Polarization resolved angular patterns in nematic liquid crystal cells

We study the angular structure of polarization of light transmitted through a nematic liquid crystal (NLC) cell by theoretically analyzing the polarization state as a function of the incidence angles. For a uniformly aligned NLC cell, the $4\times 4$ matrix formalism and the orthogonality relations are used to derive the analytical expressions for the transmission and reflection matrices. The polarization resolved angular patterns in the two-dimensional projection plane are characterized in terms of the polarization singularities: C points (points of circular polarization) and L lines (lines of linear polarization). In the case of linearly polarized plane waves incident on the homeotropically aligned cell, we present the results of detailed theoretical analysis describing the structure of the polarization singularities. We apply the theory to compute the polarization patterns for various orientational structures in the NLC cell and discuss the effects induced by the director orientation and biaxiality.Comment: pdflatex, rextex4, 22 pages, 7 figures (jpeg

Geometrically-controlled twist transitions in nematic cells

We study geometrically-controlled twist transitions of a nematic confined between a sinusoidal grating and a flat substrate. In these cells the transition to the twisted state is driven by surface effects. We have identified the mechanisms responsible for the transition analytically and used exact numerical calculations to study the range of surface parameters where the twist instability occurs. Close to these values the cell operates under minimal external fields or temperature variations

Nematic liquid crystal alignment on chemical patterns

Patterned Self-Assembled Monolayers (SAMs) promoting both homeotropic and planar degenerate alignment of 6CB and 9CB in their nematic phase, were created using microcontact printing of functionalised organothiols on gold films. The effects of a range of different pattern geometries and sizes were investigated, including stripes, circles and checkerboards. EvanescentWave Ellipsometry was used to study the orientation of the liquid crystal (LC) on these patterned surfaces during the isotropic-nematic phase transition. Pretransitional growth of a homeotropic layer was observed on 1 ¹m homeotropic aligning stripes, followed by a homeotropic mono-domain state prior to the bulk phase transition. Accompanying Monte-Carlo simulations of LCs aligned on nano-patterned surfaces were also performed. These simulations also showed the presence of the homeotropic mono-domain state prior to the transition.</p

Optically guided mode study of nematic liquid crystal alignment on a zero-order grating

B. T. Hallam and J. Roy Sambles, Physical Review E, Vol. 61, pp. 6699-6704 (2000). "Copyright © 2000 by the American Physical Society."The characterization of a liquid crystal cell, which comprises one zero-order (that is, at the wavelength of study it is nondiffractive) diffraction grating and one rubbed polyimide-coated substrate, has been performed using an optically guided mode technique. The cell is filled with nematic liquid crystal E7 (manufactured and sold by Merck, Poole, U.K.). The excitation of fully leaky guided modes within the liquid crystal layer has allowed the optical director profile to be quantified under the application of weak in-plane electric fields. The fitting of angle-dependent optical data to multilayer optical theory yields the accurate twist profile of the liquid crystal for different field strengths. Comparisons with profiles predicted from elastic continuum theory, assuming a Rapini-Papoular-type anchoring at the surfaces, allow both the azimuthal anchoring strength at each surface and the twist elastic constant of the bulk to be accurately determined. Repeating these measurements as a function of temperature allows the surface and bulk order parameters of the grating-aligned liquid crystal to be deduced

Direct Optical Quantification of Backflow in a 90° Twisted Nematic Cell

N. J. Smith, M. D. Tillin, and J. Roy Sambles, Physical Review Letters, Vol. 88, article 088301 (2002). "Copyright © 2002 by the American Physical Society."Optical guided mode observations of the transient director profile (optical tensor distribution) during the relaxation of a 90° twisted nematic cell directly reveals backflow. In the first 6 ms of the relaxation process, after a voltage across the cell is removed, the midplane tilt of the director increases, reaching a maximum value of 101° at 1.4 ms. This increase in midplane tilt is attributed to coupling between fluid flow (backflow) and director reorientation. A 270° twisted state of the opposite handedness to the 90° twisted state found at equilibrium is shown to exist during the backflow period. Good fits of theoretical models with experimentally determined time dependent director profiles yield the viscosity coefficients

The Size Ellect on the Infrared Spectra of Condensed Media Under Conditions of ID, 2D and 3D Dielectric Confinement

A general expression for the dielectric loss spectrum of an absorbing composite medium was obtained from a Maxwell-Garnett general equation. This expression was simplified for the cases of one, two and three dimensional dielectric confinement in both ordered and disordered thin layers, rods (wires) and spheres of absorbing medium which are considered as mesoparticles or mesoscopic molecules. This theoretical approach was verified experimentally using high purity organic liquids with strong absorption bands in the infrared range. Three organic liquids, namely benzene, chloroform and carbon disulphide, were measured in various dielectric confinement configurations using Fourier Transform Infrared (FTIR) spectroscopy with a Grazing Angle attachment GATRTM. A significant shift of the resonant absorption band of liquid mesoparticles was observed for various dielectric confinement geometries which is in good agreement with theoretical predictions. Possible applications of this work include investigations of industrial smoke, toxic aerosols and liquid droplets

A critical review of smaller state diplomacy

In The Peloponnesian War, Thucydides (1972: 402) highlights the effects of the general, overall weakness of smaller states vis-à-vis larger, more powerful ones in a key passage, where the Athenians remind the Melians that: “… since you know as well as we do that, as the world goes, right is only in question between equals in power. Meanwhile, the strong do what they can and the weak suffer what they must.” Concerns about the vulnerability of small, weak, isolated states have echoed throughout history: from Thucydides, through the review by Machiavelli (1985) of the risks of inviting great powers to intervene in domestic affairs, through 20th century US-led contemporary political science (Vital, 1971; Handel, 1990) and Commonwealth led scholarship (Commonwealth Secretariat, 1985). In the context of 20th century ‘Balkanization’, the small state could also prove unstable, even hostile and uncooperative, a situation tempting enough to invite the intrusion of more powerful neighbours: a combination, according to Brzezinski (1997: 123-124) of a power vacuum and a corollary power suction2: in the outcome, if the small state is ‘absorbed’, it would be its fault, and its destiny, in the grand scheme of things. In an excellent review of small states in the context of the global politics of development, Payne (2004: 623, 634) concludes that “vulnerabilities rather than opportunities are the most striking consequence of smallness”. It has been recently claimed that, since they cannot defend or represent themselves adequately, small states “lack real independence, which makes them suboptimal participants in the international system” (Hagalin, 2005: 1). There is however, a less notable and acknowledged but more extraordinary strand of argumentation that considers ‘the power of powerlessness’, and the ability of small states to exploit their smaller size in a variety of ways in order to achieve their intended, even if unlikely, policy outcomes. The pursuance of smaller state goals becomes paradoxically acceptable and achievable precisely because such smaller states do not have the power to leverage disputants or pursue their own agenda. A case in point concerns the smallest state of all, the Vatican, whose powers are both unique and ambiguous, but certainly not insignificant (The Economist, 2007). Smaller states have “punched above their weight” (e.g. Edis, 1991); and, intermittently, political scientists confront their “amazing intractability” (e.g. Suhrke, 1973: 508). Henry Kissinger (1982: 172) referred to this stance, with obvious contempt, as “the tyranny of the weak”3. This paper seeks a safe passage through these two, equally reductionist, propositions. It deliberately focuses first on a comparative case analysis of two, distinct ‘small state-big state’ contests drawn from the 1970s, seeking to infer and tease out the conditions that enable smaller ‘Lilliputian’ states (whether often or rarely) to beat their respective Goliaths. The discussion is then taken forward to examine whether similar tactics can work in relation to contemporary concerns with environmental vulnerability, with a focus on two other, small island states. Before that, the semiotics of ‘the small state’ need to be explored, since they are suggestive of the perceptions and expectations that are harboured by decision makers at home and abroad and which tend towards the self-fulfilling prophecy.peer-reviewe