Electrophoresis of sheared polyelectrolytes

ABSTRACT

A shear flow breaks the spherical symmetry of a flexible polymer, which has some interesting consequences for the electrophoresis of polyelectrolytes. In addition to introducing a chain-length dependence of the electrophoretic velocity, there is also the possibility of migration of the molecule perpendicular to the direction of coaxial gradients in pressure and electric potential. This has been shown to produce a rapid and highly localised concentration of DNA within a microfluidic capillary, with a number of potential applications to on-chip preparation and analysis of genomic DNA. In this paper, dedicated to Prof. Daan Frenkel, I will describe a calculation of the electrophoretic motion of a long polyelectrolyte under a coaxial flow and electric field.     

Ultrafast X‐ray imaging of laser–metal additive manufacturing processes

The high‐speed synchrotron X‐ray imaging technique was synchronized with a custom‐built laser‐melting setup to capture the dynamics of laser powder‐bed fusion processes in situ. Various significant phenomena, including vapor‐depression and melt‐pool dynamics and powder‐spatter ejection, were captured with high spatial and temporal resolution. Imaging frame rates of up to 10 MHz were used to capture the rapid changes in these highly dynamic phenomena. At the same time, relatively slow frame rates were employed to capture large‐scale changes during the process. This experimental platform will be vital in the further understanding of laser additive manufacturing processes and will be particularly helpful in guiding efforts to reduce or eliminate microstructural defects in additively manufactured parts.     

Elucidation of the Mechanism of Enhanced Insulin Uptake and Release from pH Responsive Hydrogels

Summary: Environmentally responsive hydrogels composed of poly(methacrylic acid-g-ethylene glycol) (P(MAA-g-EG)) have shown promise for oral insulin delivery due to their pH responsive complexation behavior. A series of hydrogel formulations were polymerized with varying amounts of crosslinker and varying monomer volume fraction. The mesh size of the network depended primarily on pH, varying from 8.0 to 27.2 nm. Insulin loading efficiency varied directly with crosslink density, ranging from 42.7 to 84.9% of available insulin loaded into the hydrogels. The release of insulin was performed with each polymer formulation at 5 pH levels ranging from 2.7 to 6.8. Insulin release was less than 20% for all formulations tested with insulin for the duration of the 3 hour release study for all pH levels considered except when the pH was 6.8, at which point the release occurred as a burst. Loading studies performed with insulin glargine, an insulin analog with an increased pI, showed the same trends as native insulin. However, the release of insulin glargine only occurred at a pH level above that of the pI of the protein. These results indicate that hydrogen bonds and ionic interactions between the protein and P(MAA-g-EG) may strongly influence its loading and release behavior in vitro.     

The Critical Fugacity for Surface Adsorption of Self-Avoiding Walks on the Honeycomb Lattice is {1+\sqrt{2}}

In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a. honeycomb) lattice is ${\mu=\sqrt{2+\sqrt{2}}}$ . A key identity used in that proof was later generalised by Smirnov so as to apply to a general O(n) loop model with ${n\in [-2,2]}$ (the case n = 0 corresponding to self-avoiding walks). We modify this model by restricting to a half-plane and introducing a surface fugacity y associated with boundary sites (also called surface sites), and obtain a generalisation of Smirnov’s identity. The critical value of the surface fugacity was conjectured by Batchelor and Yung in 1995 to be ${y_{\rm c}=1+2/\sqrt{2-n}}$ . This value plays a crucial role in our generalized identity, just as the value of the growth constant did in Smirnov’s identity. For the case n = 0, corresponding to self-avoiding walks interacting with a surface, we prove the conjectured value of the critical surface fugacity. A crucial part of the proof involves demonstrating that the generating function of self-avoiding bridges of height T, taken at its critical point 1/μ, tends to 0 as T increases, as predicted from SLE theory.     

Effect of surface corrugation on low temperature phases of adsorbed (p-H2)7: A quantum path integral Monte Carlo study

By using path integral Monte Carlo simulations coupled to Replica Exchange algorithms, various phases of (p-H₂)₇ physically adsorbed on a model graphite surface were identified at low temperatures. At T=0.5 K$T=0.5\text{K}$, the expected superfluid phase was observed for flat and slightly corrugated surfaces. At intermediate and high corrugations, a “supersolid” phase in C_7/16 registry and a solid phase in C_1/3 registry were observed, respectively. At higher temperatures, the superfluid is converted to a fluid and the “supersolid” to a solid.     

Decomposition of in vivo spatially offset Raman spectroscopy data using multivariate analysis techniques

The decomposition of spatially offset Raman spectra for complex multilayer systems, such as biological tissues, requires advanced techniques such as multivariate analyses. Often, in such situations, the decomposition methods can reach their limits of accuracy well before the limits imposed by signal‐to‐noise ratios. Consequently, more effective reconstruction methods could yield more accurate results with the same data set. In this study we process spatially offset Raman spectroscopy (SORS) data with three different multivariate techniques (band‐target entropy minimization (BTEM), multivariate curve resolution and parallel factor analysis (PARAFAC)) and compare their performance when analysing a spectrally challenging plastic model system and an even more challenging problem, the analysis of human bone transcutaneously in vivo. For the in vivo measurements, PARAFAC's requirement of multidimensional orthogonal data is addressed by recording SORS spectra both at different spatial offsets and at different anatomical points, the latter providing added dimensionality through the variation of skin/soft tissue thickness. The BTEM and PARAFAC methods performed the best on the plastic system with the BTEM more faithfully reconstructing the major Raman bands and PARAFAC the smaller more heavily overlapped features. All three methods succeeded in reconstructing the bone spectrum from the transcutaneous data and gave good figures for the phosphate‐to‐carbonate ratio (within 2% of excised human tibia bone); the PARAFAC gave the most accurate figure for the mineral‐to‐collagen ratio (20% less than excised human tibia bone). Previous studies of excised bones have shown that certain bone diseases (such as osteoarthritis, osteoporosis and osteogenesis imperfecta) are accompanied by compositional abnormalities that can be detected with Raman spectroscopy, the utility of a technique which could reconstruct bone spectra accurately is manifest. The results have relevance on the use of SORS in general. © 2014 Crown copyright. Journal of Raman Spectroscopy published by John Wiley & Sons, Ltd.     

Comparison between geometrically focused pulses versus filaments in femtosecond laser ablation of steel and titanium alloys

Kerr self-focusing of high-power ultrashort laser pulses in atmosphere may result in a structure or structures of high intensity that can propagate over long distances with little divergence. Filamentation has garnered significant interest in the nonlinear optics community due to its unique properties. Salient features of filaments include a central region of intense laser power (greater than the ionization threshold of the propagation medium) and a low temperature plasma column that lasts up to nanoseconds in duration after the passage of the laser pulse. Steel and titanium samples are ablated by filaments and by sharply focused sub-picosecond laser pulses. We then performed metrology on the samples to compare the ablation features in addition to modeling of the plasma ablation process. Ablation with filaments leads to a wider range of material responses as compared to ablation with sharply focused pulse. This results in potential complications for applications of filament ablation that depends on the rate of material removal and spectroscopic analysis.     

Gas Sorption and the Consequent Volumetric and Permeability Change of Coal II: Numerical Modeling

The permeability of coalbed methane reservoirs may evolve during the recovery of methane and injection of gas, due to the change of effective stress and gas adsorption and desorption. Experimental and numerical studies were conducted to investigate the sorption-induced permeability change of coal. This paper presents the numerical modeling part of the work. It was found that adsorption of pure gases on coal was well represented by parametric adsorption isotherm models in the literature. Based on the experimental data of this study, adsorption of pure \(\hbox {N}_2\) was modeled using the Langmuir equation, and adsorption of pure \(\hbox {CO}_2\) was well represented by the N-Layer BET equation. For the modeling of CO \(_2\) & N \(_2\) binary mixture adsorption, the ideal adsorbed solution (IAS) model and the real adsorbed solution (RAS) model were used. The IAS model estimated the total amount of mixture adsorption and the composition of the adsorbed phase based on the pure adsorption isotherms. The estimated total adsorption and adsorbed-phase composition were very different from the experimental results, indicating nonideality of the CO \(_2\) –N \(_2\) –Coal-adsorption system. The measured sorption-induced strain was linearly proportional to the total amount of adsorption despite the species of the adsorbed gas. Permeability reduction followed a linear correlation with the volumetric strain with the adsorption of pure \(\hbox {N}_2\) and the tested CO \(_2\) & N \(_2\) binary mixtures, and an exponential correlation with the adsorption of pure \(\hbox {CO}_2\) .     

Construction of multi-dimensional isotropic kernels for nonlocal elasticity based on phonon dispersion data

Kernels for non-local elasticity are in general obtained from phonon dispersion relations. However, non-local elastic kernels are in the form of three-dimensional (3D) functions, whereas the dispersion relations are always in the form of one-dimensional (1D) frequency versus wave number curves corresponding to a particular wave direction. In this paper, an approach to build 2D and 3D kernels from 1D phonon dispersion data is presented. Our particular focus is on isotropic media where we show that kernels can be obtained using Fourier–Bessel transform, yielding axisymmetric kernel profiles in reciprocal and real spaces. These kernel functions are designed to satisfy the necessary requirements for stable wave propagation, uniformity of nonlocal stress and stress regularization. The proposed concept is demonstrated by developing some physically meaningful 2D and 3D kernels that will find useful applications in nonlocal mechanics. Relative merits of the kernels obtained via proposed methods are explored by fitting 1D kernels to dispersion data for Argon and using the kernel to understand the size effect in non local energy as seen from molecular simulations. A comparison of proposed kernels is made based on their predictions of stress field around a crack tip singularity.