Calculate thickness of organic layer on wire

[Billybong]

Hello

I have done some lab work where I have coated a wire with an organic layer.

The density of the organic layer is 800kg/m^3 and the density of the wire is 2620kg/m^3. I assume 1wt% of the wire is the organic layer the rest is the wire.

The mass of the wire with organic layer is 10^(-6)kg. I assume the geometry of the wire is a cylinder with radius 8.5*10^(-6)m.

What would be the thickness of the organic layer and what volume % will it have of the whole volume?Please comment my code. Is it right what I have done?

The Attempt at a Solution

I did the following calculation where I found the thickness of the organic layer to approx 72nm.

DensitetWire_Organiclayer=800*0.01+2620*0.99; %Density of wire with organic layer

RadiusWire_Organiclayer=8.5*10^(-6)%:0.5*10^(-6):12*10^(-6); %Radius of wire with organic layer

MassWire_Organiclayer=10^(-6);%Mass of wire with organic layer

MassWire=0.99*MassWire_Organiclayer;%Mass of wire

MassOrganiclayer=0.01*MassWire_Organiclayer;%Mass organic layer

Volume=MassWire_Organiclayer/DensitetWire_Organiclayer%Volume of wire with organic layer

LengthWire_Organiclayer=Volume/(pi*RadiusWire_Organiclayer^2);% Length of wire with organic layer

VolumeWire=MassWire/2620 %Volume wire

VolumeOrganiclayer=MassOrganiclayer/800 %Volume organic layer

RadiusWire=(VolumeWire/(pi*LengthWire_Organiclayer))^(1/2) %Radius wire


RadiusOrganiclayer=RadiusWire_Organiclayer-RadiusWire % Radius organic layer

Best Regards

Robin

 

[Delphi51]

For the wire, m = density*volume = dπr²h (1)
For the coating, m = DV = D(πR²h - πr²h) = πhD(R²-r²) (2)
where r and d are the radius and density of the wire,
R and D the radius and density of the coating.
You can get the value for h from equation (1).
Then (2) can be used to find (R²-r²) and the thickness R-r. It worked out to about 40 x 10^-6 meters for me, but my calcs are not always correct!

 

[Billybong]

Dear Delphi51

Thanks for your reply. I made mistake when I described my problem. 8.5*10^(-6)m is the radius of the wire with the organic layer. Sorry

This means I have to find another method. Then I tried the code under. Do you have another method?

DensitetWire_Organiclayer=800*0.01+2620*0.99; %Density of wire with organic layer

RadiusWire_Organiclayer=8.5*10^(-6); %Radius of wire with organic layer

MassWire_Organiclayer=10^(-6);%Mass of wire with organic layer

MassWire=0.99*MassWire_Organiclayer;%Mass of wire

MassOrganiclayer=0.01*MassWire_Organiclayer;%Mass organic layer

Volume=MassWire_Organiclayer/DensitetWire_Organiclayer%Volume of wire with organic layer

LengthWire_Organiclayer=Volume/(pi*RadiusWire_Organiclayer^2);% Length of wire with organic layer

VolumeWire=MassWire/2620 %Volume wire

VolumeOrganiclayer=MassOrganiclayer/800 %Volume organic layer

RadiusWire=(VolumeWire/(pi*LengthWire_Organiclayer))^(1/2) %Radius wire


RadiusOrganiclayer=RadiusWire_Organiclayer-RadiusWire % Radius organic layer

Best Regards

Robin

 

[Delphi51]

I'm an old retired physics teacher and my memory doesn't persist long enough to follow your solution! The numbers are just a blur. I really need something more compact that I can see all at once.

What happens if you take the ratio of the two equations I wrote earlier? The ratio of the masses is .01, the height cancels out and I think you are left with a relationship between the two radii. You know one of them, so you can use it to find the other.

 

[rwisz]

Hello Robin,

Your calculations and approach seem to be correct. However, I would recommend double-checking your calculations and units to ensure accuracy. Additionally, it would be helpful to provide more context and information about your experiment, such as the specific materials and methods used, in order to accurately assess the validity of your results. Overall, it appears that you have successfully calculated the thickness and volume percentage of the organic layer on the wire. Keep up the good work!