[3dem] (mean Inner potential) Re: 3dem Digest, Vol 142, Issue 38

Vladan Lucic vladan at biochem.mpg.de
Mon Jul 1 16:00:58 PDT 2019


Hi Philip,


Let me then be more precise. You're right that the formula I mentioned 
is valid far from the dipole and that we should consider layers instead 
of single dipoles. The analytical solution for two dipole layers, valid 
far from the layers shows that the potential is proportional to the 
distance between the layers (see little calculations at 
https://datashare.biochem.mpg.de/s/4Xc18s6G9ydbAiK ), so no change there.


However strange it sounds, an electron approaching the dipoles will feel 
the dipole potential and its linear dependence on the distance between 
the layers. I don't expect this potential to be strong because it falls 
off pretty fast with the distance.


I also provide there the solution for the potential generated by a 
disk-shaped double layer of dipoles, which is valid for any distance to 
the layers, distance between layers, distance between charges within a 
dipole and the radius of the dipole layers. One can use this to 
calculate the potential due to dipole layers between the layers. The way 
I see it, it will not be constant between the layers, the highest value 
should be in the middle, but I didn't calculate it exactly.


However, my understanding is that all this doesn't matter (much) for the 
phase change of an electron passing through a material having dipole 
layers on the surfaces, because the potential between the layers 
strongly depends on the material between the dipoles (eg some type of 
C). This potential can be approximated by the mean inner potential of 
the material, which was the original reason for starting this thread. 
Reading the literature, it seems that dipoles formed on the surface have 
two effects: they add their potential, but also induce a rearrangement 
of the electrons within the material, thus modifying the mean inner 
potential.


My main point in this discussion was the sentence I quoted below that 
(erroneously or not) mentions dipoles perpendicular to the electron 
beam, which to me appears similar to an explanation for the Volta phase 
plate that was recently published (mentioned somewhere below).


Best,

Vladan


On 6/28/19 2:08 PM, Philip Köck wrote:
>
> Hi Vladan.
>
>
> I think I've spotted the problems in your argument.
>
> One is that the formula for the potential from a dipole is only valid 
> at a large distance from the dipole, r much bigger than the distance 
> between + and - in the dipole.
> The inside of a slab of matter is not necessarily very far from the 
> surface. Think of a 10 nm carbon film coated with water molecules. A 
> lot of it is quite close to the surface (compared to the charge 
> separation in a water molecule).
>
> The second problem is that you would have to integrate over the 
> surface if you want to apply your reasoning to an extended double 
> layer of dipoles.
>
>
> I would suggest a very simple model in stead: Just think of two 
> infinitely large charged planes on each face of the slab, both with 
> the negative charge closer to the inside. If you come from the vacuum 
> the potential decreases within the first bilayer and then remains 
> constant within the slab and then increases back to the vacuum value 
> in the opposite bilayer. The value inside the slab will be constant 
> and will not depend on the thickness of the slab, but only on what 
> happens in the surface bilayers.
>
>
> There's an easy way to calculate potentials numerically with an image 
> processing package (MATLAB maybe). You just create a charge 
> distribution and then apply the Poisson equation by a simple 
> manipulation in Fourier space and you get the potential.
>
> I put the formulas in my recent Ultramicroscopy paper, but you can 
> find them in many other places (papers by Spence, e.g.).
>
> If you want to try this I'd like to here what you come up with.
>
>
> There's one more thing I might have to point out since I'm not sure 
> about your last statement quoted below:
> The phase shift is proportional to the projected potential. This means 
> that it's proportional to the thickness if the potential is constant 
> inside the slab.
>
> If the potential was proportional to the thickness the phase shift 
> would be proportional to the square of the thickness.
>
>
> All the best,
>
>
> Philip
>
> ------------------------------------------------------------------------
> *From:* 3dem <3dem-bounces at ncmir.ucsd.edu> on behalf of Vladan Lucic 
> <vladan at biochem.mpg.de>
> *Sent:* Thursday, 27 June 2019 19:08:51
> *To:* 3dem at ncmir.ucsd.edu
> *Subject:* Re: [3dem] (mean Inner potential) Re: 3dem Digest, Vol 142, 
> Issue 38
>>
>> I don't see how the potential can be proportional to the distance 
>> between the dipole layers. If we think of a slab of neutral matter 
>> (as a thought experiment), which is covered first by a layer of 
>> positive charges and then an equal amount of negative charges on top 
>> of that, the following should happen: The negative charge curves the 
>> potential upwards and the potential increases, then the positive 
>> charge curves the potential down again by an equal amount. The total 
>> effect is that the potential is constant inside the slab and 
>> independent of the slab's thickness and therefore the phase shift is 
>> proportional to the thickness.
>>
> Let me try to expand on your model. Adsorbed H2O forms dipoles on the 
> surface, with positive charge towards the vacuum and the negative 
> towards the material. A potential arising from one dipole (having 
> electric dipole moment p, vector) that an electron at a distance 
> (vector) r sees is proportional to:
>
>     scalar_product(r, p) / magnitude(r)^3
>
> So you're right that it is proportional to the distance between the 
> positive and the negative charge (contained in p), but that's not all. 
> H2O dipoles form on both sides of the material and they're oriented in 
> the opposite direction. The contribution to the potential from the 
> "other side dipol" has the same form, but r needs to be replaced by 
> r+d, where (vector) d is the thickness of the material. Adding the two 
> terms (with opposite signs because of the opposite orientation), when 
> (magnitudes) r>>d leaves in the first approximation a term 
> proportional to d. That's the reason for my proportionality statement.
>
> In any case, we agree that it is clear why the phase should be 
> proportional to the thickness, at least for flat surfaces.
>
> Best,
> Vladan
>>>
>>
>
>
>
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-- 
Vladan Lucic, PhD
Max Planck Institute of Biochemistry
Department of Molecular Structural Biology
Am Klopferspitz 18
82152 Martinsried, Germany

Phone +49 89 8578-2647
Fax: +49 89 8578-2643
Web: http://www.biochem.mpg.de/277447/15_ContentSynCompl

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