Nanoparticles have attracted considerable interest because of their unique optical, electromagnetic, and catalytic properties that differ from bulk ones. The origin of these properties is due to their high surface to volume ratio and the coherent oscillation of the conduction electrons that can be induced by interactive electromagnetic fields. Properties of nanoparticles are highly size and shape-dependent; therefore, controlled synthesis of nanoparticles in terms of size and shape is a technological scaffold for their potential and fundamental studies.
Particle size distribution, morphology, and surface charge modification play a vital role in determining the optical properties of nanoparticle and there is a growing interest in the controlled synthesis of silver nanoparticles among the all noble metals. Silver has an array of properties that could be tuned through the nanoscale control of morphology. Among all the properties, localized surface plasmon resonance (LSPR) is the most important due to its application in biolabelling , surface enhanced Raman scattering (SERS) , surface enhanced fluorescence (SEF) , sensing , and fabrication of nanophotonic devices and circuits .
When the dimension of metal nanoparticles is small enough compared to the wavelength of the incident light, surface plasmon can be excited due to a collective motion of free electrons in the metal nanoparticles that resonantly couples with the oscillating electric field of the light. As a result of surface plasmon excitation, strong enhancement of the absorption, scattering, and local electric field around the metal particles arise and these feature strongly depends on particle size, shape, type of materials, and the local environment. As any change in the shape of the metal nanoparticles affect the pattern in which the free electrons are oscillating, the resonant frequency will change . Though changing the size of spherical particles can induce smaller shift in the SPR peak position, in theory and in practice, changing the shape of silver nanoparticles provide more versatility. Anisotropic silver nanoparticles can absorb and scatter light along multiple axes. It is well known that the optical absorption spectra of silver nanorods and nanodiscs are different from nanospheres. As spherical particles have strong SPR band at ~400 nm, while Ag nanorods usually show a red-shifted long-axis resonance (longitudinal plasmon band) and a slightly blue-shifted short-axis resonance (transverse plasmon band); and on the other hand, Ag nanodiscs have several resonance modes in the absorption spectra: (1) dipolar in-plane resonance, (2) dipolar out-of-plane resonance located; (3) quadrupolar out-of-plane resonance.
Much effort has been devoted to synthesize silver nanoparticles having various size and shapes. This includes zero-dimensional (0-D) spherical or tetrahedral quantum dots [7–9], one-dimensional (1-D) silver nanorods and wires [10, 11] and two-dimensional (2-D) nanoplates , nanoprisms  and nanodiscs [14, 15]. Synthesis of nanostructures via simple wet-chemical method is one of the most favoured routes towards the cost-effective large-scale production of nanobuilding blocks. Chemical synthesis of metal nanoparticles involves the reduction of metal salts followed by nucleation and growth in presence of stabilizing agents such as polymers [16, 17], thiols , CTAB , Na-AOT , SDS , unsaturated dicarboxylates , and plant extracts [23, 24]. More recently, the use of seeds to make more monodisperse metal nanoparticles along with various morphologies has been reported by various authors. Murphy and co-workers first reported the growth of citrate-stabilized gold nanoparticles by the seed-mediated method using a wide range of reducing agents and conditions [11, 25]. Using the same approach, they were able to prepare gold nanorods with tunable aspect ratios .
Synthesis of anisotropic metal nanoparticles motivates the development and innovation of theoretical methods for describing the unique properties of these nanoparticles. The study of colours of metal nanoparticles can be traced back to 19th century when Michael Faraday studied the colour of gold colloid in stained glass windows . Mie presented an analytical solution to Maxwell’s equations that describe an isolated spherical particle in 1908 . Although many extensions of Mie theory have been made for covering different aspects including magnetic and coated spheres [29, 30], this analytical method has a fundamental limitation that the exact solutions are restricted only to highly symmetric particles such as spheres and spheroids. Recently, a number of theoretical approaches have been developed, based on more advanced scattering theories for anisotropic metal nanoparticles. These include the generalized multipole technique (GMT) , the T-matrix method , the discrete dipole approximation (DDA) , and the finite different time domain (FDTD) method . The first two methods can be classified as surface-based methods where only the particle’s surface is discretized and solved numerically. The latter methods are referred to as volume-based methods where the entire volume is discretized. Among these methods, DDA has been demonstrated to be one of the most powerful and flexible electrodynamics methods for computing the optical spectra of particles with an arbitrary geometry. DDA involves replacing each particle by an assembly of finite cubical elements, each of which is small enough that only dipole interactions with an applied electromagnetic field and with induced fields in other elements need to be considered. This reduces the solution of Maxwell’s equation to an algebraic problem involving many coupled dipoles. The DDA method has been widely used to describe the shape dependence of plasmon resonance spectra, including studies of triangular prism , discs, cubes , truncated tetrahedral , shell-shaped particles , small clusters of particles , and many others . Recently, Schatz group  has carried out extensive studies showing that DDA is suited for optical calculations of the extinction spectrum and the local electric field distribution in metal particles with different geometries and environments. Again, Lee and El-Sayed  have investigated the systematic dependence of nanorod absorption and scattering on their aspect ratio, size, and medium refractive index using DDA simulation method.
This article focuses on the synthesis of silver nanostructures of different morphologies via seeding growth approach, using methyl cellulose (MC) polymer as soft-template in the growth solution. It is shown that the concentration variation of tri-sodium citrate in the growth solution plays important role in controlling the morphology of the nanoparticles. We also represent the theoretical calculations of the extinction efficiency for nanospheres, nanodiscs, and nanorods using discrete dipole approximation (DDA) methodology.