Dendrimers: Difference between revisions

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==Density profile==
==Density profile==
====Dense shell model====
====Dense shell model====
<ref>[http://dx.doi.org/10.1051/jphyslet:01983004409035100 P. G. de Gennes and H. Hervet "Statistics of «starburst» polymers", Journal de Physique Lettres '''44''' pp. 351-360 (1983)]</ref>
de Gennes and Hervet <ref>[http://dx.doi.org/10.1051/jphyslet:01983004409035100 P. G. de Gennes and H. Hervet "Statistics of «starburst» polymers", Journal de Physique Lettres '''44''' pp. 351-360 (1983)]</ref> 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
 
:<math>G_{\mathrm{max}} \approx 2.88 (\ln P + 1.5) </math>
 
====Dense core model====
====Dense core model====
Most studies support the dense core model of Lescanec and Muthukumar<ref>[http://dx.doi.org/10.1021/ma00210a026 Robert L. Lescanec and M. Muthukumar "Configurational characteristics and scaling behavior of starburst molecules: a computational study", Macromolecules '''23''' pp. 2280-2288 (1990)]</ref>
Most studies support the dense core model of Lescanec and Muthukumar<ref>[http://dx.doi.org/10.1021/ma00210a026 Robert L. Lescanec and M. Muthukumar "Configurational characteristics and scaling behavior of starburst molecules: a computational study", Macromolecules '''23''' pp. 2280-2288 (1990)]</ref>

Revision as of 16:08, 14 November 2013

Dendrimers. Dendrimers can be characterised by three parameters: functionality (), 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 [1] 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) }

Dense core model

Most studies support the dense core model of Lescanec and Muthukumar[2] [3] despite early uptake of the dense shell model.

Radius of gyration

It has been suggested that the radius of gyration (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} ) scales as [4]

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.

Ideal dendrimer

For an ideal dendrimer, consisting of non-interacting 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 R_G} is given by [5]


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}}

Specific 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

  1. ↑ P. G. de Gennes and H. Hervet "Statistics of «starburst» polymers", Journal de Physique Lettres 44 pp. 351-360 (1983)
  2. ↑ Robert L. Lescanec and M. Muthukumar "Configurational characteristics and scaling behavior of starburst molecules: a computational study", Macromolecules 23 pp. 2280-2288 (1990)
  3. ↑ David Boris and Michael Rubinstein "A Self-Consistent Mean Field Model of a Starburst Dendrimer:  Dense Core vs Dense Shell", Macromolecules 29 pp. 7251-7260 (1996)
  4. ↑ Michael Murat and Gary S. Grest "Molecular Dynamics Study of Dendrimer Molecules in Solvents of Varying Quality", Macromolecules 29 pp.1278–1285 (1996)
  5. ↑ Wilfried Carl "A Monte Carlo study of model dendrimers", Journal of the Chemical Society, Faraday Transactions 92 pp. 4151-4154 (1996)
Related reading
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