Effective field theory approach to Casimir interactions on soft matter surfaces

Abstract

We utilize an effective field theory approach to calculate Casimir interactions between objects bound to thermally fluctuating fluid surfaces or interfaces. This approach circumvents the complicated constraints imposed by such objects on the functional integration measure by reverting to a point particle representation. To capture the finite size effects, we perturb the Hamiltonian by ∆H that encapsulate the particles' response to external fields. ∆H is systematically expanded in a series of terms, each of which scales homogeneously in the two power counting parameters: λ ≡ R/r , the ratio of the typical object size (R) to the typical distance between them (r), and δ ≡ kBT /k, where k is the modulus characterizing the surface energy. The coefficients of the terms in ∆H correspond to generalized polarizabilities and thus the formalism applies to rigid as well as deformable objects. Singularities induced by the point particle description can be dealt with using standard renormalization techniques. We first illustrate and verify our approach by re-deriving known pair forces between circular objects bound to films or membranes. To demonstrate its efficiency and versatility, we then derive a number of new results: The triplet interactions present in these systems, a higher order correction to the film interaction, and general scaling laws for the leading order interaction valid for objects of arbitrary shape and internal flexibility.

Membrane-mediated interactions between rigid inclusions: An effective field theory

“…[22,23], is to extend the membrane Hamiltonian (2) to the entirety of R 2 , getting rid of the boundaries, and augment the theory with localized terms mimicking the removed boundaries and boundary conditions. To this end, we construct an effective theory…”

“…[27]. It is the quadratic order terms in the derivative expansion that are responsible for the fluctuation-induced interaction free energy of the form F = k B Tf ({r a }) [22,23]. The quadratic world line terms for axisymmetric particles are of the form (C/2)∂ m h ∂ n h| r=r a , where ∂ m h is a shorthand for a rank-m tensor made of m partial derivatives of the field.…”

“…In this article, we discuss a way to greatly facilitate these computations using an effective field theory (EFT) formalism that we introduced recently [22,23]. We note that another group recently proposed a similarly powerful method [17].…”

Effective field theory approach to fluctuation-induced forces between colloids at an interface

“…We recently introduced this generalization in Ref. [13]; here we develop the formalism in greater detail, expand on our previous results, and discuss further physical situations.…”

Scattering approach for fluctuation-induced interactions at fluid interfaces

“…Later the formalism was used to study the fluctuation-induced forces between disks and spherical colloids [17,18] as well as ellipsoidal colloids trapped at a fluid interface between two fluid phases [19,20]. In a recent work, an effective field theory method has been employed to find the asymptotic expansion of the fluctuation-induced interaction [21,22]. Around the same time, Lin et al presented a Green's function method to calculate the fluctuationinduced forces between soft and hard particles embedded in a membrane [23].…”