Vogel Equation Research Articles

Transitions in poly(vinylidene fluoride) by thermally stimulated techniques

Abstract Multiple transitions in poly(vinylidene fluoride)-PVF2 - have been studied by thermally stimulated techniques: Thermostimulated creep -TSCr - and thermostimulated current -TSCu -. The resolving power of these methods have allowed us to investigate the fine structure of transitions in PVF2. A relaxation mode is observed around the glass transition temperature -Tg -; it can be described by a distribution of relaxation times following an Arrhenius equation and it has been attributed to microbrownien motions of the amorphous chains. Another relaxation mode is revealed ∼50° higher than Tg. It corresponds to a distribution of relaxation times obeying a Vogel equation and has been assigned to the fluidification of the amorphous chains. In both cases, two sub-modes can be distinguished:The sub-mode observed at lower temperature has been attributed to the amorphous regions free from constraint, while the other one at higher temperature, has been assigned to amorphous chains under constraints from crystall...

Thermally stimulated current (TSC) study of the Tg and Tll transitions in anionic polystyrenes

AbstractThe thermally stimulated current (TSC) technique has been used to investigate three anionic polystyrenes of M̄n 17,000, 71,700, and 1.55 × 106, i.e., M < Mc, M > Mc, and M ≫ Mc, where Mc is the entanglement molecular weight. A current maximum near Tg designated TMg, has relaxation times which follow an Arrhenius equation. A second current maximum at T > Tg appears to be the Tll process and is designated TMll. Relaxation times for it follow a Vogel equation. TMg and TMll vary with molecular weight, increasing below Mc and leveling off above Mc at a temperature of about 170°C. Values of TMg and TMll are compared with values of Tg and Tll obtained from torsional braid analysis, which involves melt flow; and with differential‐scanning‐calorimetric values on fused films, where there is no transport of polymer. It is concluded from such cross‐comparisons that TSC, at least for polystyrene, is a quasistatic test which may involve microscopic viscosity. Macroscopic viscosity does not play a role. The ratio TMll/TMg is in the range 1.10–1.16, similar to Tll/Tg values by other methods. A few comments about Tll in atactic poly(methyl methacrylate) by the TSC method are given.

Multiple transitions in isotactic polypropylene around and above the glass transition

Abstract Gas chromatography, thermal expansion, dynamic mechanical relaxation and thermally stimulated current measurements were used to study multiple transitions in isotactic polypropylene. The crystalline phase relaxation Tαc was decomposed into two components, Tαc1 and Tαc1, in order of decreasing temperature. The activation energy of the Tαc mode was found to be lower than that of the relaxation observed around the glass transition temperature. Thermally stimulated current (TSC) measurements revealed the existence of an apparent double liquid-liquid transition at 39°C and 68 °C in undrawn polypropylene and at 28°C and 55°C in drawn polypropylene. These TSC peaks correspond to a relaxation time following a Vogel equation whose critical temperatures let us predict an apparent double glass transition in polypropylene.

Conformational entropy of liquid polyethylene

Abstract In previous work [I], the relationship between the conformational entropy Sc, associated with rotational isomerization about main-chain bonds, and T0, the constant in the Vogel equation for polymer liquid mobility, was derived for a three-state rotational model with independent bond rotations. The present study takes into account the exclusion of transitions between gauche states of opposite sign (the “pentane interference”).

TSC study of deuteration of polystyrene

A comparative study of natural and deuterated polysterene has been performed by thermally stimulated currents (TSC). Around the glass-rubber transition temperature ( T g a TSC peak is observed whose relaxation times obey an Arrhenius equation. At 50° above T g another TSC peak is observed whose relaxation time obeys a Vogel equation. Deuteration is found to increase the values of T g .

Rotational energetics in vinyl polymer liquids: 1. Poly(vinyl acetate)

Mobilities of liquid poly(vinyl acetate) as expressed by the Vogel equation, − Inμ = B T − T 0 ), are extrapolated to negative pressure using previously determined pressure coefficients. The extrapolations are extended to P∗ = −b ( Tait) where the liquid volume becomes ‘infinite’ and the polymer chains are in the hypothetical ‘isolated’ state. By an analysis of the rotational kinetics and relationships developed previously, this procedure leads to U∗ and V∗ for the ‘isolated’ chain, where U∗ is the energy difference between the rotational states and V∗ is an energy barrier between these states. It is found that the greatest increase occurs between U∗ for the ‘isolated’ chain and U for the liquid at atmospheric pressure, with relatively little further increase up to 2000 bars. The energy barrier V, on the other hand, increases more uniformly over the entire pressure range from P∗ to 2000 bars. On the basis of the analyses of the rotational energetics and kinetics, an approach to a unified molecular interpretation of shear-induced lowering of viscosity (non-Newtonian viscosity) and shear-induced crystallization in certain flowing polymer liquids is suggested.

A Molecular Interpretation of the Vogel Equation for Polymer Liquid Mobility

A Molecular Interpretation of the Vogel Equation for Polymer Liquid Mobility

Viscometric properties of concentrated polymer solutions. III. Dependence of viscosity on temperature and determination of the parameters of Vogel's equation

Viscometric properties of concentrated polymer solutions. III. Dependence of viscosity on temperature and determination of the parameters of Vogel's equation

Melt Viscosity of Random Copolymers of Butadiene and Styrene Prepared by Anionic Polymerization

The melt viscosity of narrow distribution, linear, random copolymers of butadiene (75%) and styrene (25%) prepared by anionic polymerization was investigated in both the Newtonian and non-Newtonian regimes of flow. The Newtonian viscosity is shown to obey the usual 3.4th power dependence on Mw The temperature dependence is represented satisfactorily by the Vogel equation, as modified by Berry and Fox. Non-Newtonian viscosities are reduced to a single master curve for all polymers, temperatures, and shear rates, using the Newtonian viscosity as the sole shift factor (η/η0 vs. η0γ̇). Comparison of this master curve with those of two narrow distribution polybutadienes of different microstructure produces agreement within 0.2 of a logarithmic unit on the η0γ̇-scale. All three master curves lie one to two decades toward higher reduced shear rates than various “universal” curves reported in the literature for polymers of broader molecular weight distribution.

The Viscosity of Carboxy-Terminated Polybutadienes

Abstract Newtonian viscosities have been determined for carboxy-terminated polybutadienes varying in microstructure, molecular weight and degree of carboxy-functionality. The latter was varied by total or partial methylation of initially di- or mono-functional polymers. The viscosity of non-functional (methylated) polybutadienes is shown to be proportional to the 3.4 power of the weight average chain length, irrespective of microstructure, provided the comparison is made at equal (T−Tg). The temperature dependence of viscosity is well represented by the Vogel equation, with constants given by Berry and Fox for polybutadiene of 8% vinyl unsaturation, again independent of microstructure. The presence of carboxy end groups increases the viscosity as a result of an association equilibrium with raises the effective molecular weight of the polymer. The absolute magnitude of the temperature coefficient of viscosity increases with carboxy-functionality, as required by the postulated association equilibrium. Theoretical calculations show that the viscosities of mono-carboxy polybutadiene and α,ω-dicarboxypolybutadiene cannot be reconciled unless some of the carboxy-associations in the latter are intramolecular. In the molecular weight range considered the glass temperature is substantially independent of carboxy-functionality.

Similarity between Oil Cooling Pipe and Heating Pipe (Rep. I & II)

I have obtained the similarity between oil cooling-pipe and oil heating-pipe, where the oil flows in a stream-line flow and its viscosity changes by temperature only and the other physical properties are constant. As a relation of viscosity and temperature, I have applied the Vogel's equation (29). I have reduced the similarity of (32) from the foundamental equations, by dimensional analysis, where θm is dimensionless mean temperature of issued oil and Wc/kN is Graetz number and s'is a dimensionless groupe which are defined by (34), and tv is a proper temperature of oil. As general liquids, these viscosities are not so large, always we can take -273 instead of tv. Then Vogel's equation becomes Andrade's equation (2) and s'becomes s (24) and similarity is (26). When change of viscosity is taken into consideration, θm is not only affected by Graetz number, but affected by dimensionless quantity s'.

The Engler Viscometer and the Theory of Laminar Flow at the Entrance of a Tube

In his lecture at the last meeting of The Society of Rheology Dr. Erk considered the Engler viscometer and pointed out that the relationship between kinematic vicosity ν and Engler degrees E is adequately represented by Vogel's empirical equation ν = E100 {7.6(1−1/E3)}. In contrast, as Dr. Erk also indicated, the theoretical equations of Mises and of the author show appreciable departures from experimental values. With regard to the equation considered by the author as an approximate equation for high viscosities, I have since found that an error was made in its derivation, so that the failure of the equation is not to be ascribed to the theory of laminar entrance-flow. Meanwhile it has been demonstrated that the theory of laminar entrance-flow, as far as one can expect it, actually agrees with observations and with Vogel's equation, as I should like to show you briefly.