Concentration dependency

It must be kept in mind that both pictures are modelistic and invoke extrather-modynamic concepts. Except mathematically, there is no such thing as a two-dimensional gas, and the solution whose osmotic pressure is calculated is not uniform in composition, and its average concentration depends on the depth assumed for the surface layer. 

Figure Bl.20.11. Force curves of DMPC/DPPE (dimyristoyl phosphatidylcholine and dipalmitoyl phosphatidylethanolainine) bilayers across a solution of PEG at different concentrations. Clearly visible is a concentration-dependent depletion attraction, with pennission from [17],...

In equation (C2.6.14) it can be seen that tire required salt concentration depends strongly on tire valency of tire ions... 

Samples can be concentrated beyond tire glass transition. If tliis is done quickly enough to prevent crystallization, tliis ultimately leads to a random close-packed stmcture, witli a volume fraction (j) 0.64. Close-packed stmctures, such as fee, have a maximum packing density of (]) p = 0.74. The crystallization kinetics are strongly concentration dependent. The nucleation rate is fastest near tire melting concentration. On increasing concentration, tire nucleation process is arrested. This has been found to occur at tire glass transition [82]. 

The chemical shifts of O—H and N—H protons are temperature and concentration dependent... 

Although the terms solute and solution are often associated with liquid samples, they can be extended to gas-phase and solid-phase samples as well. The actual units for reporting concentration depend on how the amounts of solute and solution are measured. Table 2.4 lists the most common units of concentration. 

Source Adapted from Baker, D. R. Capillary Electrophoresis. Wiley-Interscience New York, 1995. "Concentration depends on the volume of sample injected. 

As noted above, all of the partial molar quantities are concentration dependent. It is convenient to define a thermodynamic concentration called the activity aj in terms of which the chemical potential is correctly given by the relationship... 

The change in interaction energy per 1,2 pair is thus h. Aw. Next we must consider how this scales up for a large array of molecules, and particularly how to describe the concentration dependence of the result. 

At equilibrium, these concentration and pressure effects must be equal and opposite for Eq. (8.75) to apply. Equation (8.13) describes the concentration dependence of jui, and Eq. (8.12) describes the pressure effect. Assembling these results, we write... 

By describing the concentration dependence of an observable property as a power series, Eq. (9.9) plays a comparable role for viscosity as Eq. (8.83) does for osmotic pressure. 

As with the diffusion coefficient, sedimentation coefficients are frequently corrected for concentration dependence and reduced to standard conditions ... 

The concentration dependence of s is eliminated by making measurements at several different concentrations and then extrapolating to zero concentration. The limiting value is given by the symbol s°. This is the sedimentation analog of D°. 

Thus we have finally established how light scattering can be used to measure the molecular weight of a solute. The concentration dependence of r enters Eq. (10.54) through an expression for osmotic pressure, and this surprising connection deserves some additional comments ... 

A rapid increase in diffusivity in the saturation region is therefore to be expected, as illustrated in Figure 7 (17). Although the corrected diffusivity (Dq) is, in principle, concentration dependent, the concentration dependence of this quantity is generally much weaker than that of the thermodynamic correction factor d ap d a q). The assumption of a constant corrected diffusivity is therefore an acceptable approximation for many systems. More detailed analysis shows that the corrected diffusivity is closely related to the self-diffusivity or tracer diffusivity, and at low sorbate concentrations these quantities become identical. 

The Du Pont HaskeU Laboratory for Toxicology and Industrial Medicine has conducted a study to determine the acute inhalation toxicity of fumes evolved from Tefzel fluoropolymers when heated at elevated temperatures. Rats were exposed to decomposition products of Tefzel for 4 h at various temperatures. The approximate lethal temperature (ALT) for Tefzel resins was deterrnined to be 335—350°C. AH rats survived exposure to pyrolysis products from Tefzel heated to 300°C for this time period. At the ALT level, death was from pulmonary edema carbon monoxide poisoning was probably a contributing factor. Hydrolyzable fluoride was present in the pyrolysis products, with concentration dependent on temperature. 

Concentrations depend on severity of pyrolysis. At a high severity (- 2000° C) acetylene/ethylene ratio is 1, but at lower severity acetylene concentration is reduced and ethylene is increased. 

Manganate(VI) formed in the initial oxidation process must first be dissolved in a dilute solution of potassium hydroxide. The concentrations depend on the type of electrolytic cell employed. For example, the continuous Cams cell uses 120 150 g/L KOH and 50 60 g/L K MnO the batch-operated Bitterfeld cell starts out with KOH concentrations of 150 160 g/L KOH and 200 220 g/L K MnO. These concentration parameters minimize the disproportionation of the K MnO and control the solubiUty of the KMnO formed in the course of electrolysis. 

The volume of extracellular fluid is direcdy related to the Na" concentration which is closely controlled by the kidneys. Homeostatic control of Na" concentration depends on the hormone aldosterone. The kidney secretes a proteolytic enzyme, rennin, which is essential in the first of a series of reactions leading to aldosterone. In response to a decrease in plasma volume and Na" concentration, the secretion of rennin stimulates the production of aldosterone resulting in increased sodium retention and increased volume of extracellular fluid (51,55). 

When sulfuric acid is present in the mixed acids, the following ionisation reactions occur. These ionic reactions are rapid, and equiHbrium concentrations of NO2 are likely to be present at all times in the acid phase. NO2 concentrations depend mainly on the composition of the mixed acids but decrease to some extent as the temperature increases (3). 

R is hydrogen, alkenyl, or alkyne. In remote tropospheric air where NO concentrations ate sometimes quite low, HO2 radicals can react with ozone (HO2 + O3 — HO + 2 O2) and result in net ozone destmction rather than formation. The ambient ozone concentration depends on cloud cover, time of day and year, and geographical location. 

The role of specific interactions in the plasticization of PVC has been proposed from work on specific interactions of esters in solvents (eg, hydrogenated chlorocarbons) (13), work on blends of polyesters with PVC (14—19), and work on plasticized PVC itself (20—23). Modes of iateraction between the carbonyl functionaHty of the plasticizer ester or polyester were proposed, mostly on the basis of results from Fourier transform infrared spectroscopy (ftir). Shifts in the absorption frequency of the carbonyl group of the plasticizer ester to lower wave number, indicative of a reduction in polarity (ie, some iateraction between this functionaHty and the polymer) have been reported (20—22). Work performed with dibutyl phthalate (22) suggests an optimum concentration at which such iateractions are maximized. Spectral shifts are in the range 3—8 cm . Similar shifts have also been reported in blends of PVC with polyesters (14—20), again showing a concentration dependence of the shift to lower wave number of the ester carbonyl absorption frequency. 

GVD Coatings. As in PVD, the stmcture of the deposited material depends on the temperature and supersaturation, roughly as pictured in Figure 8 (12). In the case of CVD, however, the effective supersaturation, ie, the local effective concentration in the gas phase of the materials to be deposited, relative to its equiUbrium concentration, depends not only on concentration, but on temperature. The reaction is thermally activated. Because the effective supersaturation for thermally activated reactions increases with temperature, the opposing tendencies can lead in some cases to a reversal of the sequence of crystalline forms Hsted in Figure 8, as temperature is increased (12). 

In the same class of polymers, an antistat can exhibit different degrees of effectiveness. As seen in Table 6 the performance of ethoxylated oleyl amine varies among polyolefins. The data for polypropylene (PP) also shows the concentration dependence of antistats. 

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