Direct measurement of the Orderphobic Effect

Abstract

Fluctuation-induced forces, such as the Critical Casimir Effect (CCE), are fundamental mechanisms driving organization and self-assembly near second-order phase transitions. The existence of a comparable, universal force for systems undergoing a first-order transition has remained an unresolved fundamental question. The proposed Orderphobic Effect is one such potential mechanism. It arises from minimisation of the interfacial free energy between solutes that locally nucleate a disordered phase. Here, we report the first experimental demonstration and quantitative measurement of the Orderphobic Effect. Using a driven, non-equilibrium quasi-2D granular fluid undergoing a first-order order-disorder transition, we show that specifically designed solutes in an ordered phase nucleate a coexisting ``bubble'' of the disordered phase. By analysing its capillary fluctuations, we confirm that this phenomenon occurs due to the proximity to phase-coexistence, and we directly quantify the attractive force by measuring the interaction free energy between solutes. The observation of this general fluctuation-mediated force in a non-equilibrium steady state strongly supports its claimed universality. Our work establishes the Orderphobic Effect as the first-order equivalent to the CCE, providing a new, general route for controlling self-assembly and aggregation in soft matter and non-equilibrium systems.

Figures (8)

• Figure 1: Experimental results: capillary fluctuations. a) Example image of an orderphobe in the particle monolayer. b) superimposed local orientational order parameter, $|\psi_6^i|$. c) Fourier components of the interfacial radial fluctuations $\delta R_k$ for an orderphobe-nucleated bubble (blue) and one formed simply due to phase-coexistence (red) of the same size. The green vertical line indicates $k=2\pi/(2\pi R_0)$, where $R_0$ is the average radius of the interface. The purple vertical line corresponds to the coarse graining width, $k=2\pi/\xi$. The black line indicates $k^{-2}$ scaling.
• Figure 2: Qualitative demonstration of the Orderphobic Effect. Experimental images of two solutes in an otherwise ordered system. Red arrows indicate progression of time.
• Figure 3: Quantifying the effect of an orderphobic force. a) Schematic demonstrating the experimental setup. b) Image of the experiment from above. c) Probability distribution of orderphobe separations with (red) and without (blue) an order-disorder interface. The interface nucleated by the orderphobes results in a bias in the histogram towards smaller separations, demonstrating the existence of an attractive orderphobic force.
• Figure 4: Measuring the Free energy change due to the Orderphobic Effect. a) Subset of the distributions of the interfacial length for increasing pole separations, $D$. Inset, schematic illustrating the transition from one to two bubbles as the pin separation, $D$, is increased. b) Distributions of interface lengths (red line), from MBAR reweighting (see Methods). c) Proportion of time spent as one ($t_1$) or two bubbles ($t_2$) (blue circles, left scale) and the scaled free energy, $\Delta F / k_{\rm B} T_{\rm eff}$ (red circles, right scale) as a function of pole separation, $D$. Solid / dashed red lines are guides for the eye. The grey single hashed and double hashed regions are bounded by $2 R_{0}$, $2(R_{0}+\delta R_{0})$ and $2(R_{0}+2 \delta R)$ representing the distances at which the bubbles can meet via one and two standard deviations of their radial fluctuations respectively.
• Figure 5: Image showing the orderphobe (left) and its lid (right). The orderphobes are 3D printed PLA pentagons with nitrile particles attached to the edges of the pentagon. The lids are laser cut from perspex.