"Divalent Metal Nanoparticles"

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Unregistered Submission:

( February 18th, 2014 9:22am UTC )

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A summary of comments regarding this paper that happened in the pubpeer page for the related article by Stirling et al (https://pubpeer.com/publications/B02C5ED24DB280ABD0FCC59B872D04#fb6469).

This thread is clear evidence that there is at least one Unreg deliberately trying to derail the discussion with pseudo mathematics. I hope the logical fallcies made in the DeVries' article are clear from this exchange.

Nanonymous

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Unregistered Submission: ( February 14th, 2014 12:20am UTC )

Nanonymous,

Not only you are not an STM expert , you also seem to have a poor understanding of basic topology:

Poincare's hairy ball theorem states that on a two dimensional sphere there must be at least one singular point. If you have 'hairs' that are ordered in the form of stripes, then there MUST be two singularities (see this drawing: http://3.bp.blogspot.com/-x0c9FWdnDG4/TnHlUUxOntI/AAAAAAAAAx4/rvjX0wVXMzg/s400/hairy.jpg).

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Peer 1: ( February 14th, 2014 6:35am UTC )

@ The undead unreg

I'm stuck on this: "a two dimensional sphere". Can you explain the concept in a bit more detail? I'm a bit surprised that an intellectual giant like Poincare (accents don't work) actually said that.

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Unregistered Submission: ( February 14th, 2014 8:12am UTC )

Hi Unreg,

You can see that from the original paragraph from the paper:

"Monolayer protected metal NPs are supramolecular assemblies consisting of a metallic core coated with a self-assembled monolayer (SAM) composed of one or more types of thiol-terminated molecules (ligands). It is known that molecules in SAMs on flat gold surfaces form a two-dimensional (2D) crystal in which every molecule conforms to the same tilt angle and direction relative to the surface normal (19, 20) in order to maximize the van der Waals interactions with its nearest neighbors. Landman and co-workers (21) addressed the question of the morphology of the ligand shell SAM on the faceted surface of a gold NP. They found that ligand molecules conform to one single tilt angle relative to a common particle diameter rather than assuming their equilibrium tilt angle on each crystallographic facet, which would generate a large number of line defects along facet edges. That is, the vectorial projection of the tilted ligand molecules propagates around the particle. This needs to be reconciled with the fact that on a topological sphere a 2D crystal cannot exist unless two separate point defects are present (22, 23). This is commonly known as the “hairy ball theorem” that states that it is not possible to “align hairs” onto a sphere without generating two singularities (such as the whirl on the back of our heads). "

Your interpretation is plainly incorrect, and the paragraph above is clearly wrong.

You can see clearly that the authors say their theorem is true for NP's coated with *one or more* types of thiol, stripes have nothing to do with their definitions at this point.

The theorem "commonly known as the “hairy ball theorem” that states that it is not possible to “align hairs” onto a sphere without generating two singularities " is as true as the Euler characteristic of the sphere being 3.

This paragraph makes no mention of its own peculiar version of the hairy ball theorem (with no precise definitions or proofs) to be conditionally true on the existence of stripes. "Ripples" are only mentioned after the quote above.

Can you provide us with a link to the proof of the "stripy ball theorem" you are referring to?

Here is a good one on the hairy ball theorem,

http://blog.sigfpe.com/2012/11/a-pictorial-proof-of-hairy-ball-theorem.html

great introduction, and it demonstrates that there is more to it than the intuitive notion. Why would state a different theorem (with the same name, apparently) and not even cite a proof?

Nanonymous

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Unregistered Submission: ( February 14th, 2014 9:28am UTC )

Unreg also didn't seem to want to cite the source for the image. Readers can find it here:

http://www.scribd.com/doc/109912108/Professor-Stewart-s-Hoard-of-Mathematical-Treasures-Ian-Stewart

(Professor Stewart's Hoard of Mathematical Treasures By Ian Stewart)

The text in the diagram is the normal statement of the hairy ball theorem (not the the incorrect version in the paper). The relevant sentence in the text says:

"The picture shows a combed sphere with two ‘tufts’ - two places where the hairs don’t lay flat. The theorem says there can’t be no such places, but can there be only one?"

All the theorem says is that there must be more than 0 such places (*not necessarily two*), the picture is a puzzle asking the reader to figure out how to do "comb" the ball to get rid of the second tuft.

Good trolling requires skill and wit, Unreg is merely fibbing.

Nanonymous

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Unregistered Submission: ( February 14th, 2014 9:50am UTC )

I should also say this is a profound amount of effort to assert an elementary fact of topology ("elementary" since it has already been proven, Brouwer was of course brilliant and is very worth reading about).

Participants have bent over backward to demonstrate patience and willingness to critically examine Stirling's hypothesis. Essentially all of Unreg's criticisms have been the logical equivalent of "2+2=5".

I feel that it is extremely important to provide a forum and devote time to opposing voices, even if they may be singular (and of abrasive tone). Patience should really stretch to the very limit, this is the ideal that I think PubPeer aspires to.

This is the limit for me, UnReg's continued opposition at this point is nothing more that crapflooding and the value of the content no more than link spamming. I am morally fine with (effectively) censoring posts from UnReg at this point by categorizing them as spam so that they are easily ignored by the reader. I think this is an important mechanism that should be implemented in PubPeer for a trial.

Nanonymous

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Peer 4: ( February 14th, 2014 12:42pm UTC )

@Nanonymous,

Let me be the first to thank you for the time you put into researching these arguments. I do feel that with the arguments presented here we have gotten further in our own understanding.

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Philip Moriarty: ( February 14th, 2014 2:23pm UTC )

@Peer 4: ( February 14th, 2014 12:42pm UTC )

@Nanonymous

Agree entirely with Peer 4. Thanks for that link to Stewart's book, Nanonymous. I've always been a fan of his writings but had not come across the hairy ball theorem before. Your explanations of the issue have been a model of clarity.

Philip

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Unregistered Submission: ( February 14th, 2014 10:35pm UTC )

(I'm not the critical unreg)

I was thinking about this. As with you, I noticed that the theorem says "at least one", but that critical unreg (and FS) confused this to be "at least two" tufts.

One obvious way to have two tufts is if you start at the equator and comb towards either pole (either straight way or at an angle).

I was thinking that a way to only have one tuft would be if you started at the "north pole" and then combed southwards all over the ball. you end up with a "widow's peak" (baldish spot) at the top and a tuft at the bottom. I assume this is the solution for how to have only one tuft.

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Unregistered Submission: ( February 15th, 2014 1:30am UTC )

Nanonymous,

I see that you seem to understand what the hairy ball theorem says, but you don't apply it correctly. Again, all I said is

(1) Poincare's hairy ball theorem states that on a two dimensional sphere there must be at least one singular point. You agree with me on this one.

(2) If you have 'hairs' that are ordered in the form of stripes, then there MUST be two singularities (see this drawing: http://3.bp.blogspot.com/-x0c9FWdnDG4/TnHlUUxOntI/AAAAAAAAAx4/rvjX0wVXMzg/s400/hairy.jpg). You don't seem to agree with me on this one. Well, you are plain wrong.

Come on, show a sphere with aligned hairs in the form of stripes where only one singularity exists. You won't. It is impossible. That's what that paragraph from the paper you quoted says: "it is not possible to “ALIGN HAIRS” onto a sphere without generating two singularities (such as the whirl on the back of our heads)."

It's amazing to what lengths nanonymous is willing to go to try to silence criticisms to the arguments of Moriarty and Levy with lousy arguments. Again, it is obvious that you lack a solid scientific background. That Peer 4 and Moriarty praise your words also speaks of their rather modest scientific wisdom.

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Unregistered Submission: ( February 15th, 2014 8:24am UTC )

1) It isn't a matter of agreeing with you, I've understood the hairy ball theorem for some time.

2)Yes I've already taken care of providing the reference to the drawing you use (unattributed), and it has nothing to do with the notion of "stripes". I just can't parse anything after this, perhaps you should consider replying in the form of a concise mathematical proof?

E.g. "We define a stripe as a .... Given a vector field over a 2-sphere.... etc. etc."

Nanonymous

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Raphaël Lévy: ( February 15th, 2014 10:04am UTC )

Single singularity

https://twitter.com/raphavisses/status/434416568286838784

(the puzzle was not that difficult but I guess you have not even read the link provided by nanonymous and simply reposted the same link).

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Peer 4: ( February 15th, 2014 12:45pm UTC )

@Raphael:

Nice illustration. Unfortunately, topology's not my thing, which is why I don't really see how this theorem would have a grave importance on the existence of stripy nanoparticles.

@UnReg: The more you say, the more funny you sound. Especially when trying (and failing) to beat people at their own game. I fear it may be too late already, but I would advice that you do not become that scientist at the conference who is so stuck in his own beliefs that (s)he serves only as an example of how not to become. If you "understood science", as you put it, you would understand that it is damn easy to fool yourself approaching evidence with prejudice. Some of Ben Goldacre's work and warnings on this phenomenon in medicine might be worth evaluating.

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Unregistered Submission: ( February 15th, 2014 8:29pm UTC )

Levy,

That vector field you show painted on the pingpong ball is not a field that corresponds to the aligned hairs in the form of stripes. The 'aligned hairs' form parallel lines, as in here: http://us.123rf.com/400wm/400/400/itana/itana1011/itana101100102/8302429-abstract-sphere-with-stripes.jpg

With 'aligned hairs', it is obvious that there are two singularities at the poles.

This thread is clear evidence that there is at least one Unreg deliberately trying to derail the discussion with pseudo mathematics. I hope the logical fallcies made in the DeVries' article are clear from this exchange.

Nanonymous

--------------------------------------------------------------

Unregistered Submission: ( February 14th, 2014 12:20am UTC )

Nanonymous,

Not only you are not an STM expert , you also seem to have a poor understanding of basic topology:

Poincare's hairy ball theorem states that on a two dimensional sphere there must be at least one singular point. If you have 'hairs' that are ordered in the form of stripes, then there MUST be two singularities (see this drawing: http://3.bp.blogspot.com/-x0c9FWdnDG4/TnHlUUxOntI/AAAAAAAAAx4/rvjX0wVXMzg/s400/hairy.jpg).

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Peer 1: ( February 14th, 2014 6:35am UTC )

@ The undead unreg

I'm stuck on this: "a two dimensional sphere". Can you explain the concept in a bit more detail? I'm a bit surprised that an intellectual giant like Poincare (accents don't work) actually said that.

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Unregistered Submission: ( February 14th, 2014 8:12am UTC )

Hi Unreg,

You can see that from the original paragraph from the paper:

"Monolayer protected metal NPs are supramolecular assemblies consisting of a metallic core coated with a self-assembled monolayer (SAM) composed of one or more types of thiol-terminated molecules (ligands). It is known that molecules in SAMs on flat gold surfaces form a two-dimensional (2D) crystal in which every molecule conforms to the same tilt angle and direction relative to the surface normal (19, 20) in order to maximize the van der Waals interactions with its nearest neighbors. Landman and co-workers (21) addressed the question of the morphology of the ligand shell SAM on the faceted surface of a gold NP. They found that ligand molecules conform to one single tilt angle relative to a common particle diameter rather than assuming their equilibrium tilt angle on each crystallographic facet, which would generate a large number of line defects along facet edges. That is, the vectorial projection of the tilted ligand molecules propagates around the particle. This needs to be reconciled with the fact that on a topological sphere a 2D crystal cannot exist unless two separate point defects are present (22, 23). This is commonly known as the “hairy ball theorem” that states that it is not possible to “align hairs” onto a sphere without generating two singularities (such as the whirl on the back of our heads). "

Your interpretation is plainly incorrect, and the paragraph above is clearly wrong.

You can see clearly that the authors say their theorem is true for NP's coated with *one or more* types of thiol, stripes have nothing to do with their definitions at this point.

The theorem "commonly known as the “hairy ball theorem” that states that it is not possible to “align hairs” onto a sphere without generating two singularities " is as true as the Euler characteristic of the sphere being 3.

This paragraph makes no mention of its own peculiar version of the hairy ball theorem (with no precise definitions or proofs) to be conditionally true on the existence of stripes. "Ripples" are only mentioned after the quote above.

Can you provide us with a link to the proof of the "stripy ball theorem" you are referring to?

Here is a good one on the hairy ball theorem,

http://blog.sigfpe.com/2012/11/a-pictorial-proof-of-hairy-ball-theorem.html

great introduction, and it demonstrates that there is more to it than the intuitive notion. Why would state a different theorem (with the same name, apparently) and not even cite a proof?

Nanonymous

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Unregistered Submission: ( February 14th, 2014 9:28am UTC )

Unreg also didn't seem to want to cite the source for the image. Readers can find it here:

http://www.scribd.com/doc/109912108/Professor-Stewart-s-Hoard-of-Mathematical-Treasures-Ian-Stewart

(Professor Stewart's Hoard of Mathematical Treasures By Ian Stewart)

The text in the diagram is the normal statement of the hairy ball theorem (not the the incorrect version in the paper). The relevant sentence in the text says:

"The picture shows a combed sphere with two ‘tufts’ - two places where the hairs don’t lay flat. The theorem says there can’t be no such places, but can there be only one?"

All the theorem says is that there must be more than 0 such places (*not necessarily two*), the picture is a puzzle asking the reader to figure out how to do "comb" the ball to get rid of the second tuft.

Good trolling requires skill and wit, Unreg is merely fibbing.

Nanonymous

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Unregistered Submission: ( February 14th, 2014 9:50am UTC )

I should also say this is a profound amount of effort to assert an elementary fact of topology ("elementary" since it has already been proven, Brouwer was of course brilliant and is very worth reading about).

Participants have bent over backward to demonstrate patience and willingness to critically examine Stirling's hypothesis. Essentially all of Unreg's criticisms have been the logical equivalent of "2+2=5".

I feel that it is extremely important to provide a forum and devote time to opposing voices, even if they may be singular (and of abrasive tone). Patience should really stretch to the very limit, this is the ideal that I think PubPeer aspires to.

This is the limit for me, UnReg's continued opposition at this point is nothing more that crapflooding and the value of the content no more than link spamming. I am morally fine with (effectively) censoring posts from UnReg at this point by categorizing them as spam so that they are easily ignored by the reader. I think this is an important mechanism that should be implemented in PubPeer for a trial.

Nanonymous

Reply Report

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Peer 4: ( February 14th, 2014 12:42pm UTC )

@Nanonymous,

Let me be the first to thank you for the time you put into researching these arguments. I do feel that with the arguments presented here we have gotten further in our own understanding.

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Philip Moriarty: ( February 14th, 2014 2:23pm UTC )

@Peer 4: ( February 14th, 2014 12:42pm UTC )

@Nanonymous

Agree entirely with Peer 4. Thanks for that link to Stewart's book, Nanonymous. I've always been a fan of his writings but had not come across the hairy ball theorem before. Your explanations of the issue have been a model of clarity.

Philip

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Unregistered Submission: ( February 14th, 2014 10:35pm UTC )

(I'm not the critical unreg)

I was thinking about this. As with you, I noticed that the theorem says "at least one", but that critical unreg (and FS) confused this to be "at least two" tufts.

One obvious way to have two tufts is if you start at the equator and comb towards either pole (either straight way or at an angle).

I was thinking that a way to only have one tuft would be if you started at the "north pole" and then combed southwards all over the ball. you end up with a "widow's peak" (baldish spot) at the top and a tuft at the bottom. I assume this is the solution for how to have only one tuft.

Reply Report

Permalink

Unregistered Submission: ( February 15th, 2014 1:30am UTC )

Nanonymous,

I see that you seem to understand what the hairy ball theorem says, but you don't apply it correctly. Again, all I said is

(1) Poincare's hairy ball theorem states that on a two dimensional sphere there must be at least one singular point. You agree with me on this one.

(2) If you have 'hairs' that are ordered in the form of stripes, then there MUST be two singularities (see this drawing: http://3.bp.blogspot.com/-x0c9FWdnDG4/TnHlUUxOntI/AAAAAAAAAx4/rvjX0wVXMzg/s400/hairy.jpg). You don't seem to agree with me on this one. Well, you are plain wrong.

Come on, show a sphere with aligned hairs in the form of stripes where only one singularity exists. You won't. It is impossible. That's what that paragraph from the paper you quoted says: "it is not possible to “ALIGN HAIRS” onto a sphere without generating two singularities (such as the whirl on the back of our heads)."

It's amazing to what lengths nanonymous is willing to go to try to silence criticisms to the arguments of Moriarty and Levy with lousy arguments. Again, it is obvious that you lack a solid scientific background. That Peer 4 and Moriarty praise your words also speaks of their rather modest scientific wisdom.

Reply Report

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Unregistered Submission: ( February 15th, 2014 8:24am UTC )

1) It isn't a matter of agreeing with you, I've understood the hairy ball theorem for some time.

2)Yes I've already taken care of providing the reference to the drawing you use (unattributed), and it has nothing to do with the notion of "stripes". I just can't parse anything after this, perhaps you should consider replying in the form of a concise mathematical proof?

E.g. "We define a stripe as a .... Given a vector field over a 2-sphere.... etc. etc."

Nanonymous

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Raphaël Lévy: ( February 15th, 2014 10:04am UTC )

Single singularity

https://twitter.com/raphavisses/status/434416568286838784

(the puzzle was not that difficult but I guess you have not even read the link provided by nanonymous and simply reposted the same link).

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Peer 4: ( February 15th, 2014 12:45pm UTC )

@Raphael:

Nice illustration. Unfortunately, topology's not my thing, which is why I don't really see how this theorem would have a grave importance on the existence of stripy nanoparticles.

@UnReg: The more you say, the more funny you sound. Especially when trying (and failing) to beat people at their own game. I fear it may be too late already, but I would advice that you do not become that scientist at the conference who is so stuck in his own beliefs that (s)he serves only as an example of how not to become. If you "understood science", as you put it, you would understand that it is damn easy to fool yourself approaching evidence with prejudice. Some of Ben Goldacre's work and warnings on this phenomenon in medicine might be worth evaluating.

Reply Report

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Unregistered Submission: ( February 15th, 2014 8:29pm UTC )

Levy,

That vector field you show painted on the pingpong ball is not a field that corresponds to the aligned hairs in the form of stripes. The 'aligned hairs' form parallel lines, as in here: http://us.123rf.com/400wm/400/400/itana/itana1011/itana101100102/8302429-abstract-sphere-with-stripes.jpg

With 'aligned hairs', it is obvious that there are two singularities at the poles.

Enter new comment below (Please read the **How To**)

DeVries et al assume the existence of the stripy nanoparticles; our technical comment below ignores the general issues of the lack of evidence for the stripes and instead focuses on the (other) shortcomings of the Science paper.

As the list of stripy papers continued to grow, it became necessary to challenge this body of work which is based on a well known STM artefact. More here http://raphazlab.wordpress.com/stripy-guide-2014/

***

Comment on "Divalent Metal Nanoparticles"

***

Devries et al. (Reports, 19 January 2007, p. 358) claim to have placed target molecules specifically at two diametrically opposed positions in the molecular coating of metal nanoparticles. A more likely interpretation of their results is the introduction of anisotropy in nanoparticle coatings, a phenomenon already observed in various nanoparticle systems.

Self-organization of molecules within mixed monolayers provides a route to the synthesis of nanoparticle building blocks with some degree of internal complexity and is therefore of critical importance for the development of nanodevices (1, 2). DeVries and collaborators claim to have “a simple method to place target molecules specifically at two diametrically opposed positions in the molecular coating of metal nanoparticles” (3). However, to demonstrate such an extraordinary claim, one must first reject reasonable alternative explanation of the experimental data. We first point that the general theoretical underpinning for the presence of two singularities at the poles of nanoparticles is an oversimplification. We then propose a less spectacular but more likely explanation of the experimental results which is the formation of chains through dipole-dipole interaction, a phenomenon which has already been observed in various nanoparticle systems including gold nanoparticles (4-8). In the case of gold nanoparticles, the individual dipole results from anisotropy in the distribution of charges at nanoparticle’s surface.

DeVries et al’s assertion that “polar singularities must form when a curved surface is coated with ordered monolayers, such as a phase-separated mixture of ligands” is supported by a quotation of the “hairy ball theorem” stating “that it is not possible to “align hairs” onto a sphere without generating two singularities”. In fact, the theorem states that at least one singularity must exist in a vector field on a sphere (9). The Poincare theorem does not say anything about the position or number of such singularities. A large body of experimental and theoretical work has been published on positional and orientational order on a sphere (10-14). It is an extreme oversimplification to claim that “the topological nature” of the nanoparticles demonstrate the necessary existence of two polar singularities, e.g., for hexatic order, the prediction is 12 defects at the vertices of an icosahedron (14). In that context, the authors discuss molecular dynamics simulations of homogeneous monolayers of alcanethiols by Luedtke and Landman which show that the passivating molecules organize themselves into preferentially oriented molecular bundles (15). It is worth mentioning that these simulations suggest that "equatorial" ligand exchange rather than "polar" ligand exchange would be favoured in homogeneous monolayers since the ligand density has a marked minimum at the equator.

De Vries et al’s experimental work focuses on nanoparticles covered with mixed monolayers, which have been previously shown in pioneering Scanning Tunnelling Microscopy (STM) studies to form circular ripples (1, 2). The authors argue that a very fast ligand exchange happens exclusively at the pole singularities and that this can be used to label specifically these poles with carboxylic groups that can be subsequently cross-linked with a diamine. However, to prove such a fast and localized ligand exchange, it would have been necessary to characterize extensively the dynamics and extent of ligand exhange on rippled nanoparticles. The only quantitative measurement of ligand exchange given is a rate constant of 1.67 M-1s-1 obtained indirectly through ratios of aggregated nanoparticles (data not shown). The meaning and actual definition of this rate constant is not clear. The presented data certainly support the presence of fast ligand exchange in rippled nanoparticles but provide no evidence that this ligand exchange is limited to two molecules per nanoparticle.

The only indications that the ligand exchange occurs specifically at the two poles are therefore the formation of 1-D aggregates of nanoparticles, or chains and the STM images shown in Figure S6. However, both results admit more straightforward interpretation than pole functionalization. The absence of striation in the ligand exchange rippled nanoparticles images shown in Figure S6, can simply be explained by the disappearance of these structures upon ligand exchange rather by than oriented anchoring to the substrate. Spontaneous formation of nanoparticle chains has been reported in several papers and generally understood as resulting from dipole-dipole coupling (5, 8). In the case of gold nanoparticles (4, 6), the dipole is thought to be induced by an asymmetric distribution of charges at nanoparticle’s surface (7). Although DeVries et al demonstrate clearly interparticle chemical cross-linking, it does not imply that the geometry of the formed aggregate is dictated by the initial positions of the reactive molecules charges at nanoparticle’s surface. These results are perfectly compatible with a situation where partial replacement of the rippled monolayer by MUA takes place leading to dipole-dipole coupling and formation of chains during the cross-linking experiment.

1. A. M. Jackson, Y. Hu, P. J. Silva, F. Stellacci, J. Am. Chem. Soc. 128, 11135 (2006).

2. A. M. Jackson, J. W. Myerson, F. Stellacci, Nature Mater. 3, 330 (2004).

3. G. A. DeVries et al., Science 315, 358 (2007).

4. J. Y. Chang, J. J. Chang, B. Lo, S. H. Tzing, Y. C. Ling, Chem. Phys. Lett. 379, 261 (2003).

5. Z. Y. Tang, N. A. Kotov, M. Giersig, Science 297, 237 (2002).

6. J. H. Liao et al., Appl. Phys. A 76, 541 (2003).

7. S. Lin, M. Li, E. Dujardin, C. Girard, S. Mann, Adv. Mater. 17, 2553 (2005).

8. A. Y. Sinyagin, A. Belov, Z. N. Tang, N. A. Kotov, J. Phys. Chem. B 110, 7500 (2006).

9. M. Eisenberg, R. Guy, Am. Math. Mon. 86, 572 (1979).

10. T. Einert, P. Lipowsky, J. Schilling, M. J. Bowick, A. R. Bausch, Langmuir 21, 12076 (2005).

11. A. R. Bausch et al., Science 299, 1716 (2003).

12. D. R. Nelson, Nano Letters 2, 1125 (2002).

13. M. J. Bowick, D. R. Nelson, A. Travesset, Phys. Rev. B 62, 8738 (2000).

14. T. C. Lubensky, J. Prost, J. Phys. II 2, 371 (1992).

15. W. D. Luedtke, U. Landman, J. Phys. Chem. B 102, 6566 (1998).

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I've looked at the paper and the theorem is very clearly misstated. I would imagine this is deserving of a correction, surprised didn't come out in the first exchange.

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## Are you sure you want to delete your feedback?

What was Science's response to you pointing out the (mathematically completely incorrect) statement? Wouldn't they have asked a mathematician?

Nanonymous (author of Unregistered Submission: ( February 2nd, 2014 2:05am UTC ) as well)

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## Are you sure you want to delete your feedback?

******

20 February 2007

Dear Dr. Lévy,

Thank you for submitting your comment on the recent Science paper by DeVries et al. We have now received the response from the corresponding author of the original paper, which is attached for your information.

On evaluation of the comment and response, we regret to say that your comment received a lower priority rating than other technical comments under consideration. As a result, we won't be able to publish it. In general, we believe that further discussion on this topic would be more appropriate for the specialty literature.

Notwithstanding this disappointing outcome, we appreciate the chance to consider the comment, and hope that you find the author's response helpful should you decide to revise the manuscript for submission to another journal. Thank you for your interest in Science.

Sincerely,

Tara S. Marathe

Associate Online Editor, Science

tmarathe@aaas.org

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## Are you sure you want to delete your feedback?

Can you confirm my interpretation of the paper?

They begin with an non-theorem and then derive their conclusions from there....it is hard to really consider any of their statements as credible. I see experiments and photos, but they make an elementary and fundamental error at the outset. This is not inconsequential, there is no theorem that says that suggests that there are two singularities on the surface of their nanoparticle.

I can't imagine anyone reading past the intro in my paper if it said something like "the pythagorean theorem tells us that the cube of the diagonal is equal the sum of the cube of each side, therefore..."

Nanonymous

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## Are you sure you want to delete your feedback?

I've split into two parts. As far as I can understand, the 'logics' goes like this:

*** PART 1 ***

A) Ligands on NPs have a tilt angle

B) Tilt angle = vector field on a sphere if we ignore facets (and we should according to Landman's simulations, ref 21)

c) Hairy ball theorem therefore singularities in this vector field.

"This is commonly known as the “hairy ball theorem” that states that it is not possible to

“align hairs” onto a sphere without generating two singularities (such as the whirl on the back of our heads)."

*** END PART 1 ***

A) is OK.

B) It is highly disputable whether that Landman simulation is enough of a basis for ignoring the role of facets, but, let's say this is OK. The Landman paper does not show *at all* two poles with a lower ligand density. To the contrary, it shows a depletion at the equator where tilt angle reverses. See fig 3 in the said Landman paper:

http://wp.me/ajs0h-oJ

C) is plain wrong: that is not what the theorem says. The Landman paper cited just lines above is just one example showing that a continuous tilt angle on a sphere does not necessarily lead to "two singularities". My ping pong ball is another:

https://twitter.com/raphavisses/status/434416568286838784

*** PART 2 ***

starting with "Recently we have shown"

D) Particles have ripples

E) These ripples "will profoundly demarcate the two diametrically opposed singularities at the particle poles, where the rings collapse into points (Fig. 1B)."

F) Conjecture: lower density at the poles will lead to preferential ligand exchange.

*** END PART 2 ***

D) is wrong (see Stirling et al, Cesbron et al, etc); the ripples are an artifact.

E) needs a lot of unpacking.

Let's start by the end, the proof by the cartoon: Fig 1B is a cartoon that shows the singularity. If the stripes exist as shown in the cartoon then of course, the singularities exist. However, this has nothing to do with any topological theorem: it has to do with the cartoon.

Back to the beginning: "the two diametrically opposed". Note that the previous (already wrong) statement of the theorem did not mention "diametrically opposed" singularities. This wording is kind of suggesting that those singularities (which are a consequence of the cartoon), are in fact a consequence of the theorem.

F) Nice conjecture.

It would seem that at least two referees have read past the intro and liked it. And then failed as well to notice the shortcomings of the experiments which are just as abundant.

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Why a theorem about a continuous transformation has to be "reconciled" with a discrete and finite set of molecules is beyond my ken.

Nanonymous

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