Chain composition distribution

The ratio on the left-hand side can be obtained as a function of M since fw,app(M) / Mw can be determined, as described above, from experimental information. Thus, Eq. (5.7) allows determination of wa(M), the chain composition distribution when all other parameters on its right-and side are measured by differential refractometry. Once wa(M) is known, we are ready to compute v(M) from Eq. (5.3), fw(M) from Eq. (5.6), and finally Mw [59]. 

Fig. 15. Estimate of the chain composition distributions for low mass (O) and high mass (0)13% PET-PCL samples...

Sun X, Luo Y, Wang R, Li, B-G, Liu B, Zhu S. Programmed synthesis of copolymer with controlled chain composition distribution via semibatch RAFT copolymerization. Macromolecules 2007 40 849-859. 

Any number of chains per particle, 1 term, 2 term by disprop or by comb. Use of Markov chains See 1.14.13. Copolymerization, chain composition distribution... 

Palm oil[8002-75-3] is derived from the fleshy fmit of the palm tree rather than the nut as with palm kernel oil. Palm oil has a longer chain length distribution than palm kernel oil and provides properties and compositions more similar to tallow than to other vegetable oils (see Table 1). 

Any understanding of the kinetics of copolymerization and the structure of copolymers requires a knowledge of the dependence of the initiation, propagation and termination reactions on the chain composition, the nature of the monomers and radicals, and the polymerization medium. This section is principally concerned with propagation and the effects of monomer reactivity on composition and monomer sequence distribution. The influence of solvent and complcxing agents on copolymerization is dealt with in more detail in Section 8.3.1. 

The T containing sequences can be evaluated using expressions analogous to those described in Section 7.3.2.1 to provide the chain end compositions and the chain length distribution. 

In a batch reactor, the relative monomer concentrations will change with time because the two monomers react at different rates. For polymerizations with a short chain life, the change in monomer concentration results in a copolymer composition distribution where polymer molecules formed early in the batch will have a different composition from molecules formed late in the batch. For living polymers, the drift in monomer composition causes a corresponding change down the growing chain. This phenomenon can be used advantageously to produce tapered block copolymers. 

For long linear chains the second condition is supported by the Stockmayer bivariate distribution (8,9) which shows the bivariate distribution of chain length and composition is the product of both distributions, and the compositional distribution is given by the normal distribution whose variance is inversely proportional to chain length. 

Advanced computational models are also developed to understand the formation of polymer microstructure and polymer morphology. Nonuniform compositional distribution in olefin copolymers can affect the chain solubility of highly crystalline polymers. When such compositional nonuniformity is present, hydrodynamic volume distribution measured by size exclusion chromatography does not match the exact copolymer molecular weight distribution. Therefore, it is necessary to calculate the hydrodynamic volume distribution from a copolymer kinetic model and to relate it to the copolymer molecular weight distribution. The finite molecular weight moment techniques that were developed for free radical homo- and co-polymerization processes can be used for such calculations [1,14,15]. 

It should be emphasized that for Markovian copolymers a knowledge of the values of structural parameters of such a kind will suffice to find the probability of any sequence Uk, i.e. for an exhaustive description of the microstructure of the chains of these copolymers with a given average composition. As for the composition distribution of Markovian copolymers, this obeys for any fraction of Z-mers the Gaussian formula whose covariance matrix elements are Dap/l where Dap depend solely on the values of structural parameters [2]. The calculation of their dependence on time, and the stoichiometric and kinetic parameters of the reaction system permits a complete statistical description of the chemical structure of Markovian copolymers to be accomplished. The above reasoning reveals to which extent the mathematical modeling of the processes of the copolymer synthesis is easier to perform provided the alternation of units in macromolecules is known to obey Markovian statistics. 

By using two or more polymerization catalysts simultaneously, polymer chemists can produce copolymers tvith a bimodal composition distribution. This is made possible by the fact that no two catalysts incorporate monomers at exactly the same rate. The net result is that short chain branches may be preferentially incorporated into either the higher or lower molecular weight fractions. Polymer manufacturers can obtain a similar result by operating two polymerization reactors in series. Each reactor produces a resin with a different copolymer distribution, which are combined to form a bimodal product. Copolymers with a bimodal composition distribution provide enhanced toughness when extruded into films. 

Tetra Detection GPC makes further refinements with the addition of a UV or IR detector. Of course there must be a suitable chromophore in the polymer chain and a corresponding spectral window in the solvent through which to view it. It is then possible to generate the composition distribution to complement the... 

For the transformation of the macrocomposite model to a molecular composite model for the ultimate strength of the fibre the following assumptions are made (1) the rods in the macrocomposite are replaced by the parallel-oriented polymer chains or by larger entities like bundles of chains forming fibrils and (2) the function of the matrix in the composite, in particular the rod-matrix interface, is taken over by the intermolecular bonds between the chains or fibrils. In order to evaluate the effect of the chain length distribution on the ultimate strength the monodisperse distribution, the Flory distribution, the half-Gauss and the uniform distribution are considered. 

Multiblock OBCs from chain shuttling polymerization have very different architectures. The overall chains and blocks within chains have distributions of molecular weights, with MJMn approaching 2.0. The statistical shuttling process produces chains with a distribution in the number of blocks per chain. The block junctions are precise since each block is grown on a different catalyst, and the compositions are homogeneous since the OBCs are produced at steady-state in a continuous reactor. 

Odor and color instability was traced to the choice of SAI. The original Monsavon composition used an SAI blend made from 80% coconut fatty acid and 20% tallow fatty acid. A characteristic alkyl chain length distribution for the resulting SAI is shown in Table 9.4-1. 

These materials, however, as a rule exhibit rather broad chemical composition distribution. Block copolymers may contain important amounts of parent homopolymer(s) [232,244,269], In any case, it is to be kept in mind that practically all calibration materials contain the end groups that differ in the chemical composition, size, and in the enthalpic interactivity from the mers forming the main chain. In some cases, also the entire physical architecture of the apparently identical calibration materials and analyzed polymers may differ substantially. The typical example is the difference in stereoregularity of poly(methyl and ethyl methacrylate)s while the size of the isotactic macromolecules in solution is similar to their syndiotactic pendants of the same molar mass, their enthalpic interactivity and retention in LC CC may differ remarkably [258,259]. 

Here n is the average refractive index, k is Boltzman s constant, and T is absolute temperature (13). If a polyblend were to form a homogeneous network, the stress would be distributed equally between network chains of different composition. Assuming that the size of the statistical segments of the component polymers remains unaffected by the mixing process, the stress-optical coefficient would simply be additive by composition. Since the stress-optical coefficient of butadiene-styrene copolymers, at constant vinyl content, is a linear function of composition (Figure 9), a homogeneous blend of such polymers would be expected to exhibit the same stress-optical coefficient as a copolymer of the same styrene content. Actually, all blends examined show an elevation of Ka which increases with the breadth of the composition distribution (Table III). Such an elevation can be justified if the blends have a two- or multiphase domain structure in which the phases differ in modulus. If we consider the domains to be coupled either in series or in parallel (the true situation will be intermediate), then it is easily shown that... 

Gel Permeation Chromatography (GPC), also known as Size Exclusion Chromatography (SEC), is a technique used to determine the average molecular weight distribution of a polymer sample. Using the appropriate detectors and analysis procedure it is also possible to obtain qualitative information on long chain branching or determine the composition distribution of copolymers. 

Due to their multi-sited nature, Ziegler-Natta and chromium catalysts produce structurally heterogeneous ethylene homo- and copolymers. This means that the polymers have broad MWD and broad composition (short-chain branching) distribution (Fig. 9). Catalyst active sites that produce lower molecular weights also have a tendency to incorporate more comonomer... 

The results showed that all batch polymerizations gave a two-peaked copolymer compositional distribution, a butyl acrylate-rich fraction, which varied according to the monomer ratio, and polyvinyl acetate. All starved semi-continuous polymerizations gave a single-peaked copolymer compositional distribution which corresponded to the monomer ratio. The latex particle sizes and type and concentration of surface groups were correlated with the conditions of polymerization. The stability of the latex to added electrolyte showed that particles were stabilized by both electrostatic and steric stabilization with the steric stabilization groups provided by surface hydrolysis of vinyl acetate units in the polymer chain. The extent of this surface hydrolysis was greater for the starved semi-continuous sample than for the batch sample. 

Today, the majority of all polymeric materials is produced using the free-radical polymerization technique [11-17]. Unfortunately, however, in conventional free-radical copolymerization, control of the incorporation of monomer species into a copolymer chain is practically impossible. Furthermore, in this process, the propagating macroradicals usually attach monomeric units in a random way, governed by the relative reactivities of polymerizing comonomers. This lack of control confines the versatility of the free-radical process, because the microscopic polymer properties, such as chemical composition distribution and tacticity are key parameters that determine the macroscopic behavior of the resultant product. 

---