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.     

The molecular weight dependence of intrinsic viscosity of rod-like micelles of dodecyldimethylammonium chloride

It is shown that the non-linear logarithmic dependence of the intrinsic viscosity on the molecular weight for rod-like micelles of dodecyldimethylammonium chloride (as reported by Ozeki and Ikeda [1]) can be interpreted in terms of the Yamakawa-Fujii theory of worm-like chains. Characteristic parameters of the micelles are estimated: persistence length (a=14 nm), linear mass density (M _L=4800 nm^–1), diameter (d=3 nm), molecular pitch (b=0.052), and the number of surfactant chains in a layer of rod-like micellen=12. The results are compared with those derived from light-scattering measurements.     

Longitudinal volume viscosity of 1,4 cis polybutadiene

Volume flow of 1,4 cis polybutadiene (1,4 cis PB) of ¯M _n =311.900,T _g =156 K, andT _m =266 K, has been measured.Elastic modulus of the elastic wave, longitudinal volume viscosity, initial longitudinal volume viscosity, and retardation times are described at compression rates of ca. 1.0 to 200.0×10^–5 s^–1, and at temperatures of 293 K to 373 K, and pressures up to 150 MPa.Longitudinal volume viscosity decreases with increasing compression rate, and with decreasing volume deformation, the behavior being in all cases a typical non-equilibrium one. Longitudinal volume viscosity decreases with increasing temperature (except at 293 K), the volume flow activation energy being of about 18.2 KJ/mol.     

Effect of protein content on the surface activity and viscosity of emulsan

Emulsan, produced byAcinetobacter calcoaceticus RAG-1, consists of a lipoheteropolysaccharide-protein complex. The amount of protein in the complex depends on the purification procedure. Maximum hexadecane-in-water emulsifying activity of emulsan was obtained with preparations containing 8–16 % protein. Neither deproteinized preparations (apoemulsan) nor protein-rich preparations emulsified hexadecane-in-water; however, mixtures of these preparations (containing 10–15 % total protein) were potent emulsifiers.Emulsifying activity was also obtained with a mixture of apoemulsan and polysaccharide-free emulsan protein. The stimulatory role of protein in the activity of emulsan was also demonstrated by pronase treatment of the complex. The presence of protein in the complex was important for lowering interfacial tension between hexadecane and water. Apoemulsan solutions showed _i values of 30 mN/m whereas, emulsan containing more than 6% protein showed values of 13–15 mN/m. Viscosity studies showed that: (i) The higher the protein content in the complex, the lower its intrinsic viscosity, indicating that association of protein with the polysaccharide backbone results in less extended conformation; (ii) the complex appears to be stable between 30 ° and 80 °C; and (iii) mixtures of apoemulsan and emulsan had intrinsic viscosities close to the value predicted from addition of the weight-fraction contribution of the individual components. The synergistic emulsifying activity of emulsan mixtures is explained in terms of surface tension lowering by the protein component and formation of stable interfacial films by the high molecular weight polysaccharide component.Preliminary results of this work were presented at the 5th International Conference on Surface and Colloid Science, Potsdam, N.Y., June 1985.     

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.     

Influence of sodium sulfate or sodium sulfite on the solubilization of benzylalcohol in cationic micellar solutions

The enthalpy of benzylalcohol (BzOH) solution has been determined as a function of alcohol concentration in aqueous trimethyltetradecylammonium bromide (TTAB) solutions in the presence of sodium sulfite or sodium sulfate up to high salt concentration. The electrolytes studied do not seem to induce TTAB sphere-torod transition at least up to 0.6 mol/kg of salt. Comparison with the enthalpic behavior of BzOH in sodium dodecylsulfate solutions and with that of 1-pentanol in both cationic and anionic micellar solutions suggests that the solubilization of BzOH in TTAB solutions is specifically favored by intramolecular interactions between alcohol molecules within the cationic micelles. The replacement of the bromide counterions by the sulfite or sulfate ions has been studied using potentiometry with an ionselective electrode in the case of trimethylhexadecylammonium bromide (CTAB). No difference could be detected between the effects of either divalent anions on the rate of change of the bromide ion-condensation with the salt/surfactant concentration ratioR. The degree of counter-ion condensation on micellar surface depends not only on theR values, but also on the total surfactant concentration.     

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).     

Mixed micelles of tetradecyltrimethylammonium bromide and chlorhexidine digluconate in aqueous solutions of isopropyl alcohol

The influence of isopropyl alcohol (IPA) on the size and composition of the mixed micelles in mixtures of tetradecyltrimethylammonium bromide (TTAB) and chlorhexidine digluconate (CG) has been determined as a function of the composition of the systems. The addition of 0.5 M and 1.0 M IPA had little significant effect on the composition of the mixed micelles as determined both by analysis of critical micelle concentration (CMC) data using a theoretical treatment based on excess thermodynamic quantities and by an empirical treatment of conductivity data. Static and quasielastic light scattering measurements showed a progressive decrease of the aggregation number and hydrodynamic radius of TTAB micelles on addition of IPA, but minimal changes in the properties of the small CG aggregates. The results show that the micellar weight in the TTAB/CG/IPA solutions is determined by the ratio of the surfactants in the system and for each TTAB/CG ratio decreases on addition of IPA.     

The spinnability of viscoelastic solutions of tetradecyl- and hexadecyl-trimethylammonium salicylates

The spinnability was measured for aqueous viscoelastic solutions of tetradecyl- and hexadecyltrimethylammonium salicylates (C₁₄TASal, C₁₆TASal) in the absence and presence of sodium salicylate (NaSal) and sodium bromide (NaBr). The spinnability is classified into two types, D and C. While the intrinsic drawing length in type D is proportional to the drawing velocity, the drawing intrinsic length in type C decreases with the drawing velocity or is independent of it. The spinnability changes from type D to C, as the drawing velocity and the surfactant concentration increase, and the temperature lowers. The effect of salt is different between NaSal and NaBr. It can be assumed that a pseudo-network structure composed of rod-like micelles is formed in viscoelastic and spinnable surfactant solutions. Then, the spinnability depends on the balance between the elasticity and the viscosity in which the structure results.     

Small angle X-ray scattering study of an extremely elongated micelle system of CTAB-p-toluidine solution

Whenp-toluidine is added to an aqueous solution of CTAB, a remarkable increase of viscosity is accompanied by a spectacular elasticity. We detected the existence of extremely elongated rod-like micelles in electron micrographs. SAXS measurements indicate a closely packed array of cylindrical rod-like micelles, brought about when solutions flow through a thin capillary. A scattering maximum ofd=160 Å almost corresponds to the distance between the nearest neighbours of the cylindrical rod-like micelles. This value agrees with the diameter measured on electron micrographs. The second broad peak (d=75 Å) is assigned to a subsidiary maximum of the shape function of the cylinder with infinite length.     

On the shape of giant micelles in aqueous solutions of cetyltrimetylammoniumbromide (CTAB)

Low-temperature electron microscopy was used to image fracture faces of shock-frozen aqueous solutions containing the very large micelles of CTAB existing in the presence of N-methyl-N,N-diphenylamine (MDPA) and 9-anthracene carboxylic acid (9-AC) as solubilizates. When MDPA is present, large globular micelles are formed which have total aggregation numbers of the order of 10⁵ and are seen to be clusters of smaller disc-like structures containing some thousand CTAB-units. Thread-like features are visualized in solutions containing 9-AC which is known to induce the formation of micellar rods.     

The flexibility of rodlike micelles in aqueous solutions and the crossover concentrations among dilute,semidilute, and concentrated regimes

A flexibility parameter, the persistence length, has been evaluated from the radii of gyration and the contour lengths for rodlike micelles of heptaoxyethylene alkyl ethers (C _n E₇,n=12, 14, 16) and tetradecyldimethylammonium chloride (C₁₄DAC) and bromide (C₁₄DAB) at the observed crossover concentrations between dilute and semidilute regimes. The persistence length range is 43–73 nm, except for C₁₂E₇, for which it is 32 nm. The crossover concentrations between dilute and semidilute regimes for the semiflexible rodlike micelles calculated according to Ying and Chu as a function of the molecular weight, the contour length, and the persistence length are consistent with the observed values. The crossover concentration between semidilute and concentrated regimes was, on the other hand, calculated by using the same micelle parameters, including the value of thickness of cross-section of the rodlike micelles. The obtained values are at variance with the observed values. This means that rodlike micelles in semidilute and concentrated solutions might differ in size and/or flexibility from those in dilute solution.     

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.     

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     

The effect of particle concentration on zeta potential in extremely dilute solutions

The electroporetic mobility of hexadecane particles in water and in very dilute CTAB solutions was measured. The technique of microelectrophoresis was applied. Zeta potential was calculated according to the Hückel formula, applying Henry's correction factors. Electrokinetic charge density was calculated according to the formula used by Delgado et al., and previously discovered empiricaly by Loeb et al. and derived mathematicaly by Ohshima et al. It was found that the particle concentration in emulsion limits their charge in solutions of very low ion concentration (10^–7:10^–6 M), because the greater the particle concentration, the smaller the extent of the ions adsorbed at the surface of one particle. The zeta potential was found to be independent of particle concentration if the ratio of the number of bulk ions to particle number is not lower than 1.6×10⁶. This ratio depends on particle size, and the value 1.6×10⁶ relates to particles of diameter 1.6 m.     

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.     

An investigation of aging aqueous poly(vinyl alcohol) solutions by the light scattering method

Aqueous poly(vinyl alcohol) solutions of various concentrations were investigated. The aged solutions were diluted and then analyzed by the light scattering method, size exclusion chromatography, and viscometry. It was found that a relatively small quantity of supermolecular formations arise during aging; they are dispersed in the molecular solution of the predominant part of the polymeric material present. The amount of these aggregated structures and their formation rate increase with concentration of the aging solution.     

Small-angle neutron scattering on shear-induced micellar structures

Small-angle neutron scattering (SANS) experiments on sheared aqueous surfactant solutions of tetradecyltrimethylammoniumsalicylate (TTMA-Sal) are reported. A5-mM-solution without shear shows a weak correlation peak at a momentum transfer of 0.09 nm^–1 which has its origin in the micellar interaction. For shear rates above a threshold value of =40 s^–1 the scattering pattern shows an irregular increase in anisotropy. The analysis of the anisotropic pattern reveals the existence of two types of micelles: Small rodlike micelles which are weakly aligned and very large rodlike aggregates which are strongly aligned and which are present above the threshold value of. The two micelles are in equilibrium with each other and the equilibrium shifts with increasing shear rate to the side of the large oriented micelles.     

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     

Characteristics of rodlike micelles of cetyltrimethylammonium chloride in aqueous NaCl solutions: Their flexibility and the scaling laws in dilute and semidilute regimes

Static light scattering has been measured for aqueous NaCl solutions of cetyltrimethylammonium chloride (CTAC) at 25 °C. While spherical micelles are formed above the critical micelle concentration for 0–1.5 M NaCl solutions, rodlike micelles are formed at NaCl concentrations higher than 1.18 M.The aggregation number of rodlike micelles increases markedly with increasing NaCl concentration, and it is as large as 11400 in 4.0 M NaCl. Long rodlike micelles are semiflexible and behave like wormlike chains. Their contour length and persistence length have been calculated as 630 and 46.4 nm, respectively, in 4.0 M NaCl.Rodlike micelles overlap and entangle together to form a network in semidilute solutions above a threshold micelle concentration. The radius of gyration of the blob can be scaled for its molecular weight with the exponent, 0.55, coinciding with that for isolated rodlike micelles in dilute solutions. The scaling laws for the reciprocal envelope of light scattered in the semidilute regime and for the molecular weight and the radius of gyration of the blob are also discussed with reference to the micelle concentration.