Line tension in Langmuir monolayers probed by point forces

Wurlitzer, S.; Steffen, P.; Wurlitzer, M.; Khattari, Z. Y.; Fischer, Thomas M.

doi:10.1063/1.1287907

Cited by 29 publications

(31 citation statements)

References 15 publications

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“…Since the monolayer is not in a dense phase, the usual 3D viscosity η 3D of the water subphase dominates the 2D one [32,33,34], . We obtain straight lines, which proves that, at these length scales, the line tension is constant despite long-range dipolar interactions [12,13,24,30].…”

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Two-dimensional shear modulus of a Langmuir foam

et al. 2003

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Abstract. -We deform a two-dimensional (2D) foam, created in a Langmuir monolayer, by applying a mechanical perturbation, and simultaneously image it by Brewster angle microscopy. We determine the foam stress tensor (through a determination of the 2D gas-liquid line tension, 2.35 ± 0.4 pJ·m −1 ) and the statistical strain tensor, by analyzing the images of the deformed structure. We deduce the 2D shear modulus of the foam, µ = 38±3 nN·m −1 . The foam effective rigidity is predicted to be 35 ± 3 nN · m −1 , which agrees with the value 37.obtained in an independent mechanical measurement.Introduction. -A liquid foam, made of polyhedral gas bubbles separated by thin liquid walls forming a connected network [1], is a mixture of two fluids. It has nevertheless a solidlike elasticity, characterised by a shear modulus µ, proportional to the surface tension of the walls [2,3]. In fact, shearing a foam modifies the total length of the walls, thus the foam energy. The value of µ can be determined in numerical simulations [4,5,6]; however, it is still an open problem to predict analytically its value for a real foam, which has a finite fluid fraction and an inherent disorder due to its distribution of bubble sizes.Here, we compare two experimental measurements of µ. First, by global mechanical measurements on the scale of the whole foam, described in terms of elasticity of continuous media. Second, and simultaneously, by detailed imaging of the diphasic foam structure, on the local level of a few bubbles: this suggests to use two-dimensional (2D) foams. In the literature, 2D soap froths have been sheared in Couette geometry, either as bubble rafts [7,8,9] or confined in Hele-Shaw cells between two parallel plates of glass [10].We investigate the elasticity of a real 2D system: a "Langmuir foam" [11]. A monomolecular layer of amphiphilic molecules deposited at the surface of water ("Langmuir monolayer") exhibits a first order transition between a 2D gas phase and a denser 2D liquid (also called

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confidence: 74%

“…2a). The prefactor (3π 2 /4) ≈ 7.4 is calculated at the limit of vanishing surface viscosity (zero Boussinesq number) for a deformable object (here: the bubble) [35], as opposed to a solid object which would lead to a prefactor of 8 [30,34]. We then deduce λ from the balance of both forces.…”

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confidence: 99%

Two-dimensional shear modulus of a Langmuir foam

et al. 2003

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“…This relaxation has served for estimates of the line tension in a few systems, including phospholipid/cholesterol mixtures, 21 polymer mono and multilayers, 12,16 smectic liquid crystalline layers, 22 and fatty acids. 23,24 Other means of determining the line tension would be welcome. Furthermore, many of the assumptions of the models used to analyze the data may be crude; that both surface fluids are incompressible, for example.…”

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confidence: 99%

Hole dynamics in polymer Langmuir films

et al. 2006

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This article develops a model for the closing of a gaseous hole in a liquid domain within a two-dimensional fluid layer coupled to a Stokesian subfluid substrate, and compares this model to experiments following hole dynamics in a polymer Langmuir monolayer. Closure of such a hole in a fluid layer is driven by the line tension at the hole boundary and the difference in surface pressure within the hole and far outside it. The observed rate of hole closing is close to that predicted by our model using estimates of the line tension obtained by other means, assuming that the surface pressure in the gas is negligible. This result both supports the model and suggests an independent means of determining the line tension. Unlike most previous hydrodynamics models of Langmuir films, the closing of a hole necessarily involves vertical motion of the underlying incompressible fluid. Fluid is dragged along with the liquid monolayer towards the center of the hole, and must plunge away from the surface. An explicit expression is found for this vertical fluid flow in the bulk substrate.

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“…Similarly, line tension estimates were obtained from the coalescence, and subsequent relaxation, of two domains Steffen, Wurlitzer & Fischer 2001). In other experiments, the domains were instead deformed directly using silica beads at the domain edges as handles for optical tweezers (Wurlitzer, Steffen & Fischer 2000a;Wurlitzer et al 2000b).…”

Section: Line Tensionmentioning

confidence: 99%

Domain relaxation in Langmuir films

et al. 2007

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We report on theoretical studies of molecularly thin Langmuir films on the surface of a quiescent subfluid and qualitatively compare the results to both new and previous experiments. The film covers the entire fluid surface, but domains of different phases are observed. In the absence of external forcing, the compact domains tend to relax to circles, driven by a line tension at the phase boundaries. When stretched (by a transient applied stagnation-point flow or by stirring), a compact domain elongates, creating a bola consisting of two roughly circular reservoirs connected by a thin tether. This shape will then relax slowly to the minimum-energy configuration of a circular domain. The tether is never observed to rupture, even when it is more than a hundred times as long as it is wide. We model these experiments by taking previous descriptions of the full hydrodynamics, identifying the dominant effects via dimensional analysis, and reducing the system to a more tractable form. The result is a free boundary problem for an inviscid Langmuir film whose motion is driven by the line tension of the domain and damped by the viscosity of the subfluid. Using this model we derive relaxation rates for perturbations of a uniform strip and a circular patch. We also derive a boundary integral formulation which allows an efficient numerical solution of the problem. Numerically this model replicates the formation of a bola and the subsequent relaxation observed in the experiments. Finally, we suggest physical properties of the system (such as line tension) that can be deduced by comparison of the theory and numerical simulations to the experiment. Two movies are available with the online version of the paper. IntroductionIn this paper we develop a manageable model of the experimentally observed relaxation dynamics of a molecularly thin film with two fluid phases at an air/water interface. Our model refines previous work and is motivated by experimental observations. It is both analytically tractable and allows an efficient, accurate and stable numerical solution via a boundary integral technique. The model explains some observed experimental phenomena and in particular offers a more general method for measuring the line tension of the film. We neglect long-range electrostatic effects, which could be added in a straightforward manner at a later time, as well as viscosity and compressibility within the film. These approximations are reasonable for a wide but not universal range of experimental conditions, as discussed below.

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Line tension in Langmuir monolayers probed by point forces

Cited by 29 publications

References 15 publications

Two-dimensional shear modulus of a Langmuir foam

Two-dimensional shear modulus of a Langmuir foam

Hole dynamics in polymer Langmuir films

Domain relaxation in Langmuir films

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