A critical concentration

The passivating action of an aqueous solution within porous concrete can be changed by various factors (see Section 5.3.2). The passive film can be destroyed by penetration of chloride ions to the reinforcing steel if a critical concentration of ions is reached. In damp concrete, local corrosion can occur even in the presence of the alkaline water absorbed in the porous concrete (see Section 2.3.2). The Cl content is limited to 0.4% of the cement mass in steel-concrete structures [6] and to 0.2% in prestressed concrete structures [7]. 

Density. Most fillers added in rubber base formulation have a density between 2 and 2.7 g/cm-, except barium sulphate (4-4.9 g/cm- ) and zinc oxide (5.6 g/cm ). Addition of filler increases the free volume of the polymer and, in general, there is a critical concentration of filler at which the density of the formulation increases. The method of incorporation of filler in the adhesive formulation is important because air voids may appear when a poor dispersion is produced. 

The effects of inhibitive and aggressive anions on the corrosion of zinc are broadly similar to the effects observed with iron. Thus with increasing concentration, anions tend to promote corrosion but may give inhibition above a critical concentration Inhibition of zinc corrosion is somewhat... 

The effect of traps on charge carrier motion does not become noticeable until the trap concentration reaches a threshold value. One can define a critical concentration Ci/2 at which the mobility has decreased to one half of the value of the trap-free system. Eq. (12.19) predicts that. ... 

These free energies determine the critical concentrations for observing each peptide structure. In very dilute conditions, this class of peptides exist as random coil monomers in conformational flux. Above a critical concentration, C( pg, the concentration of monomer remains constant and formation of tapes occurs ... 

List B contains all compounds that form peroxides which become dangerous when they reach a critical concentration. The danger will often become apparent during distillation operations. For hydrocarbons, this is the case for deca- and tetrahydronaphthalene, cyclohexene, dicyclopentadiene, propyne and butadiene. S ondary alcohols such as 2-butanol also form part of this list. Finally, for ethers there are diethyl ethers, ethyl and vinyl ethers, tetrahydrofuran, 1,4-dioxan, ethylene glycol diethers and monoethers. 

Simha [53] made the first attempts to model the transition from a dilute to a concentrated solution. He assumed that in the range from lscaling laws a theory has been developed which allows for the prediction of the influence of Mw c and the solvent power on the screening length [54,55]. This theory is founded on the presumption that above a critical concentration, c, the coils overlap and interpenetrate. Furthermore it is assumed that in a thermody-... 

The explanation for this is that with increasing solvent power intermolecular repulsion becomes decisive. Enhancement of the polymer concentration leads therefore to coil shrinkage [64], whereas in the limiting case of a 0-solvent no concentration-induced shrinkage is to be expected. Raising c further leads to a critical concentration, c, at which the coils begin to overlap and interpenetrate. 

Below a critical concentration, c, in a thermodynamically good solvent, r 0 can be standardised against the overlap parameter c [r)]. However, for c>c, and in the case of a 0-solvent for parameter c-[r ]>0.7, r 0 is a function of the Bueche parameter, cMw The critical concentration c is found to be Mw and solvent independent, as predicted by Graessley. In the case of semi-dilute polymer solutions the relaxation time and slope in the linear region of the flow are found to be strongly influenced by the nature of polymer-solvent interactions. Taking this into account, it is possible to predict the shear viscosity and the critical shear rate at which shear-induced degradation occurs as a function of Mw c and the solvent power. 

It is a first principle of toxicology that no chemical substance is a poison at all concentrations toxicity occurs only when a critical concentration is reached within vital cells. Whether or not an economic poison will exert a particular deleterious effect depends on the relative rates of absorption as compared with detoxication and elimination, its inherent toxicity, and the physiologic status of the organism. 

The main conclusion of the percolation theory is that there exists a critical concentration of the conductive fraction (percolation threshold, c0), below which the ion (charge) transport is very difficult because of a lack of pathways between conductive islands. Above and near the threshold, the conductivity can be expressed as ... 

Dissolved oxygen (DO) in a bioreactor should be maintained above a critical concentration in order to maintain good aerobic biological activity. The minimum required DO concentration ranges between 0.2 and 2.0 mg/L with 0.5 mg/L being the most reported value. 

It is now well known that the addition of Ca2+ in aqueous solutions of these copolymers induces phase separation with precipitation of a phase constituted by a polymer-Ca complex. From turbidity measurements, it is possible to define a critical concentration ca above which this phenomenon occurs(23-25). 

The concentration at which a steep rise in this curve begins has been termed as the critical or threshold concentration (2,3). Figure 6 shows such typical curves for PTF and BTF in n-hexane. Despite the fact that different shear rates are involved in capillary viscometry, it can be qualitatively said that at a given concentration, PTF viscosified n-hexane better than BTF. It is clear from Figure 6 that the critical concentration for these two compounds is above 0.7%, while analogous tri-n-alkyltin fluorides showed a critical concentration of less than 0.4% (3). This may be due to the presence of bulky Me3Si-groups nearer to the Sn-F bond, which causes some steric hindrance to auto-association. 

There are a number of papers in the open literature explicitly reporting on the properties of boron cluster compounds for potential neutron capture applications.1 Such applications make full use of the 10B isotope and its relatively high thermal neutron capture cross section of 3.840 X 10 28 m2 (barns). Composites of natural rubber incorporating 10B-enriched boron carbide filler have been investigated by Gwaily et al. as thermal neutron radiation shields.29 Their studies show that thermal neutron attenuation properties increased with boron carbide content to a critical concentration, after which there was no further change. 

The introduced THEOS did not bring about precipitation in protein solutions. This behavior differs from that observed with common silica precursors. For example, TEOS added in such small amounts caused precipitation. By using THEOS, we could prepare homogeneous mixtures. When its amount introduced into the albumin solution was less than 5 wt.%, there was no transition to a gel state (Table 3.1). A gradual increase in THEOS concentration resulted in a rise in the solution viscosity. The transition to a gel state took place as soon as a critical concentration was reached. Its value, as demonstrated in Ref. 

Influence of Addition of Electrolyte and Increase of Temperature Addition of electrolyte or increase of temperature at a given electrolyte concentration to a sterically stabilized dispersion may result in its flocculation at a critical concentration or temperature, which in many cases coincides with the theta point for the stabilizing chain. At the theta point the mixing term in the steric interaction is zero and any yield value measured should correspond to the residual van der Waals attraction. The energy arising from van der Waals attraction may be calculated from the following approximate relationship,... 

Small, portable sensors are now available to monitor the air we breathe for such toxins as carbon monoxide, CO. As soon as the air contains more than a critical concentration of CO, the sensor alerts the householder, who then opens a window or identifies the source of the gas. 

Because there is usually a critical concentration of a chemical in the blood that is necessary to elicit either a pharmacological or toxic effect, both the rate and extent of input or availability can alter the toxicity of a compound. In the majority of cases, the duration of effects will be a function of the length of time the blood-concentration curve is above the threshold concentration the intensity of the effect for many agents will be a function of the elevation of the blood-concentration curve above the threshold concentration. 

Each of the examples mentioned above behave slightly differently and these differences are due to the detailed structure. In each case the hydrocarbon groups associate via hydrophobic bonding but HMHEC for example can show a critical concentration threshold for this to occur. HEUR on the other hand tends to associate at all concentrations. This is due to accessibility of the hydrophobes as they are at the ends of very flexible chains. In HMHEC, however, we have a much stiffer chain with the hydrophobes spread randomly along it. It is therefore a more difficult process to bring these together to form network nodes. HP AM conforms more closely to HMHEC than HEUR but, as we have groups of hydrocarbon chains at each modification site, it associates somewhat more readily. 

---