NanomaterialsNanomaterials

Nathan LiangNathan Liang

Paul MaynardPaul Maynard

Wei Li Wei Li

NanotechnologyNanotechnology

What is Nanotechnology?What is Nanotechnology?

It comprises any technological It comprises any technological developments on the nanometer scale, developments on the nanometer scale, usually 0.1 to 100 nm.usually 0.1 to 100 nm.

One nanometer equals one thousandth of One nanometer equals one thousandth of a micrometer or one millionth of a a micrometer or one millionth of a millimeter.millimeter.

It is also referred as microscopic It is also referred as microscopic technology.technology.

Molecular NanotechnologyMolecular Nanotechnology

The term nanotechnology is often used The term nanotechnology is often used interchangeably with molecular interchangeably with molecular nanotechnology (MNT)nanotechnology (MNT)MNT includes the concept of MNT includes the concept of

mechanosynthesis.mechanosynthesis.MNT is a technology based on positionally-MNT is a technology based on positionally-

controlled mechanosynthesis guided by controlled mechanosynthesis guided by molecular machine systems.molecular machine systems.

NanotechnologyNanotechnologyin Field of Electronicsin Field of Electronics

MiniaturizationMiniaturizationDevice DensityDevice Density

HistoryHistory

Richard FeynmanRichard Feynman 1959, entitled ‘1959, entitled ‘There's Plenty of Room at the BottomThere's Plenty of Room at the Bottom’’ Manipulate atoms and molecules directlyManipulate atoms and molecules directly 1/101/10thth scale machine to help to develop the next scale machine to help to develop the next

generation of 1/100generation of 1/100thth scale machine, and so forth. scale machine, and so forth.

As things get smaller, gravity would become less As things get smaller, gravity would become less important, surface tension molecule attraction important, surface tension molecule attraction would become more important.would become more important.

HistoryHistory

Tokyo Science University professor Norio Tokyo Science University professor Norio TaniguchiTaniguchi 1974 to describe the precision manufacture of 1974 to describe the precision manufacture of

materials with nanometre tolerances. materials with nanometre tolerances.

K Eric DrexlerK Eric Drexler 1980s the term was reinvented1980s the term was reinvented 1986 book 1986 book Engines of Creation: The Coming Era of Engines of Creation: The Coming Era of

NanotechnologyNanotechnology. . He expanded the term into He expanded the term into Nanosystems: Molecular Nanosystems: Molecular

Machinery, Manufacturing, and ComputationMachinery, Manufacturing, and Computation

Nanomaterial and DevicesNanomaterial and Devices

Small ScalesSmall ScalesExtreme PropertiesExtreme PropertiesNanobotsNanobots

Self-Assemble Self-Assemble

Nanodevices build themselves Nanodevices build themselves from the bottom up.from the bottom up.

Scanning probe microscopyScanning probe microscopy Atomic force microscopes Atomic force microscopes scanning tunneling microscopes scanning tunneling microscopes scanning the probe over the surface scanning the probe over the surface

and measuring the current, one can and measuring the current, one can thus reconstruct the surface structure thus reconstruct the surface structure of the material of the material

Problems in Nanotechnology Problems in Nanotechnology

how to assemble atoms and molecules how to assemble atoms and molecules into smart materials and working devices?into smart materials and working devices?Supramolecular chemistrySupramolecular chemistryself-assemble into larger structures self-assemble into larger structures

Current NanotechnologyCurrent Nanotechnology

Stanford UniversityStanford University extremely small transistorextremely small transistor two nanometers wide and regulates electric current through a two nanometers wide and regulates electric current through a

channel that is just one to three nanometers longchannel that is just one to three nanometers long ultra-low-power ultra-low-power

IntelIntel processors with features measuring 65 nanometers processors with features measuring 65 nanometers

20 nanometer transistor

Atomic structure

Gate oxide less than 3 atomic layers thick

PlasmonsPlasmons

Waves of electrons traveling along the surface of Waves of electrons traveling along the surface of metalsmetals

They have the same frequency and They have the same frequency and electromagnetic field as light.electromagnetic field as light.

Their sub-wavelength require less space.Their sub-wavelength require less space. With the use of plasmons information can be With the use of plasmons information can be

transferred through chips at an incredible speed transferred through chips at an incredible speed

Nanomaterial modeling and Nanomaterial modeling and simulation typessimulation types

What I will coverWhat I will cover

Carbon NanotubesCarbon NanotubesBio-Nano-MaterialsBio-Nano-MaterialsThermoelectric NanomaterialsThermoelectric NanomaterialsWhat is happening at UKWhat is happening at UK

Carbon NanotubesCarbon Nanotubes

What are they?What are they?Carbon molecules aligned in cylinder Carbon molecules aligned in cylinder

formationformationWho discovered them?Who discovered them?

Researchers at NEC in 1991Researchers at NEC in 1991What are some of their uses?What are some of their uses?

Minuscule wiresMinuscule wiresExtremely small devicesExtremely small devices

Potential energyPotential energyVk = Repulsive forceVk = Repulsive forceVa = attractive forceVa = attractive force

Morse potential equationsMorse potential equations

Carbon NanotubesCarbon Nanotubes

total potential of a systemtotal potential of a system

Adds the NB contributionAdds the NB contribution

Force of interactionForce of interaction

Carbon NanotubesCarbon Nanotubes

Leonard – Jones potential with von der Waals Leonard – Jones potential with von der Waals

interactioninteraction

Geen - Kudo relationGeen - Kudo relation

Bio-NanomaterialsBio-Nanomaterials

What is Bio-Nanomaterials?What is Bio-Nanomaterials? Putting DNA inside of carbon nanotubesPutting DNA inside of carbon nanotubes

What can this research give us?What can this research give us? There are lots of chemical and biological applicationsThere are lots of chemical and biological applications

Distances over timeDistances over time

Van der waals engeryVan der waals engery

Radical density profilesRadical density profiles

Thermoelectric NanomaterialsThermoelectric Nanomaterials

Concepts before modeling can begin:Concepts before modeling can begin: ZT ZT = = TTσσSS2/κ2/κ

T = temperatureT = temperature σ = electrical conductivityσ = electrical conductivity S = Seebeck constantS = Seebeck constant

κ = κph +κelκ = κph +κel K = sum of lattice and electronic contributionsK = sum of lattice and electronic contributions

Potential across thermoelectric materialPotential across thermoelectric material

Boltzmann transportBoltzmann transport

The Modeling equationsThe Modeling equations

Thermoelectric NanomaterialsThermoelectric Nanomaterials

Thermoelectric NanomaterialsThermoelectric Nanomaterials

Thermoelectric NanomaterialsThermoelectric Nanomaterials

Nanomaterials at UKNanomaterials at UK Deformation Mechanisms of Nanostructured Materials Deformation Mechanisms of Nanostructured Materials Synthesis of Nanoporous Ceramics by Engineered Synthesis of Nanoporous Ceramics by Engineered

Molecular Assembly Molecular Assembly Carbon Nanotubes Carbon Nanotubes Optical-based Nano-Manufacturing Optical-based Nano-Manufacturing The Grand Quest: CMOS High-k Gate Insulators The Grand Quest: CMOS High-k Gate Insulators Self-assembled metal alloy nanostructures Self-assembled metal alloy nanostructures Rare-earth Monosulfides: From Bulk Samples to Rare-earth Monosulfides: From Bulk Samples to

Nanowires Nanowires Thermionic Emission and Energy Conversion with Thermionic Emission and Energy Conversion with

Quantum Wires Quantum Wires Resonance-Coupled Photoconductive Decay Resonance-Coupled Photoconductive Decay

Computer Simulation of Computer Simulation of Fluorinated SurfactantsFluorinated Surfactants

Introduction to surfactant and self-assemblyIntroduction to surfactant and self-assembly

What is surfactant?What is surfactant?

What is self-assembly?What is self-assembly?

Micelles, mesophasesMicelles, mesophases

1. Davis, H. T., Bodet, J. F., Scriven, L. E., Miller, W. G. Physics of Amphiphilic Layers, 1987, Springer-Verlag, New York

Introduction to fluorinated surfactantsIntroduction to fluorinated surfactants Unique properties introduced by the strong electronegativity of Unique properties introduced by the strong electronegativity of

fluorine and the efficient shielding of the carbon atoms by fluorine fluorine and the efficient shielding of the carbon atoms by fluorine atomsatoms

Fluorocarbon chain is Fluorocarbon chain is stifferstiffer, and favors aggregates with low , and favors aggregates with low curvature (curvature (Fig from [2]Fig from [2]))

Advantages over hydrocarbon chains: higher surface activity , Advantages over hydrocarbon chains: higher surface activity , thermal, chemical, and biological inertness, gas dissolving capacity, thermal, chemical, and biological inertness, gas dissolving capacity, higher hydrophobicityhigher hydrophobicityand lipophobicityand lipophobicity

R-NC5H5+Cl- CMC(mM) @ 298 K

C12H25- 15.5 3

C8H17- 275 4

C6F13C2H4- 16.2 3

C4F9C2H4- 170 4

2. M. Sprik, U. Rothlisberger and M. L. Klein, Molec. Phys. 1999 97:3553. K. Wang, G. Karlsson, M. Almgren and T. Asakawa, J. Phys. Chem. B 1999 103:92374. E. Fisicaro, A. Ghiozzi, E. Pelizzetti, G. Viscardi and P. L. Quagliotto, J. Coll. Int. Sci. 1996 182:549

Motivations for the computer simulation of Motivations for the computer simulation of fluorinated surfactantsfluorinated surfactants

Simulations can be treated as computer experiments that serve as Simulations can be treated as computer experiments that serve as adjuncts to theory and real experimentsadjuncts to theory and real experiments

Experiment is a viable way to study the effect of chain stiffness, yet Experiment is a viable way to study the effect of chain stiffness, yet it might be expensive to do a systematic study on this topic. it might be expensive to do a systematic study on this topic.

Computer simulations might help selecting surfactants for the right Computer simulations might help selecting surfactants for the right type of mesophase, which provides a guideline for experimental type of mesophase, which provides a guideline for experimental study. study.

Monte Carlo techniques for the simulation of Monte Carlo techniques for the simulation of surfactant solutionssurfactant solutions

Off-lattice atomistic simulationOff-lattice atomistic simulation

All atoms (or small group of atoms, e.g. All atoms (or small group of atoms, e.g. CH2CH2 ) are explicitly represented) are explicitly represented Most interactions are included, more realistic, yet hard to modelMost interactions are included, more realistic, yet hard to model Can simulates molecular trajectories on a time-scale of nanosecondsCan simulates molecular trajectories on a time-scale of nanoseconds Can’t simulation the self-assembly phenomenaCan’t simulation the self-assembly phenomena

Off-lattice coarse-grainOff-lattice coarse-grain A number of atoms are grouped together and represented in a simplified A number of atoms are grouped together and represented in a simplified

mannermanner Electrostatic and dihedral angle potentials are usually absentElectrostatic and dihedral angle potentials are usually absent Can simulate process happening on a time-scale of microseconds, e.g. Can simulate process happening on a time-scale of microseconds, e.g.

micelle formationmicelle formation Can’t simulate equilibrium self-assembly structure at higher concentrationCan’t simulate equilibrium self-assembly structure at higher concentration

Monte Carlo techniques for the simulation of Monte Carlo techniques for the simulation of surfactant solutions surfactant solutions (continued)(continued)

Lattice coarse-grainLattice coarse-grain replacing the continuous space with a discretized lattice of suitable replacing the continuous space with a discretized lattice of suitable

geometrygeometry Electrostatic and intra-molecular potentials are absentElectrostatic and intra-molecular potentials are absent Fast, efficient, can simulate process happening on a time-scale of a few Fast, efficient, can simulate process happening on a time-scale of a few

hours, e.g. mesophase formationhours, e.g. mesophase formation Based on Based on Flory-Huggins TheoryFlory-Huggins Theory. Proven to be successful in polymer . Proven to be successful in polymer

science for many years for investigating universal properties of single science for many years for investigating universal properties of single chains, polymer layers and solutions and meltschains, polymer layers and solutions and melts

Utility of the model is limitedUtility of the model is limited

Choosing the right model for our simulation Choosing the right model for our simulation purpose – lattice coarse-grainpurpose – lattice coarse-grain

Most time-consuming part in a MC simulation is the evaluation of Most time-consuming part in a MC simulation is the evaluation of inter and intra-molecular potentials after each trial moveinter and intra-molecular potentials after each trial move

The speed of off-lattice models is limited, becauseThe speed of off-lattice models is limited, because It has to reevaluate the potential functions explicitly when calculate the It has to reevaluate the potential functions explicitly when calculate the

energy change after each moveenergy change after each move The speed of the simulation is determined by the complexity of the The speed of the simulation is determined by the complexity of the

potential functionspotential functions Off-lattice can at most simulate the formation of a few micellesOff-lattice can at most simulate the formation of a few micelles

Lattice models are fast, because Lattice models are fast, because Atoms (united atoms) are moving on the lattice, intra and inter-molecular Atoms (united atoms) are moving on the lattice, intra and inter-molecular

distance, bond angles are thus discretizeddistance, bond angles are thus discretized It’s possible to precalculate the potentials corresponding to certain It’s possible to precalculate the potentials corresponding to certain

distance and angles and build look-up tablesdistance and angles and build look-up tables When calculate the energy change, only need to look up the tablesWhen calculate the energy change, only need to look up the tables Can simulate the mesophase formation efficientlyCan simulate the mesophase formation efficiently

Our targeted system: mesophase formation in surfactant solutionsOur targeted system: mesophase formation in surfactant solutions

Larson’s Lattice Model – representation of Larson’s Lattice Model – representation of the systemthe system

Targeted system: a surfactant solution consists of Targeted system: a surfactant solution consists of NNAA moles water, moles water, NNBB moles oil and moles oil and NNcc moles surfactant molecules, with fixed volume moles surfactant molecules, with fixed volume and temperature (canonical ensemble)and temperature (canonical ensemble)

Surfactant: use Surfactant: use HHiiTTjj to define a linear surfactant consisting of a string to define a linear surfactant consisting of a string of consecutive of consecutive ii head units attached to consecutive head units attached to consecutive jj tail units. tail units.

Whole system resides on an N×N×N cubic lattice, periodic boundary Whole system resides on an N×N×N cubic lattice, periodic boundary conditions are appliedconditions are applied

Oil and water molecules occupy single sites on the lattice, and each Oil and water molecules occupy single sites on the lattice, and each amphiphile occupies a sequence of adjacent or diagonally adjacent amphiphile occupies a sequence of adjacent or diagonally adjacent sites (equal molar volume for all the species)sites (equal molar volume for all the species)

Number of sites occupied by surfactant is,Number of sites occupied by surfactant is,

The rest of the sites is fully occupied by water and oil according to The rest of the sites is fully occupied by water and oil according to their volume ratiotheir volume ratio

CBA

C

NjiNN

NjiN

)(

)(3

Larson’s Lattice Model – interactions Larson’s Lattice Model – interactions between speciesbetween species

Each site interacts Each site interacts onlyonly with its 8 with its 8 nearest, 9 diagonally nearest, and 9 nearest, 9 diagonally nearest, and 9 body-diagonally nearest neighborsbody-diagonally nearest neighbors

Essentially, a square well potential is Essentially, a square well potential is appliedapplied

Favorable interactions are set to be -Favorable interactions are set to be -1, while unfavorable interactions are 1, while unfavorable interactions are +1+1

Total energy is pairwise additiveTotal energy is pairwise additive ijtotal EE (i, j=water, oil, head, tail)

Square-well potential

A simple 2D lattice with 2 chains, 7 water (grey) and 6 oil (red) molecules

Larson’s Lattice Model - typical trial movesLarson’s Lattice Model - typical trial moves

Pair interchange [5]Pair interchange [5] Exchange of positions of two simple moleculesExchange of positions of two simple molecules

Chain kink [5]Chain kink [5] A surfactant segment exchanges position with A surfactant segment exchanges position with

its neighbor without breaking the surfactant its neighbor without breaking the surfactant chainchain

Chain reptation [5]Chain reptation [5] One chain end moves to a neighboring site, One chain end moves to a neighboring site,

and the rest of that chain slithers a unit to keep and the rest of that chain slithers a unit to keep the chain connectivitythe chain connectivity

Chain multiple kink [6]Chain multiple kink [6] If a kink move creates a single break in the If a kink move creates a single break in the

chain, the simple molecule will continue to chain, the simple molecule will continue to exchange with subsequent beads along the exchange with subsequent beads along the chain until beads on the chain are close chain until beads on the chain are close enough to reconnect. enough to reconnect.

5. R. G. Larson, L.E. Scriven and H. T. Davis, J. Chem. Phys. ,1985, 83, 2411

6. K.R. Haire, T.J. Carver, A.H. Windle, Computational and Theoretical Polymer Science, 2001, 11, 17

Larson’s Lattice Model – simulation processLarson’s Lattice Model – simulation process

Initialize the systemInitialize the system Put the system in a random statePut the system in a random state

Make a trial moveMake a trial move Randomly conduct a trial move according toRandomly conduct a trial move according to

its occurrence ratioits occurrence ratio Calculate the energy changeCalculate the energy change

Reevaluate the interactions of the moved Reevaluate the interactions of the moved particles with its neighbors and calculate particles with its neighbors and calculate the energy changethe energy change

Accept the trial move with the Metropolis schemeAccept the trial move with the Metropolis scheme

Keep trying the moves until system approach equilibriumKeep trying the moves until system approach equilibrium Either monitor the total energy change, or monitor the structure formed Either monitor the total energy change, or monitor the structure formed

in the simulation boxin the simulation box SamplingSampling

Sample a certain property over a certain number of configurationsSample a certain property over a certain number of configurations

01

0)exp(

E

ETk

EP

b

A simple 2D lattice with 2 chains, 7 water (grey) and 6 oil (red) molecules

Simulation of the mesophase formation - Simulation of the mesophase formation - preliminary resultspreliminary results

Simulation procedure:Simulation procedure: Start the simulation from a higher temperature and Start the simulation from a higher temperature and

equilibrate the system, in order to make the equilibrate the system, in order to make the system in a athermal state and as random as system in a athermal state and as random as possiblepossible

Anneal the system by decreasing the temperature Anneal the system by decreasing the temperature in a small amount after the system reaches in a small amount after the system reaches equilibrium at a higher temperatureequilibrium at a higher temperature

When the temperature is lower than the critical When the temperature is lower than the critical temperature, sample the density of a certain temperature, sample the density of a certain speciesspecies

Preliminary resultsPreliminary results 60vol% H4T4 surfactant, 40vol% water60vol% H4T4 surfactant, 40vol% water Should form cylindrical structure according to Should form cylindrical structure according to

Larson’s report [7]Larson’s report [7] The right figures are the same self-assembly The right figures are the same self-assembly

structure viewed from two different perspectivesstructure viewed from two different perspectives

3D density contour plot according to the oil concentration. 60% H4T4 surfactant, 40% water

7. R. G. Larson; Chemical Engineering Science, 1994, 49, 17, 2833

Add the bond overlapping constraintAdd the bond overlapping constraint

Bond overlapping may occurred Bond overlapping may occurred in the system, which is unrealisticin the system, which is unrealistic

Simulation results after adding Simulation results after adding the bond overlapping constrain the bond overlapping constrain (other conditions are the same). (other conditions are the same). Perfect hexagonal close packing Perfect hexagonal close packing cylindrical structure is formed. cylindrical structure is formed.

3D density contour plot according to the oil concentration. 60% H4T4 surfactant, 40% water

Two chains overlaps with each other

Verification of our lattice simulation program Verification of our lattice simulation program – compare with Larson’s simulation results– compare with Larson’s simulation results

Ternary phase diagram of Ternary phase diagram of HH44TT44 surfactant in water and surfactant in water and oil by Larson’s lattice Monte oil by Larson’s lattice Monte Carlo simulation [8]Carlo simulation [8]

5 data points (volume 5 data points (volume percentage)percentage) 40% water, 40% oil, 20% 40% water, 40% oil, 20%

surfactantsurfactant 20% water, 40% oil, 40% 20% water, 40% oil, 40%

surfactantsurfactant 20% water, 45% oil, 35% 20% water, 45% oil, 35%

surfactantsurfactant 60% water, 40% surfactant60% water, 40% surfactant 7.3% water, 32.7% oil, 60% 7.3% water, 32.7% oil, 60%

surfactantsurfactant 40% water, 60% surfactant40% water, 60% surfactant

8. R. G. Larson; J. Phys. II France, 1996, 6, 1441

Simulation results from our simulation Simulation results from our simulation programprogram

40% water, 40% oil, 20% 40% water, 40% oil, 20% surfactant - surfactant - BicontinuousBicontinuous mesophasemesophase

20% water, 40% oil, 40% 20% water, 40% oil, 40% surfactant - lamellar without holes surfactant - lamellar without holes mesophasemesophase

20% water, 45% oil, 35% 20% water, 45% oil, 35% surfactant - lamellar with holes surfactant - lamellar with holes mesophasemesophase

Left: oil concentration profile, Right: water concentration profile

Simulation results from our simulation Simulation results from our simulation program program (continued)(continued)

60% water, 40% surfactant – spherical 60% water, 40% surfactant – spherical structure, plot according to the structure, plot according to the surfactant tail densitysurfactant tail density

7.3% water, 32.7% oil, 60% surfactant 7.3% water, 32.7% oil, 60% surfactant – intermediate bicontinuous structure – intermediate bicontinuous structure (might be gyration structure), plot (might be gyration structure), plot according to the water densityaccording to the water density

40% water, 60% surfactant – 40% water, 60% surfactant – hexagonal close packing cylindrical hexagonal close packing cylindrical structure, plot according to the structure, plot according to the surfactant tail densitysurfactant tail density

Left: oil concentration profile, Right: water concentration profile

An application of lattice MC simulation – the effect An application of lattice MC simulation – the effect of wall textures on the self-assembly structureof wall textures on the self-assembly structure

Motivation: nanostructured materialsMotivation: nanostructured materials SiOSiO22 source, ethanol, water, catalyst + surfactants give ordered phases source, ethanol, water, catalyst + surfactants give ordered phases Mimic surfactant mesophases (coassembled)Mimic surfactant mesophases (coassembled) Calcination gives ordered mesoporesCalcination gives ordered mesopores

Figures from 9. C.J. Brinker et al. Advanced Materials 1999 11: 579

Motivations to study the textured wallsMotivations to study the textured walls

Real substrate surface may not be flatReal substrate surface may not be flat For hierarchical materials (macroporous / mesoporous), curved For hierarchical materials (macroporous / mesoporous), curved

surfaces may be presentsurfaces may be present Design of nanostructure using surface texturing – use nano-Design of nanostructure using surface texturing – use nano-

patterned substrate to control the orientation of the self-assembly patterned substrate to control the orientation of the self-assembly structurestructure Mesopores perpendicular to the substrate is desiredMesopores perpendicular to the substrate is desired Use the texture on the substrate to make the mesopores perpendicular Use the texture on the substrate to make the mesopores perpendicular

to the substrateto the substrate

Simulation results without walls and with flat Simulation results without walls and with flat wallswalls

Targeted system: Targeted system: 60% H4T4 surfactant, 40% water 60% H4T4 surfactant, 40% water

solventsolvent

The simulation without wallsThe simulation without walls Hexagonal close packing cylindrical Hexagonal close packing cylindrical

structuresstructures From the figure, d spacing = 10.7σ , From the figure, d spacing = 10.7σ ,

unit cell parameter = 12.4σunit cell parameter = 12.4σ

The simulation results with flat wallsThe simulation results with flat walls Whether walls are hydrophilic or Whether walls are hydrophilic or

hydrophobic, cylindrical structure are hydrophobic, cylindrical structure are always parallel to the wall and sits on always parallel to the wall and sits on the (1, 0, 0) planethe (1, 0, 0) plane

Self-assembly structure with hydrophobic (left) and hydrophilic (right) walls, according to oil density

The nano-structures prepared by the evaporation-induced dip-coating process

Wave-patterned wall texture applied in the Wave-patterned wall texture applied in the simulationsimulation

Walls are treated as a set of block sites, Walls are treated as a set of block sites, which can be neither occupied nor which can be neither occupied nor penetrated by any moleculespenetrated by any molecules

Interactions between wall site and other Interactions between wall site and other components in the system are set to +10 components in the system are set to +10 or -10, to emphasize the wall existenceor -10, to emphasize the wall existence

The form of the 3D wave function:The form of the 3D wave function:

Illustration of a discretized wave pattern Illustration of a discretized wave pattern with wall thickness = 2 and wave with wall thickness = 2 and wave amplitude = 2amplitude = 2

Periodic boundary conditionsPeriodic boundary conditions

Wave pattern with wall thickness = 2 and wave amplitude = 2

Lattice Monte Carlo simulation results for the Lattice Monte Carlo simulation results for the hydrophilic textured wallshydrophilic textured walls

Simulation results of 30x30x30 and Simulation results of 30x30x30 and 30x30x40 simulation box, wave 30x30x40 simulation box, wave amplitude = 1amplitude = 1

Surface pattern doesn’t change the Surface pattern doesn’t change the structure much at lower wall spacing. structure much at lower wall spacing. Walls sit on the (2 1 0) plane.Walls sit on the (2 1 0) plane.

A little calculation:A little calculation: How many layer in the horizontal plane:How many layer in the horizontal plane:

Number of layers in the vertical plane:Number of layers in the vertical plane:

Box size = 30x30x30, wave amplitude = 1, plot according to the oil density

Box size = 30x30x40, wave amplitude = 1, plot according to the oil density

47.10

43.42230

d

25.24.12

28230

a

06.34.12

38240

a

Lattice Monte Carlo simulation results for the Lattice Monte Carlo simulation results for the hydrophilic textured walls hydrophilic textured walls (continued)(continued)

Surface pattern changes the self-Surface pattern changes the self-assembly structures at higher wall assembly structures at higher wall spacingspacing

Number of layers in the vertical placeNumber of layers in the vertical place 30x30x50 box, wall sits on (1, 0, 0) 30x30x50 box, wall sits on (1, 0, 0)

planeplane

30x30x60 box, wave amplitude = 1, 30x30x60 box, wave amplitude = 1, wall sits on (1, 0, 0) planewall sits on (1, 0, 0) plane

30x30x60 box, wave amplitude = 2, 30x30x60 box, wave amplitude = 2, wall sits on (2, 1, 0) planewall sits on (2, 1, 0) plane

Box size = 30x30x50, wave amplitude = 1, plot according to the oil density

Box size = 30x30x60, wave amplitude = 1 (left) and 2(right), plot according to the oil density

49.47.10

48250

d

42.57.10

58260

d

68.44.12

58260

a

Lattice Monte Carlo simulation results for the Lattice Monte Carlo simulation results for the textured wallstextured walls

With higher wall spacing, the With higher wall spacing, the amount of planar defects amount of planar defects increases, 2 layers with a different increases, 2 layers with a different orientation formed.orientation formed.

Same phenomena are not Same phenomena are not observed in systems with observed in systems with hydrophobic wallshydrophobic walls

Box size = 30x30x100, wave amplitude = 1, plot according to the oil density

Box size = 30x30x60, wave amplitude = 1, hydrophobic walls, plot according to the oil density

ConclusionsConclusions

Cylinders always align along diagonal of texture, even with small wave Cylinders always align along diagonal of texture, even with small wave amplitudeamplitude

For hydrophilic walls, small wall spacing with small wave amplitude only For hydrophilic walls, small wall spacing with small wave amplitude only distorts structuredistorts structure

For hydrophilic walls,For hydrophilic walls, large wall spacing with small wave amplitude large wall spacing with small wave amplitude promotes (1 0 0) orientationpromotes (1 0 0) orientation

For hydrophilic walls, planar defects may be more likely if wall spacing > For hydrophilic walls, planar defects may be more likely if wall spacing > space needed for # of layersspace needed for # of layers

systems with hydrophobic walls may avoid planar defects, becausesystems with hydrophobic walls may avoid planar defects, because the deposition of a monolayer of surfactant on the wall.the deposition of a monolayer of surfactant on the wall. The chain softness mitigates the patternThe chain softness mitigates the pattern

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