Conceptual aspects of line tensions

We analyze two representative systems containing a three-phase-contact line: a liquid lens at a fluid--fluid interface and a liquid drop in contact with a gas phase residing on a solid substrate. We discuss to which extent the decomposition of the grand canonical free energy of such systems into volume, surface, and line contributions is unique in spite of the freedom one has in positioning the Gibbs dividing interfaces. In the case of a lens it is found that the line tension is independent of arbitrary choices of the Gibbs dividing interfaces. In the case of a drop, however, one arrives at two different possible definitions of the line tension. One of them corresponds seamlessly to that applicable to the lens. The line tension defined this way turns out to be independent of choices of the Gibbs dividing interfaces. In the case of the second definition,however, the line tension does depend on the choice of the Gibbs dividing interfaces. We provide equations for the equilibrium contact angles which are form-invariant with respect to notional shifts of dividing interfaces which only change the description of the system. Conceptual consistency requires to introduce additional stiffness constants attributed to the line. We show how these constants transform as a function of the relative displacements of the dividing interfaces. The dependences of the contact angles on lens or drop volumes do not render the line tension alone but a combination of the line tension, the Tolman length, and the stiffness constants of the line.Comment: 34 pages, 9 figure

Contact line stability of ridges and drops

Within the framework of a semi-microscopic interface displacement model we analyze the linear stability of sessile ridges and drops of a non-volatile liquid on a homogeneous, partially wet substrate, for both signs and arbitrary amplitudes of the three-phase contact line tension. Focusing on perturbations which correspond to deformations of the three-phase contact line, we find that drops are generally stable while ridges are subject only to the long-wavelength Rayleigh-Plateau instability leading to a breakup into droplets, in contrast to the predictions of capillary models which take line tension into account. We argue that the short-wavelength instabilities predicted within the framework of the latter macroscopic capillary theory occur outside its range of validity and thus are spurious.Comment: 6 pages, 1 figur

Free energy of colloidal particles at the surface of sessile drops

The influence of finite system size on the free energy of a spherical particle floating at the surface of a sessile droplet is studied both analytically and numerically. In the special case that the contact angle at the substrate equals $\pi/2$ a capillary analogue of the method of images is applied in order to calculate small deformations of the droplet shape if an external force is applied to the particle. The type of boundary conditions for the droplet shape at the substrate determines the sign of the capillary monopole associated with the image particle. Therefore, the free energy of the particle, which is proportional to the interaction energy of the original particle with its image, can be of either sign, too. The analytic solutions, given by the Green's function of the capillary equation, are constructed such that the condition of the forces acting on the droplet being balanced and of the volume constraint are fulfilled. Besides the known phenomena of attraction of a particle to a free contact line and repulsion from a pinned one, we observe a local free energy minimum for the particle being located at the drop apex or at an intermediate angle, respectively. This peculiarity can be traced back to a non-monotonic behavior of the Green's function, which reflects the interplay between the deformations of the droplet shape and the volume constraint.Comment: 24 pages, 19 figure

Influence of Biopsy Technique on Molecular Genetic Tumor Characterization in Non-Small Cell Lung Cancer—The Prospective, Randomized, Single-Blinded, Multicenter PROFILER Study Protocol

The detection of molecular alterations is crucial for the individualized treatment of advanced non-small cell lung cancer (NSCLC). Missing targetable alterations may have a major impact on patient’s progression free and overall survival. Although laboratory testing for molecular alterations has continued to improve; little is known about how biopsy technique affects the detection rate of different mutations. In the retrospective study detection rate of epidermal growth factor (EGFR) mutations in tissue extracted by bronchoscopic cryobiopsy (CB was significantly higher compared to other standard biopsy techniques. This prospective, randomized, multicenter, single blinded study evaluates the accuracy of molecular genetic characterization of NSCLC for different cell sampling techniques. Key inclusion criteria are suspected lung cancer or the suspected relapse of known NSCLC that is bronchoscopically visible. Patients will be randomized, either to have a CB or a bronchoscopic forceps biopsy (FB). If indicated, a transbronchial needle aspiration (TBNA) of suspect lymph nodes will be performed. Blood liquid biopsy will be taken before tissue biopsy. The primary endpoint is the detection rate of molecular genetic alterations in NSCLC, using CB and FB. Secondary endpoints are differences in the combined detection of molecular genetic alterations between FB and CB, TBNA and liquid biopsy. This trial plans to recruit 540 patients, with 178 evaluable patients per study cohort. A histopathological and molecular genetic evaluation will be performed by the affiliated pathology departments of the national network for genomic medicine in lung cancer (nNGM), Germany. We will compare the diagnostic value of solid tumor tissue, lymph node cells and liquid biopsy for the molecular genetic characterization of NSCLC. This reflects a real world clinical setting, with potential direct impact on both treatment and survival

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where "surface fields" may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given

Chaperoning Roles of Macromolecules Interacting with Proteins in Vivo

The principles obtained from studies on molecular chaperones have provided explanations for the assisted protein folding in vivo. However, the majority of proteins can fold without the assistance of the known molecular chaperones, and little attention has been paid to the potential chaperoning roles of other macromolecules. During protein biogenesis and folding, newly synthesized polypeptide chains interact with a variety of macromolecules, including ribosomes, RNAs, cytoskeleton, lipid bilayer, proteolytic system, etc. In general, the hydrophobic interactions between molecular chaperones and their substrates have been widely believed to be mainly responsible for the substrate stabilization against aggregation. Emerging evidence now indicates that other features of macromolecules such as their surface charges, probably resulting in electrostatic repulsions, and steric hindrance, could play a key role in the stabilization of their linked proteins against aggregation. Such stabilizing mechanisms are expected to give new insights into our understanding of the chaperoning functions for de novo protein folding. In this review, we will discuss the possible chaperoning roles of these macromolecules in de novo folding, based on their charge and steric features

The Flux-Line Lattice in Superconductors

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.Comment: Review paper for Rep.Prog.Phys., 124 narrow pages. The 30 figures do not exist as postscript file