Branch units, types

As described earlier, we classify dendritic poiyrotaxanes in which rotaxane building units grow like a dendrimer, as Type III rotaxane dendrimers. Depending on whether ring components are located on the branches or at the branching points. Type III rotaxane dendrimers are further classified as 111-A and 111-B, respectively. 

First of all it is necessary to determine the branching coefficient a, w hich is defined as the probability that a given functional group of a branch unit leads via a chain of bifunctional units to another branch unit. In a polymer of the type shown in Fig. 61, a is the probability that an A group selected at random from one of the trifunctional units is connected to a chain the far end of which connects to another trifunctional unit. As will be shown later, both the location of the gel point and the course of the subsequent conversion of sol to gel are directly related to a. 

If more than one type of branching unit is present, (/—I) must be replaced by the appropriate average, weighted according to the numbers of functional groups attached to the various branched units and the molar amount of each present. The critical condition can be expressed in various ways Eq. (7) is a particularly convenient form for application to condensation polymers. 

At the beginning of investigations on chiral dendrimers in our own group was the question of how to synthesize chiral, non-racemic derivatives of tris(hydroxymethyl)-methane [82], which we wanted to use as dendrimer center pieces. We have developed efficient diastereoselective syntheses of such triols [83-85] from ( R)-3-hydroxybutanoic acid, readily available from the biopolymer PHB [59,60] (cf. Sect. 2.4). To this end, the acid is converted to the dioxanone 52 [86, 87], from which various alkylation products and different aldol adducts of type 53 were obtained selectively, via the enolate (Fig. 20). These compounds have been reduced to give a variety of enantiopure chiral building blocks for dendrimers, such as the core unit 54, triply branching units 55a and 55b or doubly branching unit 56 [1,88]. 

Dendrimer architectures are largely determined by the types of branching units they display. To be realised in a dendrimer synthesis, these branching units have to fulfil certain conditions. 

The value of p 7000 makes the term (1 -a)gP a and thus gives practically the result of Kurata s estimation [ 129]. This observation leads to the conclusion that it is not the total number of branching units in the branched cluster that defines the type of the g dependence on g but very likely it is the functionality of the repeating unit. However, further experiments with/=4 have to be made before a well established statement can be made. 

The/ in Eq. 2-145 is the functionality of the branch units, that is, of the monomer with functionality greater than 2. It is not the average functionality/avg from the Carothers equation. If more than one type of multifunctional branch unit is present an average / value of all the monomer molecules with functionality greater than 2 is used in Eq. 2-145. 

These equations do not apply for reaction systems containing monofunctional reactants and/or both A and B type of branch units. Consider the more general case of the system... 

The third type of carbon-branched unit is 2-oxoisovalerate, from which valine is formed by transamination. The starting units are two molecules of pyruvate which combine in a thiamin diphosphate-dependent a condensation with decarboxylation. The resulting a-acetolactate contains a branched chain but is quite unsuitable for formation of an a amino acid. A rearrangement moves the methyl group to the (3 position (Fig. 24-17), and elimination of water from the diol forms the enol of the desired a-oxo acid (Fig. 17-19). The precursor of isoleucine is formed in an analogous way by condensation, with decarboxylation of one molecule of pyruvate with one of 2-oxobutyrate. 

The following sections are devoted primarily to the introduction of two different types of functional units. A distinction is made between dendrimers with bi-functionalised molecular periphery (Fig. 3.7 Types A, B, C, D) and those in which one function is located in the core and the other in the branching units or in the periphery (Types E, F). Multifunctional dendrimers of type G with different functional units in the core, scaffold, and periphery have so far played only a minor role and will therefore only be treated briefly here, particularly since compounds of this type will be considered in greater depth in Chapter 6. 

Dendritic hybrid architectures of the two dendrimer types - POPAM and PAMAM - designated by Majoros et al. as POMAM dendrimerf [17] are structural rarities. One such dendrimer of this type was assembled with PAMAM branching units starting from a POPAM core unit [18]. Vogtle et al. developed POPAM/PAMAM hybrid dendrimers up to the third generation (Fig. 4.8) [19]. 

Dendrimers are hyperbranched polymers that emanate from a single core and ramify outward with each subsequent branching unit [1,2]. In the commonly employed divergent synthesis, dendrimers can be prepared through sequential, alternating reactions of two smaller units, one of which has a point of bifurcation. As is described elsewhere in this volume, several classes of dendrimers are known, including polypropyleneimine (PPI), polyamidoamine (PAMAM), and Frechet-type polyether dendrimers [1,2]. 

Yeast mannan is an amorphous, homogeneous polysaccharide with a D. P. of about 500. The proposed structure of this mannan is a long chain, with radiating side-chains of one or two D-mannopyranose units. In this mannan, 2 —> 1, 3 —> 1, and 6 — 1 linkages have been found. The mannan of the seaweed Porphyra umbilicalis contains chiefly 4 —> 1 /3-d linkages, and is of the branched-chain type with about one branch for each 12 D-mannose residues. 

Other segments may also be present with one or no branch units on their ends. Gel formation will occur when at least one of the if—1) segments radiating from the end of the segment of the type shown is in turn connected to another branch unit. The probability that this will occur is l/(f—1). Thus the critical value of a for gelation is... 

Here f is the functionality of the branch units, or the avere e functionedity of all branch units if more than one type is present. 

One may relate a to the extent of reaction. If the extents of reaction for A and B groups are Pa and Pe, and the ratio of A groups on branch units to all A groups is y, the probability that a B group has reacted with a branch unit isp y with a bifunctional A, Pb(1—y). The probability that a segment of the type shown is formed is... 

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