Depletion-induced biaxial nematic states of boardlike particles

With the aim of investigating the stability conditions of biaxial nematic liquid crystals, we study the effect of adding a non-adsorbing ideal depletant on the phase behavior of colloidal hard boardlike particles. We take into account the presence of the depletant by introducing an effective depletion attraction between a pair of boardlike particles. At fixed depletant fugacity, the stable liquid crystal phase is determined through a mean-field theory with restricted orientations. Interestingly, we predict that for slightly elongated boardlike particles a critical depletant density exists, where the system undergoes a direct transition from an isotropic liquid to a biaxial nematic phase. As a consequence, by tuning the depletant density, an easy experimental control parameter, one can stabilize states of high biaxial nematic order even when these states are unstable for pure systems of boardlike particles

Free Minimization of the Fundamental Measure Theory Functional: Freezing of Parallel Hard Squares and Cubes

Due to remarkable advances in colloid synthesis techniques, systems of squares and cubes, once an academic abstraction for theorists and simulators, are nowadays an experimental reality. By means of a free minimization of the free-energy functional, we apply Fundamental Measure Theory to analyze the phase behavior of parallel hard squares and hard cubes. We compare our results with those obtained by the traditional approach based on the Gaussian parameterization, finding small deviations and good overall agreement between the two methods. For hard squares our predictions feature at intermediate packing fraction a smectic phase, which is however expected to be unstable due to thermal fluctuations. This implies that for hard squares the theory predicts either a vacancy-rich second-order transition or a vacancy-poor weakly first-order phase transition at higher density. In accordance with previous studies, a second-order transition with a high vacancy concentration is predicted for hard cubes

On the relation between adjacent inviscid cell type solutions to the rotating-disk equations

Over a large range of the axial coordinate a typical higher-branch solution of the rotating-disk equations consists of a chain of inviscid cells separated from each other by viscous interlayers. In this paper the leading-order relation between two adjacent cells will be established by matched asymptotic expansions for general values of the parameter appearing in the equations. It is found that the relation between the solutions in the two cells crucially depends on the behaviour of the tangential velocity in the viscous interlayer. The results of the theory are compared with accurate numerical solutions and good agreement is obtained

Liberalizing Trade in Environmental Goods

Trade liberalization in environmental goods is high on the agenda of the current Doha round. We examine its effects in a model with one domestic downstream polluting firm and two upstream firms (one domestic, one foreign). The domestic government sets the emission tax rate after the outcome of R&D is known. The upstream firms offer their technologies to the downstream firm at a flat fee. The effect of liberalization on the domestic upstream firm's R&D incentive is ambiguous. Liberalization usually results in cleaner production, which allows the country to reach higher welfare. However this increase in welfare is typically achieved at the expense of the environment (a backfire effect). Thus our results cast doubt on the hoped-for "win-win-win" outcome of trade liberalization in environmental goods.Pollution abatement technology, R&D, trade and environment, trade liberalization, backfire effect

Group rewards and individual sanctions in environmental policy

We examine an incentive scheme for a group of agents, where all agents are rewarded if the group meets its target. If the group does not meet its target, only the agents that meet their individual target are rewarded. In environmental policy, the EU burden sharing agreement and the UK Climate Change Agreements feature this incentive scheme. There is only a difference in outcome between group and individual rewards if emissions are stochastic. Group rewards generally lead to higher expected emissions than individual rewards. The attraction of the group reward scheme may lie in its fairness and its tough-looking targets.Team incentive scheme, stochastic pollution, UK Climate Change Agreements

Group Rewards and Individual Sanctions in Environmental Policy

We examine an incentive scheme for a group of agents, where all agents are rewarded if the group meets its target. If the group does not meet its target, only the agents that meet their individual target are rewarded. In environmental policy, the EU burden sharing agreement and the UK Climate Change Agreements feature this incentive scheme. There is only a difference in outcome between group and individual rewards if emissions are stochastic. Group rewards generally lead to higher expected emissions than individual rewards. The attraction of the group reward scheme may lie in its fairness and its tough-looking targets.Team Incentive Scheme, Stochastic Pollution, UK Climate Change Agreements

Permit Trading and Credit Trading: A Comparison of Cap-Based and Rate-Based Emissions Trading under Perfect and Imperfect Competition

This paper compares emissions trading based on a cap on total emissions (permit trading) and on relative standards per unit of output (credit trading). Two types of market structure are considered: perfect competition and Cournot oligopoly. The e?ect of combining the two schemes is also discussed. We ?nd that output and abatement costs are higher under credit trading. Combining the two schemes may give an increase in welfare. With perfect competition, permit trading always leads to higher welfare than credit trading. With imperfect competition, credit trading may out perform permit trading. Environmental policy can lead to both entry and exit of ?rms. Entry and exit have a profound impact on the performance of the schemes, especially under imperfect competition. We ?nd that it may be impossible to implement certain levels of total industry emissions. Under credit trading several levels of the relative standard can achieve the same total level of emissions.emissions trading, entry and exit, permit allocation, tradable performance standards

Density Functional Theory for Chiral Nematic Liquid Crystals

Even though chiral nematic phases were the first liquid crystals experimentally observed more than a century ago, the origin of the thermodynamic stability of cholesteric states is still unclear. In this Letter we address the problem by means of a novel density functional theory for the equilibrium pitch of chiral particles. When applied to right-handed hard helices, our theory predicts an entropy-driven cholesteric phase, which can be either right- or left-handed, depending not only on the particle shape but also on the thermodynamic state. We explain the origin of the chiral ordering as an interplay between local nematic alignment and excluded-volume differences between left- and right-handed particle pairs

Stabilizing the Hexagonal Close Packed Structure of Hard Spheres with Polymers : Phase diagram, Structure, and Dynamics

We study the phase behaviour of a binary mixture of colloidal hard spheres and freely-jointed chains of beads using Monte Carlo simulations. Recently Panagiotopoulos and coworkers predicted [Nat. Commun. 5, 4472 (2014)] that the hexagonal close packed (HCP) structure of hard spheres can be stabilized in such a mixture due to the interplay between polymer and the void structure in the crystal phase. Their predictions were based on estimates of the free-energy penalty for adding a single hard polymer chain in the HCP and the competing face centered cubic (FCC) phase. Here we calculate the phase diagram using free-energy calculations of the full binary mixture and find a broad fluid-solid coexistence region and a metastable gas-liquid coexistence region. For the colloid-monomer size ratio considered in this work, we find that the HCP phase is only stable in a small window at relatively high polymer reservoir packing fractions, where the coexisting HCP phase is nearly close packed. Additionally we investigate the structure and dynamic behaviour of these mixtures.Comment: 8 pages, 5 figure