La percolation

Clerc, Jeannine; Giraud, G; Roussenq, J.; Blanc, Robert; Carton, Jessy; Guyon, E.; Ottavi, H.; Stauffer, D.

doi:10.1051/anphys/198308080003

Cited by 35 publications

(36 citation statements)

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“…1-namely, a sharp increase at the threshold hc followed by saturation at increased hydrationis observed for all experimental conditions. This behavior is typical of percolation phenomena, where, at a critical concentration of carriers, the appearance of long-range connectivity between sites accounts for the onset of a process (3,7).…”

Section: Discussionmentioning

confidence: 86%

Proton percolation on hydrated lysozyme powders

Careri¹,

Giansanti²,

Rupley

1986

Proc. Natl. Acad. Sci. U.S.A.

115

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The framework of percolation theory is used to analyze the hydration dependence of the capacitance measured for protein samples of pH 3-10, at frequencies from 10 kHz to 4 MHz. For all samples there is a critical value of the hydration at which the capacitance sharply increases with increase in hydration level. The threshold hc = 0.15 g of water per g of protein is independent of pH below pH 9 and shows no solvent deuterium isotope effect. The fractional coverage of the surface at h, is in close agreement with the prediction of theory for surface percolation. We view the protonic conduction process described 'here for low hydration and previously for high hydration as percolative proton transfer along threads of hydrogen-bonded water molecules. A principal element of the percolation picture, which explains the invariance of hc to change in pH and solvent, is the sudden appearance of long-range connectivity and infinite clusters at the threshold ho. The relationship of the protonic conduction threshold to other features of protein hydration is described. The importance of percolative processes for enzyme catalysis and membrane transport is discussed.In a previous paper we have described the protonic conductivity induced by hydration below monolayer coverage for single molecules of the protein lysozyme (1). Under these conditions, the hydration water is severely disordered (2). Thus, it seems appropriate to consider the protonic conductivity in the framework of the percolation model (3, 4). This model has been shown applicable to a broad range of chemical and physical phenomena where spatially random processes and topological disorder are of vital importance, such as polymer gelation and the electrical conductivity of a network of conducting and nonconducting elements. One of the most appealing aspects ofthe percolation model is the presence ofa percolation transition, where a long-range connectivity among the elements of the system suddenly appears. In this paper we focus on a transition of this kind, a sharp change in dielectric properties in the low hydration region for the protein lysozyme. This analysis extends that reported for the high hydration region (1).MATERIALS AND METHODS A previous paper (1) described the preparation of protein samples of pH 3-10 and the measurement of their dielectric properties at frequencies from 10 kHz to 10 MHz and for hydration levels from wet powder (>0.35 h) to the low hydration limit (h.) where the evaporation rate is zero under these experimental conditions. The data were analyzed previously for the high hydration region, h > 0.2 (1). In this paper we analyze a similar body of data for the low hydration region.For display and analysis, the dielectric properties are presented as a function of hydration level, h. During the measurements the hydration of each sample was varied from the starting conditions, a wet powder obtained by isopiestic equilibration against pure water, to the final limiting low hydration, h.. The dielectric data were collected continuously. Hydra...

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Section: Discussionmentioning

confidence: 86%

Proton percolation on hydrated lysozyme powders

Careri¹,

Giansanti²,

Rupley

1986

Proc. Natl. Acad. Sci. U.S.A.

115

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“…5 Due to the shear, the detailed geometry of the suspension is permanently changing and fluctuations of the torque around a mean value occur. Figure 3 a shows the variations of the relative mean square deviation a, of the viscosity obtained from two different sizes of the viscometer, plotted against q~s.…”

Section: Fluctuationsmentioning

confidence: 99%

“…[4] or [5]). In the percolation problem, p is the ratio of the number of active sites to the total number of sites, its analogue here in suspensions is the ratio of the number of spheres in a given system to the maximum number of spheres i.e.…”

Section: Comparison With Percolationmentioning

confidence: 99%

Cluster statistics in a bidimensional suspension: Comparison with percolation

Blanc¹,

Belzons²,

Camoin³

et al. 1983

Rheol Acta

Self Cite

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We study the cluster statistics and the viscosity of a two-dimensional suspension of passive macroscopic spheres undergoing shear, The second moment of the finite cluster statistics exhibits a maximum for a 2-D concentration q5 s near 0.67 without measurable anomaly in the viscosity. The results of the cluster statistics are compared to those obtained in percolation.Key words: Suspension, cluster statistics, viscosity, percolation lntroductionIt was suggested by de Gennes [1] that one could try to explain the plug-flow phenomenon in suspensions [2] on the basis of an analogy with percolation. In that analysis, the dynamical clusters induced by hydrodynamical interactions between suspended particles are similar to percolation clusters. Their mean size grows with particle concentration, and one can expect a critical concentration above which an "infinite" cluster appears, a cluster which contains most of the total (finite) number of particles. So, we were led to study macroscopic passive particle suspensions with regard to their rheology (viscosity, velocity profile) as well as to their statistical cluster properties (mean size, number, length). In order to simplify the observation of clusters, we carried out the study on bidimensional suspensions; preliminary results were published elsewhere [3]. Statistical parameters of the suspensionThe suspension is a two-dimensional collection of passive spheres (diameter d = 5 mm) in a layer (thickness t = 5 mm) of a liquid, the density of which is adjusted to that of the spheres. The suspension was studied in laminar steady flow with a low Reynolds number ( R e~0 . 1 ) in a Couette viscometer (inner diameter R1 = 1.7 cm or 3.35 cm, outer diameter R2 = 9.25 cm õr 18 cm). The inner cylinder is fixed by a 911 torsion wire, the outer one rotating with angular speed f~. The 2D-concentration P s of a suspension containing N spheres is defined by d 2 Ps = N 4(R2 _ R{ )and related to the volume concentration qsv by 3 Bs = ~-~v. For 45s between 0 and 0.80, we study the relative viscosity r/r (ratio of the effective viscosity of the suspension to that of the pure liquid) and the statistical grouping of spheres, by counting from photographs of the suspension undergoing the Couette flow the number ns of clusters of s spheres in contact*), the S 2 ---~~s n « -(mass averaged) mean size. s *) Two spheres are said "in contact" when they seem adjoining within the photographic resolution that is in our case about a tenth of a sphere diameter.

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“…For discrete-particle systems such as silica, where there is strong interparticle repulsion, the porosity E obtained is relatively low (typically about 0.36). Clerq et al, 1983;Brown and Ball, 1985;van Voorst Vader and Groenweg, 1989). For gels produced by cluster aggregation, shrinkage of the network is constrained, as will be discussed, and residual gel porosities are much higher, i.e.…”

Section: 1 Gelation and Percolation Processesmentioning

confidence: 99%

Sol–gel processing

Ramsay¹

1994

Controlled Particle, Droplet and Bubble Formation

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La percolation

Cited by 35 publications

References 0 publications

Proton percolation on hydrated lysozyme powders

Proton percolation on hydrated lysozyme powders

Cluster statistics in a bidimensional suspension: Comparison with percolation

Sol–gel processing

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