This paper studies the spatio-temporal dynamics of a diffusive plant-sulphide model with toxicity delay. More specifically, the effects of discrete delay and distributed delay on the dynamics are explored, respectively. The deep analysis of eigenvalues indicates that both diffusion and delay can induce Hopf bifurcations. The normal form theory is used to set up an exact formula that determines the properties of Hopf bifurcation in a diffusive plant-sulphide model. A sufficiently small discrete delay does not affect the stability and a sufficiently large discrete delay destabilizes the system. Nonetheless, a sufficiently small or large distributed delay does not affect the stability. Both delays cause instability by inducing Hopf bifurcation rather than Turing bifurcation.

The Strength of Weak Ties is among the most influential social theories of the past 50 years. However, its prediction that weak ties are especially useful for obtaining novel information is sometimes not supported. To understand why, I investigate whether social networks typically satisfy the theory’s assumptions, and whether the theory’s prediction is robust to violations of its assumptions. First, examining a diverse corpus of 56 empirical social networks, I show that empirical social networks (nearly) satisfy some but not all of the theory’s assumptions. Second, using a simulation of information diffusion, I show that the predicted utility of weak ties is not robust to violations of these assumptions. When the assumptions of the theory are violated, as is common in social networks, access to novel information depends on bridging ties, regardless of their strength. Moreover, when they exist, strong bridges (i.e., bridges with high bandwidth) are more useful than weak bridges (i.e., bridges with low bandwidth). I conclude by recommending that research applying this theory should first consider whether its assumptions are satisfied, and that a tie’s strength and bridgeness should be measured and modeled independently.

This article explores the global spread of domestic codifications of academic freedom norms by mapping constitutional provisions over time and space. Drawing on the new Academic Freedom in Constitutions dataset, the study evaluates several hypotheses that may explain the norm’s geographically diverse, yet comparatively limited, adoption in 52 per cent of constitutions today. The descriptive analysis of constitutional adoption patterns suggests that the as yet large pockets of absence are a result of the fact that academic freedom was not included as a fundamental right from the early days of constitution-making, combined with its close link to higher education development, thus locking many countries into a path dependency of early constitutions exclusive of academic freedom norms. The availability of relevant models in nearby countries, together with higher education expansion, are key facilitators of academic freedom adoption at the critical time of a constitutional reform process. Diverse countries in different regions acted as norm entrepreneurs, often motivated to domestically protect academic freedom, thus leading to the emergence of regional and other clusters of academic freedom reference types. A sizeable proportion of insincere adopters further suggests that, in some regions, academic freedom serves as a legitimizing international norm.

The sustainability of grazed rangelands can be improved by adopting innovative management practices that enhance the ecological resilience, productivity, and long-term viability of rangeland ecosystems. This study applied a bivariate Multiple Indicator–Multiple Causation model to examine how landowner characteristics are associated with their perceptions concerning patch-burn grazing (PBG) and mixed-species grazing (MSG). Data were collected through a mail survey of landowners in the Southern Great Plains who own at least 100 acres. The significant and positive correlation between PBG and MSG suggests that their relative preference tends to change together, potentially allowing them to complement when implemented together.

The diffusion of water in the title intercalate has been measured by quasielastic neutron scattering. The diffusion coefficient (6.1 × 10−7 cm2 s−1 at 23.5°C) is one order less than that found previously for a sodium-exchanged montmorillonite which, however, contained 4 times as much water in the interlamellar space. The activation energy for the motion has been deduced to be 18 kJ mol−1. Also it has been demonstrated that upon the time scale of the neutron scattering events (faster than 10−9 s) the hydroxyl groups of the clay lattice are not in motion.

The diffusion of water in Li-montmorillonite was studied by incoherent quasielastic neutron scattering. Experiments were carried out on sedimented samples equilibrated at relative humidities of 32%, 58%, and 98%, corresponding approximately to 1, 2, and 3 molecular layers of water in the clay. At all three humidities, although the mobility of the water molecules is less than in bulk water, all water molecules in the system undergo translational diffusion, at least over short distances (>5 Å), with correlation times shorter than 5 × 10−11 sec.

Various models of molecular motion have been used to account for the exact shape of the scattering. The only completely successful model is one where a water molecule undergoes jump-translational diffusion and rotational diffusion. The mean square jump length is 10–15 Å2 with a residence time between jumps of 4–2 × 10−11 sec. The translational diffusion coefficient increases with humidity, having values of 4, 7, and 10 × 10−10 m2/sec for the three humidities. These values can be combined with values previously obtained by tracer measurements to give an estimate of 0.75–0.8 for the tortuosity factor. Although the samples are anisotropic, there is no clear evidence that the diffusion of water over distances 5–20 Å is anisotropic. An upper limit of 3 can be deduced for the rate of diffusion parallel to the direction perpendicular to the platelets.

Sorption and desorption of two neutral, nonpolar organic compounds, 1,2-dibromoethane (EDB, a soil fumigant) and trichloroethene (TCE, an industrial solvent and common ground-water contaminant), by pyrophyllite, kaolinite, illite, and smectite were investigated. For sorption, vapors of the compounds in a stream of dry N2 gas were passed through columns of the powdered clay minerals for different periods of time. The compounds retained by the clays were extracted with methanol and analyzed by gas chromatography (GC). For desorption, N2 was passed through the treated samples, and the desorbed compounds were collected in hexane traps and analyzed by GC.

Initially sorption was rapid for several hours but then proceeded at a slower rate for many hours. Surprisingly, the clays sorbed large quantities of these neutral compounds; for example, the pyrophyllite, kaolinite, illite, and smectite sorbed about 3, 5, 6, and 9% EDB, respectively, by weight. The amounts of TCE sorbed, which is more volatile than EDB, were somewhat less. Only a portion of the compounds sorbed over a period of time were desorbed in the same period of time. Desorption was rapid initially but then proceeded at a slow rate; slow desorption continued for over 100 hr from samples which had undergone sorption for only 1–2 hr. A two-compartment efflux model was used to describe the sorption behavior. A rapidly desorbing component was considered to be present on the outer surfaces of the clay aggregates and a slowly desorbing component, in the interior pores of the aggregates.

The rate of sorption of methanol (MeOH), propan-2-ol (i-PrOH), and 2-methyl-propan-2-ol (t-BuOH) onto a Wyoming montmorillonite saturated with Al3+-, Cr3+-, or Fe3+-cations has been studied by isothermal gravimetry in the temperature range 18°–105°C using samples of differing weights and grain-size distributions. The rate of sorption for all the alcohols increased with decreasing sample and grain size, demonstrating that inter-, rather than intraparticle mass transfer was the rate-limiting process. Optimization of the sample parameters (2 mg sample of < 45-μm grain size, pretreated at 120°C yielded integral diffusion coefficients at 18°C of 1.1 × 10−4 m2/s for t-BuOH for the Cr3+-form and 2.0 × 10−14 m2/s for MeOH and i-PrOH for the Al3+-form. In general, the rate of alcohol sorption decreased as MeOH ≥ i-PrOH > t-BuOH, but no temperature dependence of the sorption rate was observed. The alcohol sorption rate was dependent on the cation present, with Fe3+ < Cr3+ < Al3+.

The rate of vapor-phase sorption of tetrahydrofuran (THF), tetrahydropyran (THP), and 1,4-dioxan (DIOX) onto a Wyoming montmorillonite saturated with Al3+ or Cr3+ has been studied by isothermal gravimetry in the temperature range 18° to 105°C using samples of different weights and grain-size distributions. The rate of sorption for all the cyclic ethers increased with decreasing sample and grain size, demonstrating that inter-, rather than intraparticle mass transfer was rate-determining. Optimization of the sample parameters (2 mg sample of <45-μm grain size, pretreated at 120°C yielded integral diffusion coefficients at 18°C of 0.5 × 10−14 m2/s for DIOX for the Cr3+-clay to 3.5 × 10−4 m2/s for THF for the Al3+-clay; however, no temperature or cationic dependence of the cyclic ether uptake was observed. In general, the rate of sorption of the cyclic ethers increased as THF ≥ THP > DIOX indicating that the sorption rate of THF and THP was dependent on concentration or that DIOX sorption was retarded by bidentate coordination to aluminum ions at the edges of the clay platelets.

With the current interest in the use of transition metal-exchanged phyllosilicates as catalysts for novel organic syntheses, investigations into the factors which affect the movement of reactant, product, and solvent molecules into and out of their interlamellar region are of considerable importance. Mixed organic-water intercalates of a Wyoming montmorillonite, exemplified by the Na-montmorillonitepyridine-water system which can form four different intercalates exhibiting basal spacing of 29.3, 23.3, 19.4, and 14.8 Å depending on the pyridine: water ratio, have been used as a model system. X-ray and neutron diffraction and quasielastic neutron scattering data relating to the interconversion of interlayer species indicate that access to and exit from the interlayer space is hindered at high partial pressures of water by a water-film diffusion barrier in the interparticulate voids which exist between the aggregated silicate layers. At lower water vapor pressures the rate-limiting step for interconversion from one intercalate to another is the rate of transport of reagents and products to and from the clay particles. Under conditions where these rates are fixed, the rate-limiting step is the rate of diffusion of the pyridine molecule in the lower-spacing intercalate. Processes which involve a change in basal spacing do not necessarily proceed via a single discrete step, but are also affected by the amount of water made available to the system. In organic reactions catalyzed in the interlamellar space of various cation-exchanged montmorillonites (e.g., the conversion of alk-1-enes to di-2,2’-alkyl ethers and the reaction of alcohols to form ethers), rate-determining steps similar to those found above are likely to be operative. In particular, for reactions carried out in the liquid phase, where mass transport is facile and where phase-transfer problems are avoided, such reactions are likely to be diffusion controlled.

The isothermal solid state reactions of Na2CO3 and other salts at 550°C with montmorillonite and with 1:1 mixtures of montmorillonite-illite and montmorillonite-chlorite were investigated. At a concentration of 20 wt. %, Na2CO3 caused the complete destruction of the X-ray powder diffraction (XRD) pattern of montmorillonite alone and in mixtures with other clays. Less deterioration of the XRD pattern was found for NaOH, NaF, K2CO3, and Li2CO3. NaCl, Na2SO4, Na3PO4, MgCO3, and CuCO3 had no effect on the XRD traces of montmorillonite. The time dependence of the Na2CO3-montmorillonite interaction at 550°C suggested that the reaction is diffusion controlled in three dimensions, i.e., diffusion was directed from the surface of the particle towards its center.

Diffusion of K during analytical electron microscopy (AEM) results in anomalously low count rates for this element. As the analysis area and specimen thickness decrease, count rates become disproportionally lower. Adularia and muscovite show different diffusion profiles during AEM; for muscovite a strong dependence of diffusion on crystallographic orientation has been observed. Conditions giving rise to reliable chemical data by AEM are the use of a wide scanning area (>800 × 800 Å) and/or large beam size to reduce the effect of diffusion of alkali elements, a specimen thickness greater than about 1000 Å, constant instrument operating conditions, and the use of a homogeneous, well-characterized standard sample. The optimum thickness range was obtained by determining the element intensity ratio vs. thickness curve for given operating conditions. The standard and unknown should have a similar crystal structure and, especially for strongly anisotropic minerals such as phyllosilicates, a similar crystallographic orientation with respect to the electron beam.

Batch data for the sorption of Eu and Th on pelagic sediments may be represented by equations of the form: ln M = A ln Cs + B/T + D, where M = concentration of sorbate on sediment, Cs = concentration of sorbate in solution, T = absolute temperature, and A, B, and D = constants. Thermodynamic interpretation of this equation leads to an expression for the true thermodynamic equilibrium constant of K = m/CsA and for the enthalpy change, ΔH, of d ln(M/CsA)/d(1/T) = −ΔH/R, where R = universal gas constant.

Experimentally, the sorption of Eu onto clay-rich sediments was very rapid in the first few seconds and slowed over an interval of minutes to hours. Rate curves were similar in shape to those of α-iron hydroxide, rather than of the oxalate-extracted residual sediment, indicating the importance of oxyhydroxide-like phases in the uptake of Eu onto red-clay sediments. For clay-rich sediments, numerical modeling reproduced the general features of a series of diffusion experiments. To a first approximation, the penetration of Eu into a sediment proceeded by saturation of the sediment to the depth of penetration and produced a sharp drop-off in sorbed + dissolved Eu concentration at the diffusion front. Higher partition coefficients (Kp) resulted in greater sorbed + dissolved concentrations, but reduced penetration. For calcareous sediments, however, Eu concentrations at the surface were much higher than at depth, presumably due to the formation of an insoluble carbonate.

Clay-modified electrode research indicates that adsorbed complexes are electroactive if the adsorption sites are clay edges. Interlayer adsorbed complexes may be electroactive if a charge shuttle is added or if interlayer swelling is large. Conductivity of the film towards anionic species depends upon the swelling of the clay, which depends on the electrolyte concentration and speciation. The diffusion coefficients measured by electrochemical experiments agree well with alternative measurements.

The roles of molecular structure and charge are examined in the transport of cations within montmorillonite clay films. The series of Ru(NH3)63+, Co(NH3)3+, Co(en)33+, Co(sep)3+ and Co(bpy)33+ are examined in detail via electrochemical and spectrochemical methods. The electrochemical signal is enhanced both in minimizing the time required to develop the signal and in the magnitude of the signal for Ru(NH3)63+. In addition, the potential for the observed reduction peak is shifted negative and the current peak associated with reduction disappears with rinsing of the clay film. These observations are characteristic of a compound that is held by simple electrostatic charge characteristics. In contrast, the compounds Co(NH3)3+, Co(en)33+ and Co(sep)3+, while showing rapid and enhanced signal development, eventually evolve a signal that is diminished with respect to the bare electrode, consistent with a hydrophobic mode of retention. The signal for Co(bpy)33+ is slow to be observed, is diminished with respect to the bare electrode and is shifted positive in potential, all hallmarks of a strong, non-electrostatic mode of binding within the clay.

Diffusion of alkali and low-atomic-number elements during the microbeam analysis of some silicates by analytical electron microscopy (AEM) has been known for some time. Our repeated analyses at 300 kV of kaolinite, halloysite, smectite, biotite, muscovite and pyrophyllite, however, showed differential loss (relative to Si) of not only alkali elements (such as K, Na, Mg) and low-atomic-number elements (such as Al) but also higher-atomic-number elements (such as Fe, Ti). For AEM of these phyllosilicates, a Philips EM430/EDAX facility with a tungsten filament was used to provide a current of 0.3 nA in a stationary beam of nominal diameter 90 nm. The loss of Al in kaolin minerals during analysis is particularly severe. Kaolin crystals can be damaged by the electron irradiation over several seconds, making it the most sensitive clay to the electron beam; in general, relative phyllosilicate stabilities are kaolin < smectite < pyrophyllite < mica. A clear dependence of element loss on crystallographic orientation has been observed for layer silicates in our study; a greater element loss occurred when the plane of the specimen foil was perpendicular to the basal planes of the phyllosilicate crystals than when the foil was parallel to the basal planes. Lower beam current, larger beam diameter and thicker specimens all reduce the loss of elements. The initial stage of irradiation produces highest rates of element loss and the rate of loss can be fitted by an exponential decay law. The analyses at low temperature of phyllosilicates showed that element loss remains serious in our analytical conditions. Since the element loss appears to be instrument- and method-dependent, one should use closely related, well-characterized phyllosilicates as compositional standards to calibrate any AEM instrument that is to be used to analyze unknown phyllosilicates, and the standards and unknowns should be analyzed under identical conditions.

Dynamical and thermodynamic properties of water at room temperature in Ca- and hexade-cyltrimethylammonium- (HDTMA) exchanged bentonite were determined for 4 different water contents (~0.03–0.55 g water g-1 clay). Incoherent quasi-elastic neutron scattering (QENS) was used to measure the translational and rotational mobility of water in the clays, while chilled mirror dewpoint psychrometry measured water activity of the samples, differential scanning calorimetry (DSC) provided information about the temperature of dehydration and X-ray diffraction (XRD) quantified layer spacings for the clays. The neutron scattering data were fit to a jump diffusion model that yielded mean jump lengths, jump diffusion residence times and rotational relaxation times for water in the clays. Mean jump lengths were quite similar for the 2 different cation saturations at equivalent water contents, and decreased with increasing water content. The fitted jump lengths ranged from 0.27–0.5 nm and were 2–4 times larger than that found for bulk water (0.13 nm). Jump diffusion residence times were 3–30 times longer than that for bulk water (1.2 ps) and also decreased with increasing water content. The residence times were somewhat shorter for HDTMA-clay as compared with Ca-clay at equivalent water contents. Rotational motion was less strongly influenced than translational motion by the presence of the clay surface. The energy state of water in the 2 cation saturations were quite different; dehydration temperatures for the HDTMA-clay were approximately 30 °C lower than the Ca-clay at equal water contents, while water activities, as P/P0, were up to 0.6 units higher. A linear relationship was found between water activity and the translational diffusion coefficient, although at the highest water content, the diffusion coefficient of water for the HDTMA-clay was approximately 30% higher than that measured for bulk water.