Constrained Geometries Research Articles

Impact of Membrane Fluidity on Steric Stabilization by Lipopolymers

In this work, the impact of lipid lateral mobility on the steric interaction between membranes containing poly(ethylene glycol) (PEG) functionalized lipids was investigated using the surface force apparatus. The force-distance profiles show the presence of electrostatic and steric repulsion that arise from the presence of negatively charged PEG functionalized lipids. Fluid-phase bilayers have high lateral diffusion relative to gel-phase bilayers; however, a quantitative comparison of the interaction forces between membranes in these two different phase states demonstrates a reduced rate of diffusion in the fluid phase for the PEG-lipids under constrained geometries. Thus, the amount of polymer in the contact zone can be modulated and is reduced with fluid membranes; however, complete exclusion was not achieved. As a result, the steric repulsion afforded by PEG chains or binding affinity of ligated PEG chains can only be modestly tailored by the phase state of the liposome.

Assessing the accuracy of volume averaging effective diffusivity estimates with Brownian dynamics simulations

The volume averaging method (VAM) is widely used for estimating the effective diffusivity for solute transport in constrained geometries (e.g., porous media). Comparisons with experimental results for different geometric configurations have indicated that the VAM can provide accurate results over a wide range of porous media configurations. This work uses Brownian dynamics simulations (BDS) to estimate effective diffusivities for constrained geometries and to assess the accuracy of estimations from the VAM. For simple microscale geometric configurations, both isotropic and non-isotropic, it was found that the results predictions of effective diffusivity from VAM agree well with results from the BDS for high porosity values. However, some discrepancies are found for low porosity values, which were attributed to a smoothing effect of the VAM closure problem in the vicinity of very small apertures.

Structure–Mechanochemical Activity Relationships for Cyclobutane Mechanophores

Ultrasound activation of mechanophores embedded in polymer backbones has been extensively studied of late as a method for realizing chemical reactions using force. To date, however, there have been few attempts at systematically investigating the effects of mechanophore structure upon rates of activation by an acoustic field. Herein, we develop a method for comparing the relative reactivities of various cyclobutane mechanophores. Through the synthesis and ultrasonic irradiation of a molecular weight series of poly(methyl acrylate) polymers in which each macromolecule has a single chain-centered mechanophore, we find measurable and statistically significant shifts in molecular weight thresholds for mechanochemical activation that depend on the structure of the mechanophore. We also show that calculations based on the constrained geometries simulate external force method reliably predict the trends in mechanophore reactivity. These straightforward calculations and the experimental methods described herein may be useful in guiding the design and the development of new mechanophores for targeted applications.

An investigation of differential deposition for figure corrections in full-shell grazing-incidence X-ray optics

We are investigating differential deposition as a way of correcting small figure errors inside full-shell grazing-incidence X-ray optics. The optics in our study are fabricated using the electroformed-nickel-replication technique, and the figure errors arise from fabrication errors in the mandrel, from which the shells are replicated, as well as errors induced during the electroforming and mounting process. Combining, these give sub-micron-scale figure deviations which limit the angular resolution of the optics to 10–15 arcsec. Sub-micron figure errors can be corrected by selectively depositing (physical vapor deposition) material inside the shell. The requirements for this filler material are that it must not degrade the ultra-smooth surface finish necessary for efficient X-ray reflection (∼5 A rms), and must not be highly stressed. In addition, a technique must be found to produce well controlled and defined beams within highly constrained geometries, as some of our mirror shells are less than 3 cm in diameter. We report on our efforts to date to implement this technique.

Can X-rays provide a solution to the abundance discrepancy problem in photoionized nebulae?

Abstract We re-examine the well-known discrepancy between ionic abundances determined via the analysis of recombination lines (RLs) and collisionally excited lines (CELs). We show that abundance variations can be mimicked in a chemically homogeneous medium by the presence of dense (nH > rsim 104 cm−3) X-ray irradiated regions which present different ionization and temperature structures from those of the more diffuse medium they are embedded in, which is predominantly ionized by extreme-ultraviolet radiation. The presence of X-ray ionized dense clumps or filaments also naturally explains the lower temperatures often measured from O ii RLs and from the Balmer jump when compared to temperatures determined by CELs. We discuss the implications for abundances determined via the analysis of CELs and RLs and provide a simple analytical procedure to obtain upward corrections for CEL-determined abundance. While we show that the abundance discrepancy factor and the Balmer Jump temperature determined from observations of the Orion Nebula can simultaneously be reproduced by this model (implying upward corrections for CELs by a factor of 1.15), we find that the required X-ray fluxes exceed the known Orion's stellar and diffuse X-ray budget, if we assume that the clumps are located at the edge of the blister. We propose, however, that spatially resolved observations may be used to empirically test the model, and outline how the framework developed in this Letter may be applied in the future to objects with better constrained geometries (e.g. planetary nebulae).

A Synthetic Protein Selected for Ligand Binding Affinity Mediates ATP Hydrolysis

How primitive enzymes emerged from a primordial pool remains a fundamental unanswered question with important practical implications in synthetic biology. Here we show that a de novo evolved ATP binding protein, selected solely on the basis of its ability to bind ATP, mediates the regiospecific hydrolysis of ATP to ADP when crystallized with 1 equiv of ATP. Structural insights into this reaction were obtained by growing protein crystals under saturating ATP conditions. The resulting crystal structure refined to 1.8 A resolution reveals that this man-made protein binds ATP in an unusual bent conformation that is metal-independent and held in place by a key bridging water molecule. Removal of this interaction using a null mutant results in a variant that binds ATP in a normal linear geometry and is incapable of ATP hydrolysis. Biochemical analysis, including high-resolution mass spectrometry performed on dissolved protein crystals, confirms that the reaction is accelerated in the crystalline environment. This observation suggests that proteins with weak chemical reactivity can emerge from high affinity ligand binding sites and that constrained ligand-binding geometries could have helped to facilitate the emergence of early protein enzymes.

Structure Dependence of Hyperpolarizability in Octopolar Molecules.

Recent Hyper Rayleigh Scattering measurements report a significant increase of second-order hyperpolarizability upon introduction of positive charges at the pyridyl end groups in trispyridyl octopolar chromophores. We calculated the geometries, linear response, and first-order hyperpolarizabilities of a series of six trispyridyl molecules both in the neutral and protonated forms. The calculations were performed with ab initio and semiempirical methods. The results are in good agreement with the experimental values and a correlation between the first hyperpolarizability and two structural properties, the N-C bond elongation and the C-C bond length alternation, ⟨Δr⟩ was established. To test these effects we computed the hyperpolarizability for several constrained geometries and confirmed the importance of planarity on the hyperpolarizability values. However the ⟨Δr⟩ values alone seem to have little influence both on the hyperpolarizability and on the gap values. Replacing the triple C≡C bond by a double C=C bond in the conjugation bridge has no significant effect due to the strong hyperpolarizability dependence on the pyridyl-benzene dihedral angle.

Investigation of the Nonlinearity Thresholds of Magnetic Nanostructures by Computing the Bifurcation Points at Microwave Frequencies

The bifurcation analysis of the threshold for collective behavior, due to the instabil- ities (the parametric excitation) of magnetostatic waves (MSW) and dipole-exchange spin-waves (SW) in 3D magnetic nanostructures, is developed. The numerical method is applied to deter- mine the bifurcation points of the nonlinear Maxwell operator (the nonlinear Maxwell equations with electrodynamic boundary conditions complemented by the Landau-Lifshitz equation includ- ing the exchange term). The original computational algorithm is improved by combining it with a qualitative method of analysis, based on Lyapunov stability theory. The threshold magnitudes of the pumping electromagnetic waves (EMWs) in the magnetic particle arrays are determined by computing the bifurcation point for difierent size nanoparticles and for various separations. This technique, based on the bifurcation theory, is a pioneering approach in nano-electrodynamics, taking into account the constrained geometries. Magnetic nanocomposites of nanometer size magnetic particles embedded in a non-magnetic, insu- lating matrix provide a novel solution for low loss microwave materials up to mm wave frequencies. The electromagnetic properties of magnetic materials change drastically upon reducing the dimen- sions into the nano-range, including the early onset of nonlinear efiects, important for high power applications and non-linear signal processing. To investigate this efiect, the instability of para- metric excitation process of magnetostatic waves MSW and dipole-exchange spin-waves SW in 3D magnetic nanostructures should be simulated, taking into account the constrained geometries. In contrast to the bifurcation analysis of the instability of parametric excitation of electromag- netic oscillations in resonator structures with nonlinear planar ferrite inserts (1) and the parametric instability of MSW in thin fllm ferrite structures (2), in this work the parametric excitation of dipole-exchange SW in the arrays of magnetic nanoparticles is analyzed. For the analysis of non- linear phenomena (i.e., the parametric instability of SW) in magnetic nanoparticle systems the numerical method, developed by us earlier (3), is modifled here to determine the bifurcation points of the nonlinear Maxwell's operator including the Landau-Lifshitz equation with the exchange term.

Augmenting microgel flow viareceptor-ligand binding in the constrained geometries of microchannels

We investigated the flow dynamics of biotin-conjugated microgel capsules in avidin-conjugated microchannel constrictions. Microgels were prepared using a microfluidic assembly approach. Biotinylated microgels passing through avidin-modified constrictions slowed relative to several control systems. This effect was observed below a critical velocity of the microgels in the channel-at-large. The reduction in microgel velocity in the constriction occurred for several different sizes of microgels and orifices. Soft compliant microgels showed a lower velocity in the constriction relative to rigid microgels with the same concentration of biotin on the surface, due to the ability of the softer microgels to deform in the orifice and maximize their surface area when in contact with the orifice wall.

The influence of test duration and geometry on the creep crack initiation and growth behaviour of 316H steel

Short-term creep crack growth (CCG) tests have often been performed so that they may be incorporated into research projects with a relatively narrow time frame. Therefore tests are generally performed at relatively high loads, leading to high values of the crack-tip driving-force parameter C*, to reduce the test duration. For the case of ductile materials with relatively low yield strengths, this can lead to significant plastic strains being generated in the specimen on loading. Recently, long-term CCG tests have been performed on the low constraint double edge notch tension and high constraint compact tension specimen geometries of 316H stainless steel at 550 °C. The CCG test data is examined in terms of the experimentally determined C* parameter and compared to data available from a wide range of specimen geometries over a range of C* values. At high C* values similar CCG behaviour is observed for the various specimen geometries. A difference in CCG behaviour is observed between long and short-term tests on the compact tension geometry which may be explained by the effects of constraint loss due to plasticity effects. However, similar trends are observed in the CCG rate data of the alternative, relatively lower constrained geometries, at both high and low C* values. The influence of test duration and specimen geometry on creep crack initiation times is also studied and experimental results are compared with predictions from analytical models.

Spontaneous spin polarization and electron localization in constrained geometries: The Wigner transition in nanowires

The Wigner transition in a jellium model of cylindrical nanowires has been investigated by density-functional computations using the local spin-density approximation. A wide range of background densities ${\ensuremath{\rho}}_{b}$ has been explored from the nearly ideal metallic regime $({r}_{s}={[3/4\ensuremath{\pi}{\ensuremath{\rho}}_{b}]}^{1/3}=1)$ to the high correlation limit $({r}_{s}=100)$. Computations have been performed using an unconstrained plane wave expansion for the Kohn--Sham orbitals and a large simulation cell with up to 480 electrons. The electron and spin distributions retain the cylindrical symmetry of the Hamiltonian at high density, while electron localization and spin polarization arise nearly simultaneously in low-density wires $({r}_{s}\ensuremath{\sim}30)$. At sufficiently low density $({r}_{s}\ensuremath{\ge}40)$, the ground-state electron distribution is the superposition of well defined and nearly disjoint droplets, whose charge and spin densities integrate almost exactly to one electron and $1/2{\ensuremath{\mu}}_{B}$, respectively. Droplets are arranged on radial shells and define a distorted lattice whose structure is intermediate between bcc and fcc. Dislocations and grain boundaries are apparent in the droplets' configuration found by our simulations. Our computations aim at modeling the behavior of experimental low-carried density systems made of lightly doped semiconductor nanostructures or conducting polymers.

DNA Transport in Hierarchically-Structured Colloidal-Nanoparticle Porous-Wall Nanochannels

We report a simple approach to the formation of 3D colloidal nanoparticle structures incorporating enclosed mesoscopic structures through a simple process of spin-coating-driven directed self-assembly onto lithographically defined polymer templates. Removal of the buried polymer patterns by high temperature calcination results in the formation of hierarchically enclosed channels, continuous networks, isolated cavities, and multilayered structures with high stability and environmental resistance. These channels are used to investigate the transport of DNA molecules in constrained geometries.

Preparation of enediyne-crosslinked networks and their reactivity under thermal and mechanical conditions

The COGEF technique (COnstrained Geometries simulating External Force) was used to investigate the effects of macroscopic forces on cyclic enediynes, which can undergo Bergman Cyclization (BC). Because the forces needed to activate BC were found to be less than the forces needed for chain scission in polymer backbones, the calculations suggest that enediynes are potentially useful mechanophores. Three enediynes studied computationally were synthesized. The thermal BC reactions for these compounds were studied by DSC and found to be consistent with the predicted thermal sensitivity based on known substituent effects. However, upon incorporation of the enediynes into a polymer matrix as crosslinks, no definitive mechanical activation was observed, and conclusions about the stress-sensitivity of enediynes were unable to be drawn. Model studies suggest that insufficient force was applied to the crosslinks for mechanical activation to be observable by DSC.

Theory of relaxation dynamics in glass-forming hydrogen-bonded liquids

We address the relaxation dynamics in hydrogen-bonded supercooled liquids near (but above) the glass transition, measured via broadband dielectric spectroscopy (BDS). We propose a theory based on decomposing the relaxation of the macroscopic dipole moment into contributions from hydrogen-bonded clusters of s molecules, with s(min) < or = s < or = s(max) . The existence of s(max) is translated into a sum rule on the concentrations of clusters of size s . We construct the statistical mechanics of the supercooled liquid subject to this sum rule as a constraint, to estimate the temperature-dependent density of clusters of size s . With a theoretical estimate of the relaxation time of each cluster, we provide predictions for the real and imaginary parts of the frequency-dependent dielectric response. The predicted spectra and their temperature dependence are in accord with measurements, explaining a host of phenomenological fits like the Vogel-Fulcher fit and the stretched exponential fit. Using glycerol as a particular example, we demonstrate quantitative correspondence between theory and experiments. The theory also demonstrates that the alpha peak and the "excess wing" stem from the same physics in this material. The theory also shows that in other hydrogen-bonded glass formers the excess wing can develop into a beta peak, depending on the molecular material parameters (predominantly the surface energy of the clusters). We thus argue that alpha and beta peaks can stem from the same physics. We address the BDS in constrained geometries (pores) and explain why recent experiments on glycerol did not show a deviation from bulk spectra. Finally, we discuss the dc part of the BDS spectrum and argue why it scales with the frequency of the alpha peak, providing an explanation for the remarkable data collapse observed in experiments.

Numerical investigation of domain walls in constrained geometries

In recent years, magnetic domain wall structures in ferromagnetic nanowires have attracted growing attention, opening paths to develop novel devices which exploit magnetoresistive effects. A reduction of the domain wall length in geometrically constrained areas has been predicted and observed. In this article, we consider a rectangular constriction (width s0, length 2d0) in form of a thin film, attached to a rectangular pad (width s1) on either side. The material considered is Ni (Ms=490kA∕m) with a weak in-plane anisotropy (K1=2000J∕m3). We investigate the dependence of the domain wall length as a function of the constriction geometry. Micromagnetic simulations are used to systematically study the head-to-head domain walls between head-to-head domains (case A) and Néel walls between sidewise domain orientations (case B). We present the resulting domain wall length w as a function of 2d0 and s0 and analyze the magnetization patterns. A reduction of the domain wall length to below 11nm is found (where the corresponding unconstrained domain wall length is 69nm). For constriction lengths above a critical value (case B only), the single 180° domain wall splits into two 90° domain walls.

Effects of halogen substitution on the properties of eight- and nine-vertex closo-boranes

The symmetry constrained geometries of the eight- and nine-vertex polyhedral boranes and haloboranes BnXnz (n = 8 and 9; X = H, F and Cl; z = -2, -1 and 0) were optimized at the B3LYP/6-311+G(d) level and their nucleus-independent chemical shifts (NICS) were calculated using the GIAO method with Kohn-Sham orbitals. Substitution of halogens on borane cages was found to significantly impact not only the geometric but also magnetic properties. Multiple fluorine substituents cause a deviation from the Wade-Mingos skeletal electron rules in B8F8(2-), resulting in a distortion from the expected D2d bisdisphenoid to a C2v nido type bicapped trigonal prism. However, all of the nine-vertex cages B9X9z retain the D3h tricapped trigonal prismatic structure of B9H9(2-). The presence of halogen substituents was found to enhance the three-dimensional diatropic ring currents within the dianionic borane cages B8X8(2-) and B9X9(2-). For the neutral structures the NICS values indicate BnFn to be aromatic, BnCln to be essentially non-aromatic, and BnHn to be antiaromatic (n = 8, 9).

The toughness of laser welded joints in the ductile–brittle transition

An important feature of laser welded joints is the high level of strength and toughness mismatch developed between the weld and the parent plate. As a result, defects are frequently located in regions with high strength and toughness gradients. To address this issue, toughness tests have been performed on laser welded joints with strength mismatches in excess of 2. Toughness tests have been performed on high and low constraint mode I geometries and mixed-mode I/II configurations. In highly constrained geometries, the local toughness dominates the failure process causing the crack to deviate into harder and more brittle weld metal, while in low constraint configurations, the size of the plastic zone promotes crack deviation into the softer and tougher parent plate. In Charpy tests the crack also deviates into the tougher parent plate giving potentially misleading indications of the behaviour of defects in highly constrained joints. The experiments are modelled by a local approach technique for functionally graded materials in which the local yield strength and toughness are allowed to vary spatially.

Electronic interactions between gold nanoclusters in constrained geometries

The interactions between gold nanoclusters dispersed in decane $({\mathrm{C}}_{10}{\mathrm{H}}_{22})$ when confined in narrow gaps of a few nanometers were investigated. The diameter of the gold core was $1.8\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The clusters were capped off with alkanethiol molecules of different lengths (${\mathrm{C}}_{6}\mathrm{S}$ and ${\mathrm{C}}_{15}\mathrm{S}$) to prevent metallic contact with each other. By applying force to the gap walls, the cluster suspension was squeezed out of the gap in a nearly continuous way. In the case of the shorter ligand ${\mathrm{C}}_{6}\mathrm{S}$, the width of the minimum gap at the highest applied force was $7\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ ($\ensuremath{\sim}3$ cluster diameters). In contrast with the continuous decrease in thickness, the gap capacitance exhibited stepwise increases, which are interpreted as Mott type insulator-to-metal transition of aggregates of clusters under pressure when the average distance between the metallic cores becomes less than $\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. With longer ligands, ${\mathrm{C}}_{15}\mathrm{S}$, the thickness of the minimum gap was $12--15\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. In that case, no discontinuous steps in thickness or capacitance were observed, showing that the longer ligand effectively prevents exchange interactions between the metallic cores of the nanoclusters.

Long time behaviour of diffusing particles in constrained geometries; application tochromatin motion

Inspired by experiments that use single-particle tracking to measure the regions ofconfinement of selected chromosomal regions within cell nuclei, we have developed ananalytical approach that takes into account various possible positions and shapes of theconfinement regions. We show, in particular, that confinement of a particle into a subregionthat is entirely enclosed within a spherical volume can lead to a higher limit of themean radial square displacement value than the one associated with a particlethat can explore the entire spherical volume. Finally, we apply the theory toanalyse the motion of extrachromosomal chromatin rings within nuclei of livingyeast.

Numerical Simulation of Nonlinear and Parametric Oscillations in a Semiconductor Resonator Structure

The rigorous mathematical modeling of nonlinear oscillations in microwave strip-slot resonator structure (RS), loaded with a distributed planar Gunn diode, is based on the solution of the threedimensional diffraction boundary problem, formulated rigorously taking into account the full set of Maxwell's equations and the nonlinear equation of transport carriers in a semiconductor. Using our numerical approach to determine the bifurcation points of the solution of nonlinear Maxwell's equations, the transition region from the stationary regime of the nonlinear semiconductor device behavior (i.e., the frequency multiplication and the stable para- metric amplification) to the generation (the onset of self-oscillations) caused by the instability process in the distributed Gunn diode, was simulated taking into account constrained geometries of strip-slot RS.