Effects Of Concentration Fluctuations Research Articles

Концентрационные флуктуации в киральных ферромагнетиках Fe-=SUB=-x-=/SUB=-Mn-=SUB=-1-x-=/SUB=-Si во внешнем магнитном поле

In the framework of the theory of spin fluctuations, magnetic h-T diagrams of chiral helicoidal ferromagnets FexMn1-xSi with the Dzyaloshinskii-Moriya interaction are investigated. A specific analysis of the equations of magnetic state is carried out on the basis of a model of the electronic structure following from the LDA + U + SO DOS calculations in the virtual crystal approximation. It was shown that in the concentration range x <0.12, the Fermi level remains within the local minimum DOS. In this case, a helicoidal long-range order is realized, which undergoes a first-order transition induced by spin fluctuations, accompanied by the formation of intermediate skyrmion phases induced by an external magnetic field. With increasing x arising due to the chaotic distribution of the magnetic moments of manganese and iron over the nodes, the effects of concentration fluctuations suppress zero-point quantum spin fluctuations. In this case, the condition for the appearance of skyrmion phases is violated for x> 0.12, and the region of the helicoidal ferromagnetic order is preserved up to concentrations xc = 0.20. In the interval 0.10 <x <0.20, the transition induced by fluctuations to the paramagnetic state is accompanied by the disappearance of local magnetization and the formation of a paramagnetic state with dynamic spin correlations.

Calcium Concentration Fluctuations and Subspace Volume Influence Calcium-Regulated Calcium Channel Gating and Subspace Dynamics

Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs) and mass-action kinetics. However, spatially restricted “domains” associated with calcium influx are small enough that local signaling may involve 1-100 calcium ions. Therefore, the question arises: is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of subspace calcium concentration and channel open probability (a result that accounts for the small subspace volume and concentration fluctuations) with the corresponding deterministic model (an approximation that assumes large system size and ignores concentration fluctuations). When subspace calcium did not regulate calcium influx, the deterministic and stochastic descriptions agreed. However, when calcium-binding altered channel activity in the model, the continuous deterministic description often deviated significantly from the discrete stochastic model, unless the subspace volume is unrealistically large and/or the kinetics of the calcium binding are sufficiently fast, demonstrating that the calcium concentration fluctuations and subspace volume influence channel gating and subspace dynamics. This principle was also demonstrated using a physiologically realistic model of calmodulin regulation of L-type calcium channels introduced by Yue and coworkers [Tadross, Dick, Yue. Cell 133: 1228-40, 2008]. Additional work will consider the influence of slow and rapid buffers present in the subspace and whether and under what conditions these buffers mitigate the effects of concentration fluctuations on channel gating and subspace dynamics.

Looking for chemical reaction networks exhibiting a drift along a manifold of marginally stable states

I recently reported some examples of mass-action equations that have a continuous manifold of marginally stable stationary states [Brogioli, D., 2010. Marginally stable chemical systems as precursors of life. Phys. Rev. Lett. 105, 058102; Brogioli, D., 2011. Marginal stability in chemical systems and its relevance in the origin of life. Phys. Rev. E 84, 031931]. The corresponding chemical reaction networks show nonclassical effects, i.e. a violation of the mass-action equations, under the effect of the concentration fluctuations: the chemical system drifts along the marginally stable states. I proposed that this effect is potentially involved in abiogenesis. In the present paper, I analyze the mathematical properties of mass-action equations of marginally stable chemical reaction networks. The marginal stability implies that the mass-action equations obey some conservation law; I show that the mathematical properties of the conserved quantity characterize the motion along the marginally stable stationary state manifold, i.e. they allow to predict if the fluctuations give rise to a random walk or a drift under the effect of concentration fluctuations. Moreover, I show that the presence of the drift along the manifold of marginally stable stationary-states is a critical property, i.e. at least one of the reaction constants must be fine tuned in order to obtain the drift.

The Volumetric Particle Approach for Concentration Fluctuations and Chemical Reactions in Lagrangian Particle and Particle-grid Models

A new approach is proposed to predict concentration fluctuations in the framework of one-particle Lagrangian stochastic models. The approach is innovative since it allows the computation of concentration fluctuations in dispersing plumes using a Lagrangian one-particle model with micromixing but with no need for the simulating of background particles. The extension of the model for the treatment of chemically reactive plumes is also accomplished and allows the computation of plume-related chemical reactions in a Lagrangian one-particle framework separately from the background chemical reactions, accounting for the effect of concentration fluctuations on chemical reactions in a general, albeit approximate, manner. These characteristics should make the proposed approach an ideal tool for plume-in-grid calculations in chemistry transport models. The results are compared to the wind-tunnel experiments of Fackrell and Robins (J Fluid Mech, 117:1–26, 1982) for plume dispersion in a neutral boundary layer and to the measurements of Legg et al. (Boundary-Layer Meteorol, 35:277–302, 1986) for line source dispersion in and above a model canopy. Preliminary reacting plume simulations are also shown comparing the model with the experimental results of Brown and Bilger (J Fluid Mech, 312:373–407, 1996; Atmos Environ, 32:611–628, 1998) to demonstrate the feasibility of computing chemical reactions in the proposed framework.

Accounting for the effect of concentration fluctuations on toxic load for gaseous releases of carbon dioxide

In Great Britain, advice on land-use planning decisions in the vicinity of major hazard sites and pipelines is provided to Local Planning Authorities by the Health and Safety Executive (HSE), based on quantified risk assessments of the risks to the public in the event of an accidental release. For potential exposures to toxic substances, the hazard and risk is estimated by HSE on the basis of a “toxic load”. For carbon dioxide (CO 2), this is calculated from the time-integral of the gas concentration to the power eight. As a consequence of this highly non-linear dependence of the toxic load on the concentration, turbulent concentration fluctuations that occur naturally in jets or plumes of CO 2 may have a significant effect on the calculated hazard ranges. Most dispersion models used for QRA only provide estimates of the time- or ensemble-averaged concentrations. If only mean concentrations are used to calculate the toxic load, and the effects of concentration fluctuations are ignored, there is a danger that toxic loads and hence hazard ranges will be significantly under-estimated. This paper explores a simple and pragmatic modification to the calculation procedure for CO 2 toxic load calculations. It involves the assumption that the concentration fluctuates by a factor of two with a prescribed square-wave variation over time. To assess the validity of this methodology, two simple characteristic flows are analysed: the free jet and the dense plume (or gravity current). In the former case, an empirical model is used to show that the factor-of-two approach provides conservative estimates of the hazard range. In the latter case, a survey of the literature indicates that there is at present insufficient information to come to any definite conclusions. Recommendations are provided for future work to investigate the concentration fluctuation behaviour in dense CO 2 plumes. This includes further analysis of existing dense gas dispersion data, measurements of concentration fluctuations in ongoing large-scale CO 2 release experiments, and numerical simulations.

Dynamics of Miscible Polymer Blends: Role of Concentration Fluctuations on Characteristic Segmental Relaxation Times

We show that the time corresponding to the peak of the segmental relaxation time distribution and the mean time of that distribution for the components of several miscible polymer blends are strongly affected by both chain connectivity and concentration fluctuations. These two measures of characteristic segmental relaxation times differ from the time corresponding to the mean composition experienced by a segment, with these differences being emphasized for blends with large glass transition contrast, lower temperatures, or increased concentration fluctuations on the nanometer scale. These findings are in contrast to self-concentration models, which generally assume that concentration fluctuations affect neither the mean nor the peak segmental relaxation times and are only relevant for determining the distribution of relaxation times. Going further, we show through the inclusion of self-concentration and concentration fluctuation effects that segmental dynamics are only affected by a local environment of s...

Effect of blend composition on diffusivity and solubility of small molecules in polystyrene/poly(vinyl methyl ether) blends

AbstractThe capillary column inverse gas chromatography technique was used to determine diffusivity and solubility data for several solvents in polymer blends composed of polystyrene and poly(vinyl methyl ether) (PVME). Diffusivity behaved as expected, increasing as the concentration of PVME increased in the blend. Knowing only the free‐volume parameters for the pure polymers, the free‐volume theory was successfully applied to predict the dependence of the diffusion coefficients on the blend composition. Transport in blends above the glass transition temperature is controlled by free volume, and the effect of concentration fluctuations is minimal at the temperatures studied. Experimental data show an increase in the partition coefficient of some solvents in the blends with respect to the pure polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2071–2082, 2007

Probing self‐associated structures of the solute molecule, acrylonitrile, the solvent molecule 2Cl‐phenol and their binary complexes via concentration‐dependent Raman study and DFT calculation

AbstractRaman study of CN‐stretching mode of acrylonitrile and ring‐breathing mode of 2Cl‐phenol was made in the binary mixture of (acrylonitrile + 2Cl‐phenol) at different molar ratios of the two components. Raman spectra were recorded in the different spectral regions, 990–1070 cm−1 and 2170–2300 cm−1. Ring‐breathing mode of 2Cl‐phenol exhibited two components, which were attributed to the neat and self‐associated dimer of 2Cl‐phenol molecules. The self‐associated structure of the dimer was obtained by geometry optimization. Other structures, which were calculated, include self‐associated structure of acrylonitrile and the hydrogen‐bonded complex of (acrylonitrile + 2Cl‐phenol). All the geometry optimizations were made using density functional theory (DFT) and B3LYP functional employing the 6–31 + G(d,p) basis set. The variations of the linewidth and the peak position with concentration are explained on the basis of a model, which includes both the effect of concentration fluctuation in a microscopic volume and the influence of concentration‐dependent microviscosity based on a model proposed recently by our group. Copyright © 2006 John Wiley & Sons, Ltd.

Concentration fluctuation effects on the phase behavior of compressible diblock copolymers.

A Hartree analysis has been performed for compressible diblock copolymers of incompatible pairs to investigate the concentration fluctuation effects on their microphase separation behavior. The free energy in the Hartree analysis is obtained from the self-consistent correction to its mean-field cousin, which was recently formulated for such copolymer systems. The mean-field phase diagram is shown to be significantly affected by the fluctuation effects as the copolymer chain size N is lowered. An effective interaction chi(cRPA), which carries not only the change in contact interactions but also the compressibility difference between block components, plays a key role in understanding of the phase behavior and the pressure responses of various thermodynamic transitions for the copolymers with finite sizes. In particular, a symmetric copolymer at disorder-to-lamella transition is found to satisfy Nchi(cRPA)(q*)=10.495+41.022N(-1/3) when evaluated at a characteristic wave number q* for ordered microphases.

On the Critical Behavior of Phase Changes of a Forward-Scattered Light in a Nonpolar Binary Liquid Mixture

The effect of concentration fluctuations on the changes of azimuth and ellipticity are analytically obtained in a binary chiral liquid mixture, when the incident light is completely linearly polarized above (or below) thehorizontal at 45°. The important results are as follows; (1) When the binary liquid is in the critical region far from the critical point, the ellipticity change is proportional to isothermal compressibility factor and the fifth order of frequency. As the system approaches very close to the critical point, the change is proportional to the third order of frequency and shows the logarithmic divergence. (2) In the case that the system is in the critical region far from the critical point, the azimuth change is solely due to the molecular contribution. As the system approaches to the critical point, the effect of fluctuations becomes important. If it is in the extreme close to the critical point, the term due to the concentration fluctuations is comparable to or larger than the molecular contribution.

Correction of dopant concentration fluctuation effects in silicon drift detectors

Dopant fluctuations in silicon wafers are responsible for systematic errors in the determination of the particle crossing point in silicon drift detectors. In this paper, we report on the first large-scale measurement of this effect by means of a particle beam. A significant improvement of the anodic resolution has been obtained by correcting for these systematic deviations.

Effects of concentration fluctuations on statistical evaluations of centreline concentration estimates by atmospheric dispersion models

An investigation is undertaken of a concept expressed in a draft Guide under construction, which recommends that evaluation data having similar meteorological and physical conditions be grouped together, the modelling results and observations be separately averaged and that the evaluation shall consist of a comparison of the respective averages. It is determined that, even though large uncertainties are associated with this process, the summary conclusions reached regarding relative model performance in estimating the average centreline concentration values are preserved. It is recommended that the Guide be finalised for routine use and the concepts further tested using other testable features in the concentration pattern.

Concentration Fluctuations in Surfactant Cubic Phases: Theory, Rheology, and Light Scattering

Ternary surfactant cubic phases exhibit a sharp melting transition. We investigate the effect of concentration fluctuations in this system which are a possible driving mechanism for the phase trans...

Self-Diffusion of a Symmetric PEP−PDMS Diblock Copolymer above and below the Disorder-to-Order Transition

The self-diffusion of a lamellae-forming nonentangled PEP−PDMS diblock copolymer was investigated with pulsed field gradient (PFG) NMR in dependence on temperature. The order-to-disorder transition (ODT), which occurs at T = 64 °C, was traversed. Coming from the disordered state, a sudden increase of the width of the distribution of self-diffusivities was observed (an increase of the nonexponentiality of the echo attenuation) when crossing the ODT. This is caused by the onset of anisotropic diffusion along the lamellae whose orientations are isotropically distributed. The weakness of the nonexponentiality leads to the conclusion that the range of local order in the grains is much smaller than the grain size (determined by small-angle light scattering). In addition, the temperature dependence of the self-diffusivity shows a substantial slowing down when approaching the ODT from the disordered state which is attributed to the effect of concentration fluctuations. The self-diffusion measurements are compared with earlier measurements of the zero shear viscosity and dynamic light scattering on this polymer and with Monte Carlo simulations from the literature. The results from all of these methods are consistent.

Liquid State Theory of Thermally Driven Segregation of Conformationally Asymmetric Diblock Copolymer Melts

Thermally induced packing correlations and apparent microphase spinodal boundaries are studied for conformationally asymmetric diblock copolymer melts using the “polymer reference interaction site model” (PRISM) theory. Microphase instabilities are deduced from predictions of the collective scattering intensities and are correlated with the degree of conformational mismatch. For diblocks interacting through attractive van der Waals forces, but where the Flory mean field χ-parameter is identically zero, the predictions reveal rich dependencies of the apparent microphase spinodal boundaries on the degree of structural asymmetry between blocks which are consistent with recent polyolefin diblock melt experiments. This demonstrates the importance of the coupling between local packing correlations and attractive interactions, and the fundamental inseparability of enthalpic and entropic contributions to the effective χ-parameter governing miscibility. Length-scale-dependent “effective compositions” above and near an apparent microphase spinodal temperature are also calculated. Large enrichments of the local composition are predicted in the highly fluctuating, low temperature, regime which depend on copolymer composition, density, and nonuniversal chain structural features. Marked enhancements of this clustering relative to melt behavior are predicted for concentrated diblock solutions. The present numerical calculations are also compared to previous analytical Gaussian thread model PRISM predictions, and general qualitative consistency is found. Numerical calculations for blends of the same polymers are also performed and demonstrate a very large reduction of concentration fluctuation effects and physical clustering for this macrophase separation case.

Local and Microdomain Concentration Fluctuation Effects in Block Copolymer Solutions

On the basis of the simplest Gaussian thread model for structurally symmetric copolymers, the polymer reference interaction site model (PRISM) theory is applied to study the equilibrium properties of diblock copolymer solutions under neutral solvent conditions. Analytic predictions are obtained for the influence of local and microdomain scale concentration fluctuations on the relationship between temperature, degree of polymerization, and polymer concentration at the order−disorder transition (ODT). In the semidilute regime, PRISM predictions agree with blob scaling and fluctuation-corrected field theoretic analyses. However, in the concentrated solution and melt regime strong disagreements occur, and the naive mean field dilution approximation is found to fail. Nevertheless, apparent scaling laws emerge under concentrated conditions with effective exponents which depend on solvent quality, melt screening length, and other nonuniversal structural features. The primary origin of the dilution approximation failure is interchain nonrandom mixing, which is concentration dependent and driven by local packing effects. Microdomain scale fluctuations yield corrections of secondary importance which vanish in the long chain limit. For concentrated solutions and good solvents, the predicted apparent exponent is fortuitously in close agreement with semidilute blob scaling results, and also agrees with recent measurements on polystyrene−polyisoprene diblocks by Lodge and co-workers. Smaller effective exponents are found under ϑ solvent conditions. Systematic PRISM model calculations for properties strongly affected by microdomain scale fluctuations, such as small angle scattering intensity and local physical clustering, are also presented. Significant physical clustering is found in solutions of compositionally asymmetric diblocks even very far from the ODT.

On the scattering phenomena for various kinds of polarized light in a nonpolar binary liquid mixture

The explicit result for the Mueller matrix for the sum of single and double scatterings is obtained in a nonpolar binary liquid mixture composed of a chiral solute and an achiral solvent are obtained with the aid of the Ornstein–Zernike form for the correlation function of concentration fluctuations. The explicit result of the matrix shows that the law of reciprocity does not hold in the mixture. The scattering phenomena for six kinds of completely polarized light in a nonpolar binary liquid mixture are different from those in a pure chiral fluid because of the failure of the law and the large effect of concentration fluctuations. The scattering phenomena are in detail discussed in the region far from and near the critical point.

Concentration fluctuation induced dynamic heterogeneities in polymer blends

The presence of two distinctly different local segmental mobilities found in the case of several phase mixed polymer blends by two-dimensional 2H-NMR, dielectric spectroscopy and depolarized dynamic light scattering is rationalized through a simple concentration fluctuation model. Our primary hypothesis is that, although the probability of the occurrence of concentration fluctuations is symmetric about the mean value in a given volume, the ‘‘cooperative volume’’ over which a fluctuation must occur for it to be detected by a dynamic probe is not a constant, but rather depends on the composition of the cooperative volume. Consequently, we suggest that the cooperative volume associated with a concentration fluctuation be determined by the local composition in a self-consistent manner. In the case of systems with weak interactions and large Tg contrast, these ideas are shown to create a bimodal probability density function for dynamic concentration fluctuations, which has a local maximum corresponding to small cooperative volumes rich in the more mobile component, in addition to the bulk composition itself. We also predict the broadening of both the segmental relaxation time spectrum and the single calorimetric glass transition of the blends with increasing concentration of the slow component. Comparisons of the predictions are made for two experimental systems with different thermodynamic and kinetic effects to illustrate the present approach. Further, we predict the effects of concentration fluctuations in the case of three other blends whose segmental dynamics have not been examined experimentally to date. We predict that the dynamics of the two components approximately follow time–temperature superposition either in the case of strongly interacting blends or for systems that have closely matched Tg values and Williams–Landel–Ferry (WLF) coefficients.

Theory of the Order-Disorder Phase Transition in Cross-Linked Polymer Blends

We consider the system of a network formed by crosslinking a polymer blend. In such a system there is a competition between monomer-monomer interactions and elastic energy which may result in a microphase separation. We first treat the problem by adapting a model due to de Gennes to include the effect of concentration fluctuations 'frozen in' by the crosslinking process. This yields an expression for the scattering structure factor which gives finite scattering in the limit of low wavenumber (this has been observed in experiments on crosslinked blends). The expression also shows that the frozen-in fluctuations 'seed' the phase transition, so that the structure factor diverges as (χs - χ) -2 on approaching the spinodal. We then reconsider the problem at a molecular level. We model the network as a blend of interacting chains anchored at either end to fixed points in space. The system is treated using a variant of the Random Phase Approximation (RPA) which deals with the quenched chain-end variables but which does not resort to replica methods. The resulting structure factor has an identical form to that obtained by modifying the de Gennes model, but allows us to investigate the effect of varying composition, crosslink density, and applied strain. We find that the characteristic lengthscale for the early stages of microphase separation is controlled by the least concentrated component or the one with the shortest chain length between crosslinks, depending on which parameter shows the strongest difference between the two chain types. We also find that strain produces a phase separation with wavevectors in the direction(s) of least stretching (or greatest compression).

Concentration fluctuation effects on chain orientation dynamics of polymer blends in the critical region

Dielectric relaxation spectroscopy has been employed to investigate the normal mode relaxation of polyisoprene I chains in binary polystyrene/polyisoprene (S/I) blends over a broad temperature range in the one and two phase region. The normal mode relaxation time in the homogeneous phase near the transition is faster than expected on the basis of the average bulk composition and the distribution of relaxation times becomes bimodal in the transition region. A concentration correlation model is proposed to account for the new experimental findings in the framework of Rouse chain dynamics and mean-field static behavior. The computed normal mode relaxation times compare well with the experiment for an effective composition averaged over a microscopic scale O(nm).