4.4
Gold Nanoparticle Surface Coverage
The intensity of the diffraction pattern observed depends on the ratio ofr1/r2; the amplitude
reflectivity coefficients of the two surfaces. For the diffraction sensor r2 is fixed and equals
the reflectivity of silicon that has been through the processing stages necessary for the DNA grating fabrication. The reflectivity r1 corresponds to the reflectivity of processed silicon
with a layer of DNA oligonucleotides that is modified by hybridisation of a variable number of gold nanoparticles. By measuring the diffraction order intensities with all other variables constant the pattern observed can be correlated to a specific value ofr1/r2. Since r2 is fixed,
r1 may be calculated. Variation in the value of r1 is related to the number of hybridised Au
nanoparticles per unit area. Consequently, it is possible to quantify the number of hybridised gold nanoparticles from the diffraction order intensity distribution.
A given number of particles percm2 corresponds to a certain fractional area coverage of the surface, dependent on the particle size. The surface coverage calculations detailed below are based on a hexagonal packing structure, giving the maximum fractional area coverage by spherical particles. Figure 4.17 shows the hexagonal packing method used for calculations.
Figure 4.17: Area of surface coverage based on hexagonal packing of nanoparticles.
One nanoparticle of diameterφ is located within a hexagon, bounding a circle of radius R. As can be seen from Figure 4.17, the particles are separated by a centre to centre distance of 2R. The fractional area coverage of the surface depends on the radius of the particle (r =φ/2) compared to the hexagonal area specified byR (see Figure 4.18).
Figure 4.18: The maximum hexagonal area occupied by a nanoparticle of diameterφis determined byR.
Figure 4.19: Geometrical calculation of area of hexagonal region.
The area of a particle is 14πφ2, with the area of the hexagon given by 32l×2R. From Figure 4.19 it can be seen that R =lsin 60 ⇒ l = 2√R
3. Hence the hexagonal area can be written
as 2√3R2. The fractional area coverage (ρ) is then:
ρ= πφ 2/4 2√3R2 = π 8√3 φ R 2
Thus the maximum fractional area coverage when φ = 2R is ρ = 90.67 %. Knowing the number of particles per unit area (N/cm2) and the particle diameter, the fractional area coverageρcan be calculated along with an estimate of the average particle separation (2R). The maximum fractional area coverage of a close packed hexagonal arrangement of 10 nm
diameter particles would correspond to 1.15×1012 cm−2.
Inductively coupled plasma-mass spectroscopy (ICP-MS) was used by Dr H Yin (working with Dr J A Milton from the National Oceanography Centre, University of Southampton)
4.4 Gold Nanoparticle Surface Coverage 114 for analysis of DNA-gold nanoparticle conjugates dehybridised from DNA gratings on silicon [223]. Samples were dehybridised in 800 µl of water at 90◦C for 15 minutes. The silicon sample was removed, washed twice with 100µlof water and added to the collected solution, giving 1 ml total. The gold nanoparticles in the solution were dissolved by adding 50 µl of 0.1 M KCN and 1 mM K3Fe(CN)6 and were then diluted with 9 ml of 5 % HCl. ICP-MS
was used to determine the mass of gold in the solution, using the method developed by Pitcairnet al [224]. This was compared to the average particle mass for 1.4nm and 10nm
gold nanoparticles to quantify the number of particles dehybridised from the samples. It was determined that ‘good’ hybridisation yields approximately 6.4×109 gold nanoparticles per
cm2 (or 64 particles per square micron) for 10 nm diameter colloids and 2.15×1012cm−2
for 1.4 nm diameter particles. Fluorescent molecules were found to hybridise with a higher area density of 1.2×1013 cm−2. For 10 nm diameter gold nanoparticles, this hybridisation
density corresponds to a fractional area coverage of the surface ofρ≈0.5 % with an average separation of 134 nm(assuming an even distribution).
An area coverage of 0.5 % corresponds to a reflectivity ratio change of 2.4 % in the reflectivity of a DNA line compared to the silicon substrate. The diffraction intensity changes were predicted for a fractional area coverage of gold particles of 0.5 %, on a 40 micron period grating, with 3 : 1 mark-space ratio and a step height of 100 nm. The intensity changes predicted for each diffraction order are shown in Table 4.2.
Order ∆Im/Iinput m = 0 +0.65 % m = 1 +1.17 % m = 2 +1.18 % m = 3 +1.25 % m = 4 +0.65 % m = 5 +1.28 %
Table 4.2: Change in diffraction intensities predicted for a 40 µm period DNA grating hybridised with 10nmdiameter gold colloids.
In order to produce an approximate 10 % change in the intensities of the majority of the diffraction orders it was calculated that the surface area coverage needed would beρ≈2.6 %. This required 3.3×1010 particles/cm2, approximately 5 times higher particle hybridisation density than achieved in practice for the 10nm diameter gold.
Order ∆Im/Iinput ρ= 2.6 % ρ= 3.3 % m= 0 + 4.01 % + 5.15 % m= 1 +10.42 % +13.37 % m= 2 +10.22 % +13.12 % m= 3 +10.03 % +12.87 % m= 4 + 3.54 % + 4.55 % m= 5 +10.56 % +13.55 %
Table 4.3: Change in diffraction intensities predicted for a 40 µm period DNA grating hybridised with gold colloids. The centre column shows that an approximate 10 % change in diffraction values is predicted for a fractional area coverage of ρ = 2.6 %. The right hand column indicates the predicted change in diffraction with hybridisation of 1.4 nm diameter particles at the highest measured density of 2.15×1012cm−2, givingρ= 3.3 %.
The equivalent number for 1.4 nm gold colloids was calculated to be 1.3×1011 particles
/cm2. The diameter of the smaller gold colloids was just over 7 times smaller, so that at the same hybridisation density they would cover 51 times less surface area. However, the smaller particles were able to hybridise at a greater density, with the maximum measured value of 2.15×1012cm−2 being 336 times higher for 1.4nmparticles than for 10nmdiameter colloids. This corresponded to a fractional area coverage ofρ = 3.3 %, which was 6.6 times higher than for the 10 nm gold. The predicted change in diffraction associated with this level of fractional area coverage is shown in Table 4.3.
In genomic DNA samples, hybridisation is less likely to be as high as determined above for complementary, short oligonucleotide sequences. It is desirable to be able to empirically correlate the reflectivity ratio r1/r2, to the number of particles per cm2, by measuring the
diffraction patterns associated with different fractional area coverage of gold nanoparticles.