Trifunctional branch point

Macromolecule comprising a main chain with multiple trifunctional branch points from each of which a linear side-c/ a/n emanates. 

The main topic of interest is the properties of molecules of finite size, having no large rings, and in general having trifunctional branch-points. These are typically produced by chain-transfer with polymer in free-radical polymerizations, though they can of course be made in other ways. Molecules with branch-points of higher functionality are also of interest, especially star-shaped molecules with several arms, as these are both easy to synthesize and relatively easy to discuss theoretically. 

Near a trifunctional branch point the following statistical weight matrices are required (the term o is factored out of 3Un(- j. 

When a trifunctional branch point is present, the configuration partition function is written as Z = U1 Statistical weight matrices used are ... 

Formation of complex branches, which might arise from two intramolecular rearrangements of the Roedel type, are investigated in polyethylene. An RIS model is used for the polyethylene chain statistics, with inclusion of the effect of a trifunctional branch point on weighting of all configurations. 

Reduction of the unperturbed dimensions of the main chain is calculated when ethyl groups are attached to a polyethylene backbone. Values of most of the paramters are taken from the well-known RIS model for unperturbed polyethylene (Abe, A. Jernlgan, R. L. Flory, P, J, J, Am. Chem. Soc. 1966, 88, 631) the bond angle is 112°, gauche states are located at 60° trans 180°l. First- and second-order interactions are weighted by using o 0.43 and m 0.034 (for 300 K). An additional statistical weight, denoted by t, is required at each bond to an atom that constitutes a trifunctional branch point (Flory, P, J, Sundararajan, P. R. DeBolt, L. C. J. Am. Chem. Soc. 1974, 96, 50151. Calculations are performed with t = 0 and t = [Pg.410]

RIS theory, in the form appropriate for branched molecules, is used to calculate the mean-square unperturbed radius of gyration, < s2>0, for cross-linked polyglycine, poly(L-alanine),poly(L-proline),poly(i-alanyl-D-alanine),poly(i.-prolyl-L-pro lylglycine),poly(L-prolyl-i.-alanylglycine ,poly(glycyl-L-alanyl-L-pro line), andpoly(L-aianyl-L-alanylgIycine).Thecentral amino acid residue in each polypeptide chain is replaced by the L-cysteinyl residue involved in cross-link formation. Each cross-linked molecule is considered to contain two trifunctional branch points, the a-carbon atoms of the two... 

Gido SP, Lee C et al (1996) Synthesis, characterization, and morphology of model graft copolymers with trifunctional branch points. Macromolecules 29 7022-7028... 

Properties. The polyphosphates of the alkali or alkaline earth metals are soluble in water, the trifunctional branch points being un-... 

In general, monomer addition to a backbone radical center ( internal radical as opposed to a radical center at the end of a chain) leads to the formation of trifunctional branch points. In addition, b-scission at backbone radical centers can also produce polymer chains with TDBs. IDB polymerization leads to the formation of tetrafunctional branch points. In addition, termination by combination of two backbone radicals also leads to the formation of a tetrafunctional branch point (crosslinking again, leading to... 

For monodisperse polymers with trifunctional branch points, they obtained... 

Fig. 1. Graft Copolymers (1) random graft copolymer (identical branches randomly distributed along the backbone) (2) regular graft copolymer (identical branches equally spaced along the backbone) (3) simple graft copolymer (3-miktoarm star copolymer) and (4) graft copolymer with two trifunctional branch points. Exact graft copolymers.

Chain transfer to polymer (LCB, trifunctional branch points)... 

An analytically tractable approximation of the general equation is used to exemplify this method for a network of chains with trifunctional branch points. In addition, it is shown how actually obtained conversions of the reactive groups in non-stoichiometric compositions may be estimated, and that T reaches a maximum at the stoichiometric composition provided n side reactions occur. 

When a linear polymer containing a number of active A groups is crosslinked with a bifunctional crosslinking agent containing B groups and A reacts with a network with trifunctional branch points is foimed as shown schematically in Fig. k. 

Fig> h, A model of a network containing trifunctional branch points. The conversion y is the ratio of the branch points present over the highest number of branch points obtainable. 

Fig. 8. Continuous variation in "size" of a hifunctional cross linker transforming a network containing trifunctional branch points to a network containing tetrafunctional branch points.

It should he noted that formation of each trifunctional branch point generates also one chain end. Thus. ... 

The number of trifunctional branch points produced per unit volume at a particular conversion is... 

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