# Difference between revisions of "User:Allison K. Alix/Notebook/Thesis Research/2013/06/12"

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## AuNP synthesis

Note: These AuNPs will be used in the silica coating procedure. See calculations below.

## Calculating AuNP diameter and concentration (nM)

λspr= 527nm

d= [ln(λspr0/L1)]/L2

where λ0= 512nm, L1= 6.53, and L2=0.0216 (These are fit parameters from theoretical calculations1)

d= [ln(527nm-512nm/6.53)]/0.0216

d= 38.5nm

c = A450450

c = 1.89/(4.36x109)

c = 0.43nM

## Calculating AuNP concentration in g/L

1) Calculate the volume of 1 AuNP

Volume of 1 AuNP = 4/3πr3, where r = d/2 = 19.25nm

V= 4/3π(19.25x10-9m)3

V= 2.988x1023m3

V= 2.988x1017cm3

2) Calculate the mass of 1 AuNP

density of Au = 19.3g/cm3

19.3g/cm3 x 2.988x1017cm3 = 5.7668x10-16 g per 1 AuNP

3) Calculate # of AuNP in 20mL solution

0.43x10-9mol/L x 20mL x 1L/1000mL x 6.02x1023AuNP/1 mol = 5.219x1012 AuNP

4) Calculate mass of all AuNP in 20mL solution

5.7668x10-16 g/1 AuNP x 5.219x1012AuNP x 1/20mL x 1000mL/1L = 0.1505g/L

## Dilution of AuNP

According to Reference 1, for the silica coating procedure, 34.7mL AuNP with a radius of ~19nM must have a concentration of 0.058g/L

M1V1=M2V2

(0.1505g/L)(x)=(0.058g/L)(37.4mL)

x = 13.37mL in 21.33mL H2O

## Calculating the amount of PVP to add to AuNP

• There must be ~60PVP/1nm2AuNP

1) Calculate the surface area of 1 AuNP

Surface Area of a sphere = 4πr2

SA= 4π(19.25x10-9)2

SA= 4.657x10-15m2

SA= 4656.63nm2

2) Calculate #PVP per 1 AuNP

60PVP/1nm2 x 4656.63nm2/1 AuNP = 279397.5 PVP/1 AuNP

3) Calculate the new concentration of AuNP in nM

M1V1=M2V2

(0.43x10-9)(13.37mL) = (x)(34.7mL)

x = 1.657x10-10M = 0.1657nM

4) Calculate # AuNP in 34.7mL 0.1657nM solution

0.1657x10-9mol/L x 34.7mL x 1L/1000mL x 6.02x1023AuNP/mol = 3.46x1012 AuNP

5) Calculate #moles PVP needed to coat AuNP

279397.5 PVP/AuNP x 3.46x1012AuNP x 1 mol/6.02x1023PVP = 1.6065x10-6 mol PVP

6) Calculate concentration needed to add 0.65mL of 1.6065x10-6mol PVP

1.6065x10-6 mol PVP x 10000g/mol x 1/0.65mL x 1000mL/L = 24.7g/L

7) Calculate how many grams 10000g/mol PVP is needed to make 5mL 24.7g/L solution

24.7g/L x 5mL x 1L/1000mL = 0.1235g in 5mL H2O

## Functionalization of AuNP with PVP

1) Mix 34.7mL of 0.058g/L AuNP with 0.65mL 24.7g/L PVP (10kg/mol)

2) Stir for 24 hours at room temperature to ensure complete adsorption

## References

1) [1] with supporting information [2]