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.     

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.     

Phase behavior and dynamic properties in mixed systems of anionic and cationic surfactants: lithium perfluorooctanesulfonate/diethanolheptadecafluoro-2-undecanolmethylammonium chloride (DEFUMAC) and lithium dodecyl sulfate/DEFUMAC aqueous mixtures

Two ternary phase diagrams of the cationic perfluorosurfactant diethanolheptadecafluoro-2-undecanolmethylammonium chloride (DEFUMAC) with an anionic perfluorosurfactant lithium perfluorooctanesulfonate (LiFOS) and an anionic hydrocarbon surfactant lithium dodecyl sulfate (LiDS) have been established at 25°C. The total surfactant concentration was less than 20wt%. In a wide mixing region of the LiFOS/DEFUMAC system, a lamellar-type phase,P , was identified by its texture under a polarization microscope and by its x-ray diffraction pattern. Dispersed fragments ofP -phase are present in the dilute solutions in which one surfactant was in excess. The anisotropy of electrical conductivity, flow birefringence, dynamic light scattering, and electric briefringence demonstrate that theP fragments are disk-like with a radius of 0.7 m. The disk-likeP particles are transformed by shear into a spherical aggregate ofL above a critical shear gradient. LiDS/DEFUMAC mixed solution forms dispersed and precipitatedL in the dominant region. Radius and micropolarity of the dispersedL aggregates are decreased as the ratio of LiDS:DEFUMAC approaches 1:1. On the basis of x-ray diffraction measurement the structure of precipitatedL -phase seems to consist of monolayers.     

Effects of pressure and solvent on the diffusion of aromatic compounds through polymers

The diffusion of six azo and five anthraquinone derivatives through nylon 6, poly(ethylene terephthalate) and secondary cellulose acetate films were studied under high hydrostatic pressures of up to 3000 bar and at temperatures 80–130 °C, by analyzing the diffusion profiles yielded in a stacked multiple film, placed in the solution of the diffusant. It was found that the diffusion coefficient,D, of the diffusant decreased with increasing pressure, giving a linear relationship between InD and the pressure, the slope of which gave the activation volume for the diffusion,V . It was revealedV increased linearly with increasing intrinsic molecular volume of the diffusant,V _w , the slopes being different between the azo and the anthraquinone derivatives. The ratio ofV toV _w (V /V _w ) ranged from 0.13 to 0.93, depending in a sensitive manner on the degree of swelling of the polymer matrix which in turn was varied by the solvent. The overall results could be explained in accordance with the formulation,V _{f, local} +V =V _w , whereV _{f, local} represents the free volume contribution. It was proposed thatV _w is increased by solvation when the solvent is good for the diffusant.     

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     

Macromolecular conformations at the water-air interface: Interactions between alpha and beta conformations of polypeptides

Bidimensional miscibility between alpha and beta conformations of polypeptides was investigated at the water-air interface in the 15°–30°C temperature range. The polypeptides were poly--methyl-L-glutamate (PGMG), poly--benzyl-L-glutamate (PGBG) and poly--benzyl-L-aspartate (PBBA). The polypeptide conformations, alpha or beta, were checked by IR spectroscopy using the MIR technique.The spreading isotherms for mixed monolayers alpha-PGMG/alpha-PGBG and beta-PGMG/beta-PBBA showed bidimensional miscibility both for alpha-alpha and beta-beta mixtures.For the alpha-alpha system, attractive interactions among the polypeptide alphahelices were found (G_mix<0) and the driving factor appeared to be the entropic one (packing). Compressibility moduli and surface potential measurements showed a fluidification effect of alpha-PGBG on mixed monolayers. In the case of beta-beta mixed monolayers, ideal behaviour was observed and no fluidification effect detected.Scanning electron micrographs made on collapsed monolayers showed hexagonal structures for alpha-alpha mixtures and no well-defined or characterized features for the beta-beta system.     

Monte Carlo simulation of a lattice model for ternary polymer mixtures

Monte Carlo studies of symmetrical polymer mixturesAB, modelled by selfavoiding walks withN _A =N _B =N steps on a simple cubic lattice, are presented for arbitrary concentrations of vacancies _v in the range from _v =0.2 to _v =0.8 and chain lengthsN64. We obtained the phase diagrams and the equation of state for three choices of the ratio / _AB ( being the energy between monomers of the same kind, _AB being the energy between different monomers). Flory-Huggins theory provides only a qualitative understanding of these results. If the equation of state is fitted with an effective Flory-Huggins parameter _eff , the latter turns out to be strongly dependent on both concentration and temperature.Contributed paper delivered at the Tagung der Deutschen Physikalischen Gesellschaft, Fachausschuß Polymerphysik, Berlin, March 30–April 3, 1987.     

Adsorption behavior of polymers having phosphoric acid group on γ-Fe2O3 and magnetic characteristics in magnetic coatings

Polymers having phosphoric acid groups were prepared as a model binder for magnetic coatings, and the correlation among the adsorption behavior of the polymers onto-Fe₂O₃ particles and the dispersibility, the orientation, and the packing density of-Fe₂O₃ particles in the magnetic coatings was investigated.PMMA homopolymer molecules hardly adsorbed on-Fe₂O₃, and the interfacial tension at a water/polymer solution (toluene) interface ( _W/T) was scarcely changed compared with a water/toluene interface. Increasing with the content of polymeric phosphoric acid group, the adsorbance of polymer increased and the interfacial tension ( _W/T) decreased. When the content of polymeric phosphoric acid groups was over 0.4 mol%, the adsorbance of polymer and interfacial tension ( _W/T ) remained constant. When these polymers were used as a binder for magnetic tapes, the dispersibility of-Fe₂O₃ in the magnetic coatings was improved, increasing with the content of polymeric phosphoric acid group; however, when the content of phosphoric acid group was over 0.2 mol%, its dispersibility decreased abruptly.Studies on Recording Magnetic Materials and Magnetic Composite. XVIII.     

Theory of ring formation in a reversible system: general solutions

The enumeration theory is extended in this work into a more general theory, taking back-reactions into consideration. The solutions may faithfully reproduce real processes from arbitrary starting points to a steady-state. Therefore, the presented theory includes the equilibrium theory by Jacobson-Stockmayer, the numerical solution by Gordon-Temple, and the irreversible theory by the present authors. The solutions are described first in general forms of transition probabilities {P}, and then explicitly with the aid of rate equations; simple proofs are given. The presented theory was applied to an experimental data: the distribution of cyclic species in poly(ethylene terephthalate). We shall show that agreement between theory and experiment is nearly perfect.AB model N ₀ Total number of units - V System volume - C ₀=N ₀/N _A ·V Initial concentration (N _A : Avogadro's number) - L _x AB type chain x-mer; (AB)_x - N _x Number of AB type x-mers - R _x Ring x-mer - N _Rx Number of ring x-mers - E Small molecule eliminated by bond-formation - N _E Number of small molecules eliminated by bond-formation - h _k Number of reacted functional units (f.u.) in statek - _k Number of reacted functional units (f.u.) in chains in statek - _k Total number of units in chains in statek - D=h _k /N ₀ Extent of reaction in statek - D ^*= _k / _k Extent of reaction in chains in statek - k _L Chain-propagation rate constant - k _Rx Cyclization rate constant of chain x-mers - k _B Bond breakage rate constant of chains - k _B,Rx Bond breakage rate constant of cyclic x-mers - <k _Rx > _k Mean cyclization rate constant in statek - g(x)=k _B,Rx /k _B Ring-opening factor of cyclic x-mers - P _Lx,k Probability that a chain x-mer will be formed in statek - {P} Set of transition probabilities per single jump in forward direction or reverse direction (see the text on individual transition probabilities) AB model M _A Total AA monomer unit number - M _B Total BB monomer unit number - M ₀=M _A +M _B Total particle number - _A,i =2M _A –h _i Unreacted A functional unit (f.u.) number in statei - _B,i =2M _B –h _i Unreacted B f.u. number in statei - _Ax Unreacted A f.u. number on x-mers - h _i Number of reacted A (or B) f.u. in statei - _i Number of reacted A (or B) f.u. in chains in statei - _A,i =2M _A –h _i + _i A f.u. number in chains in statei - _B,i =2M _B –h _i + _i B f.u. number in chains in statei - _i =2(M ₀–h _i + _i ) Total f.u. number in chains in statei - D=h _i /M ₀ Extent of reaction in statei - D _A ^* = _i / _A,i Extent of reaction of A f.u. in chains in statei - D _B ^* = _i / _B,i Extent of reaction of B f.u. in chains in statei - D ^*=2 _i / _i Extent of reaction in chains in statei - L _x (AA-BB)_x-1-AA type chain x-mer;x=1,2,3,... - L _x BB-(AA-BB)_x type chain x-mer;x=0,1,2,... - L _x (AA-BB)_x type chain x-mer;x=1,2,3,... - N _x Number of type x-mers - N _x Number of type x-mers - N _x Number of type x-mers     

Dielectric properties of moist CaCO3 filled polyethylene composites

The capacitance and the dielectric loss tangents of CaCO₃ filled polyethylene composites were studied. Composite samples, prepared by polymerizing ethylene on the surfaces of fillers, pre-treated by polymerization catalysts, were compared to normal mechanical mixtures. Dielectric dispersion,, and loss, , proved to be sensitive to heating or vacuum treatment. Investigation of samples under conditions of different relative humidities showed that the dielectric dispersion is due to adsorbed water. Both and increased with decreasing frequency and the ratio of loss and dispersion was nearly constant. Dielectric data measured at different relative humidities could be represented by a single Cole-Cole plot. Samples soaked in water for different periods yielded qualitatively similar but quantitatively different Cole-Cole plots. Composite samples showed higher losses at similar humidities.Possible interpretations in terms of a molecular relaxation model, an interfacial relaxation model, including a charged double layer mechanism, percolation theory and the universal response theory were examined, but none was able to fully explain the observed phenomena.     

Dielectric properties of cleaned and monodisperse polystyrene latexes in microwaves

The dielectric behavior (, ) of three well-cleaned monodisperse polystyrene latexes having the same particle size and the same number of chemically-bound surface groups has been studied at a fixed microwave frequency (9.4 GHz), as a function of temperature and surface group (SO ₄ ^– , COO^–, OH).A large dielectric relaxation was observed in the sulfate-stabilized latex, which has the most polar surface end-group. The anomalous behavior in the thermal dependence of the hydroxyl and carboxyl-stabilized latexes (the OH latex being more pronounced than the COO^– latex) may originate from differences in the experimental conditions used for the preparation of such polymer colloids, or due to the presence of ionic species.On the basis of various dielectric models, the apparent volume fractions of the latexes were calculated. The amount of bound water around the latex particle was quantitatively correlated to the polarity of surface end-group (SO ₄ ^– > COO^– > OH). The differences between the calculated and actual values were not only a reflection of the thickness of vicinal water, but could also be indicative of the presence of oligomeric species in the suspension's medium (serum) of the latex. The permittivities of hydrated particle and of bound water were obtained with a non-linear iterative procedure.     

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     

Gas permeability of block copolymers of styrene and butadiene

The permeability of styrene-butadiene block copolymer foils with different composition prepared by casting and pressing has been investigated for the gases Ar, CO₂, and CH₄ at pressure difference of 400 mbar and at the temperature range 298 T [K] 333.The permeation process can be described by the solution diffusion mechanism. The diffusion coefficients decrease in the sequence of the gases Ar, CO₂, and CH₄ and the solubility coefficients increase in the sequence Ar, CH₄, CO₂.The dependence of the permeability on the composition of the block copolymer can be interpreted by the help of percolation theory and the effective medium theory. It follows the critical volume fraction of the percolation of the transport phase _PB ^c (= 0,23) and the coordination numberz (= 4) giving an information concerning the multiphase structure of the block copolymer.Presented in part at the 33^rd Annual Meeting of the Colloid-Gesellschaft, Graz, Austria, September 14–16, 1987.     

Phase diagram of the system dihexadecylphosphatidylcholine/dihexadecyl-phosphatidic acid/water/NaOH at pH=14

Differential-scanning-calorimetry, freeze-fracture electron microscopy, and³¹P-NMR spectroscopy were used to study the lyotropic and thermotropic properties of the system dihexadecylphosphatidylcholine/dihexadecylphosphatidic acid/water/ NaOH in dispersion with excess water at pH=14. The phase diagram showed that both phospholipids are demixed nearly completely in the gel phase. The coexistence of theP and theB -phase in the mixtures was pointed out in the freeze-fracture electron micrographs by the ripple structure (P -phase) and by the lamellar structure (B -phase).     

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.     

Theory of swelling of a crosslinked substance in equilibrium with a pure solvent in various phases. Part II: The variation of the pressure

A theory of swelling is presented which describes the equilibrium swelling of a body in a solvent in its various states. The pressure dependence of the pressure-concentration swelling curves is treated for the swelling agent occurring in the liquid, crystalline or vapor phase. The slopes of the pressureconcentration swelling curves are dependent on the differential volume of dilution of the solvent and, additionally, on the volume changes of vaporization, crystallization, and sublimation of the solvent corresponding to the state of the swelling agent. At the melting and boiling pressure of the swelling agent the swelling curves change their slopes with a discontinuity, which is most distinct at the evaporation transition. By measurements of the slopes of the swelling curves at the transition pressure the derivative ₁/w₁ at constant temperature and pressure, which is the change of the chemical potential of the solvent with its weight fraction, is obtained. Thus, a further equation is given to test statistical theories at the transition pressures. Simultaneous variations of the swelling with changes of temperature are also treated.     

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.     

X-ray diffraction studies on homologous thallium soaps below the temperature range of the neat phase 1. Calculation and comparison of the structure parameters of unit cells

The results of X-ray diffraction patterns of homologous thallium soaps TlC _n (n-8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20 and 22) in dependence on the temperature showed that the structures of the phases below the temperature range of the liquid-crystalline neat phase (so called phase C₁, phase C₂, phase I, phase II) are crystalline-like, not liquid-crystalline.As function of the chain length of the fatty acid group, we found the following phase sequences to be a function of temperature: TlC₈: phase Ineat phase: TlC₉–Tl₁₄: phase C₂phase IIphase Ineat phase; TlC₁₅, TlC₁₆: phase C₁phase IIphase Ineat phase; TlC₁₇–TlC₂₂: phase C₁phase IIneat phase.From the X-ray patterns of the thallium soaps were calculated the lattice parameters and the unit cells of these homologues at various temperatures. The comparison between the lattice parameters of the homologues showed, surprisingly, that these parameters were independent of chain length and temperature. This X-ray data are the basis for the following development of structure models of the phase C₁, phase C₂, phase I, and phase II, including the neat phase (see Part 2).     

The acceleration of decomposition of potassium persulfate in the presence of sodium dodecyl sulfate and polymer particles as a model of emulsion polymerization system

The decomposition rates of potassium persulfate (KPS) in aqueous solutions containing sodium dodecyl sulfate (SDS) in the presence of polystyrene or poly(methyl methacrylate) particles as models of emulsion polymerization systems were measured by isotachophoresis. Free SDS molecules dispersed in the monomolecular state had an ability to accelerate the KPS decomposition, but SDS molecules adsorbed onto the polymer particles did not accelerate it.Part CXX of the series of Studies on Suspension and Emulsion     

Torsional potential and strain energy distribution in an extended chain under stress

Torsional potentialV() for the single bond transformation in an extended hexadecane, subjected to elongation, has been determined by molecular mechanics calculations. The stored elastic energy significantly modifies the potentialV(), the conformational energies and the barriers of transition. Apart from the soft torsional coordinate, elastic energy is also dissipated considerably by bond stretching and angle bending. Maximal variations of the valence coordinates occur in the vicinity of the torsional defect and dampen along the chain. At higher elongation, the gauche minimum on the potentialV() disappears and the calculations predict the abrupt gauche to trans transition. The energetics of torsion of a deformed chain are compared with the experimental data on the hydrodynamic extension of polymers in dilute solution by elongational flow. The calculations also provide details of a single bond transformation mechanism at conformational interconversions in a long chain, proposed by Helfand.