizer occurred at the highest viscosity ratio. The rheological data by themselves are insufficient to reach a definitive conclusion about the mechanism of compatibilizer action. The results are consistent with the effects of flow-induced gradients in compatibilizer concentration. An alternative constitutive modeling approach that captures compatibilizer effects in terms of an interfacial dilational elasticity can reproduce the recovery curves qualitatively, but some predictions of the model contradict experimental results.

Appendix

The equations below are given by Jacobs et al. (1999). We correct a typographical error in those equations (Eq. 11 in Jacobs paper has (1 − (3/2) ϕ) in the denominator whereas (1+(3/2) ϕ) is correct).

$$\lambda _{{11}} = \frac{{R\eta _{{\text{m}}} }}{\alpha }\frac{{{\left( {19p + 16} \right)}{\left[ {2p + 3 - 2\phi {\left( {p - 1} \right)}} \right]}}}{{40(p + 1) + 2\frac{\beta }{\alpha }{\left( {23p + 32} \right)} - 2\phi {\left[ {4{\left( {5p + 2} \right)} + \frac{\beta }{\alpha }{\left( {23p - 16} \right)}} \right]}}}$$

(20)

$$\lambda _{{12}} = \frac{{R\eta _{{\text{m}}} }}{\alpha }\frac{\alpha }{\beta }\frac{{40(p + 1) + 2\frac{\beta }{\alpha }{\left( {23p + 32} \right)}-2\phi {\left[ {4{\left( {5p + 2} \right)} + \frac{\beta }{\alpha}{\left( {23p - 16} \right)}} \right]}}}{{48{\left({1-\phi} \right)}}}$$

(21)

$$\lambda _{{21}} = \frac{{R\eta _{{\text{m}}} }}{\alpha }\frac{{{\left( {19p + 16} \right)}{\left[ {2p + 3 + 3\phi {\left( {p - 1} \right)}} \right]}}}{{40(p + 1) + 2\frac{\beta }{\alpha }{\left( {23p + 32} \right)} + 3\phi {\left[ {4{\left( {5p + 2} \right)} + \frac{\beta }{\alpha }{\left( {23p - 16} \right)}} \right]}}}$$

(22)

$$\lambda _{{22}} = \frac{{R\eta _{{\text{m}}} }}{\alpha }\frac{\alpha }{\beta }\frac{{40(p + 1) + 2\frac{\beta }{\alpha }{\left( {23p + 32} \right)} + 3\phi {\left[ {4{\left( {5p + 2} \right)} + \frac{\beta }{\alpha }{\left( {23p - 16} \right)}} \right]}}}{{48{\left( {1 + 3\phi /2} \right)}}}.$$

(23)

The relaxation and retardation times are given by

$$\lambda _{{F1}} = 2\lambda _{{11}} {\left[ {1 + {\sqrt {1 - 4\frac{{\lambda _{{11}} }}{{\lambda _{{12}} }}} }} \right]}^{{ - 1}} ;\quad \lambda _{{\beta 1}} = 2\lambda _{{11}} {\left[ {1 - {\sqrt {1 - 4\frac{{\lambda _{{11}} }}{{\lambda _{{12}} }}} }} \right]}^{{ - 1}} $$

(24)

$$\lambda _{{F2}} = 2\lambda _{{21}} {\left[ {1 + {\sqrt {1 - 4\frac{{\lambda _{{21}} }}{{\lambda _{{22}} }}} }} \right]}^{{ - 1}} ;\quad \lambda _{{\beta 2}} = 2\lambda _{{21}} {\left[ {1 - {\sqrt {1 - 4\frac{{\lambda _{{21}} }}{{\lambda _{{22}} }}} }} \right]}^{{ - 1}}. $$

(25)

Equations 24 and 25 are in a slightly different algebraic form than those provided by Jacobs et al. (1999): since λ₁₁ and λ₂₁ both remain finite in the limit of β/α=0, (24) and (25) are slightly more convenient than those given by Jacobs et al. Finally, all the above times can be made dimensionless by multiplying by the steady shear rate $\dot{\gamma}_{0}:$

$$\lambda^{*}_{F1} = \dot{\gamma}_{0} \lambda_{F1}; \quad \lambda^{*}_{{\beta 1}} = \dot{\gamma}_{0} \lambda _{{\beta 1}}; \quad \lambda^{*}_{F2} = \dot{\gamma}_{0} \lambda _{F2}; \quad \lambda^{*}_{{\beta 2}} = \dot{\gamma}_{0} \lambda _{{\beta 2}}. $$

(26)