Theory of the high-frequency limiting viscosity of a dilute polymer solution

Summary A general formula for the high-frequency limiting viscosity of dilute solution of polymers is derived.N beads successively connected withN-1 bonds are employed as the model of a polymer chain and the viscosity is calculated from the sum of frictional loss of each beads, assuming that the chain is free-draining, the internal rotation of the bonds is frozen and the beads move by the hydrodynamic force under some geometrical constraints. The derived formula proves to be equivalent to the frequency-independent term in theErpenbeck-Kirkwood theory on the viscosity for the same model. The formula is applied to a freely jointed chain and it is shown that the intrinsic limiting viscosity of the chain is 2.51 times as large as that of the individual segment which consists of a single bond with two half beads at each ends. This result is compared with existing experimental values of the high-frequency viscosity of poly(L-glutamic acid) in the broken helix state and polystyrene in a highly viscous solvent.

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Zusammenfassung Eine allgemeine Formel für die Hochfrequenz-Grenzviskosität von verdünnten Polymerlösungen wird abgeleitet.N Perlen miteinander verknüpft mitN-1-Bindungen werden als Modell einer Polymerkette verwendet und die Viskosität berechnet von der Summe der Reibungsverluste aller Perlen. Dabei wird angenommen, daß die Kette frei durchströmt ist und die interne Rotation um die Bindung eingefroren ist, sowie daß die Perlen sich durch hydrodynamische Kräfte unter gewissen geometrischen Spannungen bewegen. Die abgeleitete Formel zeigt Gleichheit zu dem frequenzunabhängigen Term in derErpenbeck-Kirkwood-Theorie für die Viskosität des gleichen Modells. Die Formel wird angewendet auf freibewegliche Ketten, und es wird gezeigt, daß die intrinsic-Grenzviskosität der Kette 2,51 mal größer ist als die eines individuellen Segments, welches aus einer Einzelbindung mit zwei Halbperlen an jedem Ende besteht. Dieses Ergebnis wird mit gegebenen experimentellen Daten für die Hochfrequenzviskosität von Poly-L-glutamatsäure im Zustand der stückweisen Helix und von Polystyrol im hochviskosen Zustand verglichen.

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The viscosity anomaly of polymer mixture solution in extremely dilute concentration region

The measured reduced viscosity-concentration (η_sp/C-C) curves of compatible PPO/PS incompatible PMMA/PS mixtures with different composition in toluene all deviate linear and reveal downward turn in extremely dilute concentration region. Moreover, with the variation of composition, the η_sp/C-C curve of PS/PMMA/m-xylene solution bends downwards sometimes and bends upwards sometimes in the extremely dilute concentration region. It indicates that such viscosity anomaly should not be attributed simply to incompatibility, but be related to solvent, composition and so on. It is further suggested that, like the single polymer solution, the viscosity anomaly of polymer mixture solution be resulted mainly from the interference of wall effects on viscosity measurement, which could be eliminated quantitatively with a proposed theoretical formula.     

Memory effect in the chain-collapse process in a dilute polymer solution

The effect of temperature perturbation on a single-chain-collapse process was studied for poly(methyl methacrylate) with the molecular weight M(w)=1.05 x 10(7) in the mixed solvent of tert-butyl alcohol+water (2.5 vol %). In the chain-collapse process after a quench from the theta; temperature to a temperature T(1), the temperature was changed from T(1) to T(2) at the time t(1) after the quench and returned to T(1) at the time t(1)+t(2). In the three stages at T(1), T(2), and T(1), measurements of the mean-square radius of gyration of polymer chains were carried out by static light scattering and the chain-collapse process was represented by the expansion factor as a function of time. An effect of chain aggregation on the measurements was negligibly small because of the very slow phase separation. For the negative temperature perturbation (T(1)>T(2)), the chain-collapse processes observed in the first and third stages were connected smoothly and agreed with the collapse process due to a single-stage quench to T(1). A memory of the chain collapse in the first stage at T(1) was found to persist into the third stage at the same temperature T(1) without being affected by the temperature perturbation of T(2) during t(2). The memory effect was observed irrespective of the time period of t(2). The positive temperature perturbation (T(1)相似文献   

Thermal diffusion of dilute polymer solutions: the role of solvent viscosity

We have performed measurements of the thermal diffusion coefficient D(T) in the dilute limit on polystyrene in cyclo-octane, cyclohexane, benzene, toluene, tetrahydrofuran, ethyl acetate, and methyl ethyl ketone and of poly(dimethyl-siloxane) in toluene. These data have been combined with literature data to test various theoretical predictions. The viscosity is identified as the dominating and only relevant solvent parameter. On the polymer side, the size or mass of an effective correlated segment determines the strength of the Soret effect. Large and heavy effective segments, as found in stiffer chains, lead to higher D(T).     

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Theoretical formulas for the intrinsic viscosity and viscoelastic properties of some model branched molecules in dilute solution are calculated by means of the normal coordinate method of Rouse modified to include hydrodynamic interactions. The calculations are exact except for the usual approximation of the hydrodynamic interactions by the Kirkwood-Riseman formula. The ratio of the intrinsic viscosity of a branched molecule to that of a linear molecule of the same weight is found to vary almost as the square root of the ratio of the mean square radii, instead of as the latter ratio to three-halves power, as has been postulated before. It is proposed that this square root relation is applicable in general to branched molecules of all types. Several sets of experimental data in the literature are shown to agree well with this hypothesis.     

A theory of viscosity of dilute and moderately concentrated polymer solutions

A model theory of viscosity η for moderately concentrated polymer solutions is based on the assumption of a “local viscosity” effect and intermolecular hydrodynamic and thermodynamic interactions. It is shown that η is given by

$\text{η = η}{}_{\mathrm{o}}\text{{1 + γc[η]}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{·}\text{exp}\text{H}{}_{\mathrm{o}}\text{RT}\text{aø}\text{1 ? aø}$

where γ is 0–0.4 and depends on the quality of the solvent, a varies between 0,4 and 0.8 and depends on the fraction of the “free volume” of the systems, H₀ is the activation energy of the solvent and π is the polymer volume concentration. The dependence of η and “activation energy” of π and T for various molecular weights and qualities of solvents is described quantitatively. Anomalous dependences of [η] and of η on M for low polymer are obtained. An expression for η is proposed:

$\text{η}\text{η}{}_{\mathrm{o}}{}^{\mathrm{<mtext>1\; ?\; 2</mtext><mtext>K</mtext>}}\text{= {1 + (1 ? 2K)c[η]}F(π)}$

where K is the Huggins-Martin coefficient and F(π) = 1 for most solutions when T is > T_g. For poor solvents the H vs c curve (where H is the activation energy of η of solution) has a minimum value at moderate concentrations. For good solvents, H depends slightly on the molecular weight according to an empirical equation:

$\text{H = H}{}_{\mathrm{o}}\text{+}\text{660}\text{α}{}^3\text{1}\text{n}\text{η}\text{η}{}_{\mathrm{o}}$

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Counterion and solvent effects on the dilute solution viscosity of polystyrene ionomers

We present an analysis of data on the intrinsic viscosity [η] of sulfo-polystyrene ionomers in several solvents for a variety of sulfonation levels and counterions. For solvents of low dielectric constant, 2 < ε < 18, [η] decreases from the base polymer value [η]₀ with increasing substitution level. This behavior was attributed to intramolecular association of ionic dipoles. The ratio [η]/[η]₀ was found to depend on a single reduced variable α_Aα_Sx, where x is the fractional substitution, α_A depends only on the counterion, and α_S ∝ ε^?1 depends only on the solvent. For solvents of high dielectric constant, 36 < ε < 47, [η] increases approximately as x³, and counterion effects are small. This behavior was attributed to ionic dissociation, giving rise to a polyelectrolyte effect. Implications of the low ε results are discussed in relation to association-induced gelation behavior and possible generalizations of the reduced variables approach.     

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 Applying the technique of Brownian dynamics simulation, we have studied the fracture process of flexible polymer chains when they encounter an extensional flow field of transient character. For this purpose, a mathematical model was made of an experimental device used earlier by other authors to study fracture of polystyrene in dilute solution. The polymer/solvent system studied was a very dilute solution in theta conditions. The polymer molecule was modeled as a FENE bead-spring chain, including a modification to allow for chain fracture. The simulation results showed that the fracture yield depended strongly on flow rate and on molecular weight. We have characterized the molecular-weight dependence of the critical flow rate which is necessary for fracture to occur. The distribution of the result-ing fragments is interpreted in terms of the conformation of the chains prior to fracture. Received: 17 September 1996 Accepted: 29 May 1997     

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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.     

Influence of second virial coefficient and persistence length on dilute solution polymer conformation

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