Effect concentration

7 CHAIN CROSSOVER AND CHAIN ENTANGLEMENT 5.7.1 Concentration Effect 

So far our description of the random-coil chain basically assumes a dilute solution and we have not yet defined the term dilute solution. It has been discovered that when the concentration increases to a certain point, interesting phenomena occur chain crossover and chain entanglement. Chain crossover refers to the transition in configuration from randomness to some kind of order, and chain entanglement refers to the new statistical discovery of the self-similar property of the random coil (e.g., supercritical conductance and percolation theory in physics). Such phenomena also occur to the chain near the theta temperature. In this section, we describe the concentration effect on chain configurations on the basis of the theories advanced by Edwards (1965) and de Gennes (1979). In the next section, we describe the temperature effect, which is parallel to the concentration effect. 

In 1966, S. F. Edwards proposed classifying flie concentrations of polymer solutions into three broad types in terms of the total number of micromolecules (monomers) N, the number of polymer chains n, the effective length / of a micromolecule, the excluded volume per micromolecule U, and the total volume V. The length of the single chain L is defined as 

Edwards discussed intermediate concentrations in detail, for this is the region in which chain crossover and chain entanglement occur. To describe this region, he introduced two derived quantities  

Edwards reached a conclusion for the mean-square end-to-end distance of a polymer in intermediate solution by giving 

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In the preceding section, the choice of reactor type was made on the basis of which gave the most appropriate concentration profile as the reaction progressed in order to minimize volume for single reactions or maximize selectivity for multiple reactions for a given conversion. However, after making the decision to choose one type of reactor or another, there are still important concentration effects to be considered. 

In many cases, however, well-designed catalysts provide intrinsically different reaction paths, and the specific nature of the catalyst surface can be quite important. This is clearly the case with unimolecular reactions for which the surface concentration effect is not applicable. 

It was pointed out that a bimolecular reaction can be accelerated by a catalyst just from a concentration effect. As an illustrative calculation, assume that A and B react in the gas phase with 1 1 stoichiometry and according to a bimolecular rate law, with the second-order rate constant k equal to 10 1 mol" see" at 0°C. Now, assuming that an equimolar mixture of the gases is condensed to a liquid film on a catalyst surface and the rate constant in the condensed liquid solution is taken to be the same as for the gas phase reaction, calculate the ratio of half times for reaction in the gas phase and on the catalyst surface at 0°C. Assume further that the density of the liquid phase is 1000 times that of the gas phase. 

The fundamental assumption of SAR and QSAR (Structure-Activity Relationships and Quantitative Structure-Activity Relationships) is that the activity of a compound is related to its structural and/or physicochemical properties. In a classic article Corwin Hansch formulated Eq. (15) as a linear frcc-cncrgy related model for the biological activity (e.g.. toxicity) of a group of congeneric chemicals [37, in which the inverse of C, the concentration effect of the toxicant, is related to a hy-drophobidty term, FI, an electronic term, a (the Hammett substituent constant). Stcric terms can be added to this equation (typically Taft s steric parameter, E,). 

The concentration effect involves the AG s of mixing for the solutions of concentrations 0 and 20. We shall return to this presently. 

Since [r ] is a limiting value as Ci 0, the concentration effect it contains can be written as... 

Assuming that concentration effects have been eliminated by extrapolating Kc2/Rg to C2 = 0 (subscript c = 0), we see that Eq. (10.89) is the equation of a straight line if (Kc2/Rg)(,=o plotted against sin (0/2). The characteristic parameters of the line have the following significance ... 

An example of the concentration effect on the specific cake resistance is available (12) that reports results of some experiments with a laboratory horizontal vacuum belt filter. In spite of operational difficulties in keeping conditions constant, the effect of feed concentration on specific cake resistance is so strong that it swamps all other effects. 

Further work is needed to build a physical model that allows prediction of the concentration effect from the primary properties of the slurry or from a limited amount of slurry testing. 

Effects of Surfactants on Solutions. A surfactant changes the properties of a solvent ia which it is dissolved to a much greater extent than is expected from its concentration effects. This marked effect is the result of adsorption at the solution s iaterfaces, orientation of the adsorbed surfactant ions or molecules, micelle formation ia the bulk of the solution, and orientation of the surfactant ions or molecules ia the micelles, which are caused by the amphipathic stmcture of a surfactant molecule. The magnitude of these effects depends to a large extent on the solubiUty balance of the molecule. An efficient surfactant is usually relatively iasoluble as iadividual ions or molecules ia the bulk of a solution, eg, 10 to mol/L. 

Concentration Effects. The reactivity of ethyl alcohol—water mixtures has been correlated with three distinct alcohol concentration ranges (35,36). For example, the chromium trioxide oxidation of ethyl alcohol (37), the catalytic decomposition of hydrogen peroxide (38), and the sensitivities of coUoidal particles to coagulation (39) are characteristic for ethyl alcohol concentrations of 25—30%, 40—60%, and above 60% alcohol, respectively. The effect of various catalysts also differs for different alcohol concentrations (35). 

From known properties of solution, at measured or calculated concentration. Effective AT if a surface condenser. 

An important but frequently overlooked condition that can result in SCC involves concentration effects. These effects are of two types— stress concentration and corrodent concentration. 

Another subsidiary field of study was the effect of high concentrations of a diffusing solute, such as interstitial carbon in iron, in slowing diffusivity (in the case of carbon in fee austenite) because of mutual repulsion of neighbouring dissolved carbon atoms. By extension, high carbon concentrations can affect the mobility of substitutional solutes (Babu and Bhadeshia 1995). These last two phenomena, quenched-in vacancies and concentration effects, show how a parepisteme can carry smaller parepistemes on its back. 

This is an oversimplified treatment of the concentration effect that can occur on a thin layer plate when using mixed solvents. Nevertheless, despite the complex nature of the surface that is considered, the treatment is sufficiently representative to disclose that a concentration effect does, indeed, take place. The concentration effect arises from the frontal analysis of the mobile phase which not only provides unique and complex modes of solute interaction and, thus, enhanced selectivity, but also causes the solutes to be concentrated as they pass along the TLC plate. This concentration process will oppose the dilution that results from band dispersion and thus, provides greater sensitivity to the spots close to the solvent front. This concealed concentration process, often not recognized, is another property of TLC development that helps make it so practical and generally useful and often provides unexpected sensitivities. 

The complex distribution system that results from the frontal analysis of a multicomponent solvent mixture on a thin layer plate makes the theoretical treatment of the TLC process exceedingly difficult. Although specific expressions for the important parameters can be obtained for a simple, particular, application, a general set of expressions that can help with all types of TLC analyses has not yet been developed. One advantage of the frontal analysis of the solvent, however, is to produce a concentration effect that improves the overall sensitivity of the technique. 

Experimental results of cPBD adhesion stick and receptor concentration effects... 

Lopata, V.J., Chung, M., Janke, C.J. and Havens, S.J., Electron curing of epoxy resins initiator and concentration effects on curing dose and rheological properties. 28th Int. SAMPE Technical Conference, 901, 1996. 

Any material which contains a geometrical discontinuity will experience an increase in stress in the vicinity of the discontinuity. This stress concentration effect is caused by the re-distribution of the lines of force transmission through the material when they encounter the discontinuity. Causes of stress concentration include holes, notches, keyways, comers, etc as illustrated in Fig. 2.62. 

Hjertager, B. H., K. Fuhre, and M. Bjorkhaug. 1988a. Concentration effects on flame acceleration by obstacles in large-scale methane-air and propane-air explosions. Comb. Sci. Tech., 62 239-256. 

Concentration effects, i.e., the dependences of Vr on injected polymer concentration (Ci), represent a further complicating factor in the quantitative... 

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