Nonlinear viscoelasticity of polystyrene solutions. II. Non-Newtonian viscosity

The steady shear viscosity η(k) and the stress decay function \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \eta \left({t,k} \right)$\end{document} (the shear stress divided by the rate of shear k after cessation of steady shear flow) were measured for concentrated solutions of polystyrene in diethyl phthalate. Ranges of molecular weight M and concentration c were 7.10 × 10⁵ to 7.62 × 10⁶ and 0.112–0.329 g/cm³, respectively. Measurements were performed with a rheometer of the cone-and-plate type in the range 10^?4 < k < 1 sec^?1. The Cox–Merz relation η(k) = |η^*(ω)|_ω=k was tested with the experimental result (|^*(ω)| is the magnitude of the complex viscosity). It was found to be applicable to solutions of relatively low M or c but not to those of high M and c. For the latter η(k) began to decrease at a lower rate of shear than |η^*(ω)|_ω=k did; the Cox–Merz law underestimated the effect of rate of shear. The stress decay function was assumed to have a functional form \documentclass{article}\pagestyle{empty}\begin{document}$\tilde \eta \left( {t,k} \right) = \sum {\eta _p \left( k \right)e^{ - t/\tau p\left( k \right)} } $\end{document} where τ₁ > τ₂ > …, and the values of τ₁, τ₂ η₁ and η₂ were determined for some solutions. The relaxation times τ₁ and τ₂ were found to be independent of k and equal to the relaxation times of linear viscoelasticity. At the limit of k → 0, η₁ and η₂ were approximately 60 and 20–30%, respectively, of η and the non-Newtonian behavior was due to large decreases of η₁ and η₂ with increasing k. It was shown that η₁(k) may be evaluated from the relaxation strength G₁(s) for the longest relaxation time of the strain-dependent relaxation modulus with a constitutive model for relatively high c–M systems as well as for low c–M systems.     

Nonlinear viscoelasticity of polystyrene solutions. I. Strain-dependent relaxation modulus

Strain-dependent relaxation moduli G(t,s) were measured for polystyrene solutions in diethyl phthalate with a relaxometer of the cone-and-plate type. Ranges of molecular weight M and concentration c were from 1.23 × 10⁶ to 7.62 × 10⁶ and 0.112 to 0.329 g/cm³. Measurements were performed at various magnitudes of shear s ranging from 0.055 to 27.2. The relaxation modulus G(t,s) always decreased with increasing s and the relative amount of decrease (i.e.,–log[G(t,s)/G(t,0)]) increased as t increased. However, the detailed strain dependences of G(t,s) could be classified into two types according to the M and c of the solution. When cM < 10⁶, the plot of log G(t,s) versus log t varied from a convex curve to an S-shaped curve with increasing s. For solutions of cM > 10⁶, the curves were still convex and S-shaped at very small and large s, respectively, but in a certain range of s (approximately 3 < s < 7) log G(t,s) decreased rapidly at short times and then very slowly; a peculiar inflection and a plateau appeared on the plot of log G(t,s) versus log t. The strain-dependent relaxation spectrum exhibited a trough at times corresponding to the plateau of log G(t,s). The longest relaxation time τ₁(s) and the corresponding relaxation strength G₁(s) were evaluated through the “Procedure X” of Tobolsky and Murakami. The relaxation time τ₁(s) was independent of s for all the solutions studied while G₁(s) decreased with s. The reduced relaxation strength G₁(s)/G₁(0) was a simple function of s (The plot of log G₁(s)/G₁(0) against log s was a convex curve) and was approximately independent of M and c in the range of cM <10⁶. This behavior of G₁(s)/G₁(0) was in agreement with that observed for a polyisobutylene solution and seems to have wide applicability to many polymeric systems. On the other hand, log G₁(s)/G₁(0) as a function of log s decreased in two steps and decreased more rapidly when M or c was higher. It was suggested that in the range of cM < 10⁶, a kind of geometrical factor might be responsible for a large part of the nonlinear behavior, while in the range of cM > 10⁶, some “intrinsic” nonlinearity of the entanglement network system might be important.     

Relaxation spectra of concentrated polystyrene solutions

The relaxation modulus G(t) and the stress decay after cessation of steady shear flow were measured on concentrated solutions of polystyrenes in diethyl phthalate. Ranges of concentration c and molecular weight M of the polymer were from 0.112 to 0.329 g/ml and from 1.23 × 10⁶ to 7.62 × 10⁶, respectively. The relaxation spectrum H(τ) as calculated from G(t) for the solution of very high M was found to be composed of two parts. One, at relatively short times, was a broad distribution (plateau zone) with height proportional to c². The second, at the long-time end, was very sensitive to concentration and gave rise to a maximum in H(τ) for very high concentrations. The behavior of H(τ) at long times was examined quantitatively by evaluating the longest relaxation time τ₁⁰ and the corresponding relaxation strength G₁⁰ from G(t) and from the stress decay function, on the assumption of a discrete distribution of relaxation times at long times. The longest relaxation time was approximately proportional to M^3.5, even at relatively low concentrations where the zero-shear viscosity was not proportional to M^3.5. The strengths of relaxation modes with the longest few relaxation times are proportional to the third power of concentration.     

Dynamic mechanical properties of moderately concentrated polystyrene solutions

The storage (G′) and loss (G″) shear moduli have been measured in the frequency range from 0.04 to 630 Hz for solutions of narrow distribution polystyrenes with molecular weights (M) 19,800 to 860,000, and a few of poly(vinyl acetate), M = 240,000. The concentration (c) range was 0.014–0.40 g/ml and the viscosities of the solvents (diethyl phthalate and chlorinated diphenyls) ranged from 0.12 to 70 poise. Data at different temperatures (0–40°C) were combined by the method of reduced variables. Two types of behavior departing from the usual frequency dependence describable by the Rouse-Zimm-Tschoegl theories were observed. First, for M ? 20,000, the ratio (G″ ? ωη_s)/G′ in the neighborhood of ωτ₁ = 1 was abnormally large and the steady-state compliance J was abnormally small, especially at the lowest concentrations studied. Here ω is circular frequency, η_s solvent viscosity, and τ₁ terminal relaxation time. Related anomalies have been observed by others in undiluted polymers at still lower molecular weights. Second, at the highest concentrations and molecular weights, a “crossover” region of the logarithmic frequency scale appeared in which G″ ? ωη_s < G′. The width of this region is a linear function of log c; the frequency dependence under these conditions can be represented by a sequence of Rouse relaxation times grafted on to a sequence of Zimm relaxation times. For each molecular weight, the terminal relaxation time τ₁ was approximately a single function of c for different solvents of widely different η_s. At lower concentrations, τ₁ was close to the Rouse prediction of 6ηM/π²cRT, where η is the steady-flow viscosity; but at higher concentrations, τ₁ was proportional to η/c² and corresponded, according to a recent theory of Graessley, to an average molecular weight of 20,000 between entanglement coupling points in the undiluted polymer.     

Critical molecular weight for onset of non-newtonian flow and upper newtonian viscosity of polydimethylsiloxane

The flow curves of fractionated polydimethylsiloxanes of different molecular weights were obtained over a wide range of shear rates, from 3 × 10^?1 to 4.3 × 10⁶ sec^?1, by use of a gas-driven capillary viscometer designed to decrease the experimental error in high shear rate region. Non-Newtonian flow can occur at molecular weights below the critical molecular weight M_c for the entanglement of polymer chain. The critical molecular weight M′_c for the onset of the non-Newtonian flow is identical with that of the segment of viscous flow. For the polymer of molecular weights from M′_c to M_c, the upper Newtonian viscosity increases with an increase in molecular weight. Above M_c, the upper Newtonian viscosity is almost independent of the molecular weight.     

Rheological properties of rodlike polymers in solution. 2. Linear and nonlinear transient behavior

Rheological and rheo-optical studies are reported for isotropic solutions of the mesogenic rodlike polymer poly(1,4-phenylene-2,6-benzobisthiazole) (PBT). Several PBT samples were used with average contour lengths from 95 to 135 nm. Concentrations were varied over a range just below the concentration C_c for the formation of an ordered (nematic) state. The predictions of a single-integral constitutive equation of the BKZ type utilizing experimental estimates of the distribution of discrete relaxation times is compared with experimental data on the steady-state viscosity η_κ, the recoverable compliance function R_κ, and the steady-state flow birefringence as functions of the shear rate κ, with satisfactory results. The relaxation of the shear stress and the flow birefringence on cessation of steady-state flow at shear rate κ are also compared with the single-integral constitutive equation, and it is found that in the nonlinear response range the data can be superposed over a wide range in κ. The overall behavior is qualitatively similar to that for flexible chains, which can also be fitted by the single-integral constitutive equations over similar ranges of η₀R₀κ, with η₀ and R₀ the limiting values of η_k and R_κ for small κ. Of course, the dependence of η₀ and R₀ on concentration and molecular weight differs markedly for rodlike and flexible-chain polymers.     

Cooperative chain relaxation in miscible polymer blends

Orientation relaxation of dissimilar chains in the molten miscible blends, poly(methyl methacrylate)/poly(vinylidene fluoride) and poly(methyl methacrylate)/poly(vinylidene fluoride-co-trifluoroethylene), were investigated by measuring (1) the change of infrared dichroic ratio with time after the uniaxial stretching of film specimens, (2) the shear stress relaxation spectrum, and (3) birefringence relaxation in shear. The dissimilar polymers showed an identical time variation of the normalized Hermans orientation function. The blend showed a relaxation spectrum with a single characteristic relaxation time τ_c, depending on the blend composition. The birefringence relaxed monotonically, remaining positive. These results suggest that the dissimilar polymers do not relax independently but cooperatively. This behavior may be induced by a constraint due to the specific interactions between the dissimilar polymers, e.g., weak hydrogen bonding. For the cooperative chain relaxation, a third power relationship was found; τ_c/τ_e vprop; (M/M_e),³ where τ_e and M_e are the relaxation time and molecular weight of entanglement strand, respectively, and M is the number average molecular weight in the blend.     

Strain criterion in nonlinear creep and recovery in concentrated polymer solutions

Transient and steady-state rheological data are reported for several anionic polystyrene solutions in tritolylphosphate (1. 6 < cM/ρM_c < 7). Here c is the concentration of the solution, M is the molecular weight, ρ the density of the undiluted polymer, and M_c the molecular weight between entanglements as determined from zero-shear viscosity. The polystyrene used had M_w = 410,000 and M_w/M_n < 1.06. Data are also given for solutions of polyisobutylene and poly(vinyl acetate) with larger M_w/M_n. The results give a critical strain γ′ ∝ c⁻¹ such that linear viscoelastic behavior was obtained in a simple shear deformation with shear less than γ′. A simplified version of the constitutive equation of Bernstein, Kearsley, and Zapas is used with an empirical strain function F (γ) which contains γ′ as a parameter to discuss transient and steady-state behavior in terms of the distribution of relaxation (or retardation) times determined for linear viscoelastic responce. Features of the dependence of the steady-state viscosity η_k, recoverable compliance R_k, the first-normal stress function N_k⁽¹⁾ on shear rate k are discussed in terms of F (γ) and the distribution of relaxation times to conclude that the latter plays a dominant role in the behavior observed in the range of k usually studied. The results predict that the reduced functions η_k/η₀, R_k/R₀, and N_k⁽¹⁾/N₀⁽¹⁾ should depend on η₀R_0k, and that the functional form depends markedly on the distribution of relaxation times, at least in the range η₀R₀k < 10². Comparison with the mechanistic model of Doi and Edwards shows a similar F (γ) but substantial differences in the reduced functions caused by a very narrow distribution of relaxation times in the model.     

Relaxation dynamics of salt‐free polyelectrolyte solutions using flow birefringence and rheometry

Relaxation dynamics of salt‐free, aqueous solutions of sodium poly(styrene sulfonate) (NaPSS) were investigated by mechanical rheometry and flow birefringence measurements. Two semidilute concentration regimes were studied in detail for a range of polymer molecular weights. At solution concentrations c < 10 mg mL, limiting shear viscosity η₀ was found to scale with molecular weight and concentration as η₀ ∼ c^0.5M_w over nearly two decades in concentration. At higher solution concentrations, c > 10 mg mL, a change in viscosity scaling was observed η₀ ∼ c^1.5M, consistent with a change from simple Rouse dynamics for unentangled polyions to near‐perfect reptation dynamics for entangled chains. Characteristic relaxation times τ deduced from shear stress and birefringence relaxation measurements following start‐up of steady shearing at high rates reveal very different physics. For c < 10 mg mL, both methods yield τ ∼ c^−0.42M and τ ∼ c⁰M for c > 10 mg mL. Curiously, the concentration scalings seen in both regimes are consistent with theoretical expectations for salt‐free polyelectrolyte solutions undergoing Rouse and reptation dynamics, respectively, but the molecular weight scalings are not. Based on earlier light scattering studies using salt‐free NaPSS solutions, we contend that the unusual relaxation behavior is likely due to aggregation and/or coupled polyion diffusion. Simultaneous stress and birefringence measurements suggest that in concentrated solution, NaPSS aggregates are likely well permeated by solvent, supporting a loose collective of aggregated chains rather than the dense polymer aggregates previously supposed. Nonetheless, polyion aggregates of either variety cannot account for the inverse dependence of relaxation time on polymer molecular weight for c < 10 mg mL. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 825–835, 1999     

Experimental determination of the relationships among various measures of fluid elasticity

The viscoelastic properties of a 4% solution of monodisperse polystyrene (molecular weight 394,000) in Aroclor 1260 were determined by the following techniques: creep recovery, stress relaxation upon cessation of steady flow, dynamic measurements, and normal stress difference and shear stress measurements in steady flow. All measurements were carried out with cone and plate geometry in a Weissenberg rheogoniometer. The modification of this instrument to perform creep and creep recovery experiments by use of an air-bearing suspension and an air-turbine drive is described. A broad range of shear rates and frequencies encompassing both linear and nonlinear behavior was employed. The elastic behavior is described in terms of the recoverable shear strain s or the steady-state compliance J_e°. The first three techniques gave identical results for J_e° in the range of linear viscoelasticity for which it is defined. The normal stress difference measurements confirmed Lodge's relation s = (P₁₁ ? P₂₂)/2σ₂₁. Reasons for previous experimental disagreement with this result are discussed.     

Dynamical behavior of xanthan polysaccharide in solution

Dilute-solution hydrodynamic data for xanthan biopolymer in water suggest a rodlike molecule of dimensions 15,000 × 20 Å, and molecular weight 2.2 × 10⁶ g/mol. Upon addition of NaCl to this system, the xanthan molecules self-associate to form stable aggregates. The native xanthan conformation can be thermally denatured to a disordered coil which can be stabilized at room temperature in 4M urea. The transition to semidilute solutions is manifested by discrete changes in the concentration dependence of diffusion coefficient and zero-shear viscosity at c ≈ 2.0 × 10^?4 g/mL. At higher concentrations c ≥ 1.0 × 10^?3 g/mL, the light-scattering and shear-viscosity data are qualitatively but not quantitatively consistent with predictions of the dynamical theory of Doi and Edwards for an isotropic entangled solution of rigid-rod molecules. Measurements of latex sphere diffusion in xanthan-water solution show a sudden retardation at c ≈ 1.0 × 10^?3 g/mL, consistent with the cooperative formation of a motionally restricted network of long, thin, rigid fibers. At high shear rates, flow birefringence experiments indicate enhanced ordering of the xanthan chains in the semidilute regime.     

Application of scaling concepts to sedimentation phenomena in semidilute macromolecular solutions

Sedimentation velocity data on polystyrene in a good solvent (toluene) and in a theta solvent (cyclopentane), over a large concentration range are reported. Under good-solvent conditions the exponent β in the apparent scaling law describing the concentration dependence of the sedimentation coefficient (s ∝ c^β) in the semidiiute region is found to be concentration dependent. However, a power law fit to data for the highest molecular weight (M = 20.6 × 10⁶) in the concentration region (c < 2 kg m^?3) yields a value β = ?0.59, somewhat smaller than that (?0.54) predicted theoretically. This discrepancy and the observed curvature in logs vs. logc at higher concentrations are discussed. Under theta-solvent conditions, on the other hand, the concentration dependence of s in the semidilute regime can be represented by a simple power law, with β = ?1.0, in excellent agreement with the theoretical prediction. The crossover concentration c^*, separating the dilute and semidilute concentration regimes, was found to be well defined and located at c = 1/[η]. c^* varies with molecular weight as M^?0.73 and M^?0.50 under good-solvent and theta-solvent conditions, respectively.     

Voltammetry of immobilized cytochrome c on novel binary self-assembled monolayers of thioctic acid and thioctic amide modified gold electrodes

Horse heart cytochrome c (cyt c) was adsorbed on the binary self-assembled monolayers (SAMs) composed of thioctic acid (T-COOH) and thioctic amide (T-NH₂) at gold electrodes via electrostatic interaction. The cyt c adsorbed on the modified gold electrode exhibited well-defined reversible electrochemical behavior in 10 mM phosphate buffer solution (PBS, pH 7.0). The surface concentration (Γ) of electroactive species, cyt c, on the binary SAMs was higher than that in single-component SAMs of T-COOH, and reached a maximum value of 9.2 × 10⁻¹² mol cm⁻² when the ratio of T-COOH to T-NH₂ in adsorption solution was of 3:2, and the formal potential (E^0′=(E_pa+E_pc)/2) of cyt c was −0.032 V (vs. Ag|AgCl (3 M NaCl)) in a 10 mM PBS. The interaction between cyt c and the binary SAMs made the E^0′ shift negatively when compared with that of cyt c in solution (+0.258 V vs. NHE, i.e., +0.058 V vs. Ag|AgCl (3 M NaCl)). The fractional coverage of bound cyt c was a 0.64 theoretical monolayer. The standard electron transfer rate constant of cyt c immobilized on the binary SAMs was also higher than that on single-component SAMs of T-COOH, and the maximum value of 15.8 ± 0.6 s⁻¹ was obtained when the ratio of T-COOH to T-NH₂ in adsorption solution was at 3:2. The results suggest that the electrode modified with the binary SAMs functions better than the electrode modified with single-component SAMs of T-COOH.     

A study of the chain extending effect of elongational flow in polymer solutions

Summary The effect of elongational flow on the orientation of dissolved macromolecules has been studied by observation of localised birefringence within appropriate regions of the flow field, with the objective of linking up experimentally observed chain alignment with basic theory. Benefitting from previous experience the highest available molecular weight fractions were used, i. e. polystyrene ofM _w = 2 · 10⁶, and two opposed suck jets were employed to provide the high strain rates required. Birefringence set in above a critical strain rate and rose rapidly to a maximum value, confirming expectations from theory. Both the maximum birefringence and critical strain rate were independent of concentration indicating that the chains are independent of each other. The value of the birefringence was consistent with complete chain extension, while the critical strain rate yielded a relaxation time of 3 · 10^–5 s in accord with the value calculated fromZimm's non-free draining model. Other observations yielded an estimate of the critical entanglement concentration. The prospects and limitations of the present kind of experimental approach are discussed.With 5 figures and 2 tables     

Coil-globule transition: Self-assembly of a single polymer chain

The coil collapse problem is of interest not only because it represents the simplest model of protein folding, but also because of its fundamental importance as related to polymer nanostructures and fractionation. It is extremely difficult to observe the coil-to-globule transition experimentally because at finite concentrations in a poor solvent, the macromolecules tend to aggregate due to phase separation when the collapsed state is being achieved. In the mid-1980s, two-stage kinetics of a single-chain collapse was proposed theoretically.^1,2 The first successful experimental observation of a two-stage coil-to-globule transition was achieved by quenching a dilute solution of polystyrene (PS) in cyclohexane.³ By using a thinnest capillary tube cell with a wall thickness of 0.01 mm and a diameter of 5 mm for dynamic light scattering, two relaxation times, τ_crum for the crumpled globule state and τ_eq for the compact globule state, were determined⁴ for the first time. The relaxation times were much slower than expected. From the size of the crumpled globule and that of the compact globule and by assuming the intraglobular density to be uniform, the volume fraction of the PS chain in the crumpled globule state, ϕ_crum, and that in the compact globule state, ϕ_comp, can be estimated, with ϕ_crum = 0.02 and ϕ_comp ∼ 0.24-0.4 at 28°C for polystyrene in cyclohexane. The results imply that a single-chain globule contains a large amount of solvent. It should also be noted that ϕ_comp is temperature dependent, i.e., one would have to go to hypothetically low temperatures in order to squeeze out all the solvent (cyclohexane) in the compact PS globule. The single-chain coil collapse state could be achieved under equilibrium conditions by using a high molecular weight, M_w ∼ 1.08 × 10⁷ g/mol; M_w/M_n < 1.06) poly(N-isopropylacrylamide) (PNIPAM) in water,<⁵ even though the ten million molecular weight for PNIPAM was substantially lower than that for polystyrene (M_w ∼ 50 × 10⁶ g/mole).⁶ Under equilibrium conditions, it was feasible to determine both the hydrodynamic radius R_h and the radius of gyration R_g. The ratio of R_g/R_h changed from 1.45 to 0.77, clearly demonstrating the transition from the theta coil state to the compact globule state. At the maximum value of the scaled expansion factor α_s³ |τ| M_w^1/2, R_g/R_h = 1.33 where α_s = R_g/R_g (θ) and τ = |T-θ| / θ with θ being the theta temperature. In the compact globule, R_g/R_h was of the order of 0.7, implying that the PNIPAM compact globule in water still contained ∼80% water, of the same order of magnitude as the PS compact globule in cyclohexane at 7° below its theta temperature (35°C).     

A relativistic C.I. study on theJ=1/2 even spectrum of Sr II

We present a method for performing relativistic CI calculations in ground and excited atomic and ionic levels. An electron occupying a relativistic shellnκ in a given electronic configuration is described by a single numerical four-component Dirac-Fock orbital having the samen and κ quantum numbers to those of the shellnκ. Application of this method yields estimates for the I.P. (88 741 cm^?1) and the core correlation energy (?30916 cm^?1) for Sr II and for the total correlation energy in Sr III (?30916 cm^?1). Core-valence correlation energies for the |core 5s〉 (?4379 cm^?1), |core 6s〉 (?1191 cm^?1) and |core 13s〉 (?32 cm^?1) levels have been calculated for Sr II. Estimates for the total relativistic, Breit, vacuum polarization and self energy corrections for these levels are also reported. Configurations in which the core is not fully occupied have been found to yield significant contributions to the correlation energies of both ground and excited levels. Our results show that full scale relativistic CI calculations using numerical four-component Dirac-Fock orbitals are feasible and provide a useful ab-initio tool for the investigation of atomic properties within the framework of fully relativistic theories.     

Can the Theoretical Fitting of the Proton‐Nuclear‐Magnetic‐Relaxation‐Dispersion (Proton NMRD) Curves of Paramagnetic Complexes Be Improved by Independent Measurement of Their Self‐Diffusion Coefficients?

The self‐diffusion (D_c) coefficients of various lanthanum(III) diamagnetic analogues of open‐chain and macrocyclic complexes of gadolinium used as MRI contrast agents were determined in dilute aqueous solutions (3–31 mM ) by pulsed‐field‐gradient (PFG) high‐resolution ¹H‐NMR spectroscopy. The self‐diffusion coefficient of H₂O (D_w) was obtained for the same samples to derive the relative diffusion constant, a parameter involved in the outersphere paramagnetic‐relaxation mechanism. The results agree with an averaged relative diffusion constant of 2.5 (±0.1)×10^?9 and of 3.3 (±0.1)×10^?9 m² s^?1 at 25 and 37°, respectively, for 'small' contrast agents (M_r 500–750 g/mol), and with the value of bulk H₂O (2.2×10^?9 and 2.9×10^?9 m² s^?1 at 25° and at 37°, respectively) for larger complexes. The use of the measured values of D_c for the theoretical fitting of proton NMRD curves of gadolinium complexes shows that the rotational correlation times (τ_R) are very close to those already reported. However, differences in the electronic relaxation time (τ_SO) at very low field and in the correlation time (τ_V) related to electronic relaxation were found.     

Determination of electrochemical kinetic parameters by square-wave polarography: Polarographic reduction of Zn(II) in 1 M KCl,KBr, and KNCS solutions

A new method of determining electrochemical kinetic parameters by square-wave polarography was presented, in which the faradaic current at θ/2, θ being the half-period of superimposed square-wave voltage, was used for the analysis. The method gave the following kinetic parameters for the electrode reaction, Zn(II) + 2e(Hg), in aqueous solutions at 25° C: k_c^θ=0.0052 cm s^?1 and α_c=0.36 in 1 M KCl, k_c^θ=0.011 cm s^?1 and α_c=0.30 in 1 M KBr, and k_c^θ=0.020 cm s^?1 and α_c=0.52 in 1 M KNCS. Induced adsorption of Zn(II) on the dropping mercury electrode was suggested in solutions containing thiocyanate ions.     

The influence of shear rate, temperature and chain conformation on the critical concentration c

 When viscometry is used, a crossover phenomenon is observed separating the dilute solutions into extremely dilute solutions and dilute solutions. The critical concentration c ^**, determined from this crossover phenomenon, strongly depends on the shear rate in the solution. At very high values of shear rate the critical concentration c ^** becomes very low and depends only on the contour length of the elongated chains of different polymers. An increase of the temperature induces an increase of c ^** because the relaxation time of the chains decreases. If a polymer adopts a rodlike conformation (in a given solvent at a given temperature) the excluded volume of its chains increases and its critical concentration c ^** decreases. Received: 14 October 1996 Accepted: 3 March 1997