arXiv subjects

U. S. Schwarz

Publications and source records attributed to U. S. Schwarz.

26 records · Page 2Linked to original sources

arXiv2002

Elastic Interactions of Cells

Biological cells in soft materials can be modeled as anisotropic force contraction dipoles. The corresponding elastic interaction potentials are long-ranged ($\sim 1/r^3$ with distance $r$) and depend sensitively on elastic constants, geometry and cellular orientations. On elastic substrates, the elastic interaction is similar to that of electric quadrupoles in two dimensions and for dense systems leads to aggregation with herringbone order on a cellular scale. Free and clamped surfaces of samples of finite size introduce attractive and repulsive corrections, respectively, which vary on the macroscopic scale. Our theory predicts cell reorientation on stretched elastic substrates.

cond-mat.soft↗

arXiv2001

Bending Frustration of Lipid-Water Mesophases Based on Cubic Minimal Surfaces

Inverse bicontinuous cubic phases are ubiquitous in lipid-water mixtures and consist of a lipid bilayer forming a cubic minimal surface, thereby dividing space into two cubic networks of water channels. For small hydrocarbon chain lengths, the monolayers can be modeled as parallel surfaces to a minimal midsurface. The bending energy of the cubic phases is determined by the distribution of Gaussian curvature over the minimal midsurfaces which we calculate for seven different structures (G, D, P, I-WP, C(P), S and F-RD). We show that the free-energy densities of the structures G, D and P are considerably lower than those of the other investigated structures due to their narrow distribution of Gaussian curvature. The Bonnet transformation between G, D, and P implies that these phases coexist along a triple line, which also includes an excess water phase. Our model includes thermal membrane undulations. Our qualitative predictions remain unchanged when higher order terms in the curvature energy are included. Calculated phase diagrams agree well with the experimental results for 2:1 lauric acid/dilauroyl phosphatidylcholine and water.

cond-mat.soft↗

arXiv2000

Phase behavior and material properties of hollow nanoparticles

Effective pair potentials for hollow nanoparticles like the ones made from carbon (fullerenes) or metal dichalcogenides (inorganic fullerenes) consist of a hard core repulsion and a deep, but short-ranged, van der Waals attraction. We investigate them for single- and multi-walled nanoparticles and show that in both cases, in the limit of large radii the interaction range scales inversely with the radius, $R$, while the well depth scales linearly with $R$. We predict the values of the radius $R$ and the wall thickness $h$ at which the gas-liquid coexistence disappears from the phase diagram. We also discuss unusual material properties of the solid, which include a large heat of sublimation and a small surface energy.

cond-mat.soft↗

arXiv2000

Stability of inverse bicontinuous cubic phases in lipid-water mixtures

We investigate the stability of seven inverse bicontinuous cubic phases ($G$, $D$, $P$, $C(P)$, $S$, $I-WP$, $F-RD$) in lipid-water mixtures based on a curvature model of membranes. Lipid monolayers are described by parallel surfaces to triply periodic minimal surfaces. The phase behavior is determined by the distribution of the Gaussian curvature on the minimal surface and the porosity of each structure. Only $G$, $D$ and $P$ are found to be stable, and to coexist along a triple line. The calculated phase diagram agrees very well with experimental results for 2:1 lauric acid/DLPC.

cond-mat.soft↗

arXiv2000

Deformation and tribology of multi-walled hollow nanoparticles

Multi-walled hollow nanoparticles made from tungsten disulphide (WS$_2$) show exceptional tribological performance as additives to liquid lubricants due to effective transfer of low shear strength material onto the sliding surfaces. Using a scaling approach based on continuum elasticity theory for shells and pairwise summation of van der Waals interactions, we show that van der Waals interactions cause strong adhesion to the substrate which favors release of delaminated layers onto the surfaces. For large and thin nanoparticles, van der Waals adhesion can cause considerable deformation and subsequent delamination. For the thick WS$_2$ nanoparticles, deformation due to van der Waals interactions remains small and the main mechanism for delamination is pressure which in fact leads to collapse beyond a critical value. We also discuss the effect of shear flow on deformation and rolling on the substrate.

cond-mat.mtrl-sci↗

arXiv1999

Stability of bicontinuous cubic phases in ternary amphiphilic systems with spontaneous curvature

We study the phase behavior of ternary amphiphilic systems in the framework of a curvature model with non-vanishing spontaneous curvature. The amphiphilic monolayers can arrange in different ways to form micellar, hexagonal, lamellar and various bicontinuous cubic phases. For the latter case we consider both single structures (one monolayer) and double structures (two monolayers). Their interfaces are modeled by the triply periodic surfaces of constant mean curvature of the families G, D, P, C(P), I-WP and F-RD. The stability of the different bicontinuous cubic phases can be explained by the way in which their universal geometrical properties conspire with the concentration constraints. For vanishing saddle-splay modulus $\bar κ$, almost every phase considered has some region of stability in the Gibbs triangle. Although bicontinuous cubic phases are suppressed by sufficiently negative values of the saddle-splay modulus $\bar κ$, we find that they can exist for considerably lower values than obtained previously. The most stable bicontinuous cubic phases with decreasing $\bar κ< 0$ are the single and double gyroid structures since they combine favorable topological properties with extreme volume fractions.

cond-mat.soft↗

arXiv1999

A systematic approach to bicontinuous cubic phases in ternary amphiphilic systems

The Fourier approach and theories of space groups and color symmetries are used to systematically generate and compare bicontinuous cubic structures in the framework of a Ginzburg-Landau model for ternary amphiphilic systems. Both single and double structures are investigated; they correspond to systems with one or two monolayers in a unit cell, respectively. We show how and why single structures can be made to approach triply periodic minimal surfaces very closely, and give improved nodal approximations for G, D, I-WP and P surfaces. We demonstrate that the relative stability of the single structures can be calculated from the geometrical properties of their interfaces only. The single gyroid G turns out to be the most stable bicontinuous cubic phase since it has the smallest porosity. The representations are used to calculate distributions of the Gaussian curvature and 2H-NMR bandshapes for C(P), C(D), S, C(Y) and F-RD surfaces.

cond-mat.soft↗

arXiv1996

The lamellar-to-isotropic transition in ternary amphiphilic systems

We study the dependence of the phase behavior of ternary amphiphilic systems on composition and temperature. Our analysis is based on a curvature elastic model of the surfactant film with sufficiently large spontaneous curvature and sufficiently negative saddle-splay modulus that the stable phases are the lamellar phase and a droplet microemulsion. In addition to the curvature energy, we consider the contributions to the free energy of the long-ranged van der Waals interaction and of the undulation modes. We find that for bending rigidities of order k_B T, the lamellar phase extends further and further into the water apex of the phase diagram as the phase inversion temperature is approached, in good agreement with experimental results.

cond-mat↗