Dynamics, rheology and critical properties of colloidal fluid mixtures

Liquids under the influence of external fields exhibit a wide range of intriguing phenomena that can be markedly different from the behaviour of a quiescent system. This work considers two different systems — a glassforming Yukawa system and a colloid-polymer mixture — by Molecular Dynamics (MD) computer simulations coupled to dissipative particle dynamics. The former consists of a 50-50 binary mixture of differently-sized, like-charged colloids interacting via a screened Coulomb (Yukawa) potential. Near the glass transition the influence of an external shear field is studied. In particular, the transition from elastic response to plastic flow is of interest. At first, this model is characterised in equilibrium. Upon decreasing temperature it exhibits the typical dynamics of glassforming liquids, i.e. the structural relaxation time τα grows strongly in a rather small temperature range. This is discussed with respect to the mode-coupling theory of the glass transition (MCT). For the simulation of bulk systems under shear, Lees-Edwards boundary conditions are applied. At constant shear rates γ˙ ≫ 1/τα the relevant time scale is given by 1/γ˙ and the system shows shear thinning behaviour. In order to understand the pronounced differences between a quiescent system and a system under shear, the response to a suddenly commencing or terminating shear flow is studied. After the switch-on of the shear field the shear stress shows an overshoot, marking the transition from elastic to plastic deformation, which is connected to a super-diffusive increase of the mean squared displacement. Since the average static structure only depends on the value of the shear stress, it does not discriminate between those two regimes. The distribution of local stresses, in contrast, becomes broader as soon as the system starts flowing. After a switch-off of the shear field, these additional fluctuations are responsible for the fast decay of stresses, which occurs on a time scale 1/γ˙ . The stress decay after a switch-off in the elastic regime, on the other hand, happens on the much larger time scale of structural relaxation τα. While stresses decrease to zero after a switch-off for temperatures above the glass transition, they decay to a finite value for lower temperatures. The obtained results are important for advancing new theoretical approaches in the framework of mode-coupling theory. Furthermore, they suggest new experimental investigations on colloidal systems. The colloid-polymer mixture is studied in the context of the behaviour near the critical point of phase separation. For the MD simulations a new effective model with soft interaction potentials is introduced and its phase diagram is presented. Here, mainly the equilibrium properties of this model are characterised. While the self-diffusion constants of colloids and polymers do not change strongly when the critical point is approached, critical slowing down of interdiffusion is observed. The order parameter fluctuations can be determined through the long-wavelength limit of static structure factors. For this strongly asymmetric mixture it is shown how the relevant structure factor can be extracted by a diagonalisation of a matrix that contains the partial static structure factors. By presenting first results of this model under shear it is demonstrated that it is suitable for non-equilibrium simulations as well.

Crystal phases and glassy dynamics in monodisperse hard ellipsoids

We have performed Monte Carlo and molecular dynamics simulations of suspensions of monodisperse, hard ellipsoids of revolution. Hard-particle models play a key role in statistical mechanics. They are conceptually and computationally simple, and they offer insight into systems in which particle shape is important, including atomic, molecular, colloidal, and granular systems. In the high density phase diagram of prolate hard ellipsoids we have found a new crystal, which is more stable than the stretched FCC structure proposed previously . The new phase, SM2, has a simple monoclinic unit cell containing a basis of two ellipsoids with unequal orientations. The angle of inclination is very soft for length-to-width (aspect) ratio l/w=3, while the other angles are not. A symmetric state of the unit cell exists, related to the densest-known packings of ellipsoids; it is not always the stable one. Our results remove the stretched FCC structure for aspect ratio l/w=3 from the phase diagram of hard, uni-axial ellipsoids. We provide evidence that this holds between aspect ratios 3 and 6, and possibly beyond. Finally, ellipsoids in SM2 at l/w=1.55 exhibit end-over-end flipping, warranting studies of the cross-over to where this dynamics is not possible. Secondly, we studied the dynamics of nearly spherical ellipsoids. In equilibrium, they show a first-order transition from an isotropic phase to a rotator phase, where positions are crystalline but orientations are free. When over-compressing the isotropic phase into the rotator regime, we observed super-Arrhenius slowing down of diffusion and relaxation, and signatures of the cage effect. These features of glassy dynamics are sufficiently strong that asymptotic scaling laws of the Mode-Coupling Theory of the glass transition (MCT) could be tested, and were found to apply. We found strong coupling of positional and orientational degrees of freedom, leading to a common value for the MCT glass-transition volume fraction. Flipping modes were not slowed down significantly. We demonstrated that the results are independent of simulation method, as predicted by MCT. Further, we determined that even intra-cage motion is cooperative. We confirmed the presence of dynamical heterogeneities associated with the cage effect. The transit between cages was seen to occur on short time scales, compared to the time spent in cages; but the transit was shown not to involve displacements distinguishable in character from intra-cage motion. The presence of glassy dynamics was predicted by molecular MCT (MMCT). However, as MMCT disregards crystallization, a test by simulation was required. Glassy dynamics is unusual in monodisperse systems. Crystallization typically intervenes unless polydispersity, network-forming bonds or other asymmetries are introduced. We argue that particle anisometry acts as a sufficient source of disorder to prevent crystallization. This sheds new light on the question of which ingredients are required for glass formation.

Effect of mixing, particle interaction, and spatial dimension on the glass transition

In this thesis, the influence of composition changes on the glass transition behavior of binary liquids in two and three spatial dimensions (2D/3D) is studied in the framework of mode-coupling theory (MCT).The well-established MCT equations are generalized to isotropic and homogeneous multicomponent liquids in arbitrary spatial dimensions. Furthermore, a new method is introduced which allows a fast and precise determination of special properties of glass transition lines. The new equations are then applied to the following model systems: binary mixtures of hard disks/spheres in 2D/3D, binary mixtures of dipolar point particles in 2D, and binary mixtures of dipolar hard disks in 2D. Some general features of the glass transition lines are also discussed. The direct comparison of the binary hard disk/sphere models in 2D/3D shows similar qualitative behavior. Particularly, for binary mixtures of hard disks in 2D the same four so-called mixing effects are identified as have been found before by Götze and Voigtmann for binary hard spheres in 3D [Phys. Rev. E 67, 021502 (2003)]. For instance, depending on the size disparity, adding a second component to a one-component liquid may lead to a stabilization of either the liquid or the glassy state. The MCT results for the 2D system are on a qualitative level in agreement with available computer simulation data. Furthermore, the glass transition diagram found for binary hard disks in 2D strongly resembles the corresponding random close packing diagram. Concerning dipolar systems, it is demonstrated that the experimental system of König et al. [Eur. Phys. J. E 18, 287 (2005)] is well described by binary point dipoles in 2D through a comparison between the experimental partial structure factors and those from computer simulations. For such mixtures of point particles it is demonstrated that MCT predicts always a plasticization effect, i.e. a stabilization of the liquid state due to mixing, in contrast to binary hard disks in 2D or binary hard spheres in 3D. It is demonstrated that the predicted plasticization effect is in qualitative agreement with experimental results. Finally, a glass transition diagram for binary mixtures of dipolar hard disks in 2D is calculated. These results demonstrate that at higher packing fractions there is a competition between the mixing effects occurring for binary hard disks in 2D and those for binary point dipoles in 2D.

Wavelets in High-Capacity DWDM Systems and Modal-Division Multiplexed Transmissions

Optical communications receivers using wavelet signals processing is proposed in this paper for dense wavelength-division multiplexed (DWDM) systems and modal-division multiplexed (MDM) transmissions. The optical signal-to-noise ratio (OSNR) required to demodulate polarization-division multiplexed quadrature phase shift keying (PDM-QPSK) modulation format is alleviated with the wavelet denoising process. This procedure improves the bit error rate (BER) performance and increasing the transmission distance in DWDM systems. Additionally, the wavelet-based design relies on signal decomposition using time-limited basis functions allowing to reduce the computational cost in Digital-Signal-Processing (DSP) module. Attending to MDM systems, a new scheme of encoding data bits based on wavelets is presented to minimize the mode coupling in few-mode (FWF) and multimode fibers (MMF). The Shifted Prolate Wave Spheroidal (SPWS) functions are proposed to reduce the modal interference.

Dynamical hierarchy in transition states: Why and how does a system climb over the mountain?

How a reacting system climbs through a transition state during the course of a reaction has been an intriguing subject for decades. Here we present and quantify a technique to identify and characterize local invariances about the transition state of an N-particle Hamiltonian system, using Lie canonical perturbation theory combined with microcanonical molecular dynamics simulation. We show that at least three distinct energy regimes of dynamical behavior occur in the region of the transition state, distinguished by the extent of their local dynamical invariance and regularity. Isomerization of a six-atom Lennard–Jones cluster illustrates this: up to energies high enough to make the system manifestly chaotic, approximate invariants of motion associated with a reaction coordinate in phase space imply a many-body dividing hypersurface in phase space that is free of recrossings even in a sea of chaos. The method makes it possible to visualize the stable and unstable invariant manifolds leading to and from the transition state, i.e., the reaction path in phase space, and how this regularity turns to chaos with increasing total energy of the system. This, in turn, illuminates a new type of phase space bottleneck in the region of a transition state that emerges as the total energy and mode coupling increase, which keeps a reacting system increasingly trapped in that region.

Optimized Monte Carlo method for glasses

A new Monte Carlo algorithm is introduced for the simulation of supercooled liquids and glass formers, and tested in two model glasses. The algorithm thermalizes well below the Mode Coupling temperature and outperforms other optimized Monte Carlo methods.

Finite size effects in the specific heat of glass-formers

We report clear finite size effects in the specific heat and in the relaxation times of a model glass former at temperatures considerably smaller than the Mode Coupling transition. A crucial ingredient to reach this result is a new Monte Carlo algorithm which allows us to reduce the relaxation time by two order of magnitudes. These effects signal the existence of a large correlation length in static quantities.

First-principles quantum dynamics in interacting Bose gases II: stochastic gauges

First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analysed. In a companion paper, we showed how the positive-P representation can be applied to these problems using stochastic differential equations. That method, however, is limited by increased sampling error as time evolves. Here, we show how the sampling error can be greatly reduced and the simulation time significantly extended using stochastic gauges. In particular, local stochastic gauges (a subset) are investigated. Improvements are confirmed in numerical calculations of single-, double- and multi-mode systems in the weak-mode coupling regime. Convergence issues are investigated, including the recognition of two modes by which stochastic equations produced by phase-space methods in general can diverge: movable singularities and a noise-weight relationship. The example calculated here displays wave-like behaviour in spatial correlation functions propagating in a uniform 1D gas after a sudden change in the coupling constant. This could in principle be tested experimentally using Feshbach resonance methods.

In-fibre directional transverse loading sensor based on excessively tilted fibre Bragg gratings

We report a distinctive polarization mode coupling behaviour of tilted fibre Bragg gratings (TFBGs) with a tilted angle exceeding 45°. The ex-45° TFBGs exhibit pronounced polarization mode splitting resulted from the birefringence induced by the grating structure asymmetry. We have fabricated TFBGs with a tilted structure at 81° and studied their properties under transverse load applied to their equivalent fast and slow axes. The results show that the light coupling to the orthogonally polarized modes of the 81°-TFBGs changes only when the load is applied to their slow axis, giving a prominent directional loading response. For the view of real applications, we further investigated the possibility of interrogating such a TFBG-based load sensor using low-cost and compact-size single wavelength source and power detector. The experimental results clearly show that the 81°-TFBGs plus the proposed power-measurement interrogation scheme may be developed to an optical fibre vector sensor system capable of not just measuring the magnitude but also recognizing the direction of the applied transverse load. Using such an 81°-TFBG based load sensor, a load change as small as 1.6 × 10-2 g may be detected by employing a standard photodiode detector.

Optical fibre sensors with applications in gas and biological sensing

This thesis describes the study of various grating based optical fibre sensors for applications in refractive index sensing. The sensitivity of these sensors has been studied and in some cases enhanced using novel techniques. The major areas of development are as follows. The sensitivity of long period gratings (LPGs) to surrounding medium refractive index (SRI) for various periods was investigated. The most sensitive period of LPG was found to be around 160 µm and this was due to the core mode coupling to a single cladding mode but phase matching at two wavelength locations, creating two attenuation peaks, close to the waveguide dispersion turning point. Large angle tilted fibre gratings (TFGs) have similar behaviour to LPGs, in that they couple to the co-propagating cladding modes. The tilted structure of the index modulation within the core of the fibre gives rise to a polarisation dependency, differing the large angle TFG from a LPG. Since the large angle TFG couple to the cladding mode they are SRI sensitive, the sensitivity to SRI can be further increased through cladding etching using HF acid. The thinning of the cladding layer caused a reordering of the cladding modes and shifted to more SRI sensitive cladding modes as the investigation discovered. In a SRI range of 1.36 to 1.40 a sensitivity of 506.9 nm/URI was achieved for the etched large angle TFG, which is greater than the dual resonance LPG. UV inscribed LPGs were coated with sol-gel materials with high RIs. The high RI of the coating caused an increase in cladding mode effective index which in turn caused an increase in the LPG sensitivity to SRI. LPGs of various periods of LPG were coated with sol-gel TiO2 and the optimal thickness was found to vary for each period. By coating of the already highly SRI sensitive 160µm period LPG (which is a dual resonance) with a sol-gel TiO2, the SRI sensitivity was further increased with a peak value of 1458 nm/URI, which was an almost 3 fold increase compared to the uncoated LPG. LPGs were also inscribed using a femtosecond laser which produced a highly focused index change which was no uniform throughout the core of the optical fibre. The inscription technique gave rise to a large polarisation sensitivity and the ability to couple to multiple azimuthal cladding mode sets, not seen with uniform UV inscribed gratings. Through coupling of the core mode to multiple sets of cladding modes, attenuation peaks with opposite wavelength shifts for increasing SRI was observed. Through combining this opposite wavelength shifts, a SRI sensitivity was achieved greater than any single observed attenuations peak. The maximum SRI achieved was 1680 nm/URI for a femtosecond inscribed LPG of period 400 µm. Three different types of surface plasmon resonance (SPR) sensors with a multilayer metal top coating were investigated in D shape optical fibre. The sensors could be separated into two types, utilized a pre UV inscribed tilted Bragg grating and the other employed a post UV exposure to generate surface relief grating structure. This surface perturbation aided the out coupling of light from the core but also changed the sensing mechanism from SPR to localised surface plasmon resonance (LSPR). This greatly increased the SRI sensitivity, compared to the SPR sensors; with the gold coated top layer surface relief sensor producing the largest SRI sensitivity of 2111.5nm/URI was achieved. While, the platinum and silver coated top layer surface relief sensors also gave high SRI sensitivities but also the ability to produce resonances in air (not previously seen with the SPR sensors). These properties were employed in two applications. The silver and platinum surface relief devices were used as gas sensors and were shown to be capable of detecting the minute RI change of different gases. The calculated maximum sensitivities produced were 1882.1dB/URI and 1493.5nm/URI for silver and platinum, respectively. Using a DFB laser and power meter a cheap alternative approach was investigated which showed the ability of the sensors to distinguish between different gases and flow rates of those gases. The gold surface relief sensor was coated in a with a bio compound called an aptamer and it was able to detect various concentrations of a biological compound called Thrombin, ranging from 1mM to as low as 10fM. A solution of 2M NaCl was found to give the best stripping results for Thrombin from the aptamer and showed the reusability of the sensor. The association and disassociation constants were calculated to be 1.0638×106Ms-1 and 0.2482s-1, respectively, showing the high affinity of the Aptamer to thrombin. This supports existing working stating that aptamers could be alternative to enzymes for chemical detection and also helps to explain the low detection limit of the gold surface relief sensor.

Water diffusion into UV inscripted long period grating in microstructured polymer fibre

A long period grating was photoinscribed step-by-step in microstructured poly(methyl methacrylate) fiber for the first time using a continuous wave HeCd laser at 325 nm, irradiating the fiber with a power of 1 mW. The grating had a length of 2 cm and a period of 1 mm. A series of cladding mode coupling resonances were observed throughout the spectral region studied of 600 to 1100 nm. The resonance wavelengths were shown to be sensitive to the diffusion of water into the fiber.

Advanced fibre gratings fabricated in standard and infrared glass fibres by ultraviolet and near-infrared-femtosecond lasers

In this thesis, I describe studies on fabrication, spectral characteristics and applications of tilted fibre gratings (TFGs) with small, large and 45° tilted structures and novel developments in fabrication of fibre Bragg gratings (FBGs) and long period gratings (LPGs) in normal silica and mid-infrared (mid-IR) glass fibres using near-IR femtosecond laser. One of the major contributions presented in this thesis is the systematic investigation of structures, inscription methods and spectral, polarisation dependent loss (PDL) and thermal characteristics of TFGs with small (<45°), large (>45°) and 45° tilted structures. I have experimentally characterised TFGs, obtaining relationships between the radiation angle, central wavelength of the radiation profile, Bragg resonance and the tilt angle, which are consistent with theoretical simulation based on the mode-coupling theory. Furthermore, thermal responses have been measured for these three types of TFGs, showing the transmission spectra of large and 45° TFGs are insensitive to the temperature change, unlike the normal and small angle tilted FBGs. Based on the distinctive optical properties, TFGs have been developed into interrogation system and sensors, which form the other significant contributions of the work presented in this thesis. The 10°-TFG based 800nm WDM interrogation system can function not just as an in-fibre spectrum analyser but also possess refractive index sensing capability. By utilising the unique polarisation properties, the 81 °-TFG based sensors are capable of sensing the transverse loading and twisting with sensitivities of 2.04pW/(kg/m) and 145.90pW/rad, repectively. The final but the most important contribution from the research work presented in this thesis is the development of novel grating inscription techniques using near-IR femtosecond laser. A number of LPGs and FBGs were successfully fabricated in normal silica and mid-IR glass fibres using point-by-point and phase-mask techniques. LPGs and 1st and 2nd order FBGs have been fabricated in these mid-IR glass fibres showing resonances covering the wavelength range from 1200 to 1700nm with the strengths up to 13dB. In addition, the thermal and strain sensitivities of these gratings have been systematically investigated. All the results from these initial but systematic works will provide useful function characteristics information for future fibre grating based devices and applications in mid-IR range.

Superstructure fiber gratings via single step femtosecond laser inscription

We present the development of superstructure fiber gratings (SFG) in Ge-doped, silica optical fiber using femtosecond laser inscription. We apply a simple but extremely effective single step process to inscribe low loss, sampled gratings with minor polarization dependence. The method results in a controlled modulated index change with complete suppression of mode coupling associated with the overlapping LPG structure leading to highly symmetric superstructure spectra, with the grating reflection well within the Fourier design limit. The devices are characterized and compared with numerical modeling by solving Maxwell's equations and calculating the back reflection spectrum using the bidirectional beam propagation method (BiBPM). Experimental results validate our numerical analysis, allowing for the estimation of inscription parameters such as the ac index modulation change, and the wavelength, position and relative strength of each significant resonance peak. We also present results on temperature and refractive index measurements showing potential for sensing applications.

Superstructure fiber gratings via single step femtosecond laser inscription

We present the development of superstructure fiber gratings (SFG) in Ge-doped, silica optical fiber using femtosecond laser inscription. We apply a simple but extremely effective single step process to inscribe low loss, sampled gratings with minor polarization dependence. The method results in a controlled modulated index change with complete suppression of mode coupling associated with the overlapping LPG structure leading to highly symmetric superstructure spectra, with the grating reflection well within the Fourier design limit. The devices are characterized and compared with numerical modeling by solving Maxwell's equations and calculating the back reflection spectrum using the bidirectional beam propagation method (BiBPM). Experimental results validate our numerical analysis, allowing for the estimation of inscription parameters such as the ac index modulation change, and the wavelength, position and relative strength of each significant resonance peak. We also present results on temperature and refractive index measurements showing potential for sensing applications.

Theoretical and experimental analysis of excessively tilted fiber gratings

We have theoretically and experimentally investigated the dual-peak feature of tilted fiber gratings with excessively tilted structure (named as Ex-TFGs). We have explained the dual-peak feature by solving eigenvalue equations for TM0m and TE0m of a circular waveguide, in which the TE (transverse electric) and TM (transverse magnetic) core modes are coupled into TE and TM cladding modes, respectively. Meanwhile, in the experiment, we have verified that one of the dual peaks at the shorter wavelength is due to the TM mode coupling whereas the other one at the longer wavelength arises from TE mode coupling when a linearly polarized light launched into the Ex-TFG. We have also investigated the peak separation of TE and TM cladding mode for different surrounding medium refractive indexes (SRI), revealed that the dual peaks separation is decreasing as increasing of SRI, which agrees very well with the theoretical analysis results.