PDF version: Notes on nanoparticle self-assembly – Logan Thrasher Collins

Preparation of nanoparticle superlattices

• Nanoparticle superlattices can be prepared using solvent evaporation, solvent destabilization, or gravitational sedimentation methods.
• Solvent evaporation involves evaporating a nanoparticle-containing solvent to induce ordered aggregation of the particles. Note that many inorganic nanoparticles are insoluble in polar solvents and soluble in nonpolar solvents, though the presence of polar surface ligands can alter this behavior.
• Solvent evaporation techniques include (i) placing a small droplet of nanoparticle-containing solvent on a solid substrate and allowing for evaporation to occur, (ii) evaporating a nanoparticle-containing solvent from a tilted vial so as to control the orientation of the meniscus, (iii) placing a small droplet of polar solvent on a solid substrate and then adding a nonpolar nanoparticle-containing solvent over the top to facilitate aggregation in the thin layer of nonpolar solvent, and (iv) filling a tray with a polar solvent and adding nonpolar nanoparticle-containing solvent over the top to facilitate aggregation in the thin layer of nonpolar solvent.
• Solvent destabilization promotes gradual clustering of nanoparticle in solution via slowly changing the solvent conditions. Solvent destabilization techniques include (i) allowing for a polar and a nonpolar solvent to gradually intermingle and so facilitate a steady increase in the favorability of nanoparticle-nanoparticle interactions and (ii) heating a premixed solvent mixture that includes both polar and nonpolar components and so facilitating a controlled enrichment of the solvent with a higher boiling point. This increases the favorability of nanoparticle-nanoparticle interactions in a controlled fashion. Because many nonpolar liquids possess lower boiling points, the nanoparticle lattices prepared in this way may require nanoparticles equipped with polar surface ligands.
• Gravitational sedimentation is less common than the other techniques since many nanoparticles are small enough to remain dissolved in spite of gravitational forces. But very large nanoparticles (100-1,000 nm) often do sediment, facilitating close-packing and the assembly of superlattices.

Characterization of nanoparticle superlattices

• Transmission electron microscopy (TEM) is used to visualize nanoparticle superlattices directly. As TEM requires very thin slices, it makes 2-dimensional images of nanoparticle superlattices.
• TEM operates best when there is a high contrast between the atomic number of the nanoparticles and the atomic number of the background support structure. For instance, PbS is easily imaged on a carbon support.
• To circumvent issues that arise with atomic number contrast, ultrathin (i.e. graphene) supports or supports that possess numerous holes can be used. Ultrathin supports absorb less electrons while “holey” supports allow some nanoparticles to be positioned over the holes during imaging, preventing background absorption.
• TEM often requires a vacuum chamber and so necessitates dry samples, meaning  that superlattice structure can be visualized after removal of the solvent, but snapshots of the self-assembly process cannot be taken. However, recent investigations into designing liquid-cell TEM may circumvent this problem.
• Scanning electron microscopy (SEM) generates 3-dimensional images via a scanning electron beam and so is useful for imaging nanoparticles and nanoparticle superlattices that exhibit some kinds of notable 3-dimensional geometric characteristics.
• Atomic force microscopy, a technique in which a nanoscale probe is moved across a sample to reconstruct its shape via a “sense of touch,” has also been used for nanoparticle superlattice characterization.
• Images of repetitive superlattices are amenable to processing with two-dimensional fast Fourier transforms (FFTs) that can reveal insights about the lattice’s characteristics. Performing this form of FFT upon an image of a repetitive crystal structure creates a plot of spatial frequencies. This plot is said to display reciprocal space (or Fourier space).
• Distinct points on the reciprocal space plot correspond to certain properties of the lattice that are sometimes not apparent from the image prior to the FFT. In this way, very similar lattices can be clearly distinguished.

Kinetics of nanoparticle superlattice formation

• Homogenous nucleation occurs in solution and requires overcoming a nucleation barrier while heterogenous nucleation occurs as nanoparticles are added to a preexisting seed crystal. Homogenous nucleation typically leads to disordered solids and is typically much slower than heterogenous nucleation.
• In heterogenous nucleation, crystal growth occurs at differing rates depending on how many new contacts are formed (assuming attractive interparticle interactions). If more new contacts occur upon the addition of a nanoparticle, the process will exhibit grater energetic favorability and occur at a faster rate.
• This means that adding nanoparticles to kinks and vacancies happens more rapidly than the adsorption of nanoparticles to steps, terraces, and “adatoms” (see figure at right). As such, large scale structures that minimize surface energy tend to form.

Thermodynamics of nanoparticle superlattices

• As mentioned, if superlattice assembly occurs rapidly, disordered aggregates can form. Allowing the process to occur more slowly facilitates sampling of many states as assembly proceeds. As such, the most thermodynamically stable structures can form when gradual assembly is performed.
• Van der Waals interactions between nanoparticles are often approximated using the following pair potential equation. U is the potential energy for the interparticle interaction, C represents a proportionality constant for the interparticle interaction, ρ₁ and ρ₂ are the number of atoms per unit volume in two interacting bodies, and r is the distance between the bodies.

• For nanoparticles with volumes V₁ and V₂, the total van der Waals energy of attraction is obtained by the following integral that performs a pairwise summation of all the atomic van der Waals interactions.

• If two nanoparticles are spherical with radii R₁ and R₂, the integral can be solved analytically to give their interparticle potential energy.

• When the distance d between two nanoparticles is much less than the radius of either nanoparticle, the above equation can be approximated using the following formula.

• For many nanoparticles without chemical ligands, these van der Waals interactions would cause rapid aggregation in solution. However, the presence of certain surface ligands gives repulsion that maintains colloidal solutions of nanoparticles.
• In order to convey repulsive effects between nanoparticles, the surface ligands require a proper solvent. Such solvents exhibit negative free energy upon ligand-solvent mixing. That is, interactions between the surface ligand and the solvent are energetically favorable.
• Surface ligand repulsion includes an osmotic component and an elastic component. As the solvent molecules are sterically blocked by surface ligands, when the surface ligands of two nanoparticles start to interact, the volume that the solvent cannot enter increases. This situation is osmotically unfavorable, so osmotic repulsion occurs. When surface ligands are compressed because two nanoparticles are close to each other, elastic repulsion occurs.
• When a solution of nanoparticles with surface ligands that are attracted to each other (i.e. hydrophobic chains) is dried, the ligands begin to freeze together rather than experiencing repulsion.
• Equilibrium superlattice structures minimize the free energy G in terms of enthalpy U and entropy S according to Gibb’s equation ΔG = ΔU – TΔS.
• The contributions of cores and ligands can be decomposed into the terms ΔU_cores, ΔU_ligands, ΔS_cores, and ΔS_ligands. The energy terms can be further broken down into the components of van der Waals interactions (London dispersion forces, dipole-induced dipole interactions, and dipole-dipole interactions). The entropy terms can be further broken down into configurational, rotational, and translational components.

Reference: Boles, M. A., Engel, M., & Talapin, D. V. (2016). Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials. Chemical Reviews, 116(18), 11220–11289. https://doi.org/10.1021/acs.chemrev.6b00196

My first scientific journal article (I am the lead author)! I came up with the idea for this project during middle school. In high school, I started working at a university laboratory. Over the course of this research, I competed in the International Science and Engineering Fair three times, gave a TEDx presentation, fought through countless obstacles, ignored the naysayers, witnessed the Nobel Prize ceremonies firsthand, and brought my idea to fruition.

ACS Biochemistry: Design of a De Novo Aggregating Antimicrobial Peptide and a Bacterial Conjugation-Based Delivery System

Local copy (full text): Design of a De Novo Aggregating Antimicrobial Peptide and a Bacterial Conjugation-Based Delivery System

PDF version: Notes on computer architecture – Logan Thrasher Collins

Main memory

• Some computers store data using flip-flop circuits. Each flip-flop circuit possesses a configuration of logic gates (including AND, OR, and NOT gates) that allows switching between “on” and “off” states corresponding to 1 and 0.
• More modern machines often use conceptually similar ways of storing data that involve using tiny electric charges to represent 1 and 0 states.
• Each memory cell contains eight flip-flop circuits (or similar storage devices) that correspond to eight bits of memory. Together, eight bits are equal to one byte.
• The memory cell’s eight bits are depicted as arranged in a line. The leftmost end is called the high-order end and the rightmost end is called the low-order end. The leftmost bit is called the most significant bit and the rightmost bit is called the least significant bit.
• In order for the computer to find specific memory cells within main memory, every cell is assigned a unique numeric address. This can be visualized as a series of memory cells lined up and numbered starting with zero. In this way, individual cells are not only identifiable, but they are also ordered relative to other cells.
• Since the computer can independently access any cell that is needed for a computation (despite the cells possessing an ordered configuration), the main memory is called random access memory (RAM).
• For computers that use tiny charges (rather than flip-flop circuits) to store data, the main memory is called dynamic RAM or DRAM because the charges are volatile, dissipate quickly, and must be restored many times per second using a refresh circuit.

Central processing unit

• The central processing unit (CPU) includes an arithmetic unit that performs operations on data, a control unit that coordinates the machine’s activities, and a register unit that temporarily stores results from the arithmetic unit (and other data) in registers.
• The CPU is connected to the main memory (which is more permanent than the registers) via a collection of wires called a bus. To perform an operation on data from the main memory, the CPU uses an electronic address to find the desired data cell and send it to a set of registers. To write data into the proper location within main memory, the CPU uses a similar address system.

The stored program

• Instructions for the CPU’s data manipulation can be stored in a computer’s main memory because programs and data are not fundamentally distinct entities.
• The following steps summarize how stored programs operate.
  1. Retrieve a set of values from main memory and place each value within a register.
  2. Activate the circuitry that performs some operation upon the values (i.e. two values might be added together) and then store the result in another register.
  3. Transfer the result from its register to main memory for long-term storage. After this, stop the program.
• CPUs also store cache memory in order to increase their speed. The cache memory is a temporary copy of the portion of the main memory that is undergoing processing at a given time. Using cache memory, the CPU can rapidly retrieve relevant data without needing to go all the way to the main memory as often.

Machine language

• Data transfer group: instructions to “transfer” data from a memory cell to a register (or some similar process) are more accurately described as “copying” the data. Requests to copy data from are memory cell to a register are called LOAD instructions. Requests to copy data from a register and write it to a memory cell are called STORE instructions. Requests that control interaction of the CPU and main memory with external devices like printers and keyboards are referred to as I/O instructions.
• Arithmetic/logic group: the arithmetic/logic unit can carry out instructions that run data through basic arithmetic operations and Boolean logic gate operations (AND, NOT, OR, XOR, etc.) The arithmetic/logic unit also uses the SHIFT and ROTATE instructions. SHIFT moves bits to the left or right within a register. ROTATE is another version of SHIFT which moves bits to the slots at the other end of the register (rather than allowing them to “fall off” as would happen if SHIFT were used).
• Control group: contains instructions that direct program execution and termination. JUMP (also called BRANCH) commands cause a program to change the next action that it performs. JUMP commands can be unconditional or conditional (when conditional, they work like “if” statements). The STOP command also falls into this category.

Machine cycle

• The machine cycle involves two special purpose registers, the instruction register and the program counter.
• The instruction register contains the instruction that is undergoing execution.
• The program counter contains the address of the next instruction that will be executed and so keeps track of the machine’s place within the program.
• Using three steps, the CPU performs the machine cycle.
  1. Fetch: the CPU retrieves an instruction from the main memory at the address specified by its program counter. The program counter then increments to specify the next instruction.
  2. Decode: the CPU breaks the instruction into appropriate components based on its operational code.
  3. Execute: the CPU activates the necessary circuitry to perform the command that was requested.
• The computer’s clock is a circuit that generates oscillating pulses which control the machine cycle’s rate. A faster clock speed results in a faster machine cycle. Clock speed is measured in Hertz. Typical laptop computers (as of 2018) run at clock speeds of several GHz.
• To increase a computer’s performance, pipelining is often used. Pipelining involves allowing the steps of the machine cycle to overlap. Using pipelining, an instruction can be fetched while the previous operation is still underway, multiple instructions can be fetched simultaneously, and multiple operations can be executed simultaneously so long as they are independent of each other.

Multiprocessor machines

• Some computers possess multiple CPUs that are linked to the same main memory. This is called a multiple-instruction stream multiple-data stream (MIMD) architecture. The CPUs operate independently while coordinating their efforts by writing instructions to each other on their shared memory cells. In this way, a CPU can request another CPU to perform a specified part of a large processing task.
• Some computers use multiple CPUs that are linked together so as to perform the same sequence of instructions simultaneously upon distinct datasets. This is called a single-instruction stream multiple-data stream (SIMD) architecture. SIMD machines are useful when the application requires the same task to be performed upon a large amount of data.
• Parallel processing can also be carried out using large computers that are composed of multiple smaller computers, each with its own CPU and main memory. In these cases, the smaller computers coordinate the partitioning of resources to handle a given task.

Reference and image source: Brookshear, J. G., Smith, D. T., & Brylow, D. (2012). Computer Science: An Overview. Addison-Wesley.