Number average polydispersity

Molecular weights of polysaccharides in solution can also be measured by osmotic pressure and light scattering. Osmotic pressure yields the number average molecular weight, which can be usefully used with Mw from sedimentation equilibrium as a measure of polydispersity Preston and Wik [28] have done this for example with hyaluronic acid. The ratio Mw/Mn the polydispersity index is often given as a measure of polydispersity, and can be related to the width of a molecular weight distribution via the well-known Herdan [96] relation ... 

The inlet monomer concentration was varied sinusoidally to determine the effect of these changes on Dp, the time-averaged polydispersity, when compared with the steady-state case. For the unsteady state CSTR, the pseudo steady-state assumption for active centres was used to simplify computations. In both of the mechanisms considered, D increases with respect to the steady-state value (for constant conversion and number average chain length y ) as the frequency of the oscillation in the monomer feed concentration is decreased. The maximum deviation in D thus occurs as lo 0. However, it was predicted that the value of D could only be increased by 10-325S with respect to the steady state depending on reaction mechanism and the amplitude of the oscillating feed. Laurence and Vasudevan (12) considered a reaction with combination termination and no chain transfer. 

To run the residence time distribution experiments under conditions which would simulate the conditions occurring during chemical reaction, solutions of 15 weight percent and 30 percent polystyrene in benzene as well as pure benzene were used as the fluid medium. The polystyrene used in the RTD experiment was prepared in a batch reactor and had a number average degree of polymerization of 320 and a polydispersity index, DI, of 1.17. 

The ratio of weight-to-number average chain lengths is the polydispersity,... 

Our theoretical studies [38] showed that the hyperbranched polymers generated from an SCVP possess a very wide MWD which depends on the reactivity ratio of propagating and initiating groups, r=kjk. For r=l, the polydispersity index where P is the number-average degree of polymerization. 

Because of chromatographic dispersion, the sample fraction in the detector cell is polydisperse. The weight-average and number-average molecular weights of the polydisperse fraction are calculated as... 

The weight-average molecular weight (Mw), number-average (Mn) molecular weight, and the polydispersity ratio (P) can be calculated as 76-77... 

It should be noted that the predictions for the number average cluster size and polydispersity agree with analytical results for K(x, y) = 1, x + y, and xy. Furthermore, the short-time form of number average size in Eq. (81) matches the form of s(t) predicted by the scaling ansatz. Computational simulations (Hansen and Ottino, 1996b) also verify these predictions (Fig. 38). 

In the case of a polydisperse polymer it is still the total number n of solute molecules that is measured and the total mass m of solute molecules that is known from sample preparation, resulting in the number average molar mass M = ... 

The relative concentration of the various butadiene microstructures, (1,4 cis, 1,4 trans, and 1,2 vinyl), were determined from the infrared spectra of solid films cast on KC1.(26) The 1,2 microstructure content of all the polymers considered in this paper were between 5-8 mole percent as determined from the IR spectra. Number average and the weight average molecular weight of the polymers were obtained via osmotic pressure and HPLC. The molecular weight of all polymers is around 200,000 g/mole while the polydispersities were about 1.1 thus, all of these polymers have a relatively narrow molecular weight distribution. Note, that both the precursor diene blocks and hydrogenated copolymers... 

Tab. 5.7 Polyethers from isosorbide and 1,8-dibromo- or dimesyloctane yield and distribution data for the microwave procedure (Mn and Mw are, respectively, the number average and weight average molecular weights, the ratio Mw/Mn being the polydispersity index).

In this section, we review the properties of a series of PNIPAM-b-PEO copolymers with PEO blocks of varying length, with respect to the PNIPAM block. Key features of their solutions will be compared with those of PNIPAM-g-PEO solutions. PNIPAM-b-PEO copolymers were prepared by free-radical polymerisation of NIPAM initiated by macroazoinitiators having PEO chains linked symmetrically at each end of a 2,2/-azobis(isobutyronitrile) derivative [169,170]. The polydispersities of PEOs were low, enabling calculations of the number-average molar mass for each PNIPAM block from analysis of their H-NMR spectra (Table 2). 

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