Capillary action is vital to many biological phenomena, driving, for example, transpiration in plants to transport water from the ground, through the plant, and eventually out through its leaves. Although liquid flow through these small channels (capillaries) has been described for centuries—for instance by the Young–Laplace equation, which relates surface tension and surface curvature to the applied pressure needed to advance liquid through the capillary channel—when Lawrence Livermore scientists began experimenting with flow through smaller and smaller channels, they made stunning observations.
In their experiments, carbon nanotubes (CNTs) served as transport channels, their interiors so minuscule that only a few water molecules could pass through at once. The Young–Laplace relation suggests that such immense pressure must be applied to push water molecules through CNTs that water flow should be impossible. Yet, during experiments, the opposite was observed: the channels spontaneously filled with water, which flowed with almost no resistance.
Since scientists first documented this surprising effect in the early 2000s and started what became known as nanofluidics, this research field has matured. Resolving liquid flow through CNTs is not merely satisfying scientific curiosity. Nanofluidics research offers direct applications to the realms of bioengineering, drug delivery, and even neuromorphic computing. Now, by pairing state-of-the-art experimental setups with powerful computational resources, Livermore scientists are uncovering the curious properties of liquid transport in CNTs and using their findings to inspire new technologies.
Tubular Flow Phenomena
Nanofluidics is still a rapidly growing area of research, and Lawrence Livermore has played a vital role since the field’s inception. The Laboratory is a founding member of the Center for Enhanced Nanofluidic Transport (CENT), a virtual Department of Energy (DOE)–funded Energy Frontier Research Center now hosted at the Massachusetts Institute of Technology. Through CENT, researchers at participating universities and national laboratories address knowledge gaps concerning the properties of water under nanoconfinement in search of new, engineered materials to support liquid transport at unparalleled efficiency.
“Nanofluidic phenomena act at smaller scales than most of the effects that shape our everyday world. As such, conventional physics understanding often does not apply,” says Livermore scientist Aleksandr Noy. At the nanoscale, scientists must account for atomic-level effects to accurately predict liquid flow through CNTs. Noy’s team did not find an Achilles’ heel in the classical equations used to describe liquid flow. Rather, the equations alone could not fully describe water flow through CNTs because they simply do not capture the physical phenomena that dominate during liquid nanoconfinement.
Flow rate of a liquid is highly dependent on viscosity, a property observed, for example, in the way a liquid like milk can flow with ease over a surface while a more viscous liquid like honey crawls along. This fluid property reflects the rate at which momentum within the liquid dissipates throughout its volume. Scientists found that water exhibits extraordinary flow properties when passing through a highly constrained pathway. Noy explains, “When confined to a CNT, water molecules form a single chain as if they are part of one big molecular conga line. This chain has no width or depth, and thus no volume, so viscosity is confined in one dimension along the water chain. As a result, single-file arrangement of water molecules in CNTs is one of the fastest water transport channels that exists.”
This peculiar behavior arises from how the geometry and electrical properties of CNTs affect water molecules. The interior face of CNTs is smooth and hydrophobic, conducive to frictionless water flow. Noy’s recent research shows that flow efficiency is further influenced by the arrangement of carbon atoms constituting the CNT wall—the CNT’s chirality. CNTs with different chirality exhibit unique flow properties depending on how the carbon atoms are “wound up” into their tubular shape. Different arrangements of carbon atoms and their electronic states cause the CNT wall to become either semiconducting or fully metallic. Noy’s team observed that water flowed through metallic CNTs faster than through semiconducting CNTs. The degree of metallicity influences how water molecules interact with the wall because water molecules are polar, with partial positive and negative charges associated with their hydrogen atoms and oxygen atom, respectively. Confining water molecules to such a narrow space amplifies the interactions of their dipoles with the nanotube walls, ultimately varying the amount of friction they encounter while passing through the nanotube.
In another study, Livermore researchers detailed an ion transport mechanism that seemingly defies a second fundamental fluid mechanics equation, the Nernst–Einstein relation, which connects a particle’s tendency to diffuse into a medium to the speed of its movement under an applied electric field (electrophoretic mobility). When Noy’s team measured the efficiency of ion diffusion and ion electrophoresis in CNTs, their findings differed by orders of magnitude from what the Nernst–Einstein relation would predict. Computer simulations performed by CENT researchers completed the physics picture, revealing a dramatic mechanism of ion transport. Under an applied electric field, the CNT pore momentarily empties of water; then, small clusters of ions and water molecules speed through the nanotube similar to a bullet through a gun’s barrel. This mechanism allows the electrophoretic transport to exceed the efficiency offered by simple diffusion, thus breaking the Nernst–Einstein relation.
Nanoscale Experiments
Understanding liquid flow under nanoconfinement could open the door to revolutionary materials and technologies, but probing molecular interactions to achieve the most accurate measurements demands pioneering experimental platforms. Previous approaches to studying liquid transport through CNTs were complicated by uncertainties surrounding variability in CNT properties and how they embedded into an experimental platform. Noy’s team came up with a new platform that uses highly purified sources of CNTs with controlled geometry and electronic properties. In this platform, short snippets of CNTs called carbon nanotube porins (CNTPs) are produced through sonication (shattering long CNTs into fragments using strong ultrasound) and are embedded in a lipid membrane. CNTPs are an asset to nanofluidics experiments because they can also spontaneously migrate into a lipid bilayer used to separate two chambers in the way that the membrane of a biological cell defines the cell’s interior and exterior. Once embedded within the lipid bilayer, CNTPs resemble a class of transmembrane proteins called aquaporins.
Noy’s group applies these properties to their Droplet Interface Bilayer experimental platform. First, researchers place droplets of a lipid-laden solution into an oil bath. The lipids naturally line up on the surface of these small, circular droplets, their hydrophilic heads facing inward and their hydrophobic tails sticking out into the oil. When two droplets eventually come together, their membranes stick together and form a lipid bilayer segment that resembles a cell membrane. CNTPs added to the droplets spontaneously migrate into position and form a bridge between the conjoined vesicles, providing a channel to transport ions between those vesicles. The researchers can then characterize material transport between the vesicles by measuring the ion current between the droplets with a high-sensitivity patch-clamp amplifier. This setup is familiar to cell biologists, who use it to study transport through biological ion channels, but Noy’s group pioneered its use in carbon nanofluidics.
Modeling Every Atom
Using this precisely addressable experimental platform, the Livermore team’s strength is pairing experimental results with simulation predictions. “We can directly compare the behavior observed during experiments to the predictions made by our molecular dynamics simulations. We have learned precisely what to control and what to simulate,” says Livermore scientist Tuan Anh Pham. Computational modeling typically involves a simplified model of the structure. Engineering analysis of a macroscopic 3D structure, such as a bridge, might consider the structure as many discrete sections to study how forces affect the overall structure. “In our modeling case, however, the CNT and lipid membrane are small enough that we can model them explicitly and use the right physics,” says Noy. Instead of modeling the CNT and membrane as simplified sections, the team’s all-atomic simulations capture the dynamics of every atom in each of the system’s components: the CNT, the surrounding lipid membrane, and individual water molecules and ions flowing through the CNT’s interior.
The team utilized a combination of existing and purpose-built computing resources to achieve atomic-level modeling precision. According to Pham, commercial or open-source molecular dynamics simulation software usually suffices for estimating how atoms and molecules would interact in the experimental platform. However, the group needed to develop modeling code to simultaneously investigate finer, complicated dynamics such as the vibration of ions, mixtures of multiple ions, and quantum electronic effects that could significantly affect the overall flow dynamics. Pham’s computing efforts to explore molecular dynamics, nanostructures, and electrocatalysts on institutional computational resources have received node hours in multiple years of the Lawrence Livermore Computing Grand Challenge awards. “Much of this work can only be done here at Livermore because we have the world’s premier computing systems and simulation capabilities,” says Pham.
The primary challenge posed by atomic-level resolution is that the associated multiphysics simulations would be too resource-intensive to perform repeatedly. Atomistic simulations typically calculate dynamics on the order of picosecond (thousandths of a nanosecond) intervals to capture quantum electronic phenomena, whereas liquids flow through CNTs over the course of nanoseconds. Moreover, the team needed to capture the behavior not only of individual atoms (subnanometer-scale), but their ensemble behavior at the magnitudes-greater micrometer scale. “Accuracy and speed rarely coexist in the realm of computer simulations,” says Pham.
To contend with this trade-off, the team struck a middle ground: applying machine-learning techniques to simulate the CNT system at the necessary spatial and temporal scales while retaining the accuracy associated with quantum (atomic-level) simulations. “We found that accounting for quantum effects is essential to accurately simulating liquid transport in CNTs. Only when we took into account these effects did we discover how different materials support varying transport efficiency,” says Pham.
New Computing Paradigm
Because the membrane-embedded CNTPs at the heart of the team’s new experimental platform resemble transmembrane protein pores, the platform is ideal for developing novel membrane separation technologies and for studying controlled molecule release and efficient transport into a targeted cell for drug delivery. Increasing control of liquid flow through nanoscale channels has even broader technological implications. Livermore researchers are investigating how to use the phenomenon of ion transport through these channels to process information.
The notion is not far-fetched. Noy says that in essence, neural networks—those employed in machine-learning algorithms—are a collection of junctions through which information passes and transforms in series. These junctions are differentially weighted, meaning the output of one junction may prove more consequential to the final result than output from another junction. Neural networks encoded in electronic computer hardware are now commonplace. If the medium for passing information and performing logic is not semiconductors and transistors but rather the flow of ions through nanopores, then, the system begins mimicking the function of neurons found in the brain, giving rise to the term “neuromorphic ionic computing.”
Noy explains, “In the brain, these junctions are embodied as synapses, where neurotransmitters and ions help the signal pass from the axon of one neuron to the dendrite of another neuron.” Scientists emulate neurobiological behavior through a spiking neural network architecture whose parameters relate to charge, timing, and threshold values in similar fashion to how traditional neural networks are programmed with weights and biases.
Noy and his team are already working with researchers in Livermore’s Engineering Principal Directorate as well as colleagues at Sandia National Laboratories, the University of Southern California, and Google Research to design nanofluidics-based components and neuromorphic algorithms to carry out proof-of-principle computational tasks. Most recently, they have used nanofluidic droplet interfaces and a technique called reservoir computing to play a tic-tac-toe game. With enough development—despite being slower than silicon-based computing—biomimetic computing systems could prove more energy-efficient and parallelizable than today’s supercomputers—advantages attractive to laboratories and enterprises contending with increasing power demand as computational needs escalate.
—Elliot Jaffe
For further information contact Aleksandr Noy (925) 423-3396 (noy1 [at] llnl.gov (noy1[at]llnl[dot]gov)).
