A method of optical implementation of frequency encoded all optical logic gates based on multiphoton processes in non linear material

A novel frequency encoded all optical logic gates are proposed exploiting multiphoton processes in non linear optical medium. In the frequency encoding of the information the ‘0’ is represented by a frequency ω and ‘1’ is represented by another frequency 2ω. The gates proposed are NOT, OR, AND, NAND and NOR among which NAND and NOR are universal. Using these gates one can generate other important gates and logical function generating all optical devices. Two main three-photon processes, second harmonic generation (SHG) and parametric light generation (PLG) are used to implement the gates and the corresponding appropriate non linear material is LiB₃O₅ (LBO) which has wide operating and transparency range in the wavelength 350–3,200 nm. The source of optical frequency encoded signal may be derived from an external cavity diode laser generating a wavelength 1,560 nm for ω (‘0’ state of information) and its second harmonic 780 nm for 2ω (‘1’ state of information).     

Cavitation and the tensile strength of liquids under dynamic stressing

This paper discusses the differences between the results of various measurements of the effective tensile strength (F _c ) of liquids in experiments involving a pulse of tension (‘negative pressure’) created by the reflection of a pressure pulse at a boundary. Using a modified ‘bullet-piston’ (B-P) pulse reflection apparatus, measurements presented herein show that degassed, deionized water is capable of sustaining tensions an order of magnitude greater than previously reported in B-P work. Results are also reported for a series of Newtonian silicone oils which show a similar dependence of F _c on the shear viscosity (μ) as a previous study though the absolute values of F _c are greater.     

Rheological Behaviors of Polypropylene/Poly(1-butene) Blends

The rheological behaviors of polypropylene (PP)/poly(1-butene) (PB) blends with homo-polypropylene (PP₁) or impact polypropylene (PP₂), a poly(propylene-co-ethylene) as the PP component were studied. With increasing of PB resin content for both PP/PB blends, the blends showed higher G'(ω), G''(ω) and η*(ω) at low frequencies but lower values at high frequencies which implied that the processability was improved. A two-phase morphology was observed through the various rheological responses, including G'(ω)-ω terminal region curves, Cole-Cole plots and the weighted relaxation spectra with the PB contents up to 40?wt%. With the same PB content, the rheological parameters of the PP₂/PB blends were quite different from those of the PP₁/PB, which can be attributed to the stronger interaction between PB chains and the ethylene-co-propylene copolymer in PP₂. The impact strength of the PP₂/PB blends was improved dramatically over that of the PP₁/PB. The more significant toughening effect for the PP₂/PB blends can be attributed to the special responses of its rheological behaviors.     

Rheological Behavior of Blends of Poly(Phenylene Sulfide) with a Thermotropic Liquid Crystalline Aromatic Poly(Ether Ester)

A new type of thermotropic liquid crystalline aromatic poly(ether ester) (PEE) was prepared from 1,3-bis(4′-carboxyphenoxy)benzene, 1,4-diacetoxybenzene, and p-acetoxybenzoic acid through a melt transesterification process. The rheological behavior of blends of poly(phenylene sulfide) (PPS) with PEE was studied using a high-pressure capillary rheometer with the shear rate range of 50 s^?1 to 3000 s^?1. The results show that according to the range of shear rate, the flow curves of PEE/PPS blends can be divided into three zones: a first shear-thinning zone (n < 1, “n” represents non-Newtonian indexes), a shear-thickening zone (n > 1), and a second shear-thinning zone (n < 1), and the former two zones are more obvious with the increase of PEE content or elevated temperature. In the second shear-thinning zone, the PPS melt is close to a Newtonian fluid at high temperature and high shear rate; meanwhile the non-Newtonian behavior of the PPS melt at high temperature is enhanced with the addition of PEE. The apparent viscosity of PPS melts sharply dropped after adding PEE, especially at relatively low temperature and low shear rate. The curve of apparent viscosity vs. shear rate starts to flatten out after adding PEE, suggesting that the addition of PEE lowers the sensitivity of PPS to shear rate. As the content of PEE increases, the activation energy of the viscous flow, ΔE_η, of PPS decreases, which means that adding PEE weakens the temperature sensitivity of the apparent viscosity of the PPS melt. It can clearly be seen that the addition of PEE is beneficial to the processing of PPS.     

Raman imaging and stress quantification in self‐assembled graphene oxide fiber ‘Latin Letters’

To probe the intrinsic stress distribution in terms of spatial Raman shift (ω) and change in the phonon linewidth (Γ), here we analyze self‐assembled graphene oxide fibers (GOF) ‘Latin letters’ by confocal Raman spectroscopy. The self‐assembly of GOF ‘Latin letters’ has been explained through surface tension, π–π stacking, van der Waals interaction at the air–water interface and by systematic time‐dependent investigation using field emission scanning electron microscopy analysis. Intrinsic residual stress due to structural joints and bending is playing a distinct role affecting the E_2g mode (G band) at and away from the physical interface of GOF segments with broadening of phonon linewidth, indicating prominent phonon softening. Linescan across an interface of the GOF ‘letters’ reveals Raman shift to lower wavenumber in all cases but more so in ‘Z’ fiber exhibiting a broader region. Furthermore, intrinsic stress homogeneity is observed for ‘G’ fiber distributed throughout its curvature with negligible shift corresponding to E_2g mode vibration. This article demonstrates the significance of morphology in stress distribution across the self‐assembled and ‘smart‐integrable’ GOF ‘Latin letters’. Copyright © 2016 John Wiley & Sons, Ltd.     

The microwave conductivity of solid electrolytes

We investigate the frequency dependent conductivity σ(ω) for ω in the vicinity of the jump rate Γ₀. The most general model based on hopping diffusion predicts a σ(ω) consistent with experiment for β-Al₂O₃ but qualitatively at odds for Ag⁺ and Cu⁺ conductors. We consider the coupling of the transition rate to an external variable such as a long lived, low frequency lattice mode and show that this mechanism can give structure in σ(ω) of the form observed in Ag⁺ and Cu⁺ conductors.     

Deuteron NMR study of dynamics and order in the columnar phase of a fluorinated discotic liquid crystal

Measurements have been made of deuteron quadrupolar splitting and spin—lattice relaxation times T _1Q and T _1z in the columnar phase of a ring deuterated 1-fluoro-2,3,6,7,10,11-hexahex-yloxytriphenylene (F-HAT6) as a function of temperature and at two different Larmor frequencies. The disc-like molecules are stacked, with only short range positional order, into columns which are arranged on a 2-dimensional hexagonal lattice. To describe small step reorientations of these molecules, a rotational diffusion model which uses a space-fixed frame to diagonalize the molecular diffusion tensor is adopted. The principal diffusion constants in this so called ‘anisotropic viscosity model’ Dα and Dβ are for rotations of a molecule around and perpendicular to the columnar axis, respectively. A global target analysis of the spectral densities J ₁(ω₀) and J ₂(2ω₀) at seven temperatures and two Larmor frequencies in a single minimization procedure was carried out. It was found that Dα Dβ, which is consistent with the picture that the motion towards or away from the local director (i.e., the columnar axis) tends to disrupt the packing of molecules within the column. Furthermore, the activation energies Eαβ and Eβ_a for these motions were found to be 67.7 kJmol^?1 and 56.3kJmol^?1. That these values are higher in comparison with those for HAT6 is interesting, and believed to be a result of a strong lateral dipole in F-HAT6.     

Stimulated Raman spectra of a strong bichromatic field interacting with a three-level atom

We have studied the stimulated Raman spectra arising from the interaction of a three-level atom with two strong electromagnetic fields whose initially populated modes ω _a and ω _b are in resonance with the two atomic transition frequencies. The Green's function formalism has been used in the limit of high photon densities to calculate the excitation spectra near the frequencies ω = ± ω _ab = ± (ω _a - ω _b ). Expressions are derived for the relative intensities, which describe, apart from the usual Raman peak at the frequency ω = ω _ab , four pairs of lorentzian lines peaked at the frequencies ω - ω _ab = ± Ω _a /√2, ± Ω _b /√2, ± Ω and ± 2Ω, respectively, and having spectra widths of the order of 3γ₀/4. The parameter Ω is defined as Ω² = (Ω _a ² + Ω _b ²)/2, where Ω _a and Ω _b are the Rabi frequencies of the two laser fields and γ₀ is the spontaneous emission probability. Numerical calculations for selected values of the Rabi frequencies are graphically presented and discussed. Conditions have been established for which Raman gain processes are anticipated to take place.     

Principles of generalized spin-echo spectroscopy

The concept is proposed for determining the total dynamic scattering function of an object under study, representing a sum of odd and even parts measured by the generalized neutron spin-echo method in the form of the signals S _odd(q, t) ～ ΣS(ω, q)sin(ωt)dω and S_even(q, t) ～ ΣS(ω,q)cos(ωt)dω as functions of the momentum q transferred to the neutron and the time t corresponding to the frequency ω and the transferred energy ?ω. The principle of the generalized spin echo and the results of mathematical modeling are confirmed in experiments on inelastic scattering on magnetic fluids and polymer solutions. The developed method makes it possible to study the features of the dynamics of atomic and molecular systems, e.g., to analyze soft vibrational spectra of nanoparticle ensembles against the background of intense relaxation processes, which is inaccessible for classical spin-echo spectrometry.     

Precursor Based on Polyborylborazine for BN Fiber: Preparation and Rheology Properties

A polyborylborazine precursor for hexagonal boron nitride (h-BN) was obtained by reaction of boron trichloride with methylamine and its structure was characterized by ¹¹BNMR, ¹³CNMR, ¹HNMR, and FTIR. The results show that the molecular precursor consists of borazine rings connected via a cross-linked network. The results of shear rheological tests indicated that the polymer is capable of being melt spun at moderate temperature, which implies that the structure of the molecular chains of the precursor polymer is branched. The precursor polymer was spun into a continuous polymer fiber in the melt state and then subsequently heat-treated under NH₃ up to 1000°C for conversion into BN fibers. Its surface morphology was observed by scanning electron microscopy (SEM); the fiber was free of defects and cavities.     

Influence of Reactive Compatibilizer on the Morphology,Rheological, and Mechanical Properties of Recycled Poly(Ethylene Terephthalate)/Polyamide 6 Blends

Recycled poly(ethylene terephthalate) (R-PET) and virgin polyamide 6 (PA6) blends compatibilized with glycidyl methacrylate grafted poly(ethylene-octene) (POE-g-GMA) were melt blended. The morphological, rheological and mechanical properties of the prepared blends were investigated by scanning electron microscopy, rheology, and an electromechanical testing instrument, respectively. All of the blends showed a droplet dispersion type morphology, and the PA6 particle size decreased with increase in the POE-g-GMA concentration. The storage modulus (G′), loss modulus (G′′), and complex viscosity (η*) of the blends significantly increased at low frequency with the addition of POE-g-GMA. In addition, ‘‘Cole-Cole’’ plots showed that the elasticity of the blends was also increased by raising the compatibilizer dosage. It was also found that 10 wt% of POE-g-GMA caused 88.46 and 171.05% increments in Charpy impact strength and elongation at break with only a 21.66% decrement in tensile strength.     

Third-order optical harmonic coefficients of atomic hydrogen at low frequencies

The analytical expression is derived for the third-order optical harmonic coefficients χ⁽³⁾₁₁₁₁ (ω, ω, ω) = χ⁽³⁾₂₂₂₂ (ω, ω, ω) = χ⁽³⁾₃₃₃₃ (ω, ω, ω) of the atomic hydrogen at very low frequencies ω → 0.     

Transport coefficients of hard sphere fluids

New calculations have been made of the self-diffusion coefficient D, the shear viscosity η_s, the bulk viscosity η_b and thermal conductivity λ of the hard sphere fluid, using molecular dynamics (MD) computer simulation. A newly developed hard sphere MD scheme was used to model the hard sphere fluid over a wide range up to the glass transition (～0.57 packing fraction). System sizes of up to 32 000 hard spheres were considered. This set of transport coefficient data was combined with others taken from the literature to test a number of previously proposed analytical formulae for these quantities together with some new ones given here. Only the self-diffusion coefficient showed any substantial N dependence for N < 500 at equilibrium fluid densities (ε 0.494). D increased with N, especially at intermediate densities in the range ε ～ 0.3–0.35. The expression for the packing fraction dependence of D proposed by Speedy, R. J., 1987, Molec. Phys., 62, 509 was shown to fit these data well for N ～ 500 particle systems. We found that the packing fraction ε dependence of the two viscosities and thermal conductivity, generically denoted by X, were represented well by the simple formula X/X ₀ = 1/[1 ? (ε/ε₁)]^m within the equilibrium fluid range 0 > ε > 0.493. This formula has two disposable parameters, ε and m, and X ₀ is the value of the property X in the limit of zero density. This expression has the same form as the Krieger-Dougherty formula (Kreiger, I. M., 1972, Adv. Colloid. Interface Sci., 3, 111) which is used widely in the colloid literature to represent the packing fraction dependence of the Newtonian shear viscosity of monodisperse colloidal near-hard spheres. Of course, in the present case, X _o was the dilute gas transport coefficient of the pure liquid rather than the solvent viscosity. It was not possible to fit the transport coefficient normalized by their Enskog values with such a simple expression because these ratios are typically of order unity until quite high packing fractions and then diverge rapidly at higher values over a relatively narrow density range. At the maximum equilibrium fluid packing fraction ε = 0.494 for both the hard sphere fluid and the corresponding colloidal case a very similar value was found for η_s/η_o ?30–40, suggesting that the ‘crowding’ effects and their consequences for the dynamics in this region of the phase diagram in the two types of liquid have much in common. For the hard sphere by MD, D_o/D ～ 11 at the same packing fraction, possibly indicating the contribution from ‘hydrodynamic enhancement’ of this transport coefficient, which is largely absent for the shear viscosity. Interestingly the comparable ratio for hard sphere colloids is the same.     

Correlation functions for nematic liquid crystals

We show that the correlation functions of a system of hard ellipsoids whose axes are constrained to be parallel are simply related to the corresponding functions of a hard sphere fluid with the same packing fraction. The existence of simple, accurate approximations for the latter system make the oriented ellipsoid fluid a suitable ‘reference system’ for the nematically ordered phase of liquid crystals and other orientationally ordered molecular fluids such as polar fluids in an external field. The properties of such fluids, with a given angular distribution f(ω), may then be obtained via ‘standard’ perturbation theory. Methods for obtaining f(ω) near the perfectly ordered state are discussed.     

Dynamic Rheological Behavior of HDPE/UHMWPE Blends

The rheological behaviors of high-density polyethylene (HDPE)/ultra-high molecular weight polyethylene (UHMWPE) blends prepared by melt blending and solution blending were studied. The results showed that the rheological parameters (G′, G ^″, and η*) of both types of blends increased gradually with increasing fraction of UHMWPE, while the tanδ decreased correspondingly. Comparing blends with the same UHMWPE content, all G′, G ^″, and η* values of solution blends were higher, and the tanδ of the solution blends were remarkably lower than those of the melt blends. Combined with the scanning electron microscopy (SEM) observations, it was proved that, because of its very high melt viscosity, the UHMWPE chain is difficult to diffuse and be distributed well in the HDPE matrix by melt blending, resulting in a two-phase-like morphology. On the other hand, the blends prepared by the solution blending showed a homogeneous distribution of UHMWPE in the HDPE matrix. In addition, the state of aggregation of the UHMWPE in the HDPE matrix can be distinguished well by time–temperature superposition (TTS) curves; i.e., the two-phase-like morphology in the melt blends can be detected by the failure of TTS in the high-frequency range, which cannot be reflected by Cole–Cole plots and Han curves.     

Viscosity at small scales in polymer melts

Flows around small colloidal particles of diameter b, or in thin films, capillaries, etc., cannot always be described in terms of the macroscopic polymer viscosity. We discuss these features for entangled polymer melts, where two distinct regimes can be found: (a) the thin regime where b is smaller than the coil radius R₀, but larger than the diameter of the Edwards tube; (b) the ultrathin regime, where . We consider (i) non adsorbing particles, where slippage may occur between the melt and the solid surface; (ii) “hairy” particles, which carry some bound polymer chains. We obtain scaling predictions for mobilities of spheres, of needles, and of clusters of particles. We also discuss translational and rotational diffusion of needles. Received 19 April 1999     

The Peculiar Temperature Response of Dynamic Rheological Behaviors of Poly (Vinyl Chloride)/trioctyl Trimellitate (100/70) System

The dynamic rheological behavior, application of time-temperature superposition (TTS) and the failure mechanism of TTS are studied for the poly(vinyl chloride) (PVC)/trioctyl trimellitate (TOTM) (100/70) system. The Arrhenius equation, Williams–Landel—Ferry (WLF) equation, mathematical non-linear fitting and manual shift are applied to TTS fitting. For the PVC/TOTM (100/70) system, none of those methods can give well-superimposed master curves with either single horizontal shift or two-dimensional (horizontal and vertical) shift. The failure reason is attributed to the thermorheological complexity of the PVC/TOTM (100/70) system. Curves of the storage modulus versus the frequency can be well fitted with an empirical equation (G′=G′₀+Kω ⁿ ) usually used to describe filled polymer systems, indicating the multilevel flowing unit characteristic in this system. With the increase of test temperature, the structure of the PVC/TOTM (100/70) system changes and an apparent transition appears in the rheological behavior. Differential scanning calorimetry (DSC) results reveal that for the PVC/TOTM (100/70) system there are microcrystallites present below 220°C, but above the rheological transition temperature (190°C) the bulk of the microcrystallites melted, which corresponds to the appearance of viscous flow participating in the rheological behavior. It verifies the fact that the gel networks crosslinked by microcrystallites dominate the rheological behavior below the transition temperature in the PVC/TOTM (100/70) system. The quantity of microcrystallites remaining in the melt determines the perfection of the physical gel networks. With the increase of test temperature, the microcrystallites melted gradually and the gel networks are broken up.     

Do Solids Flow?

Are solids intrinsically different from liquids? Must a finite stress be applied in order to induce flow? Or, instead, do all solids only look rigid on some finite timescales and eventually flow if an infinitesimal shear stress is applied? Surprisingly, these simple questions are a matter of debate and definite answers are still lacking. Here we show that solidity is only a time-scale dependent notion: equilibrium states of matter that break spontaneously translation invariance, e.g. crystals, flow if even an infinitesimal stress is applied. However, they do so in a way inherently different from ordinary liquids since their viscosity diverges for vanishing shear stress with an essential singularity. We find an ultra-slow decrease of the shear stress as a function of the shear rate, which explains the apparent yield stress identified in rheological flow curves. Furthermore, we suggest that an alternating shear of frequency ω and amplitude γ should lead to a dynamic phase transition line in the (ω,γ) plane, from a ‘flowing’ to a ‘non-flowing’ phase. Finally, we apply our results to crystals, show the corresponding microscopic process leading to flow and discuss possible experimental investigations.