Comonomer, weight fractions

Molar mass determination requires the knowledge of the specific refractive index increment Ant Ac which in the case of complex polymers depends on chemical composition. Copolymer refractive index increments (dn/dc)copo can be accurately calculated for chemically monodisperse fractions, if comonomer weight fractions and homopolymer values are known ... 

Obviously, the sum of all comonomer weight fractions is unity. The accurate copolymer concentration and the distribution of the comonomers across the chromatogram can be calculated from the apparent chromatogram and the individual comonomer concentrations [3],... 

They found that the two branching factors varied linearly with comonomer weight fraction but that the slope depended strongly on the comonomer used. 

T and are the glass-transition temperatures in K of the homopolymers and are the weight fractions of the comonomers (49). Because the glass-transition temperature is directly related to many other material properties, changes in T by copolymerization cause changes in other properties too. Polymer properties that depend on the glass-transition temperature include physical state, rate of thermal expansion, thermal properties, torsional modulus, refractive index, dissipation factor, brittle impact resistance, flow and heat distortion properties, and minimum film-forming temperature of polymer latex... 

In the characterization of copolymers one distinguishes between qualitative analysis, designed to test whether the material is a genuine copolymer or only a physical mixture of homopolymers, and quantitative analysis of the weight fraction of the incorporated comonomers. 

Fig. 9.5-1, right, compares the co-monomer incorporated into the polymer, on a molecular basis. With the Ziegler-Natta, multi-site catalysts less monomer is incorporated in the high-molecular-weight fraction. The low-molecular-weight fraction is rich in co-monomer content as shown by the negative slope of curve a. In a metallocene-based polyethylene the comonomer is uniformly distributed (curve b). 

Assuming that classical chemical kinetics are valid and that the crosslinking reaction rate is proportional to the concentrations of polymer radicals and pendant double bonds, it was shown theoretically that the crosslinked polymer formation in emulsion polymerization differs significantly from that in corresponding bulk systems [270,316]. To simplify the discussion, it is assumed here that the comonomer composition in the polymer particles is the same as the overall composition in the reactor, and that the weight fraction of polymer in the polymer particle is constant as long as the monomer droplets exist. These conditions may be considered a reasonable approximation to many systems, as shown both theoretically [316] and experimentally [271, 317]. First, consider Flory s simplifying assumptions for vinyl/divinyl copolymerization [318] that (1) the reactivities of all types of double bonds are equal, (2) all double bonds... 

The Tg of a random copolymer is expressed by Eq. (2.28) (Fox equation). First we need to calculate the weight fractions of the comonomers in the copolymer. The copolymer has 20—CH3 groups per 100 main-chain carbons, which means that its content is 40% propylene comonomer, and as a consequence the weight fractions of the comonomers will be... 

In such cases, the copolymer molar mass M can be determined from the interpolation of homopolymer calibration curves M V) and the weight fractions w. of the comonomers k according to [1]... 

The following data were obtained [L. Mandelkem, G. M. Martin, and F. A. Quinn, J. Res. Natl. Bur. Stand., 58, 137 (1957)] for the glass transition temperature Tg of the copolymers of vinylidene fluoride and chlorotrifluoroethylene, as a function of the weight fraction wi of the first comonomer. 

Hint 1. One can plot the ratio versus conversion or crosslinker concentration or mole fraction of a comonomer or weight fraction of polymer, and observe how it behaves with respect to unity. 

FIGURE 12.27 Void -size distribution in freeze-dried uncollapsed and unoriented fibers as determined by mercury porosimetry. The weight fraction of comonomers methyl acrylate (MA) and sodium styrene sulfonate (SSS) are in parentheses. (From Terada, K., Sen i-Gakkaishi 29,12, T451, 1973.)... 

Fig. 26. Relationship between comonomer content and solution viscosity for molecular weight fractions from octene-1 and a butene-1 LLDPE resin [28]...

In blends of random copolymers, or in blends of a polymer with random copolymer, the presence of repulsive forces among segments (other than specific interactions discussed before) may lead to miscibility (Wang et al. 2006). The effect of ethylene-styrene cmitent on the miscibility and cocrystallization was studied extensively by Chen (2001). They showed that the miscibility of the system depends only oti the comonomer content with composition expressed as weight fraction. Based on the experimental observations, they constructed a miscibility map for binary blends (Fig. 10.34). 

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