Of branching

The problem of branching of the wavepacket at crossing points is very old and has been treated separately by Landau and by Zener [H, 173. 174], The model problem they considered has the following diabatic coupling matrix ... 

Baker J and Gill P M W 1988 An algorithm for the location of branching points on reaction paths J. Comput. Chem. 9 465... 

PdCb-CuCb catalyzes the condensation of branched-chain alkenes with formaldehyde to give the l,3-dioxanes 96a and 96b (Prins reaction)[73]. The yields are much higher than in the conventional acid-catalyzed Prins reaction. 

Treatment of the borates with iodine leads to boron- C2 migration of an alkyl group[9]. This reaction has not been widely applied synthetically but it might be more applicable for introduction of branched alkyl groups than direct alkylation of an indol-2-yllithium intermediate. 

Number the longest continuous chain m the direction that gives the lowest number to the substituent group at the first point of branching The numbering scheme... 

Higher octane gasoline typically contains a greater proportion of branched alkanes relative to unbranched ones Are branched alkanes better fuels because they give off more energy on com bustion" Explain... 

The amount of branching introduced into a polymer is an additional variable that must be specified for the molecule to be fully characterized. When only a slight degree of branching is present, the concentration of junction points is sufficiently low that these may be simply related to the number of chain ends. For example, two separate linear molecules have a total of four ends. If the end of one of these linear molecules attaches itself to the middle of the other to form a T, the resulting molecule has three ends. It is easy to generalize this result. If a molecule has v branches, it has v 2 chain ends if the branching is relatively low. Branched molecules are sometimes described as either combs or... 

If the concentration of junction points is high enough, even branches will contain branches. Eventually a point is reached at which the amount of branching is so extensive that the polymer molecule becomes a giant three-dimensional network. When this condition is achieved, the molecule is said to be cross-linked. In this case, an entire macroscopic object may be considered to consist of essentially one molecule. The forces which give cohesiveness to such a body are covalent bonds, not intermolecular forces. Accordingly, the mechanical behavior of cross-linked bodies is much different from those without cross-linking. 

Comparing Eqs. (2.68) and (2.70) suggests that the effect of branching on t might be an exponential increase with the length of the side chain, provided that the entanglement mechanism is operative for both the branched and unbranched samples being compared ... 

We must be careful in assessing the experimental results on the viscosity of branched polymers. If we compare two polymers of identical molecular weight, one branched and the other unbranched, it is possible that the branched one would show lower viscosity. Two considerations enter the picture here. First, since the side chains contribute to the molecular weight, the backbone chain... 

Criticize or defend the following proposition In dilute solutions, branching affects viscosity only inasmuch as the branched molecule has a more compact shape. At higher concentrations, the effect of branching is closer to a bulk effect. 

The effect of branching is to increase the number of chain ends and, therefore, free volume, which decreases Tg. Conversely, crosslinking ties together separate molecules, decreases the number of loose ends, and raises Tg. Copolymers show different effects on T, depending on the microstructure... 

Reaction (5.W) is interesting inasmuch as either the AA or BB monomer must be present to produce crosslinking. Polymerization of AB with only Aj- (or Bf) introduces a single branch point, but no more, since all chain ends are mis-oriented for further incorporation of branch points. Including the AA or BB molecule reverses this. The bb unit which accomplishes this in reaction (5.W) is underscored. 

Our interest from the outset has been in the possibility of crosslinking which accompanies inclusion of multifunctional monomers in a polymerizing system. Note that this does not occur when the groups enclosed in boxes in Table 5.6 react however, any reaction beyond this for the terminal A groups will result in a cascade of branches being formed. Therefore a critical (subscript c) value for the branching coefficient occurs at... 

A moment s reflection reveals that the effect on v of transfer to polymer is different from the effects discussed above inasmuch as the overall degree of polymerization is not decreased by such transfers. Although transfer to polymer is shown in one version of Eq. (6.84), the present discussion suggests that this particular transfer is not pertinent to the effect described. Investigation of chain transfer to polymer is best handled by examining the extent of branching in the product. We shall not pursue the matter of evaluating the transfer constants, but shall consider instead two specific examples of transfer to polymer. 

Plasticizer Range Alcohols. Commercial products from the family of 6—11 carbon alcohols that make up the plasticizer range are available both as commercially pure single carbon chain materials and as complex isomeric mixtures. Commercial descriptions of plasticizer range alcohols are rather confusing, but in general a commercially pure material is called "-anol," and the mixtures are called "-yl alcohol" or "iso...yl alcohol." For example, 2-ethyIhexanol [104-76-7] and 4-methyl-2-pentanol [108-11-2] are single materials whereas isooctyl alcohol [68526-83-0] is a complex mixture of branched hexanols and heptanols. Another commercial product contains linear alcohols of mixed 6-, 8-, and 10-carbon chains. 

This second reaction leads to the small amount of branching (usually less than 5%) observed in the alcohol product. The alpha olefins produced by the first reaction represent a loss unless recovered (8). Additionally, ethylene polymerisation during chain growth creates significant fouling problems which must be addressed in the design and operation of commercial production faciUties (9). 

Polygas Olefins. Refinery propylene and butenes are polymerized with a phosphoric acid catalyst at 200°C and 3040—6080 kPa (30—60 atm) to give a mixture of branched olefins up to used primarily in producing plasticizer alcohols (isooctyl, isononyl, and isodecyl alcohol). Since the olefins are branched (75% have two or more CH groups) the alcohols are also branched. Exxon, BASE, Ruhrchemie (now Hoechst), ICl, Nissan, Getty Oil, U.S. Steel Chemicals (now Aristech), and others have all used this olefin source. 

Some 2,000—3,000 t/yr of these specialty alcohols are produced ia the United States (Exxon) and ia Germany (Henkel) (28). Their high Hquidity because of branching permits use of less volatile, higher molecular weight materials, reported to be less irritating than the lower molecular weight linear alcohol materials, ia a variety of cosmetic products (29). 

Starch is a polysaccharide found in many plant species. Com and potatoes are two common sources of industrial starch. The composition of starch varies somewhat in terms of the amount of branching of the polymer chains (11). Its principal use as a flocculant is in the Bayer process for extracting aluminum from bauxite ore. The digestion of bauxite in sodium hydroxide solution produces a suspension of finely divided iron minerals and siUcates, called red mud, in a highly alkaline Hquor. Starch is used to settle the red mud so that relatively pure alumina can be produced from the clarified Hquor. It has been largely replaced by acryHc acid and acrylamide-based (11,12) polymers, although a number of plants stiH add some starch in addition to synthetic polymers to reduce the level of residual suspended soHds in the Hquor. Starch [9005-25-8] can be modified with various reagents to produce semisynthetic polymers. The principal one of these is cationic starch, which is used as a retention aid in paper production as a component of a dual system (13,14) or a microparticle system (15). 

Polyamines can also be made by reaction of ethylene dichloride with amines (18). Products of this type are sometimes formed as by-products in the manufacture of amines. A third type of polyamine is polyethyleneimine [9002-98-6] which can be made by several routes the most frequently used method is the polymeriza tion of azitidine [151 -56 ] (18,26). The process can be adjusted to vary the amount of branching (see Imines, cyclic). Polyamines are considerably lower in molecular weight compared to acrylamide polymers, and therefore their solution viscosities are much lower. They are sold commercially as viscous solutions containing 1—20% polymer, and also any by-product salts from the polymerization reaction. The charge on polyamines depends on the pH of the medium. They can be quaternized to make their charge independent of pH (18). 

Uses. Fluorosulfuric acid serves as catalyst in the alkylation (qv) of branched-chain paraffins (53—58) and aromatic compounds (59), and in the polymeriza tion of monoolefins (60) and rosin (61). Addition of strong Lewis acids, such as SbF, TaF, and NbF, to fluorosulfuric acid markedly increases... 

ALKYLATION OF ALIPHATIC COMPOUNDS The first reported alkylation of branched-chain alkanes by ethylene, over aluminum chloride (69), made it possible to alkylate alkanes (except methane and ethane) with straight chain or branched alkenes. 

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