STABILITY AND ORIENTATIONAL ORDER OF GOLD NANORODS IN NEMATIC
SUSPENSIONS: A SMALL ANGLE X-RAY SCATTERING STUDY
Thomas M. R.
1
, Hallett J.E.
1
, Klein S.
2
, Mann. S.
4
, Perriman A. W.
4,5
, Richardson R. M.
3*
.
1 Bristol Centre for Functional Nanomaterials, Centre for NSQI, University of Bristol, Tyndall
Avenue, Bristol, BS8 1FD (UK)
2 HP Labs Bristol, Long Down Avenue, Bristol BS34 8QZ (UK)
3 H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL (UK)
4 Centre for Organized Matter Chemistry, School of Chemistry, University of Bristol, Bristol, BS8
1TS (UK)
5 School of Cellular and Molecular Medicine, University of Bristol, Bristol, BS8 1TH, UK
SUPPORTING INFORMATION
Experimental:
Materials:
Compounds for the synthesis of GNRs were purchased from the suppliers described by Ye et al.
8
Acetone (CHROMASOLV® Plus, for HPLC, ≥99.9%) and ethanol (200 proof, anhydrous, ≥99.5%) were purchased from Sigma-Aldrich UK. Thiol terminated polyethylene glycol (PEG-SH) of molecular weight 1900 and 5400 were purchased from Rapp Polymere GmbH. 4-cyano-4’pentylbiphenyl (5CB) was purchased from Kingston Chemicals Ltd.
Nanoparticle synthesis :
GNRs were prepared using an aromatic additive modified synthesis as described by Ye et al.
8 GNRs of aspect ratio 5.2 were synthesized using the reduced pH promoted 5-bromosalicylic acid aromatic additive protocol with minor adjustments (9.0 g of CTAB, 1.1 g of 5-bromosalicylic acid, 60 mL
AgNO
3
(4 mM), 2.1 mL of HCl (37%), 1.25 mL L-ascorbic acid (0.064 M) and 0.8 ml of a seed solution for a 500 mL synthesis) yielding GNRs of dimensions (from TEM) of 14 nm by 75 nm with a polydispersity standard deviation of 1 and 6nm respectively.
PEGylation of the nanoparticles :
As prepared GNRs were centrifuged twice at 10,000 g while ensuring a surfactant concentration
>1 mg/mL. The GNRs were surface modified using two different thiol-terminated polyethylene glycols (1900 Mw and 5400 Mw, Rapp Polymere). This was achieved by reducing the concentration of centrifuged GNRs to < 0.03 mg/mL in Milli-Q water (50 mL) with a CTAB concentration of 1-2 mg/mL. To this, an aqueous solution of PEG-SH (5 ml) was added to yield an Au:PEG molar ratio of
1:10. The samples were then sonicated for 10 minutes and the functionalization was allowed to proceed overnight with gentle stirring at room temperature. The PEGylated samples could then be centrifuged at 10,000 g and re-dispersed in a 50% (by volume) ethanol/water mixture. This washing procedure was repeated in 1.5 mL Eppendorf Safe-Lock Tubes TM at higher concentration four times to remove trace surfactants and unbound PEG-SH. Dispersions in ethanol/water could be kept for weeks with only sedimentation due to gravity observed. Prior to phase transfer into LC hosts, these dispersions in ethanol-water were filtered through 0.2 µm Millex-HA MF membrane syringe filters.
Dispersion of the nanoparticles in isotropic 5CB :
Phase transfer into LC hosts was performed through an intermediate acetone phase. This was achieved by centrifugation at 16,000 g followed by re-dispersion into acetone. Once dispersed into acetone, samples were centrifuged at 6,000 g leading to a free-flowing pellet of GNRs. This process was

repeated a further 3 times prior to addition of typically 100

L of 5CB to 0.2 mg Au (GNRs) in 0.3 mL acetone. The sample was then left for 5 hours at 40 °C to remove the acetone while maintaining the isotropic phase of the 5CB (isotropic stock).
Dispersion of the nanoparticles in nematic 5CB :
PEGylated GNRs dispersions in the nematic phase were obtained through the addition of 10 µL of the isotropic stock by pipette quickly in to a rapidly vortexing 90 µL 5CB sample in an Eppendorf Safe-
Lock Tube TM . The nematic dispersion of GNRs was then vortexed for a further 5 seconds.
CryoTEM Characterization :
CryoTEM samples were prepared by drop-casting nematic composites on carbon coated copper grids that were rapidly frozen under liquid nitrogen using a Gatan cryotransfer stage. Imaging was performed using a JEOL TEM 2010. UV-vis spectrophotometry was performed using a Perkin Elmer
Lambda 25 spectrophotometer.
Thermogravimetric Analysis (TGA) :
Nanorod dispersions in an ethanol/water 50:50 by volume solvent system (1 mL) were washed by centrifugation 10 times to reduce the concentration of any impurities to less than 1x10 -7 of that in the initial solution. For an initial solution containing 100 mg of PEG-SH in 1 mL this would correspond to a mass of approximately 0.01 µg of PEG-SH not associated with that bound to nanorods. These suspensions were then pushed through 0.2 µm Millex-HA MF membrane syringe filters to remove any dust or other impurities picked up during the multiple centrifugation cycles. Following this filtration, the samples were centrifuged a final time to concentrate them to a reduced volume of 100
µL. These 100 µL samples were then dried at 100 °C (in a pre-weighed 300 µL volume ceramic crucible that had been calcined at 1000 °C) overnight and the mass of the PEGylated nanoparticles measured to a precision of ±1 µg. The samples were then calcined at 700 °c for 4 hours to remove the organic component yielding only the constituent gold. Samples were typically prepared to yield a mass of gold in the region of 300 µg. The surface area of the nanoparticles was determined assuming hemispherically end-capped cylinders with dimensions determined by TEM sizing and the density of gold was taken to be consistent with bulk gold, 19.3 gcm -3 .
SAXS experiments :
Data was obtained at the Diamond Light Source (Oxfordshire, UK) on Beamline I22. Electric fields between 0.18 and 1.4 Vμm−1(RMS) and frequencies from 0.01 Hz to a maximum of 2000 Hz were employed for samples contained in 1.5 mm diameter quartz glass capillaries (Capillary Tube Supplies
Ltd.), which were contained within a parallel plate (1.8mm separation) electric field sample holder.
The scattered intensity data was measured using a two-dimensional Dectris detector system.
X-ray Scattering Analysis
The scattering from the suspensions of GNRs in 5CB was modelled as a mixture of aggregates and single nanorods. The aggregates shown in CryoTEM experiments indicated a broad range of assembly architectures but on average, they all include a poorly ordered hexagonal lattice of nanorods. These assemblies were modelled with a finite para-crystalline hexagonal net with nanorods at each vertex. In the para-crystalline lattice model, the pair distribution function of adjacent lattice points has a
Gaussian shape, define d by a parameter vector and
∆ t1 and
∆ t2
 r
for radial distortion in the radial direction along the lattice
for the two transverse directions. The other parameters defining the assemblies are illustrated in the figure below.

Figure S1. Shows the stacked para-crystalline hexagonal cluster assemblies used in fitting the data for the PEGylated nanorod suspensions in 5CB.
The scattering from the suspension was modelled assuming that there was no inter-particle
I ( Q z
, Q y
)

(

P
 
S
)
2 n
R
F
R
2
( Q
// |
, Q

)

,

 n
A
F
R
2
( Q
//
, Q

) Z
A
( Q
| //
, Q

)

,

 n
S
F
S
2
( Q )
 where the y and z refer to a Cartesian frame with x along the X–ray beam, z horizontal and parallel to the applied field and y is vertical. The (

P
 
S
) factor represents the contrast in scattering length density between the particle and the solvent. In this equation, n
R
is the number of free nanorods per unit volume, n
A
is the number of aggregates per unit volume and n
S
is the number spherical particles per unit volume. The spherical impurities were modelled using the well-known formula for polydisperse spheres [1]. For the nanorods and aggregates, the angle brackets indicate a quantity that has been averaged over a distribution of orientations. The nanorods were modelled as uniform cylinders of length L
C
and radius R
C
| ( )
R
|
2 
V
P
2

 sin(
Q
Q
//
L
C
)
//
L
C


2 

2 J
1
( Q

R
C
Q

R
C
)


2 where Q is the component of Q along the nanorod axis and
//
Q
 is the perpendicular component. The polydispersity of nanorods size was incorporated by an integration over a Schultz distributions of length L
C
and radius R
C.
For the length, this was done analytically using the well known formula [2].
The structure factor, Z
A
, represents the inter-nanorod interference of an aggregate. It may be calculated from the paracrystal model for a hexagonal crystal lattice [3]. The hexagonal net factor can be calculated from the average of interference functions in each of three directions:
Y

( Q )


Y a 1
( Q ) Y a 2
( Q )

Y a 2
( Q ) Y a 3
( Q )

Y a 3
( Q ) Y a 1
( Q )

/ 3 where a 1, a 2 and a 3 refers refer to crystal axes perpendicular to the six-fold axis and at 120 degrees to each other as shown in figure S2. In a local Cartesian frame x

, y

, z
 with x
 along the a
1
crystal axis, z

along the six-fold axis and y
 perpendicular to both, the three in-plane unit cell vectors are a
1
 a
ˆ i a
2
 
1
2 a
ˆ i
 a
3
 
1
2 a
ˆ i

2
3 a
ˆ j
2
3 a
ˆ j

 rc z’
 t1c
 t2c a
3 a
2 c y’ a
1
 t2a
 t1a
 ra x’
Figure S2 showing the unit cell parameters and the distortion parameters for the hexagonal lattice.
Each interference function can be calculated from the lattice parameter and the distortion parameters that define the distribution of nearest neighbour vectors [4].
Y ai
( Q )

N ai

2
N n ai 

1

1
( N i
 n ) cos( n Q i
.
a i
) exp


( Q
2 ra
 2 ra

Q t
2
1 a
 2 t 1 a

Q t
2
2 a
 2 t 2 a
) / 2
 where N i
is the number of lattice sites along the a i
direction and a is the lattice parameter. The components of Q are: Q which is radial, along the a i
crystal axis; ra
Q t 1 a which is transverse to Q in ra the hexagonal plane and Q t 2 a which is transverse to Q and parallel to the six-fold axis. The lattice ra distortion parameters are
 ra
along a i
, and
 t 1 a and
 t 2 a
, transverse to a i
in the hexagonal plane and along the six-fold axis respectively. For simplicity, we have chosen
 t 2 a

0 and
 t 1 a
  ra
.
This means that the interference function only depends on the components of Q, perpendicular to the six-fold axis (i.e. Y

( Q )

Y

( Q

) ). It has been verified that these simplifications make a minor difference to the calculated result but it allows computational efficiencies because Z can be calculated as two independent one dimensional factors rather than as a large two dimensional array.
The function Y

( Q

) has a six-fold rotational symmetry. However, we assume there is no preferred orientation of the aggregate about the six-fold axis so we have taken a fibre average over 60 degrees.
Y  ( Q

)

6


/ 6


0
Y

( Q ,

) d


where
 is the angle between Q
 and the x
 axis. The figure S3 shows this function for a lattice parameter of 100A, and different values of the aggregate radius and the distortion parameters, Q ra and Q t 2 a
.
100
10
1
0,1
(a)
(b)
(c)
0,01
0 0,02 0,04 0,06 0,08
Q / Å -1
0,1
Figure S3 Showing Y
 factor for lattice parameter of 100A. For (a) aggregate radius of 1000A and distortion parameters of 10A, (b) aggregate radius of 1000A and distortion parameters of 20A and (c) aggregate radius of 500A and distortion parameters of 10A.
The overall structure factor is obtained by multiplication by a similar factor for the six-fold axis, Y//.
Y
//
( Q )

N c

2
N c n


1

1
( N c
 n ) cos( n Q .
c ) exp


( Q
2 t 1 c
 2 t 1 c

Q t
2
2 c
 2 t 2 c

Q
2 rc
 2 rc
) / 2
 where N c is the number of lattice sites along the c direction and c is the lattice parameter.
Here, the components of Q are: Q which is radial along the c crystal axis; rc
Q t 1 c which is transverse to Q in one direction and rc
Q t 2 c which is transverse to simplicity of computation, we have chosen and
Q in the other direction. Again, for rc
 t 1 c and
 t 2 c to be zero so that Y
//
( Q )

Y
//
( Q
//
) .
The overall structure factor is a product of the two factors.
Z ( Q )

Y  ( Q

) Y
//
( Q
//
)
The structure factor may be regarded as two parts. The first represents the coherent scattering from the whole aggregate and has a maximum of N
P
2 where N
P is the number of nanorods in one aggregate. It is the scattering expected from a hexagonal prism with N a
lattice points across and N c
lattice points along its six-fold axis. It is effectively the same as the scattering from a cylinder with dimensions, L
A and R
A
where N c
= L
A
/c and N a
~ 2R
A
/a :-
T Q
1
( )

N
P
2

 sin(
Q
Q
//
//
L
A
L
A
)


2 

2 J
1
( Q

R
A
)
Q

R
A


2

The second term contains all the interference peaks from the hexagonal structure. Their positions are determined by the centre-to-centre distances of the nanorods ( c and a ). They are broadened because of the lattice distortion parameters
 ra
(=
 ta and R
A
). The general trend is that large
) and
∆ rc
and because of the finite range of the lattice (ie L
A
 values rapidly broaden the peaks in Z until it becomes independent of Q , at a value of N
P
.
The orientational ordering of the free nanorods and the aggregates was described by a simple uniaxial distribution: where f (

)
 k

1 exp( m cos
2

)
 is the angle between the particle axis and the aligning field direction, k is a normalization constant and m is an orientation potential parameter.
The averaging over
α,β
then gives, where Q
||

Q cos

, Q

F
R
( Q
//
, Q

)

Q sin


,

and


0
 
0 f (

) F
R
( Q
||
, Q

) sin
 d
 d

is the angle between Q and a nanorod’s axis.
The order parameter of the particle orientational distribution can be calculated where,
P
2

0
 
0 f (

)

3
2 cos
2
 
1
2 sin
 d

By fitting the scattered intensity for samples aligned with an electric field with this model of a mixture of layered para-crystalline hexagonal assemblies and free nanorods, it has been possible to determine many of the characteristics of the nanorod suspensions in 5CB. These characteristics include the shape of the nanorod clusters, the centre-to-centre separation of nanorods within them as well as the fraction of free and assembled nanorods in the dispersions investigated by SAXS. Table S1 gives these parameters as determined for the two mPEG-SH lengths investigated. These distributions reflect how well defined the lattice position is and as such, how quickly Z(Q) tends towards 1 as Q increases. The lattice parameter defining the separation of the hexagonal lattices along z’ is defined as c and has been kept fixed at the length of the nanorods with a 5nm gap.
Figure S4. Scattering intensity with Q y
and Q z
plots for GNR(1900) and GNR(5400) in a 0.18 Vµm -1
(2 kHz) field and their corresponding simulated intensity fits below.
Sample
GNR(1900)
GNR(5400)
L
A
[nm]
210 ± 60
210 ± 60
R
A
[nm]
80 ± 30
60 ± 20 a [nm]
19.9 ± 0.5
19.2 ± 0.5
Δ ra
[nm]
5.0 ± 0.1
3.5 ± 0.1
% Free Nanorods
67 ± 7
53 ± 5

Table S1. Aggregate radii ( R
A
), thicknesses ( L
A
), hexagonal lattice parameter ( a ) which is the nanorod centre to centre separation, lattice distortion (
Δ ra
) and the percentage of non-aggregated nanorods obtained through data fitting.
References
1.
Kotlarchyk M and Chen S.-H., J. Chem. Phys. 79 , 2461-2469 (1983)
2.
Sheu, EY , Phys. Rev. A, 45, 2428-2438 (1992)
3.
Hosemann R and Bagghi SN, Direct Analysis of Diffraction by Matter, Netherlands: North
Holland Publ. Co.; 1962
4.
Guinier A. Crystal imperfections destroying long range order. X-ray Diffraction in Crystals,
Imperfect Crystals, and Amorphous Bodies. San Francisco: W.H. Freeman and Co.; 1963.