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     

Thermotropic gelation of ovalbumin 1. Viscoelastic properties of gels as a function of heating conditions and protein concentration at various pH values

A study has been undertaken of stress relaxation in ovalbumin thermotropic gels with a concentration of 8–20%, depending on time and temperature of heating (respectively, 20–60 min, 70°–110°C), at pH 2.5–10.0. In all instances, the dependence of the initial gel elasticity modulus on heating has a single maximum. Gelation conditions corresponding to this maximum are considered optimal. Optimal gelation time is 30 min, regardless of pH. On the other hand, the optimal heating temperature depends on pH. To the right and left of the isoelectric point of protein (2.5pH<4.0 and 5.5G) of gels on heating conditions, pH and protein concentration (X ₁,X ₂,X ₃,X ₄), as well as on time of relaxation (t) may be generally described asG(X ₁,X ₁,X ₁,X ₁,t)=G _e(X ₁,X ₂,X ₃,X ₄)f(t), whereG _e is the equilibrium value of the elasticity modulus, and f(t) the relaxation function. Thus, a change in the parameters only affects the value of the equilibrium elasticity modulus, and exerts no effect on the relaxation time spectrum. For this reason, all the relaxation curves obtained may be transformed into two normalized relaxation functions:f(t)=f(t)/f(1)=G(X ₁,X ₂,X ₃,X ₄,t)/G(X ₁,X ₂,X ₃,X ₄, 1)Each of these normalized functions corresponds to one of the homologous groups. Rheological similarity of gels in each homologous group evidently points to their structural similarity. Invariance of the gel relaxationproperties with regard to protein concentration, leads to a concentration dependence of the equilibrium modulus at various pH values. These dependences are curvilinear on a double logarithmic scale. The slope of the curve exceeds 2 in the entire concentration interval studied. In other words, the dependences obtained cannot be described by the usual law of squares. On the other hand, they adequately match Hermans theoretical relation for a network formed by random association of identical polyfunctional particles without cyclization. This simple model evidently gives a true picture of the major regularities of thermotropic gelation for ovalbumin. An agreement between this theory and experiment was achieved for a protein concentration ofC ^*=6.0±1.0% at the gel point regardless of pH. Invariance of gelpoint position with regards to pH demands further confirmation.List of symbols T _h,t _h heating temperature and time - T _h ^* ,t _h ^* optimal heating temperature and time - C protein concentration - C ^* protein concentration in gel-point - G relaxation modulus - G _e equilibrium modulus - f(t) relaxation function - t time of relaxation - f(t) normalized relaxation function - fT _A (t), f _B (t) normalized relaxation functions of groups A and B - G ₁ T _h,t _h-reduced modulus - G ₂ T _h,t _h, pH-reduced modulus - G ₃ C-reduced modulus - b ₁ T _h, t_h reduction parameter of modulus - b ₂ pH reduction parameter of modulus - b ₃ C reduction parameter of modulus - W_g gel-fraction     

The chain length dependence of self-diffusion in melts of polyethylene and polystyrene

The self-diffusion coefficients in melts of polyethylene fractions and polystyrene standards were measured by the NMR pulsed field gradient technique and compared with those measured by other techniques. The data agree very well if one takes into account the molar mass distribution of the samples and the free volume of the matrix. For molar masses much higher than the critical molar massM _c, reptation is confirmed,D M ^–2 holds. BelowM _e=M_c/2 the self-diffusion coefficients corrected for constant free volume show approximately the dependenceD M ^–1 confirming Rouse-like diffusion. This result was also obtained by investigating the self-diffusion of the molecules with different molar masses of a polyethylene fraction with a rather broad molar mass distribution aroundM _e andM _c, i. e. diffusion in a constant matrix. In the molar mass region betweenM _c and about 3 ·M _c the observed molar mass dependence of self-diffusion can be explained by tube formation. The constraint release model of Graessley seems to slightly overestimate the self-diffusion coefficients.     

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     

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.     

Structure relaxation after temperature jumps in homogeneous polystyrene/poly(styrene-co-bromostyrene) blends

Concentration fluctuations in polymer blends and their change after a temperature jump were studied by time-dependent small angle X-ray scattering experiments. Measurements were conducted on homogeneous mixtures of polystyrene and a partially brominated derivative. Structure factors in thermal equilibrium show the form given by the random phase approximation, thus enabling a direct determination of the-parameter and the mean radius of gyration. TheT-dependence of can be understood as the result of superposed enthalpic contributions and a free volume term. In theT-jump experiments, samples were quenched to temperatures near T_g. Relaxation occurs on the time scale of minutes and is nonexponential, becoming slower with time. Initial relaxation rates increase with increasing scattering vectorsq in accordance with theoretical predictions.     

On the theory of adsorption kinetics of ionic surfactants at fluid interfaces 3. Generalization of the model

It was shown that, in the case of adsorbing ions, the Boltzmann equation cannot be applied in its classical form, but has to be modified by considering the flux of adsorbing ions. From the comparison with the adsorption of nonionic surfactants a ratio results which is the measure of deceleration of adsorption kinetics due to the electric double layerr=K(y _s)/(t). At highr-values the electrostatic deceleration controls the adsorption kinetics process.     

Polymer adsorption on fine particles; the effects of particle size and its stability

The effects of particle size on polyacrylamide (PAAm,M _w =59×10⁴, 500×10⁴) adsorption were investigated using a series of well-characterized hematite (-Fe₂O₃) dispersions. The -Fe₂O₃ particles with highly monodisperse and nearly spherical shape ranged in radius from 23 nm to 300 nm. the maximum amount of PAAm adsorption (M _m ) in each system, showed a steady increase with decreasing particle radius and was influenced strongly by particle concentrations in the medium. Furthermore, it was realized that the diameter of -Fe₂O₃ particles after treatment with PAAm under different particle concentrations decreased with increasing particle concentration. The relation between particle concentration in the medium and particle size after treatment was also influenced by the medium pH, i.e., at the medium pH close to the isoelectric point of -Fe₂O₃ particles (pH^o=9.2), the particle size after treatment increased with increasing particle concentration. All these results suggest that in the system of ultra-fine particles, the mixing process between particle-particle and polymerparticle will play an important role on the conformation of adsorbed polymer layer.     

Determination of the regime in the reverse wilson chamber at critical supersaturation measurements

The pressure in the Reverse Wilson Chamber (RWC) was directly measured at different rates of compression of the gas mixture. It was shown that at compression time in the range from 0.06 to 0.3 s an intermediate, between adiabatic and isothermal, process took place in the chamber. To obtain the relative pressure increase P _m /P _at from the values of the relative gas compression V/V, a calibration of the experimental set-up was carried out. The calibration showed that the values of critical supersaturationSc for water condensation on hexadecane, estimated for intermediate regime of the gas compression, were reduced with respect to the values calculated when the adiabatic regime was assumed. This fact confirmed the conclusions made earlier [1–3] that the classical theory was not applicable in this case of heterogeneous phase formation and that the line tension < 0 should be taken into account. Moreover, in an atmosphere of very pure argon (instead of room air [1–3]) the critical supersaturation turned out to be independent of the initial state of undersaturationS _o . The more accurate values obtained for condensation of water on hexadecane were: lnS _c =0.204 (instead of the maximum value obtained earlier: lnS _c =0.26) and=–1.9×10^–5 dyne (instead of=–1.5×10^–5 dyne).     

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.     

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.     

Equilibrium and non-equilibrium melting of branched polyethylene relating to defect incorporation within crystals

New equilibrium melting point data, for polyethylene containing chain defects, are tested in the light of random copolymer predictions. A simplified expression for the melting point depression of random copolymers containing small amounts of non-crystallizable units is derived. Non-equilibrium melting data for rapidly quenched polyethylene samples are also reported. The fusion enthalpyH(X), and the surface free energy _e for crystals containing defects are evaluated using crystallinity, equilibrium meltingtemperatures and X-ray long period data. It is shown that increasing defect penetration within crystals induces a decrease ofH(X) withX in accordance with theoretical predictions. Finally _e is, similarly, shown to decrease with increasing number of chain defects attached to the crystal surface.     

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).     

Interfacial effects on the ageing behavior of high density polyethylene filled with glass spheres

The stress relaxation and creep behavior of unfilled high density polyethylene (HDPE) and HDPE filled with untreated and surface-treated glass spheres were measured at room temperature. A silane-based coupling agent capable of providing a covalent bond between HDPE and the glass spheres was used for the surface-treatment. Two different amounts of the coupling agent were employed giving silane layers on the fillers with different thicknesses. The effect of ageing time at room temperature on the viscoelastic properties after quenching from 100 °C to room temperature in ice water was also investigated. The effects of the surface treatment of the fillers and the ageing time was characterized by means of the internal stress ( _i ) concept. The _i -value increased with the degree of interaction of the filler/matrix interface and the ageing time. It was here not possible to superimpose the different flow curves with regard to the ageing time with sufficient accuracy. This is due to the variation of _i with ageing time. The surface-treatment of the filler had a marked effect on the creep behavior at high applied stress levels and on the ageing behavior of the composites, presumably due to the formation of an interphase region close to the filler surface with different properties and different ageing characteristics than that of the bulk of the matrix.     

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.     

The effect of segment length and concentration on dielectric properties of polypropyleneoxide-based polyurethanes

Three series of segmented polyurethanes based on MDI, variable chain extender, and polypropylene oxide of MW=1000, 2000, and 3000 were synthesized and their dielectric behavior examined.Dielectric relaxations in the segmented polyurethanes were investigated between –150°C and +150°C in the 100 Hz to 10 kHz range. In general, three transitions, designated as, , and were observed, and ascribed in accordance with calorimetric relaxations to glass transitions of the hard and soft segments, and Shatzki-type motions, respectively. The effect of structure variables such as soft segment size, type of chain extender (ethylene glycol, butane diol, and hexane diol) and soft segment concentration, as well as the effect of interaction of the phases on dielectric properties was discussed. It was found that a certain degree of phase mixing exists in all series, detected by the variation of theT _g of the soft segment with soft segment concentration, contrary to DSC results, which was ascribed to thermal treatment prior to the dielectric measurements. It appears that interfacial polarization becomes important only above the transition temperature.     

Determination of the surface free energy of modified carbon fibers and its relation to the work of adhesion

Surface free energy of various carbon fibers was determined by tensiometric method in three different procedures. The dispersive _s ^d and the nondispersive _s ^p components were separately determined by contact angle measurements in two-phase system, formamide-n-alkanes. The _s ^p increased by oxidation and decreased by hydrogen reduction, while the _s ^d remained almost constant.The _s ^p value determined from contact angle of water/ethyleneglycol solution tended to become higher. The critical surface free energy was in harmony with the total free energy determined from formamide-n-alkanes system as long as liquids were properly selected. The formation of oxygen-containing functional groups was evidenced by ESCA, and the surface [O]/[C] ratio was related linearly to the surface polarity defined by _s ^p [ _s ^d + _s ^p ] Oxidation in liquid phase resulted in the formation of both hydroxyls and carboxyls, while only hydroxyls were formed in gas phase. The interfacial shear strength of the fiber-epoxy resin could be closely correlated with thermodynamical work of adhesion calculated on the basis of surface free energy and its component.     

Steric repulsion of polyoxyethylene groups for emulsion stability

Rapid coalescence was studied on liquid paraffin emulsion stabilized with a series of poly(oxyethylene) dodecyl ethers [C₁₂H₂₅ (EO),n=1, 2, 3, 4, 5, 6, 7, 8] and of poly(oxyethylene) nonylphenyl ethers [C₉H₁₉(EO) _n ,n=2, 4, 5, 6, 12]. The turbidity of emulsion was measured as a function of the solution pHs at constant ionic strength of 0.1 mol dm^–3.As a result, it was found that the emulsions (which were formed with C₁₂H₂₅(EO) _n surfactants having less than four oxyethylene groups, or with C₉H₁₉ (EO) _n surfactants having less than six oxyethylene groups) brought about rapid coalescence in the bulk pH between 2.03.5, which corresponded to the zero point of charges for the emulsions of the present systems. According to the Tadros treatment for emulsion flocculation, the total flocculation potennual was estimated as a function of the distance relative to the number of oxyethelene groups in the surfactants. The critical coalescence energy was obtained as –343 ×10^–19 J for the C₁₂H₂₅(EO) _n surfactants and –2.14×10^–19) J for the C₉H₁₉ (EO) _n surfactants. Furthermore, the formation of a hole for coalescence was estimated under the simple assumption that the coalescence was caused only by the energy dissipation.     

Crystal structure of ionic and non-ionic surfactants based on polyoxyethylenated dodecanol: A13C-CP-MAS-NMR and x-ray investigation

Crystal structure of monodisperse non-ionic surfactants having the general formula C₁₂H₂₅O–(CH₂–CH₂–O)_nH (C₁₂E_n),n=7,9, 10, 15, 16 and ionic derivatives, C₁₂H₂₅–O–(CH₂–CH₂–O)_n–CH₂COONa (C₁₂E_nC),n=3,4,5,6,7,9, 12 has been investigated by¹³C-CP-MAS-NMR and x-ray diffraction. A structural model, in which aliphatic and polyether segments are segregated in bilayers stacking parallel to the elongation direction of the molecules, fits the experimental data for both series. The experimental values of the repeat distance along the stacking directiond(001) are linearly dependent onn and the slope is nearly equal to twice the repeat distance of7/2 helix conformation, which is typical for crystalline polyethyleneoxide. The values ofd(001) agree very well with the values expected for the C₁₂ segment in a planar zig-zag conformation, which is tilted with respect to the polyerther segment (7/2 helix conformation) in such a way that both the aliphatic and the polyether regions adopt the mass density of the corresponding crystalline compound. Two additional phases have been detected for C₁₂E_nC. One of them is probably characterized by the planar zig-zag conformation of the polyether chain. The meader model, previously proposed in the literature for surfactants containing polyethylene oxide segments is inconsistent with the obtained experimental data.     

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.