Jan Kierfeld

Elastometry of Deflated Capsules: Elastic Moduli from Shape and Wrinkle Analysis

Elastic capsules, prepared from droplets or bubbles attached to a capillary (as in a pendant drop tensiometer), can be deflated by suction through the capillary. We study this deflation and show that a combined analysis of the shape and wrinkling characteristics enables us to determine the elastic properties in situ. Shape contours are analyzed and fitted using shape equations derived from nonlinear membrane-shell theory to give the elastic modulus, Poisson ratio and stress distribution of the membrane. We include wrinkles, which generically form upon deflation, within the shape analysis. Measuring the wavelength of wrinkles and using the calculated stress distribution gives the bending stiffness of the membrane. We compare this method with previous approaches using the Laplace-Young equation and illustrate the method on two very different capsule materials: polymerized octadecyltrichlorosilane (OTS) capsules and hydrophobin (HFBII) coated bubbles. Our results are in agreement with the available rheological data. For hydrophobin coated bubbles, the method reveals an interesting nonlinear behavior consistent with the hydrophobin molecules having a rigid core surrounded by a softer shell.

Dislocations and the critical endpoint of the melting line of vortex line lattices

line merge. 14 In this paper we present an explanation for the existence of a critical endpoint of the first-order melting line in the presence of point disorder. Our argumentation is based on a unified description of the vortex lattice phases. We demonstrate that all phase transitions between vortex lattice phases can be described as dislocation mediatedby deriving the free energy for an ensemble of directed dislocations as a function of the dislocation density in the presence of thermal and disorder. Each of the experimentally observed phases is characterized by its inherent dislocation density or, equivalently, by the characteristic dislocation spacing RD . The elastic VG is dislocation-free and has RD5‘. The VL can be viewed as a vortex array saturated with dislocations such that RD;a, and in the amorphous VG, R D ;R a , where R a is the socalled positional correlation length on which typical vortex displacements are of the order of the lattice spacing a. 2 Within our approach each phase corresponds to one of the local minima in the dislocation ensemble free energy, and dislocation densities in these minima represent the equilibrium dislocation densities in the corresponding phases. The global minimum corresponds to the thermodynamically stable phase under the given conditions, phase transitions occur when two local minima exchange their role as global minimum. This mechanism for the transitions enables us to derive Lindemann-criteria both for the locations of the thermal melting line and for the disorder-induced instability line of the BrG. Furthermore, the characteristic scale set by the mean distance between free dislocations offers a natural explanation of the critical endpoint of the first-order melting line: While at low magnetic fieldsRa@a and the amorphous VG appears to contain significantly less dislocations than the VL, at higher field where R a 5a the two phases become thermodynamically equivalent and the first-order melting line has to terminate.

Buckling of spherical capsules.

We investigate buckling of soft elastic capsules under negative pressure or for reduced capsule volume. Based on nonlinear shell theory and the assumption of a hyperelastic capsule membrane, shape equations for axisymmetric and initially spherical capsules are derived and solved numerically. A rich bifurcation behavior is found, which is presented in terms of bifurcation diagrams. The energetically preferred stable configuration is deduced from a least-energy principle both for prescribed volume and prescribed pressure. We find that buckled shapes are energetically favorable already at smaller negative pressures and larger critical volumes than predicted by the classical buckling instability. By preventing self-intersection for strongly reduced volume, we obtain a complete picture of the buckling process and can follow the shape from the initial undeformed state through the buckling instability into the fully collapsed state. Interestingly, the sequences of bifurcations and stable capsule shapes differ for prescribed volume and prescribed pressure. In the buckled state, we find a relation between curvatures at the indentation rim and the bending modulus, which can be used to determine elastic moduli from experimental shape analysis.

Droplets, bubbles, and vesicles at chemically structured surfaces

Liquid droplets, gas bubbles, and membrane vesicles which are in contact with chemically structured substrate surfaces can undergo morphological transitions or shape transformations. The structured surfaces considered here consist of two types of surface domains, γ and δ, which attract and repel the droplets, bubbles, and vesicles, respectively. For droplets on a striped γ domain, one has to distinguish droplets with fixed end caps from those with freely moving end caps. Both types of channels undergo morphological wetting transitions. For vesicles, one has a strong adhesion regime in which the vesicle shapes have constant mean curvature and exhibit effective contact angles. One can then map the shape bifurcation diagram for vesicles onto the one for droplets if one includes the constraint of fixed membrane area. We also report preliminary experimental observations of the adhesion of vesicles to chemically structured surfaces.

Discontinuous Unbinding Transitions of Filament Bundles

The movement of motor particles consisting of one or several molecular motors bound to a cargo particle is studied theoretically. The particles move on patterns of immobilized filaments. Several patterns are described for which the motor particles undergo nondirected but enhanced diffusion. Depending on the walking distance of the particles and the mesh size of the patterns, the active diffusion coefficient exhibits three different regimes. For micrometer-sized motor particles in water, e.g., this diffusion coefficient can be enhanced by 2 orders of magnitude.

Topological order in the vortex-glass phase of high-temperature superconductors

The stability of a vortex glass phase with quasi-long-range positional order is examined for a disordered layered superconductor. The role of topological defects is investigated using a scaling argument supplemented by a variational calculation. The results indicate that topological order is preserved for some range of parameters in the vortex glass phase. The stability regime is given in terms of a simple Lindemann-like criterion and is consistent with recent experiments. {copyright} {ital 1997} {ital The American Physical Society}

Persistence length of semiflexible polymers and bending rigidity renormalization

The persistence length of semiflexible polymers and one-dimensional fluid membranes is obtained from the renormalization of their bending rigidity. The renormalized bending rigidity is calculated using an exact real-space functional renormalization group transformation based on a mapping to the one-dimensional Heisenberg model. The renormalized bending rigidity vanishes exponentially at large length scales and its asymptotic behaviour is used to define the persistence length. For semiflexible polymers, our result agrees with the persistence length obtained using the asymptotic behaviour of tangent correlation functions. Our definition differs from the one commonly used for fluid membranes, which is based on a perturbative renormalization of the bending rigidity.

A general stability criterion for droplets on structured substrates

Wetting morphologies on solid substrates, which may be chemically or topographically structured, are studied theoretically by variation of the free energy which contains contributions from the substrate surface, the fluid– fluid interface and the three-phase contact line. The first variation of this free energy leads to two equations—the classical Laplace equation and a generalized contact line equation—which determine stationary wetting morphologies. From the second variation of the free energy we derive a general spectral stability criterion for stationary morphologies. In order to incorporate the constraint that the displaced contact line must lie within the substrate surface, we consider only normal interface displacements but introduce a variation of the domains of parametrization.

Stability of liquid channels or filaments in the presence of line tension

The local stability of a cylindrical liquid channel or filament deposited on a planar homogeneous substrate is studied in the framework of an effective interface model including the line tension of the three phase contact line. We discuss the stability with respect to transversally symmetric and antisymmetric deformation modes and compute a stability diagram in terms of the contact angle and the longitudinal wavelength of these modes for different values of line tension. An increase in the line tension always leads to an increase in the local stability of liquid channels or filaments. For large positive line tension, the behaviour with pinned contact lines is recovered. As one decreases the line tension to negative values, deformation modes of arbitrary wavelength destabilize the channel or filament for sufficiently small contact angles. In addition, a negative line tension leads to a band of unstable short wavelength modes within the continuum theory considered here. It is argued that the presence or absence of these latter modes depends on the ratio of the contact line width to the molecular size.

Theory of Plastic Vortex Creep

We develop a theory for plastic vortex creep in a topologically disordered (dislocated) vortex solid phase in type-II superconductors in terms of driven thermally activated dislocation dynamics. Plastic barriers for dislocations show a power-law divergence at small driving currents j, U(pl)( j) approximately j(-&mgr;), with &mgr; = 1 for a single dislocation and &mgr; = 2/5 for creep of dislocation bundles. This implies a suppression of the creep rate at the transition from the ordered vortex phase ( &mgr; = 2/11) to the dislocated glass and can manifest itself as an observed increase of the apparent critical current (second peak). Our approach applies to general dynamics of disordered elastic media on a random substrate.