Colloidal Silver and Gold Forum

Production Techniques and Chemistry => Questions and Comments about Articles => Topic started by: PeterXXL on July 19, 2015, 07:00:58 PM

Title: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: PeterXXL on July 19, 2015, 07:00:58 PM
In order to calculate the amount of stabilizing / capping agents that is needed, it should depend on the size of the nanoparticles, as the molecules of the stabilizers attach to the outside of the nanoparticxle.

If we assume that the nanoparticles are spheres, then the volume (V) and area (A) are...

A = 4 x Pi x r2
V = ( 4 x Pi x r3 ) / 3

So for nanoparticles that are 10 nm in diameter we have...

A = 314 nm2
V = 524 nm3

And the covalent radius (the radius for atoms in molecules) for Silver is 145 pm +/- 5 pm (= 140 to 150 pm) , so this means that we also can calculate the number of the nanoparticles as...

Number of atoms in the nanoparticle = V / covalent radius
Number of atoms on the surface of the nanoparticle = A / covalent radius

So for a 10 nm nanoparticle it means...

Atoms in the nanoparticle = 524 / 0.145 (or 0.140 to 150) = 3614 (3493 to 3743)
Atoms on the surface of the nanoparticle = 314 /  0.145 (or 0.140 to 0.150) = 2166 (2093 to 2243)

And the ratio between the surface area and volume for the 10 nm particle is 2166 / 3614 = 60%. Which means, that 60% of the silver atoms are on the surface of a spherical nanoparticle of the size of 10 nm in diameter.

Based on this, we should be able to calculate how much stabilizers we need to add to, as they are attached to the surface atoms of the nanoparticles only.

The larger the nanoparticles are, the less percentage of them are on the surface.
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: PeterXXL on July 19, 2015, 08:39:53 PM
I dont think so.  Your formulas are incorrect.

In what way are the formulas wrong?

I did a check with the online calculator that I just found here...

http://www.cleavebooks.co.uk/scol/calsph.htm (http://www.cleavebooks.co.uk/scol/calsph.htm)

Entering the value 5 as radius confirms the surface area and volume.


Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: PeterXXL on July 19, 2015, 09:44:53 PM
To find out how many volumes fit in a larger volume, you obviously have to divide volume by volume, not radius.  Likewise with areas.

Ok, so for a 10 nm diameter nanoparticle we have a radius of 5 nm, and the covalent atom radius is 0.145, and the volume is 524 nm3 then, the percentage of atoms on the surface must have the same ratio as the volume of thickness of atoms on the surface to entire volume of the nanoparticle, like…

O = Outer radius of the nanoparticle (outside of the atoms on the surface) = 5 nm
I = Inner radius of the nanoparticle (inside of the atoms on the surface) = 5 – 0.145 = 4.855 nm, so…

Volume of the entire nanoparticle = 524 nm3
Volume of the “inner” part of the nanoparticle (excluding 1 layer of atoms) =

= ( 4 x Pi x I3 ) / 3 = 479 nm3 

So the outer layer of atoms on the surface have a volume of 45 nm3  (524 – 479) 

Surface ratio =  45 / 524 = 8.6%

So less than 9% of the atoms are in fact on the surface of a 10 nm diameter spherical silver nanoparticle.
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: kephra on July 19, 2015, 10:00:17 PM
If I take a bucket and fill it with golf balls, is the bucket really full? 
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: PeterXXL on July 19, 2015, 10:07:17 PM
If I take a bucket and fill it with golf balls, is the bucket really full?


It's for sure full of golf balls, but there's space in-between the golf balls there ;)


On a molecular level, if the bucket is the nanoparticle, then there's no room for other atoms in that nanoparticle, assuming that that the nanoparticle is spherical.
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: kephra on July 19, 2015, 10:10:33 PM
Quote
On a molecular level, if the bucket is the nanoparticle, then there's no room for other atoms in that nanoparticle, assuming that that the nanoparticle is spherical.
Nevertheless, all the volume of the nanoparticle is not used up. 
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: kephra on July 20, 2015, 12:02:27 PM
Take a look at this: https://en.wikipedia.org/wiki/Atomic_packing_factor
BTW, covalent bonding radius is not the correct term, its metallic bonding radius.  The values are the same though in this case.
Covalent bonding radius refers to the bond length between unlike atoms, as in sodium chloride for example.
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: PeterXXL on July 20, 2015, 03:56:08 PM
Take a look at this: https://en.wikipedia.org/wiki/Atomic_packing_factor (https://en.wikipedia.org/wiki/Atomic_packing_factor)
BTW, covalent bonding radius is not the correct term, its metallic bonding radius.  The values are the same though in this case.
Covalent bonding radius refers to the bond length between unlike atoms, as in sodium chloride for example.


Thanks for the link. As they refer to crystallography (https://en.wikipedia.org/wiki/Crystallography), I wonder if this also is the case for nanoparticles as colloids or not; are atoms packed closer as crystals than in soluble form?
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: kephra on July 20, 2015, 05:26:04 PM
The internal makeup of a particle does not depend on whether it is suspended in water or not.
Crystalline simply means the atoms are arranged in an orderly manner, instead of randomly placed.  A dissolved substance cannot be crystalline. 

Since silver nanoparticles are not soluble, your last question does not apply to them.

Applying what you learned so far, what is your new estimate for the percentage of surface atoms on a 10nm particle?
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: PeterXXL on July 20, 2015, 09:52:42 PM
The internal makeup of a particle does not depend on whether it is suspended in water or not.
Crystalline simply means the atoms are arranged in an orderly manner, instead of randomly placed.  A dissolved substance cannot be crystalline. 

Since silver nanoparticles are not soluble, your last question does not apply to them.

Applying what you learned so far, what is your new estimate for the percentage of surface atoms on a 10nm particle?


So ref. to https://en.wikipedia.org/wiki/Atomic_packing_factor (https://en.wikipedia.org/wiki/Atomic_packing_factor)

…atoms are packed, and the majority of metals have an “atomic packing factor” of 0.68 to 0.74 so this mean that we can assume that the actual size between each atom in the nanoparticle is 0.68
to 0.74 as small. So a silver atom which has an atomic radius of 0.145 we get 0.145 x 0.68 = 0.0986 to 0.145 x 0.74 = 0.1073. And based on that…

For a nanoparticle of 10 nm in diameter we have...

Surface Area = 314 nm2
Volume = 524 nm3
Atomic radius = 0.145 nm

Atomic radius corrected for “atomic packing factor” = 0.0986 or 0.1073 nm
O = Outer radius of the nanoparticle (outside of the atoms on the surface) = 5 nm
I = Inner radius of the nanoparticle (inside of the atoms on the surface) = 5 – 0.0986 = 4.9014 to 5 – 0.1073 = 4.8927 nm, so…

Volume of the entire nanoparticle = 524 nm3
Volume of the “inner” part of the nanoparticle (excluding 1 layer of atoms) = ( 4 x Pi x I3 ) / 3 = 490 to 493 nm3

So the outer layer of atoms on the surface have a volume of 31 to 34 nm3  (524 – 490 to 493) .

Compared to the total volume of the nanoparticle, this is  31 / 524 to 34 / 524 = 5.9% to 6.5% of the total volume.
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: kephra on July 20, 2015, 11:46:01 PM
Um no.  The packing factor says that only 68 to 74% of the volume of the nanoparticle would actually be silver atoms, the rest is empty space.  So the nanoparticle will have fewer atoms, not more.
Go back to the bucket of golf balls, and see all the empty space that cannot hold another golf ball.
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: PeterXXL on July 21, 2015, 01:09:21 AM
Um no.  The packing factor says that only 68 to 74% of the volume of the nanoparticle would actually be silver atoms, the rest is empty space.  So the nanoparticle will have fewer atoms, not more.
Go back to the bucket of golf balls, and see all the empty space that cannot hold another golf ball.

Ok, so for a 10 nm diameter nanoparticle we have a volume of 524 nm3 but only 68 - 74% of that consists of atoms, making the volume of atoms to 524 x 0.68 or 524 x 0.74 = 356 to 524 nm3.

And if we divide that with the volume of a silver atom, which have a radius of 0.145 nm, equal to an atomic volume of 1.28 nm3, we get 356 to 524 / 1.28 = 278 to 409 atoms in the nanoparticle.

And on the surface we have a layer of atoms with the volume of 490 to 493 nm3 (according to my previous post), but adjusted for the atomic packing factor, multiplied with 0.68 to 0.74, equal to 333 to 365 nm3

So the surface to total volume ratio (corrected for the atomic packing factor) is 333 to 365 / 356 to 524 = 64 to 94%, which confirms that most of the silver atoms atoms on a 10 nm diameter spherical nanoparticle are actually on the surface.
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: kephra on July 21, 2015, 03:07:09 AM
Quote
And if we divide that with the volume of a silver atom, which have a radius of 0.145 nm, equal to an atomic volume of 1.28 nm3, we get 356 to 524 / 1.28 = 278 to 409 atoms in the nanoparticle.
Not even close. 
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: RickinWI on July 21, 2015, 07:26:55 AM
I seem to  recall that there are about 100 -- 150 silver atoms in one of our silver particles but I have no clue how to calculate that.
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: kephra on July 21, 2015, 11:03:17 AM
There are a lot more than that. 
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: kephra on July 21, 2015, 12:49:58 PM
@PeterXXL:  Although you got the wrong answer so far, I want to tell you that I like your idea of calculating the surface atoms by subtracting the inside volume from the outside.  When I first did these calcs, I did it based on the surface area, but the packing ratio may be different for the surface atoms. 

Also, since we are comparing volumes, its unnecessary to bother with the 4/3 pi in the calcs.
So we can just cube the ratios of radii, and apply the packing ratio.
For example: A 12 nm particle has a radius of 6 nm, so the amount of atoms which will fit inside is (6/.155)3*.74 which comes out to 42923

Using your method to find the number of surface atoms, we have 42923 - ((6-.155)/.155)3* .74 = 3241
This gives a value of 7.55% for the percentage of surface atoms for a 12nm particle.
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: RickinWI on July 21, 2015, 04:00:50 PM
43,000 atoms!  WoW,  I guess I was off by a few  ;)
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: SanchoPanza on July 21, 2015, 08:14:19 PM
You might know you're a redneck if....
You have a feeling they just "make some of this stuff up" on the Forum...

Wooosh.....

But I applaud the brilliance here!

-Sancho
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: kephra on July 21, 2015, 10:31:03 PM
Well I am a redneck at heart :)  Git 'R Done!
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: PeterXXL on July 22, 2015, 12:39:08 PM
@PeterXXL:  Although you got the wrong answer so far, I want to tell you that I like your idea of calculating the surface atoms by subtracting the inside volume from the outside.  When I first did these calcs, I did it based on the surface area, but the packing ratio may be different for the surface atoms. 

Also, since we are comparing volumes, its unnecessary to bother with the 4/3 pi in the calcs.
So we can just cube the ratios of radii, and apply the packing ratio.
For example: A 12 nm particle has a radius of 6 nm, so the amount of atoms which will fit inside is (6/.155)3*.74 which comes out to 42923

Using your method to find the number of surface atoms, we have 42923 - ((6-.155)/.155)3* .74 = 3241
This gives a value of 7.55% for the percentage of surface atoms for a 12nm particle.


Based on that, I made an Excel table as follows (Silver):

Particle diameter size in nm
5
10
12
15
20
25
30
35
40
45
50
Radius
2.5
5
6
7.5
10
12.5
15
17.5
20
22.5
25
Atoms in particle
3105
24840
42923
83834
198718
388121
670672
1065003
1589742
2263519
3104965
Atoms on the surface
542
2239
3241
5091
9098
14260
20577
28049
36676
46458
57395
Percentage of atoms on the surface
17.5%
9.0%
7.6%
6.1%
4.6%
3.7%
3.1%
2.6%
2.3%
2.1%
1.8%

So we can conclude that it should be more than enough to use 17.5% of the molar weight of the silver when calculating amount of stabilizing and capping agents to use for reduced colloidal silver, as we can be sure that the particles are tat least 5 nm large (most are probably around 10 nm).
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: kephra on July 22, 2015, 01:23:55 PM
Thats a nice table.  Thanks for doing the work.

Considering that a 50nm particle has 1000 times as many silver atoms as a 5nm particle, that means for a given ppm of silver, the 50nm size has only .1% of the number of particles.  Is it any wonder that smaller particle size is way more effective just due to the greater number of nanoparticles?

Concerning the amount of stabilizer:  I think your assumption is true provided that the rate of stabilization is faster than the rate of production.  Just like the rate of anode scavenging is important, so is this, but I think it is a safe assumption to make at the low currents we home users make our colloidal silver with.  Otherwise, the particles may grow past the safe area faster than they are capped.  If that happens, the particles can continue to grow out of control.

Of course, this also assumes the presence of a separate reducing agent, since the lower amount would preclude using the stabilizer as the primary reducing agent.

I know that with some agents, the amount limits the particle size to a maximum, and increasing the amount of stabilizer results in smaller particles.  Infinite stabilizer does not result in infinitely small particles though :)

Another problem is knowing the molecular weight of the stabilizer.  Some are not defined.  Lecithin for example exists in many variations depending on the source.  Maltodextrin exists in various forms with different molecular weights.  Gelatin is another. 

Lecithin has published MWs varying from 600 to 800 daltons for example.
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: SanchoPanza on July 23, 2015, 04:01:38 AM
That's a really nice table Peter, thanks for the efforts!

Sorry to interrupt here, but I have a redneck question.
If we could make 5nm particles, what color would the colloidal silver be?

Thank you,
-Sancho
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: kephra on July 23, 2015, 11:18:50 AM
Light green.
This picture shows high ppm samples. (100+ ppm)
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: SanchoPanza on July 24, 2015, 11:21:13 PM
Thank you Sir. Excellent reference!
Looking at those samples, It appears our "yellow" results are in the 5-7nm range?
The 10nm sample looks like it would dilute down to more of a pinkish color.
The others are not even close.

Is green to small of a particle for us to consume?
Can that size still be capped effectively with Gelatin?

-Sancho
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: kephra on July 25, 2015, 12:17:01 AM
Quote
Is green to small of a particle for us to consume?
Can that size still be capped effectively with Gelatin?
Unknown.

But being light green does not guarantee that particle is spherical and 5 nm as other shapes exhibit different colors.  You see green because the particles filter out both red and blue.  A rod shaped particle does this by having a long axis (red absorber) and a short axis (blue absorber).  There have been reports with gold nanorods being toxic.  I don't know if this is the case with silver nanorods, but I am not going to risk it. 
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: PeterXXL on July 25, 2015, 01:27:26 AM
Thank you Sir. Excellent reference!
Looking at those samples, It appears our "yellow" results are in the 5-7nm range?
The 10nm sample looks like it would dilute down to more of a pinkish color.
The others are not even close.

Is green to small of a particle for us to consume?
Can that size still be capped effectively with Gelatin?

-Sancho


The 100 ppm batches (and higher concentration diluted to 100 ppm) that I've made look most similar to the picture of the 10 nm sizes to me.


Also, if there's particles in different sizes then my conclusion is that it look somewhat turbid. I've noticed that for batches of above 20 ppm when there has been too little of the stabilizing agent.
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: SanchoPanza on July 25, 2015, 03:00:48 AM
Aahh, Thank you both.
My experience is limited to 20ppm colors.
I will consider green to be not as good then.

-Sancho
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: fishing4fun on July 25, 2015, 06:53:08 AM
Light green.
This picture shows high ppm samples. (100+ ppm)
Do these colors indicate particle size no matter what process was made to achieve those colors?
There using sodium borohydride and trisodium citrate as reducing agents, Silver nitrate, sodium hydroxide, Ethyl alcohol and acetone & double deionized (DI) water.
And the process were mostly here doing is totally different so is the color the same for every process or can it be different?
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: kephra on July 25, 2015, 11:20:57 AM
The color is determined by the size and shape of the metal particle, not the chemicals used to make it .

BTW, whats with the sizeing?  Its annoying, like shouting.
Title: Re: Calculating number of atoms inside of a nanoparticle and on the surface
Post by: fishing4fun on July 25, 2015, 05:45:58 PM
The color is determined by the size and shape of the metal particle, not the chemicals used to make it .

BTW, whats with the sizeing?  Its annoying, like shouting.
Not sure why that size comes up when you copy and paste from another location but i went back and fixed it.
Thanks for the answer i just didn't know if there process or chemicals they used had anything to do with the color they came up with and if it would be different for us as we do not use the same chemicals or solutions.