Phase behavior and interfacial properties of nonadditive mixtures of Onsager rods

Within a second virial theory, we study bulk phase diagrams as well as the free planar isotropic-nematic interface of binary mixtures of nonadditive thin and thick hard rods. For species of the same type the excluded volume is determined only by the dimensions of the particles, whereas for dissimilar ones it is taken to be larger or smaller than that, giving rise to a nonadditivity that can be positive or negative. We argue that such a nonadditivity can result from modelling of soft interactions as effective hard-core interactions. The nonadditivity enhances or reduces the fractionation at isotropic-nematic ($IN$) coexistence and may induce or suppress a demixing of the high-density nematic phase into two nematic phases of different composition ($N_1$ and $N_2$), depending on whether the nonadditivity is positive or negative. The interfacial tension between co-existing isotropic and nematic phases show an increase with increasing fractionation at the $IN$ interface, and complete wetting of the $IN_2$ interface by the $N_1$ phase upon approach of the triple point coexistence. In all explored cases bulk and interfacial properties of the nonadditive mixtures exhibit a striking and quite unexpected similarity with the properties of additive mixtures of different diameter ratio.Comment: 12 pages, revised version, submitted to JC

Dynamical Monte Carlo Study of Equilibrium Polymers (II): The Role of Rings

We investigate by means of a number of different dynamical Monte Carlo simulation methods the self-assembly of equilibrium polymers in dilute, semidilute and concentrated solutions under good-solvent conditions. In our simulations, both linear chains and closed loops compete for the monomers, expanding on earlier work in which loop formation was disallowed. Our findings show that the conformational properties of the linear chains, as well as the shape of their size distribution function, are not altered by the formation of rings. Rings only seem to deplete material from the solution available to the linear chains. In agreement with scaling theory, the rings obey an algebraic size distribution, whereas the linear chains conform to a Schultz--Zimm type of distribution in dilute solution, and to an exponentional distribution in semidilute and concentrated solution. A diagram presenting different states of aggregation, including monomer-, ring- and chain-dominated regimes, is given

Modelling of non-steady-state concentration profiles at ISFET-based coulometric sensor—actuator systems

Acid or base concentrations can be determined very rapidly by performing an acid—base titration with coulometrically generated OH− or H+ ions at a noble metal actuator electrode in close proximity to the pH-sensitive gate of an ion-sensitive field effect transistor (ISFET). The ISFET is used as the indicator electrode to detect the equivalence point in the titration curve. Typical values for the time needed to reach the equivalence point are 0.5–10 s for acid or base concentrations ranging from 0.5 × 10−3 to 20 × 10−3 mol l−1.\ud \ud A model is presented, giving an analytical description of the diffusion phenomena that occur with the sensor—actuator system. The results of this analytical model description, using linearized concentration gradients, are presented together with the results of numerical simulations. Both results are in good agreement with measurements

Modelling of the migration effect occurring at an ISFET-based coulometric sensor-actuator system

The migration effect, in addition to diffusion, occurring at an ion-selective field-effect transistor (ISFET)-based coulometric sensor-actuator system has been studied. A diffusion-migration model is presented, based on the numerical solution of the Nernst-Planck equations of which a digital simulation is realized. Corresponding experiments were carried out and compared with the simulation. The results are in good agreement with the simulation.\ud Typical titration times of this system were found to be 0.5–10 s, corresponding to fully dissociated acid concentrations of 0.5×10−3−6.5×10−3 mol 1−1 with excess of supporting electrolyte. Both the simulation and experimental results show that if the concentration of the supporting electrolyte is 20 times higher than that of the species to be titrated, the deviation caused by migration is less than 5% and within the experimental error when pure diffusion is considered. At relatively low concentrations of supporting electrolyte, the migration effect should be taken into account to determine the concentrations of titrated species

Osmotic Pressure of Solutions Containing Flexible Polymers Subject to an Annealed Molecular Weight Distribution

The osmotic pressure $P$ in equilibrium polymers (EP) in good solvent is investigated by means of a three dimensional off-lattice Monte Carlo simulation. Our results compare well with real space renormalisation group theory and the osmotic compressibility K \propto \phi \upd \phi/\upd P from recent light scattering study of systems of long worm-like micelles. We confirm the scaling predictions for EP based on traditional physics of quenched monodisperse polymers in the dilute and semidilute limit. Specifically, we find $P\propto \phi^{2.3}$ and, hence, $K \propto \phi^{-0.3}$ in the semidilute regime --- in agreement with both theory and experiment. At higher concentrations where the semidilute blobs become too small and hard-core interactions and packing effects become dominant, a much stronger increase % \log(P/\phi)\approx \log(\Nav^2/\phi) \propto \phi is evidenced and, consequently, the compressibility decreases much more rapidly with $\phi$ than predicted from semidilute polymer theory, but again in agreement with experiment.Comment: 7 pages, 4 figures, LATE

Dynamic behaviour of ISFET-based sensor-actuator systems

Rapid acid-base titrations can be performed at the surface of a noble-metal electrode with coulometrically generated ions. An ISFET is used as an indicator electrode to detect the equivalence point in the resulting titration curve. The time needed to reach the equivalence point is typically 0.5 to 10 s for acid/base concentrations ranging from 0.5 × 10−3 to 20 × 10−3 mol l−1.\ud \ud A model is presented describing the concentration profiles which appear during the coulometric generation of ions. The result of this model is in good agreement with corresponding measurements. These measurements are carried out with two different actuator electrodes, of which the processing steps are described

Quasiuniversal connectedness percolation of polydisperse rod systems

The connectedness percolation threshold (eta_c) and critical coordination number (Z_c) of systems of penetrable spherocylinders characterized by a length polydispersity are studied by way of Monte Carlo simulations for several aspect ratio distributions. We find that (i) \eta_c is a nearly universal function of the weight-averaged aspect ratio, with an approximate inverse dependence that extends to aspect ratios that are well below the slender rod limit and (ii) that percolation of impenetrable spherocylinders displays a similar quasiuniversal behavior. For systems with a sufficiently high degree of polydispersity, we find that Z_c can become smaller than unity, in analogy with observations reported for generalized and complex networks.Comment: 5 pages with 3 figures + 2 pages and 4 figures of supplemental materia

Compound redistribution due to droplet evaporation on a thin polymeric film: theory

A thin polymeric film in contact with a fluid body may leach low-molecular-weight compounds into the fluid. If this fluid is a small droplet, the compound concentration within the liquid increases due to ongoing leaching in combination with the evaporation of the droplet. This may eventually lead to an inversion of the transport process and a redistribution of the compounds within the thin film. In order to gain an understanding of the compound redistribution, we apply a macroscopic model for the evaporation of a droplet and combine that with a diffusion model for the compound transport. In the model, material deposition and the resulting contact line pinning are associated with the precipitation of a fraction of the dissolved material. We find three power law regimes for the size of the deposit area as a function of the initial droplet size, dictated by the competition between evaporation, diffusion and the initial compound concentrations in the droplet and the thin film. The strength of the contact line pinning determines the deposition profile of the precipitate, characterised by a pronounced edge and a linearly decaying profile towards the centre of the stain. Our predictions for the concentration profile within the solid substrate resemble patterns found experimentally.Comment: 12 pages, 10 figure