Degree Of Positional Disorder Research Articles

Disorder-Induced Phase Transitions in the Transmission of Dielectric Metasurfaces.

Light interaction with disordered materials is both complex and fascinating at the same time. Here, we reveal disorder-induced phase transitions in a dielectric Huygens' metasurface made from silicon nanocylinders that simultaneously support an electric and magnetic dipole resonance. Depending on the degree of positional disorder and the spectral detuning of the two resonances, the phase angle of the transmission coefficient exhibits a clear phase transition from normal to anomalous dispersion. Combined with the considerations of whether the resonances of spectrally detuned particles appear as separated or overlapping, we distinguish four different phase states. We study this phenomenon analytically by employing dipole particles and disclose the entire phase diagram, support our insights with full-wave simulations of actual structures, and corroborate the findings with experimental results. Unveiling this phenomenon is a milestone simultaneously in the growing fields of metamaterial-inspired silicon nanophotonics, photonics in disordered media, and the fundamental physics of phase transitions.

Unidirectional Light Beam Splitter Based on the Square-Lattice Photonic Crystal Heterojunctions

The unidirectional light transmission characteristics of the two-dimensional square-lattice photonic crystal heterostructure consisting of air holes immersed in silicon are numerically studied by the finite-difference time-domain method. Through interlacing the air holes with different radiuses on the interface vertical to the light transmission direction, a new kind of unidirectional beam splitter is obtained. This kind of beam splitting device works well with a tolerance within 10% degree of radial disorder or 5% degree of positional disorder.

Disorders influences on the focusing effect of all-dielectric photonic crystal slab superlens

The influences of structure disorders on the subwavelength focusing properties of an all-dielectric photonic crystal slab superlens are theoretically studied. The structure disorders are considered as randomly perturbing the position or diameter of air holes of the photonic crystal slab. The results show that the photonic crystal slab superlens can tolerate within 10% degree of positional disorder or 15% degree of diameter disorder without destroying the focusing function.

The effect of static disorder on pressure-induced phase transitions and amorphization in α-quartz-type solid solutions

The high-pressure stability of α-quartz-type materials is of considerable interest for materials (piezoelectrics etc.) and Earth science. Representative compositions of two α-quartz type solid solutions SiO2–PON and AlPO4–GaPO4 were studied at high pressure by X-ray diffraction. These materials exhibit distinct high pressure behaviour as the diffraction lines of α-quartz-type Si0.56P0.44O1.56N0.44 were found to decrease in intensity above 23 GPa with the pattern becoming completely featureless above 40 GPa, whereas Al0.30Ga0.70PO4 transforms to a poorly-crystallised phase above 12 GPa. This difference in behaviour can be linked to the initial degree of positional disorder in the two solid solutions. A highly disordered, possibly amorphous, phase is favoured in the SiO2–PON system, in which positional disorder is present on all cation and anion sites. In contrast, disorder affects only ½ of the cation sites in the AlPO4–GaPO4 system. A high degree of disorder, particularly on the site occupied by phosphorus, plays a role in inhibiting the formation of ordered phases with increased cation coordination.

Phase polymorphism of [Zn(DMSO)6](ClO4)2 studied by differential scanning calorimetry

Four solid phases of [Zn(DMSO)6](ClO4)2 have been detected by differential scanning calorimetry (DSC). Specifically, the phase transitions were detected between: metastable phase KII↔supercooled phase K0 at TC3h=315 K, stable phase KIb↔stable phase KIa at TC2h=341 K, stable phase KIa↔stable phase K0 at TC1h=355 K. At Tm2=389K crystals partially and at Tm1=465K completely melts. From the entropy change values it was concluded that the phases: K0 and K0′ are the orientationally dynamically disordered phases, so called ODDIC crystals, and phases KIa, KIb and metastable KII are dynamically ordered but with some degree of positional disorder.

Positional disorder in lattices: a model for the structural order responsible for the firstsharp diffraction peak in glasses

Gaussian positional disorder has been introduced into the structure of various 2D and 3Dcrystal lattices. As the degree of positional disorder is increased, the weights of thehighest-k peaks in the orientationally-averaged structure factor are decreased first, eventuallyleaving only a single peak having significant weight, that with the lowestk-value. The orientationally-averaged real-space pair-correlation function for lattices withsuch high levels of positional disorder exhibits a corresponding power-law-damped series ofoscillations, with a single period equal to the separation between the furthest-separated,lowest-k lattice planes. This last surviving peak in the structure factor is at ak-value nearly identical to that of the experimentally-observed first sharp diffractionpeak for the corresponding real amorphous phases of such lattices (e.g. Si,SiO2). These results also have a bearing on the unsolved Gauss circle problem in mathematics.

Hole Transport in Hydrazone Doped Polymers

Hole mobilities have been measured in poly(styrene) doped with a series of hydrazone (HDZ) molecules with different dipole moments. The results are described by a formalism based on disorder. The formalism is premised on the argument that charge transport occurs by hopping through a manifold of localized states that are distributed in energy. The parameters of the formalism are σ, the energy width of the hopping site manifold or DOS (density-of-states), µ0 a prefactor mobility, and Σ the degree of positional disorder. The results show that the widths are between 0.098 and 0.113 eV, increasing with increasing dipole moment. The widths are described by an argument based on dipolar disorder. The argument is that the total width of the DOS is comprised of a dipolar component and a van der Waals component. Describing the dipolar component by the model of Young leads to the conclusion that the van der Waals components are approximately 0.091 eV. The prefactor mobilities are between 6 and 9×10-3 cm2/ Vs. Values of Σ are approximately 1.5. Compared to other classes of doped polymers with similar dipole moments, the relatively low mobilities of these materials are attributed to the high values of the van der Waals components and the low prefactor mobilities. The degree of positional disorder is similar to literature values reported for a wide range of doped polymers.

Charge Transport in Vapor-Deposited p-Diethylaminobenzaldehyde Diphenylhydrazone

Hole mobilities of vapor-deposited p-diethylaminobenzaldehyde diphenylhydrazone glasses have been measured over a range of temperatures that includes the glass transition temperature Tg. Discontinuities in the temperature dependence were observed at Tg. For T > Tg, the activation energy is approximately 1/2 its value for T < Tg. The results are described within the framework of a formalism based on disorder, due to Bässler and coworkers. The formalism is based on the assumption that charge transport occurs by hopping through a manifold of localized states that are distributed in energy and distance. The key parameters of the formalism are σ, the energy width of the hopping site manifold, Σ the degree of positional disorder, and μ0 a prefactor mobility. For T < Tg, the results yield σ = 0.106 eV, μ0 = 4.6×10—3 cm2/Vs, and Σ = 1.0. Analyzing the data for T > Tg leads to the conclusion that σ increases with increasing temperature while Σ remains constant.

Hole transport in vapor deposited enamines and enamine doped polymers

Hole mobilities have been measured of a series of vapor deposited enamine glasses and enamine doped polymers. The enamines are weakly polar donor molecules with dipole moments between 0.38 and 0.66 debye. For the vapor deposited glasses, the room temperature mobilities approach 10 −2 cm 2/V s at high fields. For the doped polymers, the mobilities are in excess of 10 −3 cm 2/V s. The results are described by a formalism based on disorder. According to the formalism, charge transport occurs by hopping through a manifold of localized states that are distributed in energy and distance. The key parameters of the formalism are σ, the energy width of the hopping site distribution, Σ the degree of positional disorder, and μ 0 a prefactor mobility. The width of the hopping site manifold is described by a model of dipolar disorder. The model is premised on the assumption than the total width is comprised of a dipolar component and a van der Waals component. For weakly polar molecules, the dipolar component vanishes and the total width gives the van der Waals component directly. For the vapor deposited glasses, the van der Waals components are 0.075 eV. Values for the doped polymers are 0.082 eV. The prefactor mobilities for the vapor deposited glasses are approximately 0.20 cm 2/V s while values for the doped polymers are between 2 and 4 × 10 −2 cm 2/V s. Values of the positional disorder parameter are approximately 1.0 for the vapor deposited glasses and 1.7 to 2.0 for the doped polymers. The high mobilities in these materials are due to the low values of the van der Waals components and the high prefactor mobilities.

Hole Transport in Triphenylmethane-Doped Poly(styrene)

Hole mobilities have been measured for a series of triphenyl-methane (TPM) derivatives with different dipole moments doped into poly(styrene) (PS). The results are described within the framework of a formalism based on disorder, due to B&#xE4;ssler and coworkers. The formalism is premised on the assumption that transport occurs by hopping through a manifold of localized states that are subject to a distribution of energies and distances. The key parameters of the formalism are the energy width of the hopping site manifold, the degree of positional disorder, and a prefactor mobility. For TPM-doped PS, the widths are between 0.104 and 0.124 eV, increasing with increasing TPM concentration and increasing dipole moment. Values of the positional disorder parameter are between 2.0 and 4.5, increasing with increasing dilution. The prefactor mobilities decrease with increasing dilution and can be described by wavefunction decay constants of approximately 1.0 &#xC5;. The energy widths are described by a model based on dipolar disorder. According to the model, the widths are comprised of a dipolar component and a van der Waals component. The dipolar components are between 0.012 and 0.067 eV, and the van der Waals components are 0.104 eV. The van der Waals components are significantly larger than literature values for PS doped with a wide range of triarylamine (TAA) molecules. The difference in the van der Waals components is the principal reason for the very considerable difference in mobility of TPM- and TAA-doped polymers. For constant dopant concentrations, the degree of positional disorder and the prefactor mobilities are essentially the same for all TPM- and TAA-doped polymers.

The Effect of Dopant Concentration on the Mobility of a Triphenylmethane Doped Polymer

Hole mobilities have been measured in poly(styrene) (PS) doped with bis(4-N,N-diethylamino-2-methylphenyl) (4-4-methoxyphenyl)methane (TPM). TPM is a weakly polar donor molecule with a dipole moment of 2.1 D. The results are described by a formalism based on disorder. The formalism is based on the assumption that charge transport occurs by hopping through a manifold of localized states with superimposed energetic and positional disorder. The parameters of the formalism are σ, the energy width of the hopping site manifold, Σ the degree of positional disorder, µ0 a prefactor mobility, and ρ0 a wavefunction decay constant. The energy widths are between 0.105 and 0.113 eV, increasing with increasing TPM concentration. The concentration dependence of the widths is described by an argument based on dipolar disorder. Values of Σ are between 2.4 and 3.8, increasing with increasing dilution. The prefactor mobilities are between 1.6×10-5 and 7.4×10-2 cm2/ Vs and can be described by a wavefunction decay constant of 1.2 Å.

Bipolar Transport in a Molecularly Doped Polymer Containing a Bifunctional Dopant Molecule

Hole and electron mobilities have been measured in N-[p-(di-ptolylamino) phenyl]-N'-(1,2-dimethylpropyl)-1,4,5,8-naphthalenetetracarboxylic diimide (TAND)- oped polycarbonate (PC). The TAND molecule contains a naphthalene diimide acceptor functionality and a triarylamine donor functionality. Both electron and hole transport are observed in TAND-doped PC with comparable mobilities. To our knowledge, this is the first literature report of bipolar transport in a doped polymer containing a bifunctional dopant molecule. The results are described by a model based on disorder, due to Bassler and coworkers. The model is premised on the assumption that charge transport occurs by hopping through a manifold of localized states with superimposed energetic and positional disorder. The key parameters of the formalism are &#x3C3;, the energy width of the hopping site manifold, and &#x3A3;, the degree of positional disorder. For TAND-doped PC, the widths are 0.130 and 0.137 eV for hole and electron transport, respectively. The corresponding values of the positional disorder are 3.7 and 3.4. The results suggest that the hole and electron transport manifolds are each independent and not influenced by the transport states of the oppositely charged carriers.

Hole transport in triarylamine doped polymers

Hole mobilities have been measured in N,N′,N″,N‴-tetrakis(4-methylphenyl)-(1,1′-biphenyl)-4,4′-diamine(TTB) and N,N′-diphenyl-N,N′-bis(3-methylphenyl)-(1,1′-biphenyl)-4,4′-diamine (TPD) doped poly(styrene) (PS). The results are described within the framework of a formalism based on disorder, due to Bässler and coworkers. The formalism is based on the assumption that charge transport occurs by hopping through a manifold of localized states with superimposed energetic and positional disorder. The key parameters are σ, the energy width of the hopping site manifold, and Σ, the degree of positional disorder. For 20% TTB and TPD doped PS, σ = 0.102 eV. The positional disorder parameter is Σ = 3.9 for TTB and Σ = 3.8 for TPD doped PS. The width of the hopping site manifold is described by a model based on dipolar disorder. The model is based on the assumption that the width is comprised of a dipolar component due to the dopant molecule and a van der Waals component. The results show that transport in both TTB and TPD can be described by disorder-controlled hopping without invoking polaronic contributions. Deviations from ideal disordercontrolled behavior have been observed for both compounds at low fields.

A comparative study of hole transport in vapor-deposited molecular glasses of N,N′,N″,N‴-tetrakis(4-methylphenyl)-(1,1′-biphenyl)-4,4′-diamine and N,N′-diphenyl-N,N′-bis(3-methylphenyl)-(1,1′-biphenyl)-4,4′-diamine

Abstract Hole mobilities have been measured in vapor-deposited layers of N,N′,N″,N‴-tetrakis(4-methylphenyl)-(1,1′-biphenyl)-4,4′-diamine (TTB) and N,N′-diphenyl-N,N′-bis(3-methylphenyl)-(1,1′-biphenyl)-4,4′-diamine (TPD). The results are described within the framework of a formalism based on disorder, due to Bassler and co-workers. The formalism is based on the assumption that charge transport occurs by hopping through a manifold of localized states with superimposed energetic and positional disorder. The key parameters of the formalism are σ, the energy width of the distribution of hopping site energies, and Σ, the degree of positional disorder. For TTB, σ = 0.078 eV and Σ = 1.7. The values for TPD are 0.077 eV and 1.6. The width of the hopping site energies can be described by a model based on dipolar disorder. The degree of positional disorder is in agreement with results observed for a wide range of vapor-deposited molecular glasses and is attributed to packing constraints. The results show that transport in both compounds can be described by simple disorder-controlled hopping without invoking polaronic contributions.

Anomalous Transition in Charge Transport Behavior of Polysilane

Anomalous transition of the dispersion parameter α was observed for the first time in poly( n-butyl- n-pentylsilane) (PBPS). Time-of-flight photocurrent (I) of PBPS was measured. The photocurrent transient was dispersive: I∝t-(1-α). The dispersion parameter α dropped around the glass transition temperature T g with increasing temperature, and became temperature-independent above T g. The mobility was described within the framework of a formalism based on disorder due to Bässler and coworkers. Both the diagonal disorder parameter σ, the variance of the density of states, and the off-diagonal disorder parameter Σ, the degree of positional disorder, decreased around T g. Nevertheless the ratio of the off-diagonal disorder parameter Σ to the diagonal disorder parameter σ was found to increase above the transition temperature. This anomalous transition is rationalized by the assumption that the off-diagonal disorder dominates charge transport in PBPS above T g.

Electron Transport in Vapor‐Deposited Layers of 2‐Methyl‐2‐Pentyl‐1,3‐Bis(Dicyanomethylene)Indane

AbstractElectron mobjlities are measured in vapor‐deposited amorphous layers of 2‐methyl‐2‐pentyl‐1, 3‐ bis(dicyanomethylene)indane, a highly polar acceptor compound with a dipole moment of 3.9 D. The results are described within the framework of a formalism based on disorder, due to Bässler and coworkers. The parameters of the formalism are σ, the variance of the hopping site energies, μ0 a prefactor mobility, and Σ, the degree of positional disorder. Experimental values of σ, μ0, and Σ are 0.112 eV, 1.6 × 10−3cm2/Vs, and 1.6. The variance of site energies can be described by a model based on dipolar disorder. A comparison of the prefactor mobility with literature values for vapor‐deposited acceptor glasses suggests that the prefactor is dependent on dipole moment, decreasing with increasing moment. The degree of positional disorder is similar to that observed in a wide range of vapor‐deposited molecular glasses and attributed to packing constraints.

Effects of the dipole moment on charge transport in disordered molecular solids

Hole mobilities have been measured in a series of donor compounds with different dipole moments. The results have been described by the disorder formalism, due to Bassler and co-workers. The formalism is based on the assumption that charge transport occurs by hopping through a Gaussian manifold of states with superimposed positional disorder. Key parameters of the model are the width of the density-of-hopping states and the degree of positional disorder. The width of the hopping site manifold increases with increasing dipole moment. This results in a sharp decrease in mobility with increasing dipole moment. The origin of this effect has been attributed to random internal fields associated with the dipole moments. The positional disorder has been attributed to packing constraints

Hole transport in p‐diethylamino‐benzaldehyde‐diphenyl hydrazone

AbstractHole mobilities have been measured in vapour‐deposited films of p‐diethylamino‐benzaldehyde‐diphenyl hydrazone (DEH). The results are described by a model based on hopping through a manifold of sites broadened by energetic and positional disorder. The application of the model leads to the conclusion that the width of the density of hopping states is influenced by dipolar disorder due to dipole moments of the DEH molecules. In comparing the results with those observed in other molecular solids, the degree of positional disorder is shown to be relatively small.