Diffusion-limited Reaction Research Articles

Surface acoustic waves (SAW) accelerated microfluidic mixing for improved microcalorimetry in biochips

By measuring very small local temperature changes, microcalorimetry is used to determine the rates of energy released or absorbed during biochemical reactions. The measurement signal-to-noise ratio can be significantly increased by accelerating the reaction kinetics by active microfluidic mixing. We present a biochip incorporating a self-referencing droplet-based microreactor consisting of a thermopile-based microcalorimeter (50 Ni/Au thermocouples in series) on a glass substrate with a surface acoustic wave (SAW)-based microfluidic mixing system on a LiNbO3 piezoelectric substrate. In our design, the SAW mechanical energy is transmitted from the piezoelectric substrate through the glass substrate to the droplets via a water film which acts as a pseudo mechanical impedance matching layer. The cumulative energy released by a standard calorimetric test reaction (sucrose dilution) is measured with the system. Results show that, by overcoming the diffusion-limited reaction rate, SAW-accelerated mixing in the droplets increases the thermal power released during the experiment by a factor 2, increasing the measurement SNR by the same factor. This enthalpy measurement accuracy improvement makes the system well-suited to sensitive thermodynamic measurements on biochip devices.

Validity of the Law of Mass Action in Three-Dimensional Coagulation Processes

Diffusion-limited reactions are studied in detail on the classical coalescing process. We demonstrate how, with the aid of a recent renormalization group approach, fluctuations can be integrated systematically. We thereby obtain an exact relation between the microscopic physics (lattice structure and particle shape and size) and the macroscopic decay rate in the law of mass action. Moreover, we find a strong violation of the law of mass action. The corresponding term in the kinetic equations originates in long-wavelength fluctuations and is a universal function of the macroscopic decay rate.

IS SUBDIFFUSIONAL TRANSPORT SLOWER THAN NORMAL?

We consider anomalous non-Markovian transport of Brownian particles in viscoelastic fluid-like media with very large but finite macroscopic viscosity under the influence of a constant force field F. The viscoelastic properties of the medium are characterized by a power-law viscoelastic memory kernel which ultra slow decays in time on the time scale of strong viscoelastic correlations τ. The subdiffusive transport regime emerges transiently for t < τ. However, the transport becomes asymptotically normal for t ≫ τ. It is shown that even though transiently the mean displacement and the variance both scale sublinearly, i.e., anomalously slow, in time, 〈δx(t)〉 ∝ Ftα, 〈δx2(t)〉 ∝ tα, 0 < α <1, the mean displacement at each instant of time is nevertheless always larger than one obtained for normal transport in a purely viscous medium with the same macroscopic viscosity obtained in the Markovian approximation. This can have profound implications for the subdiffusive transport in biological cells as the notion of "ultra-slowness" can be misleading in the context of anomalous diffusion-limited transport and reaction processes occurring on nano- and mesoscales.

Facilitated diffusion on confined DNA

In living cells, proteins combine three-dimensional bulk diffusion and one-dimensional sliding along the DNA to reach a target faster. This process is known as facilitated diffusion and we investigate its dynamics in the physiologically relevant case of confined DNA. The confining geometry and DNA elasticity are key parameters: We find that facilitated diffusion is most efficient inside an isotropic volume and on a flexible polymer. By considering the typical copy numbers of proteins in vivo, we show that the speedup due to sliding becomes insensitive to fine tuning of parameters, rendering facilitated diffusion a robust mechanism to speed up intracellular diffusion-limited reactions. The parameter range we focus on is relevant for in vitro systems and for facilitated diffusion on yeast chromatin.

Bimolecular Electron Transfer in Ionic Liquids: Are Reaction Rates Anomalously High?

Steady-state and picosecond time-resolved emission spectroscopy are used to monitor the bimolecular electron transfer reaction between the electron acceptor 9,10-dicyanoanthracene in its S(1) state and the donor N,N-dimethylaniline in a variety of ionic liquids and several conventional solvents. Detailed study of this quenching reaction was undertaken in order to better understand why rates reported for similar diffusion-limited reactions in ionic liquids sometimes appear much higher than expected given the viscous nature of these liquids. Consistent with previous studies, Stern-Volmer analyses of steady-state and lifetime data provide effective quenching rate constants k(q), which are often 10-100-fold larger than simple predictions for diffusion-limited rate constants k(D) in ionic liquids. Similar departures from k(D) are also observed in conventional organic solvents having comparably high viscosities, indicating that this behavior is not unique to ionic liquids. A more complete analysis of the quenching data using a model combining approximate solution of the spherically symmetric diffusion equation with a Marcus-type description of electron transfer reveals the reasons for frequent observation of k(q) ≫ k(D). The primary cause is that the high viscosities typical of ionic liquids emphasize the transient component of diffusion-limited reactions, which renders the interpretation of rate constants derived from Stern-Volmer analyses ambiguous. Using a more appropriate description of the quenching process enables satisfactory fits of data in both ionic liquid and conventional solvents using a single set of physically reasonable electron transfer parameters. Doing so requires diffusion coefficients in ionic liquids to exceed hydrodynamic predictions by significant factors, typically in the range of 3-10. Direct, NMR measurements of solute diffusion confirm this enhanced diffusion in ionic liquids.

Hydrogen peroxide electrochemistry on platinum: towards understanding the oxygen reduction reaction mechanism

Understanding the hydrogen peroxide electrochemistry on platinum can provide information about the oxygen reduction reaction mechanism, whether H(2)O(2) participates as an intermediate or not. The H(2)O(2) oxidation and reduction reaction on polycrystalline platinum is a diffusion-limited reaction in 0.1 M HClO(4). The applied potential determines the Pt surface state, which is then decisive for the direction of the reaction: when H(2)O(2) interacts with reduced surface sites it decomposes producing adsorbed OH species; when it interacts with oxidized Pt sites then H(2)O(2) is oxidized to O(2) by reducing the surface. Electronic structure calculations indicate that the activation energies of both processes are low at room temperature. The H(2)O(2) reduction and oxidation reactions can therefore be utilized for monitoring the potential-dependent oxidation of the platinum surface. In particular, the potential at which the hydrogen peroxide reduction and oxidation reactions are equally likely to occur reflects the intrinsic affinity of the platinum surface for oxygenated species. This potential can be experimentally determined as the crossing-point of linear potential sweeps in the positive direction for different rotation rates, hereby defined as the "ORR-corrected mixed potential" (c-MP).

Kinetics of Biotin Derivatives Binding to Avidin and Streptavidin

The on-rate constants (kon) of biotin (B) binding to avidin (AV) and streptavidin (SAV) are believed to be diffusion limited (109 M−1s−1). In this study; we asked whether these reactions were actual diffusion controlled, what association model and thermodynamic cycle describe the process, and what are the functional differences between AV and SAV. We have studied the B association by two stopped flow methodologies that used: I) fluorescent probes attached to B; and II) unlabeled B and HABA [2-(4’-hydroxyazobenzene)-benzoic acid]. The reactions were carried out at several temperatures, pH's and under pseudo first-order conditions with: oregon green biocytin (BcO), biotin-4-fluorescein (BFl), biotin-DNA duplex, and unlabeled B. We obtained the spectroscopy properties of the bound dye-biotin complexes to have an insight of the chemical environment surrounding B. The association data showed not cooperativity between the 1st and the 4th binding sites of AV. The kon values of SAV were faster than AV's, but in both cases were slower than those expected for a diffusion limited reaction. Furthermore, the Arrhenius plots revealed strong temperature dependence with large activation energies (6-15 kcal/mol) that did not correspond either to a diffusion limited process (3-4 kcal/mol). The outcomes indicated that AV binding sites were deeper and less accessibility than SAV. In addition, we are reporting, for the first time, a second order displacement rate constant of a bound SAV complex when challenged with free B; results that are relevant for the purification technology base on these proteins. Finally, we propose a simple reaction model with a single transition state whose forward energetic parameters complete the thermodynamic cycle in excellent agreement with previous studies.

Effect of Particle Size and Morphology on the Dehydration Mechanism of a Non-Stoichiometric Hydrate

A hydrated form of 7-methoxy-1-methyl-5-(4-(trifluoromethyl)phenyl)-[1,2,4]triazolo[4,3-a]quinolin-4-amine (designated Form B) exhibits moisture sorption behavior that is very strongly affected by particle size and morphology. When studied pre- and post-micronization, the simple rate of dehydration at ambient temperature is faster by >2 orders of magnitude after micronization. Complementary techniques were employed to understand this behavior including environmental X-ray powder diffractometry (XRPD), gravimetric vapor sorption (GVS), differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), hot-stage microscopy (HSM), single-crystal X-ray diffractometry (SCXRD), and solid-state nuclear magnetic resonance (SSNMR). Solid-state kinetics analysis of thermal data revealed that dehydration of the nonmicronized material follows a two-step consecutive reaction with the first step being a diffusion limited reaction and the second step being a first order reaction, whereas the micronized material ...

The H2A–H2B Dimeric Kinetic Intermediate Is Stabilized by Widespread Hydrophobic Burial with Few Fully Native Interactions

The H2A–H2B histone heterodimer folds via monomeric and dimeric kinetic intermediates. Within ∼5 ms, the H2A and H2B polypeptides associate in a nearly diffusion limited reaction to form a dimeric ensemble, denoted I2 and I2⁎, the latter being a subpopulation characterized by a higher content of nonnative structure (NNS). The I2 ensemble folds to the native heterodimer, N2, through an observable, first-order kinetic phase. To determine the regions of structure in the I2 ensemble, we characterized 26 Ala mutants of buried hydrophobic residues, spanning the three helices of the canonical histone folds of H2A and H2B and the H2B C-terminal helix. All but one targeted residue contributed significantly to the stability of I2, the transition state and N2; however, only residues in the hydrophobic core of the dimer interface perturbed the I2⁎ population. Destabilization of I2⁎ correlated with slower folding rates, implying that NNS is not a kinetic trap but rather accelerates folding. The pattern of Φ values indicated that residues forming intramolecular interactions in the peripheral helices contributed similar stability to I2 and N2, but residues involved in intermolecular interactions in the hydrophobic core are only partially folded in I2. These findings suggest a dimerize-then-rearrange model. Residues throughout the histone fold contribute to the stability of I2, but after the rapid dimerization reaction, the hydrophobic core of the dimer interface has few fully native interactions. In the transition state leading to N2, more native-like interactions are developed and nonnative interactions are rearranged.

Anomalous kinetics in diffusion limited reactions linked to non-Gaussian concentration probability distribution function

We investigate anomalous reaction kinetics related to segregation in the one-dimensional reaction-diffusion system A + B → C. It is well known that spatial fluctuations in the species concentrations cause a breakdown of the mean-field behavior at low concentration values. The scaling of the average concentration with time changes from the mean-field t(-1) to the anomalous t(-1/4) behavior. Using a stochastic modeling approach, the reaction-diffusion system can be fully characterized by the multi-point probability distribution function (PDF) of the species concentrations. Its evolution is governed by a Fokker-Planck equation with moving boundaries, which are determined by the positivity of the species concentrations. The concentration PDF is in general non-Gaussian. As long as the concentration fluctuations are small compared to the mean, the PDF can be approximated by a Gaussian distribution. This behavior breaks down in the fluctuation dominated regime, for which anomalous reaction kinetics are observed. We show that the transition from mean field to anomalous reaction kinetics is intimately linked to the evolution of the concentration PDF from a Gaussian to non-Gaussian shape. This establishes a direct relationship between anomalous reaction kinetics, incomplete mixing and the non-Gaussian nature of the concentration PDF.

Diffusion-limited reactions on disordered surfaces with continuous distributions of bindingenergies

We study the steady state of a stochastic particle system on a two-dimensional lattice, withparticle influx, diffusion and desorption, and the formation of a dimer when particles meet.Surface processes are thermally activated, with (quenched) binding energies drawn from acontinuous distribution. We show that sites in this model provide either coverage ormobility, depending on their energy. We use this to analytically map the system to aneffective binary model in a temperature-dependent way. The behavior of the effectivemodel is well understood and accurately describes key quantities of the system:compared with the case for discrete distributions, the temperature window of efficientreaction is broadened, and the efficiency decays more slowly at its ends. Themapping also explains in what parameter regimes the system exhibits realizationdependence.

Immobilization methods for developing enzyme based biosensors

Diffusion and kinetics of amperometric immobilized enzymes on the planar, cylindrical and spherical electrodes are discussed. This model is described as a set of non-linear reaction-diffusion equations consisting of a non-linear term related to Michaelis-Menten kinetics and enzyme-catalyzed reactions. In this paper, we obtain approximately the general analytical solutions for the non-linear equations that describe diffusion-limited reaction within the film by employing the Akbari-Ganji Method (AGM). The obtained analytical results for the concentration of substrate, mediator and current are compared with the available limiting case results and numerical results and found to be in satisfactory agreement. The dependence of the amperometric response on substrate and mediator concentration, enzyme concentration, electrode potential, film thickness and geometry of the electrode is analyzed.

Influence of crystal size and probe molecule on diffusion in hierarchical ZSM-5 zeolites prepared by desilication

The improvement of molecular transport properties of hierarchical H-ZSM-5 obtained by desilication was evidenced by studying the desorption of o-xylene and isooctane by in situ diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS). This technique enabled monitoring simultaneously bands associated with the molecular probes and the zeolite, using powdered sample masses as low as 1 mg. Two H-ZSM-5 samples with markedly different crystal sizes were investigated. The first sample was commercial and consisted of small crystallites ( ca. 250 nm). The second sample were laboratory-made large crystals with coffin-like shape ( ca. 17 × 4 × 4 μm 3). The hierarchical derivatives of the small and large zeolite crystals displayed 250 and 120 m 2 g −1 of mesopore surface area, respectively, in contrast to the 62 and 5 m 2 g −1 of the parent counterparts. The data based on o-xylene desorption were partly disguised by site-desorption limitations. Desorption experiments using isooctane evidenced a 4-fold reduction in the characteristic diffusion path length on both mesoporous small and large zeolites with respect to their purely microporous analogues. These results confirm the substantial potential for improvement of commercial nanocrystalline zeolites in diffusion-limited reactions upon the introduction of intra-crystalline mesoporosity by post-synthesis modification.

A new approach to diffusion-limited reaction rate theory

A new approach to the diffusion-limited reaction rate theory is developed on the base of a similar approach to consideration of Brownian coagulation, recently proposed by the author. The traditional diffusion approach to calculation of the reaction rate is critically analyzed. In particular, it is shown that the traditional approach is applicable only to the special case of reactions with a large reaction radius, \(\bar r_A \ll R_{AB} \ll \bar r_B\) (where \(\bar r_A\), \(\bar r_B\) are the mean interparticle distances), and becomes inappropriate to calculation of the reaction rate in the case of a relatively small reaction radius, \(R_{AB} \ll \bar r_A\), \(\bar r_B\). In the latter, most general case particles collisions occurmainly in the kinetic regime (rather than in the diffusion one) characterized by a homogeneous (at random) spatial distribution of particles. Homogenization of particles distribution occurs owing to particles diffusion mixing on the length scale of the mean interparticle distance with the characteristic diffusion time being small in comparison with the characteristic reaction time. The calculated reaction rate for a small reaction radius in 3D formally (and casually) coincides with the expression derived in the traditional approach for reactions with a large reaction radius, however, notably deviates at large times from the traditional result in the plane (2D) geometry.

Solvothermal synthesis and thermoelectric properties of indium telluride nanostring-cluster hierarchical structures

A simple solvothermal approach has been developed to successfully synthesize n-type α-In2Te3 thermoelectric nanomaterials. The nanostring-cluster hierarchical structures were prepared using In(NO3)3 and Na2TeO3 as the reactants in a mixed solvent of ethylenediamine and ethylene glycol at 200°C for 24 h. A diffusion-limited reaction mechanism was proposed to explain the formation of the hierarchical structures. The Seebeck coefficient of the bulk pellet pressed by the obtained samples exhibits 43% enhancement over that of the corresponding thin film at room temperature. The electrical conductivity of the bulk pellet is one to four orders of magnitude higher than that of the corresponding thin film or p-type bulk sample. The synthetic route can be applied to obtain other low-dimensional semiconducting telluride nanostructures.PACS: 65.80.-g, 68.35.bg, 68.35.bt

Diffusion-limited hyperbranched polymers with substitution effect

Highly branched structure has the essential influence on macromolecular property and functionality in physics and chemistry. In this work, we proposed a diffusion-limited reaction model with the consideration of macromolecular unit relaxations and substitution effect of monomers to study the structure of hyperbranched polymers prepared by slow monomer addition to a core molecule. The exponential relationship (R(g) ∼ N(λ)) between the radius of gyration R(g) and the degree of polymerization N, was systematically analyzed at various branching degrees. It is shown that the effective exponent λ(eff) decreases at lower N and but increases toward that of diffusion-limited aggregation (DLA) clusters (λ(DLA) = 0.4) with the degree of polymerization increasing. The substitution effect of monomers in reaction strongly influences the evolution pathway of λ(eff). With the static light scattering technique, the fractal property of internal chains was further calculated. A general law about the radial distribution of the units of diffusion-limited hyperbranched polymers was found that, at smaller reactivity ratio k(12), the radial density of all monomer units D(A) declines from the center region to the peripheral layer revealing the dense core structure; however, at larger k(12), the density distribution shows a loose-dense-loose structure. These structural characteristics are helpful to deeply understand the property of hyperbranched polymers.

Agent-based simulation of reactions in the crowded and structured intracellular environment: Influence of mobility and location of the reactants

BackgroundIn this paper we apply a novel agent-based simulation method in order to model intracellular reactions in detail. The simulations are performed within a virtual cytoskeleton enriched with further crowding elements, which allows the analysis of molecular crowding effects on intracellular diffusion and reaction rates. The cytoskeleton network leads to a reduction in the mobility of molecules. Molecules can also unspecifically bind to membranes or the cytoskeleton affecting (i) the fraction of unbound molecules in the cytosol and (ii) furthermore reducing the mobility. Binding of molecules to intracellular structures or scaffolds can in turn lead to a microcompartmentalization of the cell. Especially the formation of enzyme complexes promoting metabolic channeling, e.g. in glycolysis, depends on the co-localization of the proteins.ResultsWhile the co-localization of enzymes leads to faster reaction rates, the reduced mobility decreases the collision rate of reactants, hence reducing the reaction rate, as expected. This effect is most prominent in diffusion limited reactions. Furthermore, anomalous diffusion can occur due to molecular crowding in the cell. In the context of diffusion controlled reactions, anomalous diffusion leads to fractal reaction kinetics. The simulation framework is used to quantify and separate the effects originating from molecular crowding or the reduced mobility of the reactants. We were able to define three factors which describe the effective reaction rate, namely f diff for the diffusion effect, f volume for the crowding, and f access for the reduced accessibility of the molecules.ConclusionsMolecule distributions, reaction rate constants and structural parameters can be adjusted separately in the simulation allowing a comprehensive study of individual effects in the context of a realistic cell environment. As such, the present simulation can help to bridge the gap between in vivo and in vitro kinetics.

Development of a comprehensive mathematical model for free radical suspension polymerization of methyl methacrylate

In this work a detailed mathematical model for free radical suspension polymerization of methyl methacrylate (MMA) in water is developed. This model is based on sound principles such as the free volume theory to account for the diffusion limited reactions in suspension polymerization. Additionally, the complex polymerization kinetics process of the aqueous suspension polymerization of MMA is studied as a one-dimensional numerical experiment. For this purpose, the polymerization process is modeled as a moving boundary mass transfer problem coupled with polymerization reactions. The Galerkin finite element method is used to simultaneously solve the nonlinear governing equations. The model predictions for conversion and average molecular weights vs. time were found to be in close agreement with laboratory data. It is believed that this work, as it provides fundamental understanding of the process, it might contribute to a more rational design of polymerization reactors. POLYM. ENG. SCI., 2011. © 2010 Society of Plastics Engineers

KINETIC RESPONSE OF SURFACES DEFINED BY FINITE FRACTALS

Historically, fractal analysis has been remarkably successful in describing wide ranging kinetic processes on (idealized) scale invariant objects in terms of elegantly simple universal scaling laws. However, as nanostructured materials find increasing applications in energy storage, energy conversion, healthcare, etc., one must reexamine the premise of traditional fractal scaling laws as it only applies to physically unrealistic infinite systems, while all natural/engineered systems are necessarily finite. In this article, we address the consequences of the 'finite-size' problem in the context of time dependent diffusion towards fractal surfaces via the novel technique of Cantor-transforms to (i) illustrate how finiteness modifies its classical scaling exponents; (ii) establish that for finite systems, the diffusion-limited reaction is decelerated below a critical dimension [Formula: see text] and accelerated above it; and (iii) to identify the crossover size-limits beyond which a finite system can be considered (practically) infinite and redefine the very notion of 'finiteness' of fractals in terms of its kinetic response. Our results have broad implications regarding dynamics of systems defined by the same fractal dimension, but differentiated by degree of scaling iteration or morphogenesis, e.g. variation in lung capacity between a child and adult.

Defectivity Avoidance in Chemical Mechanical Planarization: Role of Multi-Scale and Multi-Physics Interactions

A multi-physics model encompassing chemical dissolution and mechanical abrasion effects in CMP is developed. This augments a previously developed multi-scale model accounting for both pad response and slurry behavior evolution. The augmented model is utilized to predict scratch propensity in a CMP process. The pad response delineates the interplay between the local particle level deformation and the cell level bending of the pad. The slurry agglomerates in the diffusion limited agglomeration (DLA) or reaction limited agglomeration (RLA) regime. Various nano-scale slurry properties significantly influence the spatial and temporal modulation of the material removal rate (MRR) and scratch generation characteristics. The model predictions are first validated against experimental observations. A parametric study is then undertaken. Such physically based models can be utilized to optimize slurry and pad designs to control the depth of generated scratches and their frequency of occurrence per unit area.