Prediction of the non-Newtonian viscosity and shear stability of polymer solutions

The structure-property relationships derived here permit the prediction of both the zero-shear viscosity ₀, as well as the shear rate dependent viscosity . Using this molecular modeling it is now possible to predict over the whole concentration range, independently of the molecular weight, polymer concentration and imposed shear rate. However, the widely accepted concept: dilute — concentrated, is insufficient. Moreover it is necessary to take five distinct states of solution into account if the viscous behavior of polymeric liquids is to be described satisfactorily. For non-homogeneous, semi-dilute (moderately concentrated) solutions the slope in the linear region of the flow curve (= must be standardized against the overlap parameterc · []. As with the ₀-M-c-relationship, a-M -c- relationship can now be formulated for the complete range of concentration and molecular weight. Furthermore, it is possible to predict the onset of shear induced degradation of polymeric liquids subjected to a laminar velocity field on the basis of molecular modeling. These theoretically obtained results lead to the previously made ad hoc conclusion (Kulicke, Porter [32]) that, experimentally, it is not possible to detect the second Newtonian region.Roman and Italian symbols a exponent of the Mark-Houwink relationship - b exponent of the third term of the ₀-M -c relationship - c concentration /g · cm^–3 - E number of entanglements per molecule - F(r) connector tension - f function - G _i ^A shear modulus; A indicates that it /Pa has been evaluated by a transient shear flow experiment; i is the shear rate to whichG ^A refers to - G storage modulus /Pa - G _p plateau modulus /Pa - H() relaxation spectrum /Pa - h shift factor (₀/_r) - K _H Huggins constant - K _b third constant of the ₀-M -c relationship - K constant of the Mark-Houwink relationship - M molecular weight /g · mol^–1 - M _e molecular weight between two /g · mol^–1 entanglement couplings - N number of segments per molecule - n slope in the power-law region of the flow curve - p p-th mode of the relaxation time spectrum - R gas constant /8.314 J·K^–1·mol^–1 - r direction vector - T temperature /K Greek symbols ß reduced shear rate - shear rate /s^–1 - shear viscosity /Pa·s - _s solvent viscosity /Pa·s - _sp specific viscosity - ₀ zero-shear viscosity /Pa·s - apparent viscosity at shear rate - reduced viscosity - viscosity of polymeric liquid in /Pa·s the second Newtonian region - [] intrinsic viscosity/cm³·g^–1 - screening length/m - /g·cm ^–3 density - relaxation time/s - ₀ experimentally derived relaxation time/s - angular frequency of oscillation Indices conc concentrated - corr slope corrected - cr critical - deg degradation - e entanglement - exp experimental - mod moderately concentrated/semi-dilute - n number average - p polymer - R Rouse - rep reptation - s solvent - sp specific - theo theoretical - weight average - relaxation time - o experimental or steady state - * critical - ** transition moderately conc. — conc. - + transition dilute — moderately cone. Paper presented at the 2nd bilateral U.S.-West German Polymer Symposium, Yountville, the 7th–11th September 1987.     

Characterization of water-soluble,cationic polyelectrolytes as exemplified by poly(acrylamide-co-trimethylammoniumethylethacryate chloride) and the establishment of structure-property relationships

The cationic copolymerization products of poly (acrylamide-co-trimethylammoniumethylmethacrylate chloride (PTMAC) having cationic monomer percentages of 8%, 25%, and 50% as well as the cationic homopolymer, were characterized with respect to their molecular dimensions. The light-scattering and viscometric measurements were carried out for molecular weights ranging from 200 000 to 12 800 000 g/mol in 1 M NaCl solution at 25°C. It was possible to establish a relationship between the molecular weight and the two parameters: intrinsic viscosity and radius of gyration, for all four polymers.Rheological investigations of the flow properties in 1 M NaCl solution were also carried out using the polymer with a cationic monomer of 50% (PTMAC 50). Structure-property relationships were formulated which made it possible to describe and predict the shear viscosity, both in the zero-shear region (Newtonian region) and in the shear-dependent region (non-Newtonian region) as a function of the polymer concentration, the molecular weight, and shear rate.Abbreviations a exponent of the []-M relationship - A ₂ 2^nd virial coefficient/mol·cm³·g^–2 - AAm acrylamide - b slope of the flow-curve in the shear-rate dependent region - c concentration/g·cm^–3 - dn/dc refractive index increment/cm³·g^–1 - f function - K constant of the []-M relationship/cm³·g^t-1 - m _c proportion of cationic monomers/mol % - M molecular weight/g·mol^–1 - M _w weight-average molecular weight/g·mol^–1 - M _n number-average molecular weight/g·mol^–1 - NaCL sodium chloride - PAAm polyacrylamide - PS polystyrene - PTMAC poly(acrylamide-co-trimethylammoniumethylme thacrylate chloride) - R_G ^20.5 radius of gyration/nm - TMAC trimethylammoniumethylmethacrylate chloride - shear rate/s^–1 - critical shear rate/s^–1 - viscosity/Pa·s - 0 zero-shear viscosity/Pa·s - _s solvent viscosity/Pa·s - _sp specific viscosity - [] intrinsic viscosity/cm³·g^–1 - relaxation time/s     

Viscosity B coefficients of polyethyleneglycols in water

The viscosity B coefficients of polyethylene glycols (M=62–1000) are determined at 25 °C. The B coefficient increases non-linearly with the number of ethyleneoxide (EO) units. The increase of the B coefficient per EO(0.111 dm³/mole) is less than the B value for two methylene groups (0.160 dm³/mole). This is discussed in terms of changes in the configurations of polyethylene glycols with long EO chains.Molecular size is the major factor that contributes to B at shorter chains, but solvation (hydration) becomes dominant as the number of ethyleneoxide groups increases. The hydration parameter,(gH₂O/g ethyleneglycol), shows a linear dependence on B at low mass followed by a non-linear increase at high molecular mass and the viscosity C coefficient accounts for the solute-solute interactions.Symbols absolute viscosity - _d absolute viscosity of dispersion medium - _r relative viscosity - _sp specific viscosity - ¦ _o ¦ intrinsic viscosity at infinite dilution - ¦ _c ¦ intrinsic viscosity as a function of solute concentration - partial specific volume - volume fraction - hydration (weight of H₂O hydrating 1 g of polyethylene glycol) - _c hydration as a function of solute concentration - K shape function - K _c shape function as a function of solute concentration     

Scattering from concentration fluctuations in polymer blends: A monte carlo investigation

The collective scattering function S_coll( ), which describes light (neutron-, x-ray) scattering under wavevector , is obtained from Monte Carlo simulations for a symmetrical polymer mixture. The polymers are modelled by self-avoiding walks ofN _A=N_B=N steps on a simple cubic lattice, where a fraction _V of sites is left vacant, and an attractive energy occurs if two neighboring sites are taken by the same kind of monomer. Spinodal curves are estimated from linear extrapolation of S _coll ^–1 (0) vs./k _B T, whereT is the temperature. Also the single chain structure factor is obtained and the de Gennes random phase approximation (RPA) can thus be tested. Unexpectedly, strong deviations are found if one species is very dilute. The estimation of an effective Flory-Huggins-parameter from scattering data is also discussed.Contributed paper delivered at the Tagung der Deutschen Physikalischen Gesellschaft, Fachausschuß Polymerphysik, Hamburg, March 14–16, 1987.     

Effect of thick fixed-charge layers on electrostatic interaction — a theoretical approach

The electrostatic interaction pressure of charged surface layers is considered qualitatively and quantitatively. In the case of mutual penetration of the surface layers in addition to Maxwell stress and osmotic resp. hydrostatic pressure an isotropic stress on the fixed charges carrying molecules of the surface layers has to be taken into account. The derivation of the pressure-distance equations is given starting from both thermodynamic/electrostatic and hydrostatic/electrostatic principles. A possible biological significance of the additional stress is discussed emphasizing its role in modifying the structure of surface layer molecules.List of symbols e ₀ elementary charge - k Boltzmann constant - n _i concentration of theith ionic species in the bulk solution - P hydrostatic pressure - P hydrostatic pressure in the bulk volume (× ) - P ^h integration constant, independent on ×:P ^h =P(h) - T absolute temperature - Z _i electrovalence of theith ionic species - thickness of the surface layer - , ₀ relative and absolute permittivities - II(×) osmotic pressure at position × - II osmotic pressure in the bulk solution (× ) - osmotic pressure in the symmetry plane of interacting identical surface layers (electric field strength equals zero) - integration constant, independent on ×: - _e ^h electrostatic component of the disjoining pressure _e ^h = _e (h) - (×) mobile charge density profile (cations and anions of the electrolyte) - (×) fixed charge density profile - ^t(x) total charge density profile ( ^t = +) - ¹(x) fixed charge density profile of one of the two surface layers ( ¹(×) 0 for 0×) - (×) electric potential profile     

CPS GL 799

The effect of illumination on transport of sulfonated bisazo direct dyes, CI Direct Yellow 12, and CI Direct Yellow 4, into a cellulose membrane has been studied at various temperatures. Transport of CI Direct Yellow 12, which exhibits photoinduced reversible trans-cis isomerism in aqueous solution into a cellulose membrane, was influenced by illumination. It is likely that the transport was influenced by transisomerization of the photoisomeric dye and the diffusivity was controlled by surface diffusion rather than by pore diffusion under both light and dark conditions.Notations C Concentration of dye in the pores (mol/dm³) - C _E Concentration of electrolyte in the bulk solution (mol/dm³) - C _o Concentration of dye in the bulk solution (mol/dm³) - D _p Pore diffusivity (m²/s) - D _s Surface diffusivity (m²/s) - [M] Mean concentration of dye in membrane (mol/dm³) - [M] _L Local concentration of dye in membrane (=q+ _p C) (mol/dm³) - [M] Mean concentration of dye in membrane (mol/kg) - [M] _L Local concentration of dye in membrane (=q/V+ _p C) (mol/dm³) - F Fractional attainment of equilibrium - l Thickness of membrane (m) - q Concentration of dye adsorbed on pore wall (mol/dm³) - q _o Adsorbed concentration of dye in equilibrium withC _o (mol/dm³) - q Concentration of dye adsorbed on pore wall (mol/kg) - q _o Adsorbed concentration of dye in equilibrium withC _o (mol/kg) - t Time (s) - V Volume of membrane swollen with water per unit dry cellulose (dm³/kg) - x C/C _o - y q/q _o - z Distance that the dye diffused in the membrane (m) - q _o / _o C _o - D _s /D _p - Coefficient of the Freundlich isotherm - _p Pore void fraction - z/l - _p D _p t/l ² - _s D _s t/l ²     

Solutions of alkali soaps and water in fatty acids XIII. Circumstances that regulate the extension of theL 2-phase and the role of the acid-soaps rich in fatty acid for the occurrence of the phase

A basic requirement for that type ofL ₂-phase which exists in the system sodium octanoate-octanoic acid-water is the formation of acid-soaps. In order for the phase to be formed at all, the temperature must lie above the melting point of the fatty acid so that a reaction in non-aqueous milieu between neutral soap and fatty acid is possible. In order to obtain the characteristic shape and complete extension of the phase in direction of high water content the temperature must be so high that also the hydrated acid-soaps occur in fluid state. On the other hand the temperature cannot be so high that the acid-soaps become unstable.At temperatures at which the phase has obtained its full extension those circumstances differs which in different regions regulate the location of the phase borders; they depend on the composition of the acid soaps and on their amounts. In that part of the phase where the molar ratio between octanoic acid and sodium octanoate lies between 2 and 3 and where one has a continuous transition from reversed to normal structure only the two acid octanoates 1 NaC₈ 2 HC₈ x H₂O and 1 NaC₈ 3 HC₈ x H₂O occur and both are at 20 °C in fluid state.At water contents from about 22 % to 40 % the hydrate-water molecules belonging to the first mentioned soap are capable of contributing actively to the formation of large aggregates of acid-soap, a process which however is counteracted by the inmixing of the latter acid-soap. This mixture of the two acid-soaps decides in this region where the border of the phase will lie in direction towards an increased content of sodium octanoate; the result is that in spite of the fact that the hydration is increased, the border is only slowly displaced towards a higher content of fatty acid. As soon as the hydration of the acid octanoates has been completed and the additional water occurs as unbound bulkwater, the location of the phase boundary will no longer be influenced by the water content — now it will be the amphiphilic composition of the acid-soaps that determines the location of the border and it remains at the molar ratio 2.5 between octanoic acid and sodium octanoate at water contents from about 40% and up to 82%.In the direction of decreasing content of neutral sodium octanoate and increased content of water theL ₂-phase both at the highest content of fatty acid and the highest contents of water will be in equilibrium with the water-richL ₁-phase; in the first mentioned region with theL ₁-phase below the lac where at the border it is saturated with octanoic acid and in the latter region with theL ₁-phase just above the lac, where the dilute sodium octanoate solution contains dissolved 1 NaC₈ 1HC₈ x H₂O. In the large central part of theL ₂-phase, from about 20 % to about 86 % of water, the location of the border is dominated by the acid octanoate 1 NaC₈ 3 HC₈ x H₂O and that makes an equilibrium with theL ₁-phase impossible; instead one has an equilibrium via a two-phase zone between the amphiphile-rich region of theL ₂-phase and its water-rich region. In the first region the location of the border is regulated by the decreasing capability of the hydrated acid octanoate 1 NaC₈ 3 HC₈ x H₂O to dissolve octanoic acid; in the latter it is regulated by the fact that 1 NaC₈ 3 HC₈ x H₂O is the most fatty acid-rich acid-soap that is formed and that the octanoic acid is very little soluble in water and in the aqueous solution of this acidsoap.The middle part of theL ₂-phase, especially the region between about 55 % and 82 % of water, constitutes a direct continuation of the liquid crystalline lamellarD-phase. The liquid crystalline character of theD-phase is lost at the transition, but the lamellar organization is retained. That the molecules at least up to a water content of about 40 % are of the original reversed type and have an elongated shape with a central part of hydrated polar groups, from which core the hydrocarbon chains extend in two opposite directions, is the reason to that they, at crowding, form transient layer-like agglomerates of tightly packed more or less parallel molecules; this facilitates the transformation to coherent double amphiphilic layers, in which all molecules lie with the hydrated polar groups outwards toward coherent domains of bulk-water, without another liquid phase occurs.     

An estimation of the surface ionization constant of oleic acid in aqueous sodium chloride solution

The zeta potential () measurements and the site binding theory were utilized for calculations of the parameters of the electrical double layer (edl), ionization, and complexation constants for oleic acid-aqueous sodium chloride solution interface. Assuming that is equal to the diffuse layer potential ( _d ) of the edl, the charge of the diffuse part of the edl was calculated from the Gouy-Chapman equation. The intrinsic ionizaiton constant was then determined by an extrapolation method to be . Subsequently, the surface potential ( ₀) was calculated, and it was found that ₀ changes by 50 mV per pH unit (50 mV/pH) or 42.5 mV/pH for 10^–3 and 10^–2 M NaCl, respectively. For further calculations, the integral capacity of the outer zone of the compact part of the edl was assumed to be for both ionic strengths. It was established that the intrinsic complexation constant for the binding of Na⁺ ions with the surface of oleic acid ispK _Na ^int = 2.9±0.5 if the integral capacity of the inner zone of the compact edl (K ₁) is 80 for 10^–3 M NaCl, but 280 for 10^–2 M NaCl. The use of the sameK ₁ value for both ionic strengths gives a differentpK _Na ^int for different NaCl concentrations, and also provides unrealistic surface charge ( _o ) values greaterfor 10^–3 M NaCl than for 10^–2 M NaCl, at the same pH of the solution.     

Water self-diffusion in micellar solutions and in lyotropic mesophases of the system water/Triton TX-100

Studies by Pulsed Field Gradient NMR (PFG-NMR) methods and other physico-chemical experiments have been used to clarify the processes connected with water self-diffusion in mixtures formed by water and Triton TX-100. In micellar solutions the solvent diffusive trend is related to micelle hydration and, to a much less extent, to micelle size and shape. Hydration numbers from PFG-NMR are close to those obtained by viscosity experiments. In solution phases of the reversed kind, water in oil, water self-diffusion data suggest that aqueous domains are large and bicontinuous. Water self-diffusion in the hexagonal lyotropic mesophase has been interpreted by introducing a geometrydependent contraint, , termed structural factor, which is related to the parameters of the phase.     

Iodine sorption,porosity, and wettability of carboxymethylcellulose of low degree of substitution

Cellulosic fabric was carboxymethylated by single-bath method for different durations. arrived at a maximum when plotted against the time of reaction. This might be interpreted by the dissolution of the highly substituted fractions. The fibrous character of the carboxymethylated samples remained unchanged, but the accessibility of the cellulose characterized by iodine sorption, porosity, and wettability changed significantly. The carboxymethylation had a complex effect on the investigated parameters: the values of accessibility were increasing initially, caused by opening the fibrillar structure, but decreasing later as the swollen structure was collapsing during air-drying. The studied properties were depending not only on the changes in but also on the reaction parameters.     

Adsorption kinetics with time delay

A theory of adsorption kinetics of solutes onto a solid surface from the solution phase is proposed in which a time delay is introduced into the solute concentration on the surface. Equations governing the adsorption kinetics are similar to those for membrane transport with time delay (Ohshima and Kondo, Biophys. Chem. (1989) 33: 303). It is found that introduction of time delay causes, under certain conditions, overshoot or oscillation in the solute concentrations, both in the solution phase and on the surface. The criterion for oscillation depends on the scaled delay time , the ratio of the possible maximum amount of solutes adsorbed on the surface to the total solute amountR, and the scaled binding constantK. When the number of the binding sites is small, the criterion for oscillation is expressed as >exp(–1), where =(/K) exp().     

Study of the polymer latex coalescence by dielectric measurements at microwave frequency—feasibility of the method

The measurement of the complex dielectric constant ( ^*=–j) in the dipolar absorption domain of the free water molecule (microwave region) permits us to follow quasi-specifically and precisely the water circulation during the coalescence process of a latex. Weight losses and dielectric constants variations have been simultaneously recorded upon latex drying, in a resonant cavity at 5 and 9 GHz and under controlled atmosphere and temperature. Two different latexes were studied (polybutylacrylate (PBuA) and polystyrene (PS)) from which the glass transition temperature effect was investigated. It is found that the harder the polymer particles, the more clearly evidenced the flocculation and packing points are. This method appears to be quite reliable for discriminating the various steps in the film formation process of latexes.     

Mass,size and shape of micelles formed in aqueous solutions of ethoxylated nonyl-phenols

The study was extended to analysis of mass, size and conformation of micelles formed in aqueous solutions of ethoxylated nonyl phenols. The results obtained by ultracentrifugal technique between 293 and 323 K have proved that the slightly ethoxylated nonyl phenols form micelles with high molecular mass and larger size at constant temperature, while the increasing length of the ethylene oxide chain favours formation of micelles of smaller molecular mass and size. The transformation of conformation from oblate to spherical shapes ensues with increasing temperature at constant ethoxy number or with ethoxylation at constant temperature. The second virial coefficient decreases with increasing temperature and decreasing ethoxy number. In accordance with the earlier conclucions, the change of the second virial coefficient relates to enhanced variation of monomer solubility, stabilization of micelle structure and increased deviation from ideal behaviour of a given micellar system.Symbols a major axis of micelle, Å - a _m attractivity factor, cm³ erg molecule² - b minor axis of micelle, Å - c concentration, g dm^–3 - c _b equilibrium concentration at the bottom of the cell, g dm^–3 - c _m equilibrium concentration at the meniscus of the cell, g dm^–3 - c _o initial concentration in the cell, g dm^–3 - c _M critical micellization concentration, mol dm^–3 - e eccentricity - f _IS Isihara-constant - f/f _o frictional ratio of micelle - amount of water in micelle per ethoxy group, mol H₂O/mol EO - n aggregation number, monomer micelle^–1 - n _EO number of ethoxy groups - r distance of Schlieren peak from the axis, cm - r _b distance of cell bottom from the axis, cm - r _m distance of cell meniscus from the axis, cm - R _h equivalent hydrodynamic radius of micelle, Å - s _t sedimentation coefficient, s - reduced sedimentation coefficient, s - reduced limiting sedimentation coefficient, s - ¯v _t volume of micelle, cm³ micelle^–1 - partial specific volume of solute, cm³g^–1 - partial specific volume of solute reduced to 293 K, cm³ g^–1 - B _a, B_e constants, cm³ mol g^–2 - B ₂ second virial coefficient, cm³ mol g^–2 - M _m ^a mass average apparent molecular mass of micelle, g mol^–1 - M _m mass average molecular mass of micelle corrected withB ₂, g mol^–1 - M _m ^cM mass average molecular mass of micelle belonging toc _M, g mol^–1 - M ¹ mass average molecular mass of monomer, gmol^–1 - N _A the Avogadro's number, molecule mol^–1 - R universal gas constant, erg mol^–1 K^–1 - T temperature, K - _t ^o dynamic viscosity of solvent atT temperature, g cm^–1 s^–1 - dynamic viscosity of solvent at 293 K, g cm^–1 s^–1 - _t density of solution atT temperature, g cm^–3 - _t ^o density of solvent atT temperature, g cm^–3 - density of solvent at 293 K, g cm^–3 - angular velocity, rad s^–1 - time, s     

Transient photocapacitance study in 4-nitro-4′-aminodiphenyl layers

In 4-nitro-4-aminodiphenyl (NAD) layers the photocapacitance (PhC) transients were investigated. PhC spectral distribution as well as the temperature dependences of time constants (under/_on/or after/_off/illumination) have been measured. The photocapacitance spectral distribution possesses maxima at 350, 500, and 750 nm. It was shown that _on (T) is of exponential form while _off (T) is more complicated. The values of thermal activation energies (0.65±0.05) eV of both time constants coincide. The mechanism of photocapacitance process has been disclosed in NAD layers.     

Shear-induced deformation of polystyrene coils in dilute solution from small angle neutron scattering 2. Variation of shear gradient,molecular mass and solvent viscosity

The technique of small angle neutron scattering (SANS) has been used to study the conformation of polystyrene chains in dilute solution under a constant shear gradient. The experiments reveal a distinct anisotropy of the molecular dimensions with regard to the directions parallel and perpendicular to the flow direction on the 2D-multidetector. The deformation ratio of the single polymer chain (R ²/R _iso ² )–1 as a function of the reduced shear gradient=([] · · M _w G)/RT shows a transition from the ideal ²-behaviour for dynamic infinitely flexible coils found at small gradients, to a behaviour with smaller increase at larger. These results are qualitatively consistent with the theory of Cerf for a polymer with finite internal viscosity in a shear gradient. At low(<1), a better agreement with the model of a free-draining coil (Rouse behaviour) than with the Zimm model is observed.     

Structure of gangliosides from gonads of the starfish Evasterias retifera

Mono- and disialogangliosides were isolated from gonads of the starfish Evasterias retifera. Their structures were elucidated using chemical methods, GC-MS analysis, and enzymatic hydrolysis with neuraminidase. The monosialoganglioside has the structure 8-O-Me-Neu5Gc-23-GalNAc-13-Gal-14-Glc-11-Cer, while the disialoganglioside contains an additional Neu5Ac residue which glycosylates GalNAc in position 6. The lipid moieties of both gangliosides contain phytosphingosine (mainly C_18:0) and two types of fatty acids, unsubstituted (mainly C_16:0 and C_18:0) and -hydroxy acids (mainly -hydroxy-C_16:0).     

Studies on the electrical double layer structure at the water/air interface

Effective dipole moments (calculated from experimental data of surface tension and electric surface potential) of some homologous normal alcohols and carboxylic acid were found to vary linearly with the number of carbon atoms in the hydrocarbon chain. Values of effective dipole moments were used for the determination of the effective dipole moments of water molecules , and the dielectric permittivity of the water subphase (₁), as well as in the vicinity of the hydrophobic part of adsorbed molecule (₂). The latter was found to decrease with the increase of the hydrocarbon chain length. Knowing the effective dipole moment of surface water dipoles, the average orientation angle () of water molecules at the inteface was estimated. The calculated potential drop of water varies within the range –0.038 to –2.38 V for two extreme orientations of water dipoles at the surface.     

Determination of unperturbed dimensions of polymers in binary solvent mixtures from viscosity measurements

Intrinsic viscosity measurements were carried out on poly(vinyl pyrrolidone) and poly(vinyl alcohol) in various solvents and solvent mixtures. The values of, [] andk, the latter two being the fundamental terms in the equationC/ _sp =1/kC, were utilized for the determination of the unperturbed dimensions in solution. The values of (¯r _o ² /M _w )^1/2 were calculated.     

Mechanical properties and molecular mobility in oriented polyolefines

The static modulus of elasticity (E) and the correlation time of rotation ( _c ) of 2,-2,6,6-tetramethylpiperidine-1-oxyl are studied as a function of the temperature (210<T <350°K) for oriented films of isotactic polypropylene and polyethylene of high and low density.E and _c change both upon heating and polymer orientation; this result indicates that sample properties are influenced by the microstructure of the amorphous phase where probes are localized.     

Complex polarizability as used to analyze dielectric relaxation measurements

The effect of representing dielectric properties in terms of the complex polarizability ^c = – i is examined. Loss curves ( and tan ) are shifted towards higher frequencies, revealing the existence of new relaxations and allowing the clarifications of ones already known. We have calculated the shift ratios (at maximum or tan )/ (at maximum or tan ) from the more conventional empirical equations representing the dielectric behavior. Some examples are given.