Evaluation of Huggins' Constant,Kraemer's Constant and Viscosity Concentration Coefficient of Polymer Dextran in Urea,Glycine and Glucose

Abstract

Reduced viscosity (η_sp/c) and Inherent viscosity (In η_rel/c) of dilute solution of water soluble polysaccharide polymer “Dextran” has been calculated by measuring the flow time of the polymer solution in solvents like 6(M) Urea, 2(M) Glycine and 50% Glucosc at three different temperatures ? 25°C, 30°C and 35°C. From extrapolation of curve (η_sp/c) versus (c) and (In η_rel/c) versus (c), thermo viscosity parameters like Huggins' constant (k′_H) Kraemer's constant (k″_H) and viscosity concentration coefficient (a ₂) have been estimated which enable us to know the fate of the polymer molecules in these solvents.     

The viscosities of dilute solutions of nitrocellulose

The viscosities of dilute solutions (0.05, 0.1, and 0.2 g. per 100 ml.) of relatively high nitrogen content nitrocelluloses, weight-average molecular weights ca. 100,000, have been studied using homologous series of methyl ketones, alkyl acetates, and dialkyl phthalates as solvents. The simple form of the Huggins equation, does not appear to hold, plots of η_sp/c against c being generally curved. The results are capable of expression by where A equals [η] and B the initial slope. Values of B and A appear to be related to solvent power as determined by the volume of hexane required to cause initial phase separation from solution, good solvents giving higher values of B and A than poor. The variation of B with solvent is more marked than that of [η] and may reflect differences in degree of coiling of chains in different solvents. Values of B/[η]² (Huggins k′) do not generally decrease with solvent power increase. The slopes of Martin plots divided by intrinsic viscosities are not generally related to solvent power in the manner observed by Spurlin with solutions of ethyl cellulose.     

Dilute solutions of poly(vinyl alcohol) derived from vinyl trifluoroacetate

The dilute-solution behavior of poly(vinyl alcohol) (PVA_VTFA), derived from vinyl trifluoroacetate, in water-dimethylsulfoxide (DMSO) mixtures was investigated. With solvent mixtures ranging from 10 to 20 vol % DMSO, the relation between the reduced viscosity η_sp/C and the polymer concentration C was linear for polymer concentrations above 0.2 g/dL, whereas in solutions in mixed solvents of other compositions the dependence was linear for polymer concentrations above 0.1 g/dL. The relation between the intrinsic viscosity [η] obtained for aqueous solutions of PVA_VTFA and the molecular weight M estimated from viscosity measurements in solutions of poly(vinyl acetate) (PVA_VTFA), obtained by acetylation of PVA_VTFA, was given by [η] = 7.34 × 10^?4 M^0.63. The value of [η] was greatest for the solvent mixture with 10 vol % DMSO and smallest for about 50 vol % DMSO, and Huggins constants k were smallest and greatest for these two cases, respectively. The turbidity of the solutions of low-molecular-weight PVA_VTFA, was higher than that of high-molecular-weight PVA_VTFA up to 30 vol % DMSO, and the reverse relation held for 40-70 vol % DMSO.     

Huggins constant k′ for flexible chain polymers

The Huggins constant k′ in the expression for the viscosity of dilute nonelectrolytic polymer solutions, η = η(1 + [η] c + k′[η]²c² + …), is calculated. For polymers in the theta condition, k′ is estimated to be 0.5 < k_θ′ ≤ 0.7. For good solvent systems, the Peterson-Fixman theory of k′ has been modified; the equilibrium radial distribution function in the original theory is replaced with a parametric distribution for interpenetrating macromolecules in the shear force field. Comparison of the modified theory with experimental k′ for polystyrenes and poly(methyl methacrylates) of different molecular weights in various solvents shows good agreement. An empirical equation which correlates the Huggins constant k′ and the viscosity expansion factor α_η for polymers has been found to coincide well with the modified theory.     

Determination of Chain Transfer Constant for Solvent When the Viscosity of the Polymerizing System Is Considered Important

Abstract

The chain transfer constant of the polymethyl methacrylate radical for N,N-dimethylaniline was determined in two solvents, benzene and dimethyl phthalate. Plots were made using1/P_n=k_t°R_p/k_p ²[M]²η + C_S1 [S₁]/[M] + C_S2 [S₂]/[M] +C_M where η=viscosity of monomer-solvents mixture, k_t°=rate coefficient of termination when η=1 cP, S₁=benzene or dimethyl phthalate, S₂=N,N-dimethylaniline, and other symbols have their usual meanings. The plots agreed well for the two solvents. If the plots were made without considering the viscosity term, two separate lines resulted for the two solvents. Thus it is essential to consider the viscosity of the polymerizing system in the analysis of chain transfer reactions when the termination reaction is diffusion-controlled and the viscosities of the monomer and solvent differ markedly.     

Intrinsic viscosity of polydisperse branched polymers

The relationships between molecular weight distribution and structure in polymerizations with long-chain branching were reviewed and extended. Results were applied to an experimental examination of intrinsic viscosity in polydisperse, trifunctionally branched systems. Several samples of poly(vinyl acetate) were prepared by bulk polymerization under conditions of very low radical concentration. The relative rate constants for monomer transfer, polymer transfer, and terminal double-bond polymerization were established from the variation of M _n and M _w with the extent of conversion. Average branching densities were then calculated for each sample and ranged as high as 1.5 branch points/molecule. Intrinsic viscosities [η]_B were measured in three systems: a theta-solvent, a good solvent, and one that was intermediate in solvent interaction. These results were compared with calculated viscosities, [η]_L, which would have been observed if all the molecules had been linear. The values of [η]_B/[η]_L were substantially the same in all three solvents. The variation of this ratio with branching density was compared with the theory of Zimm and Kilb as adapted to polydisperse systems. Discrepancies were noted, and the adequacy of present model distribution functions for branched polymers was questioned.     

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.     

Studies in inorganic polyelectrolytes — Part II

Viscosity behaviour of several samples ofGraham's salt with varying molecular weight has been studied. Reduced viscosity (η _sp /c) versus concentration curves were found to be characteristic of polyelectrolytes. They are dependent on the molecular weight and can be reduced to straight lines by plotting the reciprocal of the reduced viscosity against the square root of concentration. The intrinsic viscosities obtained by extrapolation were found to be proportional to the square of molecular weights. The value of reduced viscosity at any particular concentration in the concentration range between 0.25% and 4.0% was linearly related to the molecular weight. Reduced viscosities were found to decrease considerably on addition of electrolytes. Reduced viscosity versus added salt concentration curves were remarkably molecular weight dependent. The p_H of the medium seemed to have no effect at all. Bivalent salts reduce the viscosity to a much greater extent than monovalent ones. By keeping the concentration of the added salt constant and varying that ofGraham's salt, curves showing hump which disappeared at higher concentration of the added salt, were obtained. In the action of electrolytes the more important factor is the valency of cation rather than the ionic strength of the medium. Most observations confirm the already well-establishedFolding-Chain Theory of polyelectrolytes developed byKatchalsky, Fuoss and others.     

Preparation and properties of solvent-soluble bridged polybiphenylenes and related copolymers

A solvent-soluble polybiphenylene with a single hetero atom in the chain (a bridged polybiphenylene) was prepared according to the synthetic procedure for a solvent-soluble poly(4,4′-biphenylene). In addition, a related copolymer was similarly prepared by the addition of the MMA monomer in the reaction system. The thermal properties and viscosity behavior of each product were influenced by the hetero atom, especially by the introduction of MMA component in the chain. Each viscosity curve (η_sp/c vs. c) shows an anomalous peak at a specific concentration (0.3–0.002 g/100 ml DMF), depending upon the atomic group. The η_sp/c value for each homopolymer was not over 0.1 except in the neighborhood of the anomalous peak, while those for copolymers became 3–4 times larger than values for corresponding homopolymers. It is obvious that the viscosity of each copolymer increases due to an increase in flexibility due to introduction of the MMA units in the chain, since little difference in molecular weights is found between homopolymers (16,000–15,000) and copolymers (10,000–12,000).     

DILUTE SOLUTION BEHAVIOR OF CHITOSAN IN DIFFERENT ACID SOLVENTS

Dilute solution behavior of chitosan was studied in formic acid, acetic acid, lactic acid andhydrochloric acid aqueous solution under different pH values. The reduced viscosities, η_(sp)/C,ofchitosan solutions were dependent on the properties of acid and pH value of solvents. For a givenchitosan concentration, η~(sp)/C decreased with the increase of acid concentration, or decreasing pHof solvent, indicating shielding effect of excessive acid similar to adding salt into solution. Thestabilities of dilute chitosan solution in formic acid and lactic acid were better than that in acetic acid and hvdrochloric acid.     

Relation empirique entre la viscosite intrinseque et la masse moleculaire d'un polymere dissout dans un bon solvant

We propose the following empirical relationship between the intrinsic viscosity of a polymer and its molecular weight M.

$\text{{[η]?[η]}{}_{\mathrm{\theta }}\text{/[η][η]}{}_{\mathrm{\theta }}\text{=?Δρ}{}_{\mathrm{\infty }}\text{+}\text{A′}\text{M}\text{1}\text{2}$

[η] and [η]₀ are the intrinsic viscosities in a good solvent and in θ conditions respectively. Δ?, and A′ are constants characteristic of a system polymer-solvent. This relationship is valid for PS and PMMA in various good solvents and for a range of molecular weight from 3000 to 250,000. It is in this range that the Mark-Houwink-Sakurada equation is least applicable.     

Polynomial expansion of log relative viscosity and its application to polymer solutions

Solomon and Ciuta's equation has been deduced from first principles and has been shown to be merely an algebraic consequence of the definition of intrinsic viscosity. Secondly, a consequence of this equation that [η]c should be linear with \documentclass{article}\pagestyle{empty}\begin{document}$\sqrt {2\eta {\rm sp} - 2\ln \eta {\rm rel}}$\end{document} with unit slope, is found to be fairly accurate when examined against literature and our own data, and so this equation is commended not only for single-point determination of [η] but also for representing viscosity variation with concentration up to η_sp < 0.60. Thirdly, higher-order approximations are found to be less suitable. Other consequences of Solomon and Ciuta's equation are discussed.     

Limits of the dilute regime for the solution viscosity of PMMA in good and in poor solvents

The concentration (c′) marking the first deviation from linearity in the Huggins plot of specific viscosity η_sp/c vs c) has been determined for PMMA in chloroform, benzene (good solvents), acetonitrile, chlorobutane (poor solvents) and acetonitrile/chlorobutane mixtures (cosolvent). The dependence of c′ on polymer chain length and on solvent quality is given. The results are analysed in terms of the influence on c′ of incipient coil overlap, peripheral entanglements and other interactions, such as polymer association.     

Steady-shear viscosity of polydimethylsiloxanes over the range from the lower to the upper Newtonian region

The mechanism of non-Newtonian behavior for flow from the lower to the upper Newtonian region is explained by a modification of Graessley's theory. In the theory proposed here, a viscosity η_fric, which is based on friction between polymer segments and is almost shear-independent, is introduced in addition to Graessley's entanglement viscosity η_ent, which decreases with increasing shear rate. The theory is applied to previously obtained data on steady flow of polydimethylsiloxanes of different molecular weights. The agreement between calculated and experimental results is good. In polymers with the molecular weight above the critical molecular weight for entanglement M_c, the major contribution to viscosity near zero shear rate is η_ent. As the shear rate increases, the flow curve has an inflection where η_fric cannot be disregarded in comparison with η_ent. In the upper Newtonian region, η_fric has more influence on the viscosity than η_ent. The theory can also explain the experimental results on flow of polymers with molecular weight below M_c, which were shown to be slightly non-Newtonian in the previous paper.     

Determination of composition of ethylene–propylene copolymers by intrinsic viscosity

Intrinsic viscosities have been measured at 25° on five ethylene–propylene copolymer samples ranging in composition from 33 to 75 mole-% ethylene. The solvents used were n-C₈ and n-C₁₆ linear alkanes and two branched alkanes, 2,2,4-trimethylpentane and 2,2,4,4,6,8,8-heptamethylnonane (br-C₁₆). This choice was based on the supposition that the branched solvent would prefer the propylene segments and the linear solvent the ethylene segments, due to similarity in shape and possibly in orientational order. It was found that [η]_n ? [η]_br ≡ Δ[η] is indeed negative for propylene-rich copolymers, zero for a 56% ethylene copolymer, and positive for ethylene-rich copolymers. The Stockmayer–Fixman relation was used to obtain from Δ[η] a molecular-weight independent function of composition. The quantities (Δ[η]/[η])(1 + aM^?1/2) and Δ[η]/M are linear with the mole percent ethylene in the range investigated with 200 ≤ a ≤ 2000. The possibility of using these results for composition determination in ethylene–propylene copolymers is discussed. Intrinsic viscosities in the same solvents are reported for two samples of a terpolymer with ethylidene norbornene.     

Upturn effect in the Non-Newtonian intrinsic viscosity of polymer solutions. II. Polyisobutylene in polybutene oil

With an increasing gradient, the intrinsic viscosity of a high molecular weight polyisobutylene (M?_n = 7 × 10⁶) in polybutene oil L.100 (η_s = 5 poise) first drops to a minimum and then rises again. The minimum occurs at β = M[η]₀η_sG/NkT = 240, which is about ten times the value predicted by the dumbbell model. Such a shift to larger gradient is in good agreement with the more realistic necklace model of macromolecules in a good solvent. The increase of intrinsic viscosity after the minimum is nearly linear with the gradient and continues beyond the value at zero gradient. Experiments with capillaries of different length-to-diameter ratios yield identical flow curves so that one may exclude the possibility that the observed upturn is an artifact caused by end effects or time dependence of viscosity.     

Viscoelastic properties of dilute nematic mixtures containing cyclic and hyperbranched liquid crystal polymers dissolved in a nematic solvent

The twist and bend viscosities of dilute solutions of cyclic and hyperbranched liquid crystal polymers (LCP) dissolved in low molar mass nematic solvents were determined via dynamic light scattering analysis. These results were compared to those of linear chains with similar chemical repeat structures. The nematic solvent used was 4′-pentyloxy-4-cyanobiphenyl (50CB). The cyclic LCP oligomers, Cy TPB10, have a mesogenic group, 1-(4-hydroxy-4′-biphenyl)-2-(4-hydroxyphenyl) butane, separated by flexible decamethylene spacers. The twist viscosity of the cyclic Cy-TPB10 oligomers increases with molecular weight more strongly than the linear, TPB-10, suggesting that the hydrodynamic behavior of Cy-TPB10 is closer to that of a rigid rod than TPB10. Surprisingly, the intrinsic bend viscosity [η_bend] of Cy-TPB10 decreases with molecular weight, in contrast to the positive dependence for linear TPB10. This may reflect the higher strain energy in the smaller ring sizes. The hyperbranched LCP, TPD-b-8, is also based on the mesogen 10-bromo-1-(4-hydroxy-4′-biphenyl)-2(4-hydroxyphenyl) decane but with octyl groups at the chain ends. We compare the viscoelastic behavior of dilute nematic solutions of TPD-b-8 in 50CB against that of a linear main-chain LCP, TPB7, with the same mesogenic group but with heptamethylene spacers. The viscometric properties of TPD-b-8/50CB and TPB7/50CB are quite different. The results suggest that each chain is prolate (i. e., R_∥ > R_⊥) but that TPD-b-8 has a smaller chain anisotropy than that of TPB7. © 1995 John Wiley & Sons, Inc.     

Viscosity of the systems m-xylene, +1-propanol, +2-propanol, +1-butanol, +t-butanol

Viscosities, η, of the systems, m-xylene, +1-propanol, +2-propanol, +1-butanol and +t-butanol have been measured for the whole range of composition at 303.15, 308.15, 313.15, 318.15 and 323.15?K. The variation of viscosities has been plotted against mole fraction of alkanols. Viscosities have been found to increase slowly up to a considerable concentration of alkanols, followed by a rapid rise of viscosities at higher concentrations. The slow rise of viscosity is attributed to dissociation of alkanols in m-xylene, while the rapid rise of viscosity is ascribed to self-association of alkanols. Excess viscosities, η^E, have been plotted as a function of mole fraction of alkanols. The curves show negative values for the whole range of composition, with minima occurring in alkanol-rich region.?η?and η^E have been fitted to appropriate polynomial equations. The study shows the effect of branching and chain length of alkanols on?η?and η^E.     

Preparation of polyamide-imides via the phosphorylation reaction. II. Synthesis of wholly aromatic polyamide-imides from N-[p-(or m-) carboxyphenyl]trimellitimides and various aromatic diamines

Wholly aromatic polyamide-imides with high molecular weight (η_inh up to 1.7 dL/g in DMAc–5% LiCl) were obtained by the direct polycondensation reaction of N-[p-( or m-) carboxyphenyl]trimellitimide [p-(or m-)CPTMI] and aromatic diamines by means of di- or triphenyl phosphite in N-methyl-2-pyrrolidone (NMP)-pyridine solution in the presence of lithium or calcium chloride. The factors affecting the phosphorylation reaction were investigated, in particular for the reaction of p-CPTMI and 4,4'-oxydianiline (ODA). Molecular weight of polymers varied with the amount of metal salts and showed maximum values at the concentration of 10-15 wt % in the reaction mixture. Monomer concentration of 0.2 mol/L produced polymer of the highest viscosity. Higher concentrations produced gelation and yielded polymers of low molecular weight. A reaction temperature of about 120°C gave the best results. Among the solvents tested, NMP was significantly the most effective for the reaction. The highest inherent viscosity values, η_inh = 1.35 and 1.58 dL/g, were obtained with triphenyl phosphite (TPP)/monomer and diphenyl phosphite (DPP)/monomer molar ratios of 2.0. Excessive addition of phosphites did not cause a serious deleterious effect on the molecular weight of polymer. Polycondensations of several combinations of p-or m-CPTMI and aromatic diamines were carried out with satisfactory results.