Nematic liquid-crystal alignment on stripe-patterned substrates

Here, we use molecular simulation to consider the behavior of a thin nematic film confined between two identical nanopatterned substrates. Using patterns involving alternating stripes of homeotropic-favoring and homogeneous-favoring substrates, we investigate the influence of the relative stripe width and the film thickness. From this, we show that the polar anchoring angle can be varied continuously from planar to homeotropic by appropriate tuning of these parameters. For very thin films with equal stripe widths, we observe orientational bridging, the surface patterning being written in domains which traverse the nematic film. This dual bridging- domain arrangement breaks down with increase in film thickness, however, being replaced by a single tilted monodomain. Strong azimuthal anchoring in the plane of the stripe boundaries is observed for all systems

Liquid crystal films confined between patterned substrates.

In this thesis, systems of nematic liquid crystals confined between patterned substrates have been studied using molecular computer simulation. The aim of this work, done in parallel with experimentalists in Leeds, has been to investigate the use of chemical patterning as a novel method for controlling liquid crystal alignment. In the first part of this thesis, the study of confined systems of liquid crystalline particles has been addressed. Using the hard needle wall and hard gaussian overlap potentials, homeotropic and planar alignment of model molecules on the substrates has been induced. We have then extended the study of confined liquid crystals systems from the use of unpatterned symmetric susbtrates systems to hybrid anchored systems and, finally, to a system involving one patterned substrate. The results from this initial study show that surface anchoring can be controlled by changing the surface interaction parameter and that, by varying the surface interaction parameter across a model substrate, a pattern can be imposed on the confining surfaces.In the second part of this thesis, the substrate model developed in our initial stripe systems is used to simulate liquid crystal films confined between two identical patterned substrates. This is achieved through a comprehensive investigation of stripe patterned systems. In this, we show that, by varying key parameters like the stripe width, the surface interaction parameters and the film thickness, surface patterning can be used to control the polar anchoring angle and set the azimuthal anchoring. Our results show that a full range of tilt angles can be obtained by changing these key parameters.Following this work on striped systems, we extend our study to 2D patterned substrates (i.e. square and rectangle patterns). Here, the results show that by changing two key parameters, the surface interaction parameter and the shape of the pattern, it is possible to gain more complete control of the bulk tilt angle as the latter variesmonotonically as the key parameters are changed. We close the thesis with brief descriptions of some other substrate patternings that have been considered in this thesis work. These include circle and displaced/rotated stripe systems. We then draw some conclusions and comment on possible directions for future work

Competing Alignments of Nematic Liquid Crystals on Square Patterned Substrates

A theoretical analysis is presented of a nematic liquid crystal confined between substrates pat- terned with squares that promote vertical and planar alignment. Two approaches are used to eluci- date the behavior across a wide range of length scales: Monte Carlo simulation of hard particles and Frank-Oseen continuum theory. Both approaches predict bistable degenerate azimuthal alignment in the bulk along the edges of the squares; the continuum calculation additionally reveals the possi- bility of an anchoring transition to diagonal alignment if the polar anchoring energy associated with the pattern is sufficiently weak. Unlike the striped systems previously analyzed, the Monte Carlo simulations suggest that there is no "bridging" transition for sufficiently thin cells. The extent to which these geometrically patterned systems resemble topographically patterned substrates, such as square wells, is also discussed.Comment: 11 pages, 12 figure

Ordering of Oblate Hard Particles between Hybrid Penetrable Walls.

We report a Monte Carlo (MC) simulation study of a model discotic liquid crystal (DLC) confined between hybrid walls with controllable penetrability. The model consists of oblate hard Gaussian overlap (HGO) particles. Particle-substrate interactions are modeled as follows: each substrate sees a particle as a disc of zero thickness and diameter D less than or equal to that of the actual particle, σ0, embedded inside the particle and located halfway along, and perpendicular to, its minor axis. This allows us to control the anchoring properties of the substrates, from planar (edge-on) for D ≈ 0 to homeotropic (face-on) for D ≈ σ0, which can be done independently at either substrate. Depending on the values of Ds ≡ D/σ0 at the top (D s t ) and bottom (D s b ) substrates, we find domains in (D s b , D s t ) space in which particle alignment is uniform planar (UP), is uniform homeotropic (UH), or varies linearly from planar at one substrate to homeotropic at the other (Lin). These domains are separated by regions of bistability (P-Lin and H-Lin), which appear to be wider than for prolate HGOs, and there may be also a small tristable (P-H-Lin) region. Results are compared with the predictions of density functional theory, implemented at the level of Onsager's second-virial approximation with Parsons-Lee rescaling. As in the case of symmetric confinement studied previously, the agreement between theory and simulation is substantially less good than for prolate HGOs: in particular, for the investigated substrate separation L = 6σ0, the Lin configuration is never predicted. These discrepancies are likely a consequence of the fact that Onsager's theory is less accurate for discs than for rods

Competition of lattice and basis for alignment of nematic liquid crystals

Due to elastic anisotropy, two-dimensional patterning of substrates can promote weak azimuthal alignment of adjacent nematic liquid crystals. Here we consider how such alignment can be achieved using a periodic square lattice of circular or elliptical motifs. In particular, we examine ways in which the lattice and motif can combine to favor differing orientations. Using Monte Carlo simulation and continuum elasticity we find, for circular motifs, that the coverage fraction controls both the polar anchoring angle and a transition in the azimuthal orientation. If the circles are generalized to ellipses, arbitrary control of the effective easy axis and effective anchoring potential becomes achievable by appropriate tuning of the ellipse motif relative to the periodic lattice patterning. This has possible applications in both monostable and bistable liquid crystal device contexts

Interdependence, Networks, and Green Deal: The EU's Opportunity to Redefine the Landscape of Global Sustainable Development Challenges

Today's world stands at the crossroads of major global challenges, ranging from poverty and inequality to climate change and environmental degradation. These pressing issues underscore the essential role of sustainable development in forging a prosperous, equitable, and peaceful future for all. Building on the insights and findings of SDSN Senior Working Group on the European Green Deal's previous reports, namely "Transformations for the Joint Implementation of Agenda 2030 for Sustainable Development and the European Green Deal: A Green and Digital, Job-Based and Inclusive Recovery from COVID-19 Pandemic" (2021), and "Financing the Joint Implementation of Agenda 2030 and the European Green Deal" (2022), this year’s report explores in detail the multifaceted nature of sustainable development and offers invaluable insights to guide the policy decisions required to address these challenges. More specifically, in line with the work presented in 2021’s and 2022’s Reports, the current report also investigates the complicated web of factors affecting sustainable development. It emphasizes the importance of region-specific approaches to sustainable development, repeating the focus on the European Union's role presented in the previous reports. It explores the potential of the EU to redefine global sustainable development challenges and highlights the necessity of understanding interdependencies among different systems, a topic touched upon in our discussions about the close link between the European Green Deal and Agenda 2030, with the 17 SDGs. Furthermore, this report expands on the concept of 'natural capital' introduced in 2022’s Report, exploring its interconnectedness with social capital, produced capital, and cultural heritage. More specifically, it recognizes the role of aesthetic, historical, social, and spiritual values in shaping sustainable development policies. In consistence with the previous reports, this report also underscores the significance of green jobs and digital transition as drivers of sustainable development. It goes deeper into the employment trends and skill requirements in the net-zero economy and urges the importance of reskilling policies, reflecting on the job-based recovery discussed in 2021’s Report. Building upon the financial discussion in 2022’s Report, this report touches on the private sector's role in financing the SDGs, identifying SDG content in financial asset portfolios, and emphasizing the potential of carbon farming and voluntary carbon markets. These discussions further illuminate the financial strategies necessary for the successful implementation of sustainable development initiatives. In conclusion, "Transforming Our World: Interdisciplinary Insights on the Sustainable Development Goals" serves as an extension of our previous discussions. By bringing together interdisciplinary insights and understanding the interconnections between different dimensions of sustainable development, this report can guide policymakers and stakeholders to take informed decisions and targeted actions to address the complex challenges of our time, thereby contributing to a more sustainable and equitable future

Transforming Our World: Interdisciplinary Insights on the Sustainable Development Goals

Today's world stands at the crossroads of major global challenges, ranging from poverty and inequality to climate change and environmental degradation. These pressing issues underscore the essential role of sustainable development in forging a prosperous, equitable, and peaceful future for all. Building on the insights and findings of our previous reports, namely "Transformations for the Joint Implementation of Agenda 2030 for Sustainable Development and the European Green Deal: A Green and Digital, Job-Based and Inclusive Recovery from COVID-19 Pandemic" (2021), and "Financing the Joint Implementation of Agenda 2030 and the European Green Deal" (2022), this year’s report explores in detail the multifaceted nature of sustainable development and offers invaluable insights to guide the policy decisions required to address these challenges. More specifically, in line with the work presented in 2021’s and 2022’s Reports, the current report also investigates the complicated web of factors affecting sustainable development. It emphasizes the importance of regionspecific approaches to sustainable development, repeating the focus on the European Union's role presented in the previous reports. It explores the potential of the EU to redefine global sustainable development challenges and highlights the necessity of understanding interdependencies among different systems, a topic touched upon in our discussions about the close link between the European Green Deal and Agenda 2030, with the 17 SDGs. Furthermore, this report expands on the concept of 'natural capital' introduced in 2022’s Report, exploring its interconnectedness with social capital, produced capital, and cultural heritage. More specifically, it recognizes the role of aesthetic, historical, social, and spiritual values in shaping sustainable development policies. In consistence with the previous reports, this report also underscores the significance of green jobs and digital transition as drivers of sustainable development. It goes deeper into the employment trends and skill requirements in the net-zero economy and urges the importance of reskilling policies, reflecting on the job-based recovery discussed in 2021’s Report. Building upon the financial discussion in 2022’s Report, this report touches on the private sector's role in financing the SDGs, identifying SDG content in financial asset portfolios, and emphasizing the potential of carbon farming and voluntary carbon markets. These discussions further illuminate the financial strategies necessary for the successful implementation of sustainable development initiatives. In conclusion, "Transforming Our World: Interdisciplinary Insights on the Sustainable Development Goals" serves as an extension of our previous discussions. By bringing together interdisciplinary insights and understanding the interconnections between different dimensions of sustainable development, this report can guide policymakers and stakeholders to take informed decisions and targeted actions to address the complex challenges of our time, thereby contributing to a more sustainable and equitable future