A class of interface state models. I

The Green's function matching procedure of Garcia-Moliner and Rubio is applied to a class of one and three dimensional band models, based on separable Pseudopotentials, for which the Green's functions can be obtained in analytic form. Surface and interface states are obtained corresponding to the [100] and [110] surfaces for a simple cubic, single gap case.     

Hydrogenic atoms in “superstrong” magnetic fields

An estimate is made of the magnetic field above which many recent non-relativistic treatments of hydrogenic atoms in strong magnetic fields become invalid. It is argued that this value may be as low as 10¹⁰Z Gauss.     

Diffusion of Oligonucleotides from within Iron‐Cross‐Linked,Polyelectrolyte‐Modified Alginate Beads: A Model System for Drug Release

An analytical model to describe diffusion of oligonucleotides from stable hydrogel beads is developed and experimentally verified. The synthesized alginate beads are Fe³⁺‐cross‐linked and polyelectrolyte‐doped for uniformity and stability at physiological pH. Data on diffusion of oligonucleotides from inside the beads provide physical insights into the volume nature of the immobilization of a fraction of oligonucleotides due to polyelectrolyte cross‐linking, that is, the absence of a surface‐layer barrier in this case. Furthermore, the results suggest a new simple approach to measuring the diffusion coefficient of mobile oligonucleotide molecules inside hydrogels. The considered alginate beads provide a model for a well‐defined component in drug‐release systems and for the oligonucleotide‐release transduction steps in drug‐delivering and biocomputing applications. This is illustrated by destabilizing the beads with citrate, which induces full oligonucleotide release with nondiffusional kinetics.     

Ambient isobaric heat capacities, C(p,m), for ionic solids and liquids: an application of volume-based thermodynamics (VBT)

Thermodynamic properties, such as standard entropy, among others, have been shown to correlate well with formula volume, V(m), thus permitting prediction of these properties on the basis of chemical formula and density alone, with no structural detail required. We have termed these procedures "volume-based thermodynamics" (VBT). We here extend these studies to ambient isobaric heat capacities, C(p,m), of a wide range of materials. We show that heat capacity is strongly linearly correlated with formula volume for large sets of minerals, for ionic solids in general, and for ionic liquids and that the results demonstrate that the Neumann-Kopp rule (additivity of heat capacity contributions per atom) is widely valid for ionic materials, but the smaller heat capacity contribution per unit volume for ionic liquids is noted and discussed. Using these correlations, it is possible to predict values of ambient (298 K) heat capacities quite simply. We also show that the heat capacity contribution of water molecules of crystallization is remarkably constant, at 41.3 ± 4.7 J K(-1) (mol of water)(-1), so that the heat capacities of various hydrates may be reliably estimated from the values of their chemical formula neighbors. This result complements similar observations that we have reported for other thermodynamic differences of hydrates.     

Preparation and characterization of hydrophobic derivatives of TEMPO-oxidized nanocelluloses

Amidation and ionic complexation were evaluated as surface modification treatments for TEMPO-oxidized nanocelluloses (TONc), using octadecylamine (ODA) as the modifying compound. Effects of the two treatments on TONc with respect to degree of ODA substitution, surface hydrophobicity, crystalline characteristics, and thermal decomposition properties were investigated, respectively, with elemental analysis, contact angle measurements, X-ray diffraction spectroscopy, and thermogravimetric analysis. Both treatments resulted in complete substitution of TONc surface carboxyl groups with ODA, transforming TONc surfaces from hydrophilic to hydrophobic. A slightly greater than one-to-one ODA-to-carboxyl ratio was found for the ionic complexation product, giving it a more hydrophobic character than the amidation product. Furthermore, the ionic complexation product was found to be surprisingly stable in acidic environment and was able to resist dissociation at fairly low pH. TONc from both treatments could be readily dispersed in organic solvents of wide-ranging polarities, making ionic complexation an equally effective surface modification approach as amidation for the hydrophobization of TONc surfaces. It was also found, through X-ray diffraction results that the crystalline structure of TONc was preserved even after the surface modification treatments. Finally, the thermal stability of TONc was slightly increased as a result of the surface modification treatments as evidenced by slight shifts to higher values of TONc thermal decomposition temperature.     

Exact evaluation of entropic quantities in a solvable two-particle model

It has long been known that the von Neumann entropy _SN$S_N$ and the Jozsa–Robb–Wootters subentropy _QJRW$Q_{\mathit{JRW}}$ [R. Jozsa, et al., Phys. Rev. A 49 (1994) 668] are, respectively, upper and lower bounds on the accessible information one can obtain about the identity of a pure state by performing a quantum measurement on a system whose pure state is initially unknown. We determine these bounds exactly in terms of the occupation numbers of normalized natural orbitals of an externally confined interacting two-particle model system. The occupation numbers are obtained via a sign-correct direct decomposition of the underlying exact Schrödinger wave function in terms of an infinite sum of products of Löwdin?s natural orbitals, avoiding thus the solution of the eigenvalue problem with the corresponding reduced one-particle matrix.     

Critically shielded potential in a three-dimensional electron gas: The induced charge density at the origin

The induced electron density at the position of a critically shielded single point charge embedded in a three-dimensional degenerate electron gas is studied at low densities, in a comparative manner. The partial-wave expansion method for scattering states and averaging over the occupied Fermi sphere are used for an attractive potential energy of Hulthen form. The third-order differential equation of March and Murray [N.H. March, A.M. Murray, Phys. Rev. 120 (1960) 830] for the diagonal of the one-particle density matrix is also investigated, for the same continuous set of energy eigenvalues. The comparative study, performed for the s-type component of the total electron density, explicitly demonstrates the equivalence of the two methods.     

Parameter variation for the solution of two-point boundary-value problems and applications in the calculus of variations

In the parameter variation method, a scalar parameterk, k[0, 1], is introduced into the differential equations. The parameterk is inserted in such a way that, whenk=0, the solution of the boundary-value problem is known or readily calculated and, whenk=1, the problem is identical with the original problem. Thus, bydeforming the solution step-by-step throughk-space fromk=0 tok=1, the original problem may be solved. These solutions then provide good starting values for any convergent, iterative scheme such as the Newton-Raphson method.The method is applied to the solution of problems with various types of boundary-value specifications and is further extended to take account of situations arising in the solution of problems from variational calculus (e.g., total elapsed time not specified, optimum control not a simple function of the variables).     

Specific heat of electron gas of arbitrary dimensionality

The exchange contribution to the specific heat of an electron gas in d dimensions is calculated and is shown to lead to a logarithmic temperature dependence at low temperatures in all dimensions (d > 1).