Dendrimers

A single dendrimer molecule (G4 PAMAM, solvent not shown)

Dendrimers (from the aincient greek δένδρον, meaning tree ). Dendrimers can be characterised by three parameters: functionality (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} ), spacer length (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P} ) and number of generations (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle G} ). The number of monomers (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N} ) in a dendrimer is given by

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N= 1 +fP \frac{(f-1)^{G+1}-1}{f-2}}

Density profile

Dense shell model

de Gennes and Hervet calculated that for self-avoiding dendrimers in a good solvent, the density profile increases from a minimum at the centre of the dendrimer to a maximum at its outer surface, i.e. a dense outer shell with a hollow centre. Note this leads to a limit of

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle G_{\mathrm{max}} \approx 2.88 (\ln P + 1.5) }

However, recent work by Zook and Pickett has shown that the de Gennes and Hervet model was flawed.

Dense core model

Most studies support the dense core model of Lescanec and Muthukumar despite early uptake of the dense shell model. Boris and Rubinstein pointed out that the structure of the dendrimer is a result of the competition between the entropy and excluded volume , neither of which terms favouring a hollow centre.

Radius of gyration

It has been suggested that the radius of gyration ($R_{G}$) scales as

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_G \propto N^{1/3}}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N} is the number of monomers. This implies a compact structure.

Ideal dendrimer

For an ideal dendrimer, consisting of non-interacting monomers, $R_{G}$ is given by

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_{G \mathrm{ideal} } \propto \sqrt{PG}}

Chen-Cui scaling law

The Chen-Cui scaling law is given by :

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_G \propto (PG)^{1-\nu}N^{2\nu-1}}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \nu} is the Flory exponent.

Specific dendrimers

• Carbosilane
• PAMAM (also known as STARBURST^®)
• PBzE poly(benzyl ether)
• PPI (polypropylenimine)
• Tecto dendrimers

See also

• Star polymers (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle G=0} )

References

Related reading

• Matthias Ballauff and Christos N. Likos "Dendrimers in Solution: Insight from Theory and Simulation", Angewandte Chemie International Edition 43 pp. 2998-3020 (2004)
• M. R. Wilson, J. M. Ilnytskyi, L. M. Stimson and Z. E. Hughes "Computer simulations of liquid crystal polymers and dendrimers" in Computer Simulations of liquid crystals and polymers, eds. Pasini P., Zannoni C. and Zŭmer S., Kluwer pp. 57-78 (2004) (preprint)
• Mark R. Wilson, Lorna M. Stimson and Jaroslav M. Ilnytskyi "The influence of lateral and terminal substitution on the structure of a liquid crystal dendrimer in nematic solution: A computer simulation study", Liquid Crystals 33 pp. 1167 - 1175 (2006)
• Juan J. Freire "Realistic numerical simulations of dendrimer molecules", Soft Matter 4 pp. 2139-2143 (2008)
• Gustavo Del Río Echenique, Ricardo Rodríguez Schmidt, Juan J. Freire, José G. Hernández Cifre and José García de la Torre "A Multiscale Scheme for the Simulation of Conformational and Solution Properties of Different Dendrimer Molecules", Journal of the American Chemical Society (JACS) 131 pp. 8548-8556 (2009)
• J. M. Ilnytskyi, J. S. Lintuvuori, M. R. Wilson "Simulation of bulk phases formed by polyphilic liquid crystal dendrimers", Condensed Matter Physics 13 pp. 33001:1-16 (2010)