The effect of molecular-weight polydispersity

The value of the molecular quantities discussed in Chapter 5 all depend on the molecular weight of the polymer. Many actual samples of polymeric material are characterized by a distribution of molecular weights. In this section, the effect of polydispersity in the molecular weight will be discussed for each of the physical properties introduced above. 

Consider a sample of polymeric material with the same composition but with a distribution of chain lengths. Let there be N molecules in the sample. Each molecule is characterized by a mass, m,. The molecular weight for each species is given by Mj = When all the molecules are weighed, they are grouped by molecular weight and enumerated as NJ. The molecular-weight distribution is defined by the mole fraction of each species  

Because the probability distribution is based on the number fraction, the average is called the niunber average molecular weight. It is the normal mathematical definition of an average. 

Many properties depend on the weight fraction instead of the mole fraction. The weight fraction can be defined as  

The weight-averaged molecular weight is then defined as  

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The effect of molecular weight polydispersity is shown in Fig. 10 for blends of one PE with two different series of polystyrenes with constant (18,100 and 107,200) and different polydispersities. The interfacial tension decreased with increasing polydispersity in both cases, and the influence of polydispersity was higher for lower PS molecular weights. The decrease in interfacial tension could be... 

According to the concepts, given in the paper [7], a significant difference between the values of yield stress of equiconcentrated dispersions of mono- and polydisperse polymers and the effect of molecular weight of monodisperse polymers on the value of yield stress is connected with the specific adsorption on the surface of filler particles of shorter molecules, so that for polydisperse polymers (irrespective of their average molecular weight) this is the layer of the same molecules. At the same time, upon a transition to a number of monodisperse polymers, properties of the adsorption layer become different. 

Previously we have studied the effect of molecular weight and polydispersity... 

Nam KH, Jo WH (1995) The effect of molecular weight and polydispersity of polystyrene on the interfacial tension between polystyrene and polybutadiene. Polymer 36 3727-3731... 

The effect of molecular weight distribution, MWD, is somewhat more subtle but still very important. In general, commercial polymers have a rather broad molecular weight distribution, although materials produced using metallocene catalysts can have polydispersities... 

In this contribution, a series of polydisperse polystyrene sanples with various eoncentrations were electrospim from THF solution. The concentrations for the onset of fiber formation as well as the complete fiber formation were determined by SEM analysis. The rheological properties of the aforementioned polystyrene-THF solutions were also studied. The dependence of zero-shear viscosity on the weight average molecular weight as well as the solution concentrations was determined. Results are compared with the monodisperse systems. The effects of molecular weight distribution were studied. 

The effects of molecular weight distribution on the formation of electrospun polystyrene fibers in THF have been studied. A fibrous structure can be obtained at a lower concentration in polydisperse samples than in a monodisperse polymer. The higher moleeular weight fragments may contribute to entanglements even at low eoneentrations and thereby stabilize a fibrous structure. 

Instrumental band broadening or axial dispersion can cause calibration errors when employing polydisperse standards. Correction of the polydisperse standard calibration data for instrumental band broadening will minimize the effect on molecular weight analyses of polymer samples. However, as previously demonstrated in this report, when low dispersion SEC columns are employed instrumental band broadening is minimized and the effect on use of linear calibration methodology is negligible. 

The molecular weight distribution obtained from SEC analysis was also shown in Fig. 8. In order to check the effect of the estimated exponent a(-0.55) on molecular weight distribution for Ei branched PVAc, we used another a(-0.58) value to compute a new calibration curve as shown in Fig. 9. The two calibration curves almost overlapped with each other. The results are listed in Table 2. In both cases, we obtained the same weight-average molecular weight and the polydispersity index (M /M ). Thus, we could confirm that in using a two-point (Bq and %l) estimate for a, we have not introduced an appreciable error in the determination of molecular weight distribution of branched PVAc. 

Figure 1.6 Effect of molecular weight on the strength-melt flow index interrelationship of polystyrene for three polydispersity indices.

It is much easier to notice the effect of slow initiation by analysis of the evolution of molecular weights with conversion in Figs. 2 and 3. The small increase of the polymerization degree, in relation to the ideal case, disappears for the ratio / , = 0.1 at approximately 40% conversion. However, it is necessary to add subsequent portions of a monomer (conversions > 100%) for ratios / , = 0.03 and R, = 0.01 to asymptotically approach ideal M values as shown in Fig. 3. The polydispersities in systems with slow initiation depend on the ratio [M]0/[l]o and / , and are very low for R( = 1 and 10 (Af, /Af < 1.02) but approach MJMn 1.15 for the ratio... 

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