investigating self assembly of gold nanocrystal superlattices · namrata ramesh bachelors with...

Investigating Self Assembly of Gold Nanocrystal Superlattices

by

Namrata Ramesh

A dissertation submitted in partial satisfaction of the

requirements for the degree of

Bachelors with Honors

in

Physics

in the

Undergraduate Division

of the

University of California, Berkeley

Committee in charge:

Professor Naomi Ginsberg, Chair

Spring 2020

The dissertation of Namrata Ramesh, titled Investigating Self Assembly of Gold NanocrystalSuperlattices, is approved:

Chair Date

Date

Date


22 May, 2020


Copyright 2020by

Namrata Ramesh

1

Abstract


by

Namrata Ramesh

Bachelors with Honors in Physics


Professor Naomi Ginsberg, Chair

Superlattices of colloidal nanocrystals are a new class of materials that have been madeto self-assemble from a liquid suspension. Their high compositional tunability results in arange of electronic, optical, and mechanical properties [1]. Strong coupling of nanocrystalsin the superlattice - a very recent advance - leads to dramatic changes in their conductivityand, consequently, their increased applicability in electronic devices [2]. This, along withthe comparatively basic equipment needed for synthesis, makes these superlattices optimalcandidates for materials used in cost-effective solar cells or next-generation displays[3].

While our collaborators have been able to self assemble strongly coupled superlattices fromgold nanocrystals with inorganic thiostannate ligands suspended in polar solvents [4, 5],the mechanism for self assembly in this atypical system is still not as well understood asthat of more traditional, weakly coupled superlattices with organic ligands. Thus, alongwith my colleagues in the Ginsberg Group and collaborators, I was a part of an experimentconducted at the National Synchotron Light Source II (NSLS-II) in August 2019 whichused time resolved small angle x-ray scattering (SAXS) and x-ray photon correlation spec-troscopy (XPCS) to more quantitatively understand the macroscopic timescales (kinetics)and microscopic timescales (dynamics) associated with the self assembly of gold nanocrystalsuperlattices with thiostannate ligands.

In Chapter 1, I motivate the project and the aim of this thesis to show how the in-situ X-rayphoton correlation spectroscopy (XPCS) measurements from NSLS-II hint at some of thedynamics of forming superlattices during the self assembly process. In Chapter 2, I givemore background on nanocrystal superlattices and show how the self assembly mechanismof our system - gold nanocrystal superlattices with thiostannate ligands - is still not fullyunderstood, and how a more quantitative understanding could aid efforts to create stronglycoupled superlattices with semiconductor nanocrystals. In Chapter 3, I explain the theoryunderlying our primary characterization techniques – small angle X-ray scattering (SAXS)and XPCS – and how we converged on suitable x-ray beam parameters for our experiment,

2

keeping in mind a need for high signal-to-noise for XPCS and avoiding beam damage. InChapter 4, I elucidate the protocols used for self assembly, the results of preliminary char-acterizations of the system and assembly process undertaken before our beam time, andthe different self assembly protocols used. In Chapter 5, I report my analysis of the XPCSdata taken, and ultimately show that the process detected by XPCS is faster than diffusionand potentially due to the collective motions of nanocrystals in aggregates or superlatticesor the collective motions of aggregates and superlattices. The ~q-dependence of the KWWexponents in some runs and the time-dependence of KWW in another run – the exponentobtained from the fits to the intensity autocorrelation function g(2) – point to qualitativeevidence for jamming-related processes. These could arise from the motion of nanocrystalsin disordered aggregates or from superlattices and aggregates sinking and collecting into apile at the bottom of the capillary. Chapter 6 summarizes the findings of this thesis, andmotivates the exciting avenues that this analysis has.

As this experiment is the first attempt of doing XPCS and potentially also the time-resolvedSAXS on the self assembly of strongly coupled superlattices, this thesis shows for the firsttime how XPCS can be used to gain nanoscale spatial resolution and timescales on the orderof seconds to learn meaningful information about the dynamics of these novel systems. Thisthesis also shows that there is the potential to link the information about dynamics thatXPCS gives to the that about kinetics that time-resolved SAXS gives. Linking both piecesof information should provide a more informed, quantitative picture of self assembly Ausuperlattices.

i

To my parents,

who empower me to reach for the stars.

ii

Contents

Contents ii

List of Figures iv

List of Tables vii

1 Introduction 1

2 Introduction to Nanocrystal Superlattices 22.1 Definition of Nanocrystals and Superlattices . . . . . . . . . . . . . . . . . . 22.2 Strongly Coupled Superlattices . . . . . . . . . . . . . . . . . . . . . . . . . 22.3 Motivation for project and thesis . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Overview of Characterization Techniques 63.1 Small Angle X-Ray Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 63.2 X-Ray Photon Correlation Spectroscopy . . . . . . . . . . . . . . . . . . . . 103.3 Optimizing for SAXS or XPCS with acquisition parameters . . . . . . . . . . 17

4 Methods 224.1 Self Assembly protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2 Preliminary characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3 Types of Self Assembly Protocols . . . . . . . . . . . . . . . . . . . . . . . . 31

5 Results and discussion 365.1 Overview of beam time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.2 Overview of Data Examined in Thesis . . . . . . . . . . . . . . . . . . . . . 375.3 Correlations found between g(2)(~q, τ) decays and SAXS patterns . . . . . . . 455.4 Dispersion relation of ~q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.5 Implications of observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6 Conclusions 636.1 Summary of findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

iii

Bibliography 67

iv

List of Figures

2.1 Properties of Au superlattices with thiostannate ligands. Panel (a) is adaptedfrom Ref [4]. Reprinted with permission from The American Association for theAdvancement of Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Proposed self assembly mechanism. Adapted from ref [5] . . . . . . . . . . . . . 4

3.1 Cartoon explaining basics of x-ray scattering . . . . . . . . . . . . . . . . . . . . 73.2 Various contributions to 1D SAXS patterns . . . . . . . . . . . . . . . . . . . . 83.3 Ex-situ vs in-situ SAXS of self assembly of Au superlattices . . . . . . . . . . . 93.4 Adapted from ref [17]. Reprinted with permission from American Institute of

Physics.; Institute of Physics (Great Britain). . . . . . . . . . . . . . . . . . . . 113.5 Dispersion relation information. Adapted from ref [15]. Reprinted with permis-

sion from Annual Reviews, Inc. . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.6 How data is acquired for XPCS and SAXS . . . . . . . . . . . . . . . . . . . . . 173.7 Damage test with 5000 frames, 0.01 s exposure time per frame. The top row is

exposed to 20% of full beam and the bottom row is exposed to full beam . . . . 203.8 Damage test with 5000 frames, 0.002 s exposure time per frame. The top row is

exposed to 20% of full beam and the bottom row is exposed to full beam . . . . 21

4.1 Cartoon of ligand exchange process . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Overview of self assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3 Determining preflocculation concentration . . . . . . . . . . . . . . . . . . . . . 254.4 In-situ UV-Vis overview. Plots courtesy of James Utterback . . . . . . . . . . . 284.5 In-situ UV-Vis vs in-situ DLS. Plots courtesy of James Utterback and Christian

Tanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.6 Preliminary studies to determine optimal concentration of Au nanocrystals needed

for beamtime experiments. Figure (a) shows the relationship between attenuationlength of x-ray beams and the concentration of gold. Figures (b)-(d) are plotsof in-situ UV-Vis and DLS that show the concentration dependence of kinetics,with Figure (e) showing this more concretely. Plots courtesy of James Utterbackand Christian Tanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.7 Using ex-situ SAXS to determine when superlattices form . . . . . . . . . . . . 314.8 How the setups look . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.9 Steps to set up the in-situ rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

v

5.1 Presence of g(2)(~q, τ) in early and late times . . . . . . . . . . . . . . . . . . . . 385.2 How 1D SAXS and g(2)(~q, τ) decays changed with time in ic4slowinsitu100mg . . 395.3 How 1D SAXS and g(2)(~q, τ) decays changed with time in ic4slowinsitu100mgtake2 405.4 How 1D SAXS and g(2)(~q, τ) decays changed with time in jp4aggregate100mg . . 415.5 How 1D SAXS and g(2)(~q, τ) decays changed with time in jp4aggregate100mg lowligand 425.6 How 1D SAXS and g2 decays changed with time in ic5aggregate100mg prep2 . . 435.7 How 1D SAXS and g(2)(~q, τ) decays changed with time in In situ # 4 . . . . . . 445.8 Description of qualitative parameters used to find patterns in the data . . . . . 475.9 Overview of patterns found in data. Note: the term ‘trike run’ is another term

for partially in-situ self assembly . . . . . . . . . . . . . . . . . . . . . . . . . . 485.10 Patterns when there was g2. Note: the term ‘trike run’ is another term for

partially in-situ self assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.11 Patterns when there was no g(2)(~q, τ). Note: the term ‘trike run’ is another term

for partially in-situ self assembly . . . . . . . . . . . . . . . . . . . . . . . . . . 505.12 Dispersion relation analysis for ic5aggregate100mg prep2. . . . . . . . . . . . . . 525.13 1D SAXS pattern at 11 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545.14 Dispersion relation plot of KWW exponent at 11 min . . . . . . . . . . . . . . . 545.15 Dispersion relation plot of relaxation rate at 11 min. Fit parameters are A =

100± 100A2s−1.exponent = 1.361± 0.001.D = 2800± 200A2s−1 . . . . . . . . . 545.16 1D SAXS pattern at 60 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545.17 Dispersion relation plot of KWW exponent at 60 min . . . . . . . . . . . . . . . 545.18 Dispersion relation plot of relaxation rate at 11 min. Fit parameters are A =

400± 100A2s−1.exponent = 1.094± 0.001.D = 35000± 3000A2s−1 . . . . . . . . 545.19 1D SAXS pattern at 94 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545.20 Dispersion relation plot of KWW exponent at 94 min . . . . . . . . . . . . . . . 545.21 Dispersion relation plot of relaxation rate at 94 min. Fit parameters are A =

500± 200A2s−1.exponent = 1.104± 0.006.D = 37000± 3000A2s−1 . . . . . . . . 545.22 Dispersion relation analysis for ic4slowinsitu100mg . . . . . . . . . . . . . . . . 545.23 1D SAXS pattern at 6 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.24 Dispersion relation plot of KWW exponent at 6 min . . . . . . . . . . . . . . . 555.25 Dispersion relation plot of relaxation rate at 6 min. Fit parameters are A =

8± 4A2s−1.exponent = 0.6± 0.2.D = 8000± 1000A2s−1 . . . . . . . . . . . . . 555.26 1D SAXS pattern at 9 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.27 Dispersion relation plot of KWW exponent at 9 min . . . . . . . . . . . . . . . 555.28 Dispersion relation plot of relaxation rate at 9 min. Fit parameters are A =

8± 7A2s−1.exponent = 0.69± 0.05.D = 4000± 500A2s−1 . . . . . . . . . . . . . 555.29 1D SAXS pattern at 15 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.30 Dispersion relation plot of KWW exponent at 15 min . . . . . . . . . . . . . . . 555.31 Dispersion relation plot of relaxation rate at 15 min. Fit parameters are A =

1.3± 0.4A2s−1.exponent = 0.323± 0.001.D = 5600± 700A2s−1 . . . . . . . . . 555.32 Dispersion relation analysis for jp4aggregate100mg . . . . . . . . . . . . . . . . 555.33 1D SAXS pattern at 4 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

vi

5.34 Dispersion relation plot of KWW exponent at 4 min . . . . . . . . . . . . . . . 575.35 Dispersion relation plot of relaxation rate at 4 min. Fit parameters are A =

27± 5A2s−1.exponent = 0.864± 0.003.D = 7000± 700A2s−1 . . . . . . . . . . . 575.36 1D SAXS pattern at 32 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.37 Dispersion relation plot of KWW exponent at 32 min . . . . . . . . . . . . . . . 575.38 Dispersion relation plot of relaxation rate at 32 min. Fit parameters are A =

4± 2A2s−1.exponent = 0.5± 0.1.D = 4000± 500A2s−1 . . . . . . . . . . . . . . 575.39 1D SAXS pattern at 73 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.40 Dispersion relation plot of KWW exponent at 73 min . . . . . . . . . . . . . . . 575.41 Dispersion relation plot of relaxation rate at 73 min. Fit parameters are A =

500± 700A2s−1.exponent = 1.7± 0.1.D = 1400± 100A2s−1 . . . . . . . . . . . 575.42 Dispersion relation analysis for jp4aggregate100mg low . . . . . . . . . . . . . . 575.43 Overview of patterns found in dispersion relations . . . . . . . . . . . . . . . . . 595.44 Calculating g(2) at different attenuations of the beam in ic4slowinsitu100mg to

test for beam damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

vii

List of Tables

5.1 Overview of Chemical Composition of Various Samples . . . . . . . . . . . . . . 37

viii

Acknowledgments

I would like to first thank Professor Naomi Ginsberg for believing in me, for being suchan inspiration to me, and for creating a respectful and nourishing environment where theconcept of a stupid question simply does not exist, where everyone is treated equally andeveryone’s ideas matter.

Thank you to all the wonderful people I have had the privilege to meet in my two and ahalf years in the Ginsberg Group. Thank you to Alex Liebman-Pelaez, Audrey Short, Bren-dan Folie, Christian Tanner, Eniko Zsoldos, Hannah Stern, Hannah Weaver, Jack Tulyang,James Utterback, Jenna Tan, Jonathan Raybin, Jonathon Kruppe, Leo Hamerlynck, Mi-lan Delor, Rebecca Wai, Rongfeng Yuan and Trevor Roberts. A special thanks to RebeccaWai for being an incredible mentor and a great friend, to Hannah W. and Jenna for theirfriendship and the laughter that inevitably breaks out when we and Rebecca are around oneanother, to Milan Delor for his kindness and advice, and to James and Christian for theirexpertise and camaraderie with the XPCS side of the superlattice self assembly project.

I have also been fortunate to have had the opportunity to work with some of our incrediblecollaborators within and beyond Berkeley. Thank you to Andrei Fluerasu, Avishek Das,Chris Tassone, David Limmer, Dmitri Talapin, Igor Coropceanu, Josh Portner and SamTeitelbaum. A special thanks to Andrei and Sam for being so patient and insightful, and toJosh and Igor for being lovely people and for making beamtime more enjoyable.

Thank you to all the amazing people I have met through my classes, my work as theundergraduate representative to the Faculty Committee on Equity and Inclusion and throughcreating “The STEMinist Chronicles”: Amanda Dillon, Barbara Jacak, Catherine Bordel,Cecilia Lucas, Claudia Trujillo, Joelle Miles, Kathleen Cooney, Kathy Lee, Robert Birgeneau,and T. Roberts. Thank you also to Jessie Woodcock in the chemistry department for mywonderful experience as a SURS and for supporting me through my time in the GinsbergGroup.

Thank you to the family I found in Berkeley: Aditya, Mira, Sophie, Lara, Josh, Kimballand Tim, you have all made Berkeley feel like home for me, and I treasure spending the restof my life with you all in it.

Thank you to my family in the Bay Area for welcoming me and making a country halfway across the world from my own feel more like home. Thank you to my grandparentsfor instilling in me the value of hard work. Thank you to my uncle, Partha, for helping merealize that life is more interesting when you are guided by your imagination. Thank youto my parents for believing in me when I could not, for empowering me to be whatever Ichoose to put my mind to, for loving me. Amma and Appa, I love you.

1

Chapter 1

Introduction

Superlattices of colloidal nanocrystals are a new class of materials that have been madeto self-assemble from a liquid suspension. Their high compositional tunability results in arange of electronic, optical, and mechanical properties [1]. Strong coupling of nanocrystalsin the superlattice - a very recent advance - leads to dramatic changes in their conductivityand, consequently, their increased applicability in electronic devices [2, 3]. This, along withthe comparatively basic equipment needed for synthesis, makes these superlattices optimalcandidates for materials used in cost-effective solar cells or next-generation displays[3].

Recently, our collaborators in the University of Chicago have been able to create stronglycoupled superlattices by triggering self assembly in gold nanocrystals colloidally suspendedin polar solvent with inorganic thiostannate ligands. [4, 5]. While a mechanism for thisself assembly process has been proposed [5], the self assembly process is still not as wellunderstood and characterized as that of traditional, more weakly coupled superlattices withorganic ligands. Understanding the mechanism more quantitatively by characterizing bothmacroscopic and microscopic timescales can help refine the current hypothesis. A deeperunderstanding of this process can potentially clarify why these strongly coupled superlatticesonly form with metal nanoparticles and not with semiconductor ones, informing efforts toexpand the parameter space for self assembly of strongly coupled superlattices.

Our project uses small angle X-ray scattering (SAXS) and x-ray photon correlationspectroscopy (XPCS) to obtain a more quantitative insight into the kinetics (macroscopictimescales) and dynamics (microscopic timescales) of the self assembly of gold nanocrys-tal superlattices with thiostannate ligands. This thesis primarily examines data from ourexperiment conducted between August 9th - 14th 2019 at the Brookhaven National Lab’sNational Synchotron Light Source II (NSLS-II). The aim of this thesis is to explain theXPCS autocorrelation decays and to infer which processes these decays imply.

2

Chapter 2

Introduction to NanocrystalSuperlattices

2.1 Definition of Nanocrystals and Superlattices

Colloidal nanocrystals are fragments of semiconductor, metal or dielectric crystals protectedby a layer of surface-bound molecules (ligands). Ligands are present in order to suspend thenanocrystals in solution [3].

Nanocrystals can be made to self-assemble into a superlattice. Nanocrystal superlat-tices are like artificial solids, with the nanocrystals as atoms and a balance of the van derWaals attraction and repulsive Coulomb forces between them acting as weak intermolecularbonds[6].

As outlined in [3], superlattices have been self assembled from a range of nanocrystalswith different geometries, composition and ligands, and have been self assembled using avariety of environmental manipulations of the solvent. This range in superlattice structureand composition, along with relative ease of synthesis, represents an exciting new way tosynthesize materials and to tailor their properties for specific device applications [3].

2.2 Strongly Coupled Superlattices

Typically, nanocrystals in superlattices are not configured particularly close together, andtheir photoinduced electrons and holes are restricted to the nanocrystal itself (quantumconfinement). This confinement should reduce when the nanocrystals are brought sufficientlyclose together, making it easier for electronic states to couple between particles and forcharge carriers to move from one nanocrystal to the next. Charge carriers isolated on agiven nanocrystal, on application of an electrical voltage across the ensemble of nanocrystals,will typically ‘hop’ from one nanocrystal to the other. However, if the electronic couplingbetween nanocrystals is sufficiently large, the electronic wavefunctions could delocalize over

CHAPTER 2. INTRODUCTION TO NANOCRYSTAL SUPERLATTICES 3

more than one nanocrystal, which increases the electrical conductivity of the superlattice[7].

In order to make superlattices that are more compatible with device applications, it isimportant to increase their electrical conductivity. Most superlattices that have been synthe-sized are sterically stabilized with long-chain organic ligands [3]. These ligands, however, actas an electrically-insulating barrier between nanocrystals, preventing coupling between theparticles. Thus, it is important to be able to synthesize superlattices with strongly-couplednanocrystals in order to allow for more charge carrier delocalization, which increases con-ductivity.

Gold nanocrystals with thiostannate ligands

Recent synthetic developments from our collaborators at the University of Chicago, theTalapin Group, have replaced organic ligand/nonpolar solvent combinations with shorter,inorganic ionic ligands paired with polar and ionic solvents able to colloidally suspend avariety of nanoparticles (NPs) [8]. From these, metal NPs capped with chalcogenometallates(ChMs, e.g. Sn2S

4−6 ) have been coerced to form ordered superlattices (SLs) in a polar sol-

vent, achieved by destabilization using excess anionic ligands. The interparticle interactionsand self assembly driving forces in these new systems rely much more on strong Coulombinteractions than traditional NP self assembly. The ultimate formation of ordered structuresinstead of disordered agglomerates is currently limited to metallic, as opposed to semicon-ducting, NPs. These metal NP SLs exhibit strong electronic coupling, leading to strikingmetallic transport.

Properties of our system

The system studied in this thesis are gold nanocrystal superlattices with thiostannate (Sn2S4−6 )

ligands. As Figure 2.1 shows, these are highly ordered structures that are a few micrometersin size. They have an face centered cubic (FCC) crystal structure with lattice constantsusually around 7 nm.


(a) Transmission electron microscope (TEM)image of Au SLs with thiostannate ligands.

(b) 1D SAXS pattern, with red lines indicat-ing the peaks of an FCC lattice with 7 nmlattice constant

Figure 2.1: Properties of Au superlattices with thiostannate ligands. Panel (a) is adaptedfrom Ref [4]. Reprinted with permission from The American Association for the Advance-ment of Science

Hypothesis for nucleation pathway

Figure 2.2: Proposed self assembly mechanism. Adapted from ref [5]

The current hypothesis for how self assembly of thiostannate-capped Au nanocrystals sus-pended in hydrazine form into highly ordered superlattices is given in Figure 2.2. In thispathway, addition of the ligand solution past a critical concentration leads to agglomeration,where a loosely ordered state emerges that allows the nanocrystals to sample a variety oflocations before settling into a configuration that has a global energetic minimum, leadingto crystallization [5]. The self assembly is limited to metal nanoparticles, and appears to be


due to stronger Coulomb repulsion of ligand shells on metal NPs dominating van der Waalsattraction at short-range.

2.3 Motivation for project and thesis

Our current understanding of NP–solvent interactions and the effective inter-NP interactionsthat result from them in cases of strong Coulomb potentials is far less advanced than moretraditional NP SL self-assembly. It is therefore essential to reveal the relationship betweenthe underlying microscopic interactions and SL formation in order to develop a frameworkin which these new systems can be manipulated and employed to drive new geometries andfunctional assemblies. For example, at the smallest scales, an understanding of NP solvationin these complex solvents and how manipulation of solvent parameters, such as polar andionic composition, affects NP–NP interactions is critical. Identifying the key differencesbetween dielectric and metal NP solvation will also be essential to harness the power ofsemiconducting nanocrystals within strongly-coupled superstructures. While some work hasbeen done to explain pairwise interactions between NPs in ionic suspensions [9, 10, 11]understanding nonadditive effects in 2D and 3D assemblies and complex geometries is stilldifficult. Knowledge of microscopic interactions between NPs and solvent and of how theyinfluence collective ordering at larger scales is essential to drive the fundamental sciencebehind the next-generation of superassemblies that will present strong electronic coupling.

In this thesis, I will show how the in-situ X-ray photon correlation spectroscopy (XPCS)measurements in which I participated at the Brookhaven National Laboratory’s NationalSynchotron Light Source II (NSLS-II) in August 2019 hint at some of the dynamics offorming superlattices during the self assembly process. In Chapter 3, I will explain the theoryunderlying our primary characterization techniques – small angle X-ray scattering (SAXS)and XPCS – and how we converged on suitable x-ray beam parameters for our experiments.In Chapter 4, I will elucidate the protocols used for self assembly, the results of preliminarycharacterizations of the system and assembly process undertaken before our beam time, andthe different self assembly set ups used. In Chapter 5, I will report my analysis of the XPCSdata taken, and discuss the implications of these results, and in Chapter 6 I will summarizethe findings in this thesis and discuss futures avenues for the analysis.

6

Chapter 3

Overview of CharacterizationTechniques

3.1 Small Angle X-Ray Scattering

Introduction to X-Ray Scattering

When waves are incident on atoms, they get scattered off into different directions. Whenthe wavelength of these waves is incident on atoms in a lattice structure and is equal to orsmaller than the lattice constant, they undergo diffraction. The Bragg law describes howwaves get diffracted due to the periodicity of a lattice. The Bragg law is:

2d sin(θ) = nλ

where d is the distance between lattice planes, λ is the wavelength of the incident radiation,n is called the order of diffraction and is a positive integer, and θ is the angle between thelattice plane and the direction of the incident rays. This law is satisfied only when λ ≤ 2d.

The implication of the Bragg law is that for some values of θ there is constructive in-terference, whereas for others there is destructive interference. This results in the scatteredradiation looking like a series of bright and dark rings on a detector surface, centered aroundthe transmitted incident beam. The presence of such constructive and destructive interfer-ence rings occurs irrespective of the type of lattice that the radiation is incident on, butthe intensity of various orders of diffraction vary due to the particular type of lattice or theelemental composition.

The Bragg Law can be used to describe x-ray diffraction from superlattices, as the wave-length of x-rays are between 0.1 to 10 nm. As the lattice constant of our superlattices are≈ 7 nm, x-rays can be used to probe their crystal structure.

Derivation and explanation of form and structure factors

This derivation is adapted from [12].

CHAPTER 3. OVERVIEW OF CHARACTERIZATION TECHNIQUES 7

(a) X-ray scattering off of and object (b) Definition of ~q vector

Figure 3.1: Cartoon explaining basics of x-ray scattering

I will start by describing x-ray scattering from one atom (or colloidal particle). As shown

in Figure 3.1, ~k0 is the wavevector of the incident x-ray, ~k is the wavevector of the scatteredx-ray, and ~k − ~k0 = ~q.

The total amplitude, fe of the scattered electric field of the x-ray at a point P due to oneelectron at point ~rn (visualized in Figure 3.1 (a)) is:

fe =∑n

e~q· ~rn

Quantum mechanically, this expression can be written as an integral:

fe =∫e~q· ~rnρdV

where ρ is the density of electrons. Assuming this density is spherically symmetric andsumming the amplitude from each electron gives:

f =∑j

fej =∑j

∫ ∞r=0

4πr2ρj(r)sinqr

qrdr

Here, f is called the atomic scattering factor. For a solid sphere of radius R (ρ(r) = 1):

f = N4π

3R33(sin(qR)− qR cos(qR))

(qR)3

When the particles are widely separated, there is no interference. The total intensity Iof the scattered light off of widely separated atoms/particles is:

I = I0∑n

f ∗nfn = I0N |f |2 = I0P (~q)

In the unit cell of a crystal, the total amplitude of the scattered electric field at point P dueto each particle at position rn (where rn corresponds to the location of the nth lattice pointin a unit cell) is:


F =∑n

fnei~q·~r.

F is called the structure factor, and it is the sum of atomic scattering factors from all theatoms (or nanocrystals) in the unit cell.

To obtain the intensity of an entire crystal, we need to sum over all the unit cells:

I = I0FF∗ sin

2( ~q2N1 ~a1)sin

2( ~q2N2 ~a2)sin

2( ~q2N3 ~a3)

sin2( ~q2~a1)sin2( ~q

2~a2)sin2( ~q

2~a3)

= I0FF∗PP,

where PP is the peak profile, and ~a1, ~a2 and ~a3 are the basis vectors of the crystal.Plots of what the total intensity from the contributions of various components found in

our samples (colloids, aggregates and HCP and FCC crystal structures) typically look likeare shown in Figure 3.2.

SAXS pattern contributions in our data

The data that we get from x-rays scattering off of our samples is incident on our CCDdetectors as rings (referred to in this thesis as 2D SAXS patterns). When the rings in these2D SAXS patterns are averaged, the result is a 1D SAXS pattern with peaks whenever thereare bright rings caused by constructive interference.

(a) HCP contribution inglovebox sample

(b) FCC contribution inin-situ #4

(c) FCC contribution inglovebox sample

(d) Colloidal back-ground

(e) Aggregate contribu-tion in glovebox sample

Figure 3.2: Various contributions to 1D SAXS patterns

Figure 3.2 shows intensity contributions of objects with different structure factors to our 1DSAXS patterns. In each panel, the red 1D SAXS patterns indicate the structure factors of


various types of particles in our system; the blue and black 1D SAXS patterns are from thedata. Figures 3.2 (a), (b) and (c) show the contributions of HCP and FCC with two differentlattice constants respectively. Figures 3.2 (d) and (e) show the contributions from colloidaland aggregate backgrounds.

Motivation for in-situ SAXS measurement

(a) Ex situ SAXS (b) in-situ SAXS

Figure 3.3: Ex-situ vs in-situ SAXS of self assembly of Au superlattices

In order to understand the kinetics of self assembly, to put quantitative timescales to whenaggregates convert into superlattices and to when superlattice peaks contract, it is crucial tohave time-resolved SAXS information of the self-assembly process. As shown in Figure 3.3,there is a limit to the number of time points we can get 1D SAXS patterns for in an ex-situassembly, whereas for an in-situ SAXS run we are limited only by the detector’s frequencyof detection.

In-situ SAXS can also give us more information about the kinetics of self assemblythrough studying how peak intensity, peak position and peak width change over time. Peakintensity is a rough indicator of how many superlattices are present, so by tracking howthis intensity changes over time we can estimate whether the amount of superlattices isincreasing or not. The peak position is related inversely to the lattice constant of the crystal,so tracking how peak positions change can tell us whether our crystal is contracting overtime. Finally, changes in peak width over time can give us information about the annealingof superstructures or the growth of a structure.


3.2 X-Ray Photon Correlation Spectroscopy

X-ray photon correlation spectroscopy, or XPCS, is a measurement technique that looks forcorrelations in the intensity fluctuations in speckle patterns caused due to the diffraction ofcoherent x-rays. I will explain what each of these terms mean and the implications of XPCSin this section.

Coherent X-Rays and Speckle

Definition of Coherent X-Rays

In depth discussions into coherence can be found in optics textbooks [13, 14]. For thepurposes of this discussion, adapted from that in [15], there are two types of coherence:transverse and longitudinal/temporal. Transverse coherence refers to phase coherent scat-tering between two spatially separated scatterers and occurs up to a maximum separationgiven by the X-ray wavelength. Longitudinal coherence refers to coherence between X-raysarriving at different times and is limited by the wavelength spread of the incident x-rays.Both types of coherence result in an interference pattern being created at a distant detector.Both types of coherence need to be kept in mind in order to determine a coherence volume.If the scattering volume of the sample exceeds this coherence volume, then XPCS cannot bedone. According to [16], this coherence volume is determined by two transverse coherencelengths and one longitudinal coherence length. The transverse coherence lengths are givenby:

Lh,v ≈λL

2Dh,v

where λ is the wavelength of the incident x-ray, L is the distance from the source, and Dh,v

is the horizontal/vertical source size. The longitudinal coherence length is given by:

Ll =λ

2(∆λ/λ)

where ∆λ/λ is the spectral bandwidth of radiation.


Origin of Speckle from Coherent X-Rays, and the Difference between Kineticsand Dynamics

Figure 3.4: Adapted from ref [17]. Reprinted with permission from American Institute ofPhysics.; Institute of Physics (Great Britain).

This discussion is adapted from [17]. Figure 3.4 is reproduced from [17] to show how inco-herent x-ray diffraction (Figure 3.4 (a)) differs from coherent x-ray diffraction (Figure 3.4(b)). In this figure, λ is the wavelength of the scattered x-ray, a is the area of illumination,and d is the average distance between scatterers. Due to scale invariance, the two lengthscales that affect the resultant diffraction pattern are λ

dand λ

a.

In incoherent x-ray diffraction, the scattered radiation looks as described in Section 3.1,as a series of bright and dark rings on a detector surface centered around the transmittedincident beam. As incoherent illumination is independent of the area it is incident on, theresultant diffraction is only dependent on λ

d. This is visible in Figure 3.4 (a), where it is

shown how the distance between interference rings is dependent on λd.

In coherent x-ray diffraction, there is an additional feature that is governed by the λa

length scale. This is because coherent illumination is dependent on the coherence volume,described in the above subsection. These features are called speckles, and are the result ofthe wavefronts scattering from different particles interfering.

Thus, incoherent diffraction can be thought of as a spatial average over slightly differ-ent particle arrangements, while coherent diffraction results from a particular spatial andtemporal configuration of particles and therefore leads to spatiotemporal fluctuations in thespeckle pattern that are not averaged out and can be resolved. For this reason, the informa-tion encoded in the positions of maxima of the interference rings (the λ

ddependent features)

give information about the kinetics of a process like self-assembly, i.e., information about theaverage behavior of the system, while the spatiotemporal intensity fluctuations in the speckle


(the λa-dependent features) can give additional information about the more microscopic dy-

namics of the particles in any given self-assembly stage. The speckle fluctuations directlyrelate to the fluctuations of the scatterers, which are commonly referred in this context as‘dynamics,’ as opposed to kinetics.

From speckle to g(2)(~q, τ)

To extract information from the intensity fluctuations of speckle, the normalized intensityautocorrelation function g(2)(~q, τ) must be calculated. g(2) is a function of ~q (typically arange of ~q values are chosen around the desired ~q center) and τ , the time difference betweentwo consecutive time points.

Deriving sum of scattered x-ray from a scattering volume

When x-rays are incident on the scattering volume, the sum of the scattered x-rays can bederived (derivation adapted from [18]). The incident x-rays can be approximated as a planewave propagating in the z-direction:

~E(~r, t) = yEinc(x, y)exp(i(kz − ωt))

where ω is the frequency and Einc(x, y) is the magnitude of the electric field of the incidentx-ray radiation. The x-ray scattered off of a particle i is given as:

~Esca,i(~q, t) = yEinc(xi, yi)ai(~ri)exp(i(~q · ~ri − ωt)).

Summing over all N the particles in the scattering volume gives:

u(~q, t) =N∑i=1

yEinc(xi, yi)ai(~ri)exp(i(~q · ~ri − ωt)).

Deriving g(2)(~q, τ) from G(2)(~q, τ)

The intensity autocorrelation function, G(2)(~q, τ), can be calculated as a function of thescattering intensity, |u(~q, t)|2. The following derivation is adapted from [19]. G(2)(~q, τ) isdefined as:

G(2)(~q, τ) = 〈I(t)I(t+ τ)〉 = limT→∞

1

T

∫ T

0I(t)I(t+ τ)dt ∼= lim

Nfr→∞

1

Nfr

Nfr∑j=1

IjIj+n.

The discrete sum in the above equation is used, as in practical calculations there are onlya discrete number, Nfr, of frames available to do this analysis. The limits of 〈I(t)I(t+ τ)〉are:

limτ→0〈I(t)I(t+ τ)〉 = 〈I(t)I(t)〉 =

⟨I2⟩


andlimτ→∞〈I(t)I(t+ τ)〉 = 〈I(t)I(τ)〉 = 〈I〉2 .

G(2)(~q, τ) can be related to u(~q, t) through the following equation:

G(2)(~q, τ) =⟨|u(~q, t)|2

⟩ ⟨|u(~q, t+ τ)|2

⟩+ 〈u(~q, t)u(~q, t+ τ)∗〉〈u(~q, t)∗u(~q, t+ τ)〉 .

The first term,⟨|u(~q, t)|2

⟩ ⟨|u(~q, t+ τ)|2

⟩, can be re-expressed as:

⟨|u(~q, t)|2

⟩ ⟨|u(~q, t+ τ)|2

⟩= 〈I(~q, t)I(~q, τ)〉 = 〈I(~q, t)〉2 = G(2)(τ →∞)

.The second term, 〈u(~q, t)u(~q, t+ τ)∗〉〈u(~q, t)∗u(~q, t+ τ)〉, can be re-expressed as:

〈u(~q, t)u(~q, t+ τ)∗〉〈u(~q, t)∗u(~q, t+ τ)〉 =∣∣∣G(1)(~q, τ)

∣∣∣2 ,where G(1)(~q, τ) is the field correlation function.

Thus, G(2)(~q, τ) can be re-expressed as:

G(2)(~q, τ) = 〈I(~q, t)〉2 +∣∣∣G(1)(~q, τ)

∣∣∣2 = G(2)(τ →∞) +∣∣∣G(1)(~q, τ)

∣∣∣2 .Dividing both sides of this equation by G(2)(τ →∞) gives the Siegert relation:

g(2)(~q, τ) = 1 +∣∣∣g(1)(~q, τ)

∣∣∣2 ,where

g(2)(~q, τ) =G(2)(~q, τ)

G(2)(τ →∞)=G(2)(~q, τ)

〈I(~q, t)〉2

and

g(1)(~q, τ) =G(1)(~q, τ)

〈I(~q, t)〉As described in [20], there is a coherence factor β that has a maximum value of 1 and a

minimum value of 0. It is a measure of the signal-to-noise ratio in the data, as it indicateshow well the speckle can be resolved. Accounting for β in the above equation gives:

g(2)(~q, τ) = 1 + β∣∣∣g(1)(~q, τ)

∣∣∣2 .


Functional form used to fit g(2)(~q, τ)

Assuming that the system under consideration has identical particles undergoing Brownianmotion in a dilute suspension, it can be shown in [21] that g(1)(~q, τ) can be expressed as:

g(1)(~q, τ) = exp(−q2D0τ)

where D0 is the diffusion coefficient for a sphere moving in a medium of viscosity η. D0 isdefined by the Stokes-Einstein equation:

D0 =kBK

6πηrp

where kB is the Boltzmann constant, rp is the radius of the particle and K is the temperature.Thus, in this case, g(2)(~q, τ) can be found by fitting to the following functional form:

g(2)(~q, τ) = 1 + f exp(−q2D0τ)

However, it is possible for the functional form of the second term to deviate from a simpleexponential - in such cases the Kohlrausch-Williams-Watts (KWW) function or stretchedexponential can be used. In such cases:

g(1)(~q, τ) = e−(τ/τ0)α

where 1τ0

is the relaxation rate and α is the KWW exponent. Some studies, outlined in [22],

have used KWW functions to model g(1)(~q, τ) in liquids that formed glass or had capillarywaves. The functional form of g(2)(~q, τ) in this case is:

g(2)(~q, τ) = 1 + βe−(τ/τ0)α

My data analysis fits this function to the data using the following fitting parameters:

g(2)(~q, τ) = baseline+ βe−2(τ/τ0)α

where baseline is a value predominantly close to 1 and β is the coherence factor.

Information that g(2)(~q, τ) provides

Length scales implied by a given ~q

To understand what findings at a given ~q correspond to in real space, it is useful to startwith defining the wavevector number ~k:

~k =2π

λ

where λ is the wavelength of the incident x-ray. As derived in Section 3.1:


~q = ~kscattered − ~kincidentwhere kscattered is the wavevector number of the scattered x-ray and kincident is the wavevectornumber of the incident x-ray. The magnitude of ~q is thus:

|~q| = 4π sin θ

λ

where θ is the same angle that is in the Bragg law as:

2d sin θ = nλ.

Thus, this relationship between the wavelength of the incident x-rays and the magnitude of~q points to a relationship between a real space distance and ~q. As the Bragg condition issatisfied only when λ < 2d, where d is the distance between lattice planes, smaller values ofλ can be used to probe smaller spacing between scatterers.

In a lattice or perfect crystal, the magnitude of ~q can also be defined as:

|~q| = 2π∣∣∣~d∣∣∣where d is the distance between lattice planes.

Thus, the range of ~q over which g(2) is calculated probes intensity fluctuations caused byscatterers moving spatially relative to one another, for example, fluctuations in inter-particledistances. If the value of ~q, for example, is 0.005 A−1, then the corresponding separationbetween particles is ∼ 130 nm. This could point to the distance between two nanocrystals(∼ 4 nm in diameter) or the distance between superlattices and aggregates (few micrometersacross).

Relaxation rate versus ~q and interpreting KWW exponent α

To understand what type of process is causing the stretched exponential decays, typicallystudies (summarized in [15] and [22]) have plotted each of the relaxation time (τ0) and theKWW exponent α versus a series of ~q-centers. Figure 3.5 from [15] is a log-log plot of thetime scale τ (the inverse of which is the relaxation rate) versus the length scale (the definitionfor which is in the previous section). As depicted in the green and red lines in the figure,processes that are diffusive have a slope of 2, while processes that have a slope lesser than2 are faster than diffusion (indicated by the blue line, which represents the speed of sound,and the grey line, which is the speed of light). Processes that have a slope greater than 2are those that are slower than diffusion.

When processes have a KWW exponent α, typically α is plotted against the same ~q-centers. As outlined in [21], an α consistently greater than 1 implies that the decay is fasterthan a pure exponential, while an α lesser than 1 implies that the decay is slower thanan exponential. As [15] and [22] show, typically the information given by the dispersion


relations of both the relaxation time and α help determine what kind of process is occurring– when a process is thought to be faster than diffusion, the slope of the dispersion relationof relaxation time is lesser than 2 and the KWW exponent is greater than 1.

Section 5.4 will show my analysis of the dispersion relation of the relaxation time and ofthe disperion relation of α. I fitted the log of the relaxation rate to the dispersion relationof a diffusive process

log(D) + 2 log(q)

where D is the diffusion coefficient. I also fitted log(~q) to a general power law:

log(A) + exponent× log(q)

.

Figure 3.5: Dispersion relation information. Adapted from ref [15]. Reprinted with permis-sion from Annual Reviews, Inc.


3.3 Optimizing for SAXS or XPCS with acquisition

parameters

How data is acquired for XPCS and SAXS

Figure 3.6: How data is acquired for XPCS and SAXS

Figure 3.6 shows how data is acquired in our experiment. The figure shows how, whenscattered x-rays are incident on the detector, the detector acquires the data in a series offrames separated by δt, also known as τ . The strength of the beam, the number of frames,Nfr, and the exposure time of each frame, tfr, are the main acquisition parameters tuned toimprove signal-to-noise, optimize for SAXS/XPCS and to avoid effects due to beam damage.

Improving signal-to-noise

The ratio of signal-to-noise of g(2)(~q, τ) as derived in [23], is:

SNR = βIpix√N

where β is the coherence factor (also known as the speckle contrast), Ipix is the averageintensity per pixel, and

√Ntot is: √

Ntot =√NpixNfrNrep

where Npix is the number of pixels, and Nrep is the number of repetitions. As Nfr = T/tfr,where T is the total time taken to collect all the frames, the signal-to-noise ratio can also berepresented as:


SNR ∝ Fc√tfrT = Fctfr

√Nfr

where Fc is the coherent flux and is related to Ipix. At NSLS-II, the coherent flux is ≈1011ph/s.

Thus, in order to increase signal-to-noise, the three parameters that can be altered are Fc,tfr and Nfr. Fc in our experiment can only be attenuated - the two fluxes used predominantlywere those at full beam and at 20% attenuation of the beam. Increasing tfr and Nfr canincrease the signal-to-noise, but both parameters must also be optimized keeping in mindthe purpose of a particular measurement (whether it is geared towards SAXS or XPCS) andbeam damage.

Burst versus continuous mode

There are two types of acquisition modes, depending on whether the purpose of the measure-ment is for XPCS or acquiring high signal-to-noise SAXS measurements. While it is possibleto average the frames obtained from XPCS and get a SAXS pattern, if the purpose of themeasurement is solely to obtain high-quality SAXS data then a different set of parametersneeds to be used.

For XPCS, a higher number of frames is required in order to have enough time pointsto calculate g(2)(~q, τ) with good signal-to-noise. This is referred to as a burst. Continuousmode is used to acquire high quality SAXS data, using a longer exposure time per frame.

To ensure that no part of the dynamics of self-assembly is missed, the exposure time forXPCS and the number of frames for SAXS is chosen such that the total time per measurementis adequately short. The burst parameters for XPCS were finalized based on beam damagetests, which will be discussed in the next subsection.

Accounting for beam damage

There is a critical dose, Dc within which radiation induced damage starts to degrade thesample. Referred to in [23], the formula for this dose is:

Dc =FcE(1− Tsamp)Td(E)Abeamρ

where 1− Tsamp is the sample absorption, d(E) is the distance dependent sample thickness,T is the total exposure time, Abeam is the area of the beam, E is the energy of the photonand ρ is the density of the sample. Assuming all these mentioned parameters are constant,Dc can also be re-expressed as:

Dc ∝ FcNfrtfr.

Fc can be controlled by attenuating the beam - thus, longer timescales can be found withlower attenuation of the beam. The total time of exposure, T = Nfrtfr needs to be chosen for


a given beam attenuation such that this does not exceed the critical dose for damage. Thus,there must be a compromise between picking a large enough Nfr for calculating g(2)(~q, τ)and picking a high enough tfr for getting good signal-to-noise.

To determine T = Nfrtfr within these constraints and conditions, we needed to find whatcombinations of Nfr and tfr gave g(2)(~q, τ) decays that were independent of the intensity ofthe x-ray beam used. If the presence of the decay is dependent on the strength of the x-raybeam, then this is a good indication that the decay found is due to beam damage. This isbecause Dc ∝ Fc (on fixing Nfr and tfr), so if Fc is a value that increases the dose beyondthe critical value for damage, then a corresponding g(2)(~q, τ) will be present at this dose ofthe beam. Conversely, if there is a g(2)(~q, τ) decay that is independent of the attenuationof the x-ray and, thus, the strength of the dose, the decay probably stems from a physical,non-beam damage related process.

Figures 3.7 and 3.8 depict how we ascertained a good combination of Nfr and tfr. Bothfigures depict the results of two bursts, each done on distinct points on a capillary filled withsuperlattices in solution. Figures 3.7 shows the results of bursts with 5000 frames and 0.01s exposure time per frame, while Figures 3.8 shows the results of bursts with 5000 framesand 0.002 s exposure time per frame. 5000 frames were chosen so that there were enoughtime points for good signal-to-noise in calculating g(2)(~q, τ). The top row of each Figure isa burst using 20% of the full flux of the beam, and the bottom row is a burst using the fullflux of the beam. g(2)(~q, τ) in both bursts was calculated for five ~q centers (represented asvertical lines in the SAXS patterns (a) and (c) in both figures).

Figure 3.7 shows a g(2)(~q, τ) decay that is clearly dependent on the attenuation of thebeam. As panels (b) and (d) show, the decays found in (d) have much shorter values of τ0and more pronounced decays. This indicates that the decays present are dependent on theattenuation of the beam. However, Figure 3.8 (b) and (d) show decays that look unchangedat different values of attenuation of the beam, with similar values of τ0 .

This analysis showed us that a good acquisition parameter to pick that took into accountthe need for good signal-to-noise to calculate g(2)(~q, τ) and the need to account for beamdamage was to conduct bursts with 5000 frames and with exposure time per frame lower than0.002 s. We picked 0.00134 s as this was the fastest exposure time available. A discussion onhow to make sure that the specific g(2)(~q, τ) decays analysed in Chapter 5 is not due to beamdamage is given in Section 5.5. The beam was also rastered on the order of 10-20 µm aftereach burst so that each spot chosen on the sample received a dose lower than the damagethreshold. Similar to the tests at different exposure time per frame illustrated in Figures 3.7and 3.8, we experimented with the distance between spots scanned on the sample to arriveat the 10-20 µm range. We also rastered the beam along the bottom of the capillary, wherewe expected the accumulation of the forming SLs and other aggregates due to them sinkingto the bottom.


(a) (b)

(c) (d)

Figure 3.7: Damage test with 5000 frames, 0.01 s exposure time per frame. The top row isexposed to 20% of full beam and the bottom row is exposed to full beam


(a) (b)

(c) (d)

Figure 3.8: Damage test with 5000 frames, 0.002 s exposure time per frame. The top row isexposed to 20% of full beam and the bottom row is exposed to full beam

22

Chapter 4

Methods

4.1 Self Assembly protocol

Our collaborators in the Talapin Group have developed protocols and hypotheses to describehow Au nanocrystals, with thiostannate ligands that electrostatically stabilize them in polarsolvents, can be triggered to self assemble into strongly-coupled Au nanocrystal superlattices.In this section, I will summarize these insights about the process. The protocols outlined herewere used for both our in-house characterizations and during our beam time experiments.These protocols were developed by members in the Talapin Group, and the insights andhypotheses about the process reference those outlined in Dr. Eric Janke’s PhD thesis [5].

Ligand Exchange

The first step in this process is to exchange the native organic 1-dodecanethiol (DDT) lig-ands of the Au nanocrystals with inorganic thiostannate ligands through a two-phase ligandexchange process. The two phases are toluene (a non-polar solvent) and our ligand solutionin hydrazine (a polar solvent). Figure 4.1 is a cartoon of how these two phases visually looklike, with the left of the cartoon representing a two-phase separation with Au nanocrystalswith DDT ligands in the top phase, and the right showing the two-phase seperation withAu nanocrystals with thiostannate in the bottom phase. Although the exact stoichiometryof the reaction of this process is not necessarily well-defined, it can be loosely thought of as:

4DDT−Au + (N2H5)4Sn2S6,solution → Sn2S4−6 bound + 4(N2H5)DDTsolution,

CHAPTER 4. METHODS 23

Figure 4.1: Cartoon of ligand exchange process

where solution and bound refer respectively to the ligand states in solution and bound to aAu NP surface. The entire process was undertaken in a nitrogen or argon filled glovebox, dueto the flammability and toxicity of hydrazine. We typically did the ligand transfer processtwice each time, using a 20 mL scintillation vial with our bottom phase consisting of 4 mLof 25 mM ligand in hydrazine and our top phase consisting of 100 mg of Au nanocrystals in12 mL of toluene.

In the first round of ligand transferring, we let the solution with both phases stir forat least 24 hours at room temperature. After this the top phase was clear and the bottomphase was a bit cloudy or aggregated. In order to recover the solids from the bottom phase,we needed to pipette off the toluene phase, replace it with fresh toluene, and stir for anotherhour. The reason for this is to remove excess organic ligands that are free to move betweenthe phases.

After repeating this procedure a few more times and finally discarding the toluene phase,we apportioned the bottom phase into small centrifuge tubes, each one having 1 mL ofthis mixture. Adding 0.4 mL of acetonitrile (MeCN) to each these centrifuge tubes andcentrifuging them at 5000 rpm caused pellets to form at the bottom of the tubes.

We then removed the excess liquid, re-dissolved the pellets in hydrazine, put the contentsback in a vial to repeat the ligand transfer process. After another 24 hours, the distinctionbetween the phases became much clearer, just as the right half of Figure 4.1 shows. Afteranother round of pipetting out the top toluene phase and centrifuging the bottom one withMeCN, the pellets in centrifuge tube were then ready to be redissolved in hydrazine. Afterpipetting out the supernatant, we added 0.4 mL of hydrazine to each centrifuge tube andconsolidated them into two tubes, each with 0.8 mL of Au nanocrystals with thiostannateligands.

Self Assembly

In this section, I describe both the self assembly protocol used for in house characterizationsand for beam time experiments, and reasons for why certain choices were made about theprotocol.


Overview of self assembly protocol

Self assembly occurs in an air-free environment, and is induced in electrostatically stabilizedAu nanocrystals suspended in hydrazine with thiostannate ligands by slowly adding excessligand solution ((N2H5)4Sn2S6), which is above a critical concentration (≈150 mM). Using100 mg/mL of these Au nanocrystals, we typically reached a final ligand concentration be-tween 250-325 mM. Flocculation of the nanocrystals can be achieved either with a one stageaddition of the ligand solution at the final concentration (which was primarily used for inhouse characterization experiments), or in two stages with the addition of a preflocculationstage, where some ligand solution of a concentration below the critical threshold for floccula-tion is injected into the Au solution and left for a period of time, the remainder being addedlater to trigger self assembly. The reason for using the preflocculation stage, especially forour beamline experiment, is explained at a later point in this section.

Figure 4.2: Overview of self assembly

After reaching the final concentration of ligand, it takes about two hours to form fullyassembled superlattices, although superlattices can be seen in our experiments (outlined inChapter 5) and in our preliminary characterizations (outlined in Section 4.2) within thefirst ten minutes of injecting the full ligand concentration. As seen in Figure 4.2, whichis a cartoon that illustrates the steps in a self assembly protocol inside the glovebox, it ispossible to see this process by eye. Within ten minutes of injecting the critical amount ofligand solution, it is possible to see brown substances starting to collect at the bottom ofthe reactor. Within two hours, the original purple color of the solution starts to become lessintense (due to the lowering concentration of freely suspended colloidal Au) and more brownmaterial (superlattices and aggregates) forms at the bottom of the reactor.

Preflocculation

For our beamtime experiment, we decided to preflocculate our samples as doing so tended toimprove the results we saw in our 1D SAXS patterns. We also realized, through the course ofour experiments, that only certain preflocculation–flocculation concentration combinations


were best suited to generate sharp 1D SAXS peaks. As seen in Figure 4.3, while the twoblue colored 1D SAXS patterns each originates from a different sample but with the samepreflocculation–final ligand concentrations (150 mM preflocculate – 275 mM final ligandconcentrations), they both have similarly sharp peaks. The other SAXS patterns do nothave as pronounced peaks as the blue SAXS patterns’. Another important point is thatcertain preflocculation–final ligand concentrations created more reproducible results thanothers. While the blue SAXS patterns are reproducibly found in two different samples, thegreen SAXS patterns have the same composition (50 mM preflocculated – 275 mM finalconcentration) and yet do not have similar SAXS patterns. In the end, we converged on150 mM preflocculated–325 mM final ligand concentrations for our in-situ set up (furtherinformation on this set up is given in Section 4.3).

Figure 4.3: Determining preflocculation concentration

Our hypothesis for why preflocculation is necessary is that, through increasing the lig-and coverage of the nanocrystals before flocculation, this step makes the colloidal particlesmore consistently repulsive at short range, thus increasing reproducibility. It could also beremoving any impurities that still remain on the surface of the Au nanocrystals, which couldalso aid with reproducibility.

Size of Au nanocrystals used

For the beamtime experiment, Au nanocrystals 4 nm in diameter were mainly used. Rudi-mentary investigations with 5 nm and 6 nm Au particles showed that they aggregate on a


similar time scale as 4 nm Au particles. However, the ordering of the superlattices foundwas incomplete and did not appear to continue on a longer time scale.

Choice of electrolyte used for flocculation

The reason why we use our ligand solution itself to induce flocculation is that it has beenobserved that the chemical identity of the compound that increases ionic strength and triggersself assembly matters [5]. It has been observed that when chalcogenide metal (ChM) saltsabove a critical concentration are used to increase the ionic strength, self assembly into highlyordered superlattices occurs [5]. Using any other salt that ionizes in polar solvents (creatinganions such as NO3−) results in the formation of low-density and branching aggregates [5].The common features amongst all the electrolytes that trigger self assembly into superlatticesare that they have multivalent anions, monovalent cations, undergo a decomposition reactionthat results in a metal chalcogenide (more on such a reaction in the following sections), andbind strongly to Au [5].

Effect of nanocrystal composition on self assembly

It has also been observed that this self assembly pathway occurs only in metallic nanocrystalswith ChM ligands, and not with semiconductor nanocrystals (even if they have same ligands)[5]. The hypothesis for this so far is that metallic particles, due a larger dielectric mismatchbetween the electrolyte and the nanocrystal, have a much higher density of ChM− anionssurrounding them; this creates the short-range repulsive force needed for proper self assemblywith such short ligands [5].

Hypothesis for why lattice contraction occurs and why cation size of electrolytedoes not matter

The superlattices, over the timescale of a few hours, are observed to contract in size. Theirformation is also independent of the size of the cation of the electrolyte. The hypothesis forwhy this is true is due to this rearrangement pathway:

(cation)4Sn2S6 → 2SnS2 + 2(cation)2S,

which expels the cation from the lattice and converts the bulky anions into a more compactmetal chalcogenide framework [5].


4.2 Preliminary characterization

In order to have a rough sense of what timescales to optimize acquisition parameters forin our beamtime experiments and to carefully pick the right concentration of gold thatwould inform the thickness of the glassware we would need to use, we conducted a series ofpreliminary characterization experiments. These are outlined in this section.

Using UV-Vis and DLS to determine rough early timescales ofkinetics

We conducted in-situ optical experiments to determine how fast the processes that occurredwithin the first few minutes of initiating self assembly were. The methods we used wereUV-Vis spectroscopy in kinetics mode at a wavelength where gold has its lowest level ofabsorbance (750 nm, as seen in Figure 4.4 (a)), and dynamic light scattering (DLS), whichoperates under the same principles as XPCS but uses light rays instead of x-rays. For bothexperiments, we were limited to using low concentrations of Au (between 1-10 mg/mL), asanything higher than this would simply extinguish all of the incident light.

UV-Vis

To conduct experiments with UV-Vis, we first attempted to do ex-situ UV-Vis character-ization (Figure 4.4 (a)), where we first looked at the absorption spectrum of just colloidalAu, and then looked at absorption spectrum of Au superlattices. The motivation behindthis attempt is that, as the superlattices have nanocrystals that are strongly coupled to oneanother, this would cause the peak of the spectrum to redshift. However, we were unable toget conclusive results here due to sinking of the superlattices and aggregates formed.

We then turned to using UV-Vis in its kinetics mode, which is an acquisition mode thattracks changes in absorption over time at a specified wavelength. We picked a wavelength atwhich gold absorbs light the least and thus scatters more light (750 nm). The motivation forthis technique is that, by tracking how absorbance changes in a low-absorbance regime, wecan track how the scattering of light off the Au colloids changes as they self-assemble intoaggregates and superlattices. As the amount of scattered light is proportional to the diameterof the object it is incident on, this method serves as an indirect way to track the growth ofthe superlattice. To do this, we also modified a cuvette (Figure 4.4 (c)) to be air-tight andallowed for the ligand to be mixed with the colloidal Au in the UV-Vis spectrometer.

What we noticed was, at 1 mg/mL of Au concentration, that ≈ 30 s was the initialtime constant. This initial time constant, defined as the half life, (τhalf ), is qualitativelydetermined as the time at which the intensity of absorption is half that of the flat regionseen in Figure 4.4 (b) between 10 and 100 minutes). τhalf is used as a qualitative metricof how fast the process at early times of self-assembly is, allowing us to compare this rateacross other runs.


(a) UV-Vis Spectra of superlattices and col-loidal Au

(b) UV-Vis extinction curve tracking growthof particle

(c) In-situ cuvette

Figure 4.4: In-situ UV-Vis overview. Plots courtesy of James Utterback

The extinction curve levels out at ≈ 10 minutes and increases slowly until 2 hours, whenthe particles crash out of solution (seen as the downward slope following the peak at ≈ 100min in Figure 4.4 (c)).

Dynamic Light Scattering (DLS)

Dynamic Light Scattering (DLS) tracks correlations in the intensity fluctations of scatteredvisible light to calculate g(2) and is the optical analogue of XPCS. DLS measures fluctuationsin the scattered light intensity at a specific angle (or ~q). We calculate g(2) based on thesefluctuations, and fit it to a simple exponential with

f1 = exp(−2Dq2t)

where D is the diffusion coefficient.Instead of resolving g(2) at multiple values of ~q, DLS is often done at a single value of ~q.

From the fit, D is extracted and then, using the Einstein-Stokes equation, the radius of theparticle can be found. This makes DLS suited for easily tracking the growth of particles overtime. As DLS uses visible light, it cannot resolve the crystal structure on nm lengthscales,unlike XPCS.


(a) In-situ UV-Vis extinction curve trackinggrowth of particle indirectly

(b) In-situ DLS calculating growth of parti-cle by calculating particle size

Figure 4.5: In-situ UV-Vis vs in-situ DLS. Plots courtesy of James Utterback and ChristianTanner

Figure 4.5 compares the extinction curve found from UV-Vis (Figure 4.5 (a)) with theparticle size versus time plot found using DLS (Figure 4.5 (b)), both using 1 mg/mL con-centration of Au. Both UV-Vis and DLS tell us similar information about these timescales.There is a ≈ 1 min τhalf for growth (which is ≈ 30 s in UV Vis), the particle size then levelsout at a size of 700 nm at 10 min (which is the same as UV Vis). The one place where DLSand UV-Vis differ is that in DLS, the particles slowly increase in size to 900 nm over 4 hours.As our particles sink within 2 hours in UV-Vis, this is not a timescale that has meaning inUV-Vis.

Using UV-Vis and DLS to determine optimal concentration ofgold for beamline experiments

Glass capillaries were used for either runs of fully and partially in-situ self assembly or forruns of samples fully assembled in the glovebox (all of which are described in Section 4.3).In order to ascertain what the thickness of our capillary’s glass needed to be, we needed tounderstand how the concentration of gold affected the attenuation length of x-ray beamsand the speed of kinetics observed. Figure 4.6 (a) is a chart that shows how the attenuationlength of x-ray beams is affected by the concentration of gold (this chart assumes that thesample is bulk gold - to be rigorous one would account for the volume fraction of the goldin superlattices). The smaller the attenuation length, the thinner our glassware needed tobe for good signal to noise. Figures 4.6 (b)-(d) show how in-situ UV-Vis and DLS indicatethat kinetics of self assembly speed up with higher concentrations of gold. Figure 4.6 (c), inparticular, shows how both the τhalf and τcrash in UV-Vis become shorter, indicating that the


Figure 4.6: Preliminary studies to determine optimal concentration of Au nanocrystalsneeded for beamtime experiments. Figure (a) shows the relationship between attenuationlength of x-ray beams and the concentration of gold. Figures (b)-(d) are plots of in-situ UV-Vis and DLS that show the concentration dependence of kinetics, with Figure (e) showingthis more concretely. Plots courtesy of James Utterback and Christian Tanner

processes are speeding up with higher concentrations of Au. Figure (e) is a table that showsthis more concretely and shows what it would be for 100 mg/mL of gold (extrapolating usingthe relation τ = 1

[Au]. We finally decided to go with 100 mg/mL of gold concentration, as

we were able to get glassware thin-enough for this purpose so that the attenuation length atthis concentration of Au was no longer an issue, and knew that such a high concentration ofAu would improve our signal-to-noise as there would be a lot more Au to scatter.

Using ex-situ SAXS to obtain rough late timescales of kinetics

Before attempting our beamline experiments, we conducted an experiment where we didex-situ SAXS at different time points along the time course of self-assembly. To achieve this,we started the self assembly procedure in a vial, and at specific time points we would draw


a small amount out of the vial and put this in eppendorf tubes, each time point with itsown tube. We would then add some MeCN to freeze the assembly in each eppendorf tube.Finally, once we had collected all our time points, we centrifuged these tubes to make pellets,which we scraped out onto kapton tape after pipetting out the supernatant. We then sentthese kapton tapes to the University of Chicago tabletop SAXS setup to see when we startedto see superlattice peaks.

Figure 4.7: Using ex-situ SAXS to determine when superlattices form

As seen in Figure 4.7, we started to see FCC superlattice peaks by the ten minutemark, and these peaks only got higher in intensity and sharpness by the 2 hour mark.This, along with out UV-Vis and DLS studies, made us realize that a lot of the kineticswere occurring within the first ten minutes of self-assembly, enabling us to optimize ouracquisition parameters for those few minutes.

4.3 Types of Self Assembly Protocols

At the beamline a variety of different self assembly protocols were used for different purposes,as described in this section.


(a) in-situ setup (b) Samples assembled in glovebox set up

Figure 4.8: How the setups look

Fully assembled in glovebox

Some of our samples were fully self assembled in the glovebox, which meant that self assemblywas triggered in a vial and was left to occur in that environment for over two hours. Suchsamples were used as controls for our in-situ runs, and to run tests for the optimal chemicalcomposition of our samples. Once we let these samples fully self assemble in the glove box,we would draw them up in a capillary, seal both ends with melted paraffin wax, and transportthem to perform x-ray experiments using secondary containment.

Partially in-situ self assembly

Partially in-situ self assembled runs refer to when samples were triggered to self-assemblein the glovebox and brought to the x-ray hutch within a matter of minutes, transported ina similar way as those fully-assembled in the glovebox. These samples were partially in-situas the rest of the self assembly would occur in the x-ray beam. The motivation for creatingsuch samples was to probe what was happening at around the ten minute regime of selfassembly, and was a preliminary step before our fully in-situ self assembly set up.

Fully in-situ self assembly set up

We were able to attempt 7 fully in-situ self assembly experiments through our beamtimeshifts. Each experiment gave us the opportunity to observe, from the moment of injection,both the kinetics and the dynamics of self-assembly. Below, I have described what goes intosetting up and disassembling the sample reactor for such an experiment.


Step 1: Pre-glovebox set up

To set the needles up before loading everything into the glovebox, we first threaded two longneedles (30 gauge, 150 mm) through two teflon balls, and attached them to gas tight syringebarrels. We then attached the shorter needle (22 gauge, 2 inches) to our outlet syringe barrel.As in Figure 4.9 (a), all the elements (the needles and syringes, the black syringe bracketthat fitted into the syringe pump, and the silver magnetic holder that kept our set up firmlyheld in front of the xray) were brought into the glovebox.

Step 2: Loading syringes with chemicals and into the capillary

Once all the elements were in, we first withdrew a small amount of hydrazine from stocksolution into a 2 mL vial to wet both our syringes with hydrazine. This step just allowedus to more smoothly draw up our Au and ligand solutions. We then drew up a volume ofpreflocculated Au (varied between 35-44 uL depending on the run), along with some argonas head space, into one syringe. Into the other, we drew up an equal volume of ligand andhead space.

After loading our two syringes with chemicals, we needed to insert these needles into thefunnel of the capillary. On doing this, we pushed the second teflon ball as far back from thecapillary as possible. To ensure air-tightness, we did two layers of sealing this entrance. Wefirst filled the opening of the capillary with the needles with melted paraffin wax, and thenepoxy-glued around this seal, letting it sit for five minutes. We similarly sealed the openingof the outlet syringe on the other side of the capillary, which we inserted after sealing thefirst two syringe needles in. To ensure the seal was tight, we pushed the outlet syringefurther into the capillary while the epoxy was still wet. We epoxied both joints again for anadditional protective layer for at least 5 minutes. The setup would look like Figure 4.9(b).

Step 3: Fitting the setup with styrofoam and into the rig

Using pre-cut tubes of styrofoam, we carefully fitted these over the joints of the epoxiedneedles. We then placed the styrofoamed syringes-capillary set up into bracket, where theinlet syringes rested on the white smaller bracket (as seen in 4.9(c). We then placed theentire rig into a larger secondary container to take it out of the glovebox.

Step 4: Mounting the capillary onto the rig

Once brought out of the glovebox, the capillary and attached needles were secured into therig. Each part was tailored to the dimensions of our glassware, so we were able to create asecure rig for our in-situ assembly. To transport the set up to the x-ray hutch, the woodenboard shown in 4.9(e) allowed all parts of the set up to be rigid for safe transportation.


Step 5: Clean up after an in-situ run

To clean up after a run, we needed to unscrew all the components. We then took our setupto a fume hood and took out all the liquid inside the capillary using the outlet syringe. Wethen used acetone to weaken the epoxy at the joints, which let us slide the needles out of thecapillary. The liquid in the outlet syringe was quenched in a large volume of water, whichrendered the hydrazine in the liquid harmless. The capillary was rinsed before disposal ina waste designated for hydrazine-contaminated waste, and all our syringes and needles werepurged several times with water. We dried them off using nitrogen from a nitrogen gun, andfinally threaded our needles to keep them clean and ready for reuse.


(a) Pre-glovebox set up (b) Loading syringes withchemicals and into the capil-lary

(c) Fitting the setup with sty-rofoam and into the rig

(d) Set up without screws (e) Set up with screws andbrown board

Figure 4.9: Steps to set up the in-situ rig

36

Chapter 5

Results and discussion

5.1 Overview of beam time

This thesis examines data from our experiments conducted between August 9th - 14th 2019at the Brookhaven National Lab’s National Synchotron Light Source II (NSLS-II). Our maingoal was to gain more quantitative information about the kinetics of self-assembly of stronglycoupled NP SLs through our in-situ self assembly runs. We also conducted XPCS alongsideour SAXS runs to determine the dynamics of the forming superlattices at the various stagesof self-assembly. This chapter will focus on analyzing the XPCS data that we collectedthrough our beamtime.

Before delving into the XPCS data, I will first give a brief summary of the runs conductedat our beamtime. To enable this and consequent discussion, the nomenclature used to namesamples will be briefly discussed. Samples were generally named with the following conven-tion: [Initials of maker][4, 5, or 6 nm nanoparticles][self assembly protocol][concentration]. Inthe samples discussed in this thesis, “slowinsitu” and “aggregate” are used interchangeablyto describe partially in-situ experiments. I will also refer to the only fully in-situ experimentdiscussed in this thesis as In Situ # 4, as the original name (jp4insitu100trial20190813-0437)is very long.

We started our beam time with the goal of optimizing beam parameters to avoid damageand get good signal-to-noise (described in Section 3.3), and tweaking the chemical compo-sition of our samples to get optimally sharp and high intensity superlattice peaks in our1D SAXS patterns (described in Section 4.1). An example of a sample used for the pur-pose of optimizing both beam and chemical parameters is ic5agg100mg prep2, which will bediscussed more in Section 4.2, as a burst in this run had promising g(2)(~q, τ) decays.

In preparation for our full in-situ runs, we conducted four partially in-situ runs. TheXPCS results of these will be examined closely in this thesis (ic4slowinsitu100mg, ic4slowinsitu100mgtake2,jp4aggregate100mg, jp4aggregate100mg lowligand) as most of the g(2)(~q, τ) decays foundwere in these runs. The description of this self-assembly set up is given in Section 3.3 inChapter 3.

CHAPTER 5. RESULTS AND DISCUSSION 37

In addition, we conducted 7 fully in-situ runs (descriptions of this protocol are alsogiven in Section 3.3 in Chapter 3) and accompanying glovebox controls, samples that hadthe same chemical composition as their in-situ counterparts. We used glovebox controls tocheck if there was any effect that the x-ray beam had on the self-assembly process. We alsoperiodically took SAXS data of capillaries with hydrazine, ligand solution and colloidal Aurespectively to better analyze our SAXS data.

The in-situ run with the most promising time-resolved SAXS and XPCS was In Situ #4, a run that I closely look at in this thesis.

5.2 Overview of Data Examined in Thesis

In this section I will summarize when we found g(2)(~q, τ) decays with respect to time in theselect runs described in the above section. The g(2)(~q, τ) decays in this section are all thosefound at 0.006 A−1, with a width of 0.001 A−1, and with the incident x-rays at full-beam.This ~q-value was chosen as we found a series of g(2)(~q, τ) decays in the low ~q region (0.005- 0.018 A−1) of ic4slowinsitu100mg. My goal was to understand whether such a decay alsoexisted in other partially in-situ runs, and in other runs with different self-assembly protocols(the fully glove box self assembled ic5agg100mg prep2 and In Situ #4).

The bursts used to get g(2)(~q, τ) decays generally consisted of 5000 images with 0.00134seconds of exposure time each, as discussed in Section 3.3 (with the exception of ic5agg100mg prep2,which had frame exposure times of 0.01 seconds).

The chemical compositions of each of these samples is given in Table 5.1. An overviewof how g(2)(~q, τ) decays found in our samples changed with time is presented in Figure 5.1.

Sample nameGold size(nm)

Gold conc.(mg/mL)

Pre-flocc.ligand conc.(mM)

Wait time forpre-flocc.(min)

Final ligandconc. forself assembly(mM)

Self AssemblySetup

When inX-ray beam(min sinceinjection)

ic4slowinsitu100mg 4 100 23 30 250 Partially insitu 10ic4slowinsitu100mgtake2 4 100 23 30 260 Partially insitu 11jp4aggregate100mg 4 100 150 96 275 Partially insitu 6jp4aggregate100mglowligand

4 100 50 105 275 Partially insitu 4

ic5agg100mg prep2 5 100 NA NA1:1Au:ligand

Gloveboxassembled

NA

In Situ #4 4 100 150 136 325 In situ rig 0

Table 5.1: Overview of Chemical Composition of Various Samples


Fig

ure

5.1:

Pre

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ofg(2) (~q,τ)

inea

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late

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es


ic4slowinsitu100mg

(a) 1D SAXS 10 minutes from self assemblyinitiation

(b) g(2)(~q, τ) decay 10 minutes from self as-sembly initiation

(c) 1D SAXS 94 minutes from self assemblyinitiation

(d) g(2)(~q, τ) decay 94 minutes from self as-sembly initiation

Figure 5.2: How 1D SAXS and g(2)(~q, τ) decays changed with time in ic4slowinsitu100mg

ic4slowinsitu100mg was self-assembled using a partially in-situ protocol. Chemically, itconsisted of 4 nm Au colloids of 100 mg/mL concentration. This sample was preflocculatedin a vial in the glovebox for 30 minutes at a ligand concentration of 23 mM. After this period,it was flocculated to a final ligand concentration of 250 mM, drawn up into a capillary,quickly sealed and transported in a secondary container to the x-ray hutch. The first burstmeasurement was taken at ≈ 10 minutes after initiation of self assembly, and the last burstwas taken at ≈ 120 minutes. The first five XPCS bursts were acquired with a minute betweeneach one, and after this the remaining bursts were taken every four to ten minutes.

The predominant 1D SAXS patterns looked like those in Figure 5.2, and these SAXSpatterns stayed the same through all the time points. For each of these bursts, we found ag(2)(~q, τ) decay with τ0 mainly between 0.2 - 1 seconds. The exception of a few bursts (the


g(2)(~q, τ) decay found in the first burst, reproduced in Figure 5.2 (b), had a time constant of6.702 seconds.

ic4slowinsitu100mgtake2

(a) 1D SAXS 11 minutes from injection (b) g(2)(~q, τ) decay 11 minutes from injection

(c) 1D SAXS 58 minutes from injection (d) g(2)(~q, τ) decay 58 minutes from injection

Figure 5.3: How 1D SAXS and g(2)(~q, τ) decays changed with time inic4slowinsitu100mgtake2

ic4slowinsitu100mgtake2 was self-assembled using a partially in-situ protocol. Chemically,it was almost identical to ic4slowinsitu100mg. The only difference is that the final concen-tration of ligand in this sample is 260 mM, as opposed to 250 mM, which was intended todeliberately drive the self assembly harder. The first burst was taken at ∼ 11 minutes afterinitiation of self assembly, and the last burst was taken at ∼ 98 minutes. The first thirteenXPCS bursts were acquired with a minute between each one, and after this the remainingbursts were taken every four to ten minutes.


The predominant 1D SAXS patterns looked like those in Figure 5.3, and these SAXSpatterns stayed the same through all the time points. We were not able to see any meaningfulg(2)(~q, τ) decays in any of these bursts.

jp4aggregate100mg



Figure 5.4: How 1D SAXS and g(2)(~q, τ) decays changed with time in jp4aggregate100mg

jp4aggregate100mg was self-assembled using a partially in-situ protocol. Chemically, itconsisted of 4 nm Au colloids of 100 mg/mL concentration. This sample was preflocculatedin a vial in the glovebox for 96 minutes at a concentration of 150 mM. After this period, itwas flocculated to a final concentration of 275 mM, drawn up into a capillary, quickly sealedand transported in a secondary container to the x-ray hutch. The first burst was taken at≈ 6 minutes after initiation of self assembly, and the last burst was taken at ≈ 50 minutes.All the bursts were taken with about a minute between them.

The predominant 1D SAXS patterns in the early bursts looked like those in Figure 5.7(a), and these started to become like the 1D SAXS pattern in 5.7 (c) towards the later time


points. g(2)(~q, τ) decays were found whenever the 1D SAXS pattern looked like Figure 5.7(a), with τ0 between 2-4 seconds in the early time bursts.

jp4aggregate100mg lowligand



Figure 5.5: How 1D SAXS and g(2)(~q, τ) decays changed with time injp4aggregate100mg lowligand

jp4aggregate100mg lowligand was self-assembled using a partially in-situ protocol. Chem-ically, it was similar in composition to jp4aggregate100mg, except that it had a lowerpreflocculation ligand concentration (50 mM compared to 150 mM). The reason for thechange in preflocculated ligand concentration from jp4aggregate100mg was to see if the lig-and concentration for pre-flocculation would affect the final superlattice formation. Bothjp4aggregate100mg and jp4aggregate100mg lowligand had the same final ligand amount –the only difference between the two was their pre-flocculated ligand concentrations.

The first burst was taken at ≈ 4 minutes after initiation of self assembly, and the lastburst was taken at ≈ 140 minutes. Acquisition of the data was altered between getting an


XPCS burst and SAXS continuous mode (differences between both acquisition modes areoutlined in Section 2.3 of Chapter 2).

The predominant 1D SAXS patterns in the early bursts looked like those in Figure 5.5(a), but as time progressed these 1D SAXS patterns started to become more like that ofFigure 5.5 (c). g(2)(~q, τ) decays in early time points had τ0 values between 2-4 seconds, butas time progressed τ0 values increased.

ic5aggregate100mg prep2

(a) 1D SAXS of burst 8344ba5a (b) g(2)(~q, τ) at 0.006 A−1, 0.001 A−1 widthof burst 8344ba5a

(c) 1D SAXS of burst 87112cdd (d) g2 at 0.006 A−1, 0.001 A−1 width of burst87112cdd

Figure 5.6: How 1D SAXS and g2 decays changed with time in ic5aggregate100mg prep2

ic5aggregate100mg prep2 was a control sample that was fully assembled in the glovebox.Chemically, 5 nm colloidal Au with a concentration of 100 mg/mL was used, with a 1:1Au:ligand solution volume ratio. This sample was not created to observe self assembly ofsuperlattices, but simply to test some beam parameters and chemical parameters out.


Only two bursts of XPCS were taken of this sample. As seen in Figures 5.6 (a) and (b),only one of these bursts had a strong 1D SAXS pattern with defined peaks and a g(2)(~q, τ)with a τ0 of 3 seconds. The other burst has a g(2)(~q, τ) decay with a τ0 of 100 seconds.

In situ # 4



Figure 5.7: How 1D SAXS and g(2)(~q, τ) decays changed with time in In situ # 4

In situ # 4 was self assembled fully in-situ. Chemically, it consisted of 4 nm colloidal Au withconcentration of 100 mg/mL that was preflocculated with 150 mM concentration of ligandsolution. After a preflocculation time of 136 minutes, the final concentration of 325 mM ofthe ligand was reached via simultaneous injection of two syringes (one with preflocculatedAu, and the other with ligand solution) into a capillary in front of the x-ray beam. This setup is described in Section 3.3 of Chapter 3.

The acquisition scheme alternated between XPCS bursts and SAXS continuous mode,first at full beam for the first 5 minutes, and then we repeated a triple sequence of a burst at20% full beam, a burst at full beam, and finally a SAXS continuous mode acquisition at full


beam until minute 117. One full cycle of these 3 modes took ∼ 2 min to complete. Whilewe found good time-resolved SAXS for this sample, we were unable to find any meaningfulg(2)(~q, τ) decays.

5.3 Correlations found between g(2)(~q, τ ) decays and

SAXS patterns

Definition of qualitative parameters

After carefully looking for which runs had g(2)(~q, τ) decays and how they varied in time ineach sample, I decided to see if there were patterns present across samples with g(2)(~q, τ)decays. To understand this, I defined a few qualitative parameters, which are outlined inFigure 5.8.

The four parameters that I qualitatively defined were:

1. The self assembly set up used (whether it was self asssembled fully in the glovebox,partially in-situ in front of the x-ray beam or fully in-situ in front of the x-ray beam).

2. The signal strength of our scattered x-rays (qualitatively defined as strong, medium orweak).

This was qualitatively assessed based on the contrast of the 2D SAXS pattern, as seenin Figure 5.8 (b).

3. The presence of a colloidal and/or aggregate background in the 1D SAXS pattern.

This parameter was assessed qualitatively by looking for the signature features in the1D SAXS pattern of colloidal and aggregate backgrounds which arise due to theirstructure factors. Figure 5.8 (c) shows how the aggregate and colloidal backgrounds(red curves in both plots) contribute to the blue and black 1D SAXS patterns. Whenlooking for an aggregate background in our 1D SAXS patterns, I noticed that thesesamples had a distinct dip between q values of 0.1-0.15 A−1. As the plot in the left ofFigure 5.8 (c) shows, this dip is due to the shape of the structure factor of aggregates.Similarly, when looking for a colloidal background, I looked for a signature slope inthe 1D SAXS plot between ~q values of 0.02-0.1 A−1 (as seen in the plot in the right ofFigure 5.8 (c)). This slope is also present due to the structure factor of the colloids.

4. The crystal structure present (FCC, HCP or FCC and HCP).

Figure 5.8 (d) shows the contributions of FCC and HCP crystal structure factors (inred) to the 1D SAXS patterns found in the data (in blue). It is possible to qualitativelytell the crystal structure of the samples due to the distinctly different structure factorsof hexagonal close packed (HCP) and FCC crystals. FCC crystal structures in oursamples tend to have a 1D SAXS pattern with two main peaks, the peak at low ~q


higher in intensity than the other (these peaks are circled in purple in the left andmiddle plots in Figure 5.8 (d)). We were able to see HCP peaks in our sample only in1D SAXS patterns that looked like the middle and right plots in Figure 5.8 (d), withthis peak circled with pink.

Patterns observed

Figure 5.9 summarizes all the patterns that I was able to find using these qualitative pattern.

When meaningful g(2)(~q, τ) decays were present

I was able to see g(2)(~q, τ) decays present whenever there were high amounts of signal.g(2)(~q, τ) decays with high signal-to-noise ratio were present only in the samples that wereself assembled in the glovebox, which included both the fully assembled in the gloveboxsample and three of the four partially in-situ self assembled samples (at all time points inthe run of ic4slowinsitu100mg and in early time points in the runs of jp4aggregate100mg andjp4aggregate100mg lowligand). What was common among all their 1D SAXS patterns wasthat they had an aggregate background, and had the presence of FCC crystal peaks. Thesepatterns can be seen more clearly in Figure 5.10, which specifically shows representative 1Dand 2D SAXS patterns and high signal-to-noise g(2)(~q, τ) decays.

When g(2)(~q, τ) decays were not present

I was not able to see any g(2)(~q, τ) decays present whenever there were low amounts ofsignal. These low-signal samples were present in all time points of the partially in-situself assembly sample ic4slowinsitu100mgtake2, in later time points of partially in-situ selfassembly sample jp4aggregate100mg, and in In Situ # 4. What was common among alltheir 1D SAXS patterns was that they had either a pronounced colloidal background orneither colloidal nor aggregate background, and had low intensity FCC crystal peaks. Thesepatterns can be seen more clearly in Figure 5.11, which specifically shows representative 1Dand 2D SAXS patterns and g(2)(~q, τ) decays from samples without g(2)(~q, τ) decays.


(a) Self assembly set up

(b) Qualitatively determining signal strength

(c) Qualitatively distinguishing between colloidal and aggregate back-grounds

(d) Qualitatively determining crystal structure

Figure 5.8: Description of qualitative parameters used to find patterns in the data


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bly


5.4 Dispersion relation of ~q

In order to see if g(2)(~q, τ) decays I found were due to a diffusive process or not, for eachchosen XPCS burst (in the runs of samples ic5aggregate100mg prep2, ic4slowinsitu100mg,jp4aggregate100mg, jp4aggregate100m lowligand) I did a qualitative analysis of the relax-ation rates ( 1

τ0) obtained from ten g(2)(~q, τ) decays at ten different ~q values (between 0.005-

0.018 A−1

, with a width of 0.00065 A−1

for each ~q). I also qualitatively plotted the KWWexponent versus each of these ~q-centers.

This analysis is qualitative as I did not account for whether the source of some of thesedecays are due to beam damage or not, even though most of the runs used beam acquisitionparameters that were optimized for reducing damage. A more in depth discussion about thisis in Section 5.5. A discussion of whether these dispersion relations are due to a physicalprocess or due beam damage is given in Section 5.5.


Analysis of dispersion relations of relaxation rate and α

ic5aggregate100mg prep2

(a) 1D SAXS pattern (b) Dispersion relation plot of KWW expo-nent

(c) Dispersion relation plot of relaxationrate. Fit parameters are A = 190 ±20A2s−1× exponent = 1.2± 0.1.D = 6200±600A2s−1

Figure 5.12: Dispersion relation analysis for ic5aggregate100mg prep2.

Figure 5.12 shows the dispersion relation analysis for ic5aggregate100mg prep2. (a) showsthe 1D SAXS pattern of the sample, with blue vertical lines indicating the location of ~q-centers used of g(2) analysis. As discussed in Section 5.3, the crystal structure indicated bythis SAXS pattern is FCC, and an aggregate background is also present.

Figure 5.12 (b) is a plot of the dispersion relation the the KWW constant α versus the~q-centers, where the orange markers represent the data and the blue line is a line inserted toshow when α= 1. The α values are consistently below 1 at ∼ 0.8, indicating that the decayis slower than a simple exponential decay.


Figure 5.12 (c) is a log-log plot of relaxation rate (1/τ0) versus the ~q-centers, where thered line is the fit for a diffusive process, 2 log(~q) + log(D0), the blue markers represent thedata and the blue line is the best fit for the data, exponent∗ log(~q) + log(A), the parametersof which are in Figure 5.12 (d). The exponent of the best fit is 1.2, which is smaller thanthe exponent for diffusion, which is 2. This could indicate that the process is faster thandiffusion.

ic4slowinsitu100mg

Figure 5.22 shows the dispersion relation analysis for ic4slowinsitu100mg. Figures 5.13, 5.16and 5.19 show the 1D SAXS pattern of the sample at various time points in the run referencedto the initiation time of self assembly, with blue vertical lines indicating the location of ~q-centers used of g(2) analysis. As discussed in Section 5.3, the crystal structures indicated bythis SAXS pattern are a combination of both FCC and HCP, with an aggregate backgroundalso present.

Figures 5.14, 5.17 and 5.20 are plots of the dispersion relation the the KWW constant αversus the ~q-centers, where the orange markers represent the data and the blue line is a lineinserted to show when α= 1. The α values are generally above 1 before the 11 minute timemark, but then become below 1 at both the 60 minute and 94 minute time marks. Whatthis changing α could imply is discussed in 5.5.

Figures 5.15, 5.18 and 5.21 are log-log plots of relaxation rate (1/τ0) versus the ~q-centers,where the red line is the fit for a diffusive process, 2 log(~q) + log(D0), the blue markersrepresent the data and the blue line is the best fit for the data, exponent ∗ log(~q) + log(A),the parameters of which are in the captions. The exponent of the best fit across all timespoints is between 1.1-1.3, which is smaller than the exponent for diffusion, which is 2. Thiscould indicate that the process is faster than diffusion.

jp4aggregate100mg

Figure 5.32 shows the dispersion relation analysis for jp4aggregate100mg. Figures 5.23, 5.26and 5.29 show the 1D SAXS pattern of the sample at various time points in the run referencedto the initiation time of self assembly, with blue vertical lines indicating the location of ~q-centers used of g(2) analysis. As discussed in 5.3, the crystal structures indicated by thisSAXS pattern are a combination of both FCC and HCP, with an aggregate background alsopresent.

Figures 5.24, 5.27 and 5.30 are plots of the dispersion relation the the KWW constantα versus the ~q-centers, where the orange markers represent the data and the blue line is aline inserted to show when α= 1. The α values are generally above 1 at the 6 minute timemark, but then shows a decreasing trend from above to below 1 at both the 9 minute and15 minute time marks. What a changing α could imply is discussed in 5.5.

Figures 5.25, 5.28 and 5.31 are log-log plots of relaxation rate (1/τ0) versus the ~q-centers,where the red line is the fit for a diffusive process, 2log(~q) + log(D0), the blue markers


Fig

ure

5.13

:1D

SA

XS

pat

tern

at11

min

Fig

ure

5.14

:D

isp

ersi

onre

lati

onplo

tof

KW

Wex

pon

ent

at11

min

Fig

ure

5.1

5:

Dis

per

sion

rela

tion

plo

tof

re-

laxati

on

rate

at

11

min

.F

itpara

met

ers

are

A=

100±

100A

2s−

1.expon

ent

=1.3

61±

0.0

01.D

=2800±

200A

2s−

1

Fig

ure

5.16

:1D

SA

XS

pat

tern

at60

min

Fig

ure

5.17

:D

isp

ersi

onre

lati

onplo

tof

KW

Wex

pon

ent

at60

min

Fig

ure

5.1

8:

Dis

per

sion

rela

tion

plo

tof

re-

laxati

on

rate

at

11

min

.F

itpara

met

ers

are

A=

400±

100A

2s−

1.expon

ent

=1.0

94±

0.0

01.D

=35000±

3000A

2s−

1

Fig

ure

5.19

:1D

SA

XS

pat

tern

at94

min

Fig

ure

5.20

:D

isp

ersi

onre

lati

onplo

tof

KW

Wex

pon

ent

at94

min

Fig

ure

5.2

1:

Dis

per

sion

rela

tion

plo

tof

re-

laxati

on

rate

at

94

min

.F

itpara

met

ers

are

A=

500±

200A

2s−

1.expon

ent

=1.1

04±

0.0

06.D

=37000±

3000A

2s−

1

Fig

ure

5.22

:D

isp

ersi

onre

lati

onan

alysi

sfo

ric

4slo

win

situ

100m

g


Fig

ure

5.23

:1D

SA

XS

pat

tern

at6

min

Fig

ure

5.24

:D

isp

ersi

onre

lati

onplo

tof

KW

Wex

pon

ent

at6

min

Fig

ure

5.2

5:

Dis

per

sion

rela

tion

plo

tof

re-

laxati

on

rate

at

6m

in.

Fit

para

met

ers

are

A=

8±

4A

2s−

1.expon

ent

=0.6

±0.2.D

=8000±

1000A

2s−

1

Fig

ure

5.26

:1D

SA

XS

pat

tern

at9

min

Fig

ure

5.27

:D

isp

ersi

onre

lati

onplo

tof

KW

Wex

pon

ent

at9

min

Fig

ure

5.2

8:

Dis

per

sion

rela

tion

plo

tof

re-

laxati

on

rate

at

9m

in.

Fit

para

met

ers

are

A=

8±

7A

2s−

1.expon

ent

=0.6

9±

0.0

5.D

=4000±

500A

2s−

1

Fig

ure

5.29

:1D

SA

XS

pat

tern

at15

min

Fig

ure

5.30

:D

isp

ersi

onre

lati

onplo

tof

KW

Wex

pon

ent

at15

min

Fig

ure

5.3

1:

Dis

per

sion

rela

tion

plo

tof

rela

x-

ati

on

rate

at

15

min

.F

itpara

met

ers

are

A=

1.3±

0.4A

2s−

1.expon

ent

=0.3

23±

0.0

01.D

=5600±

700A

2s−

1

Fig

ure

5.32

:D

isp

ersi

onre

lati

onan

alysi

sfo

rjp

4agg

rega

te10

0mg


represent the data and the blue line is the best fit for the data, exponent ∗ log(~q) + log(A),the parameters of which are in the captions. The exponent of the best fit across all timespoints is between 0.6-0.7 for the two early time points and decreases to 0.3 at the late timepoint,all of which are smaller than the exponent for diffusion, which is 2. This could indicatethat the process is faster than diffusion.

jp4aggregate100mg lowligand

Figure 5.42 shows the dispersion relation analysis for jp4aggregate100mg lowligand. Figures5.33, 5.36 and 5.39 show the 1D SAXS pattern of the sample at various time points in the runfrom initiation of self assembly, with blue vertical lines indicating the location of ~q-centersused of g(2) analysis. As discussed in 5.3, the crystal structures indicated by this SAXSpattern are a combination of both FCC and HCP, with an aggregate background.

Figures 5.34, 5.37 and 5.40 are plots of the dispersion relation the the KWW constantα versus the ~q-centers, where the orange markers represent the data and the blue line is aline inserted to show when α= 1. The α values are generally above 1 in the 4 minute timemark, but then shows a decreasing trend from above to below 1 in both the 32 minute and73 minute time marks. What a changing α could imply is discussed in 5.5.

Figures 5.35, 5.38 and 5.41 are log-log plots of relaxation rate (1/τ0) versus the ~q-centers,where the red line is the fit for a diffusive process, 2log(~q) + log(D0), the blue markersrepresent the data and the blue line is the best fit for the data, exponent ∗ log(~q) + log(A),the parameters of which are in the captions. The exponent of the best fit for time points of4 minutes and 32 minutes is lesser than 1, whereas the exponent for time point 73 min is1.7, closer to 2 than the other time points. When the exponent is lesser than 2, this couldindicate that the process is faster than diffusion.

Commonalities observed in dispersion analyses across runs

Two main commonalities emerge from the dispersion relation analysis of these four runs.The first is the similarities between ic5aggregate100mg prep2 (ic5) and ic4slowinsitu100mg(ic4). In the best fits of the relaxation rates versus ~q, both have exponents between 1.1-1.3.In the plot of the KWW exponent α versus ~q, both ic5 and in the middle and late timepoints of ic4 have α values below 1. These similarities are particularly interesting giventhat ic5 had acquisition parameters of 5000 frames and 0.01 s exposure time per frame -parameters that we expected to cause damage in the sample - compared to beam damageoptimized parameters of 5000 frames and 0.00134 s for the same two parameters in ic4. Thesesimilarities are also striking given that the crystal structures of both samples are different -ic5 has predominantly FCC superlattices, whereas ic4 has a combination of FCC and HCPcrystal structures; both have aggregate backgrounds.

The second commonality exists between jp4aggregate100mg (jp4) and jp4aggregate100mg lowligand(jp4 low). In the plot of the KWW exponent α versus ~q, both have scalings for the relaxationrate dispersion best fit that are weaker than q−2. jp4a has a scaling between 0.6-0.7 in the


Fig

ure

5.33

:1D

SA

XS

pat

tern

at4

min

Fig

ure

5.34

:D

isp

ersi

onre

lati

onplo

tof

KW

Wex

pon

ent

at4

min

Fig

ure

5.3

5:

Dis

per

sion

rela

tion

plo

tof

rela

x-

ati

on

rate

at

4m

in.

Fit

para

met

ers

are

A=

27±

5A

2s−

1.expon

ent

=0.8

64±

0.0

03.D

=7000±

700A

2s−

1

Fig

ure

5.36

:1D

SA

XS

pat

tern

at32

min

Fig

ure

5.37

:D

isp

ersi

onre

lati

onplo

tof

KW

Wex

pon

ent

at32

min

Fig

ure

5.3

8:

Dis

per

sion

rela

tion

plo

tof

re-

laxati

on

rate

at

32

min

.F

itpara

met

ers

are

A=

4±

2A

2s−

1.expon

ent

=0.5

±0.1.D

=4000±

500A

2s−

1

Fig

ure

5.39

:1D

SA

XS

pat

tern

at73

min

Fig

ure

5.40

:D

isp

ersi

onre

lati

onplo

tof

KW

Wex

pon

ent

at73

min

Fig

ure

5.4

1:

Dis

per

sion

rela

tion

plo

tof

rela

x-

ati

on

rate

at

73

min

.F

itpara

met

ers

are

A=

500±

700A

2s−

1.expon

ent

=1.7

±0.1.D

=1400±

100A

2s−

1

Fig

ure

5.42

:D

isp

ersi

onre

lati

onan

alysi

sfo

rjp

4agg

rega

te10

0mg

low


first two time points and 0.3 at the late time point; in jp4 low there is more variation in thisvalue but this is still consistently lower than 2. Both also seem to have the same behaviorwith respect to the dispersion relation of α. The value of α decreases in value with increasing~q generally; in the earliest time point for both samples all the values of α are above 1, whilethe middle and late time points show this go below 1.

These commonalities can be seen more clearly in Figure 5.43, which is a collection ofselect 1D SAXS patterns, plots of α versus ~q and plots of relaxation rate versus ~q from allfour runs. The first commonality, which involves the similarities between ic4 and ic5, canbe seen in the first (analysis of ic5) and third (analysis of ic4) columns of the chart. Thesecond column, analysis of ic4 at another time point, is present to show the anomalous pointin this comparison as its α values are above 1. The second commonality, which involves thesimilarities between jp4 and jp4 low, can be seen in columns 4 (analysis of jp4 low) and 5(analysis of jp4).


Fig

ure

5.43

:O

verv

iew

ofpat

tern

sfo

und

indis

per

sion

rela

tion

s


5.5 Implications of observations

Discussion about whether observations are caused by beamdamage

Figure 5.44: Calculating g(2) at different attenuations of the beam in ic4slowinsitu100mg totest for beam damage

Even though, as discussed in Section 5.3, the acquisition parameters were tuned to accountfor beam damage, it is still important to test whether beam damage is the origin of theobserved dispersion relations for every run. As also discussed in Section 5.3, one way to ruleout beam damage is to perform XPCS bursts on two different points of the sample at differentstrengths of the beam. Figure 5.44 shows the results of such a test on ic4slowinsitu100mg


(ic4). Panels (a) and (b) show the g(2) decays unchanged at time point ∼ 50 minutes, evenwith changes in the strength of the beam from full beam in (a) to 20% of full beam in (b).This is also observed at time point ∼ 2 hours. This indicates that beam damage is probablynot the source of dispersion relations and g(2) observed in this run.

However, such tests were not performed during the experiment on the other three samples.As I discuss in Chapter 6, another way to test whether beam damage is the origin of thesedecays would be to recompute g(2) with a lower number of frames. If the decay is unaffectedby the number of frames, then beam damage is probably not the origin of these decays.

Hypotheses about results of dispersion relation analysis

The consistency of exponents between 1.1-1.3 observed in ic5 and ic4 indicates that the pro-cess responsible for this exponent is independent of the crystalline composition of the sample.As the process is detected using both acquisition parameters that induce damage (in ic5)and those that do not (in ic4), this indicates that the process occurs even if the compositionis changed due to beam effects. Thus, qualitative evidence points to the process underlyingthe near-unity value of the exponent to be independent of the microscopic structure (ie:ordered/disordered of constituents) in the sample.

As discussed in Section 3.2, when the exponent of the best fit power law for the ~q-dependence of the relaxation rate is lesser than 2, the processes associated with this relaxationare superdiffusive (faster than diffusion). This is observed in all dispersion relations ofrelaxation rate. As noted in Section 3.2, it has been empirically observed that dispersionrelationships of the relaxation rate which are faster than diffusive are associated with fasterthan exponential decay of the g(2) (KWW exponent > 1) [22, 15]. The initial hypothesisabout this observation has been proposed by Cipelletti et al., who proposed that the presenceof a ballistic relaxation rate dispersion relation and KWW exponent of 1.5 is a universalbehavior associated with aging/jamming in ‘glassy’ systems [24]. However, in both theobserved sets of correlations in our data there exists KWW exponents that are lesser than1, and even changes with ~q from greater to lesser than 1 (as seen in the second correlationobserved in jp4 and jp4 low).

The presence of a KWW exponent lesser than one and a ~q-dependence of the KWWexponent for some bursts - even with superdiffusive relaxation rate dispersion relations -has been observed in early time points of an aging process in colloidal gels [25]. This workproposed that since KWW > 1 indicates a jammed system, based on other empirical findings,a transition from KWW < 1 in early time points of the experiment to KWW > 1 in latetime points is evidence of a jamming transition. The work also notes that the reverse trend- of KWW > 1 in early time points and KWW < 1 has been observed in other systems.This trend can be seen in ic4, when KWW > 1 in the earliest time point and KWW < 1 atthe middle and late time points. This could indicate a process that moves from more to lessjamming over time - however, analysis of the KWW exponent dispersion relation at morefinely-spcaed time points in ic4 could shed more light on this process.


The study also notes that some intermediate time points of the aging process had KWWexponents with a ~q-dependence, with KWW > 1 in smaller ~q’s and the value of KWWdecreasing to 1 in larger values ~q, calling this process “unjamming”. The origin of thisprocess was conjectured to be due to small length-scale rearrangements of the gel network.We could be observing a process of “unjamming” in the second set of correlations observedbetween jp4 and jp4 low, which had KWW exponents > 1 for smaller ~q values.

The main conclusions that can be drawn about our system is that there is a hyper-diffusiveprocess occurring that could be independent of the crystalline ordering of the superlatticesformed (this is especially apparent in ic4 and ic5). Based on the intriguing behavior of theKWW exponent, moving from values greater to lesser than 1 (more to less jammed) overtime in ic4 and over ~q for every time point in jp4 and jp4 low, another conclusion is thatjamming could be playing a role in the dynamics observed. As the ~q-range is 0.005-0.018 A−1(∼ 30-120 nm length scales), this process could correspond to perhaps collective motion ofseveral nanoparticles (4 nm diameter each) within a superlattice or aggregate (on the orderof a few micrometers), or sinking/other relative motion of the aggregates and superlattices.Jamming could manifest in these systems as nanocrystals frozen in a disordered aggregate,or superlattices and aggregates in a pile at the bottom of the capillary (which we visuallyobserved and thus rastered our beam at the bottom of the capillary for good signal-to-noise).An understanding of how the KWW exponent changes for more closely spaced time points inthe runs of the four samples (ic4, ic5, jp4, jp4 low) could potentially aid in understanding therole of jamming in the collective motions of nanoparticles or aggregates/superlattices, andpotentially help distinguish between the origins of this jamming (either due to nanocrystalsin an aggregate or superlattices and aggregates in a pile).

63

Chapter 6

Conclusions

6.1 Summary of findings

The aim of this thesis, as Chapter 1 explains, is to explain the autocorrelation decays ob-tained in XPCS experiments conducted at NSLS-II on the in-situ self assembly of nanocrystalsuperlattices and to infer which processes these decays implied. In preparation for conduct-ing the experiment, my lab colleagues and I conducted preliminary characterizations of theself assembly process using optical techniques like UV-Vis and DLS. We used these char-acterizations to obtain a rough sense of the macroscopic timescales of self assembly for thepurpose of knowing which parts of the self assembly to optimize for with our acquisitionscheme. We also used these techniques to understand the effect of the concentration ofcolloidal gold on the macroscopic timescales for self assembly. Understanding what goldconcentration to use (100 mg/ml) helped us establish the thickness of the capillary neededfor good signal-to-noise ratio from our data collection. My colleagues and I also explored theparameter space of the self assembly protocol before and during the experiment to optimizethe signal-to-noise ratio for both SAXS and XPCS. Finally, my colleagues and I worked oncreating reactors for in-situ self assembly for both UV-Vis preliminary characterization andthe NSLS-II experiment.

On obtaining the data, my task was to understand which of the runs of the experi-ment contained viable g(2) decays, and at what range of ~q were they present. I found g(2)

decays at a ~q value of 0.006 A−1 in four samples – three partially in-situ self assembled sam-ples ic4slowinsitu100mg (ic4), jp4aggregate100mg (jp4) and jp4aggregate100mg lowligand(jp4 low), and one fully glove-box self assembled sample ic5agg100mg prep2 (ic5). I alsoanalyzed samples without g(2) decays – a fully in-situ self assembled sample In Situ # 4and another partially in-situ self assembled sample ic4slowinsitu100mgtake2(ic4 2) – to un-derstand what the samples that had g(2) decays had in common. I defined four qualitativeattributes (the self assembly setup used, the signal strength of the scattered x-rays, the pres-ence of colloidal and/or aggregate backgrounds, and the crystal structure present) to aid infinding these connections. The samples that had g(2) decays were present only when the sam-

CHAPTER 6. CONCLUSIONS 64

ple was partially or fully assembled in the glovebox, had high intensity scattered x-rays, hadan aggregate background and not a colloidal one, and had some FCC supercrystals present(ic5 and In Situ # 4 had only FCC, the other three had FCC and HCP crystal structures).Taken together, these findings suggest that the x-ray beam affects the self assembly processin some capacity, which must be taken into account, especially since decreasing the x-rayflux of the bursts too much clearly precludes obtaining g(2) decays. Furthermore, given thatthe presence of an aggregate signal correlates strongly to high overall signal-to-noise ratiog(2) decays, it must be a primary contributor to these decays themselves. It is possible thatthe colloidal background appears only when it is not overtaken by this aggregate signal butthat it is actually present in all cases, albeit not detectable unless the signal from othercontributions is strong.

The next step was to find the dispersion relations of the relaxation rates and KWWexponents (α) obtained from fitting g(1) (obtained from the g(2) decays using the Siegertrelation) to the KWW function. These decays were found between ten equally spaced ~qcenters from 0.005 to 0.018 A−1. I conducted this dispersion relation analysis on the fourruns that contained g(2) decays, and picked three time points at early, middle and late stagesof self assembly (the two exceptions to this were ic5, as it contained only one usable burst,and jp4, which had bursts with good signal-to-noise for only the first 15 minutes of selfassembly).

On doing this analysis I found two main commonalities. The first one was between ic5and ic4, which both had relaxation rates that depended on ~q with a scaling between 1.1-1.3,and had values of α lesser than 1. However, ic4 had values of α greater than 1 in the earliesttime point analyzed, which became lesser than 1 in middle and late time points. The secondconnection was between jp4 and jp4 low, which both predominantly had scalings of ~q withrespect to the relaxation rate that were lesser than 1. Both also had values of α that showeda ~q dependence, with values being greater than 1 at low ~q and dipping to below 1 at highervalues of ~q.

The conclusions that I drew from this analysis were that the process occurring couldbe independent of the crystalline structure of the sample. This is particularly evident inic4 and ic5, which had similar scaling of ~q with respect to the relaxation rate irrespectiveof their different crystal structures and different acquisition parameters (ic5 had parametersthat caused beam damage, ic4 had beam damaged optimized parameters). The decays foundin all four of the samples correspond to length scales between ∼ 30-120 nm, which couldbe due to perhaps collective motion of several nanoparticles (4 nm diameter each) withina superlattice or aggregate (on the order of a few micrometers), or sinking/other relativemotion of the aggregates and superlattices. The process is faster than diffusion as ~q roughlyscales linearly with the relaxation rate. The qualitative assessment of a change in values of αfrom greater to lesser than 1 (indicating a move from higher to lower jamming) over time inic4 and over values of ~q in jp4 and jp4 low is evidence for the role of jamming in the system,as explained in Section 5.5. Given that we interrogated the bottom of the XPCS capillary,where we expected the accumulation of the forming SLs and other aggregates, these findingslikely explain how such species enter (sink into) the beam volume or how they shift or relax


upon landing on one another, or could explain how nanocrystals in a disordered aggregatemove.

6.2 Future work

The analysis of the XPCS data has revealed some very interesting findings, and it alsoprovided ample opportunity to delve deeper into the work.

The first future step would be to make this analysis more quantitative by accounting morerigorously for beam damage. While ic5 has acquisition parameters that showed damage inour tests in Section 3.3, to be sure this burst (along with jp4 and jp4 low) must be analyzedfor impacts of beam damage. As briefly discussed in Section 5.5, another way to test whetherbeam damage is the origin of these decays would be to recompute g(2) with a lower numberof frames taken from either the first part or the latter part of a burst. If the resulting g(2)

decay is comparable to that obtained from the full burst then beam damage is probably notthe origin of these decays. The reason why this can be used to rule out beam damage is forthe same reason why checking for the dependence of the decay on beam attenuation is usedas a test of beam damage. Since the critical dose for damage is proportional to Nfr ∗ tfr ∗Fc,reducing Nfr would reduce the dose received by the sample. If one choice of Nfr is belowthe critical dose and the other is above Nfr, then there should be an associated decay thatwould only be present for the latter or there should be a difference between the two g(2)s.

Another exciting avenue would be to extend this analysis to our data with lower signalstrength to be able to analyze the dynamics, for example, in the fully in-situ runs. If thehypothesis that this thesis presents is true, that there are quasi-ballistic processes occurringin both aggregates and superlattices or in the nanocrystals within these structures, then theonly reason why we are unable to see this process in other samples is due to poor signal-to-noise ratio. One way to circumvent this is to average the g(2)’s of several bursts in eachsample to compensate for the noise.

Finally, what would be very fascinating is a quantitative analysis that carefully examinesthe dispersion relations of α and the relaxation rate at more closely spaced time pointsfrom self assembly initiation. Tracking changes in α more granularly and with error barscould help tease apart the similarities and differences between the processes occuring inic4/ic5 and jp4/jp4 low, and it would clarify whether we are seeing processes related tojamming. If a deeper insight into how α changes with respect to various time points revealsconcrete jamming processes, this could either point to the collective motions of superlatticesand aggregates sinking to a pile at the bottom of the capillary or, more excitingly, couldpotentially shed light into collective motions of nanocrystals in superlattices and aggregates,providing key insight into the dynamics of self assembly.

Tracking changes in both α and relaxation rate more closely could also help us relatethe dynamics we are seeing with XPCS to the kinetics that time-resolved SAXS allowsus to see. Linking both pieces of information could potentially give us a more informed,quantitative picture of self assembly Au superlattices. Understanding the self assembly of


these strongly coupled superlattices is more crucial than ever, as this understanding couldreveal the path to creating strongly coupled semiconductor superlattices with highly tunablebandgaps. As these systems would address the ever-increasing demand for developing cost-effective materials for technologies like solar-cells, the need to spatially and temporally resolvethe self assembly of strongly coupled superlattices is equally pressing and crucial for a moresustainable future.

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