Boundary Frustration in Double-Gyroid Thin Films.

Self-consistent field theory for thin films of AB diblock polymers in the double-gyroid phase reveals that in the absence of preferential wetting of monomer species at the film boundaries, films with the (211) plane oriented parallel to the boundaries are more stable than other orientations, consistent with experimental results. This preferred orientation is explained in the context of boundary frustration. Specifically, the angle of intersection between the A/B interface and the film boundary, the wetting angle, is thermodynamically restricted to a narrow range of values. Most termination planes in the double gyroid cannot accommodate this narrow range of wetting angles without significant local distortion relative to the bulk morphology; the (211)-oriented termination plane with the "double-wave" pattern produces relatively minimal distortion, making it the least frustrated boundary. The principle of boundary frustration provides a framework to understand the relative stability of termination planes for complex ordered block polymer phases confined between flat, nonpreferential boundaries.

Probing physical properties of single amyloid fibrils using nanofluidic channels.

Amyloid fibril formation is central to the pathology of many diseases, including neurodegenerative disorders such as Alzheimer's and Parkinson's disease. Amyloid fibrils can also have functional and scaffolding roles, for example in bacterial biofilms, and have also been exploited as useful biomaterials. Despite being linear protein homopolymers, amyloid fibrils can exhibit significant structural and morphological polymorphism, making it relevant to study them on the single fibril level. We here introduce the concept of nanofluidic channel analysis to the study of single, fluorescently-labeled amyloid fibrils in solution, monitoring the extension and emission intensity of individual fibrils confined in nanochannels with a depth of 300 nm and a width that gradually increases from 300 to 3000 nm. The change in fibril extension with channel width permitted accurate determination of the persistence length of individual fibrils using Odijk's theory for strongly confined polymers. The technique was applied to amyloid fibrils prepared from the Alzheimer's related peptide amyloid-ß(1-42) and the Parkinson's related protein α-synuclein, obtaining mean persistence lengths of 5.9 ± 4.5 µm and 3.0 ± 1.6 µm, respectively. The broad distributions of fibril persistence lengths indicate that amyloid fibril polymorphism can manifest in their physical properties. Interestingly, the α-synuclein fibrils had lower persistence lengths than the amyloid-ß(1-42) fibrils, despite being thicker. Furthermore, there was no obvious within-sample correlation between the fluorescence emission intensity per unit length of the labelled fibrils and their persistence lengths, suggesting that stiffness may not be proportional to thickness. We foresee that the nanofluidics methodology established here will be a useful tool to study amyloid fibrils on the single fibril level to gain information on heterogeneity in their physical properties and interactions.

Gaming self-consistent field theory: Generative block polymer phase discovery.

Block polymers are an attractive platform for uncovering the factors that give rise to self-assembly in soft matter owing to their relatively simple thermodynamic description, as captured in self-consistent field theory (SCFT). SCFT historically has found great success explaining experimental data, allowing one to construct phase diagrams from a set of candidate phases, and there is now strong interest in deploying SCFT as a screening tool to guide experimental design. However, using SCFT for phase discovery leads to a conundrum: How does one discover a new morphology if the set of candidate phases needs to be specified in advance? This long-standing challenge was surmounted by training a deep convolutional generative adversarial network (GAN) with trajectories from converged SCFT solutions, and then deploying the GAN to generate input fields for subsequent SCFT calculations. The power of this approach is demonstrated for network phase formation in neat diblock copolymer melts via SCFT. A training set of only five networks produced 349 candidate phases spanning known and previously unexplored morphologies, including a chiral network. This computational pipeline, constructed here entirely from open-source codes, should find widespread application in block polymer phase discovery and other forms of soft matter.

Thermodynamics and morphology of linear multiblock copolymers at homopolymer interfaces.

Block copolymers at homopolymer interfaces are poised to play a critical role in the compatibilization of mixed plastic waste, an area of growing importance as the rate of plastic accumulation rapidly increases. Using molecular dynamics simulations of Kremer-Grest polymer chains, we have investigated how the number of blocks and block degree of polymerization in a linear multiblock copolymer impacts the interface thermodynamics of strongly segregated homopolymer blends, which is key to effective compatibilization. The second virial coefficient reveals that interface thermodynamics are more sensitive to block degree of polymerization than to the number of blocks. Moreover, we identify a strong correlation between surface pressure (reduction of interfacial tension) and the spatial uniformity of block junctions on the interface, yielding a morphological framework for interpreting the role of compatibilizer architecture (number of blocks) and block degree of polymerization. These results imply that, especially at high interfacial loading, the choice of architecture of a linear multiblock copolymer compatibilizing surfactant does not greatly affect the modification of interfacial tension.

Liquid-Like States in Micelle-Forming Diblock Copolymer Melts.

Large cell self-consistent field theory (SCFT) solutions for a neat, micelle-forming diblock copolymer melt, initialized using the structure of a Lennard-Jones fluid, reveal the existence of a vast number of liquid-like states, with free energies of order 10-3 kBT per chain higher than the body-centered cubic (bcc) state near the order-disorder transition (ODT). Computation of the structure factor for these liquids at temperatures below the ODT indicates that their intermicellar distance is slightly swollen compared to bcc. In addition to providing a mean-field picture of the disordered micellar state, the number of liquid-like states and their near-degeneracy with the equilibrium bcc morphology suggest that self-assembly of micelle-forming diblock copolymers navigates a rugged free energy landscape with many local minima. This picture provides a basis for the anomalously slow ordering kinetics of particle-forming diblock copolymer melts observed in experiments.

Diffusion of knots in nanochannel-confined DNA molecules.

We used Langevin dynamics simulations without hydrodynamic interactions to probe knot diffusion mechanisms and the time scales governing the evolution and the spontaneous untying of trefoil knots in nanochannel-confined DNA molecules in the extended de Gennes regime. The knot untying follows an "opening up process," wherein the initially tight knot continues growing and fluctuating in size as it moves toward the end of the DNA molecule before its annihilation at the chain end. The mean knot size increases significantly and sub-linearly with increasing chain contour length. The knot diffusion in nanochannel-confined DNA molecules is subdiffusive, with the unknotting time scaling with chain contour length with an exponent of 2.64 ± 0.23 to within a 95% confidence interval. The scaling exponent for the mean unknotting time vs chain contour length, along with visual inspection of the knot conformations, suggests that the knot diffusion mechanism is a combination of self-reptation and knot region breathing for the simulated parameters.

Tuning conformational asymmetry in particle-forming diblock copolymer alloys.

Self-consistent field theory is employed to compute the phase behavior of binary blends of conformationally asymmetric, micelle-forming diblock copolymers with miscible corona blocks and immiscible core blocks (a diblock copolymer "alloy"). The calculations focus on establishing conditions that promote the formation of Laves phases by tuning the relative softness of the cores of the two different Laves phase particles via independent control of their conformational asymmetries. Increasing the conformational asymmetry of the more spherical particles of the Laves structure has a stabilizing effect, consistent with the expectations of increased imprinting of the Wigner-Seitz cells on the core/corona interface as conformational asymmetry increases. The resulting phase diagram in the temperature-blend composition space features a more stable Laves phase field than that predicted for conformationally symmetric systems. The phase field closes at low temperatures in favor of macrophase separation between a hexagonally-packed cylinder (hex) phase and a body-centered cubic phase. Companion calculations, using an alloy whose components do not produce a hex phase in the neat melt state, suggest that the Laves phase field in such a blend will persist at strong segregation.

Dynamics and Equilibration Mechanisms in Block Copolymer Particles.

Self-assembly of block copolymers into interesting and useful nanostructures, in both solution and bulk, is a vibrant research arena. While much attention has been paid to characterization and prediction of equilibrium phases, the associated dynamic processes are far from fully understood. Here, we explore what is known and not known about the equilibration of particle phases in the bulk, and spherical micelles in solution. The presumed primary equilibration mechanisms are chain exchange, fusion, and fragmentation. These processes have been extensively studied in surfactants and lipids, where they occur on subsecond time scales. In contrast, increased chain lengths in block copolymers create much larger barriers, and time scales can become prohibitively slow. In practice, equilibration of block copolymers is achievable only in proximity to the critical micelle temperature (in solution) or the order-disorder transition (in the bulk). Detailed theories for these processes in block copolymers are few. In the bulk, the rate of chain exchange can be quantified by tracer diffusion measurements. Often the rate of equilibration, in terms of number density and aggregation number of particles, is much slower than chain exchange, and consequently observed particle phases are often metastable. This is particularly true in regions of the phase diagram where Frank-Kasper phases occur. Chain exchange in solution has been explored quantitatively by time-resolved SANS, but the results are not well captured by theory. Computer simulations, particularly via dissipative particle dynamics, are beginning to shed light on the chain escape mechanism at the molecular level. The rate of fragmentation has been quantified in a few experimental systems, and TEM images support a mechanism akin to the anaphase stage of mitosis in cells, via a thin neck that pinches off to produce two smaller micelles. Direct measurements of micelle fusion are quite rare. Suggestions for future theoretical, computational, and experimental efforts are offered.

DNA in nanochannels: theory and applications.

Nanofluidic structures have over the last two decades emerged as a powerful platform for detailed analysis of DNA on the kilobase pair length scale. When DNA is confined to a nanochannel, the combination of excluded volume and DNA stiffness leads to the DNA being stretched to near its full contour length. Importantly, this stretching takes place at equilibrium, without any chemical modifications to the DNA. As a result, any DNA can be analyzed, such as DNA extracted from cells or circular DNA, and it is straight-forward to study reactions on the ends of linear DNA. In this comprehensive review, we first give a thorough description of the current understanding of the polymer physics of DNA and how that leads to stretching in nanochannels. We then describe how the versatility of nanofabrication can be used to design devices specifically tailored for the problem at hand, either by controlling the degree of confinement or enabling facile exchange of reagents to measure DNA-protein reaction kinetics. The remainder of the review focuses on two important applications of confining DNA in nanochannels. The first is optical DNA mapping, which provides the genomic sequence of intact DNA molecules in excess of 100 kilobase pairs in size, with kilobase pair resolution, through labeling strategies that are suitable for fluorescence microscopy. In this section, we highlight solutions to the technical aspects of genomic mapping, including the use of enzyme-based labeling and affinity-based labeling to produce the genomic maps, rather than recent applications in human genetics. The second is DNA-protein interactions, and several recent examples of such studies on DNA compaction, filamentous protein complexes, and reactions with DNA ends are presented. Taken together, these two applications demonstrate the power of DNA confinement and nanofluidics in genomics, molecular biology, and biophysics.

DNA fragmentation in a steady shear flow.

We have determined the susceptibility of T4 DNA (166 kilobase pairs, kbp) to fragmentation under steady shear in a cone-and-plate rheometer. After shearing for at least 30 min at a shear rate of 6000 s - 1 , corresponding to a Reynolds number of O ( 10 3 ) and a Weissenberg number of O ( 10 3 ) , 97.9 ± 1.3 % of the sample is broken into a polydisperse mixture with a number-averaged molecular weight of 62.6 ± 3.2 kbp and a polydispersity index of 1.29 ± 0.03 , as measured by pulsed-field gel electrophoresis (with a 95% confidence interval). The molecular weight distributions observed here from a shear flow are similar to those produced by a (dominantly extensional) sink flow of DNA and are qualitatively different than the midpoint scission observed in simple extensional flow. Given the inability of shear flow to produce a sharp coil-stretch transition, the data presented here support a model where polymers can be fragmented in flow without complete extension. These results further indicate that DNA fragmentation by shear is unlikely to be a significant issue in microfluidic devices, and anomalous molecular weight observations in experiments are due to DNA processing prior to observation in the device.

Stabilizing a Double Gyroid Network Phase with 2 nm Feature Size by Blending of Lamellar and Cylindrical Forming Block Oligomers.

Molecular dynamics simulations are used to study binary blends of an AB-type diblock and an AB2-type miktoarm triblock amphiphiles (also known as high-χ block oligomers) consisting of sugar-based (A) and hydrocarbon (B) blocks. In their pure form, the AB diblock and AB2 triblock amphiphiles self-assemble into ordered lamellar (LAM) and cylindrical (CYL) structures, respectively. At intermediate compositions, however, the AB2-rich blend (0.2 ≤ x AB ≤ 0.4) forms a double gyroid (DG) network, whereas perforated lamellae (PL) are observed in the AB-rich blend (0.5 ≤ x AB ≤ 0.8). All of the ordered mesophases present domain pitches under 3 nm, with 1 nm feature sizes for the polar domains. Structural analyses reveal that the nonuniform interfacial curvatures of DG and PL structures are supported by local composition variations of the LAM- and CYL-forming amphiphiles. Self-consistent mean field theory calculations for blends of related AB and AB2 block polymers also show the DG network at intermediate compositions, when A is the minority block, but PL is not stable. This work provides molecular-level insights into how blending of shape-filling molecular architectures enables network phase formation with extremely small feature sizes over a wide composition range.

Alternating Gyroid in Block Polymer Blends.

Alternating gyroid is a lower symmetry variant of the double gyroid morphology, where the left-handed and right-handed chiral networks are physically distinct. This structure is of particular interest for photonic applications owing to predictions of a complete photonic band gap subject to the requirement of a large dielectric contrast between the individual networks and sufficient optical matching between one of the networks and the matrix. We provide evidence, via self-consistent field theory (SCFT), that stoichiometric blends of double-gyroid-forming AB and BC diblock copolymers with relatively immiscible A and C blocks should form an alternating gyroid morphology with complementary three-dimensional A and C networks that have a free energy that is nearly degenerate with two phase-separated double gyroid states. Solvent casting offers the potential for trapping this binary mixture of diblock copolymers in this metastable alternating gyroid phase. Theory further predicts that the addition of a minuscule amount (<1%) of ABC triblock terpolymer will open an alternating gyroid stability window in the resulting ternary-phase diagram. The surfactant-like stabilization produced by the triblock is relatively insensitive to its exact composition provided the B-block forms a sufficiently long bridge between the A-rich and C-rich networks. This blending strategy provides significant synthetic and material processing advantages compared to prevailing methods to produce an alternating gyroid phase in block polymers.

Interactions between two knots in nanochannel-confined DNA molecules.

Experimental data on the interaction between two knots in deoxyribonucleic acid (DNA) confined in nanochannels produced two particular behaviors of knot pairs along the DNA molecules: (i) widely separated knots experience an attractive interaction but only remain in close proximity for several seconds and (ii) knots tend to remain separated until one of the knots unravels at the chain end. The associated free energy profile of the knot-knot separation distance for an ensemble of DNA knots exhibits a global minimum when knots are separated, indicating that the separated knot state is more stable than the intertwined knot state, with dynamics in the separated knot state that are consistent with independent diffusion. The experimental observations of knot-knot interactions under nanochannel confinement are inconsistent with previous simulation-based and experimental results for stretched polymers under tension wherein the knots attract and then stay close to each other. This inconsistency is postulated to result from a weaker fluctuation-induced attractive force between knots under confinement when compared to the knots under tension, the latter of which experience larger fluctuations in transverse directions.

The C36 Laves phase in diblock polymer melts.

The C14 and C15 Laves phases form as micelle packing structures in many types of soft matter, but the related C36 phase, which consists of alternating C14-type and C15-type layers, has not been observed in any such system. To understand this absence in the context of diblock polymers, we used self-consistent field theory to relate the morphology and energetics of C36 to other known mesophases. Two case studies were conducted: blends of AB diblock polymers with A homopolymers (where A forms the micelle core), in which C14 and C15 have stability windows, and neat AB diblock melts, in which Laves phases are metastable. Laves phases exhibit nearly identical micelle morphologies and nearly degenerate free energies, with the free energy of C36 being a near-perfect bisector of the C14 and C15 free energies in all cases, revealing an intrinsic symmetry in free energy that is attributed solely to the structural relationship between the phases in which the packing of C36 is intermediate between C14 and C15. Based on this connection between structure and free energy, C36 is thus not expected to form in flexible diblock polymers, since C14 and C15 can always form instead via facile mass transfer.

Open-source platform for block polymer formulation design using particle swarm optimization.

Facile exploration of large design spaces is critical to the development of new functional soft materials, including self-assembling block polymers, and computational inverse design methodologies are a promising route to initialize this task. We present here an open-source software package coupling particle swarm optimization (PSO) with an existing open-source self-consistent field theory (SCFT) software for the inverse design of self-assembling block polymers to target bulk morphologies. To lower the barrier to use of the software and facilitate exploration of novel design spaces, the underlying SCFT calculations are seeded with algorithmically generated initial fields for four typical morphologies: lamellae, network phases, cylindrical phases, and spherical phases. In addition to its utility within PSO, the initial guess tool also finds generic applicability for stand-alone SCFT calculations. The robustness of the software is demonstrated with two searches for classical phases in the conformationally symmetric diblock system, as well as one search for the Frank-Kasper [Formula: see text] phase in conformationally asymmetric diblocks. The source code for both the initial guess generation and the PSO wrapper is publicly available.

Modeling of Quasi-Static Floating-Gate Transistor Biosensors.

Floating-gate transistors (FGTs) are a promising class of electronic sensing architectures that separate the transduction elements from molecular sensing components, but the factors leading to optimum device design are unknown. We developed a model, generalizable to many different semiconductor/dielectric materials and channel dimensions, to predict the sensor response to changes in capacitance and/or charge at the sensing surface upon target binding or other changes in surface chemistry. The model predictions were compared to experimental data obtained using a floating-gate (extended gate) electrochemical transistor, a variant of the generic FGT architecture that facilitates low-voltage operation and rapid, simple fabrication using printing. Self-assembled monolayer (SAM) chemistry and quasi-statically measured resistor-loaded inverters were utilized to obtain experimentally either the capacitance signals (with alkylthiol SAMs) or charge signals (with acid-terminated SAMs) of the FGT. Experiments reveal that the model captures the inverter gain and charge signals over 3 orders of magnitude variation in the size of the sensing area and the capacitance signals over 2 orders of magnitude but deviates from experiments at lower capacitances of the sensing surface (<1 nF). To guide future device design, model predictions for a large range of sensing area capacitances and characteristic voltages are provided, enabling the calculation of the optimum sensing area size for maximum charge and capacitance sensitivity.

Free Energy Trajectory for Escape of a Single Chain from a Diblock Copolymer Micelle.

We use umbrella sampling to compute the free energy trajectory of a single chain undergoing expulsion from an isolated diblock copolymer micelle. This approach elucidates the experimentally unobservable transition state, identifies the spatial position of the maximum free energy, and reveals the chain conformation of a single chain as it undergoes expulsion. Combining umbrella sampling with dissipative particle dynamics simulations of A4B8 micelles reveals that the core block (A) of the expelled chain remains partially stretched at the transition state, in contrast with the collapsed state assumed in some previous models. The free energy barrier increases linearly with the Flory-Huggins interaction parameter χ up to large interaction energies, where the structure of the otherwise spherical core apparently deforms near the transition state.

Order and Disorder in ABCA' Tetrablock Terpolymers.

Self-assembly of poly(styrene)-block-poly(isoprene)-block-poly(lactide)-block-poly(styrene) (PS-PI-PLA-PS' or SILS') tetrablock terpolymers, where the volume fractions of the first three blocks are nearly equivalent, was studied both experimentally and using the self-consistent field theory (SCFT). SCFT indicates that addition of the terminal PS' chain to a low-molecular-mass, hexagonally packed cylinders forming, SIL precursor can produce a disordered state due to preferential mixing of the polystyrene end-blocks with the PI and PLA midblocks in the SILS' tetrablock, alleviating the unfavorable contact between the highly incompatible PI and PLA segments. In contrast, SCFT predicts that higher-molar-mass triblock precursors will maintain an ordered morphology upon addition of the terminal PS' block due to stronger overall segregation strengths. These predictions were tested using three sets of SILS' polymers that were synthesized based on three precursor SIL triblock polymers differing in total molar mass (14, 30, and 47 kg mol-1) and varying the length of the terminal PS' chain. In the lowest-molar-mass set of tetrablock polymers, the shift from order to disorder was observed in the materials at ambient temperature as the molar mass of the terminal PS' block was increased, consistent with SCFT calculations. Disorder with longer S' chain lengths was not found in the two higher-molar-mass polymer sets; the medium-molar-mass set showed both microphase separation and long-range order based on transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS), while the largest of these block polymers microphase separated but showed limited long-range order. The combination of the experimental and theoretical results presented in this work provides insights into the self-assembly of ABCA'-type polymers and highlights potential complications that arise from frustration in accessing well-ordered materials.

3D Printing-Enabled DNA Extraction for Long-Read Genomics.

Long-read genomics technologies such as nanopore sequencing and genome mapping in nanochannels extract genomic information in the kilobase to megabase pair range from single DNA molecules, thereby overcoming read-length limitations in next-generation DNA sequencing. Long-read technologies start with long DNA molecules as the input and thus benefit from universal sample preparation methods that are fast and shear-free and present a scope of automation and direct upstream integration. We describe a 3D printing-assisted poly(dimethylysiloxane)-based DNA sample preparation device, where diffusive chemical lysis followed by electrophoresis produces circa 100 ng of long DNA directly from cells with less than 5 min of labor. Assessment of the product DNA by confinement in nanochannels reveals that the DNA sizes are commensurate with the requirements for long-read single-molecule technologies. Microfluidics not only expedites sample preparation, but also offers the opportunity for integration with genomics technologies to eliminate DNA fragmentation and loss during transfer to the genomic device.