On the spectrum of fluctuations of a liquid surface: From the molecular scale to the macroscopic scale

We show that to account for the full spectrum of surface fluctuations from low scattering vector qd << 1 (classical capillary wave theory) to high qd > 1 (bulk-like fluctuations), one must take account of the interface's bending rigidity at intermediate scattering vector qd = 1, where d is the molecular diameter. A molecular model is presented to describe the bending correction to the capillary wave model for short-ranged and long-ranged interactions between molecules. We find that the bending rigidity is negative when the Gibbs equimolar surface is used to define the location of the fluctuating interface and that on approach to the critical point it vanishes proportionally to the interfacial tension. Both features are in agreement with Monte Carlo simulations of a phase-separated colloid-polymer system.Comment: 18 pages, 11 figures, accepted for publication in The Journal of Chemical Physic

The existence of a bending rigidity for a hard sphere liquid near a curved hard wall: Helfrich or Hadwiger?

In the context of Rosenfeld's Fundamental Measure Theory, we show that the bending rigidity is not equal to zero for a hard-sphere fluid in contact with a curved hard wall. The implication is that the Hadwiger Theorem does not hold in this case and the surface free energy is given by the Helfrich expansion instead. The value obtained for the bending rigidity is (1) an order of magnitude smaller than the bending constant associated with Gaussian curvature, (2) changes sign as a function of the fluid volume fraction, (3) is independent of the choice for the location of the hard wall.Comment: 19 pages, 5 figures, to appear in Physical Review

On the spectrum of fluctuations of a liquid surface: From the molecular scale to the macroscopic scale

We show that to account for the full spectrum of surface fluctuations from low scattering vector qd 1 (bulk-like fluctuations), one must take account of the interface's bending rigidity at intermediate scattering vector qd = 1, where d is the molecular diameter. A molecular model is presented to describe the bending correction to the capillary wave model for short-ranged and long-ranged interactions between molecules. We find that the bending rigidity is negative when the Gibbs equimolar surface is used to define the location of the fluctuating interface and that on approach to the critical point it vanishes proportionally to the interfacial tension. Both features are in agreement with Monte Carlo simulations of a phase-separated colloid-polymer system.Comment: 18 pages, 11 figures, accepted for publication in The Journal of Chemical Physic

Polymer Adsorption on Curved Surfaces: Finite chain length corrections

The structural properties of polymers adsorbed onto a surface have been widely investigated using self-consistent mean-field theories. Recently, analytical mean-field theories have been applied to study polymer adsorption on curved surfaces but all in the context of the ground state dominance approximation in which the polymer chain length (N) is essentially infinite. Using an expression for the free energy by Semenov, we determine leading order (in 1/N) corrections due to the finiteness of the polymer chain length on surface tension, spontaneous curvature, and rigidity constants.Comment: 24 pages, 7 figures. Accepted for publication in Macromolecule

Density Functional Theory of a Curved Liquid-Vapour Interface: Evaluation of the rigidity constants

It is argued that to arrive at a quantitative description of the surface tension of a liquid drop as a function of its inverse radius, it is necessary to include the bending rigidity k and Gaussian rigidity k_bar in its description. New formulas for k and k_bar in the context of density functional theory with a non-local, integral expression for the interaction between molecules are presented. These expressions are used to investigate the influence of the choice of Gibbs dividing surface and it is shown that for a one-component system, the equimolar surface has a special status in the sense that both k and k_bar are then the least sensitive to a change in the location of the dividing surface. Furthermore, the equimolar value for k corresponds to its maximum value and the equimolar value for k_bar corresponds to its minimum value. An explicit evaluation using a short-ranged interaction potential between molecules, shows that k is negative with a value around minus 0.5-1.0 kT and that k_bar is positive with a value which is a bit more than half the magnitude of k. Finally, for dispersion forces between molecules, we show that a term proportional to log(R)/R^2 replaces the rigidity constants and we determine the (universal) proportionality constants.Comment: 28 pages; 5 figures; accepted for publication in J. Phys.: Condens. Matter (2013

Tension, rigidity and preferential curvature of interfaces between coexisting polymer solutions

The properties of the interface in a phase-separated solution of polymers with different degrees of polymerization and Kuhn segment lengths are calculated. The starting point is the planar interface, the profile of which is calculated in the so-called 'blob model', which incorporates the solvent in an implicit way. The next step is the study of a metastable droplet phase formed by imposing a chemical potential different from that at coexistence. The pressure difference across the curved interface, which corresponds to this higher chemical potential, is used to calculate the curvature properties of the droplet. Interfacial tensions, Tolman lengths and rigidities are calculated and used for predictions for a realistic experimental case. The results suggest that interfaces between phase-separated solutions of polymers exhibit, in general, a preferential curvature, which stabilizes droplets of low molecular mass polymer in a high molecular mass macroscopic phase.Comment: 21 pages; 8 figures; accepted for publication in Macromolecule

Tolman lengths and rigidity constants of multicomponent fluids: Fundamental theory and numerical examples

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Is Radiation Superior to Indomethacin to Prevent Heterotopic Ossification in Acetabular Fractures?: A Systematic Review

Heterotopic ossification is a well-known complication after fixation of an acetabular fracture. Indomethacin and radiation therapy are used as prophylaxis to prevent heterotopic ossification. It is unclear, however, whether either is superior, although this may relate to lack of power in individual studies. To compare the effectiveness of indomethacin with the effectiveness of radiation therapy, we conducted a systematic review in which all published prospective studies were evaluated. We performed a literature search in PubMed®, MEDLINE®, EMBASE™, and the Cochrane Controlled Trial Register. The retrieved studies were analyzed and categorized according to the quality and validity score of Jadad et al. We found five appropriate prospective studies, describing 384 patients. Although the quality of the available studies made a proper meta-analysis inappropriate, the incidence of heterotopic ossification was significantly lower in patients treated with radiation than in patients receiving indomethacin (five of 160 versus 20 of 224, respectively). Until further information is available, we believe the evidence supports radiation therapy as the preferred method for preventing heterotopic ossification after operative treatment of acetabular fractures

Fusion Pores Live on the Edge.

Biological transmission of vesicular content occurs by opening of a fusion pore. Recent experimental observations have illustrated that fusion pores between vesicles that are docked by an extended flat contact zone are located at the edge (vertex) of this zone. We modeled this experimentally observed scenario by coarse-grained molecular simulations and elastic theory. This revealed that fusion pores experience a direct attraction toward the vertex. The size adopted by the resulting vertex pore strongly depends on the apparent contact angle between the adhered vesicles even in the absence of membrane surface tension. Larger contact angles substantially increase the equilibrium size of the vertex pore. Because the cellular membrane fusion machinery actively docks membranes, it facilitates a collective expansion of the contact zone and increases the contact angle. In this way, the fusion machinery can drive expansion of the fusion pore by free energy equivalents of multiple tens of k &lt;sub&gt;B&lt;/sub&gt; T from a distance and not only through the fusion proteins that reside within the fusion pore