A Triangular Tessellation Scheme for the Adsorption Free Energy at the Liquid-Liquid Interface: Towards Non-Convex Patterned Colloids

We introduce a new numerical technique, namely triangular tessellation, to calculate the free energy associated with the adsorption of a colloidal particle at a flat interface. The theory and numerical scheme presented here are sufficiently general to handle non-convex patchy colloids with arbitrary surface patterns characterized by a wetting angle, e.g., amphiphilicity. We ignore interfacial deformation due to capillary, electrostatic, or gravitational forces, but the method can be extended to take such effects into account. It is verified that the numerical method presented is accurate and sufficiently stable to be applied to more general situations than presented in this paper. The merits of the tessellation method prove to outweigh those of traditionally used semi-analytic approaches, especially when it comes to generality and applicability.Comment: 21 pages, 11 figures, 0 table

Orientational and phase-coexistence behaviour of hard rod-sphere mixtures

Results are presented from Monte Carlo simulations of bulk mixtures of Hard Gaussian Overlap particles with an aspect ratio of 3:1 and hard spheres with diameters equal to the breadths of the rods. For sphere number-concentrations of 50% and lower, compression of the isotropic fluid results in formation of a homogeneous (i.e. compositionally mixed) nematic phase. The volume fraction of this isotropic-nematic transition is found to increase approximately linearly with sphere concentration. On compression to higher volume fractions, however, this homogeneous nematic phase separates out into coexisting nematic and isotropic phases.</p

Nematic-Wetted Colloids in the Isotropic Phase: Pairwise Interaction, Biaxiality and Defects

We calculate the interaction between two spherical colloidal particles embedded in the isotropic phase of a nematogenic liquid. The surface of the particles induces wetting nematic coronas that mediate an elastic interaction. In the weak wetting regime, we obtain exact results for the interaction energy and the texture, showing that defects and biaxiality arise, although they are not topologically required. We evidence rich behaviors, including the possibility of reversible colloidal aggregation and dispersion. Complex anisotropic self-assembled phases might be formed in dense suspensions.Comment: 4 pages, 6 figure

Assessing measurement invariance in the EORTC QLQ-C30

PURPOSE: We aimed to investigate measurement invariance (MI) in the European Organisation for research and treatment of cancer quality of life questionnaire core 30 (EORTC QLQ-C30) in a heterogeneous sample of patients with cancer. METHODS: Data from 12 studies within the PROFILES registry were used for secondary analyses (n = 7007). We tested MI by successive restrictions on thresholds, loadings, and intercepts across subgroups based on primary cancer sites, age, sex, time since diagnosis, and life stage, using multigroup confirmatory factor analysis (MGCFA) for ordered categorical measures. We also evaluated the impact of potentially miss-specified parameter equality across groups on latent factor means by releasing threshold and loading equality constraints for each item at a time. RESULTS: Results showed that the highest level of MI (invariance of thresholds, loadings, and intercepts) was found across groups based on time since diagnosis and life stage and to a lesser extent across groups based on sex, age, and primary tumor site. On item level, however, changes in the item’s associated factor means were relatively small and in most cases canceled each other out to some extent. CONCLUSIONS: Given only a few instances of non-invariance in our study, there is reason to be confident that valid conclusions can be drawn from between-group comparisons of QLQ-C30 latent means as operationalized in our study. Nonetheless, further research into MI between other subgroups for the QLQ-C30 (i.e., treatment effects and ethnicity) is warranted. We stress the importance of including MI evaluations in the development and validation of measurement instruments. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s11136-021-02961-8

Effective Interactions and Volume Energies in Charged Colloids: Linear Response Theory

Interparticle interactions in charge-stabilized colloidal suspensions, of arbitrary salt concentration, are described at the level of effective interactions in an equivalent one-component system. Integrating out from the partition function the degrees of freedom of all microions, and assuming linear response to the macroion charges, general expressions are obtained for both an effective electrostatic pair interaction and an associated microion volume energy. For macroions with hard-sphere cores, the effective interaction is of the DLVO screened-Coulomb form, but with a modified screening constant that incorporates excluded volume effects. The volume energy -- a natural consequence of the one-component reduction -- contributes to the total free energy and can significantly influence thermodynamic properties in the limit of low-salt concentration. As illustrations, the osmotic pressure and bulk modulus are computed and compared with recent experimental measurements for deionized suspensions. For macroions of sufficient charge and concentration, it is shown that the counterions can act to soften or destabilize colloidal crystals.Comment: 14 pages, including 3 figure

Beware of density dependent pair potentials

Density (or state) dependent pair potentials arise naturally from coarse-graining procedures in many areas of condensed matter science. However, correctly using them to calculate physical properties of interest is subtle and cannot be uncoupled from the route by which they were derived. Furthermore, there is usually no unique way to coarse-grain to an effective pair potential. Even for simple systems like liquid Argon, the pair potential that correctly reproduces the pair structure will not generate the right virial pressure. Ignoring these issues in naive applications of density dependent pair potentials can lead to an apparent dependence of thermodynamic properties on the ensemble within which they are calculated, as well as other inconsistencies. These concepts are illustrated by several pedagogical examples, including: effective pair potentials for systems with many-body interactions, and the mapping of charged (Debye-H\"{u}ckel) and uncharged (Asakura-Oosawa) two-component systems onto effective one-component ones.Comment: 22 pages, uses iopart.cls and iopart10.clo; submitted to Journal of Physics Condensed Matter, special issue in honour of professor Jean-Pierre Hanse

The osmotic pressure of charged colloidal suspensions: A unified approach to linearized Poisson-Boltzmann theory

We study theoretically the osmotic pressure of a suspension of charged objects (e.g., colloids, polyelectrolytes, clay platelets, etc.) dialyzed against an electrolyte solution using the cell model and linear Poisson-Boltzmann (PB) theory. From the volume derivative of the grand potential functional of linear theory we obtain two novel expressions for the osmotic pressure in terms of the potential- or ion-profiles, neither of which coincides with the expression known from nonlinear PB theory, namely, the density of microions at the cell boundary. We show that the range of validity of linearization depends strongly on the linearization point and proof that expansion about the selfconsistently determined average potential is optimal in several respects. For instance, screening inside the suspension is automatically described by the actual ionic strength, resulting in the correct asymptotics at high colloid concentration. Together with the analytical solution of the linear PB equation for cell models of arbitrary dimension and electrolyte composition explicit and very general formulas for the osmotic pressure ensue. A comparison with nonlinear PB theory is provided. Our analysis also shows that whether or not linear theory predicts a phase separation depends crucially on the precise definition of the pressure, showing that an improper choice could predict an artificial phase separation in systems as important as DNA in physiological salt solution.Comment: 16 pages, 5 figures, REVTeX4 styl

Inhomogeneous magnetization in dipolar ferromagnetic liquids

At high densities fluids of strongly dipolar spherical particles exhibit spontaneous long-ranged orientational order. Typically, due to demagnetization effects induced by the long range of the dipolar interactions, the magnetization structure is spatially inhomogeneous and depends on the shape of the sample. We determine this structure for a cubic sample by the free minimization of an appropriate microscopic density functional using simulated annealing. We find a vortex structure resembling four domains separated by four domain walls whose thickness increases proportional to the system size L. There are indications that for large L the whole configuration scales with the system size. Near the axis of the mainly planar vortex structure the direction of the magnetization escapes into the third dimension or, at higher temperatures, the absolute value of the magnetization is strongly reduced. Thus the orientational order is characterized by two point defects at the top and the bottom of the sample, respectively. The equilibrium structure in an external field and the transition to a homogeneous magnetization for strong fields are analyzed, too.Comment: 17 postscript figures included, submitted to Phys. Rev.

A coil-globule transition of a semiflexible polymer driven by the addition of spherical particles

The phase behaviour of a single large semiflexible polymer immersed in a suspension of spherical particles is studied. All interactions are simple excluded volume interactions and the diameter of the spherical particles is an order of magnitude larger than the diameter of the polymer. The spherical particles induce a quite long ranged depletion attraction between the segments of the polymer and this induces a continuous coil-globule transition in the polymer. This behaviour gives an indication of the condensing effect of macromolecular crowding on DNA.Comment: 12 pages, 4 figure