Dynamics of phase separation and critical phenomena in polymer mixtures

The phenomenological mean-field theory for statics and dynamics of polymer mixtures is described, generalizing the approaches of Flory-Huggins, Cahn-Hilliard and de Gennes. Predictions are made for critical behavior, spinodal decomposition and homogeneous nucleation. The validity of the mean-field approximations is discussed with Ginzburg criteria. The results of the theory are compared to computer simulations and recent experiments.Invited talk delivered at the Tagung der Deutschen Physikalischen Gesellschaft, Fachausschu\ Polymerphysik, Kaiserslautern, 12–14 March 1986, and at the Gordon Research Conference on Polymer Physics, Andover, New Hampshire, 14–18 July 1986.The author is grateful to Dieter W. Heermann, Alla Sariban, Harry L. Frisch, Josef JÄckie and Thomas Schichtel for their fruitful collaboration on this research described in this review. He thanks them and Arthur BaumgÄrtner for allowing to present partially unpublished material, and for stimulating discussions. Furthermore the author has benefitted from discussions with P. G. de Gennes, P. Pincus, H. Sillescu and G. R. Strobl. This research is supported in part by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 41.     

The rheological properties of concentrated cetyltrimethylammonium bromide-salicylic acid solutions in water

Data on the rheological properties of the hexadecyl-trimethylammonium salicylate system (CTAB-SA) in water are reported. Three concentrations were used (0.1, 0.01, and 0.001 M). For the highest concentration, the effect of temperature on the rheology was studied in detail.The rheology of the 0.1 M CTAB-SA solution indicates a very uniform micellar size. By contrast with concentrated polymethyl methycrylate dispersions studied by the author, there was a strong divergence between the viscosity-shear rate and viscosity-frequency data, although the plateau low shear rate and frequency values agreed over a wide range of temperature. This effect could be explained by a shear rate dependent diffusion constant. The large temperature variation of the plateau viscosity and elasticity modulus values could be explained by a combination of micellar number concentration and flexibility changes as the temperature varies.At lower concentrations, the rheological data shows evidence of polydispersity in micellar size. Strong shear thickening and extensional viscosity effects are also evident, probably due to micellar overlap and cluster formation in strong shear fields and the alignment of the very long micelles in elongational flow. The shear thickening effects take some 200 s to relax (0.01 M solution). Recovery of the elasticity after shearing the 0.1 M solution is rapid (a few hundred milliseconds).     

The association of urethane-polyethyleneoxide (HEUR) thickeners,as studied by NMR self-diffusion measurements

The concentration and molecular weight dependence of the self-diffusion coefficient (D _self) of associative polymers of HEUR-type in aqueous solution have been investigated using FT-PGSE-NMR technique. The idea of three-dimensional network formation as a result of aggregation of the hydrophobic end-groups of the polymer in junctions is supported through the observed dramatic lowering ofD _self with increased concentration. The network-formation efficiency depends on the polymer molecular weight as well as the hydrophobicity of the end-groups.A double logarithmic dependence of the self-diffusion coefficient versus concentration (c) has been observed:D _selfc ^–a1,a2 . The first exponent,a ₁, is valid at low concentration, <1% polymer per weight solution, and ranges from 0.5 to 1, whereas the second exponent,a ₂, describing systems of higher concentration, ranges from 2 to 2.7.     

The complex rheological behavior of an aqueous cationic surfactant solution investigated in a Couette-type viscometer

In this paper the behavior of an aqueous surfactant solution in a rotational Couette viscometer is investigated. It is shown that this behavior depends strongly upon time, upon the way in which the flow curve is obtained (with increasing or decreasing shear rate), upon the temperature, and upon the concentration of the solution. Furthermore, the results also reveal a pronounced dependence upon the size of the actual measuring system used. It is shown that the slip-velocity concept is not applicable to explain this dependence.     

The behaviour of drag-reducing cationic surfactant solutions

The behaviour of two types of drag reducing surfactant solutions was studied in turbulent flows in pipes of different diameters. Our surfactant systems contained rod-like micelles; they consisted of equimolar mixtures ofn-tetradecyltrimethylammonium bromide,n-hexadecyltrimethylammonium bromide, and sodium salicylate. The structure of the turbulence was studied using a laser-Doppler anemometer in a 50 mm pipe. In the turbulent flow regime both surfactant solutions exhibited characteristic flow regimes. These flow regimes can be influenced by changing the amount of excess salt, the surfactant concentration, or the temperature. Shear viscosity measurements in laminar pipe and Couette flows show the occurrence of the so-called shear-induced state, where the viscosity increases and the surfactant solution becomes viscoelastic. The shape of the turbulent velocity profile depends on the flow regime. In the turbulent flow regime at low Reynolds numbers, velocity profiles similar to those observed for dilute polymer solutions are found, whereas at maximum drag reduction conditions more S-shaped profiles that show deviations from a logarithmic profile occur. An attempt is made to explain the drag reduction by rod-like micelles by combining the results of the rheological and the turbulence structure measurements.     

Self-diffusion of polystyrene in solution 2. Discussion of experimental results on the basis of the reptation mechanism and entanglements

The expressions for polymer self-diffusion in semidilute solutions, theoretically derived from the reptation mechanism, the blob concept and scaling considerations, are discussed and compared against experimental data from the authors' investigations and the literature. In the nonentangled (from viscoelastic data) semidilute solution, the experimentally observed concentration and molar mass exponents are in fair agreement with those derived theoretically. However, a quantitative estimation shows that the experiments cannot be explained by reptation. Experiments with polymer mixtures also give strong evidence against reptation. It is concluded, that in the nonentangled semidilute solution, the polymer self-diffusion is more complicated than simple reptation. This is also supported by recently observed long-range density fluctuations or cluster formation in this concentration region detected by scattering techniques and NMR-PFGT. In the entangled semidilute solution, the self-diffusion data are in accordance with the reptation mechanism; reptation being within a tube having approximately 20 blobs between entanglements.     

Temperature dependence of the non-Newtonian viscosity of elongated micellar solutions

We report in this work new results of the study on the non-Newtonian viscosity of aqueous micellar solutions of cetyltrimethylammonium bromide (CTAB) in the presence of potassium bromide (KBr), in the concentration range where the elongated micelles overlap. The experiments have been performed as a function of the surfactant concentration, temperature and shear rate by use of a Couette-viscosimeter.In the non-Newtonian range, at relatively low surfactant concentration (0.25 M/l), our results show that the flow curves obtained at different temperatures converge to a single liner curve with a characteristic slope varying with the surfactant concentration. These same data can be superposed on a master curve when appropriate reduced variables are used. The shape of the flow curves obtained at different temperatures for a sufficiently high surfactant concentration is similar to that obtained for monodisperse polymer solutions at different molecular weights. The slope obtained of about –1 is also predicted by Graessley's model in the theory of microviscoelasticity based on the concept of entanglement for polymer solutions. However, at surfactant concentration higher than 0.25 M/l our results show an unusual behavior. Above some critical shear rate it is possible to obtain an increase of the apparent viscosity with temperature. One possible explanation of this effect can be found in the increase of the entanglement with concentration coupled with the temperature and direct now effects on scission and recombination rate of the micelles.     

Theory of shear-induced crystallization of polymer melts

In the presented model elements of polymer melt rheology and polymer crystallization kinetics are combined. In particular, the proneness of the melt to the special type of crystallization which is characteristic for shear treatment is supposed to emerge only gradually during shear flow. Following Avrami's early ideas on crystal growth, an induction time is introduced. In principle, the model can be applied to any flow and temperature history. The special case of isothermal flow at constant shear rate is covered in greater detail: A favorable comparison is made with experimental results, as published by Lagasse and Maxwell [10].Dedicated to Prof. J. Meissner on the occasion for his 60th birthday.     

Gaussian approximation for Hookean dumbbells with hydrodynamic interaction: Translational diffusivity

The recently developed Gaussian approximation for the hydrodynamic interaction is used to discuss the translational diffusivity of polymers in dilute solutions undergoing homogeneous flows. For the Hookean dumbbell model, we derive the diffusion tensors associated with (i) the average polymer velocity caused by external forces; (ii) the mean-square displacement of a single polymer caused by the Brownian forces; and (iii) the polymer mass flux caused by concentration gradients. We discuss the model predictions for these diffusion tensors for steady shear flow in detail.This paper was presented at the Frühjahrstagung des Fachausschusses Polymerphysik der Deutschen Physikalischen Gesellschaft in Hamburg (West Germany), March 14–16,1988.     

The rheology and microstructure of charged colloidal suspensions

The effects of electric charge interation and particle correlations on suspension rheology are examined. A one-component fluid analysis using a Smoluchowski equation for the equilibrium structure is applied to charged suspensions of spherical colloids under shear. The frequency dependent modulus and viscosity, predicted as functions of particle and added salt concentrations, are compared with published rheological measurements on model suspensions. Recent improvements in the statistical mechanical theories for the equilibrium microstructure, its nonequilibrium deformation, and the bulk shear stresses are included. The direct electrostatic interaction is found to drive the divergence in the shear viscosity near the liquid-solid phase transition. Extensions of the theory predict the elastic modulus of binary mixtures of charged colloids. Estimates of the primary electroviscous effect, hydrodynamic interactions, and errors in the Yukawa limiting form for the potential and applications of asymptotic theories are presented. Predictions for the rheology based on effective hard-sphere models are found to be reasonable when using a parameter fit from the equilibrium phase behavior. Mean-field mode coupling theories predict larger relaxation times than calculated from the Smoluchowski equation (=SE). A study of binary mixing effects on elasticity shows non-ideal behavior. It is noted that equilibrium structural information can be used to resolve discrepancies between the theoretical predictions and the measured rheology.     

Studies of polymer solvation by dielectric relaxation spectroscopy II: Polyethylene glycol in methyl pyrrolidone

Frequency domain dielectric spectroscopy (30 MHz to 72 GHz) is utilized to study solvation in polyethylene glycol (PEG) — methyl pyrrolidone (MPy) mixtures over the whole mixture range at 20 °C, in particular with PEG 200. Further pure PEGs (200 to 400) and butyl glycol (in the pure state and in benzene and n-hexane solution) are considered for comparison to facilitate the assessment of PEG relaxational behavior. It turns out that the PEG-MPy mixtures can be described in terms of a simple solvation model which takes into account only the bulk and the solvating solvent state. The solvation number per repeat unit is about 0.85 in the dilute solution limit. It decreases gradually with increasing PEG concentration in accordance with a solvation equilibrium model.     

Small-angle neutron scattering of colloidal silica dispersions in a non-polar solvent

Small-angle neutron scattering studies were performed on dilute dispersions of colloidal silica spheres in mixtures of h₁₂- and d₁₂-cyclohexane. The particles consisted of a SiO₂-core and a layer of stearyl alcohol molecules terminally attached with a chemical bond (Si-O) to the particle surface. The contrast variation method was applied to reveal the internal structure of the particles. The matchpoints determined with this method were in accordance with those calculated from the mass density of the particles and the atomic composition, as determined with elemental analysis.For a detailed interpretation of the scattering curves, we assumed that the particles were spherosymmetrical and consisted of two concentric layers. With the relation we derived between the radius of gyration and the reciprocal contrast for such a model, it was possible to determine all the parameters characterizing the particle in terms of this model. The model calculations performed using these parameters fitted very well to the experimental intensities for high contrasts. For lower contrasts, the fit was somewhat less good. This is probably due to random fluctuations in the scattering length density within the particle core.The different radii as found by neutron scattering, agreed very well with those determined using other techniques, such as light scattering (static and dynamic) and electron microscopy.     

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.     

Solubilization of oleyl alcohol by pure and mixtures of surfactants

The solubilization behavior of oleyl alcohol by pure and mixtures of surfactants systems have been studied in terms of the maximum additive concentration (MAC), the solubilizing power, and the particle sizes of micelles with or without oleyl alcohol. The surfactants used are amphoteric (N,N-dimethyl-N-lauroyl lysine, DMLL; N,N,N-trimethyl-N-lauroyl lysine, TMLL; N,N-dimethyl-N-(carboxymethyl)-lauryl ammonium, DMCL), anionic (sodium dodecyl sulfate, SDS) and nonionic (alkyl polyoxyethylene ethers).The maximum additive concentration of oleyl alcohol by pure surfactants is larger by nonionic surfactants than by others.For a nonionic surfactant system mixed with DMLL, the mixing effect of surfactant on the increase in the MAC is not recognized. While, for DMLL mixed with SDS, the MAC becomes larger than that by pure surfactants. This may be attributed to the fact that the large micellar size will result in increasing the maximum additive concentration.     

Far-from-equilibrium fluctuations triggering RNA de novo synthesis

The fluctuations for very low total template concentration (5–10⁴ molecules/cm³) are calculated theoretically for a self-replicating RNA system catalyzed by highly purifiedQ replicase, by means of a center manifold stochastic treatment. The results provide an explanation of the experimental observation that at 0.15 mM nucleoside triphosphate concentration, no RNA can be synthesizedde novo, although the templatedirected synthesis proceeds normally. The role of intrinsic template fluctuations, under far-from-equilibrium conditions; in triggeringde novo (template-free) replication is elucidated.     

Effect of inorganic electrolyte concentration on anionic-cationic adsorption films Part 1. Decylpyridinium chloride + sodium octylsulphonate + sodium chloride

The effect of NaCl on simultaneous adsorption of decylpyridinium chloride (R₁₀PyCl) and sodium octylsulphonate (R₈SO₃Na) on the free surface of their aqueous solutions has been examined. The surface excess of each component was determined on the basis of a suitable form of the Gibbs adsorption equation. The ionic strength effect on the adsorption of particular components of mixtures, as well as on the composition of anionic-cationic films adsorbed from equimolar solutions, is small. This is due to little difference in surface activity of surfactants investigated.     

Shear field modification of strongly flocculated suspensions — Aggregate morphology

Rheological and microscopical studies have been made to elucidate the effects of shear fields on the morphology of concentrated, aggregated model colloids. The models employed are well-characterised, predominantly chargestabilised polymer latices, coagulated by the addition of excess electrolyte. Continuous shear rheological and viscoelastic measurements indicate a very significant decrease in shear yield stress, apparent viscosity and shear modulus following prolonged shearing.Electron microscopy reveals the source of these changes. Freshly coagulated suspensions form networks that are porous, strong and qualitatively similar to simulated structures for diffusion limited aggregation. Following protracted shearing, the network structure is rearranged to yield discrete, tightly packed aggregates with a characteristic size, which is principally a function of the primary particle size.     

Role of ionic species and valency on the steady shear behavior of partially hydrolyzed polyacrylamide solutions

Polyacrylamides are anionic polymers with a large number of charges along the polymer chains. The rheological properties of aqueous polyacrylamide solutions can be significantly modified by varying the solvent environment with the addition of salt. The presence of cations substantially reduces the inter- and intra-molecular interactions of the macroions. It was found that the valency of the cation has a strong effect on the rheological behavior of polyacrylamide solutions, but the size and type of salt have a negligible effect.The reduction in the solution viscosity with di-valent salts (e.g., CaCl₂, MgCl₂, BaCl₂, and MgSO₄) can be as high as an order of magnitude compared with mono-valent salt (KI, KC1, NaCl, and NaBr), depending on the salt concentration and shear rate. An identical viscosity function can be obtained for different types of polyacrylamide solutions by varying the salt content in solution. This interesting feature provides a useful means in the development and preparation of certain ideal fluids for simulation studies of complex flow problems.     

Investigations of the influence on the phase morphology of PP-EPDM-blends on their mechanical properties

This work covers the dependence of the mechanical properties of polymer blends on their composition and their phase morphology. Blends of EPDM-elastomers and polypropylene were prepared covering the whole concentration range. The phase morphology was varied strongly by employing different mixing techniques and its morphology was characterized by means of electron microscopy and light microscopy, as well as by x-ray scattering and calorimetry.Mechanical properties such as the complex shear modulus, the tensile modulus as well as the stress strain behavior were investigated as a function of the composition of the blends and their phase morphology. The experimental finding is that the complex modulus, the tensile modulus, the yield stress, and the ultimate stress are rather insensitive with respect to the phase morphology and vary continuosly with the composition. The elongation at break, on the other hand, as well as the impact strength were found to depend on the phase morphology and to vary discontinously with the composition. One conclusion to be drawn is that one is not always forced to control the phase morphology tightly during processing in order to obtain materials with sufficiently good mechanical properties. Rather, simple theoretical approaches, neglecting details of the phase morphology are frequently able to satisfactorily predict mechanical properties of multiphase blends.