Chain composition calculation

The mean-square dipole moments of PPCS chains are calculated as a function of stereochemical composition using the RIS analysis recently published for PS. The calculations are in good agreement with the average of experimental results for atactic PPCS chains estimated to contain ca. 35% meso diads. The temperature coefficient is calculated to be negative in agreement with available experiments. 

Fig. 6.45 Two-dimensional phase diagram as a function of chain composition for a blend of two diblocks (

It was shown [49, 60] that the composition distribution within the framework of both models mentioned are described by the same formulae. However, the values of the parameters of this distribution — mean copolymer composition and index of sequence homogeneity D — are estimated for each of the models essentially in different ways. So in the case of the complex-radical mechanism, the first of these parameters is derived from relations (3.8) and (3.19), and the latter one is equal to the sum of indices of sequential homogeneity in the chain of the colored units. These indices for such a Markov chain are calculated in the usual manner [6]. 

The parameters a = l/rij5 the number of which equals m(m — IX are reciprocal reactivity ratios (2.8) of binary copolymers. Markov chain theory allows one, without any trouble, to calculate at any m, all the necessary statistical characteristics of the copolymers, which are formed at given composition x of the monomer feed mixture. For instance, the instantaneous composition of the multicomponent copolymer is still determined by means of formulae (3.7) and (3.8), the sums which now contain m items. In the general case the problems of the calculation of the instantaneous values of sequence distribution and composition distribution of the Markov multicomponent copolymers were also solved [53, 6]. The availability of the simple algebraic expressions puts in question the expediency of the application of the Monte-Carlo method, which was used in the case of terpolymerization [85,99-103], for the calculations of the above statistical characteristics. Actually, the probability of any sequence MjMjWk. .. Mrl 4s of consecutive monomer units, selected randomly from a polymer chain is calculated by means of the elementary formula ... 

Ttp 4 Chain microstructure and propagation reactions. Propagation reactions are mainly responsible for the development of polymer chain microstructure (and control chain composition and sequence length distribution in copolymerizations). In free radical polymerization, the stereoregularity of a high molecular weight homopolymer chain depends on polymerization temperature almost exclusively. It is usually independent of initiator type and monomer concentration. Calculations on stereoregularity... 

The two analysis methodologies illustrated above (HPLC-FAB and TG-FAB) have been applied to the complex PHA samples, i.e., multicomponent copolymers (containing from 3 to 7 comonomers). Chain statistics calculations showed a random distribution of monomeric units within these polymeric materials, allowing one to calculate their composition. ... 

In the field-theoretic SCMF method [46,47], the external mean field acting on a polymer chain is calculated self-consistently with the composition profile. The utilization of the SCMF simulation scheme demands several important assumptions. Polymers are represented by phantom ehains (thread-like space curves) of statistical segments that pass through the spatial domain in the mean field produced by other components of the system (polymers and solvents). The interactions between pairs of segments are determined by phenomenological Flory-Huggins parameters x-... 

The first theories for block copolymers were introduced for the strong segregation limit (SSL) and the essential physical principles underlying phase behaviour in the SSL were established in the early 1970s [1]. Most notably, Helfand and coworkers [27-29] developed the self-consistent field (SCF) theory, this permitting the calculation of free energies, composition profiles and chain conformations. In the SCF theory, the external mean fields acting on a polymer chain are calculated self-consistently with the composition... 

If the steric structures of both comonomer imits in random copolymers are similar, the melting temperature depression equation will be the same as Eq. 1, with the interaction parameter calculated with Eq. 4. For a given copolymer, the crystallizabilities of copolymer chains in dilute solution strongly depend on the chain composition. From thermodynanuc considerations, this can be explained from the fact that changes in copolymer composition alter the value of the interaction parameter de ed by Eq. 4. For copolymers with two chemically similar comonomers, xia will be very dose to xiB, ind Xab will approach zero, hi this system, one can simply use Eq. 1 with Xl = XiA Xib-... 

The composition calculated for a maximum packing density in terms of Fig. 6 and 7 coincides very well the analytical data of the polymer oxidized to its optimum conductivity. Some workers in the field favour an alteirnative structural model which consists again of sheets of polymer chains but with the zig-zag-plane in the plane of the sheet. This model is based on the assumption that there will be an appreciable interaction between the TT-electrons of the chain and the counterions, notably with I -ions in the case of iodine-oxidized poly(aceSylene).,48,49 the same time this model negates appreciable electronic interactions between adjacent chains. 

Benzene, chlorobenzene, dichlorobenzene and trichlorobenzene are four major products formed in the pyrolysis of vinylidene chloride/vinyl chloride copolymer. To make the composition calculation, the first assumption is that all trimer peak intensities generated from the Py-GC after correction for pyrolysis efficiency and detection efficiency accurately represent the triad distribution of the vinylidene chloride/vinyl chloride copolymer. If a close relationship exists between the triad distribution in the polymer chain and the production of trimers in pyrolysis, the composition and number average sequence length can be calculated on the basis of the trimer production in the pyrolysis. Results were in good agreement with those obtained by H-NMR (Table 4.11). Copolymers containing 11 wt% and 5 wt% vinyl chloride and 5% and 89% vinylidene chloride were successfully analysed. 

The problem was solved quantitatively by the decomposition of the IR optical stretching mode of the three-atom chain by model calculations taking the possible compositions and the frequency shift depending on the mass distribution in natural and isotope-enriched boron carbide into account (57). The determined concentrations of B12 and BnC icosahedra and C—B—C and C—B—B chains are shown in Fig. 26. Other chain compositions can be excluded. Toward the boron-rich limit of the homogeneity range, an increasing number of unit cells without chains arise. Two alternative models are compatible with the optical spectra completely chain-free unit cells and unit cells in which single B atoms saturate the outer bonds of the equatorial atoms of the adjacent icosahedra. Theoretical calculations of reaction kinetics based on the second version (132) satisfactorily confirm the results in Fig. 26. 

If the dependence on temperature as well as on composition is known for a solution, enthalpies and entropies of adsorption may be calculated from the appropriate thermodynamic relationships [82]. Neam and Spaull [147] have, for example, calculated the enthalpies of surface adsorption for a series of straight-chain alcohols. They find an increment in enthalpy of about 1.96 kJ/mol per CH2 group. 

Measurement of Unsaturation. The presence of double bonds in a fatty acid side chain can be detected chemically or through use of instmmentation. Iodine value (IV) (74) is a measure of extent of the reaction of iodine with double bonds the higher the IV, the more unsaturated the oil. IV may also be calculated from fatty acid composition. The cis—trans configuration of double bonds may be deterrnined by infrared (59) or nmr spectroscopy. Naturally occurring oils have methylene-intermpted double bonds that do not absorb in the uv however, conjugated dienes maybe deterrnined in an appropriate solvent at 233 nm. 

The actual experimental moduli of the polymer materials are usually about only % of their theoretical values [1], while the calculated theoretical moduli of many polymer materials are comparable to that of metal or fiber reinforced composites, for instance, the crystalline polyethylene (PE) and polyvinyl alcohol have their calculated Young s moduli in the range of 200-300 GPa, surpassing the normal steel modulus of 200 GPa. This has been attributed to the limitations of the folded-chain structures, the disordered alignment of molecular chains, and other defects existing in crystalline polymers under normal processing conditions. 

The composites with the conducting fibers may also be considered as the structurized systems in their way. The fiber with diameter d and length 1 may be imagined as a chain of contacting spheres with diameter d and chain length 1. Thus, comparing the composites with dispersed and fiber fillers, we may say that N = 1/d particles of the dispersed filler are as if combined in a chain. From this qualitative analysis it follows that the lower the percolation threshold for the fiber composites the larger must be the value of 1/d. This conclusion is confirmed both by the calculations for model systems [27] and by the experimental data [8, 15]. So, for 1/d 103 the value of the threshold concentration can be reduced to between 0.1 and 0.3 per cent of the volume. 

A molecule of composition S4O has not been observed yet. Ab initio MO calculations indicate that a cyclic and an open-chain structure have almost the same energy but no details have been released yet [58]. 

In POLYM the output data of KINREL are used with compositional information to calculate the number and mass average molecular masses (Rn and Rm, respectively) and number and end-group average functionalities (fp and fg> respectively) in the pre-gel region in all stages. In addition, the network characteristics such as sol fraction, mj, and the number of elastically active network chains per monomer (5), Ng, are calculated in the post-gel regime of stage 3. 

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