User:Allison K. Alix/Notebook/Thesis Research/2013/06/12
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(→Calculating the amount of PVP to add to AuNP) 
(→Calculating the amount of PVP to add to AuNP) 

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5) Calculate #moles PVP needed to coat AuNP  5) Calculate #moles PVP needed to coat AuNP  
  279397.5 PVP/AuNP x 3.46x10<sup>12</sup>AuNP x 1 mol/6.02x10<sup>23</sup>PVP = 1.6065x10<sup>6</sup> mol PVP  +  279397.5 PVP/AuNP x 3.46x10<sup>12</sup>AuNP x 1 mol/6.02x10<sup>23</sup>PVP = '''1.6065x10<sup>6</sup> mol PVP''' 
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+  6) Calculate concentration needed to add 0.65mL of 1.6065x10<sup>6</sup>mol PVP  
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+  1.6065x10<sup>6</sup> mol PVP x 10000g/mol x 1/0.65mL x 1000mL/L = 24.7g/L  
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+  7) Calculate how many grams 10000g/mol PVP is needed to make 5mL 24.7g/L solution  
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+  24.7g/L x 5mL x 1L/1000mL = 0.1235g in 5mL H<sub>2</sub>O  
Revision as of 14:22, 12 June 2013
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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)λ_{spr}= 527nm d= [ln(λ_{spr}λ_{0}/L_{1})]/L_{2} where λ_{0}= 512nm, L_{1}= 6.53, and L_{2}=0.0216 (These are fit parameters from theoretical calculations^{1}) d= [ln(527nm512nm/6.53)]/0.0216 d= 38.5nm c = A_{450}/ε_{450} c = 1.89/(4.36x10^{9}) c = 0.43nM Calculating AuNP concentration in g/L1) Calculate the volume of 1 AuNP Volume of 1 AuNP = 4/3πr^{3}, where r = d/2 = 19.25nm V= 4/3π(19.25x10^{9}m)^{3} V= 2.988x10^{23}m^{3} V= 2.988x10^{17}cm^{3} 2) Calculate the mass of 1 AuNP density of Au = 19.3g/cm^{3} 19.3g/cm^{3} x 2.988x10^{17}cm^{3} = 5.7668x10^{16} g per 1 AuNP 3) Calculate # of AuNP in 20mL solution 0.43x10^{9}mol/L x 20mL x 1L/1000mL x 6.02x10^{23}AuNP/1 mol = 5.219x10^{12} AuNP 4) Calculate mass of all AuNP in 20mL solution 5.7668x10^{16} g/1 AuNP x 5.219x10^{12}AuNP x 1/20mL x 1000mL/1L = 0.1505g/L Dilution of AuNPAccording to Reference 1, for the silica coating procedure, 34.7mL AuNP with a radius of ~19nM must have a concentration of 0.058g/L M_{1}V_{1}=M_{2}V_{2} (0.1505g/L)(x)=(0.058g/L)(37.4mL) x = 13.37mL in 21.33mL H_{2}O Calculating the amount of PVP to add to AuNP
1) Calculate the surface area of 1 AuNP Surface Area of a sphere = 4πr^{2} SA= 4π(19.25x10^{9})^{2} SA= 4.657x10^{15}m^{2} SA= 4656.63nm^{2} 2) Calculate #PVP per 1 AuNP 60PVP/1nm^{2} x 4656.63nm^{2}/1 AuNP = 279397.5 PVP/1 AuNP 3) Calculate the new concentration of AuNP in nM M_{1}V_{1}=M_{2}V_{2} (0.43x10^{9})(13.37mL) = (x)(34.7mL) x = 1.657x10^{10}M = 0.1657nM 4) Calculate # AuNP in 34.7mL 0.1657nM solution 0.1657x10^{9}mol/L x 34.7mL x 1L/1000mL x 6.02x10^{23}AuNP/mol = 3.46x10^{12} AuNP 5) Calculate #moles PVP needed to coat AuNP 279397.5 PVP/AuNP x 3.46x10^{12}AuNP x 1 mol/6.02x10^{23}PVP = 1.6065x10^{6} mol PVP 6) Calculate concentration needed to add 0.65mL of 1.6065x10^{6}mol 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 H_{2}O
