Viscosity of amorphous polymers

At the high polymer concentration used in plasticized systems the viscosity of amorphous polymer is given by the modified Rouse theory at low molecular weight, M - 2Mr [from equation (47)] and by the modified Doi-Edwards equation at high molecular weight. In the first case... 

What is the relationship Newtonian viscosity of amorphous polymers and their chain length ... 

If the viscosity of amorphous polymers is measured at two different temperatures T and Tg, the above expression becomes... 

Fig. 5. Schematic illustration of general form of temperature dependence of zero-shear melt viscosities % of amorphous polymers. It is seen that % has a non-Arrhenius universal shape for Tg S T < 1.2Tg, where the reduced temperature TITg serves as the corresponding states variable. This universal behavior is lost above 1.27 g. The curves for different polymers separate from each other, as shown below for three polymers. For T 1.2T g, an Arrhenius-like (activated flow) regime is approached asymptotically. The activation energy in the extrapolation to the hypothetical limit of inflnite temperature depends on the chemical structure of the polymer.

The flexibility of amorphous polymers above the glassy state, where segmental mobility is possible, is governed by the same forces as melt viscosity and is dependent on a wriggling type of segment motion in the polymer chains. This flexibility is increased when many methylene groups (—CH2—) or oxygen atoms (—O—) are present. Thus, the flexibility of aliphatic polyesters usually increases as m is increased ... 

Aharoni has recently proposed a theory of flow based on entanglements between loops on the surface of collapsed coils (43, 228). The basic picture of amorphous polymer structure is almost certainly incorrect (see Section 2), and the derivation of viscosity is even more speculative than the others in this section. 

For concentrated solutions of amorphous polymers, Bueche s mathematical model shows the ratio of zero shear viscosities of branched and linear polymer above the critical molecular weight in the entanglement region to be (28) ... 

Inoue T, Okamoto H, Osaki K (1991) Birefringence of amorphous polymers. 1 Dynamic measurements on polystyrene. Macromolecules 24 5670—5675 Isayev AI (1973) Generalised characterisation of relaxation properties and high elasticity of polymer systems. J Polym Sci A-2 116 2123—2133 Ito Y, Shishido S (1972) Critical molecular weight for onset of non-Newtonian flow and upper Newtonian viscosity of polydimethylsiloxane. J Polym Sci Polym Phys Ed 10 2239— 2248... 

Paul W, Smith GD (2004) Structure and dynamics of amorphous polymers computer simulations compared to experiment and theory. Rep Prog Phys 67 1117-1185 Peterlin A (1967) Frequency dependence of intrinsic viscosity of macromolecules with finite internal viscosity. J Polym Sci A - 2 5(1) 179-193 Peterlin A (1972) Origin of internal viscosity in linear macromolecules. Polym Lett 10 101— 105... 

The activation energies for the backbone motion of P(4HB) and the 3HB and 4HB units in the P(3HB-co-4HB)s, derived from the DEM model analysis, are found to be similar and in the range 42-47 kJ/mol [79]. This range is typical of amorphous polymers at temperatures above Tg, but they are greater than typical ones for polymers in solution, possibly due to the increased apparent viscosity exerted by the amorphous matrix on the moving backbone segment [79]. The activation energy observed for the backbone motion of P(3HB) in chloroform solution is 17 kJ/mol [72]. 

The glass transition temperature (Tg) is the key material parameter in determining the temperature dependence of the melt viscosity. An amorphous polymer will typically be "solidlike" below Tg, "rubberlike" between Tg and a crossover temperature Tx above but not too far from 1.2-Tg, and "molten" with viscous flow over the range of temperatures above Tx. 

The Arrhenius equation has been employed as a first approximation in an attempt to define the temperature dependence of physical degradation processes. However, the use of the WLF equation (Eq. 3.6), developed by Williams, Landel, and Ferry to describe the temperature dependence of the relaxation mechanisms of amorphous polymers, appears to have merit for physical degradation processes that are governed by viscosity. 

Kanaya, T and Kaji, K. Dynamcis in the Glassy State and Near the Glass Transition of Amorphous Polymers as Studied by Neutron Scattering. Vol. 154, pp. 87-141. Kandyrin, L. B. and Kuleznev, V. N. The Dependence of Viscosity on the Composition of Concentrated Dispersions and the Free Volume Concept of Disperse Systems. Vol. 103, pp. 103-148. 

This polyamide is prepared somewhat differently. Salts of the diamine isomers with terephthalic acid are only partially polycondensed and the reaction is completed during extrusionj because the melt viscosity of the polymer is very high. The product is amorphous and exhibits greater light trasmittancy. It melts at 200 °C and is sold under the trade name of Trogamid T. 

Many different molecular weight grades of VP-based polymers, characterized by viscosity, are available commercially. The determination of viscosity is historically satisfactory for quality assurance purposes however, most physical properties of polymers are directly related to molecular weight. For example, the glass transition temperature and tensile strength of amorphous polymers are known to depend on molecular weight. The melt viscosity of polymers and the bulk viscosity of concentrated polymer solutions are also known to depend on molecular weight. 

The entanglement of the polymer chains at the weld line is related to their diffusion rate, which is a function of temperature and melt viscosity of the polymer [95]. The holding pressure in the cavity and the injection speed can also affect the weld line strength [96]. Many predictive models for the weld line strength of thermoplastic amorphous polymers in relation to the viscoelastic properties and processing conditions such as the melt temperature, the mold temperature, and the holding time, have been proposed [97-99]. 

Another consideration in the selection of technology platform is the polymer chosen for the amorphous solid dispersion formulation. The fact that many pharmaceutical polymers degrade, crosslink, or lose functionality at high temperatures has already been discussed. However, the melt viscosity of a polymer is critical to the ability to extrude the amorphous solid dispersion within the capabilities of the extrusion equipment. The melt viscosity as a function of temperature and shear rate varies considerably across pharmaceutical polymers (Chokshi et al. 2005). Formulation melt viscosities in the range of 10-100,000 Pa s are generally acceptable for HME, although the range depends heavily on the torque limit capability of the particular extruder. 

The fusion of amorphous polymer particles above their Tg is a slow coalescence process most likely driven by surface energy, which reduces the free volume and the total surface area (Rosenzweig and Narkis 1983 Palzer 2011). Since amorphous dispersions often have a polymeric component, the sintering of amorphous polymer colloids occurs at/or above the Tg which is dependent on the particle size and packing fraction within the polymer as determined by the melt viscosity (Mazur et al. 1997). 

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