Photo-thermal effects in gold nanorods / DNA complexes
Luciano De Sio1*, Giulio Caracciolo2, Ferdinanda Annesi3, Tiziana Placido4, 5, Daniela Pozzi2, Roberto
Comparelli5, Alfredo Pane3, Maria Lucia Curri5, Angela Agostiano4,5, Nelson Tabirian 1
Roberto Bartolino3, 6, 7
1
Beam Engineering for Advanced Measurements Company, Winter Park, Florida 32789, USA
2
Dipartimento di Medicina Molecolare, Sapienza Università di Roma, Viale Regina Elena 291, 00161, Roma
3
CNR-IPCF UOS Cosenza - 87036 Arcavacata di Rende, Italy
Università degli Studi di Bari – Dip. Chimica, Via Orabona 4, 70126 - Bari, Italy
4
5
CNR-IPCF Istituto per i Processi Chimici e Fisici, Sez. Bari, c/o Dip. Chimica Via Orabona 4, 70126 - Bari, Italy
6
Department of Physics - University of Calabria Centre of Excellence for the Study of Innovative Functional Materials 87036 Arcavacata di Rende, Italy
7
Centro Linceo of the National Academy dei Lincei, Rome
*Corresponding author: luciano@beamco.com
Dynamic Light Scattering experiments
Theoretical background
The temporal autocorrelation function of dynamic light scattering (DLS) intensity, G2, is given by:
G2 ( ) 
I (t ) I (t   )
I (t ) I (t )
(1)
where I(t) is the intensity of the scattered light at time t and τ is the time delay. G 2 is related to the
temporal autocorrelation function of local density fluctuations, g1, by the Siegert relationship: [1]
G2 ( )  1   g1 ( ) 2
(2)
For a dispersion of polydisperse distribution of spherical particles:
k
g1 ( )   Ai e i
(3)
i 1
where Ai are coefficients proportional to the intensity scattered from the ith class of particles, and
i  q 2 Di
(4)
are decay coefficients, proportional to the diffusion coefficients Di and to the modulus of the scattered
wave vector q=4π/λ*sin(θ/2). For spherical particles, the diffusion coefficient Di and hydrodynamic
radius RHi are related by the Stokes-Einstein equation:
i 
K BT
6 RHi
(5)
where KB is the Boltzmann constant, T is the temperature and η is the solvent viscosity. For rod like
particles the temporal autocorrelation function g1 becomes:
g1 ( )  S0 (qL)e q Dt  S1 (qL)e ( q Dt 6 Dr )  ......
2
2
(6)
where S0 and S1 are the scattering amplitudes, Dt and Dr are the translational and rotational diffusion
coefficients, L is the axis length and q is the scattered radiation wave vector. If the cylinder dimensions
are known (L is the axis length and d is the diameter), translational and rotational diffusion coefficients,
Dt and Dr, can be calculated by the following relations:
Dt 
K BT
(ln( p)   )
3 L
(7)
Dr 
3K BT
(ln( p)   )
 L3
(8)
where p = L/d, while υ and δ are end correction parameters. For 2<p<20, υ and δ are given by the
following expressions: [2]
  0.316  0.582 / p 0.05 / p 2
(9)
  0.662  0.917 / p 0.05 / p 2
(10)
Size determination by DLS involves the selection of an approximating function that reflects the
physical model of the particle population.
Experimental results
DLS experiments were performed at 37 °C by means of a Malvern NanoZetaSizer spectrometer
equipped with a 5 mW HeNe laser (λ = 632.8 nm) and a digital logarithmic correlator. Scattered light is
collected at θ=173°, the angle between incident radiation and scattered light wave vectors.
Figure S1. Representative autocorrelation function of the DLS intensity collected from a solution (blue solid line is the best
fit to the data obtained by using equation 6) (a). Hydrodynamic radius of GNRs/DNA complexes as a function of W (b).
Note: in (b) results are reported as average value ± standard deviation
Figure S1 shows a representative autocorrelation function (g1) obtained from a dispersion of GNRs.
Experimental results (Figure S1a, red circles) were well fitted by the autocorrelation function of rodlike particles reported in equation 6 (Figure S1a, blue solid line). From the fitting parameters, the
translational (Dt) and rotational (Dr) diffusion coefficients for the GNRs were obtained. For
comparison, experimental values were compared with the theoretical values calculated by using
equation 7 (Dt) and 8 (Dr) (Table S1).
Experimental values
Theoretical values
Dt (µm2s-1)
10.2370.939
12.407
Dr (s-1)
12351524
11644
Table S1. Experimental and theoretical values for the translational and rotational diffusion coefficients of the GNRs/DNA
complexes.
As a matter of fact, results reported in Table S1 show that the experimental diffusion coefficients are in
good agreement with the theoretical values. The observed slight deviation is most likely due to the fact
that, according to TEM analysis (Figure 1c), GNRs are not perfectly cylindrical in shape. DLS analysis
enables the discrimination between two different complexation regimes separated by a vertical dashed
line in Figure S1b. At low GNRs/DNA molar ratio (“excess DNA regime”, typically W<10-6), DLS
data were analyzed by the CONTIN method, [3] which is based on the assumption that the dispersion is
made by particles spherical in shape. In that case, the autocorrelation function of local density
fluctuations, g1(τ), was well fitted by equation 3. This gave us a distribution of diffusion coefficients
(equation 4) that, in turn, resulted in a distribution of hydrodynamic radii (equation 5). The goodness of
the fitting procedure means that, for W<10-6, negatively charged DNA works as a molecular glue
between positively charged GNRs resulting in the formation of large spherical clusters (RH ≈300 nm).
At high GNRs/DNA molar ratio (typically W>10-6), the CONTIN method did not meet enough fitting
quality criteria (i.e. fitting g1(τ) by equation 3 was not accurate). This observation means that, a low
DNA content (means high GNRs/DNA molar ratio), GNRs/DNA complexes are not spherical in shape.
On the other side, the autocorrelation function of local density fluctuations was well reproduced by the
autocorrelation function of rod-like particles reported in equation 6. This means that, for W>10-6, the
shape of GNRs/DNA complexes resembles that of bare GNRs. Most likely, in this regime, DNA can
partially decorate the surface of GNRs with the result that GNRs/DNA complexes exist as monomers
(i.e. do not aggregate each other) thus keeping the original rod-like shape of GNRs. In that case, the
reported hydrodynamic radius is that of an equivalent sphere (RH ≈ 50 nm) with the same translational
diffusion coefficient as determined by the above explained procedure. For each GNRs/DNA molar
ratio, W, the best fitting procedure (i.e. the CONTIN method or data fitting by Equation 6) was chosen
by goodness-of-fit tests, thus allowing to clarify the role of the GNRs/DNA molar ratio in shaping the
population.
References
[1] B. J. Berne, R. Pecora, Dynamic Light Scattering. Courier Dover Publications (2000)
[2] D. Lehner, H. Lindner, O. Glatter, Langmuir 2000, 16, 1689.
[3] S. W. Contin Provencher, Comput. Phys. Commun. 1982, 27, 229.