Temperature viscosity-molecular weight relationship

Kar, F. and Arslan, N. 1999b. Effect of temperature and concentration on viscosity of orange peel pectin solutions and intrinsic viscosity-molecular weight relationship, Carbohydr. Polym., 40 277-284. 

This reference (1) contains constants for intrinsic viscosity-molecular weight relationships that have been determined for a number of molecular weight ranges, solvents, and temperatures. 

Notice the similarity between the relationship for liquid viscosity [Eq. (4.7)] and that for gaseous viscosity [Eq. (4.6)]. They both have a square root dependence on temperature and molecular weight and depend on the inverse square of the collision diameter [can you prove this for Eq. 4.7) ]. So, at least in principle, there is a fundamental relationship between the structure of a liquid and its viscosity. 

Fox TG, Flory PJ (1948) Viscosity-molecular weight and viscosity-temperature relationships for polystyrene and polyisobutylene. J Am Chem Soc 70(7) 2384-2395 Freed KF, Edwards SF (1974) Polymer viscosity in concentrated solutions. J Chem Phys 61(9) 3626-3633... 

The molecular weight of the polymer formed is a function of the reaction temperature used during the polymerization. Lower temperatures favor increased molecular weights. The relationship between polymerization temperature and molecular weight of resin (as expressed by relative viscosity) is shown in Figure 6. In commercial practice, the molecular weight is controlled by reaction temperature, and the reaction rate is controlled by the selection of the initiator and its concentration. 

Other evidence for the model of molecular stretching comes from the qualitative relationship between onset and molecular time scale [7,8]. The solution viscosity, temperature, and molecular weight all change onset in the way predicted by the time scale hypothesis. The magnitude of the change is not exactly as predicted, but the experiments did not attempt to control the variables previously listed. Concentrations were much larger than the individual molecule limit which also means that the time scale would depend upon concentration. Since the direction of the change is correct, the time scale relationship to onset must be correct also. 

Fox TG, Hory PJ. Viscosity-molecular weight and viscosity-temperature relationships for polystyrene and polyisobutylene. J Am ChemSoc 1948 70 2384-95. 

Section C gives the limiting viscosity number -molecular weight relationships for polymers, in various solvents and at various temperatures. The table eontains the constants of the equation... 

The analysis of the main properties of aqueous solutions of polyacrylamide and copolymers of acrylamide has been reviewed [4,5]. The main characteristics of aqueous solutions of polyacrylamide is viscosity. The viscosity of aqueous solutions increases with concentration and molecular weight of polyacrylamide and decreases with increasing temperature. The relationship between the intrinsic viscosity [q]) in cmVg and the molecular weight for polyacrylamide follows the Mark-Houwink equations ... 

In some cases the relationship between polymer intrinsic viscosity ([n]) and molecular weight (M) has been established for the SEC solvent and temperature conditions i.e., the empirical Mark-Houwink coefficients (2)(K,a) in the equation... 

The longest relaxation time. t,. corresponds to p = 1. The important characteristics of the polymer are its steady-state viscosity > at zero rate of shear, molecular weight A/, and its density p at temperature 7" R is the gas constant, and N is the number of statistical segments in the polymer chain. For vinyl polymers N contains about 10 to 20 monomer units. This equation holds only for the longer relaxation times (i.e., in the terminal zone). In this region the stress-relaxation curve is now given by a sum of exponential terms just as in equation (10), but the number of terms in the sum and the relationship between the T S of each term is specified completely. Thus... 

For the solubility of TPA in prepolymer, no data are available and the polymer-solvent interaction parameter X of the Flory-Huggins relationship is not accurately known. No experimental data are available for the vapour pressures of dimer or trimer. The published values for the diffusion coefficient of EG in solid and molten PET vary by orders of magnitude. For the diffusion of water, acetaldehyde and DEG in polymer, no reliable data are available. It is not even agreed upon if the mutual diffusion coefficients depend on the polymer molecular weight or on the melt viscosity, and if they are linear or exponential functions of temperature. Molecular modelling, accompanied by the rapid growth of computer performance, will hopefully help to solve this problem in the near future. The mass-transfer mechanisms for by-products in solid PET are not established, and the dependency of the solid-state polycondensation rate on crystallinity is still a matter of assumptions. 

Since the intrinsic viscosity depends not only on the size of the macromolecule but also on its shape, on the solvent, and on the temperature, there is no simple relationship for the direct calculation of molecular weights from viscosity measurements. However, the Mark-Houwink-Kuhn equation gives a general description of how the molecular weight can be calculated from the intrinsic viscosity ... 

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