Divergent method

Diphenyl sulfone (DPS), 338 Diphenyl terephthalate-diphenyl isophthalate-bisphenol-A melt poly esterification, 111-112 Direct polyesterification, 63-69 Distinctness of image (DOI), 245 Divergent method, 8... 

A large family of new dendrimers has been synthesized following this divergent method. Hawker and Frechet developed polyaryl(-benzyl)ether dendrimers [27], Miller andNeenan [28], and also Moore and Xu [29] prepared hydrocarbon dendrimers. The latter have reported the largest monodisperse organic hydrocarbon dendrimer with a molecular mass of 18 kDa and a diameter of 12.5 nm [30]. 

Historically, early developments in the field were based on divergent methods. 

The convergent growth approach to dendrimers [1] first introduced [2] in 1989 at the IUPAC meeting on macromolecules in Seoul, Korea, has provided a useful alternative to the divergent methods exemplified by the work of Tomalia et al. on PAMAM dendrimers [3] and Meijer et al. on polypropylene imine) dendrimers [4], Today several hundred papers have exploited the convergent approach to dendrimers to prepare a variety of synthetic functional macromolecules of unparalleled structural precision. 

The fourfold cycloaddition of an excess of cyclopentadienone dendron 27 to the tetraethynyltetraphenylmethane 4 in diphenylether at 200°C affords dendri-mer 2 in 85% isolated yield, respectively (see Scheme 7). Dendrimer 2 corresponds to the second-generation polyphenylene dendrimer made by the divergent method [30]. It should be mentioned that while the addition of dendron 27 to the biphenyl core 9 takes two days the addition to the tetraphenylcore 4 takes one week. This can be explained by the higher mobiUty of the biphenylic core compared to the stiff tetrahedral core, which allows the proper orientation of the ethynyl functions for reactions with the bulky dendrons. 

In the divergent method (Fig. 4), the molecule is assembled from the core to the periphery, while in the convergent method, the molecule is synthesized from the periphery to the core. In either method, the synthesis requires a stepwise process, attaching each layer to the previous one, purifying and then changing functional groups for the next stage of reaction. 

The divergent method is illustrated in Fig. 2-22 for the synthesis of polyamidoamine (PAMAM) dendrimers [Tomalia et al., 1990]. A repetitive sequence of two reactions are used—the Michael addition of an amine to an a,P-unsaturated ester followed by nucleophilic substitution of ester by amine. Ammonia is the starting core molecule. The first step involves reaction of ammonia with excess methyl acrylate (MA) to form LXIII followed by reaction with excess ethylenediamine (EDA) to yield LXIV. LXV is a schematic representation of the dendrimer formed after four more repetitive sequences of MA and EDA. 

The convergent method takes an inverse way with the divergent method. The top surface is first prepared, and a coupling reaction of two semi-spheres is the final reaction. In this method, a unique unsymmetric nanoparticle can be obtained. 

Opposite to the divergent method, the convergent method [3] consists in the stepwise synthesis of dendrimer branches first. They are then attached to the core yielding the dendrimer. Today the name dendrimer has been extended to... 

Synthesis of a dendrimer according to the divergent method (Fig. 2.1) proceeds stepwise starting from a multi-functionalised core building block, to whose reac-... 

An advantage of the divergent method - which was the first to be developed [1] - is the attainable high-molecular (nano)scaffold architecture as well as the possibility of automation of the repetitive steps. The divergent method is therefore the method of choice for - commercially available - POP AM and PAMAM dendrimers (see Section 4.1). 

Within the framework of the AsiaFlux program, Saigusa et al. (2005) measured the C02 fluxes since 1993 in the forest ecosystem of Takayama using an aerodynamic method to estimate the vertical gradient of C02 concentration and a vortex divergence method to calculate the coefficient of diffusion over the forest canopy. Also, measurements were made of vortex fluxes of sensible heat, water vapor, and C02. 

Path A, the divergent method, was introduced by Vogtle et al. [2] and extensively applied by Tomalia and his coworkers at Dow [3]. Working on an inside-... 

A numerical method is said to be convergent if the global discretization error tends to zero when the step size tends to zero. The global discretization error is the difference between the computed solution (neglecting round-off errors) and the theoretical solution. Convergence is a minimal property of a numerical method and there is no use of a divergent method. Most numerical methods are convergent if they are consistent and stable. 

Fig. 1. Reaction steps of the divergent method for the synthesis of PAMAM dendrimers...

More recent examples of this type of polymerization have involved AB2 type monomers leading to completely aromatic, polyester, organo-metallic and silicone containing hyperbranched systems. In general the final products are substantially more polydispersed than products from the controlled divergent method with branching idealities ranging from 50-75%. 

In order to synthesize polyfpropylene imine) dendrimers onto polystyrene via the divergent method, well-defined primary amine functionalized polystyrene had to be prepared as the core molecule. The anionic polymerization technique was chosen for the preparation of polystyrene (PS), because of the possibility of control over molecular weight and end group functionalization. An indirect amination procedure was developed [50], In this procedure a standard quantitative end-cap reaction with CO2 is used and a spacer is created between polystyrene and the primary amine function. The obtained polystyrene-COOH (PS-COOH), with Af around 3kgmol and values around 1.05, could be quantitatively reduced to the... 

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