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.