Session H49: Focus Session: Fluctuation-Induced Forces in Soft Matter & Polymeric Systems - Casimir and Interfacial Forces

Casimir Interaction at Soft Interfaces

We study Casimir interaction due to the thermal fluctuations between colloidal particles on the membranes and fluid interfaces. To calculate the Casimir energy we employ the scattering formalism. In this technique the shape and material properties of the colloids are encoded in their scattering matrices. The energy is calculated by combining the scattering matrices with the universal translation matrices, which convert between the bases used to compute scattering for each colloid, but otherwise are independent of the physical and chemical properties of the colloids and the interface. We show that in the scattering formalism one can easily implement various geometries and material properties and more importantly calculate the energy for all separation regimes.   

Critical Casimir Interactions: New fluctuation forces in colloidal science

Casimir forces arise from the confinement of fluctuations between two walls. Critical Casimir forces provide thermodynamic analogues of quantum-mechanical Casimir forces and arise from the confinement of concentration fluctuations of a critical solvent. These forces act also between colloidal particles that are suspended in this solvent, giving rise to temperature-dependent attractive interactions between the particles. We use these temperature-dependent forces to control colloidal phase transitions. In this talk, I will present a new index and density-matched model system that allows direct observation of these phase transitions with confocal microscopy. In three dimensions and real time, we follow how a colloidal gas freezes into a colloidal liquid, and the colloidal liquid freezes into a solid, all driven by critical Casimir forces. We measure the critical Casimir particle pair potential directly from the pair correlation function, and use Monte Carlo simulations to map the complete gas-liquid-solid phase diagram. Excellent agreement with the experimental observations is obtained. Our measurements include microgravity experiments on board the International Space Station (ISS) to elucidate non-equilibrium assembly of the particles achieved by controlled temperature quench.   

Thermodynamic Casimir effect in the large-$n$ limit: Exact results for slabs with free surfaces

The $O(n)$ $\phi^4$-model for a three-dimensional slab of thickness $L$ and infinite lateral extension is investigated in the large-$n$ limit. The effective (Casimir-like) forces that are induced between the two confining boundary planes by thermodynamic fluctuations in such systems at and near bulk criticality are studied. While systems with periodic or antiperiodic boundary conditions perpendicular to the planes are translationally invariant and thus can be treated analytically, the physical relevant case of free boundary conditions leads to a breaking of translational invariance perpendicular to the boundary planes. In the large-$n$ limit one arrives at a spherical model with separate constraints for each layer parallel to the confining surfaces. The resulting self-consistent Schr\"odinger-type equation is solved numerically at and near the bulk critical temperature to obtain the large-$n$ limit of the scaling functions of the Casimir force and the excess free energy. The Casimir amplitude is calculated with high accuracy to take the value $\Delta_{\mathrm{C}}=-0.01077340685025(10)$. The Casimir force scaling function shows a minimum below the bulk critical temperature similar to the $n=2$ result.   

Fluctuation-induced forces in a fluid membrane under tension

We develop an exact method to calculate thermal Casimir forces between inclusions of arbitrary shapes and separation, embedded in a fluid membrane whose fluctuations are governed by the combined action of surface tension, bending modulus, and Gaussian rigidity. Each object's shape and mechanical properties enter only through a characteristic matrix, a static analog of the scattering matrix. We calculate the Casimir interaction between two elastic disks embedded in a membrane. In particular, we find that at short separations the interaction is strong and independent of surface tension.   

The Casimir forces between inclusions in a fluid membrane

We discuss the fluctuation-induced force, a finite-temperature analogue of the Casimir force, between two foreign inclusions embedded in a stretchable fluid membrane. Specifically, we suggest a Green's-function-based method to calculate the Casimir interaction in cases where the fluctuations of a planar membrane are governed by Helfrich Hamiltonian, including the surface tension $\sigma$ and both bending $\kappa$ and Gaussian $\bar\kappa$ rigidities. For two circular inclusions in a fluid membrane, the Casimir energy scales as the inverse power law of the separation and is greatly reduced beyond the characteristic length $\ell_0=\sqrt{\kappa_0/\sigma_0}$. The impact of line tension is also discussed.   

Aspect-ratio dependence of thermodynamic Casimir forces

We consider the three-dimensional Ising model in a $L_{\perp}\times L_{\parallel}\times L_{\parallel}$ cuboid geometry with finite aspect ratio $\rho=L_{\perp}/L_{\parallel}$ and periodic boundary conditions along all directions. For this model the finite-size scaling functions of the excess free energy and thermodynamic Casimir force are evaluated numerically by means of Monte Carlo simulations [1]. The Monte Carlo results compare well with recent field theoretical results for the Ising universality class at temperatures above and slightly below the bulk critical temperature $T_{\mathrm{c}}$. Furthermore, the excess free energy and Casimir force scaling functions of the two-dimensional Ising model are calculated exactly for arbitrary $\rho$ and compared to the three-dimensional case. We give a general argument that the Casimir force vanishes at the critical point for $\rho=1$ and becomes repulsive in periodic systems for $\rho>1$. \\[4pt] [1] Alfred Hucht, Daniel Gr\"uneberg, and Felix M. Schmidt, Phys. Rev. E 83, 051101 (2011)   

Field-Theoretic Simulations of Bicontinuous Microemulsions in Polymer Blends

Long diblock copolymers introduced into a blend of thermodynamically incompatible homopolymers can act as a surfactant to supress macroscopic phase separation of the blend. As the fraction of diblock copolymer is varied, an isotropic Lifshitz tricritical point is observed in the mean-field equations, demarking the crossover from macrophase to microphase separation. Close to the Lifshitz point, fluctuations are strong enough to supress the low-temperature formation of a well-ordered microphase leading to the appearance of a long-lived bicontinuous microemulsion characterized by micron-scale continuous domains. In this work, we discuss computational strategies for simulating the equilibrium formation of the microemulsion using field-theoretic methods. We address the challenges involved with accurately localizing the order-disorder transition in a fluctuating theory, and the handling of strong fluctuations close to the Lifshitz point.   

Looking Down at Adsorption Dynamics: Filament Height Measurements with TIRFM

Polymer adsorption is important in several contexts such as chromatography, colloid stabilization, and bio-fouling. Despite a cross-disciplinary interest in the subject, there are not many techniques to observe single-molecule absorption events in real time. We use TIRF microscopy to accomplish this using the biological polymer f-actin adsorbed to a microscope slide via the well-known depletion interaction. We find TIRFM is able to quantitatively measure filament height, and we compare our results to theoretical predictions and previous results obtained from other systems.   

Partial osmotic compressibility of binary mixtures of colloidal nanoparticles and PEG

Proposed originally by Oosawa and Asakura, polymer crowding-induced attractive force between colloidal particles is being used in a variety of applications ranging from protein crystallization to nanoparticle sorting. While the force has been well studied for a pair of micro particles in the presence of polymers, direct measurement of such force between nanoparticles is very difficult. To investigate effects of crowding polymers, we propose an approach to measure the colloidal osmotic compressibility and viral coefficients in the presence of polymers and compare experimental results with theoretical models. The materials we investigated are binary mixtures of fluorescent polystyrene nanospheres (100 -- 210 nm in diameter) and polyethylene glycol (PEG). Using fluorescence microscopy to examine the change of the particle concentration in an optical trap, which exerts no force upon PEG, allows us to measure the partial osmotic compressibility of the particles. The measured partial compressibility and its virial expansion are compared with theoretical calculations to elucidate the competing effects of polymer crowding and adsorption.