Effect of concentration on the viscosity of dilute solutions

Simha, Robert

doi:10.6028/jres.042.036

Cited by 94 publications

(22 citation statements)

References 3 publications

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“…Although this observation is contrary to theoretical predictions (14), it is recognized that the concentrations employed are such that polymer-polymer interactions will be of importance. Statistical treatments of the hydrodynamic behavior of long chain molecules are usually applied to the idealized condition that the particles are well separated in the solvent.…”

Section: Fig 1 Red~iced Viscosity Versus Concentration Plots For Grcontrasting

confidence: 61%

“…A similar explanation has been given to observed increases in k' for soluble fractioils of styrene -diviilyl benzene copolymers (10,17) where branching occurs through the unreacted double bonds of the diolefirlic units i l l the polymer chain. Theoretical calculatioils (14) have supported this contention. However, the results of Thurmo~id and Zimm (16) show no detectable difference in the slope constant of the Huggills equatioil between fractions of a styrene-divinyl benzene copolymer and a polystyrene prepared under identical conditions.…”

Section: I-mentioning

confidence: 81%

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Graft Copolymers of Styrene and Methyl Methacrylate: Part Ii: Viscosity Behavior

Jones¹

1956

Can. J. Chem.

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PART 11: VISCOSITY ABSTRACTA study of the viscosity behavior of the graft copolymers described in Part I has been made with dilute solutions in benzene a t 25OC. Although the slope constants of the Huggins equation increase with the frequency of branching when measurements are made in a capillary viscometer under 'free fall' conditions, this is shown to be attributable to the depertdence of viscosity on shear gradient. At a constant shear rate, the Huggins k' values approximate to those of linear polymers. I t is suggested that the marked increase in viscosity observed with decreasing shear rate for the graft copolymers is due t o molecular entanglemel~t.

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Section: Fig 1 Red~iced Viscosity Versus Concentration Plots For Grcontrasting

confidence: 61%

Section: I-mentioning

confidence: 81%

Graft Copolymers of Styrene and Methyl Methacrylate: Part Ii: Viscosity Behavior

Jones¹

1956

Can. J. Chem.

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“…Th e con cen tration dependence of [r)] c may be illustrated on the basis of th e Bakel' equa tion (2). I t yi eld s (13) Thus with in creasing c, for n > O, as is th e case in all solutions of lar ge polymers investigated, as far as we know, [r)] c decreases, bu t to a lesser degree in a pOOl' solven t in which n is large, as was shown in section 4. We may recall also that for cellulose deriv~tives n is larger than for polystyrene, at least m a goo d solvent [24].…”

Section: Discussionmentioning

confidence: 60%

“…terms. This has b een shown previously as far as th e Al coefficient [13]. These populations m ay b e formally expressed in terms of "equilibrium constants".…”

Section: Discussionmentioning

confidence: 60%

Viscosity of dilute and moderately concentrated polymer solutions

Weissberg¹,

Simha²,

Rothman³

1951

J. RES. NATL. BUR. STAN.

172

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The viscosit ies of solut ions of t hree polysty rene fractions in t hree solve nts of v ar y ing solvent power were m easured at t wo temperat ures. The relat ive vi scosit ies of the syst em s investigated ranged from 1.03 to 43.The appli cability of two empirical expressions for the concen tration depende nce, nam ely t he Martin equation and t he Baker relation, is examined . In addit ion, t he results are represented by m eans of poly nomials of suitable degr ee. The numerical procedures for t he e valuatio n of t he coeffi cien ts are discussed in detail. In t he concent ration r an ge investigated , t he in troduction of a reduced co ncen t rat ion scale S = ['1] c, places t he viscosity-con cen t ration curves for different molec ular weights in t he same solven t on a more nearly common scale. This scale, S, is simply rela ted t o another reduced scale c/co. H ere Co represen ts t he concentration a t which t he equivalent spher es of t he coiling m olec ul es, a s d efin ed at infinite dilu tion, would just begin to o verlap . At c/co « 1, t he con cent ration dependence can be described in terms of hydrody namic in teract ion. This intera ction involves single molecul es and can also involve t he int rinsic v iscosity and interactions of aggregates of low order . An a ttempt is made t o d educe from t he viscosi ty data and on t he basis of cer tain hydrody namic results, t he equilibrium constant s and relative p opulations of s uch aggregates. R easonable values are obt ained . On approaching Co, t he a verage volume a vailable t o a chain molec ule in a good solve nt is redu ced because of t he cage form ed by its nearest neighbors. The effective press ure is just t he internal osmo tic press ure. This leads to an expression for t he concent rat ion depe ndence of t he viscosi ty, in terms of t he vi rial coeffi cie nts of osmotic press ure, luolec ular weight, and size. These equat ions are s hown to be in satisfactory agreemen t wi t h t he experimen tal data. In part icul ar , in t he neighborhood of Co one obtains r easo nabl e values for t he molec ular exte nsio n f actors of t he chain .

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“…Reduced viscosities a t various concentrations of sodium ligninsulphonates in 2 N sodium chloride. The nlolecular weights of the various fractions are listed in Table I. expressed by the equation of Simha (32) and Huggills (19) derived for noncharged interacting particles:…”

mentioning

confidence: 99%

Physicochemical Studies of Ligninsulphonates: Ii. Behavior as Polyelectrolytes

Gardon¹,

Mason²

1955

Can. J. Chem.

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Conductivity, dyestuff adsorption, and viscosity measurements on aqueous solutions of fractionated ligninsulphonate samples having various molecular weights indicate that they behave as flexible polyelectrolytes. There is evidence that ligninsulphonates of nlolecular mcight less than 5000 associate in solution in a manner analogous to rnicelle formation in colloidal electrolytes. From t h e variation of intrinsic viscosity with molecular weight, it may be collcluded that the degree of molecular branching of the high molecular weight ligninsulphonates is greater than that of the low molecular wcight fractions.

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Effect of concentration on the viscosity of dilute solutions

Cited by 94 publications

References 3 publications

Graft Copolymers of Styrene and Methyl Methacrylate: Part Ii: Viscosity Behavior

Graft Copolymers of Styrene and Methyl Methacrylate: Part Ii: Viscosity Behavior

Viscosity of dilute and moderately concentrated polymer solutions

Physicochemical Studies of Ligninsulphonates: Ii. Behavior as Polyelectrolytes

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