Effect of diffusion

In addition to these limits of a solvent acting as an inert medium or as an active chemical or electronic species in the transition state, we will see a number of other effects of a more physical nature can occur, as will be discussed in the following sections. 

Wood [3], while collisions between molecules in the gas phase are separated by reasonable time intervals in liquids, collisions occur in groups of rapid sequences, known as encounters. 

In each encounter between two reactants, the molecules undergo at least four collisions, until they manage to escape the cage of solvent molecules which surround them. However, the frequency of these encounters is about 100 times lower than that for collisions of the same molecules in the gas phase. 

Based on this, a reaction in solution can be broken down into three steps (1) diffusion of reactants from bulk solution to the collision distance (2) chemical reaction of the reacting species within the solvent cage and (3) diffusion of the products from the solvent cage to bulk solution. We can represent these processes in the following kinetic scheme  

The rate of reaction, measured by the decrease in concentration of species A, is given by the expression  

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Since the blocked gas inside of the capillary is dissolving in the liquid and then diffusing towards the exit of the channel, the meniscus of the liquid crosses the position l and goes deeper. This second stage of capillary filling with liquid is called diffusive imbibition and plays an important role in PT processes. The effect of diffusive imbibition upon PT sensitivity has been studied in [7]. 

Carr H Y and Purcell E M 1954 Effects of diffusion on free precession in nuclear magnetic resonance experiments Rhys. Rev. 94 630-8... 

Concentration gradient for the analyte showing the effects of diffusion and convection as methods of mass transport. 

Ordinary diffusion involves molecular mixing caused by the random motion of molecules. It is much more pronounced in gases and Hquids than in soHds. The effects of diffusion in fluids are also greatly affected by convection or turbulence. These phenomena are involved in mass-transfer processes, and therefore in separation processes (see Mass transfer Separation systems synthesis). In chemical engineering, the term diffusional unit operations normally refers to the separation processes in which mass is transferred from one phase to another, often across a fluid interface, and in which diffusion is considered to be the rate-controlling mechanism. Thus, the standard unit operations such as distillation (qv), drying (qv), and the sorption processes, as well as the less conventional separation processes, are usually classified under this heading (see Absorption Adsorption Adsorption, gas separation Adsorption, liquid separation). 

According to this approximation, the drift velocity is proportional to the square of the electric field. This is a clear indication of the importance of the electric field inside an electrostatic precipitator. Equation (13.60) is a valid approximation for large particles [dp > 0.5 m), provided that particle charge is close to the saturation level. In the case of small particles, the effect of diffusion charging must be taken into account. 

The last boundary condition results from the assumption that for the relatively short contact times occurring in real systems, the effect of diffusion at b is negligible, and, therefore, a change in concentration at this point results only from chemical reaction. 

Kishinev ski/23 has developed a model for mass transfer across an interface in which molecular diffusion is assumed to play no part. In this, fresh material is continuously brought to the interface as a result of turbulence within the fluid and, after exposure to the second phase, the fluid element attains equilibrium with it and then becomes mixed again with the bulk of the phase. The model thus presupposes surface renewal without penetration by diffusion and therefore the effect of diffusivity should not be important. No reliable experimental results are available to test the theory adequately. 

Various improvements of the DCDT [40,41] approach have been considered to correct for the effects of diffusion, based largely around extrapolation to l/ /i) 0. 

The effects of diffusion and catalyst decay cause yields from a continuous backmix reactor to be 25 to 30% lower than from a semibatch reactor at the same residence time. This yield penalty can be reduced by staging backmix reactors in series. 

Rebenne, H. E., and Bhat, D. G., Effect of Diffusion Interface on Adhesion and Machining Performance of TiN-Coated Silicon-Nitride Cutting Tools, Proc. ThirdInt. Conf. on Surface Modification Technologies, Neuchatel, Switzerland (Aug., 1989)... 

The effects of diffusion control on cross-hnk kinetics were investigated by Dusek [102] within the context of polymerization reaction kinetics. 

Another important factor in diffusion measurements that is often encountered in NMR experiments is the effect of time on diffusion coefficients. For example, Kinsey et al. [195] found water diffusion coefficients in muscles to be time dependent. The effects of diffusion time can be described by transient closure problems within the framework of the volume averaging method [195,285]. Other methods also account for time effects [204,247,341]. 

A semi-permeable membrane, which is unequally permeable to different components and thus may show a potential difference across the membrane. In case (1), a diffusion potential occurs only if there is a difference in mobility between cation and anion. In case (2), we have to deal with the biologically important Donnan equilibrium e.g., a cell membrane may be permeable to small inorganic ions but impermeable to ions derived from high-molecular-weight proteins, so that across the membrane an osmotic pressure occurs in addition to a Donnan potential. The values concerned can be approximately calculated from the equations derived by Donnan35. In case (3), an intermediate situation, there is a combined effect of diffusion and the Donnan potential, so that its calculation becomes uncertain. 

The effects of diffusion of cations due to a concentration gradient or of the convection of cations and solvent are very small. 

A general transport equation describing the rate of change of the radon activity concentration in the pore space results from combining the effects of diffusion and convection ... 

We should remember (1) that the activation energy of eh reactions is nearly constant at 3.5 0.5 Kcal/mole, although the rate of reaction varies by more than ten orders of magnitude and (2) that all eh reactions are exothermic. To some extent, other solvated electron reactions behave similarly. The theory of solvated electron reaction usually follows that of ETR in solution with some modifications. We will first describe these theories briefly. This will be followed by a critique by Hart and Anbar (1970), who favor a tunneling mechanism. Here we are only concerned with fe, the effect of diffusion having been eliminated by applying Eq. (6.18). Second, we only consider simple ETRs where no bonds are created or destroyed. However, the comparison of theory and experiment in this respect is appropriate, as one usually measures the rate of disappearance of es rather than the rate of formation of a product. 

The total current density, J —Jx +J2> and a rather complicated formula may be obtained by straightforward algebra. In fact, for many practical purposes, the value of a>D is sufficiently large for us to neglect the effects of diffusion. This is equivalent to putting otl = ct2 = 1 in the formulae above,... 

Unless the coverage of adsorbate is monitored simultaneously using spectroscopic methods with the electrochemical kinetics, the results will always be subject to uncertainties of interpretation. A second difficulty is that oxidation of methanol generates not just C02 but small quantities of other products. The measured current will show contributions from all these reactions but they are likely to go by different pathways and the primary interest is that pathway that leads only to C02. These difficulties were addressed in a recent paper by Christensen and co-workers (1993) who used in situ FT1R both to monitor CO coverage and simultaneously to measure the rate of C02 formation. Within the reflection mode of the IR technique used in this paper this is not a straightforward undertaking and the effects of diffusion had to be taken into account in order to help quantify the data obtained. 

While there have been several studies on the synthesis of block copolymers and on the molecular weight evolution during solution as well as bulk polymerizations (initiated by iniferters), there have been only a few studies of the rate behavior and kinetic parameters of bulk polymerizations initiated by iniferters. In this paper, the kinetics and rate behavior of a two-component initiation system that produces an in situ living radical polymerization are discussed. Also, a model that incorporates the effect of diffusion limitations on the kinetic constants is proposed and used to enhance understanding of the living radical polymerization mechanism. 

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