Scaling analysis of cotton cellulose/LiCl·DMAc solution using light scattering and rheological measurements

Semidilute solution of cotton lint (CC1) in 8 wt % LiCl/N,N‐dimethylacetamide was investigated using static light scattering (SLS) and rheological measurements. The reduced osmotic modulus estimated by SLS measurements for CC1 solutions are proportional to c^1.16 in the semidilute region. From the exponent of 1.16, de Gennes' scaling theory derives the relationship between radius of gyration, R_g, and molecular weight, M_w, of CC1 as R_g ∝ M^0.62 This corresponds to the Mark‐Houwink‐Sakurada exponent of 0.86. This exponent is very close to that estimated from scaling analysis of zero shear rate viscosity, that is 0.85. Apparent radius of gyration, R_g,app, estimated by SLS measurements for CC1 solutions are proportional to c^?0.5 in the semidilute region. R_g,app indicates the mesh size of polymer entanglement in the semidilute region. On the assumption of the Gaussian behavior of CC1 molecule in the semidilute region, the exponent of ?0.5 gives the relationship between the molar mass between entanglements, M_e, and c as following relationship: M_e ∝ c^?1. This agrees with the concentration dependence on plateau modulus estimated from the dynamic viscoelastic measurements. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2155–2160, 2006     

Investigation on the interaction between C16TAB and NaCMC in semidilute aqueous solution based on rheological measurement

The rheological behavior of unentangled and entangled semidilute solution of anionic polyelectrolyte sodium carboxymethyl cellulose (NaCMC) containing cationic surfactant cetyltrimethylammonium bromide (C₁₆TAB) was investigated. The results reveal that the rheological properties of these semidilute NaCMC solutions depend on the amount of C₁₆TAB added. In the unentangled semidilute NaCMC solution (0.5 g/L), the viscosity decreases with the increase of C₁₆TAB amount in the low surfactant concentration region (below the critical aggregation concentration, CAC). However, in high surfactant concentrations (above CAC), the viscosity decreases sharply with the increase in C₁₆TAB amount. It is found that viscosity change of NaCMC solution could be described using Colby’s model when surfactant concentrations are between CAC and saturated concentration (C_s), suggesting that no inter-polymer interaction exists between C₁₆TAB and NaCMC in the unentangled semidilute solution. However, for the entangled semidilute NaCMC solution (5 g/L), the addition of C₁₆TAB leads to an increase in viscosity. Meanwhile, the solution exhibits an enhanced shear thinning behavior due to adding more C₁₆TAB than 1 mM. The viscosity increase is ascribed to the physical cross linking of surfactant micelles with NaCMC chains. Furthermore, it is suggested that the enhanced shear thinning behavior results from weak interaction between NaCMC chains and C₁₆TAB micelles.     

Viscoelasticity and rheology in the regimes from dilute to concentrated in cellulose 1-ethyl-3-methylimidazolium acetate solutions

Dynamic rheological behaviors of α-cellulose 1-ethyl-3-methylimidazolium acetate ([Emim]Ac) solutions were investigated in a large range of concentrations (0.1–10 wt %) at 25 °C. On the basis of data from the dynamic viscoelastic test, the exponents of the specific viscosity η _sp versus concentration c were determined as 1.0, 2.0 and 4.7 for dilute, semidilute unentangled and entangled regimes respectively, which were in accordance with the scaling prediction for neutral polymer in θ solvent. The intrinsic viscosity [η] of the solution was determined to be 253 mL/g at 25 °C. The linear viscoelastic response of the dilute and semidilute unentangled solutions could be described successfully by the Zimm and Rouse model (ν = 0.5 for θ solution) respectively, suggesting that the motion of cellulose chain in [Emim]Ac changed from Zimm to Rouse model with increasing concentration. At low concentrations, failure of the Cox–Merz rule with steady shear viscosity larger than complex viscosity was observed. While as the concentration increased, the deviation from the Cox–Merz rule disappeared due to the formation of homogeneous entanglement structure in cellulose solution.     

Vinyl polymerization. 275. Polymerization of vinyl monomers photosensitized by tetramethyltetrazene

A study of the photopolymerization of vinyl monomers in the presence of tetramethyltetrazene (TMT) was made. TMT was found to act as an effective sensitizer. In the photopolymerization of vinyl monomers such as methyl methacrylate or styrene the rate of polymerization was expressed by the equation: R_p = k[TMT]^1/2[monomer]. The chain-transfer constant of TMT under ultraviolet irradiation was estimated to be 3.8 × 10^?2 for the above monomers. A linear correlation was found to exist between the reactivity of dimethylamino radical toward the vinyl monomers and e values for the corresponding monomers.     

Electrospinning of nylon-6,6 solutions into nanofibers: Rheology and morphology relationships

The relationship between the rheological properties of nylon-6,6 solutions and the morphology of their electrospun nanofibers was established. The viscosity of nylon-6,6 in formic acid(90%) was measured in the concentration range of 5 wt%-25 wt% using a programmable viscometer. Electrospinning of nylon-6,6 solutions was carried out under controlled parameters. The chemical structure, morphology and thermal properties of the obtained nanofibers were investigated using Fourier transform infrared spectroscopy(FTIR), scanning electron microscopy(SEM) and differential scanning calorimetry(DSC), respectively. Entanglement concentration(ce) was found to be 15 wt% and a power law relationship between specific viscosity and solution concentration was observed with exponents of 2.0 and 3.3 for semi-dilute unentangled(c ce) and semi-dilute entangled(c ce) regimes, respectively. The diameter and uniformity of the nanofibers were found to be dependent on the viscosity. Moreover, the average diameter of electrospun nanofibers was found to be dependent on zero shear rate viscosity and normalized concentration(c/ce) in a power law relationship with exponents of 0.298 and 0.816, respectively. For nylon-6,6 solutions, the entanglement concentration(ce = 15 wt%) provides the threshold viscosity required for the formation of a stable polymeric jet during electrospinning and producing uniform beadless fibers. For concentrations less than ce, beaded fibers with some irregularities are formed. DSC analysis showed an increase in crystallinity of all electrospun samples compared to original polymer. Furthermore, Based on FTIR spectroscopy, α phase is dominant in electrospun nanofibers and minor amount of β and γ phases is also available.     

Effects of composition drift on the effectiveness of random copolymer reinforcement at polymer–polymer interfaces

Random copolymer layers are surprisingly effective at reinforcing polymer–polymer interfaces. One hypothesis is that composition drift during synthesis can account for the higher than expected toughening. To test this hypothesis, we polymerized a series of poly(d‐styrene‐r‐2‐vinylpyridine) (dPS_f‐r‐PVP_1?f) copolymers with various fractions (f) of deuterated styrene to only 10% completion to avoid composition drift. The fracture energies (G_c) of polystyrene/dPS‐r‐PVP/poly(2‐vinylpyridine) interfaces with relatively thick layers of dPS‐r‐PVP were measured. G_c decreased relative to interfaces reinforced with composition‐drifted dPS‐r‐PVP. Conversely, G_c increased when two or more copolymers were blended together. In such samples, the copolymers form distinct layers with multiple interfaces characterized by the difference in f (Δf) between adjacent layers. We find that G_c is governed by Δf_max, the largest difference in adjacent compositions, and, therefore, by the width of the narrowest interface (w_min). G_c increases strongly as w_min increases from 3 to 5 nm. Remarkably, these w_min values are about half the entanglement spacing in bulk polystyrene. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2363–2377, 2001     

Reentrant behavior of poly(vinyl alcohol)–borax semidilute aqueous solutions

 The reentrant behavior of Poly(vinyl alcohol) (PVA)–borax aqueous semidilute solutions with a PVA concentration of 20 g/l and borax concentrations varies from 0.0 to 0.20 M was investigated using dynamic light scattering (DLS) and dynamic viscoelastic measurements. Two (fast and slow modes) and three (fast, middle, and slow) relaxation modes of PVA semidilute aqueous solutions without and with the presence of borax, respectively, were observed from DLS measurements. The fast and middle relaxation modes were q ²-dependent (q is the scattering vector) characteristic of diffusive behavior; however, the slow modes were q ³-dependent, characteristic of intraparticle dynamics. The experimental results showed that the slow relaxation mode dominates the DLS relaxation. The DLS slow mode relaxation time, τ_s, and the viscoelastic modulus G′(ω) and G′′(ω) data had a similar trend and demonstrated reentrant behavior as the borax concentration was increased from 0.0 to 0.20 M, i.e. τ_s, G′(ω), and G′′(ω) fluctuated with increasing borax concentration. The excluded-volume effect of polymers, charge repulsion among borate ions bound on PVA molecules, and intermolecular cross-linking didiol–borate complexation caused an expansion of the polymer chain; however, the screening effect of free Na⁺ ions on the negative charge of the borate ions bound on PVA and intramolecular cross-linking didiol–borate complexation led to a shrinkage of the polymer chain. The reentrant behavior was the consequence of the balance between expansion and shrinkage of the PVA–borate complex. Received: 26 March 1999/Accepted in revised form: 3 September 1999     

Linear viscoelasticity of poly(acrylonitrile-co-itaconic acid)/1-butyl-3-methylimidazolium chloride extended from dilute to concentrated solutions

The solution rheology of poly(acrylonitrile-co-itaconic acid) (poly(AN-co-IA)) in 1-butyl-3-methylimidazolium chloride ([BMIM]Cl) spanning dilute, semidilute unentangled and entangled regimes were investigated. The exponents in the specific viscosity η_sp ～ overlap parameter c[η] power law were 1, 2 and 4.7 for dilute, semidilute unentangled and entangled regimes, respectively, which were found to be consistent with the scaling prediction for neutral linear polymers in θ-solvent. For dilute solutions (lower than 0.9 wt.%), the linear viscoelastic responses were observed to be in good agreement with the Zimm model (Flory exponent ν = 0.5). While for semidilute unentangled solutions (between 0.9 and 8 wt.%), results obtained had been found to be consistent with Rouse model. Considering Flory exponent ν = 0.5 and the concentration dependences of the specific viscosity and relaxation time, it had been evaluated that poly(AN-co-IA) in [BMIM]Cl behaves as a neutral polymer in θ-solvent. It had also been suggested that according to the unusual deviation of Cox-Merz rule, poly(AN-co-IA)/[BMIM]Cl solutions are typical neutral polymeric liquids for the concentrated solutions but have shown a more complicated behavior at high deformation rates.     

Elucidating Factors Manipulated the Formation of Multiply Charged Protein Homomultimeric Complexes by Electrospray Ionization

Native non‐covalently bonded protein‐protein and protein‐substrate complexes are of great interest and have been extensively studied by electrospray ionization mass spectrometry (ESI‐MS). Multiply charged protein homomultimeric complexes are shown to form by ESI‐MS. This study addresses factors that can artificially induce the formation of multiply charged protein homomultimeric complexes. Cytochrome c (Cyt c) and ubiquitin, which are monomers in solution, were found to generate (Cyt c)_mⁿ⁺ by electrospray ionization (ESI). The homomultimeric complexes were not limited to dimeric complexes but include also multiply charged trimers, tetramers, and pentamers. The observation of these homomultimeric complexes has never been revealed from a Cyt c solution at the concentration as low as 10 μM. Increasing the concentration of Cyt c enhanced the formation of (Cyt c)_mⁿ⁺ as expected; however, the protein concentration does not affect the relative intensities of monomeric and dimeric complexes. Additionally the enrichment of NH₄OH also promotes the formation of (Cyt c)_mⁿ⁺. Notably, source collision‐induced dissociations (source‐CID) of (Cyt c)_mⁿ⁺ alter the charge state distribution (CSD) and may lead to an incorrect interpretation of Cyt c conformations. Hence, extra care should be taken when using CSD to interpret the conformation of a protein derived from ESI‐MS.     

Relationship between the positive temperature coefficient of resistivity and dynamic rheological behavior for carbon black‐filled high‐density polyethylene

Studies on the relationship between resistivity and dynamic rheological properties of carbon black‐filled high‐density polyethylene (CB/HDPE) composites were carried out. Change of resistivity ρ is associated with the dynamic modulus before the positive temperature coefficient/negative temperature coefficient (PTC/NTC) transition temperature. When the temperature approaches the melting point of HDPE, ρ increases rapidly with a decreasing modulus, corresponding to PTC transition. The resistivity‐dynamic viscoelasticity relationship in the PTC region can be divided into two parts in which the changes of ρ with storage modulus G′ and loss modulus G″ can be described by the scaling laws given by the critical storage modulus and loss modulus G′_c and G″_c; adjustable parameters ρ′_1c, ρ′_2c, ρ″_1c and ρ″_2c; and nonlinear exponents n and m, respectively. The accordance between the experimental data and the scaling functions of the dimensionless quantities (G′/G′_c ? 1) and (G″/G″_c ? 1) in the PTC transition region suggests that the ρ jump may be the result of a modulus‐induced percolation. G′_c and G″_c increase, but the four scaling resistivitis, ρ′_1c, ρ′_2c, ρ″_1c, and ρ″_2c, decrease with increasing CB concentration, implying that the microstructure change of the composites is the determinant factor for the PTC behavior and the resistivity‐dynamic modulus relationship. However, ρ′_2c and ρ″_2c exhibit no scaling dependence. It is suggested that a threshold concentration exists for the modulus of the composites on the basis of examining the plot of both G′_c and G″_c against CB concentration. The scaling laws G′ ～ Φ^x and G″ ～ Φ^y hold for the concentration dependence of the critical modulus when Φ > Φ_c and the estimated values of x and y are 1.10 ± 0.10 and 0.89 ± 0.29, respectively. The resistivity‐dynamic modulus can shift to form a master curve. The horizontal factors a_G′ and a_G″ and the vertical factors a′ and a″ are relevant to the concentration dependence of the dynamic modulus or PTC behavior. It is believed that the former would be involved in changing the mechanical microstructure formed by the complicated interaction of CB particle and polymer segments, and the latter would be involved in the overall changes of conducting a network during the PTC transition region. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 983–992, 2003     

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     

The influence of variant PE‐b‐PEO segments on physical properties of LLDPE graft copolymers

A method was adopted to fix a series of polymers of PE‐b‐PEO with different PEO/PE segments on the chains of LLDPE. Maleic anhydride (MA) reacting with hydroxyl group of PE‐b‐PEO (mPE‐b‐PEO) was used as the intermediate. The structures of intermediates and graft copolymers were approved by ¹H NMR and FTIR. XPS analysis revealed a great amount of oxygen on the surface of grafted copolymers although the end group of PEO was fixed on the LLDPE chains through MA. Thermal properties of the graft copolymers as determined by differential scanning calorimetry (DSC) showed that PE segments in the grafted monomers could promote the heterogeneous nucleation of the polymer, increase T_c, and crystal growth rate. While the amorphous PEO segments which attached to the crystalline PE segments in LLDPE, impaired their ability to fit the crystal lattice, and depressed the crystallization of LLDPE backbones. In this study, it was also verified through the dynamic rheological data that increasing M_n of grafted monomers significantly increased the complex viscosity and enhanced the shear‐thinning behavior. Long‐branched chains formed by grafted monomers enhanced the complex moduli (G′ and G″) value and retarded relaxation rate. However, there were little influence on the rheological properties when increasing the amounts of PEO segments (or decreasing PE segments) of grafted monomers with similar molecular weight. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 506–515, 2008     

Electrical conductivity of some cationic polysaccharides. I. Effects of polyelectrolyte concentration,charge density,substituent at the ionic group,and solvent polarity

Electrolytic conductivity behavior of some cationic polysaccharides in water, methanol, and the mixtures water/methanol is presented. The polyelectrolytes investigated contain quaternary ammonium salt groups, N‐alkyl‐N,N‐dimethyl‐2‐hydroxypropyleneammonium chloride, attached to a dextran backbone. This study considers the influences of polymer concentration (1 × 10^?6 < C < 1 × 10^?2 monomol L^?1) and the charge density (ξ = 0.48–3.17) modified either by changing charge distance (b) or dielectric constant of the solvent (ε) on polyion–counterion interaction in salt‐free solutions. Above the critical value, ξ_c = 1, the variation of the equivalent conductivity (Λ) as a function of concentration is typical for a polyelectrolyte behavior. The conductometric data in water were analyzed in terms of the Manning's counterion condensation theory. The presence of longer alkyl chains at quaternary N atoms was found to have a negligible influence on the Λ values. The results show that the decrease of the medium polarity results in the decrease of the number of free ions and, consequently, of the equivalent conductivity values. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3584–3590, 2005     

Self‐diffusion of styrene, 2,2′‐azobisisobutyronitrile,and polystyrene in bulk polymerization by pulsed‐gradient spin‐echo nuclear magnetic resonance spectroscopy

The self‐diffusion of styrene, polystyrene, and 2,2′‐azobisisobutyronitrile has been determined in the bulk polymerization of styrene with pulsed‐gradient spin‐echo nuclear magnetic resonance at 25 °C. Data on small molecules are discussed with respect to recent diffusion models. They can fit self‐diffusion coefficient data of small molecules in dilute or semidilute polymer solutions; in concentrated solutions, however, there is a breakdown. A semiempirical model based on scaling laws is used to describe the self‐diffusion of styrene and 2,2′‐azobisisobutyronitrile over the whole range of concentrations studied. The dependence of the polystyrene self‐diffusion coefficient on the polymer concentration is described with a stretched exponential function, D = D₀ exp(?αc^ν), where α depends on the molecular weight of the polymer and ν depends on the kind of solvent. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1605–1614, 2003     

Oligonucleotide Analogues with Integrated Bases and Backbone. Part 15

The self‐complementary (Z)‐configured U*[c_e]A⁽*⁾ dinucleotide analogues 6, 8, 10, 12, 14 , and 16 , and the A*[c_e]U⁽*⁾ dimers 19, 21, 23, 25, 27 , and 29 were prepared by partial hydrogenation of the corresponding ethynylene linked dimers. Photolysis of 14 led to the (E)‐alkene 17 . These dinucleotide analogues associate in CDCl₃ solution, as evidenced by NMR and CD spectroscopy. The thermodynamic parameters of the duplexation were determined by van't Hoff analysis. The (Z)‐configured U*[c_e]A⁽*⁾ dimers 14 and 16 form cyclic duplexes connected by Watson–Crick H‐bonds, the (E)‐configured U*[c_e]A dimer 17 forms linear duplexes, and the U*[c_e]A⁽*⁾ allyl alcohols 6, 8, 10 , and 12 form mixtures of linear and cyclic duplexes. The C(6/I)‐unsubstituted A*[c_e]U allyl alcohols 19 and 23 form linear duplexes, whereas the C(6/I)‐substituted A*[c_e]U* allyl alcohols 21 and 25 , and the C(5′/I)‐deoxy A*[c_e]U⁽*⁾ dimers 27 and 29 also form minor amounts of cyclic duplexes. The influence of intra‐ and intermolecular H‐bonding of the allyl alcohols and the influence of the base sequence upon the formation of cyclic duplexes are discussed.     

Sol-Gel Transition and Equilibrium Shear Modulus of Poly(vinyl chloride) and Plasticizers

The elasticity of poly(vinyl chloride) gels with molecular weight distribution (M_w/M_n), of 2.16 have been studied in the region beyond their gel points. Dynamic storage modulus G′, and equilibrium gel shear modulus of elasticity G_e, at low frequencies (ω) have specific developments as a function of polymer concentrations c, and plasticizers. The scaling elasticity from G_e = kε^z equation holds at different PVC plasticizer gels. The scaling exponent z, and constant k. ε is defined as the relative distance, ε = (|c − c_g|)/c_g, the calculated z = 2.45 ± 0.15. Furthermore, this analysis provides constant k with certain informations about the dependency of gel elasticity on the kind of plasticizer. Near the sol-gel transition temperature T, G_e decreases rapidly with increasing temperature. The normalized moduli G_eM/cRT, of the gels at different temperature, and/or c were dependent on the relative distance from the gelation point ε, and PVC and plasticizers concentration respectively. These results suggested mesh size of gel network near the gelation point for PVC with bis(2-ethylhexyl) phthalate (DOP) or di-n-butyl sebacate (DBS) plasticizers that has been newly reported.     

Diffusion of Nanoparticles in Semidilute Polymer Solutions: A Multiparticle Collision Dynamics Study

The diffusion of nanoparticles immersed in semidilute polymer solutions is investigated by a hybrid mesoscopic multiparticle collision dynamics method. Effects of polymer concentration and hydrodynamic interactions among polymer monomers are focused. Extensive simulations show that the dependence of diffusion coefficient D on the polymer concentration c agrees with Phillies equation D-exp (-αc^δ) with a scaling exponent δ≈0.97 which coincides with the experimental one in literature. For increasing nanoparticle size, the scaling prefactor α increases monotonically while the scaling exponent always keeps fixed. Moreover, we also study the diffusion of nanoparticle without hydrodynamic interactions and find that mobility of the nanoparticle slows down, and the scaling exponent is obviously different from the one in experiments, implying that hydrodynamic interactions play a crucial role in the diffusion of a nanoparticle in semidilute polymer solutions.     

Free volumes in simple and polymeric liquids

Values of ε₀ν₀ the vaporization energy and volume in the hypothetical liquid state at 0°K., are derived for some simple polar and nonpolar molecules used as models for vinyl polymers. The following empirical relationship between the free volume fraction, f = (v ? v₀)/v, and the liquid compressibility coefficient β is demonstrated: ?f² ∝? This is applied to several vinyl polymer liquids near their glass transition temperatures, T_g, giving. f_g ? 0.17, if the “hard-core” volume v^* is considered to be independent of pressure and temperature, (i.e., v^* = v₀); or, f_g ?0.12, if the P,T dependence of v^* is considered to be the same as that of the glass. These agree with f_g values derived by Simha and Boyer from thermal expansion coefficients for the two analogous cases. An empirical viscosity-free volume equation of the Doolittle form: η = ATⁿe^b/f is applied to the glass transition, on assuming that this is an isoviscosity state and with the use of reported values for the expansion and compressibility coefficients and dT_g/dP for three polymers: polystyrene, poly(methyl methacrylate), and poly(vinyl acetate). Reasonable values of b/n are thus obtained. This viscosity equation is critically examined in the light of molecular theories of liquid viscosity.     

The stability of silver iodide sols in the presence of polyacrylic acids of various molecular weights

Summary The effect of a series of polyacrylic acids, ranging in molecular weight from 1.67×10⁴ to 2.36×10⁶, on the stability of positively charged silver iodide particles has been examined. Flocculation of the sol occurred at a well defined concentration of polyacrylic acid,c _f , and a further increase in concentration of the polyelectrolyte caused restabilization of the sol. Over the range examinedc _f appeared to be related to the viscosity average molecular weight of the acid,M _v , by an equation of the form,c _f =a ·M _v ^{– b} wherea andb are constants.