Editing Dendrimers

[[Image:single_dendrimer.png|thumb|right|A single dendrimer molecule (G4 [[PAMAM (dendrimer) | PAMAM]], solvent not shown)]]
'''Dendrimers''' (from the aincient greek δένδρον, meaning tree) . Dendrimers can be characterised by three parameters: functionality (<math>f</math>), spacer length (<math>P</math>) and number of generations (<math>G</math>). The number of monomers (<math>N</math>) in a dendrimer is given by

:<math>N= 1 +fP \frac{(f-1)^{G+1}-1}{f-2}</math>
==Density profile==
====Dense shell model====
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>

However, recent work by Zook and Pickett <ref>[http://dx.doi.org/10.1103/PhysRevLett.90.015502 Thomas C. Zook and Galen T. Pickett "Hollow-Core Dendrimers Revisited", Physical Review Letters '''90''' 015502 (2003)]</ref> 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<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>
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]]
<ref>[http://dx.doi.org/10.1021/ma960397k 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)]</ref>, neither of which terms favouring a hollow centre.

==Radius of gyration==
It has been suggested that the [[radius of gyration]] (<math>R_G</math>) scales as <ref>[http://dx.doi.org/10.1021/ma951219e Michael Murat and Gary S. Grest "Molecular Dynamics Study of Dendrimer Molecules in Solvents of Varying Quality", Macromolecules '''29''' pp.1278–1285 (1996)]</ref>

:<math>R_G \propto N^{1/3}</math>

where <math>N</math> is the number of monomers. This implies a compact structure.
====Ideal dendrimer====
For an ''ideal'' dendrimer, consisting of non-interacting monomers, <math>R_G</math> is given by <ref>[http://dx.doi.org/10.1039/FT9969204151 Wilfried Carl "A Monte Carlo study of model dendrimers", Journal of the Chemical Society, Faraday Transactions '''92''' pp. 4151-4154 (1996)]</ref>


:<math>R_{G \mathrm{ideal} } \propto \sqrt{PG}</math>

====Chen-Cui scaling law====
The Chen-Cui scaling law is given by <ref>[http://dx.doi.org/10.1021/ma9514636 Zheng Yu Chen and Shi-Min Cui "Monte Carlo Simulations of Star-Burst Dendrimers", Macromolecules '''29''' pp. 7943-7952 (1996)]</ref>:


:<math>R_G \propto  (PG)^{1-\nu}N^{2\nu-1}</math>

where <math>\nu</math> is the [[Flory exponent]].

==Specific dendrimers==
*[[Carbosilane dendrimer | Carbosilane]]
*[[PAMAM (dendrimer) | PAMAM]] (also known as STARBURST<sup>&reg;</sup>)
*[[PBzE (dendrimer) | PBzE poly(benzyl ether)]]
*[[PPI (dendrimer) | PPI (polypropylenimine)]]
*[[Tecto dendrimers]]
==See also==
*[[Star polymers]] (<math>G=0</math>)
==References==
<references/>
;Related reading
*[http://dx.doi.org/10.1002/anie.200300602     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 [http://www.springer.com/west/home/materials?SGWID=4-10041-22-33832832-0 Computer Simulations of liquid crystals and polymers], eds. Pasini P., Zannoni C. and Zŭmer S., Kluwer pp. 57-78 (2004) [http://www.dur.ac.uk/mark.wilson/papers/mrw_erice_poly.pdf (preprint)]
*[http://dx.doi.org/10.1080/02678290600973113 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)]
*[http://dx.doi.org/10.1039/B804687E Juan J. Freire "Realistic numerical simulations of dendrimer molecules", Soft Matter '''4''' pp. 2139-2143 (2008)]
*[http://dx.doi.org/10.1021/ja901275d 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)]
*[http://dx.doi.org/10.5488/CMP.13.33001  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)]


[[category: liquid crystals]]
[[category: polymers]]
[[category: complex systems]]