Interfacial Fluid Rheology of Soft Particles

In situ interfacial rheology and numerical simulations are used to investigate microgel monolayers in a wide range of packing fractions, ${\zeta }_{2D}$. The heterogeneous particle compressibility determines two flow regimes characterized by distinct master curves. To mimic the microgel architecture and reproduce experiments, an interaction potential combining a soft shoulder with the Hertzian model is introduced. In contrast to bulk conditions, the elastic moduli vary nonmonotonically with ${\zeta }_{2D}$ at the interface, confirming long-sought predictions of reentrant behavior for Hertzian-like systems.

Figure 1

Compression isotherms reporting the surface pressure $\pi$ (squares) and plateau of the elastic modulus $G_p$ (circles), normalized by $k_{B}T/{\xi }^2$, as a function of generalized packing fraction ${\zeta }_{2D}$. Lines are guides to the eye. Different colors identify different regimes of the compression isotherms.

Figure 2

Master curves obtained by the flow curves measured in the different compression stages where the stress $\sigma$ is normalized by the apparent yield stress ${\sigma }_y$ and the shear rate $\dot{\gamma }$ is normalized by ${\gamma }_y^2$, where ${\gamma }_y^2$ is the threshold strain amplitude between liquidlike and solidlike behavior. Solid and dashed lines correspond to $\sigma /{\sigma }_y=1+k(\gamma /{\gamma }_y^2{)}^u+k^{\prime }(\gamma /{\gamma }_y^2{)}^p$ with $p\simeq 0.2$ and $u\simeq 1.1$ and $p\simeq 0.3$ and $u\simeq 1.65$, respectively. Inset: ${\sigma }_y$, normalized by $k_{B}T/{\xi }^2$ as a function of the generalized area fraction, ${\zeta }_{2\mathrm{D}}$. The different regimes of the compression isotherms in Fig. 1 are indicated by different colors.

Figure 3

(a) Comparison between the 2D Hertzian potential (red curve) and the square-shoulder Hertzian model (SSH) (blue curve), where we highlight the three different regions of the particle: corona (light blue), compressible core (green), and incompressible core (gray). Corresponding colors are used in the background of the panel; (b) apparent yield stress ${\sigma }_y$ normalized to the values of the first maximum of ${\sigma }_y$ (${\sigma }_{y,1\mathrm{stpeak}}$) as a function of ${\zeta }_{2\mathrm{D}}$; (c) scaling flow curves, $\sigma /{\sigma }_y$ vs $\dot{\gamma }/{\gamma }_y^2$, obtained from simulations using the monodisperse Hertzian (diamonds) and the polydisperse SSH (triangles) potential.