Values Of Kθ Research Articles

The Role of Polymer Chain Stiffness and Guest Nanoparticle Loading in Improving the Glass Transition Temperature of Polymer Nanocomposites.

The impact of polymer chain stiffness characterized by the bending modulus (kθ) on the glass transition temperature (Tg) of pure polymer systems, as well as polymer nanocomposites (PNCs), is investigated using molecular dynamics simulations. At small kθ values, the pure polymer system and respective PNCs are in an amorphous state, whereas at large kθ values, both systems are in a semicrystalline state with a glass transition at low temperature. For the pure polymer system, Tg initially increases with kθ and does not change obviously at large kθ. However, the Tg of PNCs shows interesting behaviors with the increasing volume fraction of nanoparticles (fNP) at different kθ values. Tg tends to increase with fNP at small kθ, whereas it becomes suppressed at large kθ.

Effect of Changing Unit Weight and Decomposition on Unsaturated Hydraulics of Municipal Solid Waste in Bioreactor Landfills

The effects of compression and decomposition on the water retention curve (WRC) and unsaturated hydraulic conductivity (Kθ) of municipal solid waste (MSW) were evaluated in the laboratory and field. Laboratory measurements of the WRC and Kθ were made using the multistep outflow (MSO) method. Numerical inversion of data collected during the Deer Track Bioreactor Experiment (DTBE) was used to estimate field-scale unsaturated hydraulic properties. For the MSW tested in this study, data indicated that increasing dry unit weight resulted in an increase of the air-entry suction. Increasing levels of decomposition had the opposite effect, reducing air-entry suction for MSW at constant dry unit weight. Multiple mechanisms likely resulted in the observed changes in air-entry suction, including reduction in pore size during compression and changes in overall MSW hydrophobicity during decomposition. At field-scale, air-entry suction tended to remain constant as MSW compressed and decomposed simultaneously indicating that the two processes, which had opposite effects in the laboratory, also may have opposing effects the field. For fresh MSW, van Genuchten’s n, which is inversely related to the variance of the pore size of a porous medium, ranged between 1.3 and 2.5 and decreased as the dry unit weight increased in laboratory-scale tests. For decomposed MSW, n ranged from 1.1 to 1.3 and did not vary systematically with dry unit weight. This indicated that for degraded MSW, the variance of the pore-size distribution did not change substantially with increasing dry unit weight. The value of Kθ decreased with increasing dry unit weight for MSW in this study, consistent with observations for saturated hydraulic conductivity in MSW. However, Kθ tended to increase in laboratory tests with increasing levels of decomposition at constant dry unit weight, consistent with observed increases in void ratio. At field scale, observed changes in Kθ varied consistently with changes in saturated hydraulic conductivity as decomposition and densification occurred simultaneously.

What happens to full-f gyrokinetic transport and turbulence in a toroidal wedge simulation?

In order to save the computing time or to fit the simulation size into a limited computing hardware in a gyrokinetic turbulence simulation of a tokamak plasma, a toroidal wedge simulation may be utilized in which only a partial toroidal section is modeled with a periodic boundary condition in the toroidal direction. The most severe restriction in the wedge simulation is expected to be in the longest wavelength turbulence, i.e., ion temperature gradient (ITG) driven turbulence. The global full-f gyrokinetic code XGC1 is used to compare the transport and turbulence properties from a toroidal wedge simulation against the full torus simulation in an ITG unstable plasma in a model toroidal geometry. It is found that (1) the convergence study in the wedge number needs to be conducted all the way down to the full torus in order to avoid a false convergence, (2) a reasonably accurate simulation can be performed if the correct wedge number N can be identified, (3) the validity of a wedge simulation may be checked by performing a wave-number spectral analysis of the turbulence amplitude |δΦ| and assuring that the variation of δΦ between the discrete kθ values is less than 25% compared to the peak |δΦ|, and (4) a frequency spectrum may not be used for the validity check of a wedge simulation.

Wind tunnel tests on wind loads acting on an angled steel triangular transmission tower

Wind tunnel tests on scaled models of a triangular transmission tower body made by angled steel members were carried out. The drag coefficients of the total tower body or single frames at nine different test cases were obtained. The experimental results from wind tunnel tests were also mutually validated by computational fluid dynamics (CFD) analysis. The parameters for calculating wind loads on triangular tower bodies determined by wind tunnel tests were compared with the calculated values by some applicable design standards. For the regular triangular tower body with an equivalent solidity ratio for three lateral faces, the experimental curves of the skewed wind load factor Kθ approximately appear like W shape and symmetrical to the axis of θ=60°. Kθ is decreased to the minimum value when the wind incidence angle is 40° or 80°. When the solidity ratio of face A is different from the other two faces, the symmetry axis of the skewed wind load factor Kθ is shifted to θ=50°. Kθ is decreased to the minimum value when the wind incidence angle is 30° or 70°. The varying trend of Kθ, especially for the wind incidence angle corresponding to the minimum Kθ value in British standard, are quite different from the experimental results. Based on a combination of the drag coefficient of single frames and the shielding effect factor, a calculation method for the effective projected areas of triangular tower bodies was proposed. Especially for the wind incidence angle θ of 0° or 120°, the calculated values of the effective projected areas agree well with the experimental values obtained from the total tower-body models.

Unperturbed dimension, interaction parameters, zeta potential and rheology of sodium alginate in binary solvent mixtures

The intrinsic viscosity [η] of sodium alginate having different molecular weights (high molecular weight (type A), medium molecular weight (type B) and low molecular weight (type C)) is measured at 293–303 K temperature in various mixtures of water (good solvent), acetone (ACE, poor solvent) and water-ethoxy ethanol (EE, poor solvent). The observed result particularly the Huggins constant (K H) values shows a significant variation of cosolvency as a function of solvent composition (ΦACE/ΦEE) and the temperature. Unperturbed dimensions (K θ) under non-theta condition have been calculated using various equations in different water-acetone and water-ethoxy ethanol mixtures. The value of K θ obtained from three different methods of measurements viz., Burchard-Stockmayer and Fixman (BSF), Berry and Inagaki-Suzuki-Kurata (ISK) agree well with each other except in a few compositions of solvents. The molecular extension factor (α n) and actual end-to-end distance (α n K θ) have also been computed herein. Further, the shear thinning nature of the sodium alginate solutions (representative illustration: type A) in water and water-acetone mixed systems has been investigated at increasing strain rate. Results show that the viscous modulus G″ predominates over the elastic modulus G′ and the systems behave as viscoelastic fluids under present conditions. Higher value of G′ in acetone-water mixed solvent system compared to that in pure water undoubtedly indicates enhancement of the elasticity in alginate system in the presence of acetone. Finally, zeta potential measurement demonstrates that the polymeric surface of sodium alginate (representative illustration: type A) is essentially negatively charged and the zeta potential of the polymer is more responsive to the composition of ethoxy ethanol than that of acetone in the aqueous-organic mixed solvents.

Fibre orientation of novel dynamically sheet formed discontinuous natural fibre PLA composites

This paper describes work carried out to fabricate and to assess the fibre orientation in PLA reinforced by aligned discontinuous harakeke and hemp fibre mats produced using a dynamic sheet former (DSF). These mats were combined with PLA sheets to make composites with fibre contents of 5–40wt% using a hot press. It was found that the fibre orientation factors (Kθ) for both harakeke and hemp fibre composites were higher than those values seen in the literature for composites prepared using injection moulding and hot pressed using randomly oriented fibre mats, but slightly lower than the highest values obtained with aligned fibre nonwoven preform composites utilising more processing stages. The highest Kθ values for harakeke and hemp fibres in this work were found to be 0.58 and 0.44 respectively. Kθ decreased, reflecting increased fibre misalignment as fibre content increased, believed to be due to fibre agglomeration and the higher pressure required during processing.

Unperturbed dimensions and interaction parameters of poly(vinyl alcohol)s in water–acetone and water–tetrahydrofuran mixtures

The intrinsic viscosities [η] of poly(vinyl alcohol)s (PVAs, which are biocompatible polymers)—with different (high, medium, and low) molecular weights were measured at 293–303 K in water (good solvent)–acetone (ACE, poor solvent) and water–tetrahydrofuran (THF, poor solvent) mixtures. The results observed, particularly the values of the Huggins constant (KH), indicated that the solvency of each PVA varied as a function of solvent composition (ΦACE/ΦTHF) and temperature. The unperturbed dimensions (Kθ) of the PVAs under nontheta conditions in a variety of water–acetone and water–tetrahydrofuran solutions were also calculated using various equations. The values of Kθ obtained via three different equations, i.e., those of Burchard–Stockmayer–Fixman (BSF), Berry, and Inagaki–Suzuki–Kurata (ISK), agreed well except for a few solvent compositions. The molecular extension factor (αn) and actual end-to-end distance (αnKθ) of each PVA were also computed.

Molecular characterization and chain flexibility of linear polyacetals containing poly‐perfluoro(oxymethylene‐ran‐oxyethylene) macromers

AbstractProper samples of polyacetals containing poly‐perfluoro(oxymethylene‐ran‐oxye‐thylene) macromers were synthesized by polycondensation of a fluorinated macrodiol (Fomblin ®ZDOL) and formaldehyde and fractionated by solvent/non‐solvent separation. Of eight selected fractions, whose compositional homogeneity was checked by 19F and 13C NMR spectroscopy, the following measurements were performed: Mw by static light scattering; retention volume Vr at GPC; [η] by conventional capillary viscometry; glass transition temperature by DSC. 1,1,2‐Trichlorotrifluoroethane was used for solution measurements, from which the second virial coefficient A2, the linear Mw−Vr equation of GPC calibration, and the [η]‐Mw Mark‐Houwink‐Sakurada constants K and a were determined. From [η] and Mw data, the Kθ value (unperturbed state) was estimated by the Stock‐mayer‐Fixman‐Burchard extrapolation procedure, and the characteristic ratio C∞ of polyacetals containing poly‐perfluoro(oxyethylene‐ran‐oxymethylene) macromers was calculated through the Fox‐Flory equation. Factors related to chain flexibility were finally discussed and compared with those of corresponding fully perfluorinated copolyethers.

Spectral estimation of plasma fluctuations. II. Nonstationary analysis of edge localized mode spectra

Several analysis methods for nonstationary fluctuations are described and applied to the edge localized mode (ELM) instabilities of limiter H-mode plasmas. The microwave scattering diagnostic observes poloidal kθ values of 3.3 cm−1, averaged over a 20 cm region at the plasma edge. A short autoregressive filter enhances the nonstationary component of the plasma fluctuations by removing much of the background level of stationary fluctuations. Between ELM’s, the spectrum predominantly consists of broadband 300–700 kHz fluctuations propagating in the electron diamagnetic drift direction, indicating the presence of a negative electric field near the plasma edge. The time-frequency spectrogram is computed with the multiple taper technique. By using the singular value decomposition of the spectrogram, it is shown that the spectrum during the ELM is broader and more symmetric than that of the stationary spectrum. The ELM period and the evolution of the spectrum between ELM’s varies from discharge to discharge. For the discharge under consideration which has distinct ELM’s with a 1 ms period, the spectrum has a maximum in the electron drift direction which relaxes to a near constant value in the first half millisecond after the end of the ELM and then grows slowly. In contrast, the level of the fluctuations in the ion drift direction increases exponentially by a factor of 8 in the 5 ms after the ELM. High frequency precursors are found which occur 1 ms before the ELM’s and propagate in the ion drift direction. These precursors are very short (∼10 μs), coherent bursts, and they predict the occurrence of an ELM with a high success rate. A second detector, measuring fluctuations 20 cm from the plasma edge with kθ values of 8.5 cm−1, shows no precursor activity. The spectra in the ion drift direction are very similar on both detectors, while the ‘‘electron’’ spectrum level is significantly larger on this second detector.

Solution Properties of Poly(vinylpyrrolidone) in Cosolvent Systems

For solutions of well fractionated poly(vinylpyrrolidone) (PVP) samples of different relative molar mass M, intrinsic viscosities [η] have been measured at 298.15 K in pure water and water/acetone mixtures. Upon mixing water (good solvent) and acetone (poor solvent), thermodynamically better solvents could be obtained. The cosolvancy was detected from the viscosity measurements. Several graphical procedures have been utilized for deriving the unperturbed dimensions of PVP expressed as Kθ (in the relationship [η]=KθM1/2α3, where α is the expansion factor). It was found that the unperturbed dimensions were not constant and differed from those measured in the θ-solvent (water/acetone mixture having volume fraction of acetone (φACT)=0.668) in which Kθ was found to be 74×10−3 dm3 kg−1. A solvent-dependent parameter has been utilized to correct the Kθ values derived from Stockmayer-Fixman plot, in each solvent, for the sake of achieving a constant value of Kθ via these plots. Values ranging between 73×10−3 and 75×10−3 dm3 kg−1 with a mean of 74×10−3 dm3 kg−1 were obtained by utilizing the proposed correction, thus yielding 0.666 Å g−(1/2) mol1/2 for unperturbed polymer dimensions, (〈r2〉0/M)1/2.

Monoalkylitaconates–vinylpyrrolidone copolymers. 2. Reactivity ratios and viscometric behaviour in dilute solutions

AbstractCopolymerization of mono‐n‐decyl and mono‐n‐decyl and mono‐n‐dodecyl itaconate with vinylpyrrolidone (MOI‐VP, MDI‐VP and MDoI‐VP) was carried out using AIBN as initiator. The monomer reactivity ratios were determined by the Fineman‐Ross and Kelen‐Tüdös methods. Values of r1 and r2 were found to be less than unity for MOI‐VP, MDI‐VP and MDoI‐VP, corresponding to random copolymers with some tendency to alternance. Copolymers of various compositions were studied in solution, and Mark‐Houwink‐Kuhn‐Sakurada relationships were established in ethanol for MOI‐VP and MDI‐VP copolymers, and in 1‐propanol for MDoI‐VP. The rigidity factors s̀ and the characteristic ratio C∞ were obtained from Kθ values determined by using the Stockmayer‐Fixman relation. In all the copolymers the introduction of vinylpyrrolidone units produces flexibility of the polymer chain relative to the poly(monoitaconate) homopolymers, and the solution properties of these copolymers can be described by assuming a random coil model instead of a rigid rod or wormlike model as in poly(monoitaconates).

Flexibility and hydrodynamic properties of poly(vinylpyrrolidone) in non-ideal solvents

At 298.15K, intrinsic viscosity [η] has been measured for poly (vinylpyrrolidone), PVP, samples of different relative molar masses M in pure water and eight different binary solvents. These solvents were water/acetone mixtures having different volume fractions of acetone (ACT). The solvation power of these mixtures showed a cosolvancy effect. The maximum solvation power was found for the mixture containing 0.2 volume fraction of ACT. The value of Kθ=74×10-3 dm3kg-1 was utilized for calculating the unperturbed dimensions, u.d., steric factor, σ, the characteristic ratio, C∞, and the persistence length, ap. Values of 0.666 Ao, 2.28, 10.38 and 8.76 Ao, respectively, were obtained for PVP in theta-solvent. The calculated values of the effective radius (Re), effective unit length (b) and the effective hydrodynamic radius of monomeric unit (ro) showed the complete impermeability of polymer molecules. Some errors in the polymer handbook and CRC, water-soluble synthetic polymers, were demonstrated with its logical corrections.

Evaluation of unperturbed dimensions parameter from intrinsic viscosity data of any binary or ternary polymer system

AbstractTaking into account the dependency on molar mass of the viscometric interaction parameter B, the modified Stockmayer‐Fixman‐Burchard equation ([η]/M1/2) = KΘ + C″ · A2 · M1/2 is obtained. It relates the intrinsic viscosity, [η], to the second virial coefficient, A2, and to the unperturbed dimensions parameter, KΘ, with C″ being a constant. Hereupon, KΘ can be determined from [η] and A2 data of any binary (solvent/polymer) and/or ternary (solvent 1/solvent 2/polymer) system, BPS and/or TPS. Because of the scarcity of reliable sets of [η] and A2 values mostly for TPS, the application of the above equation to obtain KΘ coefficients rests limited. This limitation can be surmounted by an A2 evaluation from [η] data and trial KΘ values through two‐parameter theories taking into account the interpenetrating factor between chains, ψ, as evaluated from the Flory‐Krigbaum‐Orofino (FKO) theory, from a modified FKO theory, or from the Kurata‐Yamakawa theory. An interative process is followed until coincidence between assumed and evaluated KΘ values is reached. The method has been applied to the KΘ evaluation from [η] with literature data for diverse BPS and TPS of polystyrene, poly(methyl methacrylate), poly(dimethylsiloxane), poly(2‐vinylpyridine) and poly(1‐vinyl‐2‐pyrrolidone), with the respective KΘ values 7,5 · 10−2, 5,8 · 10−2, 8,2 · 10−2 and 6,4 · 10−2, 7.2·10−2 and · 6,4 · 10−2 mL · mol1/2 · g−3/2 being obtained. Moreover, a single C″ value, mainly C″ = 0,52, holds for all five polymers.

Unperturbed dimensions of polymers in binary and ternary systems

AbstractThe unperturbed dimensions parameter KΘ is one of the most important characteristics of a polymer chain. For binary systems (polymer/solvent) and mostly for ternary systems (polymer/solvent(1)/solvent(2)) the KΘ values show large discrepancies with respect to those under thetaconditions in a single solvent. These discrepancies can be explained by considering that the interaction parameter χ (and consequently the coil dimensions or the number of intramolecular contacts between polymer segments) changes with molecular weight M. Assuming this dependency, a modified Stockmayer‐Fixman equation is proposed from which a unique value of KΘ for a given polymer, independent of M, is obtained. The use for ternary polymer systems of an interaction parameter between polymer and the solvent mixture (χ3M) which depends on M, allows to calculate a single KΘ value for a polymer in different mixtures of solvents and justifies the proportionality found between KΘ deviations and the excess Gibbs free energy between both solvents of the solvent mixture.

Coil expansion and dimensions of poly(dimethylsiloxane) in alkane/2‐butanone mixtures

AbstractThe intrinsic viscosities, [η], for the ternary systems alkane (1)/2‐butanone (2)/poly(dimethylsiloxane) (PDMS)(3), with the alkanes decane, dodecane and hexadecane, are determined at 20,0°C. The constants a of the Mark‐Houwink equation and the constant of the unperturbed dimensions, KΘ, of the polymer are evaluated over the whole composition range of the binary solvent mixture. [η] shows a pronounced maximum at intermediate compositions as found in cosolvent mixtures. In these cosolvent mixtures, the numerical values of KΘ are higher than in the single‐component solvents, because the cosolvent mixtures correspond to a mixed solvent with an excess free energy, GE ≥ 0, the increase in KΘ being only moderate though. A new procedure taking into account ternary interactions, to evaluate the intrinsic viscosity in ternary systems from GE values is proposed. The influence of ternary interactions through a constant (1–2aχ) is also investigated. From these new expressions the constant of the apparent polymer unperturbed dimensions, K, and (1–2aχ) are calculated and compared with those directly evaluated from second virial coefficients.

Solution Properties of Low Molecular Weight Fractions of Poly(2-vinylpyridine)

Abstract The relationships between the weight-average molecular weight Mw and the intrinsic viscosity [η] of poly(2-vinylpyridine) [P2VP] in benzene and methyl alcohol at 25 °C, were investigated by the use of fractions with molecular weights ranging from 2.1×103 to 2.3×104. The exponent ν in the Mark-Houwink-Sakurada equation, [η]=K0Mwν, was 0.5 in both solvents when Mw was lower than about 104. A constant K0 was approximately in accord with Flory’s Kθ value for ordinary high-molecular-weight P2VP, obtained earlier in respective solvents. By measuring [η] for these low-molecular-weight fractions in several solvents at different temperatures, the temperature coefficients of an unperturbed dimension, dln\barr20⁄dT, of this polymer were estimated and averaged to be −2.3×10−3 K−1. These are quite different from the positive values calculated from the Kθ’s by Dondos et al. which were estimated using the extrapolation method for non-θ-solvents. Our results were further corroborated after adding a Kθ value which was directly determined at another θ-state; i.e. in toluene at 63.7 °C, to that in benzene at 16.2 °C published earlier, which was found from phase-separation experiments in this work.

A Modified Method for Estimating Unperturbed Dimensions of Macromolecules from Viscosity Data

Abstract A new empirical equation is presented which modifies the Krigbaum equation for calculating Kθ values from measurements of intrinsic viscosity in good solvents. This is found to fit the molecular weight data better for the polymer systems investigated.

Viscometric and preferential adsorption behaviour of poly(4-tert-butylphenyl methacrylate) in tetrahydrofuran/chloroform

The viscometric behaviour of poly(4-tert-butylphenyl methacrylate) in the solvent mixture tetrahydrofuran/chloroform has been investigated. There is qualitative agreement between variations in [η] and predictions from the Dondos and Patterson theory. The role of the preferential adsorption of one of the solvents on the polymer was considered. The experimental adsorption coefficients λ∗ are discussed in this particular mixture where GE < 0. In this binary solvent rthe kθ values of the polymer are similar in the three different mixed solvent compositions studied.

Thermoplastic urethane elastomers. VI. Dilute solution properties in various solvents

AbstractA thermoplastic urethane elastomer prepared from a polycaprolactone diol, 4,4′‐diphenylmethane diisocyanate, and 1,5‐pentanediol was fractionated and the solution properties of the fractions were characterized in terms of viscosity and sedimentation. Mark‐Houwink relations were established for data obtained at 30° in various solvents: In dimethylacetamide, tetramethylurea, and N‐methyl pyrrolidone, the value of Kθ increased systematically in the range (1.7 to 2.0) × 10−3. Lower values of Kθ were obtained in dimethylformamide (0.8 × 10−3) and meta‐cresol (0.9 × 10−3). The molecular expansion coefficients in the various solvents were approximated from the experimental viscosity data. Short‐range interactions between the solvent molecules and polymer chains are suggested as possible causes for differences in the hydrodynamic parameters.

Properties of vinylpyrrolidone‐tert‐butylphenyl methacrylate copolymers in solution

AbstractCopolymers of vinylpyrrolidone‐p‐tert‐butylphenyl methacrylate (VP‐MBPh) of several compositions were prepared by polymerization in benzene at 50°C using α′α′‐azobisisobutyronitrile as initiator. Three of the copolymers were fractionated. Number‐average molecular weights of fractionated samples were determined by osmotic pressure in benzene or 2‐propanol. Kuhn–Mark–Houwink relations were established in benzene, chloroform, and 2‐propanol. From the relation between Mn and the intrinsic viscosity (η), it appears that these random copolymers behave as predicted by the theory for flexible polymers. Abnormal viscometric behavior shown by one of the copolymers in nitromethane at 29°C (the theta temperature) is discussed. The Stockmayer–Fixman semiempirical method was used for estimating unperturbed dimensions from viscosity data obtained in chloroform, a good common solvent. Values of the viscosity parameter Kθ increase with the content of p‐tert‐butylphenyl methacrylate. In general, experimental Kθ values are higher than those calculated for the homopolymers. Excluded‐volume parameters are estimated and discussed in relation to repulsive interactions between unlike monomer units.