Viscosity of linear polymers

The status of current theories of the low shear-rate viscosities (rj0) of polymer melts (and concentrated solutions) was reviewed by Berry and Fox in 1968 (52), since when there has been little development. The viscosity of linear polymers of low MW at constant temperature (or more precisely constant free volume is proportional to Mw, but at high MW it is proportional to a higher power M, where x is empirically about 3.4-3.5 the change of slope of a ogt]0/logMw plot is fairly abrupt The high exponent 3.4—3.5 is attributed to the effects of chain... 

Godunov SK, Romenskii El (1972) Non-steady state equation of non-linear theory of elasticity in Euler co-ordinates. Zh Prikl Mech Technich Phys 6 124-144 (in Russian) Golovicheva IE, Sinovich SA, Pyshnograi GV (2000) Effect of molecular weight on shear and elongational viscosity of linear polymers. Prikl Mech Tekhnich Fiz 41(2) 154-160 (in Russian)... 

Pyshnograi GV (1996) An initial approximation in the theory of viscoelasticity of linear polymers and non-linear effects. J Appl Mech Techn Phys 37(1) 123—128 Pyshnograi GV (1997) The structure approach in the theory of flow of solutions and melts of linear polymers. J Appl Mech Techn Phys 38(3) 122—130 Pyshnograi GV, Pokrovskii VN (1988) Stress dependence of stationary shear viscosity of linear polymers in the molecular field theory. Polym Sci USSR 30 2624—2629 Pyshnograi GV, Pokrovskii VN, Yanovsky YuG, Karnet YuN, Obraztsov IF (1994) Constitutive equation on non-linear viscoelastic (polymer) media in zeroth approximation by parameter of molecular theory and conclusions for shear and extension. Phys — Doklady 39(12) 889-892... 

Viscosity of linear polymer calculated from Monte Carlo simulations. Filled circles are repton model data from M. Rubinstein, Phys. Rev. Lett. 59,1946 (1987), with data range extended by D. Shirvanyants and open squares are Evans-Edwards model data from J. M. Deutsch and T. L. Madden,... 

The intrinsic viscosity of linear polymers in good solvents may be written as... 

The intrinsic viscosity (or limiting viscosity number) can be obtained by measuring the relative viscosity at different concentrations and then taking the limit of the specific viscosity when the concentration is extrapolated to zero (Fig. 17.7). The behavior of the intrinsic viscosity with concentration depends on the nature of both the specific polymer molecule and the solvent. Since the intrinsic viscosity of linear polymers is related to the MW, for linear macromolecules intrinsic viscosity measurements provide a simple method for the determination of MW when the relationship between viscosity and MW is known. 

Takahashi, Y, Isono, Y, Noda, L, and Nagasawa, M., Zero-shear viscosity of linear polymer solutions over a wide range of concentrations. Macromolecules, 18,1002-1008 (1985). 

Solution viscosities of linear polymers relate empirically to their molecular weights. This is used in various ways to designate the size of polymers. The efflux time / of a polymer solution through a capillary is measured. This is related to the efflux time to of the pure solvent. Typical viscometers, like those designed by Ubbelohde, Cannon-Fenske, and other similar ones, are used in a constant temperature bath. The following relationships are used ... 

A dependence of the intrinsic viscosity on the molar mass for branched polymers was already shown in Fig. 5.11. The intrinsic viscosity of branched polymers is lower than the intrinsic viscosity of linear polymers with the same molar mass. 

Most properties of linear polymers are controlled by two different factors. The chemical constitution of tire monomers detennines tire interaction strengtli between tire chains, tire interactions of tire polymer witli host molecules or witli interfaces. The monomer stmcture also detennines tire possible local confonnations of tire polymer chain. This relationship between the molecular stmcture and any interaction witli surrounding molecules is similar to tliat found for low-molecular-weight compounds. The second important parameter tliat controls polymer properties is tire molecular weight. Contrary to tire situation for low-molecular-weight compounds, it plays a fimdamental role in polymer behaviour. It detennines tire slow-mode dynamics and tire viscosity of polymers in solutions and in tire melt. These properties are of utmost importance in polymer rheology and condition tlieir processability. The mechanical properties, solubility and miscibility of different polymers also depend on tlieir molecular weights. 

It has been shown" that branched polymers have lower melting points and viscosities than linear polymers of the same molecular weight. The viscosity of the silicone fluids is much less affected by temperature than with the corresponding paraffins (see Figure 29.2). 

Solution viscosity is empirically related to molecular weight for linear polymers. Intrinsic viscosity ([17]) is (risp/Qc-a< where is (rj, - 1) and C is a concentration of the polymer in solution. The quantity Vr represents J7/170, where rj and tjq are the viscosity of the polymer solution and pure solvent, respectively. Inherent viscosity (T i h) is ln(VQ-... 

Fig. 7. a Mark-Houwink plot of highly branched PMMA obtained by SCVCP of MMA with the inimer 12. (-)RI signal ( ) intrinsic viscosity of feed, ( ) intrinsic viscosity of linear PMMA (O) contraction factor, g. b Separation of feed polymer into fractions by preparative SEC. (-) RI signal of fractions (-) accumulated RI signals (.) RI signal of feed polymer. (Repro-... 

The addition of potassium bromide (0.01M) suppressed the sharp rise in reduced viscosity at low concentration and a linear relationship was obtained. By extrapolation of the line, the intrinsic viscosity of the polymer was found to be 0.15 dL/g. 

Lai et al. [100] proposed the use of the Dow Rheology Index (DRI) as an indicator for comparing branching level in industrial polymers. For a linear polymer molecule, like unbranched polyethylene, the viscosity of the polymer as a function of the applied shear rate is given by the Cross equation [84,100],... 

The dilution properties of hyperbranched polymers also differ from those of linear polymers. In a comparison between two alkyd resin systems, where one was a conventional high solid alkyd and the other based on a hyperbranched aliphatic polyester, the conventional high solid alkyd was seen to exhibit a higher viscosity [113]. A more rapid decrease in viscosity with solvent content was noted for the hyperbranched alkyd when the polymers were diluted. 

Another very special feature of these polymers is the relationship between molecular weight and melt viscosity. For linear polymers, the increase in melt viscosity with molecular weight is linear with a transition to a 3.4 power law when the molecular weight reaches the critical mass for entanglements, M. For hyperbranched polymers, the increase in viscosity follows a different curve it is less pronounced and levels off at higher molecular weights [117] (Fig. 11). 

The prediction for the diffusion constant at Eq. (4) is in very good agreement with measurements of the self-diffusion constants of polymer melts [14] while results on the viscosity have consistently given a stronger dependence of the characteristic times and viscosities on molecular weight of approximately The investigation of these discrepancies in the context of linear polymers has de-... 

The viscosity of some polymers at constant temperature is essentially Newtonian over a wide shear rate range. At low enough shear rates all polymers approach a Newtonian response that is, the shear stress is essentially proportional to the shear rate, and the linear slope is the viscosity. Generally, the deviation of the viscosity response to a pseudoplastic is a function of molecular weight, molecular weight distribution, polymer structure, and temperature. A model was developed by Adams and Campbell [18] that predicts the non-Newtonian shear viscosity behavior for linear polymers using four parameters. The Adams-Campbell model is as follows ... 

The Newtonian viscosity of some polymers increases essentially linearly with the weight average molecular weight, and for other polymers the Newtonian viscosity increases with an exponential power of the molecular weight. The exponential power is found to be about 3.4, but this power does deviate for some polymers. These two transitions, Newtonian to pseudo-plastic and linear to 3.4 power in the Newtonian range are often related to molecular structure as demonstrated in Fig. 3.31 [22]. The polystyrene data used to develop the Adams-Campbell viscosity function showed almost no shear thinning at [18]. That is why the power law slope, s, is a function of and M. At the slope is zero and the material would be essentially Newtonian. 

The reciprocal of the intrinsic viscosities of the polymer would be a unique and linear function of the amount of ethyl groups (deriving from ethylaluminum found in the polymer. 

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