TKP4190 - Fabrikasjon og anvendelse av nanomaterialer

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)
  • Convergent (top-down)