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At least 91 records · Page 5

Insights into Preceramic Polymer-Based Additive Manufacturing Inks via Rheological and Scattering Studies of Preceramic Polymer-Grafted Nanoparticles Suspended in Polycarbosilane

Preceramic polymers (PCPs) offer advantages in producing ceramics due to their processability and ability to tailor the final chemistry of the produced material. However, challenges such as volumetric shrinkage and mass loss during pyrolysis often result in polymer-derived ceramics containing pores and cracks. PCP-grafted ceramic nanoparticles (PCPGNPs) have been proposed and studied as a route to mitigate the shrinkage issues associated with neat PCPs. Prior studies on PCPGNPs have principally focused on the synthesis and characterization of neat materials. Dispersing PCPGNPs in commercial preceramic polymer is another attractive, but underexplored, route to control the rheological and char yield properties of PCP systems. In this work, a systematic rheological study of commercial PCP (SMP-877) and PCPGNP (silica with poly(1,1-dimethylpropylsilane) corona) mixtures was executed to develop design rules for the processing of such systems. A rheological study demonstrated the effect of increasing particle concentration on network formation with percolation occurring between 50 and 60 wt %. Samples above the percolation threshold exhibited higher viscosities and rapid shear thinning thus demonstrating their direct-write printability. X-ray photon correlation spectroscopy (XPCS) corroborated the rheology and showed two diffusive modes when the material was above percolation. Mixtures of PCPGNPs and SMP-877 had synergistically higher char yields upon thermal treatment and pyrolysis. XPCS and rheological measurements during thermal treatment identified thermal jamming of the polymer grafts as a key factor in improving the char yield. In conclusion, with the insights gained here, we expect these mixed systems to provide attractive feedstocks for polymer-derived ceramics, with proof-of-principal application as feedstocks for direct ink write (DIW) additive manufacturing.

36 MATERIALS SCIENCE↗

Probing Supercritical Phase Transition using Ultrafast X-ray Diagnostics (Final Technical Report)

Over recent years, several hypotheses have been put forward to elucidate supercritical transition states. Despite significant progress on the fundamental understanding of fluids at these supercritical conditions, important questions concerning the microstructure and dynamical processes remain. A particular research issue is hereby the fundamental understanding of the morphology of the molecular microstructure and its effect on the macroscopic behaviour and thermodynamic response functions. It is widely believed that the supercritical state is homogeneous without structural and dynamic observables to distinguish between a liquid and a vapor. However, recent investigations have identified regions of distinct liquid-like or vapor-like properties even under supercritical conditions. Specifically, it was shown that the transition between liquid-like and vapor-like states occurs across an extension to the coexistence line, marked by almost discontinuous changes in fluid properties. This transition was first identified experimentally by Nishikawa and Tanaka and stands in contrast to the classical presentation of the supercritical state space as a featureless, homogeneous domain. Structurally, the most important properties of supercritical fluids are the dynamic heterogeneities and local density fluctuations that are present within the fluid state at the microscopic level. These inhomogeneities are associated with the formation of molecular clusters of various sizes with liquid-like properties separated by voids of unbound gas-phase molecules which continuously restructure itself at picosecond timescales. By utilizing ultrafast X-ray Photon Correlation Spectroscopy (XPCS) at the Linac Coherent Light Source (LCLS) and X-ray synchrotron measurements as an experimental probe of these structural changes at the molecular level we seek to elucidate the higher-order phase transition from a liquid-like to a vapor-like state in the region extending the critical point. Open questions we seek to address particularly with XPCS are: (i) the underlying mechanisms responsible for the density fluctuations at supercritical conditions and how these dynamical processes at the molecular level affect the thermodynamic response functions and (ii) on what timescales do dynamical processes evolve that are associated with thermalization, molecular diffusion, and intermolecular cluster transfer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Anomalous fast atomic dynamics in bulk metallic glasses

It is believed that the strong glass formers tend to be dense packing and have rather slow atomic dynamics. Here, we report that the anomalous fast atomic dynamics exist in an Au 55 Cu 20 Ag 5 Si 20 metallic glass (MG) with good glass forming ability (GFA) by combining X-ray photon correlation spectroscopy measurements with ab initio molecular dynamics simulations. The fast dynamics are mainly originated from the increased mobility of Cu atoms by Ag addition. Ag atoms are inclined to locate at Cu-centered <0, 2, 8, 1> motifs, which slow or accelerate the dynamics of shell Cu atoms, depending on whether Ag atoms appear at the first shells or not, leading to the formation of structural heterogeneity at the atomic level. The results enrich the understanding of atomic dynamics in Cue-Ag-containing MGs and will trigger more studies on the dynamics-GFA relationship in MGs.

74 ATOMIC AND MOLECULAR PHYSICS↗

Microscopic dynamics of stress relaxation in a nanocolloidal soft glass

Here, we report x-ray photon correlation spectroscopy (XPCS) experiments with in situ rheometry performed on a soft glass composed of a concentrated suspension of charged silica nanoparticles subjected to step strains that induce yielding and flow. The XPCS measurements characterize the particle-scale and mesoscale motions within the glass that underlie the highly protracted decay of the macroscopic stress following the step strains. These dynamics are anisotropic, with slow, convective particle motion along the direction of the preceding shear that persists for surprisingly large times and that is accompanied by intermittent motion in the perpendicular (vorticity) direction. A close correspondence between the convective dynamics and stress relaxation is demonstrated by power-law scaling between the characteristic velocity of the collective particle motion and the rate of stress decay.

36 MATERIALS SCIENCE↗

Influence of TMAO as co-solvent on the gelation of silica-PNIPAm core-shell nanogels at intermediate volume fractions

We study the structure and dynamics of poly(N-isopropylacrylamide) (PNIPAm) core-shell nanogels dispersed in aqueous trimethylamine N-oxide (TMAO) solutions by means of smallangle X-ray scattering and X-ray photon correlation spectroscopy (XPCS). Upon increasing the temperature above the lower critical solution temperature of PNIPAm at 33°C, a colloidal gel is formed as identified by an increase of I(q) at small q as well as a slowing down of sample dynamics by various orders of magnitude. With increasing TMAO concentration the gelation transition shifts linearly to lower temperatures. Above a TMAO concentration of approximately 0.40 mol/L corresponding to a 1:1 ratio of TMAO and NIPAm groups, collapsed PNIPAm states are found for all temperatures without any gelation transition. This suggests that reduction of PNIPAm-water hydrogen bonds due to the presence of TMAO results in a stabilisation of the collapsed PNIPAm state and suppresses gelation of the nanogel.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A versatile pressure-cell design for studying ultrafast molecular-dynamics in supercritical fluids using coherent multi-pulse x-ray scattering

Supercritical fluids (SCFs) can be found in a variety of environmental and industrial processes. They exhibit an anomalous thermodynamic behavior, which originates from their fluctuating heterogeneous micro-structure. Characterizing the dynamics of these fluids at high temperature and high pressure with nanometer spatial and picosecond temporal resolution has been very challenging. The advent of hard x-ray free electron lasers has enabled the development of novel multi-pulse ultrafast x-ray scattering techniques, such as x-ray photon correlation spectroscopy (XPCS) and x-ray pump x-ray probe (XPXP). These techniques offer new opportunities for resolving the ultrafast microscopic behavior in SCFs at unprecedented spatiotemporal resolution, unraveling the dynamics of their micro-structure. However, harnessing these capabilities requires a bespoke high-pressure and high-temperature sample system that is optimized to maximize signal intensity and address instrument-specific challenges, such as drift in beamline components, x-ray scattering background, and multi-x-ray-beam overlap. We present a pressure cell compatible with a wide range of SCFs with built-in optical access for XPCS and XPXP and discuss critical aspects of the pressure cell design, with a particular focus on the design optimization for XPCS.

47 OTHER INSTRUMENTATION↗

Dynamics of a fractal set of first-order magnetic phase transitions in frustrated Lu 2 CoMnO 6

The axial next-nearest-neighbor Ising model predicts a fractal (infinite) set of phases with incommensurate wave vectors that are separated by first-order phase boundaries. This complexity results from a simple frustration condition between nearest- and next-nearest-neighbor interactions along a chain of Ising spins. Using x-ray photon correlation spectroscopy (XPCS), we investigate the surprising antiferromagnetic dynamics that emerge from such a complex phase diagram over a wide range of temperatures. In this work, we present XPCS measurements of the frustrated magnetic chain compound Lu 2 CoMnO 6 and Monte Carlo simulations. Incommensurate magnetic Bragg peaks slide towards commensurate “up-up-down-down” spin order with decreasing temperature and increasing time. Both simulation and experiment support a counterintuitive “upside-down” temperature dependence of the magnetic dynamics: at higher temperatures in the region of first-order phase boundaries, slower dynamics are observed where the speckle maintains its coherence. At the lowest temperatures, where part of the sample adopts commensurate order, the dynamics speed up and result in fast decoherence.

36 MATERIALS SCIENCE↗

Efficient end-to-end simulation of time-dependent coherent X-ray scattering experiments

Physical optics simulations for beamlines and experiments allow users to test experiment feasibility and optimize beamline settings ahead of beam time in order to optimize valuable beam time at synchrotron light sources like NSLS-II. Further, such simulations also help to develop and test experimental data processing methods and software in advance. The Synchrotron Radiation Workshop ( SRW ) software package supports such complex simulations. We demonstrate how recent developments in SRW significantly improve the efficiency of physical optics simulations, such as end-to-end simulations of time-dependent X-ray photon correlation spectroscopy experiments with partially coherent undulator radiation (UR). The molecular dynamics simulation code LAMMPS was chosen to model the sample: a solution of silica nanoparticles in water at room temperature. Real-space distributions of nanoparticles produced by LAMMPS were imported into SRW and used to simulate scattering patterns of partially coherent hard X-ray UR from such a sample at the detector. The partially coherent UR illuminating the sample can be represented by a set of orthogonal coherent modes obtained by simulation of emission and propagation of this radiation through the coherent hard X-ray (CHX) scattering beamline followed by a coherent-mode decomposition. GPU acceleration is added for several key functions of SRW used in propagation from sample to detector, further improving the speed of the calculations. The accuracy of this simulation is benchmarked by comparison with experimental data.

36 MATERIALS SCIENCE↗

Focusing a round coherent beam by spatial filtering the horizontal source

This paper illustrates the use of spatial filtering with a horizontal slit near the source to enlarge the horizontal coherence in an experimental station and produce a diffraction-limited round focus at an insertion device beamline for X-ray photon correlation spectroscopy experiments. Simple expressions are provided to guide the optical layout, and wave propagation simulations confirm their applicability. The two-dimensional focusing performance of Be compound refractive lenses to produce a round diffraction-limited focus at 11 keV capable of generating a high-contrast speckle pattern of an aerogel sample is demonstrated. The coherent scattering patterns have comparable speckle sizes in both horizontal and vertical directions. The focal spot sizes are consistent with hybrid ray-tracing calculations. Producing a two-dimensional focus on the sample can be helpful to resolve speckle patterns with modern pixel array detectors with high visibility. This scheme has now been in use since 2019 for the 8-ID beamline at the Advanced Photon Source, sharing the undulator beam with two separate beamlines, 8-ID-E and 8-ID-I at 7.35 keV, with increased partially coherent flux, reduced horizontal spot sizes on samples, and good speckle contrast.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Long-Term Aging in Miscible Polymer Nanocomposites

Here we find that the initial, solvent-cast state of nanoparticles (NPs) in a polymer matrix temporally evolves during thermal annealing such that, at steady state, NPs maximize their distance from each other subject to mass balance constraints. The observed timescales for this unexpected structural reorganization, as probed by small-angle X-ray scattering, are temperature-dependent and can be prohibitively large, especially at temperatures around and below 1.2Tg. X-ray photon correlation spectroscopy measurements during reorganization reveal that the collective NP dynamics slow down with annealing at constant temperature; this is accompanied by changes in the low-frequency regime in macroscopic viscoelastic measurements in equilibrated materials. By ruling out other potential sources for these effects (i.e., electrostatic interactions, adsorbed layers), we attribute these results to a long-ranged repulsive force between the NPs caused by fluctuations in the polymer phase, i.e., the "anti-Casimir" effect proposed by Obhukhov and Semenov [Long-range interactions in polymer melts: The anti-Casimir effect. Phys Rev Lett 2005, 95 (3), 038305]. Thus, our results highlight the important role of long-term, slow NP reorganization on the structure and, subsequently, the properties of polymer nanocomposites (PNCs), even in the case of nominally miscible polymer nanoparticle hybrids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Random Walks and Sticky Surfaces: Single-Molecule Measurements of Solute Diffusion in Ethanol/Water-Filled Anodic Alumina Nanopores

Nanoporous anodic aluminum oxide (AAO) membranes are now being explored for use in advanced chemical separations, including in the dehydration of biofuels such as ethanol. Optimization of membrane performance requires an in-depth understanding of how solvent mixtures and solutes behave under nanoconfinement. In this work, the diffusion of rhodamine B (RhB) dye through 10 nm and 20 nm AAO nanopores filled with a series of ethanol/water mixtures (0 - 33% water) is explored by fluorescence correlation spectroscopy (FCS). RhB was found to diffuse through the pores by two distinct mechanisms with mean diffusion coefficients, $D_f$ and $D_s$, reflecting fast and slow diffusive motions, respectively, with values that differ by nearly two orders of magnitude. Further, both $D_f$ and $D_s$ increased with pore size and were significantly smaller than $D_b$, the RhB diffusion coefficient in bulk liquid. Mean $D_f$ values follow a composition-dependent trend that closely mimics the viscosity dependence of $D_b$. Additional slowing of fast RhB diffusion is attributed to both hydrodynamic drag and electrostatic interactions with the nanopore surface. The mean $D_s$ values exhibit a different trend with increasing water content, revealing an increase in $D_s$ and a decrease in the contributions of slow diffusion to the observed dynamics. The fluorescence time transient data used in the analysis show that the slow diffusion process is strongly hindered and likely involves frequent adsorption of RhB to the pore surfaces. These results provide new insights into the detailed molecular-level mechanisms of mass transport in nanoporous AAO membranes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Microscopic ergodicity breaking governs the emergence and evolution of elasticity in glass-forming nanoclay suspensions

We report a study combining x-ray photon correlation spectroscopy (XPCS) with in situ rheology to investigate the microscopic dynamics and mechanical properties of aqueous suspensions of the synthetic hectorite clay Laponite, which is composed of charged, nanometer-scale, disk-shaped particles. The suspensions, with particle concentrations ranging from 3.25 to 3.75 wt%, evolve over time from a fluid to a soft glass that displays aging behavior. The XPCS measurements characterize the localization of the particles during the formation and aging of the soft-glass state. The fraction of localized particles f 0 increases rapidly during the early formation stage and grows more slowly during subsequent aging, while the characteristic localization length r loc steadily de- creases. Despite the strongly varying rates of aging at different concentrations, both f 0 and r loc scale with the elastic shear modulus G' in a manner independent of concentration. During the later aging stage, the scaling between r loc and G' agrees quantitatively with a prediction of naive mode coupling theory. Breakdown of agreement with the theory during the early formation stage indi- cates the prevalence of dynamic heterogeneity, suggesting the soft solid forms through precursors of dynamically localized clusters.

36 MATERIALS SCIENCE↗

Relaxation and Aging of Nanosphere Assemblies at a Water–Oil Interface

The relaxation and aging of an assembly of spherical nanoparticles (NPs) at a water-oil interface are characterized in situ by grazing incidence X-ray photon correlation spectroscopy. The dynamics of the interfacial assembly is measured while the interface saturates with NPs. Weak attractions between NPs lead to gel-like structures in the assembly, where the in-plane ordering is inhibited by the broad size distribution of the NPs. Structural rearrangements on the length scale of the NP-NP center-to-center distances proceed by intermittent fluctuations instead of continuous cooperative motions. Here, the coexistence of rapid and slow NP populations is confirmed, as commonly observed in soft glass-forming materials. Dynamics are increasingly slowed as the NPs initially segregate to the locally clustered interface. The structural relaxation of the NPs in these localized clusters is 5 orders of magnitude slower than that of free particles in the bulk. When the interface is nearly saturated, the time for relaxation increases suddenly due to the onset of local jamming, and the dynamics slow exponentially afterward until the system reaches collective jamming by cooperative rearrangements. This investigation provides insights into structural relaxations near the glass transition and the evolution of the structure and dynamics of the assemblies as they transition from an isotropic liquid to a dense disordered film.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Influence of Thermal Treatment on Preceramic Polymer Grafted Nanoparticle Network Formation: Implications for Thermal Protection Systems and Aerospace Propulsion Components

Preceramic polymer grafted nanoparticles (PCP GNPs) offer potential advantages in the production of polymer-derived ceramic composites compared to neat preceramic polymers (PCPs), such as reduced thermal shrinkage and increased char yield. In comparison to traditional composites (particles + free polymer), PCPs avoid issues of compatibility, agglomeration, and phase separation during processing and provide routes to control nanoparticle arrangement. Prior literature has established that the conversion efficiency of PCPs and PCP GNPs to ceramics and ceramic composites is linked to the thermal pretreatment of these precursor polymers (e.g., curing). In this paper, we investigate the material transformations that occur when exposing PCP GNPs to a low-temperature thermal treatment (≤250 °C) prior to pyrolysis. The PCP GNPs explored in this study possessed silica nanoparticle cores but were distinct in their PCP coronas, having poly(1,1-dimethylpropylsilane) (allyl-GNP)- or poly(1,1-dimethylbenzylethylsilane) (styryl-GNP)-grafted polymers. After undergoing low-temperature thermal treatment, these PCP GNPs exhibited increased char yield at 800 °C; however, unlike commercial PCPs (e.g., allylhydridopolycarbosilane (SMP-10)), obvious cross-linkable sites are not present in the PCP corona structure. Differential scanning calorimetry, oscillatory rheology, and X-ray photon correlation spectroscopy were utilized to elucidate the thermally induced material changes in the allyl- and styryl-GNPs. Thermally induced changes to the structure and behavior of the PCP GNPs were determined to be linked to the chemical structure of the grafted polycarbosilane chains. Styryl-GNPs experienced a curing event between 180 and 250 °C, effecting the formation of a network, which contributed to char yield improvement (at 800 °C). The nanoscale dynamics of this material also shows a transition from diffuse behavior to ballistic behavior because of the cross-linking event. Conversely, the allyl-GNPs did not exhibit a curing event under heat treatment but did show an increase in thermally induced physical cross-linking. The allyl-GNP physical network is stronger after the first cycle of thermal treatment, and it is considered that this contributed to the improvement in char yield post thermal treatment. The advancements in the understanding of the cross-linking behavior of these hybrid materials are expected to advance the application of these materials to turbine engine, advanced friction, and heat-shielding components.

36 MATERIALS SCIENCE↗

Adsorption and Solvation Modulate Rhodamine B Diffusion in Ethanol/Water-Filled Anodic Alumina Nanopores

Confinement of solvents and solutes within nanoporous materials frequently leads to the emergence of unique mass transport behaviors that, once fully understood, may lead to improved chemical separations. Here, the diffusion of Rhodamine B (RhB) dye within 10 and 20 nm diameter anodic aluminum oxide (AAO) nanopores filled with binary ethanol/water mixtures is investigated. Mixture compositions spanning from pure ethanol to pure water are employed. The results of confocal fluorescence correlation spectroscopy studies reveal that RhB diffusion occurs by a two-component mechanism comprising composition-dependent fast and slow motions, characterized by diffusion coefficients D f and D s . The results are consistent with those of previous studies performed under more limited conditions [J. Phys. Chem. C, 2023, 127, 411-420]. The fast component scales with mixture viscosity and is assigned to hindered bulk-like diffusion in central pore regions. Slow diffusion likely involves adsorption of RhB to the pore surface and may be described by a desorption mediated mechanism. The occurrence of RhB adsorption to the AAO surface is verified at the single-molecule level by wide-field fluorescence imaging of membrane cross-sectional surfaces. Unique composition dependent trends in the autocorrelation amplitude and in D s that mimic bulk RhB solubility are revealed. D s is found to be smallest in pure ethanol and pure water and largest in intermediate mixtures. These results suggest that RhB surface adsorption is strongest in the pure liquids and weakest in mixtures of intermediate composition, where the dye is least soluble, and most soluble, respectively. As a result, molecular dynamics simulations reveal that a water layer appears on the pore surface under most conditions, while RhB is solvated primarily by ethanol. The composition dependence of RhB diffusion is concluded to reflect its solvation dependent interactions with the pore walls.

36 MATERIALS SCIENCE↗

Bridging microscopic dynamics and rheology in the yielding of charged colloidal suspensions

The yielding of soft materials is critical to many natural and industrial processes, yet experimental insights into microscopic aspects of yielding are limited. This study combines angle X-ray scattering, X-ray photon correlation spectroscopy, and in situ rheology (Rheo-SAXS-XPCS) with fast lubrication dynamics simulations to examine how interparticle interactions influence yielding in charged colloidal suspensions. By tuning attraction through salt addition, we compare repulsive and attractive systems under deformation. Repulsive suspensions yield uniformly with Andrade-like creep and minimal structural change. In contrast, attractive suspensions show complex behaviors, including shear banding, delayed yielding, and resolidification, governed by transient dynamics at shear band interfaces. These results directly link microscopic particle dynamics to macroscopic flow and demonstrate how interaction potentials control rheological behavior. This work offers a framework for designing soft materials with tailored properties for applications in coatings, food processing, drug delivery, and other technologies requiring precise mechanical control.

Molecular Dynamics Simulation↗

Dynamic Nanoscale Spatial Heterogeneity in a Perovskite-to-Brownmillerite Topotactic Phase Transformation

Phase transitions are omnipresent in modern condensed matter physics and its applications. In solids, first-order phase transformations typically occur by nucleation and growth under nonequilibrium conditions. Under constant external conditions, e.g., constant annealing temperature and pressure, the nucleation and growth dynamics are often thought of as spatially and temporally independent. Here, in situ Bragg X-ray photon correlation spectroscopy (XPCS) reveals nanoscale spatial and dynamical heterogeneity in the perovskite-to-brownmillerite topotactic phase transformation in La 0.7 Sr 0.3 CoO 3 thin films annealed under constant reducing conditions over a time span of multiple hours. Specifically, a time scale associated with domain growth remains stable, with a corresponding domain wall speed of v d = 6 ± 0.5 × 10 –4 nm/s (2 ± 0.2 nm/h), while a slower time scale, associated with temperature-driven depinning of domains, leads to accelerating dynamics with time scales following an aging power law with exponent −2.2 ± 0.5. This experiment demonstrates that Bragg XPCS is a powerful tool to study nanoscale dynamics in structural phase transformations, with the ability to extract quantitative average values related to nanodomain motion in situ. Furthermore, the results are relevant for phase engineering of phase-change devices, as they show that nanoscale dynamics, linked to domain and domain-wall motion, can continuously evolve and speed up with time, even hours after the initiation of the phase transformation, with potential repercussions on electrical performance.

X-ray photon correlation spectroscopy↗

Memory in aging colloidal gels with time-varying attraction

Here, we report a combined rheology, x-ray photon correlation spectroscopy, and modeling study of gel formation and aging in suspensions of nanocolloidal spheres with volume fractions of 0.20 and 0.43 and with a short-range attraction whose strength is tuned by changing temperature. Following a quench from high temperature, where the colloids are essentially hard spheres, to a temperature below the gel point, the suspensions form gels that undergo aging characterized by a steadily increasing elastic shear modulus and slowing, increasingly constrained microscopic dynamics. The aging proceeds at a faster rate for stronger attraction strength. When the attraction strength is suddenly lowered during aging, the gel properties evolve non-monotonically in a manner resembling the Kovacs effect in glasses, in which the modulus decreases and the microscopic dynamics become less constrained for a period before more conventional aging resumes. Eventually, the properties of the gel following the decrease in attraction strength converge to those of a gel that has undergone aging at the lower attraction strength throughout. The time scale of this convergence increases as a power law with the age at which the attraction strength is decreased and decreases exponentially with the magnitude of the change in attraction. A model for gel aging in which particles attach and detach from the gel at rates that depend on their contact number reproduces these trends and reveals that the non-monotonic behavior results from the dispersion in the rates that the populations of particles with different contact number adjust to the new attraction strength.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗