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Laser cavity-solitons can appear in systems comprised of a nonlinear microcavity nested within an amplifying fiber loop. These states are robust and self-emergent and constitute an attractive class of solitons that are highly suitable for microcomb generation. Here, we present a detailed study of the free-running stability properties of the carrier frequency and repetition rate of single solitons, which are the most suitable states for developing robust ultrafast and high repetition rate comb sources. We achieve free-running fractional stability on both optical carrier and repetition rate (i.e., 48.9 GHz) frequencies on the order of [Formula: see text] for a 1 s gate time. The repetition rate results compare well with the performance of state-of-the-art (externally driven) microcomb sources, and the carrier frequency stability is in the range of performance typical of modern free-running fiber lasers. Finally, we show that these quantities can be controlled by modulating the laser pump current and the cavity length, providing a path for active locking and long-term stabilization.

In this work, we introduce a versatile metal-wire waveguide geometry, namely a four-wire waveguide, which is capable of sustaining two independent and orthogonally polarized fundamental modes, thus acting as a broadband polarization-division multiplexer. By integrating multiscale-structured grooves into the wires of such a waveguide, we demonstrate the independent manipulation of polarization-division terahertz signals.

The fracture initiation in engineering thermoplastics resulting from chemical degradation is usually observed in the form of a microcrack network within a surface layer of degraded polymer exposed to a combined action of mechanical stresses and chemically aggressive environment. Degradation of polymers is usually manifested in a reduction of molecular weight, increase of crystallinity in semi crystalline polymers, increase of material density, a subtle increase in yield strength, and a dramatic reduction in toughness. An increase in material density, i.e., shrinkage of the degraded layer is constrained by adjacent unchanged material results in a buildup of tensile stress within the degraded layer and compressive stress in the adjacent unchanged material due to increasing incompatibility between the two. These stresses are an addition to preexisting manufacturing and service stresses. At a certain level of degradation, a combination of toughness reduction and increase of tensile stress result in fracture initiation. A quantitative model of the described above processes is presented in these work. For specificity, the internally pressurized plastic pipes that transport a fluid containing a chemically aggressive (oxidizing) agent is used as the model of fracture initiation. Experimental observations of material density and toughness dependence on degradation reported elsewhere are employed in the model. An equation for determination of a critical level of degradation corresponding to the offset of fracture is constructed. The critical level of degradation for fracture initiation depends on the rates of toughness deterioration and build-up of the degradation related stresses as well as on the manufacturing and service stresses. A method for evaluation of the time interval prior to fracture initiation is also formulated.

Small-angle X-ray scattering (SAXS) was used to obtain solution parameters of a weak polyelectrolyte in water in the absence of any additives, such as neutralizing agents or salt. Poly(acrylic acid) (PAA) was used as a weak polyelectrolyte from which SAXS data were obtained in the dilute region of 1-10 mg cm -3 . An intrinsic viscosity of 15.7 dL g -1 was obtained from a plot of reciprocal reduced viscosities versus the concentration. The application of the SAXS data, that is, the contour length (L = 1.97 x 10 4 A), the persistence length (a* = 58.5 A), and the molecular weight (M = 5.9 x 10 5 Da), to the Yamakawa-Fujii equation suggested that PAA in water at 25 °C could be described as a wormlike chain having a cylindrical body of d = 6 A. An end-to-end distance (r = 1.6 x 10 3 A) was calculated from r = 2a*L - 2(a*) 2 . The nonisotropic expansion factor (α = 2.9) was calculated for PAA expanding from the random coil in dioxane at 30 °C Θ) temperature) to the wormlike chain in water at 25 °C.

We report on experimental evidence of parametric spatial solitons in a quadratic crystal with randomized periodic ferroelectric poling. Two-color self-focusing via quadratic cascading overcomes the diffractive nature of both fundamental and frequency-doubled beams. (C) 2010 Optical Society of America

Small-angle X-ray scattering (SAXS) has been applied in obtaining the solution parameters (molecular mass M, radius of gyration Rg, radius of gyration of cross-section Rq, mass per unit length Mu, and persistence length a ∗ ) of a poly(acrylic acid) (PAA) sample in dioxane at 25°C. The M and Rg values measured from SAXS were 552 000 Da (daltons) and 292 A, respectively. These values are in reasonable agreement with those obtained from solution viscometry measurements on the same sample of PAA in dioxane at 30°C ( M = 567 000 Da and R g = 227 A ). The Rq and a ∗ values obtained from SAXS were 6.1 A and 14.4 A, respectively. The Mu value measured from SAXS is 27.9 Da A−1, in excellent agreement with the model (theoretical) value of 28.6 Da A−1 calculated from the structure and molecular mass of the monomer unit. The length L (= M/Mu = 19 790 A) obtained from SAXS thus corresponds to the contour length of the molecule and not to the ‘hydrodynamic’ length (i.e. the length the chain assumes in the fluid medium).

A new CMOS current mirror is presented which has the static characteristic of the cascode current mirror and a high-frequency performance equivalent to or better than that of the simple current mirror. Moreover, the circuit proposed does not present the instability problem of the improved cascode utilized to increase the high-frequency response. The circuit is designed using CMOS 2 μm technology with various aspect ratios and simulated with the SPICE programme.

To establish the parameters for converting sheet molding compounds (SMCs) to useful products, various technical approaches, viz., solvent extraction, hydrolysis, and pyrolysis, have been explored. Thermogravimetric analysis of an SMC sample indicated that it contains about 25% by weight organics and 75% inorganics, mainly glass fibers and CaCO3 as filler. Solvent extraction of ground SMC with acetone, methylene chloride, chloroform, or chloroform : benzene (1 : 1 vol) yielded low quantities of a gummy, viscous extract. Hydrolysis of the extracted SMC sample under strong alkaline conditions was also studied. A unit structure was postulated for the hydrolysate based upon elemental and molecular weight analysis. Pyrolysis of both extracted and unextracted SMCs in nitrogen at 500°C and in air at 400°C yielded organic oils. These oils were characterized for their calorific values. The products of pyrolysis consisted of mainly aromatics along with some oligomers. The extract and the oil from pyrolysis appear to be compatible with epoxy systems. Their use as an extender for epoxy systems, while that of the inorganic residue (glass fibers and CaCO3) as a filler for epoxy system, have been explored. © 1993 John Wiley & Sons, Inc.

Isotactic and atactic poly(4-methyl-1-pentene) powders were degraded in the presence of pure oxygen at temperatures of 145° and 175°C. The functional groups present in the nonvolatile products were identified using infrared spectroscopy. The volatile products that formed were identified by means of a relativly new technique which combines gas chromatography and mass spectroscopy. In this study, seventeen volatile products were detected and identified and their relative abundance estimated. The results obtained could readily be reproduced. Various oxidation mechanisms for these products are postulated.

Several procedures have been previously reported whereby non-isothermal TG (NITG) data can be analyzed for values of the activation energy ( E ) independent of values of the reaction order ( n ). In this paper, other expressions will be derived for the estimation of E which are essentially independent of n -values and are valid at relatively low degrees of conversion. These equations are applied to NITG data for a siloxane and teflon, as well as for theoretical data. The resulting computer and graphical procedures are both utilized to estimate E -values. Limitations of the methods are also mentioned.

Determination des expressions possibles des evaluations simultanee de E et n, qui gardent intacte la fonction d'Arrhenius, mais qui utilisent une expression derivee numerique approximative de l'estimation des courbes de thermogravimetrie

By applying the restriction that α (conversion) = constant to non-isothermal TG (NITG), isothermal TG (ITG) and a combination of both (NITG/ITG), various corresponding expressions have been derived for the evaluation of the activation energy, E . By means of a computer, all the expressions developed were tested against data which was generated from theoretical equations. Also, changes were made in the number of significant figures (s.f.) of data in order to ascertain their effects on values of E . Data were generated and tested for the three theoretical mechanisms, A 2 , F 1 and R 2 .

The kinetics of the acid degradation of Streptococcus salivarius levan was studied by observing changes in the number-average molecular weight, Mn, using end-group analysis. Rate constants for the hydrolysis are presented and a tentative mechanism is forwarded. The data has been analysed according to a statistical model for a polymer with trifunctional branching and it is shown that the hydrolysis of levan proceeds through a mechanism quite different to that reported for the polysaccharide dextran.

A fraction of low molecular weight from a partially acid-hydrolyzed S. salivarius levan was examined in aqueous solution at 25° by the method of small-angle X-ray scattering (SAXS). The weight-average molecular weight of 26,570 and radius of gyration of 47.6 A are in good agreement with the values obtained previously from sedimentation equilibrium and light scattering, respectively. Although this fraction behaves hydrodynamically as a linear random coil, the higher mass per unit length [(mu)b] of 45.82 daltons/A (obtained from SAXS), compared with the calculated value of (mu)l = 28.94 for linear levan, confirms its branched structure. The g-factor, a measure of branching, was computed as 0.63 from the derived expression, g = (mu)l/(mu)b = L/Ll, where L and Ll are the hydrodynamic length (stretched length) of the backbone of the branched levan and linear levan, respectively. The values for persistence length (a* = 17.7 A), radius of gyration of the cross-section (Rq = 8.2 A), and L = 534 A were also obtained for the levan hydrolysate. The lower values of (mu)b = 35.1 A and Rq = 2.3 A, and the higher value of g = 0.90 for the L. mesenteroides dextran hydrolysate of comparable molecular weight, show that the levan hydrolysate is more branched. The higher value of a* = 26.2 A for the dextran suggests that its molecules are stiffer than those of the levan.

The proteoglycan subunit (PGS) from bovine nasal cartilage was examined in water and in 0.15 N LiCl by small-angle x-ray scattering (SAXS). The molecular weight of 2.5 × 106 and the radius of gyration, Rg = 493 A, in 0.15 N LiCl, obtained by SAXS, are in good agreement with values reported by others for similar preparations. Values of the radius of gyration of the cross section, mass per unit length, and persistence length of the PGS are also reported. The low value of intrinsic viscosity ([η]) found in 0.15 N LiCl, and a comparison of the experimental distance distribution function to that of the theoretical distance distribution function for sphere, suggest that the PGS in salt solution approaches spherical symmetry. The much higher value of [η] in water suggests a prolate ellipsoid of low axial ratio.

Bovine heparin was fractionated according to molecular weight by fractional precipitation utilizing a method described previously. The solution data from sedimentation analysis, intrinsic viscosities and partial specific volumes at pH 2·5 and in 0·5 M NaCl were treated according to the Mandelkern and Flory theory for random coil in calculating the constant β. It was found that the calculated β values for all the fractions were in close agreement with the theoretical value. Based on this observation, the solution data were then treated in light of various hydrodynamic theories for linear polymers to calculate various dimensional and other physical parameters, e.g., ( r 2 ) 1 2 , α (expansion factor), A 2 . In comparing ( r 2 ) 1 2 of a fraction to that calculated from the experimental value of ( s 2 ) 1 2 obtained from low angle X-ray scattering for a comparable molecular weight sample, it was found that heparin in solution with suppressed charges may best be described as approximating the closely related models of Debye and Bueche, Flory and Fox, or Kuhn and Kuhn.

Comparaison avec les methodes graphiques. Utilisation pour la determination des mecanismes de reactions

Solution characterization of four samples of high molecular weight linear polystyrene (HMWLPS) in the molecular weight range of 1.61 × 106 to 9.71 × 106 in methyl ethyl ketone (MEK) at 25°C. was assessed from light scattering (LS), viscosity, and small-angle x-ray scattering (SAXS) under five different entrance-slit (E) /counter-slit (Z) combinations of 20/50, 30/75, 60/150, 100/250, and 150/375 μ, using the Kratky camera. The molecular weights and radii of gyration ( 1/2) obtained from SAXS under various slit combinations were then compared to the values obtained from LS. Further, the calculated values of 1/2based on the theoretical relationship between size, entrance-slit and counter slit openings were compared to he experimental values of 1/2 of each sample. Thus establishing the upper limits of size for a given E/Z combination.

A novel procedure is presented for the evaluation of kinetic parameters, activation energy ( E ) and reaction order ( n ), from thermogravimetric (TG) traces. From given values of conversion (α) and corresponding temperatures ( T ) are calculated values of E corresponding to various arbitrary values of n . Then, the resulting arbitrary E -values may be plotted against respective n -values and the region bounded by intersecting curves used to simultaneously estimate E and n . This procedure was tested against theoretical data, teflon, sodium bicarbonate, and magnesium hydroxide, and was found to be satisfactory. Some advantages of this method are: it is relatively simple to use; it allows the user to readily discern whether the data are homogeneous and, if not, at what conversions the data deviate. A less sensitive ancillary procedure is also described which can dispense with plotting in the estimation of E and n .

All materials are subject to aging, a process of long-term degradation, but not at the same rate or affected in the same manner. The wide variation in susceptibility (or resistance) of polymers to various degradative agents, e.g., oxidative, thermal, mechanical, chemical, biological, depend on their chemical composition and structure. Accordingly, the chemical, physical, and energy considerations inherent in the pure polymer are discussed in relation to degradative stability.

Isotactic poly(1-pentene) was degraded in the presence of pure oxygen at 115°C. The functional groups present in the non-volatile products were identified using infra-red spectroscopy. The volatile products formed were identified by means of a relatively new technique which combines thermal and mass chromatography. In this study, fourteen volatile products were detected and identified and their relative abundance estimated. The results obtained could readily be reproduced. Various oxidation mechanisms for these products are postulated.

The use of linear correlation coefficients to ascertain mechanism from TG data was shown to be unsatisfactory. This is in agreement with results reported by others who also indicated the necessity of using additional isothermal techniques for determining mechanism. Two methods, Reich—Stivala (R—S) and double-log (D-L), were employed to distinguish one mechanism from among 15 theoretical possibilities for heterogeneous solid-state reactions using theoretical TG data. With a certain degree of accuracy of TG data and for relatively large E/RT values (above 18), the R—S method was shown to be superior to the D-L method and a good indicator of a most probable mechanism. In this respect, the utilization of supplemental isothermal techniques may not be necessary when the R—S method is used under certain conditions.

A light-scattering study of unfractionated and five fractions of Streptococcus salivarius levan was performed in dimethyl sulfoxide. The weight-average molecular weights Mr in dimethyl sulfoxide, after adequate dissolution, agree with those obtained in water within a mean difference of 7%. The intrinsic viscosities [η] and root-mean-square z-average radii of gyration (Rg2)z1/2 are significantly higher in dimethyl sulfoxide than in water, reflecting the higher hydrodynamic volume in the former. The Mr, [η], and (Rg2)z1/2 of the fractions suggest that levan has a low polydispersity. The exponent of 0.12 of the Mark-Houwink plot and model analysis confirm the branched and compact structure of levan.

Solution characterization of heparin with high affinity (HA) and low affinity (LA) for antithrombin III was performed using the methods of small-angle x-ray scattering (SAXS), viscometry, and aqueous gel permeation chromatography (GPC). SAXS provided various topological parameters including the radius of gyration ([S2]1/2), radius of gyration of cross-section ([S2]q1/2), persistence length (a*), contour length (L), and mass parameters, e.g., overall molecular mass (Mr), and mass per unit length (Mq). The molecular weights of HA and LA pig mucosal heparins were found to be 14,900 and 11,500 and the respective radii of gyration were 40.1 and 33.6 A. The persistence lengths of HA and LA were 21.3 and 20.3 A, respectively. These parameters were compared to SAXS data of heparin [S. S. Stivala, M. Herbst, O. Kratky, and I. Pilz (1968) Arch. Biochem. Biophys. 127, 795-802] fractionated according to molecular weight only. It was found that the various experimental values of this heparin lie somewhere in between those of HA and LA heparins. It appears that there are no appreciable differences in the physico-chemical properties, including conformation, among the heparins in H2O at 25 degrees C.

The viscosity of heparin was examined in pure glycerol, formamide and in mixtures of the two solvents. This study confirms that the equation η sp c = [η] ∞ [1 + k (c) 1 2 ] , where [η]∞ is the shielded intrinsic viscosity, adequately describes the concentration dependence of the reduced viscosity of the polyelectrolyte, heparin. The [η]∞ linearly increases with the dielectric constant of the solvent.

Small-angle x-ray scattering from solutions was applied in assessing branching using well-characterized dextran hydrolyzates. It was found that the longitudinal and cross-sectional properties of the polysaccharides vary in a manner predictable by the molecular topology of the chains. A hydrodynamically equivalent linear model for dextran is proposed and it has been shown that this model correctly predicts values of Φ and K, Flory's universal hydrodynamic constant and the Flory–Fox–Schaefgen parameter, respectively.

The kinetics of the thermal oxidation of isotactic poly(1-pentene) was studied in the bulk phase. The experimental data were obtained from the quantitative estimation of carbonyl groups formed in the non-volatile oxidation products using infra-red spectroscopy. Reaction temperature varied from 100° to 115° and oxygen concentrations from 10% to 100% by volume. A general kinetic scheme and mathematical expressions previously reported for the thermal autoxidation of polyolefins satisfactorily explained the experimental results. Activation energies of this polymer for various steps in the kinetic scheme were compared with polypropylene and poly(1-butene).

Small-angle X-ray scattering, SAXS, measurements were obtained from 12-arm near-monodisperse star polystyrenes in methyl ethyl ketone at 25°C. Calculations from the SAXS data yielded information on the molecular weight, Ms, the radius of gyration, Rg, mass per unit length, mu, radius of gyration of the crosssection, Rq, and persistence length, a∗. Values of Ms and Rg from SAXS were in good agreement with values obtained from light scattering. A branching parameter in terms of a∗, s = a∗1a*b where subscripts l and b refer to linear and branch, respectively, is introduced and related in terms of functionability, f, or g, where g = (Rg)b(Rg)l.

A method is described which allows the precise estimation of molecular weight distribution parameters p and A which pertain to free-radical polymerizations. Thus, expressions are developed which allow the estimation of (1 − p) by means of a programmable calculator using molecular weight distribution data derived from GPC. Values of A may subsequently be calculated by means of a plot of one of the expressions given. Values of (1 − p) and A obtained in this paper were checked using theoretical values as well as by a comparison between calculated and observed values. The agreement between calculated and theoretical or experimental values indicates that the method presented for the estimation of (1 − p) and A is both reliable and relatively rapid. Previously reported methods for the estimation of (1 − p) and A have involved curve-fitting trial calculations as well as more precise interpolation procedures. However, the latter are based on single-peak maximum values.

The kinetics of the thermal oxidation of isotactic and atactic poly(4-methyl-1-pentene) were studied in the bulk phase using infra-red (i.r.) spectroscopy. The rates of formation of the non-volatile products were assessed from the i.r. bands of the carbonyl groups at different temperatures and various oxygen concentrations. Reaction temperature varied from 120° to 185°C and oxygen concentrations from 10 to 100%, by volume. A general kinetic scheme and mathematical expressions, previously reported for the thermal oxidation of polyolefins, satisfactorily explained the experimental results. Single activation energies for the major oxidation stages in the scheme, were estimated from various Arrhenius plots.

The thermal degradation of the polysaccharide Levan, of various molecular weights, was studied by means of isothermal and dynamic TG, X-ray diffraction, and IR measurements. From dynamic TG traces, two main degradation stages were observed for HL-Levans (hydrolyzed) whereas, three such stages were observed for UL-Levans (unhydrolyzed). These stages were correlated with branching effects, an interpenetrating network, and ring-fragmentation and other reactions in the late stages of the thermal degradation which result in the formation of infusible material that chars on further heating. Isothermal curves obtained for the first stage indicated the possibility of a random type of thermal degradation. Anticipated linear plots were obtained, using expressions from random degradation theory, which added further support for this type of degradation for Levan (stage 1). Various parameters were obtained for the thermal degradation of Levan, e.g., activation energies, and various experimental observations have been correlated in terms of postulated microstructures for Levan and in terms of parameters such as entropy of activation.

A fractionated sample of S. salivarius levan was examined in aqueous solution at 25° by the method of small-angle X-ray scattering. The high molecular weight of 16.9 × 10 6 and low radius of gyration of 395 A suggest that this levan is branched. The mass per unit length [( m u ) b ] was found to be 72.94 daltons/A. Based on the molecular weight of the monomer unit (2,6-anhydro-β- d -fructofuranose) and its length, the mass per unit length of a linear levan [( m u ) l ] was calculated as 28.94 daltons/A. The observation that ( m u ) b > ( m u ) l is a positive indication of branching. The g -factor, a measure of branching, was computed as 0.39 from the derived expression, g = ( m u ) l /( m u ) b = L/L l , where L and L l are the hydrodynamic length (total stretched length) of the backbone of the branched levan and linear levan, respectively. Values of 42.79 A for persistence length, L = 2.313 × 10 5 A, and 22 A for the radius of gyration of the cross-section were also obtained for the branched levan.