Binary chain

This formula describes dilute solutions (Cp < 1/vN2) fairly well despite the fact that it ignores macromolecular shape changes during binary chain interactions. 

This work focuses on the behaviour of an intrinsically fractal, binary chain, showing a rich structure in its vibrational spectrum, clearly distinct from that of conventional quasi-periodic chains. Furthermore, an approximate solution is given in the weak-coupling limit and the relationship with fractal chains, the discrete analogue of fractal strings, is emphasised. 

The behaviour of a binary chain with intrinsic fractal structure is studied numerically. 

Finally, one should mention the results obtained by iterating until self-consistency at least the valence electron densities in the case of the whole finite binary chain in the framework of the matrix block NFC technique (see the end of Section 4.4.2). The units were... 

As mentioned in Section IX-2A, binary systems are more complicated since the composition of the nuclei differ from that of the bulk. In the case of sulfuric acid and water vapor mixtures only some 10 ° molecules of sulfuric acid are needed for water oplet nucleation that may occur at less than 100% relative humidity [38]. A rather different effect is that of passivation of water nuclei by long-chain alcohols [66] (which would inhibit condensation note Section IV-6). A recent theoretical treatment by Bar-Ziv and Safran [67] of the effect of surface active monolayers, such as alcohols, on surface nucleation of ice shows the link between the inhibition of subcooling (enhanced nucleation) and the strength of the interaction between the monolayer and water. 

Alkanethiols and other sulfur-bearing hydrocarbons covalently attach to metal surfaces alkanethiol onto gold is the most widely studied of these systems [27-29,31,32,45]. These SAMs are ordered provided the alkane chain contains nine or more carbons [32]. Binary solutions of two alkanethiols also appear... 

In the limit that the number of effective particles along the polymer diverges but the contour length and chain dimensions are held constant, one obtains the Edwards model of a polymer solution [9, 30]. Polymers are represented by random walks that interact via zero-ranged binary interactions of strength v. The partition frmction of an isolated chain is given by... 

Atre S V, Liedberg B and Allara D L 1995 Chain length dependenoe of the struoture and wetting properties in binary oomposition monolayers of OH and CHj-terminated alkanethiolates on gold Langmuir 3882-93... 

The general equation can be further reduced to the case of infinite dilution limit, a binary mixmre, ionic solutions, and so on. These equations are supplemented by closure relations such as the Percus-Yevick (PY) and hypernetted chain (HNC) approximations. 

Fig. 63. Molecular arrangement in (a, c) plane of a mixed ethylene-chlorine binary crystal illustrating (a) radical pair formation, (b) single chain growth and (c) chain growth in the vicinity of product line. Molecules labelled 1-4 are ethylene (C2H4), chlorine, chloroethyl radical (C2H4CI) and anti 1,2-dichloroethane (C2H4CI2), respectively.

It may be noted here that it is frequently possible to polymerise two monomers together so that residues from both monomers occur together in the same polymer chain. In addition polymerisation this normally occurs in a somewhat random fashion and the product is known as a binary copolymer. It is possible to copolymerise more than two monomers together and in the case of three monomers the product is referred to as a ternary copolymer or terpolymer. The term homopolymer is sometimes used to refer to a polymer made from a single monomer. 

Since all of the chains are intiated at about the same time and because growth continues until all of the styrene has been consumed, the chains will have similar lengths, i.e. there will be a narrow molecular weight distribution. In addition the chains will still have reactive ends. If, subsequently, additional monomer is fed to the reactor the chain growth will be renewed. If the additional monomer is of a different species to the styrene, e.g. butadiene, a binary diblock copolymer will be formed. 

When comparable amounts of oil and water are mixed with surfactant a bicontinuous, isotropic phase is formed [6]. This bicontinuous phase, called a microemulsion, can coexist with oil- and water-rich phases [7,1]. The range of order in microemulsions is comparable to the typical length of the structure (domain size). When the strength of the surfactant (a length of the hydrocarbon chain, or a size of the polar head) and/or its concentration are large enough, the microemulsion undergoes a transition to ordered phases. One of them is the lamellar phase with a periodic stack of internal surfaces parallel to each other. In binary water-surfactant mixtures, or in... 

There are notable differences in both structures and stabilities for binary N-O and S-N anions (Section 5.4). The most common oxo-anions of nitrogen are the nitrite [N02] and the nitrate anion [NOs] the latter has a branched chain structure 1.1. The sulfur analogue of nitrite is... 

Figure 10 Schematics of two-dimensional chain conformations of the block copolymer and the microsphere in a binary blend [36].

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