Elasticity Dominated Surface Segregation of Small Molecules in Polymer Mixtures

We study the phenomenon of migration of the small molecular weight component of a binary polymer mixture to the free surface using mean field and self-consistent field theories. By proposing a free energy functional that incorporates polymer-matrix elasticity explicitly, we compute the migrant volume fraction and show that it decreases significantly as the sample rigidity is increased. A wetting transition, observed for high values of the miscibility parameter can be prevented by increasing the matrix rigidity. Estimated values of the bulk modulus suggest that the effect should be observable experimentally for rubberlike materials. This provides a simple way of controlling surface migration in polymer mixtures and can play an important role in industrial formulations, where surface migration often leads to decreased product functionality.

Figure 1

Schematic figure showing a mixture of low (black) and high (red) molecular weight polymers, with the low molecular weight component migrating to the free interface $z=0$. A semi-infinite geometry is assumed. The volume fraction of the migrant in bulk and at the surface is denoted by ${\varphi }_{\infty }$ and ${\varphi }_1$, respectively. Inset shows migrant concentration profiles for different values of $\chi N$. For low values of $\chi N$ a monotonically decreasing concentration profile is observed (dashed line). As $\chi N$ increases, a wetting transition characterized by a macroscopically thick migrant layer (solid line with a break) is observed.

Figure 2

The variation of ${\chi }_c$ on the elastic modulus $\tilde{B}$ of a phase separating the binary mixture with elastic interactions for different values of the bulk migrant volume fraction ${\varphi }_{\infty }$. Main figure shows ${\chi }_c$ increases with $\tilde{B}$ (as $\sim \sqrt{\tilde{B}}$) indicating that softer systems are more susceptible to phase separation and decreases with ${\varphi }_{\infty }$ for a fixed $\tilde{B}$. Inset shows phase diagram of polymer mixtures without elastic interactions (see text).

Figure 3

Migrant concentration profiles $\varphi (z)$ for the SB model including the elasticity obtained by minimizing Eq. (4) for ($\chi =0.320$ and $N_A=10$) and increasing $\tilde{B}$. A wetting transition is not observed in this model. Inset shows concentration profiles for the SB model without elasticity for the symmetric case $N_A=N_B=10$ with increasing $\chi$. The black solid line with a break indicates the formation of a macroscopic wetting layer.

Figure 4

Migrant concentration profiles $\varphi (z)$ for different elastic moduli $\tilde{B}$ of the polymer matrix. The amount of material flowing to the surface decreases with increasing $\tilde{B}$. The dependence of the surface fraction ${\varphi }_1$ as a function of $\tilde{B}$ for different surface free energy $F_s$ is shown in the inset. As expected, the volume fraction decreases for system with higher $F_s$.

Figure 5

Cahn construction showing first order wetting transition for the Flory Huggins free energy functional, $F_{fh}$ [Eq. (1)]. An intersection between $F_{fh}({\varphi }_1)$ and $F_s^{\prime }({\varphi }_1)$ at three points demarcate areas $S_1$ and $S_2$, such that $S_1>S_2$ indicates a first-order wetting transition. A similar graphical construction for the elastic Flory-Huggins functional $F_{fhe}$ [Eq. (3)] with $\tilde{B}=0.17$ shows one intersection, indicating the absence of the wetting transition.