Distribution curves/index molecular weight

Other analysis methods dependent on multiple detectors can be implemented using this automated system. Two methods under development are the use of a continuous viscometer detector with a refractive index detector to yield absolute molecular weight and branching, utilizing the universal calibration curve concept (4), and the use of a UV or IR detector with the refractive index detector to measure compositional distribution as a function of molecular weight. 

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. 

The GPC analysis of block copolymers is handicapped by the difficulty in obtaining a calibration curve. A method has recently been suggested to circumvent this difficulty by using the calibration curves of homopolymers. This method has been extended so that the calibration curves of block copolymers of various compositions can be constructed from the calibration curve of one-component homopolymers and Mark-Houwink parameters. The intrinsic viscosity data on styrene-butadiene and styrene-methyl methacrylate block polymers were used for verification. The average molecular weight determined by this method is in excellent agreement with osmometry data while the molecular weight distribution is considerably narrower than what is implied by the polydispersity index calculated from the GPC curve in the customary manner. 

If all species in a polymer sample have same molecular weight (that is, the polymer is monodisperse) then Mn = M i — Mz- Such monodispersity is, however, unknown in synthetic polymers and it is always true that Mz > Mw > Mn- The ratio Mu,/M , or (A/ /M ) , is commonly taken to be a measure of the polydispersity of the sample. This ratio, called the polydispersity index (PDI), is not a sound statistical measure, however, and it is easy to make incorrect inferences from the magnitude of the M a/Mn ratio. The breadth and shape of the distribution curve are characterized most efiiciently with parameters derived from the moments of distribution. 

When an on-line viscometer is used together with the refractive index detector to generate the intrinsic viscosity [t]] in order to build the universal calibration curve. Sec. II.B, the intrinsic viscosity [t]] can also be used to determine the presence and degree of branching. This is done by plotting the log of [t]] versus log molecular-weight for each slice of the distribution. This plot is called the viscosity law plot, or the Mark-Houwink plot. It is described by the equation... 

The order of these three types of molecular weight is > M . The distributions of the polymer molecular weight are indicated by polydlspersity The polydlsperslty of the molecular weight of the polymer can be represented by a distribution curve or distribution index. Figure 1.3 is a typical distribution curve of the molecular weight. The relative sizes... 

Quantitative comparisons were made by fitting the Williamson model to the flow curve data. The zero-shear viscosity and rate index are two parameters obtained from the Williamson model fits. The zero-shear viscosity is the viscosity valne extrapolated to infinitely low shear rate, while the rate index is the slope of the viscosity versus shear rate relationship in the shear-thinning region at high shear rates. These two parameters are very sensitive to differences in the molecular weight distributions of the resins. Table 15-Tl lists the zero-shear viscosities and rate indexes of the two resin samples. 

Zeichner and coworkers [33,34] developed a measure of the breadth of the molecular weight distribution that is based on the curves of storage and loss moduli versus frequency. Based on data for a series of polypropylenes made by Ziegler-Natta catalysts and degraded by random chain scission, they found that the polydispersity index, i.e., the ratio Af /M , was related to the crossover modulus, G, as shown in Eq. 5.8... 

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