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At least 595 records · Page 33

ALMA Band-to-band Phase Referencing: Imaging Capabilities on Long Baselines and High Frequencies

High-frequency long-baseline experiments with the Atacama Large Millimeter/submillimeter Array were organized to test the high angular resolution imaging capabilities in the submillimeter wave regime using baselines up to 16 km. Four experiments were conducted, two Band 7 (289 GHz) and two Band 8 (405 GHz) observations. Phase correction using band-to-band (B2B) phase referencing was used with a phase calibrator only [[Formula]] away observed in Band 3 (96 GHz) and Band 4 (135 GHz), respectively. In Band 8, we achieved the highest resolution of 14 × 11 mas. We compared the synthesis images of the target quasar using 20 and 60 s switching cycle times in the phase referencing. In Band 7, the atmosphere had good stability in phase rms (<0.5 rad over 2 minutes), and there was little difference in image coherence between the 20 and 60 s switching cycle times. One Band 8 experiment was conducted under a worse phase rms condition (>1 rad over 2 minutes), which led to a significantly reduced coherence when using the 60 s switching cycle time. One of our four experiments indicates that the residual phase rms error after phase referencing can be reduced to 0.16 rad at 289 GHz in using the 20 s switching cycle time. Such conditions would meet the phase correction requirement of image coherence of >70% in Band 10, assuming a similar phase calibrator separation angle, emphasizing the need for such B2B phase referencing observing at high frequencies.

79 ASTRONOMY AND ASTROPHYSICS↗

Measurement of Thermal Conductivity in a Supercooled Hydrogel-Salt Complex Near Its Phase Transition

Solid-liquid phase transitions, i.e. solidification processes, have applications in data storage, development of novel thermoelectric materials, cooling of microelectronic substrates and air conditioning condensers. Standard analyses of solidification (Stefan problem) assume constant thermal properties of the solid and liquid sides. It is not known how these properties change across the spatial transition interface, though most studies report a discontinuity in the solid and liquid properties through the transition temperature [1]. When the phase transition releases enthalpy, recent research has shown if the phonon or electron transport time is of the same order of magnitude as the time scale of the atomic transformation, this increases the heat capacity of the solid material at temperatures near the phase transition temperature [2]. A fundamental understanding of the phase transition may help shed light on the molecular origins of supercooling and spontaneous nucleation, which will help with applications involving them. We report studies of supercooling and nucleation of sodium sulfate decahydrate, a salt hydrate which is of recent interest in thermal storage, and of a hydrogel-sodium sulfate complex which shows limited supercooling. We will also report the measurement of their thermal properties during the phase transition process. This will be done with a hot-wire setup which produces small temperature changes of the order of ~1 C.

crystallization, phase transformation, thermal con↗

SILCC – VII. Gas kinematics and multiphase outflows of the simulated ISM at high gas surface densities

ABSTRACT We present magnetohydrodynamic (MHD) simulations of the star-forming multiphase interstellar medium (ISM) in stratified galactic patches with gas surface densities Σgas = 10, 30, 50, and 100 $\mathrm{M_\odot \, pc^{-2}}$. The silcc project simulation framework accounts for non-equilibrium thermal and chemical processes in the warm and cold ISM. The sink-based star formation and feedback model includes stellar winds, hydrogen-ionizing UV radiation, core-collapse supernovae, and cosmic ray (CR) injection and diffusion. The simulations follow the observed relation between Σgas and the star formation rate surface density ΣSFR. CRs qualitatively change the outflow phase structure. Without CRs, the outflows transition from a two-phase (warm and hot at 1 kpc) to a single-phase (hot at 2 kpc) structure. With CRs, the outflow always has three phases (cold, warm, and hot), dominated in mass by the warm phase. The impact of CRs on mass loading decreases for higher Σgas and the mass loading factors of the CR-supported outflows are of order unity independent of ΣSFR. Similar to observations, vertical velocity dispersions of the warm ionized medium (WIM) and the cold neutral medium (CNM) correlate with the star formation rate as $\sigma _\mathrm{z} \propto \Sigma _\mathrm{SFR}^a$, with a ∼ 0.20. In the absence of stellar feedback, we find no correlation. The velocity dispersion of the WIM is a factor ∼2.2 higher than that of the CNM, in agreement with local observations. For $\Sigma _\mathrm{SFR} \gtrsim 1.5 \times 10^{-2}\, \mathrm{M}_\odot \, \mathrm{yr}^{-1}\, \mathrm{kpc}^{-2}$ the WIM motions become supersonic.

Astronomy & Astrophysics↗

First-principles investigation of phase stability in layered Na x ⁢CrO 2

Layered oxide intercalation compounds continue to attract interest as electrode materials for Na-ion batteries. However, many of these materials undergo complex phase transitions during cycling that influence battery performance but are still not completely understood. We have conducted a first-principles study of layered Na x ⁢CrO 2 (0 ≤ x ≤ 1) to assess phase stability between various Na-vacancy ordered phases in the O3 and P3 host structures. We predict that many of the low-energy phases belong to families of Na orderings that follow specific patterns. At high x, we identify families of vacancy row orderings in O3, which may also couple to magnetic orderings of the Cr spins. We predict similar orderings at intermediate x in P3 that contain antiphase boundaries between regions of the x = 1/2 ordering. In both cases, the average spacing between rows/boundaries is set by the overall composition. At x = 0, we find a strong preference for charge disproportionation and migration of Cr to tetrahedral sites in the intercalation layers. Finally, we obtain generally good agreement with experimental observations and rationalize key discrepancies.

25 ENERGY STORAGE↗

SDSS-IV MaNGA: Unveiling Galaxy Interaction by Merger Stages with Machine Learning

We use machine-learning techniques to classify galaxy merger stages, which can unveil physical processes that drive the star formation and active galactic nucleus (AGN) activities during galaxy interaction. The sample contains 4690 galaxies from the integral field spectroscopy survey SDSS-IV MaNGA and can be separated into 1060 merging galaxies and 3630 nonmerging or unclassified galaxies. For the merger sample, there are 468, 125, 293, and 174 galaxies (1) in the incoming pair phase, (2) in the first pericentric passage phase, (3) approaching or just passing the apocenter, and (4) in the final coalescence phase or post-mergers. With the information of projected separation, line-of-sight velocity difference, Sloan Digital Sky Survey (SDSS) gri images, and MaNGA Hα velocity map, we are able to classify the mergers and their stages with good precision, which is the most important score to identify interacting galaxies. For the two-phase classification (binary; nonmerger and merger), the performance can be high (precision > 0.90) with LGBMClassifier . We find that sample size can be increased by rotation, so the five-phase classification (nonmerger, and merger stages 1, 2, 3, and 4) can also be good (precision > 0.85). The most important features come from SDSS gri images. The contribution from the MaNGA Hα velocity map, projected separation, and line-of-sight velocity difference can further improve the performance by 0%–20%. In other words, the image and the velocity information are sufficient to capture important features of galaxy interactions, and our results can apply to all the MaNGA data, as well as future all-sky surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

The Origin and Evolution of the Normal Type Ia SN 2018aoz with Infant-phase Reddening and Excess Emission

SN 2018aoz is a Type Ia SN with a B-band plateau and excess emission in infant-phase light curves ≲1 day after the first light, evidencing an over-density of surface iron-peak elements as shown in our previous study. Here, we advance the constraints on the nature and origin of SN 2018aoz based on its evolution until the nebular phase. Near-peak spectroscopic features show that the SN is intermediate between two subtypes of normal Type Ia: core normal and broad line. The excess emission may be attributable to the radioactive decay of surface iron-peak elements as well as the interaction of ejecta with either the binary companion or a small torus of circumstellar material. Nebular-phase limits on Hα and He ι favor a white dwarf companion, consistent with the small companion size constrained by the low early SN luminosity, while the absence of [O ι] and He ι disfavors a violent merger of the progenitor. Of the two main explosion mechanisms proposed to explain the distribution of surface iron-peak elements in SN 2018aoz, the asymmetric Chandrasekhar-mass explosion is less consistent with the progenitor constraints and the observed blueshifts of nebular-phase [Fe ιι] and [Ni ιι]. The helium-shell double-detonation explosion is compatible with the observed lack of C spectral features, but current 1D models are incompatible with the infant-phase excess emission, $B_{max}$--$V_{max}$ color, and weak strength of nebular-phase [Ca ιι]. Although the explosion processes of SN 2018aoz still need to be more precisely understood, the same processes could produce a significant fraction of Type Ia SNe that appear to be normal after ~1 day.

79 ASTRONOMY AND ASTROPHYSICS↗

Iodine Capture with Metal-Functionalized Polyacrylonitrile Composite Beads Containing Ag 0 , Bi 0 , Cu 0 , or Sn 0 Particles

The capture of radioiodine from nuclear processes and the mitigation of environmental release are important topic areas of research. Some of the more commonly employed chemisorption-type iodine scavengers reported in the literature are based on metal-exchanged porous sorbents such as Ag-zeolites or metal-functionalized aerogels and xerogels. However, another option is to use zero-valent metals directly that have known high affinities for iodine gas [i.e., I2(g)]. In this study, fine metal particles of Ag0, Bi0, Cu0, and Sn0 were embedded in porous polyacrylonitrile (PAN) substrates at 75 mass% metal loadings within the form of ellipsoidal beads with maximum diameters of ~2–3 mm. These composite beads showed extremely high iodine loadings that are directly related to the metal particle loadings. The X-ray diffraction (XRD) analyses of Ag0, Bi0, Cu0, and Sn0 particles as well as metal-PAN composite beads reacted with iodine gas at 120 ± 1 °C showed phases of AgI, BiI3, CuI, and SnI4, respectively. For the Ag-PAN, Cu-PAN, and Sn-PAN beads, no other crystalline peaks were observed in XRD for unreacted metal or oxidized metals after 48 h in saturated I2(g) at 120 ± 1 °C, whereas unreacted metallic Bi0 was observed within the Bi-PAN composites. However, after a 72 h exposure at 120 ± 1 °C, both the Bi0 particles and the Bi-PAN composites showed full conversion from Bi0 to BiI3 with XRD. Comparisons between mass uptake data and X-ray absorption spectroscopy were used to better understand the phase distribution of the Bi phases present in the Bi-PAN+I composites. The iodine loadings (mg iodine per g sorbent, or qe) for these materials were 1120 (Ag-Particle), 1382 (Bi-Particle-72h), 1033 (Cu-Particle), 3000 (Sn-Particle), 753 (Ag-PAN), 1012 (Bi-PAN-72h), 1457 (Cu-PAN), and 1669 (Sn-PAN). It is possible that inexpensive sorbents such as these could be deployed to help limit or prevent release of radioiodine to the environment.

36 MATERIALS SCIENCE↗

Electrochemical control over stoichiometry via cation intercalation into Chevrel-phase sulphides (Cu x Mo 6 S 8 , x = 1-3)

Herein this work presents a systematic investigation of the electrochemical intercalation of aqueous copper cations into the Chevrel phase (CP) Mo 6 S 8 and its effect on the host's electronic and structural characteristics as a function of stoichiometry. The electrochemical potentials at which copper intercalates into the CP Mo 6 S 8 host in 1 M CuSO 4 were identified for Cu x Mo 6 S 8 (x = 1–3) as 0.23 V, 0.11 V, and 0.055 V (vs. Cu/Cu 2+ ) for Cu 1 Mo 6 S 8 , Cu 2 Mo 6 S 8 , and Cu 3 Mo 6 S 8 , respectively, and correlated via ex situ PXRD to stoichiometric content. Potentials were also identified that yield non-stoichiometric phases with traceable Cu content-dependent structural changes. Ab initio DFT calculations were performed to probe thermodynamic stability of Cu x Mo 6 S 8 CP compositions and the metal-to-semiconductor transitions as a function of copper content. Lastly, we demonstrate that the SK-pre-edge intensity is a successful probe for intercalant content: as copper equivalents increase, so does charge transfer to the partially occupied S 3p orbitals, resulting in a decrease in the pre-edge intensity corresponding to the excitation of a S 1s-to-3p/Mo 4d hybridized orbital.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermal Conductivity of a Novel Salt-Hydrogel Complex as a Phase Change Material for Building Thermal Management

Use of electricity for space heating, ventilation and air conditioning in buildings may be better managed through temporary energy storage. Compared with electrochemical storage, the levelized cost of thermal energy storage systems can be lower depending on geographical location and thermophysical properties [1]. In any phase change material (PCM), the rate of absorption and release of thermal energy increases with higher thermal conductivity [2]. However, leading PCMs like paraffin waxes have thermal conductivities on the order of 0.1 W/mK. Glauber’s salt, a salt hydrate, possesses a relatively high thermal conductivity but suffers from supercooling and phase segregation. Research has shown that polymer-based composites with salt hydrates can prevent phase segregation and limit supercooling over hundreds of cycles [3] though the thermal conductivity of the composite may be reduced leading to low energy storage rates. Here, we report thermal conductivity measurements on polymer hydrogels which are stable in solutions of Glauber’s salt. To measure thermal conductivity of soft gels, we use a 3-omega method [4] where heat flows bidirectionally through a substrate below and through a gel placed on top. This suits measurements of both gels and liquids unlike transient plane heat source or transient hot wire methods. We report measurements of thermal conductivity of salt-hydrogel complexes as a function of temperature, cross-linking and salt concentration. In addition, we present modeling of thermal conductivity of sodium sulfate solutions with available theories. We finally employ polarized optical microscopy to observe inside the transparent hydrogel networks, showing that precipitating crystals may influence thermal conductivity measurements for high salt concentrations. Our thermal conductivity results combined with enthalpy of phase change, mass density and specific heat are essential to accurately design thermal storage systems for energy-efficient buildings.

composite, thermal conductivity↗

Formation of Mn-rich interfacial phases in Co 2 Fe x Mn 1-x Si thin films

Here, we report the formation of Mn-rich regions at the interface of Co 2 Fe x Mn 1-x Si thin films grown on GaAs substrates by molecular beam epitaxy (MBE). Scanning transmission electron microscopy (STEM) with electron energy loss (EEL) spectrum imaging reveals that each interfacial region: (1) is 1–2 nm wide, (2) occurs irrespective of the Fe/Mn composition ratio and in both Co-rich and Co-poor films, and (3) displaces both Co and Fe indiscriminately. We also observe a Mn-depleted region in each film directly above each Mn-rich interfacial layer, roughly 3 nm in width in the x = 0 and x = 0.3 films, and 1 nm in the x = 0.7 (less Mn) film. We posit that growth energetics favor Mn diffusion to the interface even when there is no significant Ga interdiffusion into the epitaxial film. Element-specific X-ray magnetic circular dichroism (XMCD) measurements show larger Co, Fe, and Mn orbital to spin magnetic moment ratios compared to bulk values across the Co 2 Fe x Mn 1-x Si compositional range. The values lie between reported values for pure bulk and nanostructured Co, Fe, and Mn materials, corroborating the non-uniform, layered nature of the material on the nanoscale. Finally, SQUID magnetometry demonstrates that the films deviate from the Slater-Pauling rule for uniform films of both the expected and the measured composition. The results inform a need for care and increased scrutiny when forming Mn-based magnetic thin films on III-V semiconductors like GaAs, particularly when films are on the order of 5 nm or when interface composition is critical to spin transport or other device applications.

36 MATERIALS SCIENCE↗

Switching of Hybrid Improper Ferroelectricity in Oxide Double Perovskites

In ABO 3 -type perovskite oxides with Pnma symmetry, rotation (Q R+ , a 0 a 0 c + ) and tilt (Q T , a – a – c 0 ) of BO 6 octahedra are the two primary order parameters. These order parameters establish an inherent trilinear coupling with anti-ferroelectric A-site displacement (Q AFE ) to form the low-symmetry phase. The symmetry is further lowered in double perovskite oxides (DPOs) due to A/A' cation ordering. It in turn makes these systems polar via hybrid improper ferroelectric mechanism, primarily driven by Q R+ and Q T . Naturally, it has been believed that functionalities such as polarization can also be switched by tuning these primary order parameters. However, mystery around finding switching mechanism still remains. Our study based on density functional theory calculations combined with finite-temperature molecular dynamics simulations shows that the polarization switching is a two-step process, driven by out-of-phase rotation (Q R– , a 0 a 0 c – when Q T = 0 or, a – a – b – when Q T ≠ 0). A series of polar DPOs such as KLnFeOsO 6 [Ln = Sm, Gd, Dy, Tm (lanthanides) and Y (rare earth)], all belonging to P2 1 symmetry, are considered in this investigation. The polarization switching P ($\overrightarrow{P}$) occurs at a very high temperature of ~1150 K through a phase transition, from a polar (P2 1 ) phase with $\overrightarrow{P}$(+) to $\overrightarrow{P}$(-) via a non-polar P4/n phase. The switching itself is metastable in nature. The switching (both polarization and spin state) is only observed for a very short period of time (~23 ps) that poses limitation on using such a mechanism in memory device realization. We demonstrate a concurrent heating–cooling procedure to overcome such shortcoming. In conclusion, simulations conducted at 600 K further imply that long lasting switching can be achieved, at least for 1.2 ns for 600 K, and ideally for an infinite time, if the material is heated just above the T c followed by rapid cooling to a temperature below T c .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Superconducting properties of MoTe 2 from ab initio anisotropic Migdal-Eliashberg theory

Molybdenum ditelluride (MoTe 2 ) is attracting considerable interest since it is the archetypal type-II Weyl semimetal and a candidate for topological superconductivity. In this work, we investigate the superconducting phase diagram of two MoTe 2 polymorphs using the ab initio anisotropic Migdal-Eliashberg theory, and we show that the superconducting dome originates from the synergistic contribution of the density of states at the Fermi level and the transverse acoustic Te modes in the 1$\textit{T}’$ phase. We find that the electron and hole pockets carry trivial $\textit{s}$-wave order parameters of slightly different magnitude, reminiscent of a two-gap structure as suggested by recent experiments. We suggest that a possible route for enhancing the superconducting critical temperature, and realizing $s_{+ –}$ pairing, in the $T_d$ phase is to exploit its nontrivial band topology via electron doping.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Shape-stabilized phase change materials for energy storage based on hierarchically porous calcium magnesium carbonate

A composite phase-change material containing a hierarchically porous Ca 1-x Mg x CO 3 and having pores loaded with a phase change material is described. The heat storage material has a latent heat of melting 123 to 221 J/g, a latent heat of freezing of 107 to 201 J/g, and a thermal conductivity of 0.22 to 0.45 W·m −1 ·K −1 . The phase change material may be polyethylene glycol, and the polyethylene glycol does not leak from the pores of the hierarchically porous Ca 1-x Mg x CO 3 when heating or cooling over phase transitions.

25 ENERGY STORAGE↗

Two-component electronic phase separation in the doped Mott insulator Y 1-x Ca x TiO 3

One of the major puzzles in condensed matter physics has been the observation of a Mott-insulating state away from half-filling. Several theoretical proposals aimed to elucidate this phenomenon have been put forth, a notable one being phase separation and an associated percolation-induced Mott insulator-metal transition. In the present work we study the prototypical doped Mott-insulating rare-earth titanate YTiO 3 , in which the insulating state survives up to a large hole concentration of 35%. Single crystals of Y 1-x Ca x TiO 3 with 0 ≤ x ≤ 0.5, spanning the insulator-metal transition, are grown and investigated. Using x-ray absorption spectroscopy, a powerful technique capable of probing element-specific electronic states, we find that the primary effect of hole doping is to induce electronic phase separation into hole-rich and hole-poor regions. The data reveal the formation of electronic states within the Mott-Hubbard gap, near the Fermi level, which increase in spectral weight with increasing doping. From a comparison with DFT+U calculations, we infer that the hole-poor and hole-rich components have charge densities that correspond to the insulating x = 0 and metallic x ~ 0.5 states, respectively, and that the new electronic states arise from the metallic component. Our results indicate that the doping-induced insulator-metal transition in Y 1-x Ca x TiO 3 is indeed percolative in nature, and thus of inherent first-order character.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Spatially varying seasonal modulation to tidal stream energy potential due to mixed tidal regimes in the Aleutian Islands, AK

We provide an assessment of the tidal stream energy resource of the Aleutian Islands, Alaska via a validated barotropic tidal numerical model of the region. Eight island passes are identified as energy “hotspots”. The annual mean kinetic energy fluxes, KEF , calculated at each pass vary from 1000 to 11,000 MW, while the annual available energy, AAE , varies from 5 to 42 MWh m −2 . Notable seasonal modulation to monthly power density averages and ranges are noted at some passes and not others. Seasonal adjustment is linked to the semi-annual solar declination cycle which enhances (dampens) diurnal (D 1 ) tidal amplitudes in summer/winter (spring/fall) as well as the time-varying phase lag between D 1 and semidiurnal (D 2 ) fortnightly tidal cycles. Annual variability in monthly mean power density scales with the tidal current form factor, F u , with the largest seasonal change occurring for F u > 1 (D 1 dominated tide). The spread in power density over a month is on average smaller for passes with mixed tides (F u = 1 ) than those with D 1 or D 2 dominance, as changes to fortnightly phase lag become influential to net power density ranges when tides are mixed. This study outlines overlooked, but relevant, long-term modulation to tidal streams in regions with mixed tides.

16 TIDAL AND WAVE POWER↗

Phase evolution during conventional and reactive flash sintering of (Mg,Ni,Co,Cu,Zn)O via in situ X-ray diffraction

Reactive flash sintering (RFS) enables the simultaneous synthesis and sintering of ceramics and has been shown to affect the reaction pathway of different materials. Herein, in situ synchrotron X-ray diffraction (XRD) is used to investigate the (Mg,Ni,Co,Cu,Zn)O entropy-stabilized oxide formation during: (i) conventional heating and (ii) RFS under current rate-controlled mode. The same reaction pathway is verified in both instances: the starting rock-salt (RS), spinel (Co 3 O 4 ), tenorite (CuO), and wurtzite (ZnO) phases transform into a single RS phase with a (1 1 1) to (2 0 0) intensity ratio of 0.67, consistent with a random distribution of the cations into the structure. Pt lattice peak shift from the XRD patterns is used as standard to monitor the sample surface temperature, revealing a strong endothermic reaction during the RS single-phase formation (Pt peaks shift toward higher angles while increasing sample temperature/current density). Furthermore, in RFS, the single-phase RS structure is formed in just 60 s at a furnace temperature of 600°C and a current rate of 220 mA mm -2 /min. Therefore, RFS greatly accelerates the synthesis of (Mg,Ni,Co,Cu,Zn)O, however, it does not play a role in the reaction pathway for this material formation.

36 MATERIALS SCIENCE↗

Amantadine interactions with phase separated lipid membranes

Amantadine, a small amphilphic organic compound that consists of an adamantane backbone and an amino group, was first recognized as an antiviral in 1963 and received approval for prophylaxis against the type A influenza virus in 1976. Since then, it has also been used to treat Parkinson’s disease-related dyskinesia and is being considered as a treatment for corona viruses. Since amantadine usually targets membrane-bound proteins, its interactions with the membrane are also thought to be important. Biological membranes are now widely understood to be laterally heterogeneous and certain proteins are known to preferentially co-localize within specific lipid domains. Does amantadine, therefore, preferentially localize in certain lipid composition domains? To address this question, here, we studied amantadine’s interactions with phase separating membranes composed of cholesterol, DSPC (1,2-distearoyl-sn-glycero-3-phosphocholine), POPC (1-palmitoyl-2-oleoyl-glycero-3-phosphocholine), and DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine), as well as single-phase DPhPC (1,2-diphytanoyl-sn-glycero-3-phos-phocholine) membranes. From Langmuir trough and differential scanning calorimetry (DSC) measurements, we determined, respectively, that amantadine preferentially binds to disordered lipids, such as POPC, and lowers the phase transition temperature of POPC/DSPC/cholesterol mixtures, implying that amantadine increases membrane disorder. Further, using droplet interface bilayers (DIBs), we observed that amantadine disrupts DPhPC membranes, consistent with its disordering properties. Finally, we carried out molecular dynamics (MD) simulations on POPC/DSPC/cholesterol membranes with varying amounts of amantadine. Consistent with experiment, MD simulations showed that amantadine prefers to associate with disordered POPC-rich domains, domain boundaries, and lipid glycerol backbones. Since different proteins co-localize with different lipid domains, our results have possible implications as to which classes of proteins may be better targets for amantadine.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗