Scaling and the Smoluchowski Equations

The Smoluchowski equations, which describe coalescence growth, take into account combination reactions between a j-mer and a k-mer to form a (j+k)-mer, but not breakup of larger clusters to smaller ones. All combination reactions are assumed to be second order, with rate constants K jk. The K jk are said to scale if K λj,γk =λ μγ μK jk for j ≤ k. It can then be shown that, for large k, the number density or population of k-mers is given by Ak ae -bk, where A is a normalization constant (a function of a, b, and time), a=-(μ+ ν), and b μ+ν-1 depends linearly on time. We prove this in a simple, transparent manner. We also discuss the origin of odd-even population oscillations for small k. A common scaling arises from the ballistic model, which assumes that the velocity of a k-mer is proportional to 1/ √m k (Maxwell distribution), i.e., thermal equilibrium. This does not hold for the nascent distribution of clusters produced from monomers by reactive collisions. By direct calculation, invoking conservation of momentum in collisions, we show that, for this distribution, velocities are proportional to m k -0-.577. This leads to μ+ν=0.090, intermediate between the ballistic (0.167) and diffusive (0.000) results. These results are discussed in light of the existence of systems in the experimental literature which apparently correspond to very negative values of μ+ν

Application of Scaling and Kinetic Equations to Helium Cluster Size Distributions: Homogeneous Nucleation of a Nearly Ideal Gas

A previously published model of homogeneous nucleation [Villarica et al., J. Chem. Phys. 98, 4610 (1993)] based on the Smoluchowski [Phys. Z. 17, 557 (1916)] equations is used to simulate the experimentally measured size distributions of 4He clusters produced in free jet expansions. The model includes only binary collisions and does not consider evaporative effects, so that binary reactive collisions are rate limiting for formation of all cluster sizes despite the need for stabilization of nascent clusters. The model represents these data very well, accounting in some cases for nearly four orders of magnitude in variation in abundance over cluster sizes ranging up to nearly 100 atoms. The success of the model may be due to particularities of 4He clusters, i.e., their very low coalescence exothermicity, and to the low temperature of 6.7 K at which the data were collected

Effect of Solvent on Properties of the Liquid Metal Surface

We calculate the difference in the surface potentials between the free surface of a liquid metal and the same metal in an ideally polarizable interface at the point of zero charge. This difference, δXm, is due to the deformation of the electronic cloud of the metal by the solvent molecules. The simple model used for the free (metal-metal vapor) surface yields qualitatively correct work functions for a number of metals (Hg, Cd, In, Zn, Pb, Ga, A1). Two simple ways to model the metal-solvent interaction are proposed and calculations of δXm made for each. One, the dielectric film model, considers only an electrostatic interaction between metal electrons and solvent, while the other, the repulsive core model, considers only the exchange repulsion between metal electrons and the cores of solvent molecules. For Zn, Cd and Hg the dielectric film model, with parameters chosen according to conventional electrochemical wisdom, gives values for δXm which are close to those estimated in the literature. For Ga and A1, the effect of the solvent is much greater because of the larger electron density and smaller ion size. The repulsive core model can give similar results, but there is an arbitrariness in the choice of the barrier strength parameter. Again, Ga is more sensitive to the presence of solvent. The effect of changing certain parameters in both models, and of combining the two, is considered

On Surface Properties of the One-component Plasma

We consider a plasma of point ions in the presence of a non-uniform neutralising background. This background. the source of an external field, may have some of its parameters (density, form of surface profile, etc) modified, as long as the total charge is maintained. By considering such modifications in the context of the density-functional formalism for the ions, we prove sum rules giving the first and second moments of the ion density p(z) in terms of other properties (bulk pressure and temperature derivative of surface tension). The Poisson-Boltzmann functional is considered in detail. We show that the first and second momenr conditions on p(z) are verified. We calculate p ( z ) exactly for this system, and also perform variational calculations: comparison shows the importance of respecting the asymptotic behaviour of p(z). Variational calculations have been performed, using the density-functional formalism in the square-gradient approximation. for systems with plasma parameter r from 1 to 10. For r \u3e 3, important oscillations appear in the profile, as shown by recent Monte Carlo calculations. The profiles calculated variationally also show increasing oscillations. but are not in good agreement with the Monte Carlo results. The surface energies are poor even for r = 1 showing the inadequacy of the square-gradient expansion for this system

Understanding how the platinum anticancer drug carboplatin works: From the bottle to the cell

Carboplatin, a platinum anticancer drug used to treat many types of human cancer, contains a bidentate dicarboxylate chelate leaving ligand, a structural feature that makes it much less chemically reactive than the first-generation platinum anticancer drug cisplatin, which contains two monodentate chloride leaving ligands. In water, carboplatin exists in a monomer–dimer equilibrium with an association constant of K (M−1) ≈ 391, a property that accounts for the long-term stability of its ready-to-use infusion solution. When administered in the clinic, carboplatin is believed to exert its biological effects by interacting with genomic DNA and proteins. The slower substitution kinetics of carboplatin, compared to cisplatin, has prompted investigators to focus on mechanisms by which the compound can be activated in vivo. Carbonate, which is in equilibrium with hydrogen carbonate, carbonic acid, and dissolved carbon dioxide, is ubiquitous in biological systems, and is found in high concentrations in the blood, the interstitial fluid, and the cytosol. Activation of carboplatin by carbonate, CO32− (k1 = 2.04 ± 0.81 × 10−6 in 24 mM carbonate buffer, pH 7.5 at 37 °C), for example, leads to the formation of platinum species that are more cytotoxic than the parent drug. This short review focuses on the reason for the unusual stability of carboplatin in its aqueous ready-to-use infusion solution, describes the reactions of the drug with biologically common nucleophiles and summarizes the activation chemistry that make the drug more reactive toward substances present in the biological system

Understanding How the Platinum Anticancer Drug Carboplatin Works: From the Bottle to the Cell

Carboplatin, a platinum anticancer drug used to treat many types of human cancer, contains a bidentate dicarboxylate chelate leaving ligand, a structural feature that makes it much less chemically reactive than the first-generation platinum anticancer drug cisplatin, which contains two monodentate chloride leaving ligands. In water, carboplatin exists in a monomer-dimer equilibrium with an association constant of K (M -1) ≈ 391, a property that accounts for the long-term stability of its ready-to-use infusion solution. When administered in the clinic, carboplatin is believed to exert its biological effects by interacting with genomic DNA and proteins. The slower substitution kinetics of carboplatin, compared to cisplatin, has prompted investigators to focus on mechanisms by which the compound can be activated in vivo. Carbonate, which is in equilibrium with hydrogen carbonate, carbonic acid, and dissolved carbon dioxide, is ubiquitous in biological systems, and is found in high concentrations in the blood, the interstitial fluid, and the cytosol. Activation of carboplatin by carbonate, CO 3 2- (k 1 = 2.04 ± 0.81 × 10 -6 in 24 mM carbonate buffer, pH 7.5 at 37 °C), for example, leads to the formation of platinum species that are more cytotoxic than the parent drug. This short review focuses on the reason for the unusual stability of carboplatin in its aqueous ready-to-use infusion solution, describes the reactions of the drug with biologically common nucleophiles and summarizes the activation chemistry that make the drug more reactive toward substances present in the biological system

Simultaneous, noninvasive observation of elastic scattering, fluorescence and inelastic scattering as a monitor of blood flow and hematocrit in human fingertip capillary beds

We report simultaneous observation of elastic scattering, fluorescence, and inelastic scattering from in vivo near-infrared probing of human skin. Careful control of the mechanical force needed to obtain reliable registration of in vivo tissue with an appropriate optical system allows reproducible observation of blood flow in capillary beds of human volar side fingertips. The time dependence of the elastically scattered light is highly correlated with that of the combined fluorescence and Raman scattered light. We interpret this in terms of turbidity (the impeding effect of red blood cells on optical propagation to and from the scattering centers) and the changes in the volume percentages of the tissues in the irradiated volume with normal homeostatic processes. By fitting to a model, these measurements may be used to determine volume fractions of plasma and RBCs

Determination of a Wave Function Functional

In this paper we propose the idea of expanding the space of variations in standard variational calculations for the energy by considering the wave function $\psi$ to be a functional of a set of functions $\chi: \psi = \psi[\chi]$, rather than a function. In this manner a greater flexibility to the structure of the wave function is achieved. A constrained search in a subspace over all functions $\chi$ such that the wave function functional $\psi[\chi]$ satisfies a constraint such as normalization or the Fermi-Coulomb hole charge sum rule, or the requirement that it lead to a physical observable such as the density, diamagnetic susceptibility, etc. is then performed. A rigorous upper bound to the energy is subsequently obtained by variational minimization with respect to the parameters in the approximate wave function functional. Hence, the terminology, the constrained-search variational method. The \emph{rigorous} construction of such a constrained-search--variational wave function functional is demonstrated by example of the ground state of the Helium atom.Comment: 10 pages, 2 figures, changes made, references adde

Noninvasive, In-Vivo, Tissue Modulated Near Infrared Spectroscopy of Fingertips: Resonance Raman Spectrum of Human Hemoglobin

Tissue modulation refers to using external stimuli such as mechanical pressure and temperature to produce various spatiotemporal distributions of blood and conceivably other fluids in tissues. Having the capacity to execute tissue modulation1 allows forms of difference spectroscopy to be used to isolate spectroscopic signals from specific components of the tissues noninvasively and in vivo. In the case of human fingertips we can think of the tissues present in the probed volume as being static tissue, plasma and red blood cells (RBCs). Static tissues deform under mechanical pressure based tissue modulation and the only possible fluid motions2 involve plasma and RBCs. Figure 1 shows the difference spectrum produced, negative modulated fluorescence and positive modulated Raman, when simultaneously a small amount of RBCs move into and some plasma is move out of the probed volume. We present spectra for all limiting forms of tissue modulation and show prototypical spectra that include fluorescence Rayleigh/Mie and Raman scattering

Cisplatin Carbonato Complexes. Implications for Uptake, Antitumor Properties, and Toxicity

The reaction of aquated cisplatin with carbonate which is present in culture media and blood is described. The first formed complex is a monochloro monocarbonato species, which upon continued exposure to carbonate slowly forms a biscarbonato complex. The formation of carbonato species under conditions that simulate therapy may have important implications for uptake, antitumor properties, and toxicity of cisplatin