Approximate solutions of M nonlinear equations in N unknowns for M greater than N
Approximate solutions of M nonlinear equations in N unknowns
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Approximate solutions of M nonlinear equations in N unknowns
Abstract Atomically dispersed and nitrogen coordinated single metal sites (M‐N‐C, M=Fe, Co, Ni, Mn) are the popular platinum group‐metal (PGM)‐free catalysts for many electrochemical reactions. Traditional wet‐chemistry catalyst synthesis often requires complex procedures with unsatisfied reproducibility and scalability. Here, we report a facile chemical vapor deposition (CVD) strategy to synthesize the promising M‐N‐C catalysts. The deposition of gaseous 2‐methylimidazole onto M‐doped ZnO substrates, followed by an in situ thermal activation, effectively generated single metal sites well dispersed into porous carbon. In particular, an optimal CVD‐derived Fe‐N‐C catalyst exclusively contains atomically dispersed FeN 4 sites with increased Fe loading relative to other catalysts from wet‐chemistry synthesis. The catalyst exhibited outstanding oxygen‐reduction activity in acidic electrolytes, which was further studied in proton‐exchange membrane fuel cells with encouraging performance.
A real-space method using generating integers is used to determine possible commensurate lattice Moiré patterns for a bilayer of two equal hexagonal lattices, which can in principle be extended to lattice mismatched bilayers. These Moiré patterns can be classified by a pair of relatively prime integers (n,m), wherein a rotation θ(n,m) of the top hexagonal lattice maps its lattice vector (n,m) to (m,n) of the bottom lattice. Within this formulation, the area of the commensurate supercell is proportional to (n2+m2+nm) and the number of coincident lattice sites per supercell is given by (n−m)2. Taking bilayer boron nitride (BN) as an example, we present how to systematically generate Moiré patterns and explore the differences in local chemistry in the interstitial region by impurity intercalation. Systematic calculations of the properties of intercalated 3d transition metals were performed in an h-BN (4,3) bilayer, corresponding to a rotation of 9.43 degrees. These calculations reveal that local symmetry in the intercalated region significantly affect the energetics and magnetization of the intercalated species. These results highlight that Moiré pattern physics is not limited to optoelectronic/electronic phenomena, such as interfacial exciton formation or magic angle superconductivity, but it also produces chemical and magnetic atomic site selectivity, which may play important roles in adsorption, catalysis, or quantum information.
Advances in wurtzite nitride ferroelectrics of Al 1-x M x N ( M = Sc or B) have led to novel capabilities, which must be integrated into existing fabrication processes. In the case of electronics operating > 200°C, a movement toward SiC-based platforms enables better performance over conventional Si, primarily due to the higher bandgap and lower intrinsic carrier concentration of SiC. Hence, the challenge is to develop a deposition process to integrate Al 1-x M x M x N ferroelectrics with elevated temperature-compatible materials for high temperature electronics such as the non-volatile memory component. We demonstrate epitaxial Al M N/Mo/SiC heterostructures, which provides both the crystalline and surface features that promote high-quality ferroelectric nitride film growth. Omega scans of the Mo (110) reflection exhibit a full width at half max of < 0.02° (40 arc sec) and the (0002) peak of the subsequently grown nitride film had a value of 1.1° for 160 nm thick Al 0.7 Sc 0.3 N and 1.3° for 400 nm thick Al 0.94 B 0.06 N. The crystallographic relationships found between the Al M N, Mo, and SiC layers indicate an advancement in sputter deposition of epitaxial films. Ferroelectric switching is also shown at 400 °C in both samples via polarization-electric field hysteresis and pulsed measurements, which exhibited P r values >100 μC cm -2 and E c between 3 and 4 M V cm -1 , despite a large presence of oxygen in both Al M N films ranging between 4 and 5 at.%, revealed by compositional analysis. This study demonstrates the process for synthesizing high-crystal quality ferroelectric nitride films, which can be used in extremely high temperature applications.
A family of coordination complexes of the type [Ru(SO 2 )(NH 3 ) 4 X] m+ Y n – (m, n = 1 or 2) exhibit optical switching capabilities in their single-crystal states. This striking effect is caused by the light-induced formation of SO 2 -linkage photoisomers, which are metastable if kept at suitably cool temperatures. We modeled the dark- and light-induced states of these large crystalline complexes via plane-wave (PW)- and molecular-orbital (MO)-based density functional theory (DFT) and time-dependent DFT in order to calculate their structural and optical properties; the calculated results are compared with experimental data. We show that the PW-DFT-based periodic models replicate the structural properties of these complexes more effectively than the MO-DFT-based molecular-fragment models, observing only small deviations in key bond lengths relative to the experimentally derived crystal structures. The periodic models were also found to more effectively simulate trends seen in experimental optical absorption spectra, with optical absorbance and coverage of the visible region increasing with the formation of the photoinduced geometries. The contribution of the metastable photoisomeric species more heavily focuses on the lower-energy end of the spectra. Spectra generated from the molecular-fragment models are limited by the geometry of the fragment used and the number of excited-state roots considered in those calculations. In general, periodic models outperform the molecular-fragment models owing to their ability to better appreciate the periodic phenomena that are present in these crystalline materials as opposed to MO approaches, which are finite methods. We thus demonstrate that PW-DFT-based periodic models should be considered as a more than viable method for simulating the optical and electronic properties of these single-crystal optical switches.
Proton-exchange membrane fuel cells (PEMFCs) are efficient and clean hydrogen energy technologies for transportation and stationary applications. Highly active and durable low-cost cathode catalysts for the oxygen-reduction reaction (ORR) under challenging acidic environments are desperately needed to address the cost and durability issues of PEMFCs. The most promising platinum group metal (PGM)-free catalysts for the ORR in acidic media are atomically dispersed and nitrogen-coordinated metal site catalysts denoted as M–N–C, M = Fe, Co, or Mn. Due to significant efforts in the past few decades, these catalysts have demonstrated much-improved ORR activity and promising initial fuel cell performance approaching traditional Pt/C catalysts. However, the insufficient long-term stability (up to 5000 h) under PEMFC operation represents a primary technical barrier to making current PGM-free catalysts less viable yet in PEMFCs. In this Account, we highlight recent advances in synthesizing efficient PGM-free catalysts for the ORR in PEMFCs, emphasizing effective strategies to improve mass and intrinsic activity and the possible degradation mechanisms. In particular, a chemical doping method based on the zeolitic imidazolate framework (ZIF)-8 represents the key to developing efficient M–N–C catalysts containing atomically dispersed and nitrogen-coordinated single metal active sites (i.e., MN 4 ). The newly acquired understanding of the formation mechanism of MN 4 active sites during the thermal activation and its correlation to catalytic properties guide the rational catalyst design rather than relying on current trial-and-error approaches. Considerable efforts have further been invested in increasing the active site density and enhancing intrinsic activity by regulating carbon-phase structures and the local coordination environment. Furthermore, these highly active catalysts usually suffer from significant activity loss during the ORR. Therefore, breaking the activity–stability trade-off is the key to simultaneously achieving activity and stability in one catalyst, which is discussed on the basis of our recent successes in regulating local carbon structures surrounding active single metal sites. Significant research efforts toward understanding the degradation mechanisms and improving the lifetime of PGM-free catalysts are still crucial for viable applications in the future. Novel electrode designing strategies are needed to translate the PGM-free catalysts’ ORR activity to solid-state electrolyte-based membrane electrode assemblies (MEAs) with robust three-phase (i.e., gas–liquid–solid) interfaces for efficient charge and mass transports for performance improvement. On the basis of our effort at the University at Buffalo supported by ElectroCat Consortium associated with U.S. DOE’s Hydrogen and Fuel Cell Technologies Office, we provide a perspective on PGM-free cathode catalysts concerning remaining bottlenecks and future opportunities, aiming to inspire the community in both mechanistic understanding and technological development.
The N 4 -methylation of cytidine (m 4 C and m 4 2 C) in RNA plays important roles in both bacterial and eukaryotic cells. In this work, we synthesized a series of m 4 C and m 4 2 C modified RNA oligonucleotides, conducted their base pairing and bioactivity studies, and solved three new crystal structures of the RNA duplexes containing these two modifications. Our thermostability and X-ray crystallography studies, together with the molecular dynamic simulation studies, demonstrated that m 4 C retains a regular C:G base pairing pattern in RNA duplex and has a relatively small effect on its base pairing stability and specificity. By contrast, the m 4 2 C modification disrupts the C:G pair and significantly decreases the duplex stability through a conformational shift of native Watson-Crick pair to a wobble-like pattern with the formation of two hydrogen bonds. This double-methylated m 4 2 C also results in the loss of base pairing discrimination between C:G and other mismatched pairs like C:A, C:T and C:C. The biochemical investigation of these two modified residues in the reverse transcription model shows that both mono- or di-methylated cytosine bases could specify the C:T pair and induce the G to T mutation using HIV-1 RT. In the presence of other reverse transcriptases with higher fidelity like AMV-RT, the methylation could either retain the normal nucleotide incorporation or completely inhibit the DNA synthesis. These results indicate the methylation at N 4 -position of cytidine is a molecular mechanism to fine tune base pairing specificity and affect the coding efficiency and fidelity during gene replication.
M g 3 N 2 is a promising material for light-emitting-diode applications. However, the microscopic origin of the broad yellow photoluminescence in M g 3 N 2 remains unknown. In this study, defect properties and defect-related optical transitions are investigated based on the hybrid functional calculation. Our results show that the nitrogen vacancy introduces multiple localized defect states within the band gap, which play a dominant role in luminescent properties of M g 3 N 2 . Common impurities like hydrogen, oxygen, and carbon and their complexes with native defects are also studied. Compared with isolated V Mg , V Mg -H and V Mg – O N complexes have shallower transition levels. Our calculated optical excitation and emission peaks associated with isolated V N are in good agreement with those observed in experiments. In addition, the impurity C N is also a potential source for the observed yellow emission in M g 3 N 2 .
The invention relates to a process for sorting and separating a mixture of (n, m) type single-wall carbon nanotubes according to (n, m) type. A mixture of (n, m) type single-wall carbon nanotubes is suspended such that the single-wall carbon nanotubes are individually dispersed. The nanotube suspension can be done in a surfactant-water solution and the surfactant surrounding the nanotubes keeps the nanotube isolated and from aggregating with other nanotubes. The nanotube suspension is acidified to protonate a fraction of the nanotubes. An electric field is applied and the protonated nanotubes migrate in the electric fields at different rates dependent on their (n, m) type. Fractions of nanotubes are collected at different fractionation times. The process of protonation, applying an electric field, and fractionation is repeated at increasingly higher pH to separated the (n, m) nanotube mixture into individual (n, m) nanotube fractions. The separation enables new electronic devices requiring selected (n, m) nanotube types.
A search for the production of pairs of heavy Majorana neutrinos (N ℓ ) from the decays of Z' bosons is performed using the CMS detector at the LHC. The data were collected in proton-proton collisions at a center-of-mass energy of $\sqrt s$ = 13 TeV, with an integrated luminosity of 138 fb –1 . The signature for the search is an excess in the invariant mass distribution of the final-state objects, two same-flavor leptons (e or μ) and at least two jets. No significant excess of events beyond the expected background is observed. Upper limits at 95% confidence level are set on the product of the Z' production cross section and its branching fraction to a pair of N ℓ , as functions of N ℓ and Z' boson masses (m N ℓ and m Z' , respectively) for m Z' from 0.4 to 4.6 TeV and m N ℓ from 0.1 TeV to m Z' /2. In the theoretical framework of a left-right symmetric model, exclusion bounds in the m N ℓ -m Z' plane are presented in both the electron and muon channels. The observed upper limit on m Z' reaches up to 4.42 TeV. These are the most restrictive limits to date on the mass of N ℓ as a function of the Z' boson mass.
The Pathfinding for Airspace with Autonomous Vehicles (PAAV) Concept Document, version 1.0, lays out the key challenges and potential solutions for the use of uncrewed aircraft (UA) technology for future regional air cargo operations. The challenges and solutions described in this document were informed by communications with the UA industry community (e.g., RTCA, the Federal Aviation Administration, and regional air cargo business operators), as well as the PAAV team’s research activities during the last two years including four tabletop exercises, a human-in-the-loop simulation study, a numerical simulation study, a functional allocation study, and flight data analysis (Appendix A). This document first describes the expected operational context of PAAV (Section 2), such as the flight mission, baseline UAS components, nominal operations, m:N operations (i.e., "m" remote pilots per "N" aircraft), and off-nominal operations. This context sets the scope for the PAAV concept development work. PAAV concept development assumes that UA operations will be increasingly autonomous. Thus, near- and far-term assumptions are defined (Section 3). PAAV identified seven key challenges for UA operations (Section 4): - Flight route planning - Separation and flow management - Traffic pattern integration - Contingency management - Taxi, takeoff, and landing - m:N operations - Communications operations The following 13 potential solutions to these challenges are then described (Section 5): - Scalable communications architecture - Data link - Designated UAS corridors - Crew planning for m:N operations - Flight route optimization - Traffic load-level control - Trajectory solutions with data link - Automated hazard avoidance for m:N operations - Traffic pattern integration (TPI) tool - Standard lost command and control (C2) link (LC2L) procedures - Automated hazard avoidance under LC2L - Auto-taxi, auto-takeoff, and auto-land - Ground control station (GCS) user interface for m:N operations The document attempts to link each of these solutions to one or more of the challenge areas. Novel solutions involving numerous automation technologies are needed to mitigate traffic and airspace management challenges, especially for realizing m:N operations and ensuring safety under LC2L conditions. The purpose of this document is to help understand alternatives and tradeoffs among potential solutions and provide a foundation for a cohesive PAAV concept that will be described and refined in subsequent concept versions.
The speciation of strong acids like HNO 3 under conditions of restricted hydration is an important factor in the rates of chemical reactions at the air-water interface. Here we explore the trade-offs in play when HNO 3 is attached to alkali ions (Li + -Cs + ) with four water molecules in their primary hydration shells. This is achieved by analyzing the vibrational spectra of the M + ∙(HNO 3 )(H 2 O) 5 clusters cooled to about 20 K in a cryogenic photofragmentation mass spectrometer. The local acidity of the acidic OH group is estimated by the extent of the red shift in its stretching frequency when attached to a single water molecule. Here, the persistence of this local structural motif (HNO 3 -H 2 O) in all of these alkali metal clusters enables us to determine the competition between the effect of the direct complexation of the acid with the cation, which acts to enhance acidity, and the role of the water network in the first hydration shell around the ions, which acts to counter (screen) the intrinsic effect of the ion. Analysis of the vibrational features associated with the acid molecule as well as those of the water network reveal how cooperative interactions in the micro hydration regime conspire to effectively offset the intrinsic enhancement of HNO 3 acidity afforded by attachment to the smaller cations.
We report Mononuclear nickel(II) and nickel(III) complexes of a bisamidate-bisalkoxide ligand, (NMe 4 ) 2 [Ni- II (HMPAB)] (1) and (NMe 4 )[Ni III (HMPAB)] (2), respectively, have been synthesized and characterized by various spectroscopic techniques including X-ray crystallography. The reaction of redox-inactive metal ions (M n+ = Ca 2+ , Mg 2+ , Zn 2+ , Y 3+ , and Sc 3+ ) with 2 resulted in 2-M n+ adducts, which was assessed by an array of spectroscopic techniques including X-ray absorption spectroscopy (XAS), electron paramagnetic resonance (EPR), and reactivity studies. The X-ray structure of Ca 2+ coordinated to Ni(III) complexes, 2Ca 2+ T, was determined and exhibited an average Ni-Ca distance of 3.1253 angstrom, close to the metal ions' covalent radius. XAS analysis of 2-Ca 2+ and 2-Y 3+ in solution further revealed an additional coordination to Ca and Y in the 2-M n+ adducts with shortened Ni-M distances of 2.15 and 2.11 Å, respectively, implying direct bonding interactions between Ni and Lewis acids (LAs). Such a short interatomic distance between Ni(III) and M is unprecedented and was not observed before. EPR analysis of 2 and 2-M n+ species, moreover, displayed rhombic signals with g av > 2.12 for all complexes, supporting the +III oxidation state of Ni. The Ni III /Ni II redox potential of 2 and 2-M n+ species was determined, and a plot of E 1/ 2 of 2-M n+ versus pK a of [M(H 2 O) n ] m+ exhibited a linear relationship, implying that the Ni III /Ni II potential of 2 can be tuned with different redox-inactive metal ions. Reactivity studies of 2 and 2-M n+ with different 4-X-2,6-ditert-butylphenol (4-XDTBP) and other phenol derivatives were performed, and based on kinetic studies, we propose the involvement of a proton-coupled electron transfer (PCET) pathway. Analysis of the reaction products after the reaction of 2 with 4-OMe-DTBP showed the formation of a Ni(II) complex (1a) where one of the alkoxide arms of the ligand is protonated. A pK a value of 24.2 was estimated for 1a. The reaction of 2-M n+ species was examined with 4-OMe-DTBP, and it was observed that the k 2 values of 2-M n+ species increase by increasing the Lewis acidity of redox-inactive metal ions. However, the obtained k 2 values for 2-M n+ species are much lower compared to the k 2 value for 2. Such a variation of PCET reactivity between 2 and 2-M n+ species may be attributed to the interactions between Ni(III) and LAs. Our findings show the significance of the secondary coordination sphere effect on the PCET reactivity of Ni(III) complexes and furnish important insights into the reaction mechanism involving high-valent nickel species, which are frequently invoked as key intermediates in Ni-mediated enzymatic reactions, solar-fuel catalysis, and biomimetic/synthetic transformation reactions.
The critical mission tasks assessments effort seeks to determine the physical performance requirements that astronauts must meet in order to safely and successfully accomplish lunar exploration missions. These assessments will determine astronaut preflight strength, fitness, and flexibility requirements, and the extent to which exercise and other countermeasures must prevent the physical deconditioning associated with prolonged weightlessness. The purpose is to determine the flexibility and strength that crewmembers must possess in order to reach Crew Exploration Vehicle controls during maneuvers that result in sustained acceleration levels ranging from 3.7G to 7.8G. An industry standard multibody dynamics application was used to create human models representing a 5th percentile female, a 50th percentile male, and a 95th percentile male. The additional mass of a space suit sleeve was added to the reaching arm to account for the influence of the suit mass on the reaching effort. The human model was merged with computer models of a pilot seat and control panel for the Crew Exploration Vehicle. Three dimensional paths were created that guided the human models hand from a starting position alongside its thigh to three control targets: a joystick, a keyboard, and an overhead switch panel. The reaching motion to each target was repeated under four vehicle acceleration conditions: nominal ascent (3.7G), two ascent aborts (5.5G and 7.8G) and lunar reentry (4.6G). Elbow and shoulder joint angular excursions were analyzed to assess range of motion requirements. Mean and peak elbow and shoulder joint torques were determined and converted to equivalent resistive exercise loads to assess strength requirements. Angular excursions for the 50th and 95th percentile male models remained within joint range of motion limits. For the 5th percentile female, both the elbow and the shoulder exceeded range of motion limits during the overhead reach. Elbow joint torques ranged from 10 N-m (nominal ascent) to 60 N-m (ascent abort). Shoulder joint torques ranged from 65 N-m (nominal ascent) to 280 N-m (ascent abort). Maximal equivalent exercise loads reached 30 lb in tricep extension, 9 lb in bicep curl, 110 lb in unilateral pullover and unilateral bench press for nominal conditions (lunar reentry), and 188 lb in unilateral pullover and unilateral bench press. The location of the pilot seat was found to be inadequately located to allow a 5th percentile female to reach the switches on the overhead panel. Elbow strength requirements were found to be well within population norms. Shoulder strength was found to be a limiting factor. Reaching under nominal ascent and lunar reentry conditions was found to require near maximal shoulder strength. Reaching under ascent abort conditions requires shoulder strength well beyond population norms. Pilot seats must adjust to accomodate a 5th percentile female. Exercise countermeasures must maintain maximal pullover and bench press strength to allow pilots to reach and operate controls during lunar reentry. Reaching will not be possible during ascent abort conditions. Flight controls should be built into armrests or flight control must be accomplished by autonomous systems during acceleration exceeding 4.6G.
Here, polyethylenes of varying molecular weight and branch density, as well as polypropylenes of varying molecular weight and tacticity, were catalytically converted to lower-molecular-weight liquid products to showcase how these various properties in a mixed waste plastic stream could affect the final product. A Pt nanoparticle on a strontium titanate nanocuboid (Pt/STO) catalyst was used under solvent-free conditions in the presence of 170 psi of H 2 at 300 °C for hydrogenolysis. The initial molecular weight of polyethylene was found to have a moderate effect on the yield to the final product (ranging from 55 wt% for M n ~ 7600 Da to 67 wt% for M n ~ 50,950 Da). The microstructure, defined as the length and density of branches in a polymer, of higher-molecular-weight polymers was the dominant factor in determining the yield (ranging from 67 wt% for M n ~ 50,950 Da for linear low-density polyethylene (LLDPE) with C 2 branches to 97 wt% for M n ~ 38,850 Da for LLDPE with C 6 branches). The same products (M n = C 29 –C 46 , Ð = 1.1–1.6) and distribution of undesired light gases (C 1 –C 4 ≈ 90 mol%, C 5 –C 8 ≈ 10 mol%) are obtained from conversions of PE of varying molecular weight. The tacticity of polypropylene at a given molecular weight had a significant effect on the molecular weight of the final product, while not strongly affecting conversion. Hydrogenolysis of isotactic polypropylene (iPP) produced ≈C 18 with a wider polydispersity (Ð ~ 1.4) compared to the narrow ≈C 64 (Ð ~ 1.0) and ≈C 54 (Ð ~ 1.0) products from atactic (aPP) and syndiotactic (sPP) polypropylene, respectively. The stereochemistry of the methyl groups dictates the shape and structure of the polymer in the melt, which in turn affects how the hydrocarbon chain interacts with the catalyst surface, thereby impacting the number of C–C scissions. These results show how various characteristics such as the molecular weight and structure of a waste plastic stream could affect the final product.
Atomically dispersed platinum-group metal-free catalyst and method for synthesizing the same. According to one embodiment, the catalyst is made by a method in which, in a first step, a metal oxide/zeolitic imidazolate frameworks (ZIF) composite is formed by combining (i) nanoparticles of an oxide of at least one of iron, cobalt, nickel, manganese, and copper, (ii) a hydrated zinc salt, and (iii) an imidazole. Then, in a second step, the metal oxide/ZIF composite is thermally activated, i.e., carbonized, to form an M-N—C catalyst. Thereafter, the M-N—C catalyst may be mixed with a quantity of ammonium chloride, and then the M-N—C/NH 4 Cl mixture may be pyrolyzed. The foregoing NH 4 Cl treatment may improve the intrinsic activity of the catalyst. Then, a thin layer of nitrogen-doped carbon may be added to NH 4 Cl-treated M-N—C catalyst by chemical vapor deposition (CVD). Such CVD treatment may improve the stability of the catalyst.
The added technological potential of bimetallic clusters and nanoparticles, as compared to their pure (i.e., one-component) counterparts, stems from the ability to further fine-tune their properties and, consequently, functionalities through a simultaneous use of the “knobs” of size and composition. The practical realization of this potential can be greatly advanced by the knowledge of the correlations and relationships between the various characteristics of bimetallic nanosystems on the one hand and those of their pure counterparts as well as pure constituent components on the other hand. Here, in this study, we present results of a density functional theory based study of pure Pt n and Mo n clusters aimed at revisiting and exploring further their structural, electronic, and energetic properties. These are then used as a basis for analysis and characterization of the results of calculations on two-component Pt n-m Mo m clusters. The analysis also includes establishing relationships between the properties of the Pt n-m Mo m clusters and those of their Pt n-m and Mo m components. One of the particularly intriguing findings suggested by the calculated data is a linear dependence of the average binding energy per atom in sets of Pt n-m Mo m clusters that have the same fixed number m of Mo atoms and different number n-m of Pt atoms on the fractional content (n-m)/n of Pt atoms. We derive an analytical model that establishes the fundamental basis for this linearity and expresses its parameters—the m-dependent slope and intercept—in terms of characteristic properties of the constituent components, such as the average binding energy per atom of Mo m and the average per-atom adsorption energy of the Pt atoms on Mo m . The conditions of validity and degree of robustness of this model and of the linear relationship predicted by it are discussed.
Blending block copolymers (BCP) with additives is a useful approach for controlling BCP morphology and properties. In athermal systems, blends of BCPs with polymer additives having very high molecular (M n ) mass generally result in macrophase separation. Bottlebrush polymers, which consist of a linear backbone and grafted side chains, present an interesting alternative where the overall M n of the system can be very large but the low M n side chains may drive miscibility with the BCP. Here, in this study, a bottlebrush with a polynorbornene backbone and polystyrene (PS) side chains is blended with PS-b-poly(methyl methacrylate) (PS-b-PMMA) of varying M n , and the resulting morphologies are examined in both the bulk and thin films. Two different M n of PS-b-PMMA were used in the bulk study, and the analysis of small-angle X-ray scattering data shows that the blends were miscible and lamellar at all concentrations. This deviates from reference series of both low and high M n linear polymer additives, which either showed morphological transitions from lamellae to cylinders (low M n ) or were immiscible at all mass fractions studied (high M n ). The relative molecular mass of the side chain (N SC ) and the corresponding component in the BCP (N A ) dictate the distribution of the bottlebrush throughout the BCP, analogous to BCP/linear blends or grafted nanoparticles in a homopolymer matrix. The studies on thin films show a thickness dependence for bottlebrush mass fractions at or above 0.17, a behavior which may be driven by conformational changes of the bottlebrush upon confinement.