# Project Summary

Research objective

# Introduction

Nanoscale materials have the potential to solve many of today’s biggest problems such as peak oil, the global water crisis, and the burden of cancer. Faraday’s discovery of colloidal ruby gold producing different colored solutions in 1857 (Faraday 1857, Thompson 2007) has inspired generations of nanoscale science. Controlled synthesis of nanocrystals, namely quantum dots, was invented by Bawendi et al. in 1993 (Hakimi 1993, Murray 2000). They paved the way for the utilization of well-defined nanocrystals in various fields ranging from heterogeneous catalysis (Astruc 2008, Astruc 2006) to photovoltaics (Atwater 2010), DNA sequencing (McNally 2010), batteries (Panniello 2014), hydrogen storage (Jena 2011, Ramos-Castillo 2015), and cancer therapeutics (Jain 2010, Kim 2010).

Nanocrystals can be grown to specific sizes and shapes, but the question of what is the growth controlling mechanism remains elusive. This is important because numerous properties of metal nanocrystals are found to depend on their size (Roduner 2006) and shape (Xia 2008). In catalysis for instance, tetrahedral Pt nanocrystals are more active than spherical and cubic Pt nanocrystals as the catalyst for electron-transfer reactions (Narayanan 2005). The controlling mechanism for various systems have been studied using both experimental and computational techniques. Experimentalists have employed techniques such as in situ transmission electron microscopy (Liao 2014, Woehl 2014), X-ray photoelectron spectroscopy (Gao 2004, Park 2014, Huang 1996, Kedia 2012, Bonet 2000), and variation of reaction parameters (Personick 2013, Xia 2012, Zeng 2010, Zhang 1996, Chang 2011, Zhu 2011) to elucidate the controlling mechanism. Theorists address this important question using techniques such as density functional theory (Kilin 2008, Al-Saidi 2012, Saidi 2013, Zhang 2008) and molecular dynamics (Zhou 2014).

However, previous work in the literature have not yet adequately addressed the mechanism of shape control in the solution phase. Despite much excellent experimental and theoretical work, there is no quantitative evidence in the facet selective adsorption of structure-directing agents and their role in shape control. Without such evidence, we are left with an incomplete description of the shape control mechanism that creates the condition for ill-informed reaction engineering for scale-up. To date, only a few syntheses have been scaled up to the gram-scale, and yet they still have poor quality control (Jana 2005, Lohse 2013). This study will remedy this gap in the literature by elucidating the role of structure-directing agents using molecular dynamics simulation, in which explicit solvent is computationally feasible and observations in the atomic resolution can be made. Using enhanced sampling methods, I will provide quantitative evidence that will support or refute the facet selective adsorption hypothesis and further examine its implications.

The scope of my investigation is limited to the synthesis of colloidal metal nanocrystals, particularly silver (Ag). The polyol synthesis is a popular solution-phase synthesis of Ag nanocrystals (Skrabalak 2007). The typical reaction temperature is 150$$^{\circ}$$C. In the polyol synthesis, ethylene glycol acts as both the solvent and the reducing agent. The source of Ag is from silver nitrate ($$AgNO_3$$) that is dissolved in ethylene glycol. Ag seeds may be added in order to disentangle growth from nucleation, enhancing control of nanocrystal size and shape. Structure-directing agents, typically polyvinylpyrrolidone (PVP), are added to prevent aggregation of nanocrystals and to promote the formation of {100}-faceted nanocrystals. The reaction conditions such as temperature, the concentration of $$AgNO_3$$, and the molar ratio of PVP to $$AgNO_3$$ is critical to the formation of different nanocrystal shapes. These shapes can range from cubes (Xia 2012, Zhang 2010), triangular plates (Lofton 2005, Liu 2012), and five-fold twinned pentagonal wires (Zhu 2011, Zhang 2008, Sun 2002). It was hypothesized that PVP promotes the formation of {100} facets by preferentially binding to {100} facets over {111} facets (Xia 2012, Sun 2002), also known as facet specific adsorption.

Binding of PVP to Ag surfaces can be characterized by the potential of mean force (PMF) profiles, which can be calculated by umbrella sampling (Torrie 1977, Kästner 2011). The PMF represents the free energy of a system as the function of one collective variable. Adsorption processes can be described by the free energy of the adsorbate as the function of the orthogonal distance from the surface where adsorption occurs. Binding energies can be obtained from the difference between the PMF of the adsorbate at the adsorbing state and at the solvent phase. In addition, kinetics of the adsorption process can be obtained from the energy barrier for adsorption in the PMF profile. The limitations of this method are the collective variable must be accurately chosen to represent the physical nature of the system and the multidimensional energy landscape is reduced to one dimension thus it may not give the complete description of the system.