Polydisperse intrinsic viscosity

Another uncertainty arises from the influence of polydispersity. Intrinsic viscosity data were mostly obtained from fractions but the second virial coefficient data were chosen from unfractionated samples. The resulting error is probably not large since A2 depends only slightly on the width of the distribution [183, 184]. 

Denomination Provider Molecular weight Polydispersity Intrinsic viscosity... 

Hven fractionated polymer samples are generally polydisperse, which means that the molecular weight determined from intrinsic viscosity experiments is an average value. The average obtained is the viscosity average as defined by Eqs. (1.20) and (2.40) as seen by the following argument ... 

Figures 4 and 5 show that the degree of polymerization and the intrinsic viscosity increase with increasing the comonomer concentration. Thus, the increase in the comonomer concentration would increase DP and, consequently [rj] Eq. (2). However, the exponent of the monomer concentration for the degree of polymerization decreases at a high comonomer concentration. The abrupt change in the exponent at comonomer concentration >2.1 M/L (Eq. 9) may be ascribed to polydispersity. This was found by others [34] to be at 2.1 and 2.2 M/L, although it starts theoretically at 2.0 M/L.

For polydisperse samples, the weight average intrinsic viscosity [p])w is measured (Equation (8)) and the so-called viscosity averaged molar mass is obtained ... 

GPC measurements were used to demonstrate that a monomodal molecular weight distribution with a polydispersity of approximately 2 was obtained. The glass transition temperature was determined on a Perkin-Elmer DSC-2 using a heating rate of 10 C/min and the intrinsic viscosity was determined in NMP at 25°C. These data are summarized in Table I. 

The observed decrease in [ri] (see Fig. 16) can be understood when recalling that due to Marriman and Hermans [98] the intrinsic viscosity of polydisperse macromolecules is given by the ratio of two number averages... 

In order to determine g as a function of molecular weight, one approach is to use universal calibration with SEC analysis of molecular-weight polydisperse samples (31-33). For a multiarm (MA) branched material, the intrinsic viscosity of polymer eluting in v is ... 

If Equation (11) represents the relationship between [77] and M for a monodisperse polymer sample, then the intrinsic viscosity for a polydisperse sample containing weight fraction Wi with a molecular weight Mj will be... 

As specific viscosities are additive in the limit of infinite dilution, the weight average intrinsic viscosity is obtained for a polydisperse polymer and My is defined as... 

If intrinsic viscosity is used to evaluate the molecular weight of a polydisperse sample, the molecular weight so obtained is an average value. Equation (1.20) defined the viscosity average, which is the kind of average obtained. We are now in a better position to see how this comes about. 

The polydispersity factor p is evaluated with the aid of any of the well-known viscosity-molecular weight relationships. From eq. (3.60) a proportionality of the intrinsic viscosity to the half power of the molecular weight is expected, as this theory holds for 0-solvents. However, based on the conclusion of Section 3.5, viz. that the reduced steady-state compliance of a monodisperse polymer is insensitive to the excluded... 

From eq. (3.78) it becomes evident that the polydispersity factor depends on the solvent power. According to eq. (3.75a) the same holds for the reduced steady-state compliance p of the polydisperse system, in contrast to that of a monodisperse system (cf. the conclusion of Section 3.5). The reason for this paradoxical fact is that, actually, superpositions along the /S-axis are prescribed by eq. (3.74a), /3 being a function of intrinsic viscosity which is a function of solvent power. 

Since intrinsic viscosity but not concentrated solution viscosity is known to be sensitive to polydispersity (10, 19), a correction has been applied to g according to the calculations of Berger and Shultz (20). A value of zero was taken for b, exponent a was set equal to 0.75, and Qbi/Qlin was related to Mw/Mn using Equation 21 of Shultz (19). The branching factor corrected for polydispersity, g corr, is given by... 

Values for g corr are included in column 7 of Table IIL In essence, g corr is the ratio of the intrinsic viscosity of the branched polymer to the intrinsic viscosity of the linear polymer having a similar polydispersity. 

Both of these relations are shown by the solid lines in Figure 3 for the ratio of intrinsic viscosities uncorrected for polydispersity and in Figure 4... 

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. 

Elory and Leutner, working with monodisperse specimens of PVOH differing from one another in molar mass over a wide range (obtained by fractionating polydisperse commercial PVOH), established a correlation between the molar mass, as determined from osmotic pressure measurements, and the intrinsic viscosity. They found that for PVOH in aqueous solution at 25°C,... 

SEC data for the unknown polydisperse sample can then be obtained on the same instrument using the same solvent and temperature in other words we measure V. and determine Jr Then, as long as we know the values of the intrinsic viscosity parameters K and a for the unknown sample, the molecular weight distribution (the s) and the number... 

A. Assume that the GPC curve of Polymer A is that of a poly disperse linear polystyrene. Calculate the weight and number molecular weight averages, the polydispersity and the intrinsic viscosity of the polystyrene. 

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