Sequential distribution

Figure 3. Diagram depicting interprocessor communication in the case of sequential distribution of K states with two per processor. The figure illustrates J = 15, odd parity. The eight processors are labeled i = 0,1..., 7 and the corresponding K states that they contain to the right of each i. Arrows indicate communication between processors for each of the K states. Note that this model involves less communication than the wrapped model.

Note Where appropriate, adjectives specifying the types of copolymer may be applied to pseudo-copolymer. The term statistical pseudo-cqpo/ywer, for instance, may be used to describe an irregular polymer in the molecules of which the sequential distribution of configurational units obeys known statistical laws. 

Copolymer consisting of macromolecules in which the sequential distribution of the monomeric units obeys known statistical laws. 

Statistical copolymers are copolymers in which the sequential distribution of the monomeric units obeys known statistical laws e.g. the monomeric-unit sequence distribution may follow Markovian statistics of zeroth (Bemoullian), first, second or a higher order. Kinetically, the elementary processes leading to the formation of a statistical sequence of monomeric units do not necessarily proceed with equal a priori probability. These processes can lead to various types of sequence distribution comprising those in whieh the arrangement of monomeric units tends towards alternation, tends towards... 

S. Losio, P. Stagnaro, T. Motta, M.C. Sacchi, F. Piemontesi, and M. Gal-imberti, Penultimate-unit effect in ethene/4-methyl-l-pentene copolymerization for a sequential distribution of comonomers, Macromole-cules, 41 (4) 1104—1 111, 2008. 

The factor x corrects for the fact that each step in the reaction does not lead to a chain end with i units of monomer Mi, but only some do. We can safely assume that the sequential distribution of the chain lengths of the unreactive and reactive sequences is the same. Under all ordinary conditions the concentration of radicals assumes a value such that the... 

Temple holes 2-5 sequential holes (V32-3/32 in. in diameter) in the selvedges randomly placed holes, pressure marks, or sequentially distributed pin-sized holes in the selvedges... 

Macromolecular properties of alginates are highly dependent on G/M ratio and sequential distribution of G and M residues within homopolymeric blocks. Poly-guluronate blocks are stiffer than polymannuronate and alternating blocks, which in turn are more soluble at low pH [6]. 

The composition and sequential distribution of M and G residues within alginate polymer vary according to the seaweed species, and also according to seasons and growth conditions [5]. Indeed, alginates are tailor-made by Nature to give different mechanical properties to different seaweeds and even to different tissues within a given seaweed (Table 1) [7]. 

Strictly speaking, random copolymers are copolymers in which the distribution of repeating units is truly random. They should be considered only as a special type of statistical copolymer, because the term statistical copolymer includes all copolymers in which the sequential distribution of the repeating units may follow different statistical laws such as zero-, first- or second-order Markov, depending on the specific reactants and the method of synthesis. However, most literature references use the terra random copolymer independent of the type of statistical distribution, which is seldom known.)... 

Alginates are composed of (1—>4)-linked (3-D-mannuronic acid (M units) and a-L-guluronic acid (G units) monomers (Figure 16.9), with different sequential distribution along the polymer chain [142]. The composition, sequence, and molecular weight generally determine the physical properties of alginate [143]. 

The selective reaction of optical antipodes of NCA should reflect the stereoregularity or the sequential distribution of the antipodal residues in the polymer formed. Infrared spectral studies of the polymer have been known to provide useful information on the stereoregularity and the local conformation. As seen in Fig. 16 and Table 10 for the polymerization of y-benzyl 87%-S-glutamate NCA in dimethylformamide (48), the strength of the absorption at 795 cm"1, which has been reported to depend on the antipodal content of the polymer (50), changes with conversion through a maximum, corresponding to the observed selection of the antipode (Table 10). 

The kinetics of cooperative processes in macromolecular structures, synthetic or biological, was developed further with his student R. H. Lacombe [Simha and Lacombe, 1971]. The authors also examined cooperative equilibria in copolymer systems of specified sequence structures. This implied solutions of the classical Ising problem for linear lattices. It had already been treated by the methods of statistical mechanics for homogeneous chains and, most recently, for copolymers. Lacombe and Simha showed how these problems could be dealt with advantageously by the method of detailed balancing of opposing rates [Lacombe and Simha, 1973,1974]. The results were examined for a spectrum of linear structures, chain lengths, and sequential distributions, such as he had computed, for example, with Jack Zimmermann for polypeptides [Zimmerman et al., 1968]. 

If both A-type monomeric units and both B-type monomeric units have the same reactivity and/or fast trans reactions such as transesterification, transamidation, etc., can occur, then the A and A" or B and B" residue distribution is always random. If the reactivities differ and chain transfer reactions do not occur, then kinetically controlled sequential distributions are obtained. In the simplest case, two groups, A and A can each react with a group, B, with reactions between A and A, A and A, A and A, as well as between B and B being excluded. An example is the reaction between a diol and two different diacyl chlorides. The decrease with time in A and A concentrations is then given as... 

If the reaction rates of the SS and HS inclusion on the increasing macromolecular chain are equal, it results a HS-SS statistical sequential distribution. If the two... 

Ansa-metallocenes with C2 and Cs symmetries generate random copolymers containing norbornene microblocks [43, 44, 61, 62, 64-68, 92]. Copolymers with norbomene content well above 50 mol% and Tg values as high as 220°C can be synthesized. Metallocene symmetry and ligand substituents dictate polymerizatiOTi activity, tacticity, and sequential distribution. The type of bridge has an influence oti polymerization activity, norbornene content, and molar masses (Fig. 5). 

Carbon-13 nuclear magnetic resonance (NMR) is the most useful method of assessing tacticity. By C-13 NMR it is possible to assess the different sequential distributions of adjacent configurational units that are called dyads, triads, tetrads and pentads. The two possible dyads are shown in Fig. 1.5. A chain with 100% meso dyads is perfectly isotactic whereas a chain with 100% racemic dyads is perfectly syndiotactic. A chain with a 50/50 distribution of meso and racemic dyads is atactic. 

Statistical copolymers are copolymers in which the sequential distribution of the repeat units obeys known statistical laws (e.g. Markovian). Random copolymers are a special type of statistical copolymer in which the distribution of repeat units is truly random (some words of caution are necessary here because older textbooks and scientific papers often use the term random copolymer to describe both random and non-random statistical copolymers). A section of a truly random copolymer is represented below... 

In a variation which certainly provides block copolymers, different types of similarly bifunctional oligomers in admixture are linked by a bifunctional co-reactant (equation 6). As with random block copolymer syntheses, this methodology leads to a statistical sequential distribution of the component oligomer units along the chain. 

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