Dendrimers - Revision history

Carl McBride: Added a publication

2014-03-05T12:31:11Z

Added a publication

← Older revision		Revision as of 14:31, 5 March 2014
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	[[Image:single_dendrimer.png\|thumb\|right\|A single dendrimer molecule (G4 [[PAMAM (dendrimer) \| PAMAM]], solvent not shown)]]		[[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		'''Dendrimers''' (from the aincient greek δένδρον, meaning tree <ref>[http://dx.doi.org/10.1002/anie.199001381 Donald A. Tomalia, Adel M. Naylor and William A. Goddard III "Starburst Dendrimers: Molecular-Level Control of Size, Shape, Surface Chemistry, Topology, and Flexibility from Atoms to Macroscopic Matter", Angewandte Chemie International Edition in English '''29''' pp. 138-175 (1990)]</ref>). 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>		:<math>N= 1 +fP \frac{(f-1)^{G+1}-1}{f-2}</math>

Carl McBride: Added dendron in greek

2014-03-05T12:11:47Z

Added dendron in greek

← Older revision		Revision as of 14:11, 5 March 2014
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	[[Image:single_dendrimer.png\|thumb\|right\|A single dendrimer molecule (G4 [[PAMAM (dendrimer) \| PAMAM]], solvent not shown)]]		[[Image:single_dendrimer.png\|thumb\|right\|A single dendrimer molecule (G4 [[PAMAM (dendrimer) \| PAMAM]], solvent not shown)]]
	'''Dendrimers'''. 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		'''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>		:<math>N= 1 +fP \frac{(f-1)^{G+1}-1}{f-2}</math>

Carl McBride: /* Radius of gyration */ Added Chen-Cui result

2013-11-14T17:25:56Z

Radius of gyration: Added Chen-Cui result

← Older revision		Revision as of 19:25, 14 November 2013
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	:<math>R_G \propto N^{1/3}</math>		:<math>R_G \propto N^{1/3}</math>

	where <math>N</math> is the number of monomers.		where <math>N</math> is the number of monomers. This implies a compact structure.
	====Ideal dendrimer====		====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>		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>
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	:<math>R_{G \mathrm{ideal} } \propto \sqrt{PG}</math>		:<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==		==Specific dendrimers==

Carl McBride: Added an internal link

2013-11-14T16:36:45Z

Added an internal link

← Older revision		Revision as of 18:36, 14 November 2013
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	[[Image:single_dendrimer.png\|thumb\|right\|A single dendrimer molecule (G4 PAMAM, solvent not shown)]]		[[Image:single_dendrimer.png\|thumb\|right\|A single dendrimer molecule (G4 [[PAMAM (dendrimer) \| PAMAM]], solvent not shown)]]
	'''Dendrimers'''. 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		'''Dendrimers'''. 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

Carl McBride: Added image

2013-11-14T16:33:10Z

Added image

← Older revision		Revision as of 18:33, 14 November 2013
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			[[Image:single_dendrimer.png\|thumb\|right\|A single dendrimer molecule (G4 PAMAM, solvent not shown)]]
	'''Dendrimers'''. 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		'''Dendrimers'''. 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

Carl McBride: /* Dense shell model */

2013-11-14T15:31:44Z

Dense shell model

← Older revision		Revision as of 17:31, 14 November 2013
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	:<math>G_{\mathrm{max}} \approx 2.88 (\ln P + 1.5) </math>		:<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====		====Dense core model====

Carl McBride: /* Dense core model */

2013-11-14T15:20:33Z

Dense core model

← Older revision		Revision as of 17:20, 14 November 2013
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	====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>
	<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> ~~despite early uptake~~ of ~~the dense shell model~~.		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==		==Radius of gyration==

Carl McBride: /* Dense shell model */

2013-11-14T15:08:36Z

Dense shell model

← Older revision		Revision as of 17:08, 14 November 2013
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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>

Carl McBride: /* Ideal dendrimer */

2013-11-14T14:37:00Z

Ideal dendrimer

← Older revision		Revision as of 16:37, 14 November 2013
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	where <math>N</math> is the number of monomers.		where <math>N</math> is the number of monomers.
	====Ideal dendrimer====		====Ideal dendrimer====
	For an ''ideal'' dendrimer, consisting of non-interacting monomers, 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>		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>		:<math>R_{G \mathrm{ideal} } \propto \sqrt{PG}</math>

	==Specific dendrimers==		==Specific dendrimers==

Carl McBride at 13:30, 14 November 2013

2013-11-14T13:30:21Z

← Older revision		Revision as of 15:30, 14 November 2013
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	~~{{stub-general}}~~
	'''Dendrimers'''. 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		'''Dendrimers'''. 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

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	where <math>N</math> is the number of monomers.		where <math>N</math> is the number of monomers.
	====Ideal dendrimer====		====Ideal dendrimer====
	For an ''ideal'' dendrimer, consisting of non-interacting monomers, is given by		For an ''ideal'' dendrimer, consisting of non-interacting monomers, 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>		:<math>R_{G{\mathrm{ideal}} \propto \sqrt{PG}</math>