Classical Scaling Theory Research Articles

Why Single-Chain Nanoparticles from Weak Polyelectrolytes Can Be Synthesized at Large Scale in Concentrated Solution?

Here, the unresolved question of why single-chain nanoparticles (SCNPs) prepared from a weak polyelectrolyte (PE) precursor can be synthesized on a large is addresses, unlike SCNPs obtained from an equivalent neutral (nonamphiphilic) polymer precursor. The combination of the standard elastic single-chain nanoparticles (ESN) model -developed for neutral chains- with the classical scaling theory of PE solutions provides the key. Essentially, the long-range repulsion between electrostatic blobs in a weak PE precursor restricts the cross-linking process during SCNPs formation to the interior of each blob. Consequently, the maximum concentration at which PE-SCNPs can be prepared without interchain cross-linking is not determined by the full size of the PE precursor but, instead, by the smaller size of its electrostatic blobs. Therefore, PE-SCNPs can be synthesized up to a critical concentration where electrostatic blobs from different chains touch each other. This concentration can be 30 times higher than that for non-PE polymer precursors. Upon progressive dilution, the size of PE-SCNPs synthesized in concentrated solution increases until it reaches the bigger size of PE-SCNPs prepared under highly diluted conditions. PE-SCNPs do not adopt a globular conformation either in concentrated or in diluted solution. It shows that the main model predictions agree with experimental results.

The Effect of Particle Necks on the Mechanical Properties of Aerogels.

Mechanical properties of open-porous materials are often described by constructing a cellular network with beams of constant cross sections as the struts of the cells. Such models have been applied to describe, for example, thermal and mechanical properties of aerogels. However, in many aerogels, the pore walls or the skeletal network is better described as a pearl-necklace, in which the particles making up the network appear as a string of pearls. In this paper, we investigate the effect of neck sizes on the mechanical properties of such pore walls. We present an analytical and a numerical solution by modeling these walls as corrugated beams and study the subsequent deviations from the classical scaling theory. Additionally, a full numerical model of such pearl-necklace-like walls with concave necks of varying sizes are simulated. The results of the numerical model are shown to be in good agreement with those resulting from the computational one.

Wall-attached clusters for the logarithmic velocity law in turbulent pipe flow

The logarithmic law of the mean velocity is considered a fundamental feature of wall-bounded turbulent flows. The logarithmic velocity law is used widely to model the near-wall turbulence and to predict skin friction. Although classical scaling theory has been used to verify that the velocity profile in the overlap region follows the logarithmic behavior asymptotically, and thus recent experiments have attempted to assess the logarithmic law in large-scale facilities, there is a lack of understanding of the structural basis for the logarithmic law. Here, we show the logarithmic law by extracting the wall-attached structures of the streamwise velocity fluctuations through direct numerical simulation of turbulent pipe flow. The wall-attached structures exhibit self-similar behavior according to their height and have an inverse-scale population density, reminiscent of Townsend’s attached-eddy hypothesis. The wall-normal distributions of the streamwise velocity within the identified structures are conditionally averaged with respect to their height. The velocity profile is reconstructed by superimposing the velocity distributions of the objects that follow the inverse-scale population density. The indicator function of the resulting velocity profile shows a complete plateau for the high-speed structures due to their higher local Reynolds number. These findings provide strong evidence that the identified coherent structures are directly related to the logarithmic velocity law and serve as the structural basis for the inertial layer.

Universal Equation of State for Flexible Polymers Beyond the Semidilute Regime.

We reconsider the isothermal equation of state (EOS) for linear homopolymers in good solvents, p=p(c,T), which relates the osmotic pressure p of polymers with the bulk concentration c and the temperature T. The classical scaling theory predicts the EOS in dilute and semidilute regimes. We suggest a generalized EOS that extends the universal behavior of polymer solutions up to the highly concentrated state and confirm it by molecular dynamics simulations and available experimental data. Our conjecture implies that properties of polymer chains dominate the EOS in the presence of many-body interactions. Our theoretical approach is based on a viral expansion in terms of concentration blobs leading to a superposition of two power laws in the regime of concentrated solutions.

Quantum-Based Simulation Analysis of Scaling in Ultrathin Body Device Structures

We present self-consistent solutions of ultrathin body device structures to understand the influence of quantum-mechanical confinement on the predictions of classical scaling theory. We show that two-dimensional (2-D) electrostatics considerations play a more dominant role than quantum-mechanical effects in the subthreshold behavior of ultrathin fully depleted silicon-on-insulator structures. We also show how modifications to the doping profile can be used to alleviate 2-D short-channel effects.

Classical scaling theory of quantum resonances.

The quantum resonances occurring with delta-kicked particles are studied with the help of a fictitious classical limit, establishing a direct correspondence between the nearly resonant quantum motion and the classical resonances of a related system. A scaling law which characterizes the structure of the resonant peaks is derived and numerically demonstrated.

Stable Boundary-Layer Modelling: Established Approaches and Beyond

In the light of Large Eddy Simulation and other recent work, this paper discusses methods of stable boundary-layer modelling that are established in numerical weather prediction and potentially relevant to other applications, e.g., to dispersion. It is argued that classical scaling theory is best expressed in terms of the local Richardson numbers. The theory can then be extended to treat cases where classical assumptions break down. There are indications that Richardson number models with suitable boundary conditions can mimic, at least qualitatively, some features of the ‘very stable boundary layer’. Despite advances in research modelling, detailed observational validation remains essential.

Theory of metal-semiconductor transitions in random impurity bands.

In Si:P a metal-semiconductor transition occurs homogeneously with randomly distributed impurities. Neither classical percolation theory nor classical scaling theory describes this transition, but it is explained by set theory and the quantum theory of measurement. These concepts explain all aspects of the conductivity transition as well as the absence of accompanying transitions in the specific heat and the magnetic susceptibility.

Sum rules in inelastic gas-surface scattering

An explanation for sum-rules observed in gas-surface scattering is offered via a classical scaling theory for inelastic collisions.

Classical trajectory analysis in atom—triatom collisions: Continuous quantization and scaling behaviour

A method of analysing classical trajectory data, based on recently derived scaling principles, is applied to a model atom-triatom collinear collision system. Apart from the utility of the scaling idea in extending trajectory computations, the analysis of the scaling coefficients in terms of transition probabilities increases the scope of the classical scaling theory as a means of obtaining (at the very least) qualitative quantum-mechanical information from classical trajectories. As an useful adjunct, the method of continuous quantization is applied to generate approximate transition probabilities. These results are semiquantitative; thus a combination of classical scaling and continuous quantization affords a powerful means of modeling complex collision cases with a minimum of computational effort.

Collision dynamics of non-integrable systems: Validity of classical scaling

Abstract The classical collision dynamics of a model atom—molecule non-integrable collision system is studied, and the energy transfer (ET) moment is examined as a function of the initial semiclassical level of the molecule. A recently derived classical scaling theory is shown to be valid in the case when the molecular motion remains regular throughout the collision, and the ET variation is then characterized by a polynomial dependence on the initial (semiclassical) quantum numbers. When chaotic motions participate, the ET no longer follows the scaling law. The utility of the scaling theory in providing the proper interpolation form for extending classical trajectory data in non-integrable collision systems is discussed.

On the surface temperature dependence of non-equilibrium translational energy accommodation coefficients

The formalism of classical scaling theory is applied to the process of translational energy accommodation in the gas-solid surface system. The scaling provides a systematic description of energy transfer as a function of the initial occupation numbers of the solid. This yields a relatively simple equation for the surface temperature variation of the non-equilibrium EAC, α( T g, T s), at fixed gas temperature. Various limits, including high temperatures and near-equilibrium, and special models of the solid surface are investigated. The quantitative accuracy of a simplified scaling formula appropriate for the case of single phonon processes is demonstrated by comparison with the results of Lennard-Jones-Devonshire-Strachan theory.

Application of classical scaling theory to vibrational inelasticity in atom-Morse oscillator collision systems

Application of classical scaling theory to vibrational inelasticity in atom-Morse oscillator collision systems

Concerning the scaling behavior in the classical mechanics of non-reactive collisions: an analytic investigation

The classical mechanical treatment of non-reactive scattering processes is cast into a convenient formalism for describing the changes in the internal linear momentum affected by a collision. The dependence of these changes on the initial internal linear momentum and coordinate is shown to be weak. Combining this result with the classical virial theorem leads to a classical scaling theory for internal energy changes. In its simplest form, this theory explicitly exhibits the dependence of the internal energy transfer on four factors: (1) the initial internal energy; (2) the initial internal coordinate; (3) the bound state potential; and (4) the average momentum transfer. At a given initial kinetic energy, these four quantities suffice to characterize the systematic variation of the internal energy transfer with initial internal energy and coordinate. The combination of the classical scaling theory with the quasiclassical histogram quantization method is determination of all other transition probabilities P n → Δ, Δ = 1, 2, …, n. This includes classically forbidden processes for which the scaling theory yields an exact value of zero