TKP4190 - Fabrikasjon og anvendelse av nanomaterialer
Innhold
- 1 Pensum Del I (Jens-Petter Andreassen)
- 2 Pensum Del II (Sondre Volden)
- 3 Pensum Del III (Tor Grande)
- 4 Pensum Del IV (May-Britt Hägg)
- 5 Pensum Del V (Magnus Rønning)
Pensum Del I (Jens-Petter Andreassen)
Crystallization fundamentals
Supersaturation
Concentration driving force: <math>\Delta c = c - c^*</math> where c is the solution concentration and c* is the equilibrium saturation at a given temperature. Supersaturation ratio S is given as <math>S = \frac{c}{c^*}</math> and the relative supersaturation ratio <math>\sigma = \frac{\Delta c}{c^*} = S-1</math>
- Size dependant crystal growth
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.
<math>\Delta G = \Delta G_S + \Delta G_V = 4\pi r^2 \gamma + \frac{4}{3}\pi r^3 \Delta G_v</math>
Here <math>\Delta G_S</math> is the surface excess free energy, <math>\gamma</math> is the interfacial tension between the phases, <math>\Delta G_V</math> is the volume excess free energy and <math>\Delta G_v</math> is the same per unit volume.
At the point where the <math>\Delta G</math>-curve is at its max, we find the critical nucleus size: above this radius the nucleus is stable. Finding this size is straightforward: <math>\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</math>
Inserting <math>-\Delta G_v = \frac{k_B T \ln{S}}{\nu}</math> the critical energy for nucleation is <math>\Delta G_{crit} = \frac{16 \pi \gamma^3 \nu^2}{3(k_B T \ln{S})^2}</math>
This energy originates from random fluctuations. Rate of nucleation can thus be expressed as an Arrhenius equation:
<math>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})</math>
Heterogeneous nucleation
Critical energy changed due to availability of a solid surface. <math>\Delta G_{crit,hetr} = \phi\Delta G_{crit,hom}, \phi = \frac{1}{4}(2+\cos{\theta})(1-\cos{\theta})</math>
Growth rate limits
Diffusion controlled growth
Growth as change of particle radius per time is given as <math>\frac{dr}{dt} = D(C-C_S)\frac{V_m}{r}</math> where r is the radius, D is the diffusion coefficient of the growth species, C is the bulk concentration, <math>C_S</math> is the solubility concentration and <math>V_m</math> is the molecular volume. Solving gives <math>r^2 = 2D(C-C_S)V_mt + r_0^2</math>
- Diffusion controlled growth promotes unisized particles
- Can be obtained by increasing viscosity or introducing a diffusion barrier
Radius difference between particles decreases with time: <math>\delta r = \frac{r_0\delta r_0}{\sqrt{k_Dt + r_0^2}}</math>
Surface integration controlled growth
Growth given by <math> G = k_g(S-1)^g</math>
- Spiral growth (most common): g = 2 at very low supersaturation and g = 1 at large supersaturation
- 2D Nucleation: g > 2
- Rough growth: g=1
Mononuclear growth (layer by layer): <math>\frac{dr}{dt} = k_mr^2 \Rightarrow \frac{1}{r}=\frac{1}{r_0} - k_mt</math> and radius difference increases with time <math>\delta r = \frac{\delta r_0}{(1-k_mr_0t)^2}</math>
Polynuclear growth (multiple layers growing at once): <math>\frac{dr}{dt} = k_p \Rightarrow r=k_pt+r_0</math> and radius difference remains unchanged <math>\delta r = \delta r_0</math>
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.
- Affects morphology
- From other factors (Very specific examples in the text)
- Chloride ion concentration affects syntehsis of Pt nanoparticles from <math>H_2PtCl_6</math>
- 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 needs to be anisotropic
- Evaporation-condensation: Reduction in chemical potential by consumption of supersaturation
- Vapor-liquid-solid / Solution-liquid-solid (VLS/SLS)
- 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
- Vapor-phase deposition
- Performed under vacuum
- Liquid based growth
Initial nucleation
- Island growth / Volmer-Weber growth
- Layer growth / Frank-van der Merwe growth
- Island layer / Stranski-Krastonov growth
Pensum Del II (Sondre Volden)
Optical properties of metallic nanoparticles
LSPR
- Localized surface plasmon resonance
- Depends on size, morphology, metal, surroundings
Quasi-static approximation
- Energy levels treated as a quasi-continuum of states
- Assuming
- <math>D \le \frac{\lambda}{10}</math>
- D larger than 2 nm (more than 100 atoms)
- Volume fraction small enough to treat particles as independent
- Intensity through a medium of thickness L:
- <math>I_t=I_0\exp(-\alpha L)</math>, where <math>\alpha(\omega)</math> is the absorption coefficient
- For normal medium, <math>\alpha(\omega)=2\frac{\omega}{c}\Kappa(\omega)</math>
- For a matrix + nanosphere system, <math>\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)</math>, where p is the volume fraction of nanoparticles, and <math>\epsilon_1</math> is the complex dielectric constant of the matrix and <math>\epsilon_2</math> is the complex dielectric constant of the nanoparticles.
- <math>|f(\omega)|^2</math> represents enhancement of <math>E_i</math>. Enhancement occurs when <math>|f(\omega)|^2 > 1</math>, which happens if the contribution to the dielectric constant from conduction electrons is dominant.
- <math>\alpha(\omega)</math> expresses extinction by both absorption and scattering
- <math>S_{scatt} = \frac{24\pi^3V^2_{np}\epsilon^2_m}{\lambda^4}|\frac{\epsilon - \epsilon_m}{\epsilon + 2\epsilon_m}|^2</math> and <math>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</math>
- Ratio varies as volume of nanoparticles: <math>\frac{S_{scatt}}{S_{ext}} \propto (D/\lambda)^3</math>
- If resonance condition <math>\epsilon_1(\Omega_R)+2\epsilon_m =0</math>, SPR frequency is <math>\Omega_R = \frac{\omega_p}{\sqrt{\epsilon^{ib}_1(\Omega_R)+2\epsilon_m}}</math>
- SPR shifted towards red with increasing <math>\epsilon_m</math>
- Red shift = bathochromic shift = higher wavelength and lower energy
- Blue shift = hypsochromic shift = lower wavelength and higher energy
Mechanisms for optical properties
Intraband
- Optical transitions without change of band
- Due to quasi-free electrons in conduction band
- Described by Drude model: <math>\epsilon_{Drude} = 1-\frac{\omega_p^2}{\omega(\omega+i\gamma_0)}</math> where <math>\omega_p^2 = \frac{n_ee^2}{\epsilon_0m_e}</math>
- 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
The Mie Model
- For larger sizes, variations across the size of object must be considered
Synthesis procedures
Turkevich reaction
- Citrate reduction of chloride precursor <math>(HAuCl_4)</math>, 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
- <math>BH_4^-</math> 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
One-pot synthesis
- Using stimuli-responsive polymers
- Using tiopronin or co-enzyme A
- Using globular proteins
- Using starch-glucose
- Using viral templates
Functionalization of metallic nanoparticles
- Ag or Au 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
Adsorption
- 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
- Fractional surface coverage <math>\theta = \frac{number\;of\;molecules\;adsorbed\;onto\;surface}{number\;of\;molecules\;adsorbed\;at\;monolayer\;coverage} = \frac{N}{N_{mono}}</math>
Self-assembled monolayers (SAMs)
- One head group interacts with substrate, the other determines properties.
Macromolecular adsorption
Entropy of mixing: <math>S=k\ln{\Omega}</math>, where <math>\Omega = \frac{(n_A + n_B)!}{n_A!n_B!}</math>. Given that <math>x_j</math> is the mole fraction of j, we have <math>-\Delta S_{mix} = k[n_a\ln{x_A} + n_B\ln{x_B}]</math>.
Assume nearest neighbour interactions only. We get the Flory-Huggins free energy of mixing: <math>\frac{\Delta G_{mix}}{RT} = n_A\phi_Bx+n_A\ln\phi_A+n_B\ln\phi_B</math>. Theory is a bit limited by approximations, shapes of monomers and solvents, and application areas.
Formation of an adsorbed layer happens in three steps: Diffusion towards surface, attachment, and spreading.
Adsorption rate: <math>\frac{\delta\Gamma}{\delta t} = k(c^b-c^s)</math> where <math>\Gamma</math> is the surface coverage, k is the diffusion and hydrodynamic rate coefficient, <math>c^s</math> is the subsurface concentration and <math>c^b</math> is the bulk concentration.
New drug delivery vectors
- Desirable size: 10-30 nm for access to nucleus
- Active vs passive
Approaches
- 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
- Challenging to add functions
- 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
- Biologically degradable
Dendrimers
- Superbranched polymers
- Core: chemical species in specific nanoenvironment
- Interior monomer layers: encapsulation of molecular species
- Multifunctional surface: determines macroscopic properties
- 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
- Advantages
- Uniform tunable size
- Hydrophilic exterior, hydrophobic interior
- More stable than micelles
- Tunable surface functionalization
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.
Targeting mechanisms
- Enhanced permeability and retention (EPR)
- There are increased amounts of biofluids around tumors
- High weight polymers accumulate in solid tumor tissue
- Passive targeting
- Tumor receptor / antigen targeting
- Tumors often have unique receptors / antigens
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
Pensum Del III (Tor Grande)
Micro- meso- and macroporous materials
- Adsorption isotherms: Amount of adsorbed gas as a function of pressure.
- Macropores: d>50nm
- Mesopore: 2nm<d<50nm
- Micropores: d<2nm
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
Synthesis of nanocrystalline particles, core-shell structures
- Silica-coated metal nanoparticles
- Catalysis, drug delivery