Molar mass weight average

Gelation occurs at relatively low conversions of monomer to polymer hence the number-average molar mass at the gel point is low. By contrast, however, the weight-average molar mass becomes infinite at the gel point. 

Alternatively we can define the weight-average molar mass where we take terms inM , i.e. 

Figure 14 Neutron scattering data from branched polystyrene fit to the unified equation [83]. Reprinted with permission from Beaucage [83]. Copyright 2004, American Physical Society. (Both the branched PS fractions were synthesized using divinyl benzene as a comonomer. Fraction F2 has a weight average molar mass of 18 x 108 g/mol and fraction F5 has a weight average molar mass of 2.0 x 108 g/mol, see Ref. 147.)...

Fig. 7 Concentration dependence of (R ) (open symbols) and weight-average molar mass ((Mw)) (filled symbols) of the aggregates at 45 °C a PNIPAM-g-PEO-6 and b PNIPAM-g-PEO-7 [170]...

Fig. 10a Average hydrodynamic radii ((Rh)agg) and b weight-average molar mass ((Mw)agg) of the aggregates in aqueous block copolymer solutions at different polymer concentrations (c given in moles of PNIPAM blocks) at 45 °C a NE-A, b NE-B, c NE-C, d NE-1, e NE-2, and/ NE-3. (Reprinted with permission from Ref. [169] copyright 2002 American Chemical Society)... 

Fig. 8. Variationof the weight-average molar mass Mw ( ) and z-average hydrodynamic diameter in toluene dz (o) with the emulsifier concentration in the emulsion polymerization of 1,4-DVB [83]. Polymerization temperature = 70 °C, initiator = AIBN, water/monomer ratio = 12.5.

Fig. 55. Gel-permeation chromatogram(GPC) of a microgel sample of Mw = 10X106 g/mol obtained in the anionic polymerization of EDMA in toluene. Microgel concentration = 1 g/L solvent = butyl acetate elution temperature = 70 °C is the weight-average molar mass of linear polystyrene used for comparison. [Reproduced from Ref. 256 with permission, Huthig Wepf Publ., Zug, Switzerland].

Furthermore, polymeric samples are usually a mixture of macromolecular chains terminated by different end-groups and thus, an interesting quantity to be determined (in order to characterize the mixture) is the relative abundance of end-groups [1—3]. Other two important quantities are Mn and Mw, the number-average and the weight-average molar masses [1—3]. 

In a similar manner, the weight-average molar mass, Mw, is given by ... 

The leading parameter that characterizes the distributions of randomly branched samples is an exponent Tthat is defined in the next section. The average procedures for the z-average of the mean square radius of gyration and the weight average molar mass results in the relationship [7]... 

Figure 5.1 An experimental Zimin plot (equation (5.26)) for an aqueous solution of high-methoxy pectin (DE 58%) (pH = 8.0, 0.3 mol/dm3 NaCl, 0.01 mol/dm3 mercaptoethanol, 25 °C). The measurements were made at various pectin concentrations ch c2, etc., and at various scattering angles 0. The intersection point on the ordinate for c - 0 and - 0 is the reciprocal weight-average molar mass, 1 /Mw. Replotted from Semenova et al. (1990).

Figure 6.10 Effect of CITREM on the molecular and thermodynamic parameters of maltodextrin SA-2 (DE = 2) in aqueous medium (phosphate buffer, pH = 7.2, ionic strength = 0.05 M 20 °C) (a) weight average molar mass, Mw (b) radius of gyration, Ra (c) structure sensitive parameter, p, characterizing die architecture of maltodextrin associates (d) second virial coefficient, A2 or A2, on the basis of the weight ( ) and molal (A) scales, respectively. The parameter R is defined as the molar ratio of surfactant to glucose monomer units in the polysaccharide. The indicated cmc value refers to the cmc of the pure CITREM solution. Reproduced from Anokhina et al. (2007) with permission.

If a mixture is made of individual polymer chains and polymer clusters, the measurement of static LLS will lead to an apparent weight-average molar mass Mw>app which is expressed by... 

Figure 16 shows G(D) of a simulated polymer mixture at two scattering angles ("Q", 14° and 17°). The mixture consists of two polystyrene standards having distinctly different weight average molar masses (3.Ox 105 and 5.9x 106 g/mol) and a high mass polystyrene which is used to simulate the polymer cluster [66]. The area ratio Ar of the two peaks is expressed by... 

In static LLS [43], the angular dependence of the excess absolute time-averaged scattering intensity, known as the Rayleigh ratio Rw(< )> is measured. For a dilute solution measured at a relatively small angle (6), Rw(q) can be related to the weight average molar mass (Mw), the root mean square... 

Fig. 1 Typical angular dependence of KC/Ryy(q) of PNIPAM in water at two different temperatures, where the weight-average molar mass (Mw) and concentration (C) of PNIPAM are 1.3 x 107 g/mol and 6.7 x 10-7 g/mL, respectively. The insert shows the corresponding hydrodynamic radius distributions f(R ) of the PNIPAM chains respectively in the coiled and the globular states [38]...

Fig. 3 Dissolving kinetics (in terms of average hydrodynamic radius Rh) of collapsed single-chain PNIPAM globules, where t is the standing time after the solution temperature was quenched from 33.02 to 30.02 °C and the dashed line represents a stable average value of Rh of individual PNIPAM random coils at 30.02 °C. The weight-average molar mass (Mw) of the PNIPAM sample used is 1.08 x 107g/mol with a polydispersity index (Mw/Mn) less than 1.1 [32]...

Fig.6 Temperature dependence of z-average root-mean square radius of gyration ((Pg>) and average hydrodynamic radius ( Rh)) of copolymers NIPAM-co-VP/60/5 and NIPAM-co-VP/30/5 in water, where the weight average molar masses are 2.9 x 106 and 4.2 x 106 g/mol, respectively [56]...

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