# TKP4190 - Fabrikasjon og anvendelse av nanomaterialer

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# Faglig innhold

Emnet tar for seg det termodynamiske grunnlaget og kinetikken for nukleering og vekst av nanopartikler med fokus på felling fra væskesystemer. Ulike mekanismer for nukleering og krystallvekst med tilhørende beregninger av nukleerings- og veksthastigheter gir grunnlag for design av partikkelpopulasjoner og anvendelsen av disse partiklene i i ulike systemer relevant for forskning og industri. Funksjonalisering av overflater vil bli behandlet.

Emnet tar videre for seg metoder for framstilling av katalysator og katalysatorbærere basert på utfelling, samt andre metoder som har spesiell relevans i forhold til katalysatorenes nanostruktur og funksjonalitet, for eksempel sol-gel og kolloidbasert framstilling. Relevante eksempler der stor betydning av partikkel- eller porestørrelse er påvist gjennomgår (Au, Co, Ni- katalysator og karbon nanofibre (CNF)). Det gis også en kort innføring i katalytiske modellsystemer og overflatevitenskap og deres eksperimentelle og teoretiske anvendelse innen katalyse.

# Pensumlitteratur

• Alle bøker er tilgjengelig som e-bok gjennom innsida
• En god del forskningsartikler som blir lastet opp på its-learning
• Pensumoversikten under (sist oppdatert i 2016)

# Pensum Del I (Jens-Petter Andreassen)

## Crystallization fundamentals

Morphology is the external shape of a crystal. Polymorphism is the internal crystal structure of a crystal.

#### Calcium Carbonate

CaCO3 has three basic forms, here ordered by decreasing solubility. Calcite is the least soluble, and therefore also most thermodynamically stable.

• Vaterite (hexagonal)
• Aragonite (rod-like)
• Calcite (cubic)

### Supersaturation

Supersaturation is the driving force for both nucleation and growth Concentration driving force: $\Delta c = c - c^*$ where c is the solution concentration and c* is the equilibrium saturation at a given temperature. Supersaturation ratio S is given as $S = \frac{c}{c^*}$ and the relative supersaturation ratio $\sigma = \frac{\Delta c}{c^*} = S-1$

Supersaturation can be created in three ways

• By dissolving reactant at high temperature, and then owering the temperature
• Only works if solubility is temperature-dependent
• By reduction of ionic precursor in solution
• By evaporating solvent to increase concentration of precursor
• By adding antisolvent to decrease the solubility of the precursor in the solution

## Nucleation

### Homogeneous nucleation

The free energy associated with nucleation consists of two parts working against each other; the energetically favorable formation of solids and the unfavorable formation of new surfaces. $\Delta G = \Delta G_S + \Delta G_V = 4\pi r^2 \gamma + \frac{4}{3}\pi r^3 \Delta G_v$ Here $\Delta G_S$ is the surface excess free energy, $\gamma$ is the interfacial tension between the phases, $\Delta G_V$ is the volume excess free energy and $\Delta G_v$ is the same per unit volume. At the point where the $\Delta G$-curve is at its max, we find the critical nucleus size: above this radius the nucleus is stable. Finding this size is straightforward: $\frac{\delta \Delta G}{\delta r} = 0 \Rightarrow r_{crit} = \frac{-2\gamma}{\Delta G_v} \Rightarrow \Delta G_{crit} = \frac{16 \pi \gamma^3}{3(\Delta G_v)^2} = \frac{4}{3}\pi r^2_{crit} \gamma$
Inserting $-\Delta G_v = \frac{k_B T \ln{S}}{\nu}$ the critical energy for nucleation is $\Delta G_{crit} = \frac{16 \pi \gamma^3 \nu^2}{3(k_B T \ln{S})^2}$
This energy originates from random fluctuations.

### Heterogeneous nucleation

Critical energy changed when a solid surface with lower surface energy is awailable. This can also bee seeds in solution.

$\Delta G_{crit,hetr} = \phi\Delta G_{crit,hom}, \phi = \frac{1}{4}(2+\cos{\theta})(1-\cos{\theta})$

theta is the contact angle found by Young's equation.

### Nucleation rate

Rate of nucleation can be expressed as an Arrhenius equation:

$J = A \exp(\frac{-\Delta G}{k_B T}) = A \exp(\frac{16 \pi \gamma^3 \nu^2}{3(k_B T \ln{S})^2})$

J can be changed by gamma-3, T3 and ln(S)2. A is the pre-exponential factor determined mainly by monomer addition frequency.

J is increased by

• Decreasing gamma
• add surfactant or change solvent
• Increasing T
• Faster monomer diffusion, but watch out for lower S
• Increasing S
• Often preferred because S can be varied by several orders of magnitude

#### Induction time

As counting the number of nucleus in a highly dynamic system is hard, induction time tind is introduced. tind is the time when the system has transitioned from its metastable state. It is an experimental value that varies depending on experimental technique. As tind is proportional to J-1, a plot of tind can reveal the change in nucleation rate for different parameters.

## Growth

### Diffusion controlled growth

Growth as change of particle radius per time is given as $\frac{dr}{dt} = D(C-C_S)\frac{V_m}{r}$ where r is the radius, D is the diffusion coefficient of the growth species, C is the bulk concentration, $C_S$ is the solubility concentration and $V_m$ is the molecular volume. Solving gives $r^2 = 2D(C-C_S)V_mt + r_0^2$

• Diffusion controlled growth promotes unisized particles
• Can be obtained by increasing supersaturation (driving force), increasing viscosity or introducing a diffusion barrier

Radius difference between particles decreases with time: $\delta r = \frac{r_0\delta r_0}{\sqrt{k_Dt + r_0^2}}$

### Surface integration controlled growth

Growth rate given by $G = \frac{dr}{dt}= k_g(S-1)^g$

• Spiral growth (most common): g = 2 at very low supersaturation and g = 1 at large supersaturation
• 2D Nucleation: g > 2
• Rough growth: g=1 (diffusion controlled)

Mononuclear growth (layer by layer): $\frac{dr}{dt} = k_mr^2 \Rightarrow \frac{1}{r}=\frac{1}{r_0} - k_mt$ and radius difference increases with time $\delta r = \frac{\delta r_0}{(1-k_mr_0t)^2}$
Polynuclear growth (multiple layers growing at once): $\frac{dr}{dt} = k_p \Rightarrow r=k_pt+r_0$ and radius difference remains unchanged $\delta r = \delta r_0$

### Growth determined morphology

• Low S - Spiral growth dominates by monomer integration at inherent stacking faults in the crystal.
• S above critical value for 2D-nucleation - Nucleuses form and monomers are added around these.
• High S - Surface nucleation happens quickly, leading to diffusion control and dendriting growth. S is consumed at corners and edges, leading to monocrystalline, symmetric, dendriting crystals forming
• Very high S - Monomer integration is no longer crystallographic and polycrystalline spherulites form

### Phase stability and size

Ostwald rule of stages states that when crystals grow, the polymorph with the fastest growth kinetics will form first. Over time the most thermodynamically stable form will grow by leeching from the other forms. For the CaCO3 system, amorphous calcium will first form, then vaterite, then aragonite followed by calcite, which is the most stable form.

These kinetics can be manipulated in many ways

• Slow the growth rate to have more stable crystals form faster.
• Add structure directing agents that bind selectively to specific sites to stop one polymorph from growing
• Such as alginate G-blocks to Calcium carbonate. (although the mechanism is debated)
• Such as Mg, which will incorporate into and lower the stability of calcite until aragonite is more stable
• Add capping ligands that stops growth and ostwald ripening alltogether

### Size dependent solubility

Due to the Thomsom-effect particles with higher curvature (small radius) will be more soluble than lower curvature particles (large radius). Small particles will therefore dissolve and shrink and large particles will grow larger. This process is called Ostwald ripening and is generally unwanted because it leads to less monodisperse particles.

### Mechanism behind spherulitic particles

Spherulitic particles are polycrystalline particles. There are two theories for their formation: non-classical nucleation (nano-aggregation) or by classical growth.

Requirements to claim non-classical nucleation

• Nucleation rate is fast enough to account for the high number of small nucleus required to build the sperulite crystals.
• These small nucleus should be detectable in solution

According to work by Jens-Petter S is not high enough to form enough nuclei for non-classical nucleation. In addition spherulitic growth was observed by time-resolved SEM microscopy.

## Synthesis of metallic nanoparticles

• Metal complexes in dilute solutions are reduced
• Stronger reducing agent --> smaller particles
• Polymers used as stabilizers and diffusion barriers

### Mechanisms for formation of spherical crystalline particles

• Aggregation
• Crystal Growth

### Influences on the synthesis

• From reducing agents
• Weak reduction agent: slow reaction rate, large particles. Slow reaction could lead to continuous formation of nuclei --> wide size distribution.
• Strong reduction agent: smaller particles.
• The growth rate affects morphology and polymorphism
• From other factors (Very specific examples in the text)
• Chloride ion concentration affects syntehsis of Pt nanoparticles from $H_2PtCl_6$
• Low concentration of reactant --> decreased reduction rate
• From polymer stabilizers
• Introduced to form a monolayer on nanoparticle surface to prevent agglomeration (stabilizer)
• Adsorption of polymer occupies growth sites --> growth reduced
• Diffusion barrier
• May also react with solute, catalyst or solvent

## 1-D nanostructures

### Techniques for growing

• Spontaneous growth (Bottom-up): Driven by reduction of chemical potential (like nanoparticles) only now anisotropic
• Evaporation-condensation growth: Supersaturation driven growth
• Different facets have different growth rates
• Dislocations in certain directions
• Poisoning of impurities (structure-directing agents) on specific facets
• Vapor-liquid-solid / Solution-liquid-solid (VLS/SLS)
• Precursor gas or solution is dissolved in liquid catalyst particle and upon saturation, selectively crystalized in one direction, growing out from the catalyst.
• Stress-induced recrystallization
• Template-based synthesis (Bottom-up)
• Electroplating and electrophoretic deposition
• Colloid dispersion, melt or solution filling
• Conversion with chemical reaction
• Electrospinning (Bottom-up)
• Lithography (Top-down)

## 2-D nanostructures

### Techniques for growing

• CVD
• Liquid based growth

### Initial nucleation

• Island growth / Volmer-Weber growth
• contact angle larger than 0
• Layer growth / Frank-van der Merwe growth
• contact angle equal 0
• homoepitaxy, when lattice constant is equal
• Island layer / Stranski-Krastonov growth
• heteroepitaxy for slightly different lattice constants
• lattice mismatch induces strain energy that must be included in the free energy of nucleation
• stress is released by forming islands on top of the layer

### Film crystalinity

• single-crystalline film
• high T, low impinging flux of growth species (flux), clean substrate, good lattice match
• polycrystalline film
• medium T, medium flux
• amorphous film
• low T, very high flux

# Pensum Del II (Estelle Marie M. Vanhaecke)

## Catalysis

Nobel price winner W. Ostwald defined it as "A catalyst is a substance that enhances the rate of a reaction without itself being consumed."

Note the concept of non-functionality:

• A catalyst can not change the thermodynamic equilibrium of a reaction, only the rate at which the equilibrium is approached.

Here are some useful concepts for describing a catalyst:

• Activity
• Amount of reactant converted per amount of catalyst per time.
• Selectivity
• Amount of product per amount of reactant converted. If it creates bi-products, it has poor selectivity.
• How long a catalyst can maintain a certain activity or selectivity.
• Turnover Frequency (TOF)
• # reactant molecules converted / (#sites x time)

### Heterogenous catalysis

We mainly consider heterogenous catalysis in this course, that is catalyst that are in a different phase than the reactant.

The main steps of heterogenous catalysis are (in order)

• Can be dissocisative or non-dissociative
• Can be in multiple steps
• At total free energy lower than the product
• Desorption
• If desorption is not fast enough, the catalyst will become saturated and stop functioning.

Note that diffusion to the catalyst and on the catalyst is also very important.

#### Examples of heterogenous catalysis

You have to remember at least three examples

• Ammonia synthesis
• Oil refineries
• Natural gas production
• Polymer production
• Industrial chemicals
• Exhaust clea-up (Tree-way Catalyst)

### Three-way catalyst (TWC)

TWC are found in engines an exhaust systems in order to reduce CO, hydrocarbons and NOx to less harmful substanses.

The main active phases are

• Pt or Pd for CO
• Pt or Pd for hydrocarbons
• Rh or Pd for NOx

As these three reactions are strongly dependent on the amount of oxygen awailable, CeOx (ceria) is also needed as an oxygen buffer. The engine must also be fitted with an electrical system to regulate the oxygen amount (a $\lambda$-probe).

## Catalyst materials

Catalytically active materials are the transition metals.

### Structure

Solid catalyst particles are metals with a periodic structure characterized by crystal structures.

In this course we mainly consider

• Simple cubic
• Body centered cubic (bcc)
• Fe
• Face centered cubic (fcc)
• Rh, Pd, Pt, Au ++
• Hexagonally close packed (hcp)
• Co
• Note that the 100 plane of hcp has the same packing as the 111 plane of fcc

The bulk structure translates to the surface by exposing certain faces.

#### Model systems

Real catalyst will continously be changing their shape, so when we model it as a single crystal with defined crystal structure, we call this a model system

• A model system is single crystalline
• It has minimized surface free energy, according to the Wullf construction.
• It is nice for modeling structure sensitive reactions (reactions that can only occur on specific surfaces or sites)

### Overlayer nomenclature

Adsobates can position themselves in different positions relative to the atoms on the face of a crystal.

On top, long bridge, bridge, four-fold hollow, three-fold hollow and three-fold hollow hcp. Adsorbates form a new 2D primitive unit cell that is denoted by using the primitive unit vecors of the crystal face below. For example: insert example

### Particle size

Reactions only happen on the surface, so we want to maximize the amount of surface.

Dispersion is the # of surface atoms per # of atoms in total

Dispersion is measured by

• Gas chemisorption
• Normally H2 (dissociative) or CO (non-dissociative) is floated through the catalyst, and the amount of adsorbed gas is measured.
• There is roughly one surface atom per adsorbed gas molecule.
• Pulse chemisorption
• Short pulse of gas through the material. Goes faster, but has higher probability for falsely measuring physisorption (weak bands)
• Grivmetric analysis
• Basically the same as chemisorption, but the whole system is contiously weighted to monitor the amount of adsorbed species.

## Supports

The support is what the catalyst particles is deposited on. A good support has

• Large specific surface area
• Good mechanical, chemical and thermal stability
• Helps the catalysis by holding particles separated, affect the functionality of the metal, act as a co-catalyst
• Is easy to manufacture in large quanta

Support materials to know are Alumina, Silica, carbon and zeolites.

### Porosity

Supports are porous with the different sizes

• Macropores: d>50nm
• Mesopore: 2nm<d<50nm
• Micropores: d<2nm

Mesopores are most common, as too small pores will lead to obstruction and blocking of parts of the porous network

### BET isotherm

The BET technique is used to find the specific surface area of your support, and is very important to know in detail. It uses N2 at 77 K in vacuum at pressures lower that the EQ pressure of N2 (P0).

The machine flows a stream of the probe molecule through the support and measures how much comes out on the other side. This is done at different pressures (driving force for chemisorption), to find where the adsorbed amount of gas is stable. At this point a monolayer is assumed to have been formed, and one can find the number of molecules needed to cover the support. From the area per molecule (16.2 Å2 for N2), the specific surface area is found.

The main assumptions are (and the limitations spring out of this)

• Energy for monolayer formation is lower than energy for subsequent layers (interactions with substrate is stronger than interaction between probe molecules)
• Energy of formation for the subsequent layers are equal
• Rate of adsorption and desorption are equal
• All sites are equivalent
• The surface do not change during adsorption

Measure P and Va and plot it as the BET equation: P / Va (P0 - P) as a function of P / P0 to get a linear line. Do some exam problems to know this method in and out.

After the support is fabricated it needs to be loaded with the active catalyst particles.

Name Used for Description Benefits
Wet impregnation Large mesoporous support Dip the support in catalyst solution, dry, and repeat until desired loading No capillary forces that may break the pore structure
Dry impregnation (incipient wetness) Powder mesoporous support Drip catalyst solution of desired volume onto the powder, dry and repeat until desired loading Loading measurable by mass change
Deposition precipitation Small pores Support is suspended in solution and catalyst is nucleated directly onto the support Better dispersion control
Co-precipitaiton When you have time Difficult method where both particle and support are catalyzed simultaneously High loading and high dispersion

### Activation

After being loaded, the catalyst has been through many chemical processes and does not function optimally. Calcination (heating) is often required to reshape the particles, get rid of oxides, and make them ready for use. Watch out for aggregation and reduced dispersion during this step.

## Zeolites

Zeolites are made of O, Al and Si. Tetrahedra O-blocks are linked together by alternately Al3+ and Si4+ to form sodalite cages. These cages are self assembled to form large, highly ordered microporous networks with pore sizes down to 4 Å.

### Selectivity mechanisms

Due to the extremely small pore size, zeolites can function as molecular sieves, where only selected

• reactants are allowed into the network
• products are allowed to leave the network
• transition states are allowed, and the speccificity of the catalyst is therefor enhanced

### Charge compensation

Zeolites can become basic or acidic when Al3+ replaces Si4+ in the structure. The network compensates by binding cations or protons, and thus becomes more reactive and can donate or accept groups to weaken or (preferetially) enhance the catalysis process.

## Carbon

Carbon allotropes include graphite, diamond, carbon black, graphene, carbon nanotubes (CNT), multiwall carbon nanotubes (MWCNT), carbon nanofibers (CNF).

Previously carbon formation was associated with decreased performance in catalysators and were unwanted. Now we use the same catalysts to make them on purpose due to their intriguing properties.

### Catalytic decomposition

CNF are synthesized using gas precursor and a catalytic particle or substrate in a process called catalytic decomposition.

• Gass precursors are methane, CO or other more complex structures.
• H2 athmosphere at low pressure to remove oxides
• Catalyst particles are Ni, Fe, Co...
• Catalyst substrates are Ni, Cu and Fe

Happens in a CVD. Important parameters are:

• Temperature range 500-1000 C
• Direction of insertion, rate of insertion, distanse to catalyst, type of catalyst, time for growth, instrument used +++

### Catalyst pretreatment

Catalyst pretreatment is so important that it requires its own heading. Heating or gas flow over the deposited catalyst to change it from oxidized to metallic state, which alters both shape and lattice constant.

### Functionalization

Functionalization of CNTs are done because they are

• Difficult to disperse
• Insoluble in water and organic solvents
• Hydrophobic (resistant to wetting)
• and to remove the catalyst

It is done by

• Acid/base treatment to remove catalyst metal (oxidative purification)
• Acid treatment to create defects for functional groups to bind to (Defect functionalization)
• Halogenation by F, Cl or N

### Fuel cells (FC)

Carbon nanostructures can be used as electrocatalyst support and as electrode material. The main goal is (as always) to minimize the Pt used. Some terms:

• MEA - Membrane Electrode Assembly
• APU - Auxiliary Power Unit
• ESA - Electrochemical Surface Area
• PEMFC - Polymer Electrolyte/Membrane Fuel Cell
• DMFC - Direct Metanol Fuel Cell
• Anode reactions: H2 -> 2 H+ + 2e-
• CH3OH + H2O -> CO2 + 6H+
• Cathode reaction: O2 + 4 H+ + 4 e- -> H2O

CNF is a good support because of

• Good CO tollerance, but very low sulfur tollerance
• High conductivity
• Large electroactive surface area
• 3D mesophorous and good Pt dispersion
• Hydrophobic
Important fuel cell properties that must be remembered
Fuel cell type Operating temperature [C] Operating pressure [bar] Anode material Catode material
PEMFC 80-120 up to 10 Pt/C Pt/C
DMFC 150 up to 3 Pt-Ru/C Pt/C
Alkaline (classic) 100-250 ~5 Ni-Al, Pt or Ag Pt

### Cyclic voltametry

During cyclic voltametry a potential is raised from a starting level E1 to a final level E2, with a certain rate v. The current is measured as a function of V.

Electrochemists use this to find ESA.

## Micro- meso- and macroporous materials

• Adsorption isotherms: Amount of adsorbed gas as a function of pressure.

## Types of porous solids

• Zeolites (crystalline aluminosilicates)
• Hydrothermal synthesis: Solvent, precursors and a mineralizing agent. A structure-directing agents (cations or organic molecules) fill up pores and balance the charge of the framework. Needs to be removed later.
• Applications: Molecular sieves, chromatography, heterogeneous catalysis, ion exchange, sensing
• Metal organic frameworks (MOF)
• Low density
• May have permanent porosity if solvent can be removed
• Synthesis: Hydrothermal or solvothermal
• Applications: Gas adsorption and storage
• Ordered mesoporous oxides (Amorphous materials with ordered pores)
• Synthesis: Like zeolite, milder conditions. Needs a source for framework element oxide, a surfactant, a solvent, and a pH modifier
• Size of pores controlled by surfactant size
• Applications: Gas separation, catalysis, gas adsorption. Also, sensing, biosensing, drug delivery, optics, batteries, fuel cells.
• Sol-gel derived oxides (random mesoporous solids)
• Nano-crystalline Titanium Oxide
• Photocatalycic applications (pollutant degradation, water splitting)
• Porous silicon technology
• Preparation: etching
• Applications: sensing technology, support for CNT growth

# Pensum Del III (Sulalit Bandyopadhyay)

## Synthesis procedures

### Reduction of metallic particles in solution

#### Turkevich reaction

• Citrate reduction of chloride precursor $(HAuCl_4)$, aqueous phase
• Citrate acts as reducing agent and passivating ligand
• Most common commercially available method
• Typically at 100 degrees C
• Sizes 2-200nm
• Wide array of surface functionalities through ligand exchange

#### Brust reaction

• $BH_4^-$ reduction of chloride precursor
• 1.5-8nm size
• Very stable particles
• Wide array of surface functionalities through ligand exchange

#### Goia reaction

• Reduction of auric acid with iso-ascorbic acid
• Stabilizer-free, like with citrate
• Room temperature, aqueous phase, rapid nucleation and growth
• Tunable particle size through pH, reaction ratios, concentration
• 30-100 nm, or 80-5000 nm if in presence of gum arabic and high Au concentration

### Colloidal templating

Reverse micelles as spherical nanoreactors. Two micelle solutions of gold salt and reducing agent respectively. Mixed, and micelles come together by Brownian motion. NP is formed and micelle split into compartments equal to the original size.

A rule of thumb is that the NP size is controlled by the micelle size. The micelle size can be controlled by varying the water-surfactant ratio. More water gives larger reverse micelles.

### Sol-Gel Method

Hydrolysis and polycondensation in parallel steps yielding molecular level homogeneity at low processing temperature. (But don't you have to mill it afterwards?)

### One-pot synthesis

• Using stimuli-responsive polymers
• Using globular proteins
• Using viral templates

### By microorganisms

It is being done.

### Nucleotide-mediated synthesis

By using either nucleotides, sugar backbone, DNA, RNA, or synthetic derivatives, selective metal binding can be achieved. The suggested process goes as follows:

• Initiation
• Growth
• Termination
• Passivation
• Solubilization

#### SELEX

"Natural selection" of biomolecules capable of nanoparticles formation by screening millions of peptides at once, and selecting those who adhere to the metal surface. Multiply these, and repeat to select those who bind strongest.

### Electrochemical deposition

Top-down approach connected to cyclic voltametry

### Dendrimers

• Superbranched polymers
• Core: chemical species in specific nanoenvironment
• Interior monomer layers: encapsulation of molecular species
• Multifunctional surface: determines macroscopic properties
• Each spherically symetric nitrogen helps separate the generations (G)

#### Synthesis

• Divergent (bottom-up)
• Large structures available, lengthy separation procedures, limited by exponentially growing number of end groups
• Convergent (top-down)
• Max 4G, more economically viable, limited by steric constraints

### =Properties

• Monodispersity
• Biocompatibility
• Size and shape
• Polyvalency
• Interior compartment
• Uniform tunable size
• Hydrophilic exterior, hydrophobic interior
• More stable than micelles
• Tunable surface functionalization

#### Biocompatibility

Dendriers with cationic surface groups are cytotoxic, and more so with increasing generations. Anionic less so. Hydroxy- and methoxyterminated dendrimers non-toxic. Cytotoxicity can be reduced by cloaking, but some cationic functionality is desired to interact with negatively charged cell membranes.

Release from the "dendritic box" can be done by hydrolysis. Partial hydrolysis releases small molecules, total hydrolysis will release all molecules. Otherwise, the spatial configuration of the dendrimer alters with pH and iconic strength, which can be used for release - especially remembering the pH difference between healthy tissue and tumor tissue.

## Functionalization of metallic nanoparticles

• Metallic nanoparticles need a surface layer of a passivating ligand to be stable
• Direct functionalization: Reducing agent is passivating ligand
• Post-synthesis functionalization: Passivating ligand added after synthesis
• Can displace or bind to existing ligand

• Chemisorption
• Covalent / ionic bonds, high binding energy
• "Irreversible**
• Monolayer
• Physisorption
• van-der-Waals interactions, low binding energy
• Reversible
• Mono or multilayer
• Driven by reduction of free energy
• Surfactant adsorption on hydrophobic surfaces
• Monolayer
• Hemi-micelles
• Surfactant adsorption on hydrophilic surfaces
• At high concentrations: double layer
• Alternatively, close packed micelles

The Langmuir adsorption isotherm describes how many molecules (often surfactants) that bind to the surface at a given concentration. You get the fractional surface coverage $\theta = \frac{number\;of\;molecules\;adsorbed\;onto\;surface}{number\;of\;molecules\;adsorbed\;at\;monolayer\;coverage} = \frac{N}{N_{mono}}$ This equation must be derived.

The assumptoins of the Langmuir model are

• Only monolayer formation
• Homogenous and flat surface
• No surface diffusion after adhesion
• Adsorption independent on surface coverage (no latteral interaction)

Formation of an adsorbed layer happens in three steps: Diffusion towards surface, attachment, and spreading. Adsorption rate: $\frac{\delta\Gamma}{\delta t} = k(c^b-c^s)$ where $\Gamma$ is the surface coverage, k is the diffusion and hydrodynamic rate coefficient, $c^s$ is the subsurface concentration and $c^b$ is the bulk concentration.

Macromolecules, such as polymers and proteins may not comply with the Langmuir assumptions due to

• Strong interactions between polymers (H-bonds, hydrophobic interactions) can lead to
• More layers forming
• Interactions with neighbours by blocking active sites
• Strong affinity towards surface leads to
• spreading on the surface, and thereby latteral diffusion

## Optical properties of metallic nanoparticles

### LSPR

• Localized surface plasmon resonance
• Depends on size, morphology, metal, surroundings
• Red shift = bathochromic shift = higher wavelength and lower energy = larger particles
• Blue shift = hypsochromic shift = lower wavelength and higher energy = smaller particles

### Quasi-static approximation

• Energy levels treated as a quasi-continuum of states
• Assuming
• $D \le \frac{\lambda}{10}$ for the EM field to be treated as uniform within each spherical particle.
• Particles are small enough - the time of propagation in each sphere is small compared to the oscillation period of the EM field
• D larger than 2 nm (more than 100 atoms) for the separation of energy levels close to the particle surface to be comparable to that of the bulk metal
• Volume fraction small enough to treat particles as independent
• We can introduce an effective dielectric constant for the medium

### UV-vis

Intensity through a medium of thickness L is given by Beer-Lamberts law:

• $I_t=I_0\exp(-\alpha L)$, where $\alpha(\omega)$ is the absorption coefficient. [There is missing a concentration in the exponent.]

Beer Lamberts law is only valid for these systems

• The solution is homogenous
• The molecules do not interact
• The molecules do not change by being exposed light
• The molecules should not aggregate and thereby scatter more light

### The Mie Model

• For larger sizes, variations across the size of object must be considered

## Drug delivery

Pharmacology-pharmacodynamics-pharmacokinetics-pharmacogenetic

The golden rules for Drug Delivery

• Monodisperse
• To avoid undesired effects
• In general 5nm < L < 200nm
• Biocompatible
• Not cytotoxic
• Long circulation time
• Target specific
• Active vs passive targeting
• Delivery of cargo

The main steps through the body are

• Distribution
• Metabolism
• Encymatic cleavage of the backbone to reduce the size is essential
• Elimination
• Must be 10-15nm in order to go through the kidney

### Targeting mechanisms

• Passive targeting: Enhanced permeability and retention (EPR)
• Leaky blood channels around infections
• High weight polymers accumulate in solid tumor tissue
• Active targeting
• Tumors often have unique receptors / antigens that our vector can bind to

After vectors have aggregatet, they can be heated by photothermal therapy to kill cells. They can also be heated by hyperthermal therapy to get even more local heat.

### New drug delivery vectors

• Viral: proteines, peptides
• Very efficient
• Not easy to tune, size restricted
• Elicits strong immune responses
• Can mutilate, can be cytotoxic
• Incapable of delivering chemotherapy agents or short oligonucleotides
• Non-viral: Often passive, liposomes, polymers, dendrimers, microspheres
• Inefficient
• Possibly to control immune reactions
• Not infectious, often cytotoxic
• Capable of delivering chemotherapy agents or short oligonucleotides
• Combination vectors: metallic nanoparticle vectors
• Tunable efficiency
• Easy to incorporate different functions
• Size tunable
• Not infectious, controllable cytotoxicity
• Capable of delivering chemotherapy agents or short oligonucleotides

### Gold nanoparticles

Can be seen in differential interference contrast microscopy (DIC). Even though the particles are 5-30nm, they appear as reflections of 200-400nm, while cellular structures appear actual size.

• Functionalization methodologies:
• Attachment of payload through protein intermediate (Bovine Serum Albumin, BSA): Peptide-BSA-MBS-Au
• Direct attachment of payload to substrate through thiol chemistry
• Plasmonically heated Au nanoparticles
• LSPR excited nanomaterials are heated by adsorbed light
• Localized increase in temperatures --> hyperthermal therapy
• LSPR should be in near-infrared because body is more transparent there

### Dealing with Cancer

• Cancer cells overexpress certain receptors, but receptor targetting still targets healthy cells
• Due to lactic acid buildups, cancer cells have lower pH than healthy tissue
• Core-shell hydrogel swelling can be tuned to within 0.1 pH
• Nanoparticles suspended within gel, and released upon pH changes

### Plant virus nanotechnology

• Don't inherently target human cells
• Can be used to carry chemotherapeutic agents with little risk

### Dendrimers as drugs

• Antiviral: Competes with cells for viruses. Can inhibit influenza, herpex simplex, HIV.
• Antibacterial: Adheres to and damages bacterial cell membranes
• Photodynamic therapy: Photoactivated, generates reactive oxygen species

## Magnetic Resonance Imaging

A large magnetic field forces hydrogen proton spins to align. By applying a radifrequency pulse, the proton magnetization can be momentarily switched before it relaxes back to the direction of the magetic field, releasing energy in the process. The relaxation happens by two independent processes

• longitudinal relaxation (T1- recovery)
• transverse relaxation (T2-decay)

The difference between T1 and T2 varies with the surrounding tissue and chemical environment and is what creates the contrast in MRI scanning.

### Contrast enhancement

In the presence of magnetic NPs, both T1 and T2 will be shortened. Shortening of T1 can be reduced by usinger a thicker coating. T2 can be shortened by using superparamagnetic NPs. With a little signal trick you can get hypointense contrast (which probably means very good contrast).

## Core-shell structures

### Heteroepitaxial semiconductor core-shell structures

One semiconductor grown epitaxially on particles of another semiconductor. (Formation of shell material on the particle core is a continuation of particle growth, but with different chemical composition.)

### Metal-oxide structures

For gold nanoparticles coated with silica, a polymer layer functionalized to bind to gold on one end and silica on the other needs to be in between.

### Metal-polymer structures

Prepared by emulsion polymerization or membrane based synthesis.

### Oxide-polymer structures

Prepared by polymerization at surface or adsorption.

# Removed from curriculum

Entropy of mixing: $S=k\ln{\Omega}$, where $\Omega = \frac{(n_A + n_B)!}{n_A!n_B!}$. Given that $x_j$ is the mole fraction of j, we have $-\Delta S_{mix} = k[n_a\ln{x_A} + n_B\ln{x_B}]$. Assume nearest neighbour interactions only. We get the Flory-Huggins free energy of mixing: $\frac{\Delta G_{mix}}{RT} = n_A\phi_Bx+n_A\ln\phi_A+n_B\ln\phi_B$. Theory is a bit limited by approximations, shapes of monomers and solvents, and application areas.

## Extinction

• For normal medium, $\alpha(\omega)=2\frac{\omega}{c}\Kappa(\omega)$
• For a matrix + nanosphere system, $\alpha(\omega) = \frac{9p \omega\epsilon^{3/2}_m}{c}\frac{\epsilon_2}{(\epsilon_1+2\epsilon_m)^2 + \epsilon_2^2} = \frac{\omega}{\epsilon^{1/2}_mc}p|f(\omega)|^2 \epsilon_2(\omega)$, where p is the volume fraction of nanoparticles, and $\epsilon_1$ is the complex dielectric constant of the matrix and $\epsilon_2$ is the complex dielectric constant of the nanoparticles.
• $|f(\omega)|^2$ represents enhancement of $E_i$. Enhancement occurs when $|f(\omega)|^2 > 1$, which happens if the contribution to the dielectric constant from conduction electrons is dominant.
• $\alpha(\omega)$ expresses extinction by both absorption and scattering
• $S_{scatt} = \frac{24\pi^3V^2_{np}\epsilon^2_m}{\lambda^4}|\frac{\epsilon - \epsilon_m}{\epsilon + 2\epsilon_m}|^2$ and $S_{ext} = \frac{18\pi V_{np}\epsilon^{3/2}_m}{\lambda}\frac{\epsilon}{|\epsilon + 2\epsilon_m |^2} = \frac{2\pi V_{np}}{\lambda\epsilon^{1/2}_m} |f(\omega)|\epsilon_2$
• Ratio varies as volume of nanoparticles: $\frac{S_{scatt}}{S_{ext}} \propto (D/\lambda)^3$
• If resonance condition $\epsilon_1(\Omega_R)+2\epsilon_m =0$, SPR frequency is $\Omega_R = \frac{\omega_p}{\sqrt{\epsilon^{ib}_1(\Omega_R)+2\epsilon_m}}$
• SPR shifted towards red with increasing $\epsilon_m$

### Mechanisms for optical properties

#### Intraband

• Optical transitions without change of band
• Due to quasi-free electrons in conduction band
• Described by Drude model: $\epsilon_{Drude} = 1-\frac{\omega_p^2}{\omega(\omega+i\gamma_0)}$ where $\omega_p^2 = \frac{n_ee^2}{\epsilon_0m_e}$
• Absorption must be assisted by a third particle - another electron or a phonon, to conserve energy and momentum
• Dominates in red and infrared

#### Interband

• Optical transitions between electronic bands
• From filled bands to conduction band or from conduction band to empty bands of higher energy
• Dominates in visible and ultraviolet

## Basics of membrane materials and separation

• Microporous membrane: Separation according to selective surface flow - largets molecule permeates
• Dense polymers: Permeability P equal to diffusion times solution, P=DS
• Influenced by state of polymer, type of gas, pressure, temperature
• Other polymeric membranes: SFTM (selective facilitated transport membrane).
• Molecular sieving: Separation according to molecular size (smallest molecule goes through.)
• P=DS but diffusion factor most important
• Basic equations for membrane separation
• $P = DS$ where $D [cm^2/s]$is diffusivity and $S [cm^3(STP)/cm^3 bar]$ is solubility
• Selectivity $\alpha = P_i/P$
• Production rate (flux) $\frac{q}{A_m} = J_i = \frac{P_i}{l}(p_hx_0 - p_ly_p)$ where $A_m$ is the membrane area, $l$ is the membrane thickness, $p_h,p_l$ are feed and permeate pressures and $x_0,y_p$ are mole fractions of component i.

Total feed flow given by material balance, $L_f = L_0 + V_p$, where $L_f$ is the feed in, $L_0$ is the reject feed out and $V_p$ is the permeate out.

## Selected nanostructured membranes

### Mixed Matrix Membranes

• Polymeric matrix with dispersed porous inorganic particles

### Carbon Molecular Sieve Membranes

• Improved flux and selectivity
• Tailoring pore size by adjusting pyrolysis parameteres and post treatment (oxidation to increase pore size or organic vapor deposition to decrease pore size)

### Glass Membrane

• Surface of glass pore can be functionalized to improve flux and selectivity

## Types of porous solids

• Zeolites (crystalline aluminosilicates)
• Hydrothermal synthesis: Solvent, precursors and a mineralizing agent. A structure-directing agents (cations or organic molecules) fill up pores and balance the charge of the framework. Needs to be removed later.
• Applications: Molecular sieves, chromatography, heterogeneous catalysis, ion exchange, sensing
• Metal organic frameworks (MOF)
• Low density
• May have permanent porosity if solvent can be removed
• Synthesis: Hydrothermal or solvothermal
• Applications: Gas adsorption and storage
• Ordered mesoporous oxides (Amorphous materials with ordered pores)
• Synthesis: Like zeolite, milder conditions. Needs a source for framework element oxide, a surfactant, a solvent, and a pH modifier
• Size of pores controlled by surfactant size
• Applications: Gas separation, catalysis, gas adsorption. Also, sensing, biosensing, drug delivery, optics, batteries, fuel cells.
• Sol-gel derived oxides (random mesoporous solids)
• Nano-crystalline Titanium Oxide
• Photocatalycic applications (pollutant degradation, water splitting)
• Porous silicon technology
• Preparation: etching
• Applications: sensing technology, support for CNT growth