Quadratic Concentration Dependence Research Articles

The Microrheology of Sickle Hemoglobin Gels

Sickle cell disease is a rheological disease, yet no quantitative rheological data exist on microscopic samples at physiological concentrations. We have developed a novel method for measuring the microrheology of sickle hemoglobin gels, based on magnetically driven compression of 5- to 8-μm-thick emulsions containing hemoglobin droplets ∼80 μm in diameter. Using our method, by observing the expansion of the droplet area as the emulsion is compressed, we were able to resolve changes in thickness of a few nanometers with temporal resolution of milliseconds. Gels were formed at various initial concentrations and temperatures and with different internal domain structure. All behaved as Hookean springs with Young's modulus from 300 to 1500 kPa for gels with polymerized hemoglobin concentration from 6 g/dl to 12 g/dl. For uniform, multidomain gels, Young's modulus mainly depended on the terminal concentration of the gel rather than the conditions of formation. A simple model reproduced the quadratic dependence of the Young's modulus on the concentration of polymerized hemoglobin. Partially desaturated samples also displayed quadratic concentration dependence but with a smaller proportionality coefficient, as did samples that were desaturated in steps; such samples were significantly less rigid than gels formed all at once. The magnitude of the Young's modulus provides quantitative support for the dominant models of sickle pathophysiology.

Miccrorheology of Sickle Hemoglobin Gels

Sickle cell disease is a rheological disease, yet no quantitative rheological data exists on microscopic samples. We have developed a novel method for probing the microrheology of sickle hemoglobin gels, based on magnetically driven compression of 5-8 μm thick emulsions containing hemoglobin droplets of ∼100 μm diameter. By observing the expansion of the droplet area as the emulsion is compressed, our method can resolve changes in thickness of a few nm with temporal resolution of ms. Carbon monoxide bound to sickle hemoglobin was dissociated by laser illumination allowing the resulting deoxyhemoglobin to form gels in target droplets. The amount of polymer formed was determined by observing, in the target droplet, the residual concentration in a small region that was unilluminated by the laser. Thickness was monitored by observing a non-photolyzed reporter droplet adjacent to the target droplet.Gels were formed at different initial concentrations, temperatures and fractional saturation with CO. In addition, some gels were formed in small spatial regions which then were allowed to grow to the full extent of the target droplet, to contrast with the same sample gelled completely in the target droplet ab initio, thereby creating a different domain structure in the gel. We find that all the gels behave as Hookean springs with linear and repeatable dependence of thickness on force. This allowed us to determine Young's modulus, which ranged from 300 to 1500 kPa for the gels which varied in polymerized hemoglobin concentration from 6 g/dl to 12 g/dl. A highly simplified model for the gel, treating it as a simple lattice with fixed junctions, describes the observed quadratic concentration dependence of Young's modulus data. These measurements provide a quantitative rationale for pathophysiology in the disease.

The IR emitting centers in Bi-doped Mg-Al-Si oxide glasses

The properties of IR emission centers are investigated in Bi-doped Mg-Al-silicate glasses having moderate melting temperatures to be fabricated by routine melting in alumina crucibles. The quadratic concentration dependence of absorption in the visible range indicates that the considered optical centers can be Bi2 dimers forming in a balanced chemical reaction in the glass melt. Their formation enthalpy is evaluated from their concentration variations with the synthesis temperature. The high (up to 85% at low concentrations) luminescence quantum yield and wide emission spectrum makes this glass a promising material for tunable lasers.

Concentration dependence in coherent Raman scattering

We investigate the concentration dependence of the femtosecond coherent anti-stokes Raman scattering (CARS) signals collected from several mixtures of molecules. We demonstrate a clear quadratic dependence of the transmitted CARS signal on the number of molecules of pyridine in water by looking at the Raman signal at 1030 cm−1. Using a backscattering configuration we study the quadratic concentration dependence in solid mixtures of dipicolinic acid, calcite, and gypsum in powder form.

Equation of State Mixing Rules That Incorporate Only the Residual Part of the UNIQUAC Model

New mixing rules that incorporate the residual part of the UNIQUAC activity coefficient model and the correct quadratic concentration dependence of the second virial coefficient are presented. Following our recent approach, only the attractive part of the excess Helmholtz energy derived from the equation of state (EOS) is related to the excess Gibbs energy. It is recognized that, in the extension of this concept to the UNIQUAC model, the interpretation of the physical contributions of the combinatorial and residual parts must be considered. We conclude that the attractive forces are related only to the residual part of the UNIQUAC model. This allows the formulation of a class of mixing rules that are independent of the repulsive term in the EOS and are applicable to both cubic and noncubic EOS. The proposed mixing rules are applied to different low-pressure systems, exhibiting vapor−liquid and liquid−liquid equilibria, and to two near critical and supercritical systems.

Simple new EOS mixing rules which incorporate lattice fluid excess functions

New mixing rules which incorporate lattice fluid excess functions (for example Wilson and NRTL) and the correct quadratic concentration dependence of the second virial coefficient are presented. It is shown that the excess Gibbs functions derived for activity coefficient models correspond to the attractive part of the excess Helmholtz energy derived from EOS. This allows the formulation of a class of mixing rules which are independent of the repulsive term in the EOS, and are applicable to both cubic and noncubic EOS. The mixing rules are applied to different low-pressure phase equilibria and to two near-critical and supercritical systems.

Pseudolattice theory of strong electrolyte solutions

The quadratic concentration dependence of the logarithmic activity coefficient and relative partial molar enthalpies of concentrated strong electrolyte solutions can be explained by assuming the solution to have a pseudolattice structure and taking short-range interactions into account through a hard-core potential with an attractive 1/r6 tail. The pseudolattice model is shown to reproduce the experimental data of activity coefficients and relative partial molar enthalpies with a great degree of accuracy over a large range of concentration. The validity of the short-range potential is explicitly tested with experimental data for a number of substances.

EOS mixing rules and the quadratic concentration dependence of the second virial coefficient

The usual one-fluid mixing rule applied to the Alder-polynomial is generally not consistent with the required quadratic concentration dependence of the second virial coefficient. Consistency might have been achieved by refitting the constants, but it does not agree with argon data. The mixing rule written directly to the compressibility factor does not suffer from the consistency problem, but it involves separate mixing rules for different power combinations of u and V 0.

An exact solution of the diffusion equation with shrinking

An exact solution for diffusion from a shrinking slab of finite thickness, assuming a constant mutual diffusion coefficient, has been obtained. This has been accomplished by first casting the appropriate differential equation into the form of an equation describing diffusion in a semi-infinite slab with a fixed domain of integration but with a quadratic concentration dependence of the diffusivity and then making use of Fujita's analytical solution for that equation. The present results are of potential interest in the fields of drying, dyeing, ion exchange and solid—liquid extraction.

Doppler-free measurement of the calcium 4 s21S0-4 s4 p1P1 transition at 422.673 nm by degenerate four-wave mixing in a demountable cathode discharge atomizer

Doppler-free laser spectroscopic measurement of the calcium 4 s 2 1 S 0-4 s4 p 1 P 1 transition at 422.673 nm by degenerate four-wave mixing is reported using an excimer-pumped dye laser as the excitation light source. The use of a demountable hollow cathode discharge cell operated at relatively low pressure levels (1–10 torr) minimizes Lorentzian (pressure) broadening and hence further improves the Doppler-free signal. The analyte (as small as 0.32 μg calcium) is deposited inside the cylindrical microcathode where the three input laser beams are directed. Important characteristic properties of degenerate four-wave mixing are discussed, including cubic energy dependence, quadratic concentration dependence, and dependence of signal on different discharge gases, buffer gas pressure and discharge current.

Concentration effects on the up-conversion from the [formula omitted] level of Er 3+ in YAG

A quantitative study of the up-conversion process ( 4I 13 2 → 4I 15 2 ) + ( 4I 13 2 → 4I 9 2 → 4 I case11 2 ) , essential in the 3 μm emission of Er 3+ in YAG, over a large concentration range (0.1 to 100 at% Er 3+) and pumping energy has been performed. The concentration and sample dependence of the “intrinsic” lifetime of 4I 13 2 and 4I 13 2 laser levels is tentatively explained by energy transfer to aleatory impurities. The quadratic concentration dependence of the up-conversion parameter, obtained experimentally, and the possibility to describe the up-conversion process by rate equations are explained by large migration effects and effective interactions between nearest neighbours.

Dynamics in regular solutions: Concentration and viscosity dependence of orientational correlation time of a benzene molecule

The conformal solution theory by Longuet-Higgins was extended to the dynamic problem through the first-order perturbation theory for the interpretation of the concentration dependence of dynamic solution properties; molecular similarity and dissimilarity are reflected by the linear ideal terms and the quadratic regular terms, respectively. To test the theory, the orientational correlation times τ2R were determined for benzene-d6 in the three regular solutions of benzene (B) with toluene (T), carbon tetrachloride (C), and cyclohexane (H) as a function of the concentration (mole fraction x, 0≤x≤1) at 25 °C by measuring the spin-lattice relaxation time of the quadrupole nucleus 2H. The temperature effect was also studied in the BC solution. The τ2R–x curve is linear in BT and BC whose excess enthalpies HE are small, but it is quadratic in BH with a larger HE. The quadratic concentration dependence indicates the important effect of liquid structure on the orientation dynamics as well as the viscosity. The validity of the Stokes–Einstein–Debye (SED) law was tested with respect to the linear relation between τ2R and η/T (T the temperature, η the solution viscosity). The SED law holds when η is varied only by T or x under some limited conditions. The conditions for this simple relation have been clarified using the extended conformal solution theory.

Many-body energy-transfer processes between Er3+ ions in yttrium aluminum garnet.

The results of the luminescence-quenching measurements of the $^{4}$${\mathit{S}}_{3/2}$ level of ${\mathrm{Er}}^{3+}$ in yttrium aluminum garnet are reported. Decay data in a large temperature (10--300 K) and concentration range (0.1--100 at.%) are analyzed. The quenching process depends strongly on concentration and temperature. At low ${\mathrm{Er}}^{3+}$ content (\ensuremath{\le}3 at.%) the quenching is dominated by two-ion dipole-dipole cross-relaxation processes. It is shown that the previous proposed mechanisms can only explain the high-temperature data, and a possible active mechanism at low temperatures is proposed. At higher concentrations the quenching process depends strongly on temperature, the migration on donors playing an essential role, especially at low temperatures, where the supermigration regime is observed. The quadratic concentration dependence of the transfer parameters at high ${\mathrm{Er}}^{3+}$ content is connected with the three-ion cross-relaxation processes. The temperature dependences of the supermigration rates are consistent with two types of three-ion processes, i.e., one phonon-assisted process at low temperatures (T100 K) and another very efficient resonant one [${(}^{4}$${\mathit{S}}_{3/2}$${,}^{2}$${\mathit{H}}_{11/2}$)${\ensuremath{\rightarrow}}^{4}$${\mathit{I}}_{15/2}$${]}_{\mathit{D}}$+[${(}^{4}$${\mathit{I}}_{15}$ $_{/2}\ensuremath{\rightarrow}^{4}$${\mathit{I}}_{13/2}$${)}_{\mathit{A}1}$+${(}^{4}$${\mathit{I}}_{15/2}$${\ensuremath{\rightarrow}}^{4}$${\mathit{I}}_{9/2}$${)}_{\mathit{A}}$ at high temperatures (Tg150 K). It is shown that at 300 K for Cg10 at.% ${\mathrm{Er}}^{3+}$ the transfer is of direct donor-acceptor type, due to the above cross relaxation. Thus, at 300 K, the energy from the pumping $^{4}$${\mathit{S}}_{3/2}$ level is transferred to the 3-\ensuremath{\mu}m laser levels ${(}^{4}$${\mathit{I}}_{11/2}$ and $^{4}$${\mathit{I}}_{13/2}$) by a three-ion cross relaxation. This study has emphasized the possibility of very efficient three-ion processes in the luminescence quenching of rare earth elements at large activator concentrations.

Kinetics of hydrogen desorption from the first wall of a thermonuclear reactor

A simple model is proposed for the description of hydrogen desorption from a TNR first wall in steady conditions, taking account of radiationally stimulated desorption. An expression is obtained for the degree of cover of the surface. It is shown that, in TNR conditions, the main contribution to the desorbed flux is from the recombinational term, Radiationally stimulated desorption leads to a slight correction. The dependence of the desorbed flux on the hydrogen flux close to the surface is investigated. In a series of cases which are of practical importance, the general Eq. (7) may be simplified. As well as a quadratic concentration dependence of the thermodesorbed flux, a linear dependence is also possible. Equations (13) and (14) may be used in calculating the hydrogen permeability and tritium accumulation in the TNR first wall.

ESR determination of lipid translational diffusion coefficients at low spin-label concentrations in biological membranes, using exchange broadening, exchange narrowing, and dipole-dipole interactions

Spin-spin interactions between phosphatidylcholine nitroxide spin labels in fluid-phase dimyristoyl phosphatidylcholine bilayers have been studied in the concentration range 0.1–2.0 mol%. The total line broadening has been separated into its Gaussian and Lorentzian components. The Gaussian linewidth exhibits exchange narrowing of the unresolved proton hyperfine structure, with an approximate quadratic concentration dependence for the square of the linewidth, over this spin-label concentration range. The Lorentzian linewidth has a linear dependence on the spin-label concentration over the same range. The temperature dependence of the gradient of the Lorentzian broadening with respect to spin-label concentration is biphasic over the range 30–80°C, indicating a dominant contribution from magnetic dipole-dipole broadening at the lower temperatures. The contributions from the dipole-dipole and exchange interactions to the Lorentzian broadening have been separated by fitting the temperature dependence using an unconstrained optimization procedure and assuming a single effective activation energy for both diffusion-controlled processes. The lipid lateral diffusion coefficient has been determined from the concentration dependence of both the exchange broadening of the nitrogen hyperfine structure and the exchange narrowing of the proton hyperfine structure using a two-dimensional lattice diffusion model, and also from the concentration dependence of the dipole-dipole interaction using a three-dimensional Fick's law diffusion model. All three methods yield consistent values for the diffusion coefficient, although because of the approximate nature of some of the theoretical models the exchange broadening is expected to give the most reliable results. An experimental protocol for determining the actual spin concentration in the membrane sample is also presented.

Automatic computation of diffusion rates

The equations for diffusion due to gravity, thermal, and concentration gradients in a multi-component, quiescent plasma are so complicated that the calculation of the diffusion rate(s) should be automated. I give an automated calculation scheme that utilizes the inherent reliability of computers in conducting repeated operations, but does not require simultaneous solution of many linear equations for each time step. In the first part of the scheme, the quadratic concentration dependence of the individual coefficients in Burger's diffusion equation is exploited to automate the computation of the numerical coefficients that multiply these concentrations.

Internal friction of diluteAl/Cu alloys in homogenized and precipitated states between 100 and 350 °C

The activation energy of the Zener relaxation due to Cu pairs was found to be 31.4 kcal/mol, with τ0 = 10−15.6 s. The results show that the relaxation strength of this effect obeys the quadratic concentration dependence. The small peak around 180 °C, at about 1 Hz, appearing in the presence of the θ″-phase, has «Zener» character. In the case of the θ′-phase a broad peak near 160°C is attributed to the misfit dislocations around the semi-coherent precipitates. The activation energy of this relaxation is 23 kcal/mol, with τ0 = 10−12.4 s. From the spectra of specimens pre-annealed at 300°C, or above, we infer that in this temperature range mostly θ-phase was formed. The results are complemented by measurements on plastically deformed specimens. In order to investigate the stability and transformations of different precipitated phases, internal-friction measurements were also made after various, subsequent heat treatments.

A pair-mode in the far infrared absorption spectrum of KI:Cl -

A new resonance at 36 cm -1 has been observed in the far infrared absorption spectrum of KI:Cl -. The quadratic concentration dependence of the line strength indicates that the absorption is due to pairs of chlorine ions. A simple molecular model calculation indicates that a large softening of the short range force constants occurs around the defect, in agreement with previous single ion calcualtions.

Many-Body Processes in Nonradiative Energy Transfer between Ions in Crystals

It is shown that many-body interactions can play a dominant role in nonradiative energy transfer processes between ions in crystals. These interactions formally arise from the Coulomb and exchange interactions between the electrons of the donor ion and two or more acceptor ions. In particular, three-body transfer processes arising from the dipole-dipole perturbation Hamiltonian through virtual transitions are considered in some detail. Such processes are manifested by the quadratic concentration dependence of the per-ion nonradiative energy transfer rate observed in concentration quenching and sensitized luminescence experiments. Many-body interactions are important in rare-earth ions because of the narrow widths of the 4fn crystal states and because of the large moments of the virtual transitions involving the opposite parity 4fn−1 5d states.

Infrared Absorption by Impurity-Pair Resonant Modes in NaCl: F

New resonant-mode infrared absorption lines have been observed in NaCl with high concentrations of fluorine impurities. The quadratic concentration dependence of the strength of these lines indicates that they are due to pairs of fluorine impurities. At the resonant frequencies, the motion of some host ions appears to be as important as the motion of the impurities themselves.