Contribution of chain

This quadratic in Rp is of the form required by the data for styrene-benzoyl peroxide shown in Fig. 14. The first term, corresponding to the intercept, represents the creation of chain ends through transfer with monomer. It occurs to an extent which is independent of the polymerization rate. The second term corresponds to 1/2 according to Eq. (27) it represents the pairs of ends created at the initiation step. Its coefficient is given by the initial slope of the line in Fig. 14. The third term, which accounts for the curvature at higher rates, represents the contribution of chain transfer with benzoyl peroxide. This becomes more prominent at higher rates because of the larger amounts of the initiator which are present. The marked rise in the curves for... 

A new stress-relaxation two-network method is used for a more direct measurement of the equilibrium elastic contribution of chain entangling in highly cross-linked 1,2-polybutadiene. The new method shows clearly, without the need of any theory, that the equilibrium contribution is equal to the non-equilibrium stress-relaxation modulus of the uncross-linked polymer immediately prior to cross-linking. The new method also directly confirms six of the eight assumptions required for the original two-network method. 

It is seen that K 2) x [Kd ]2, and, since In Kd = AF, the contribution to the free energy by the number of functional groups is additive. This feature can be explained by the fact that the size of the large macromolecule becomes in narrow pores (60 A) comparable with the size of the pore. This is the reason for the statistical independence and additive contribution of chain ends to the free energy change AF. 

Because in many cases the quantitative information on the contribution of chain-breaking reactions is not yet available, we decided to use the term controlled/living polymerization to describe the still existing ambiguity and uncertainty in these systems. 

The important point is that cyclic oligomers are not formed concurrently with linear polymer, chain transfer to polymer is slow as compared to propagation and its contribution is becoming noticeable only after keeping the reaction mixture unterminated for a prolonged period of time. Thus, within a time scale required to complete the polymerization, the contribution of chain transfer to polymer can be neglected. 

This characteristic feature of cationic polymerization of THF allows the important synthetic application of this process for preparation of oli-godiols used in polyurethane technology and in manufacturing of block copolymers with polyesters and polyamides (cf., Section IV.A). On the other hand, the cationic polymerization of THF not affected by contribution of chain transfer to polymer is a suitable model system for studying the mechanism and kinetics of cationic ring-opening polymerization. 

The branched sulfonium ions are not reactive, thus Reaction (130) is an irreversible termination. The measured ratios of rate constants kp/k, [(rate constant of propagation to rate constant of termination according to Eq. (130)] reflect the general phenomenon that by increasing the number and size of the substituents the contribution of chain transfer to polymer may be considerably reduced [161] (Table 12). 

Higher intrapellet residence times increase the contribution of chain initiation by a-olefins to chain growth pathways. This intrapellet delay, caused by the slow diffusion of large hydrocarbons, leads to non-Flory carbon number distributions and to increasingly paraffinic long hydrocarbon chains during FT synthesis. But intrapellet residence time also depends on the effective diameter and on the physical structure (porosity and tortuosity) of the support pellets. The severity of transport restrictions and the probability that a-olefins initiate a surface chain as they diffuse out of a pellet also de-... 

The contribution of chain transfer with OAC in the case of TiCl4/MgCl2 is insignificant since the type and concentration of OAC do not influence the molecular mass of polyethylene >. Using titanium trichloride, the contribution of chain transfer with AlEtj increases with decreasing polymerization temperature, and at 50 °C chain transfer becomes the dominating process Mn propylene polymerization its contribution is several times lower... 

In conclusion, microhardness evaluation is a method capable of measuring the molecular reorganization taking place above and below Tg. On one hand it detects the contribution of chain mobility with increasing annealing time and temperature leading to a more compact structure (physical ageing). On the other hand, the hardness measures the influence of a thermal expansion. 

The activity predictions associated with the structures of the pseudoproference are deduced from the regularities detected in the experimental population P. In our example, two regularities are detected for primary sites. Thus the regular contribution of chain-lengthening sites (Pti and i4 jM is assigned to two sites of the same type departing from the trace plPgi)— P( ll) 0.26,... 

It is very probable that the energetics favoring the left-handed helix are also effective when the molecule is in solution. These forces, therefore, would also affect the contribution of chain stiffness and form to the optical rotation. The relation between these two phenomena and the conformation revealed by x-rays remains to be explored. A preliminary attempt at relating the conformation of /3-d-(l— 4)-linked polysaccharides to simple conformational concepts in carbohydrate chemistry has focused on the carbon-oxygen bond sequence between the residues (see Fig. 22) that form the well-known molecule methylal. Measurements of dipole moments of methylal show that the conformation shown in Fig. 22A is favored here, the group moments are in partial opposition, and the O-C-4 bond is gauche, relative to C-1-0-5. This is exactly the con-... 

The rate constant of the reaction of cobalt(III) acetate with benzaldehyde in the absence of dioxygen was determined in independent experiments. It turned out to be virtually the same as the rate constant of the chain initiation in the oxidation reaction in the presence of O2- However, the contribution of chain initiation to the radical formation is insignificant in the developed oxidation process. The radicals are mainly formed in the reactions of the intermediates in the process of degenerate chain branching. These reactions are also catalyzed by transition metal ions. Especially well studied is the acceleration of radical decomposition of intermediately formed hydroperoxides (see, e.g., [10]). 

B. The chemical factor. This factor depends on the chain length v. The energy efficiency is higher, when the reaction chain is long and the contribution of chain initiation stage (5- 111) is relatively low ... 

The Carnahan-Starling formulation is used for A and the segment-segment dispersion A p is described using a fourth-order perturbation term [62] the contribution of chain formation as well as the association term is accounted for based on the work of Wertheim [63]. 

In recent papers Kuhn has considered the influence of the presence of potential barriers on the time which a long chain molecule needs to change its shape to a considerable extent. These considerations lead to the concept inner viscosity of the molecular chain, which determines the velocity with which changes in shape will take place under the influence of external forces. A brief account is given on p. 114 in connection with the treatment of the viscosity contribution of chain molecules in solution. 

Table 3 shows some typical values of Gx and Gs for common polymers. In general, an increase in the degree of substitution of the carbon backbone increases the contribution of chain scission. 

One of the most important parameters in ATRP is the dynamics of exchange, and especially the relative rate of deactivation. If the deactivation process is slow in comparison with propagation, then a classic redox initiation process operates, leading to conventional, and not controlled, radical pol5mierization. Polydispersi-ties in ATRP are defined by the following equation, when the contribution of chain... 

Formula weight of ethyl acrylate = 1(X) g/mol. Neglecting contribution of chain ends to polymer molecular weight, DP of poly(ethyl acrylate) of M = 5000 is 50001100 = 50. From Eq. (11.10),... 

Batsberg W, Kramer O (1981) A direct experimental determination of the elastic contribution of chain entangling in a tightly cross-linked elastomer. J Chem Phys 74(ll) 6507-6508... 

In an isotropic polycrystalline polymer whose microstructure consists of stacked lamellae arranged in the form of spherolites, the slip systems activated depend on the local orientation of the lamellae with respect to the applied stress and, as deformation proceeds, these orientations are modified. To calculate the evolution of the crystalline texture, one can consider the polymer to behave as a crystalline aggregate. Although the entropic contribution of chain orientation in the amorphous regions may also need to be considered, the major contribution to work hardening in tension is rotation of the slip planes toward the tensile axis, so that the resolved shear stress in the slip direction diminishes. This results in a fiber texture in the limit of large deformations, such that the crystallites are oriented with their c axis (the chain axis) parallel to the stretch direction. Despite the relative success of such models, they do not explicitly address the micro-mechanisms involved in the transformation of the spherulitic texture into a fiber texture. One possibility is that the... 

The good agreement between the prediction of the miscibility gap from liquid/ gas equilibria with the actual behavior is a further example of the utility of this approach. The extension of the Flory-Huggins theory by incorporating further contributions of chain connectivity and accounting for the phenomenon of... 

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