Exponential Rate Law Research Articles

Study on diffusion of oxygen in coral concrete under different preloads

The diffusion law of oxygen in coral concrete under different loading conditions was investigated in this study. Compressive strength of nine groups of C30 coral concrete was measured to determine the ultimate compressive strength of coral concrete. Then, loads of 0, 25, 45, or 65% of the compressive strength were applied, and the damage to the specimens was quantitatively characterized via an ultrasonic method. Further, the oxygen diffusion coefficient of coral concrete was measured under different loads. Next, numerical simulations were carried out by using COMSOL software to verify and improve the oxygen diffusion test of coral concrete. The results show that the damage of the coral concrete increases with increasing load, while the ultrasonic velocity gradually decreases. Owing to its higher porosity, coral concrete exhibits a greater oxygen diffusion coefficient than mortar specimens with the same mix ratio, and the diffusion of oxygen in coral concrete follows an exponential rate law. With increasing pre-applied load on the specimen, an increase in the damage and the number of microcracks of the specimens as well as in the oxygen transmission rate and the final oxygen diffusion coefficient could be observed. The calculated values of the model obtained by using the numerical simulations exhibit a good correlation with the test results, which verifies the accuracy of the model established in this study.

On the Effectiveness of Using the Real Law of Solid Propellant Burning Rate As a Function of Solid Rocket Motor Pressure

This paper presents a comparative analysis of the maximum possible solid rocket motor pressures obtained using the exponential and real laws of the propellant burning rate as a function of pressure. It is shown that at high exponents in the burning rate law, there is a large (tens of percent) difference between the maximum motor pressure obtained by the above two methods. In the case where the exponent is in the range 0.3–0.4, the exponential burning rate law overestimates the motor pressure by only 2–3%.

Temperature dependence of calcite dissolution kinetics in seawater

Knowledge of calcite dissolution kinetics in seawater is a critical component of our understanding of the changing global carbon budget. Towards this goal, we provide the first measurements of the temperature dependence of calcite dissolution kinetics in seawater. We measured the dissolution rates of ^(13)C-labeled calcite in seawater at 5, 12, 21, and 37°C across the full range of saturation states (0 < Ω = Ca^(2+)[CO_3^(2-)/Ksp'< 1). We show that the dissolution rate is non-linearly dependent on Ω and that the degree of non-linearity both increases with temperature, and changes abruptly at “critical” saturation states (Ω_(crit_). The traditional exponential rate law most often utilized in the oceanographic community, R=k(1-Ω)^n, requires different fits to k and n depending upon the degree of undersaturation. Though we calculate a similar activation energy to other studies far from equilibrium (25±2 kJ/mol), the exponential rate law could not be used to mechanistically explain our near equilibrium results. We turn to an alternative framework, derived from crystal nucleation theory, and find that our results are consistent with calcite dissolution kinetics in seawater being set by the retreat of pre-existing edges/steps from Ω=1-0.9, defect-assisted etch pit formation from Ω=0.9-0.75, and finally homogenous etch pit formation from Ω=0.75-0. The Ω_(crit) s for each mechanism are shifted significantly closer to equilibrium than they occur in dilute solutions, such that ocean acidification may cause marine carbonates to enter faster dissolution regimes more readily than would be expected from previous studies. We use the observed temperature dependence for each dissolution mechanism to calculate step kinetic coefficients (β, cm/s), densities of active nucleation sites (n_s, sites/m^2), and step edge free energies (α, mJ/m^2). Homogenous dissolution is well explained within the surface nucleation framework, but defect-assisted dissolution is not. Dissolution is initiated via step-propagation at all temperatures, but the defect-assisted mechanism is skipped over at 5°C, potentially due to a lack of nucleation sites. The surface nucleation framework enhances our understanding of calcite dissolution in seawater, but our results suggest that a complete theory will also need to incorporate the role of solution/surface speciation and complexation.

Wear and oxidation resistances of AlCrFeNiTi-based high entropy alloys

Based on the AlCoCrFeNi high entropy alloy, by replacing Co with Ti, new cobalt-free high entropy alloys AlCrFeNiTi and its derivative AlCrFeNiTiMn0.5 were designed and prepared by arc melting, and as-cast microstructures, wear and oxidation behaviors were investigated. The results show that two alloys are all composed of an ordered body centered cubic (BCC) and a disordered BCC phases, and typical dendritic structures including dendritic (DR), interdentritic (ID) and ‘eutectic phase’ areas were observed, implying the feature of near-eutectic high entropy alloys for AlCrFeNiTi and AlCrFeNiTiMn0.5. Adhesive wear mechanisms for these two alloys are indentified mainly as delamination wear, while oxidative wear is gradually dominated in AlCrFeNiTi. The wear resistance declines with addition of a half mole of Mn into AlCrFeNiTi due to rising wear coefficients of alloys. The oxidation kinetics of AlCrFeNiTi and AlCrFeNiTiMn0.5 alloys oxidized at 900 °C meet the exponential rate law, and the oxidation rate of AlCrFeNiTi is lower than that of AlCrFeNiTiMn0.5, suggesting a better oxidation resistance. Comparing with AlCrFeNiTi, a new Mn2O3 subscale was formed between the outer TiO2 scale and the underlying Al2O3 subscale on surfaces of AlCrFeNiTiMn0.5, which is consistent with theoretical analysis from the view of forming ability level by the first principles calculations.

Crystal Growth Mechanism of Vaterite in the Systems Containing Charged Synthetic Poly(Amino Acids)

Negatively ionisable poly-L-glutamic acid (pGlu) and poly-L-aspartic acid (pAsp), considered as analogues of the naturally occurring acidic macromolecules involved in biomineralization processes, were used as additives in the calcium carbonate precipitation systems in order to investigate their interactions with the vaterite crystallites. Poly-L-lysine (pLys), a positively ionisable poly(amino acid), was also used in order to elucidate the impact of the side chain charge. The growth kinetics of vaterite was found parabolic, indicating that the integration of growth units into the spiral step at the vaterite crystal surfaces is the rate-determining mechanism. The presence of small amounts of pGlu and pAsp inhibited the crystal growth. At the highest concentrations of both acidic macromolecules the exponential rate law was observed, which indicates the surface nucleation as the rate controlling mechanism. The addition of pLys in the range of applied concentrations did not significantly influence the crystal growth of the vaterite. Thus, the kinetic results, corroborated by morphological observations, pointed out to the significance of the negative charge of the side chains of selected polypeptides in the interfacial interactions with mineral planes.

Kinetics of zirconium saturation with nitrogen during high-temperature nitridation

Zirconium samples in the form of ribbons 60 mm in length and 3.0 × 0.5 mm in cross section were heated in a nitrogen atmosphere at temperatures of 1500, 1800, 1965, and 2400°C. The nitridation time at each temperature was 4, 6, 11, 21, 30, 40, 50, and 60 min. It has been shown that, under the thermal conditions studied, the process of saturation with nitrogen involves two stages: the first stage (in which the metallic phase disappears) can be represented by an exponential rate law, and the second (corresponding to an increase in nitrogen content up to the stoichiometric composition of ZrN) has a linear rate law.

Quantitative determination by SRET measurements of pit dissolution rate of AISI 304 stainless steel in natural sea water

Pit dissolution rate on samples of an AISI 304 stainless steel (SS) in natural sea water was assessed using a scanning reference electrode technique (SRET) and compared with chronoamperometric measurements. Corrosion pits generated in AISI 304 SS samples under potentiostatic control at room temperature and smooth surface presented an empirical exponential growth rate law. The quantity of dissolved metal per pit as a function of polarisation time determined using SRET and chronoamperometric measurements presented acceptable agreement. Considering the capabilities and limitations of scanning techniques, this study presents an approach of the pit growth rate determination from SRET measurements demonstrating the possibility to perform real time quantitative determination of localised dissolution rate.

Kinetics of Magnetic Field‐Induced Orientational Ordering in Block Copolymer/Superparamagnetic Nanoparticle Composites

The combination of external potential dynamics and Brownian dynamics is introduced to study the kinetics of orientational ordering in block copolymer/superparamagnetic nanoparticle composites where the particles are smaller than the domain spacing and preferentially segregate into one block of the copolymer. This simulation method accounts for both excluded volume interactions and dipolar interactions between particles to quantify alignment kinetics. Two-dimensional simulations reveal that higher dipolar interaction strengths lead to faster alignment of the block copolymer, where the orientation kinetics obeys an exponential rate law. The observed rate of alignment increases with increasing dipolar interaction strength and is dependent on the initial state of the block copolymer. The primary mechanism of orientational ordering is found to be the redistribution of monomer segments leading to bridging and growth of the block copolymer domains around the nanoparticles.

Measurement and Analysis of the Burning Rate of HAN-Based Liquid Propellants

A new device for measuring the linear burning rate of liquid propellants at high pressures is reported. High-pressure environments were generated by the combustion of solid propellants. The coated propellants, which burn progressively, were introduced to maintain the approximate constant-pressure environments. By use of ion probe transducers, measurements were made of the spread velocity of the flame surface, i.e. the apparent linear burning rate of the HAN-based liquid propellant LP1846 (HAN =hydroxylammonium nitrate) was measured quantitatively at pressures from 6 to 28 MPa. The results show that it follows the exponential burning rate law. The burning rate coefficient and exponent were fitted by least-squares methods. Based on the experiment, a simplified model of the linear burning rate of HAN-based liquid propellants at high pressures was developed. The numerical simulation is found to be in good agreement with the experimental data.

Pyromellitamide Gelators: Exponential Rate of Aggregation, Hierarchical Assembly, and Their Viscoelastic Response to Anions

The gelation and aggregation properties of a newly synthesized structurally simplified tetrahexyl pyromellitamide 2 have been studied and compared to the previously reported tetra(ethylhexanoate) pyromellitide 1, indicating that the ester groups in the latter significantly impede its aggregation. Morphology studies (AFM and TEM) on the aggregates formed by tetrahexyl pyromellitamide 2 in cyclohexane revealed highly uniform aggregates with different dimensions at different starting concentrations, suggesting that this molecule aggregates in a hierarchical fashion from a one-dimensional supramolecular polymer through hollow tubes or compressed helices to a network structure and then to a gel. This hypothesis is further supported by viscosity measurements that indicate a crossover point where individual supramolecular fibers get entangled at concentrations above ca. 3 mM in cyclohexane. Addition of 1 equiv of tetraalkylammonium salts of chloride or bromide, however, caused the viscosities of these pyromellitamide solutions to drop by a factor of 2-3 orders of magnitude, demonstrating the sensitivity of these aggregates to the presence of small anions. The sensitivity to anions does depend on the solubility of the salts used as small anion salts with little solubility in cyclohexane did not show this effect. Time-dependent viscosity studies showed that the aggregation of pyromellitamide 2 follows an exponential rate law, possibly related to the columnar rearrangements that are associated with the observed 6 angstroms contraction in d spacing in the XRD pattern of these gels. These results, particularly on the importance of kinetics of aggregation of self-assembled pyromellitamide gels, will be useful for future development of related materials for a number of applications, including tissue engineering and drug delivery.

Conditioning-Annealing Studies of Natural Organic Matter Solids Linking Irreversible Sorption to Irreversible Structural Expansion

The assumption of reversibility underpins the sorption term in current models dealing with the fate and impact of organic compounds in the environment, yet experimentally sorption of organic compounds in soils and sediments often shows "irreversible" behaviors such as hysteresis and the conditioning effect (enhanced repeat sorption). The objective of this study was to test whether a glassy polymer irreversibility model applies to natural organic matter (NOM) solids. Irreversible sorption in polymers is believed to be caused by irreversible expansion and creation of internal micropores by penetrating molecules, leading to enhanced affinity during desorption or subsequent resorption. Using chlorobenzene as a conditioning agent and polychlorinated benzenes as test compounds in a second sorption step, we observed conditioning effects for a peat soil, a soil humic acid, and a model glassy polymer, poly- (vinyl chloride), but not for a model rubbery polymer, poly- (ethylene). The conditioning effect for the two natural solids, probed bythe enhancement in the sorption distribution coefficient of 1,2,4-trichlorobenzene, relaxed upon sample annealing between 45 and 91 degrees C in a manner similar to the relaxation of free volume and enthalpy of glassy polymers. Relaxation of the conditioning effect in the NOM solids depended on annealing temperature and, at a given temperature, followed a double additive exponential rate law with a nonzero constant term descriptive of the final state that depends inversely on temperature. At environmentally relevant temperatures, the conditioning effect may "never" completely relax. The results provide compelling evidence for the glassy, nonequilibrium nature of natural organic matter solids and for irreversible structural expansion as a cause of irreversible sorption.

Hydration of phenylketene revisited: a counter-intuitive result.

In previous work (Can. J. Chem. 1987, 65, 1719-1723 and J. Am. Chem. Soc. 1995, 117, 9165-9171), flash photolysis of diazoacetophenone or phenylhydroxycyclopropenone in aqueous solution was found to produce phenylketene as a short-lived transient species with absorbance at lambda congruent with 260 nm, which decayed with single-exponential kinetics. It has now been discovered that, in the acidity region [H(+)] = 0.000 01 to 0.06 M, this decay is preceded by a faster absorbance rise, and that the overall change conforms well to a double exponential rate law. Analysis of the new data produces rate profiles whose general shapes, as well as the numerical values of their constituent rate constants, plus the form of buffer catalysis, indicate that this newly discovered absorbance rise represents ketonization of phenylacetic acid enol, and that the subsequent absorbance decay represents addition of water to phenylketene. The chemistry of the system, however, requires ketene hydration to precede enol ketonization in a time sequence opposite from that of the absorbance changes. This seemingly counter-intuitive result is nevertheless consistent with the rate law that governs the time evolution of the central species in a two-step rise and decay, such as that observed here.

Probing the presence of hydrophobic sites in anionic polyelectrolytes with tris(polypyridine)chromium(III) complexes

The emission properties of tris(polypyridine)chromium(III) complexes, [Cr(LL) 3] 3+ (LL=2,2′-bipyridine (bpy), 1,10-phenanthroline (phen), 4,7-dimethylphenanthroline (dim), and 4,7-diphenylphenanthroline (dip)), in air-saturated aqueous solutions, are dramatically modified in the presence of anionic polyelectrolytes. Investigated polyions included poly(acrylic acid) (PAA), poly(methacrylic acid) (PMA), and sodium poly(styrenesulfonate) (PSS). All four chromium complexes displayed tunable emission properties in the polyelectrolyte microenvironment, in a degree that depended on the hydrophobic character of both the macromolecule and the polyamine. The largest effect was observed for 2.5×10 −5 M aqueous solutions of [Cr(dip) 3] 3+ in 4×10 −3 M PMA at approximately pH 5 and t=15°C, where I PMA/ I w=25.66 ( I PMA=emission intensity in aqueous solutions containing PMA; I w=emission intensity in water). Decay lifetimes revealed that [Cr(dip) 3] 3+ units are distributed in hydrophobic and hydrophilic sites of the PMA, giving rise to short and long-lived intermediates. Distribution of [Cr(dip) 3] 3+ units in PAA and PSS is homogeneous throughout the polyelectrolyte, and the excited-state intermediates decay following a first order exponential rate law. All other investigated chromium polypyridines showed a homogeneous distribution in solutions containing PMA, PAA or PSS.

Growth of Ca-D-malate crystals in a bioreactor.

To develop a bioreactor for solid-to-solid conversions, the conversion of solid Ca-maleate to solid Ca-D-malate by permeabilized Pseudomonas pseudoalcaligenes was studied. In a bioreactor seeded with product (Ca-D-malate) crystals, growth of Ca-D-malate crystals is the last step in the solid-to-solid conversion and is described here. Crystal growth is described as a transport process followed by surface processes. In contrast to the linear rate law obeyed by the transport process, the surface processes of a crystal-growth process can also obey a parabolic or exponential rate law. Growth of Ca-D-malate crystals from a supersaturated aqueous solution was found to be surface-controlled and obeyed an exponential rate law. Based on this rate law, a kinetic model was developed which describes the decrease in supersaturation due to Ca-D-malate crystal growth as a function of the constituent ions, Ca(2+) and D-malate(2-). The kinetic parameters depended on temperature, but, as expected (surface-controlled), they were hardly affected by the stirring speed.

A physico-chemical method to calculate time-dependent reaction mixtures

A method is proposed to calculate multicomponent chemical reaction mixtures as a series of sequential, time-dependent thermochemical states. The procedure is based on the two general principles of physical chemistry, viz., decreasing Gibbs-energy for a natural process and the exponential Arrhenius rate law for the overall reaction kinetics. The calculation is performed in repeated sequences for a closed system element with known heat transfer to its surroundings. The temperature of each sequential reactor element is determined by a Gibbs-energy minimization routine (SOLGASMIX) connected to the closed system enthalpy balance iteration. The extent of overall reaction is limited by the Arrhenius kinetics, while the possible side reactions may reach equilibrium. The mass balance relations forming the subsidiary constraints of the Lagrange method are modified to facilitate the Gibbs-energy minimization for the intermediate “reactor states”. The well-known reaction of titanium (IV) chloride oxidation to titanium dioxide with such side reactions as chlorine dissociation and oxychloride formation is given as a calculational example.

The effect of dodecylammonium chloride on crystal growth of calcium oxalate

The effect of dodecylammonium chloride (DDACl) on the growth of calcium oxalate crystals from high ionic strength solutions has been investigated. At DDACl concentrations below the critical micelle concentration (CMC) adsorption of dodecylammonium ion (DDA +) at the crystal surface was insufficient to affect the crystallization. In the presence of DDACl at a concentration equal to or higher than the CMC a strong inhibition of the crystal growth is observed. It is caused by strong DDA + adsorption on some crystal faces. Furthermore, it was shown that the rate control mechanism changed from exponential rate law (in the control system and at the concentration of DDACl < CMC) to the linear rate law (at DDACl concentrations #62; CMC).

Crystal growth of lead fluoride using the constant composition method II. The effect of Pb/F activity ratio on the kinetics of crystal growth

A potentiometric pF-stat method has been used for the investigation the kinetics of lead fluoride crystal growth on seeds (α-PbF2) at 25°C. The kinetics was studied as a function of ionic strength, pH and lead-to-fluoride ions activity ratio, which were changed only by changing Pb(NO3)2 and KF concentrations. Depending on the excess of lead(II) nitrate or potassium fluoride in supersaturated solution two different crystal phases grow: (a) In solutions with large excess of Pb(NO3)2 and corresponding pH=4.35−5.00, a large needle-like crystals with some sponge-like precipitate are grown. The effective order of crystallization of this mixture is 1.55, indicating preferentially one-dimensional growth of needles. (b) In solutions with KF in excess, and consequently with pH=5.0–7.0, however, voluminous bipyramids of orthorhomic α-PbF2 crystals are grown. The effective order of crystallization of this known phase is 4.0, i.e. presumably an exponential rate law is valid.

Electrolyte crystal growth mechanisms

When very soluble electrolytes crystallize from aqueous solution they usually grow by a linear rate law - the rate being proportional to the difference between the concentration and the solubility. The rate is controlled by the transport of the ions in the bulk solution or by the adsorption process. Sparingly soluble electrolytes mostly grow by a parabolic or exponential rate law at small or moderate supersaturations, and may change to transport control at larger concentrations. Both with parabolic and with exponential rate laws the rates can be accounted for in terms of the classical theories of surface spirals caused by screw dislocation, and surface nucleation, respectively, when it is assumed that the rate-determining molecular mechanism is the integration of the cations into crystal lattice positions at kinks in the surface steps (whether caused by dislocations or surface nucleation). The rate of integration at a kink is of the order of one thousandth of the rate of dehydration of the cation. The factor 10 -3 is interpreted as due to the activation energy of diffusion, as an ion, in order to integrate, must dehydrate and make a diffusional jump at the same time. The theory is confirmed by application to 20 electrolytes following the parabolic rate law, and two electrolytes following the exponential law.

Analysis of crystal growth characteristics in a conventional vertical Bridgman configuration

The growth behavior in a conventional vertical Bridgman system was studied experimentally using gallium-doped germanium. The effects of varying modes of heat extraction from the seed end, the charge lowering rate, and the temperature distribution in the furnace on growth were investigated. It was found that the microscopic growth rate is transient at all times and that the growth interface remains concave into the solid. Initial transients follow a first order exponential rate law in most thermal configurations; extended configurational rate transients could be attributed to thermal end effects. The location of the control thermocouple was found to critically affect the growth behavior.

The monoclinic-to-trigonal transformation in selenium

The conversion of monoclinic selenium to trigonal selenium is studied by x-ray diffraction, optical microscopy, and thermal analysis between 343 and 487 K. Below the melting temperature of the monoclinic crystal the process is topochemical, but not topotactic. The melting of the monoclinic crystals to the pure Se8- ring melt occurs at 413 K (with a heat of fusion of 2.8 kJ/mole Se, and an entropy of fusion of 6.8 J/K/mole Se). The nucleation of the trigonal phase in the monoclinic single crystal is athermal and occurs in crystalline register with the monomer, either through the nature of the nucleating defect or through epitaxy. The time for the appearance of the fixed temperature-independent number of nuclei is governed by an activation energy of about 100 kJ/mole. The subsequent growth occurs by crystallization during polymerization in the direction of the macromolecular helix axis, independent of the host crystal. Above 360–380 K, the trigonal phase branches to spherulitic crystals with radial c-axis orientation. The linear crystal growth is described over the whole analyzed temperature range by the same exponential (−1/T) rate law with an activation energy of 113 kJ/mole, which indicates that ring opening is the rate-determining step.