Experimental evidences

Direct experimental proof that the true driving force for diffusive transport is the gradient of chemical potential rather than the concentration gradient is provided by the experiments of Haase and Siry who studied diffusion in binary liquid mixtures near the consolute point. At the consolute point the chemical potential (and the vapor pressure) are independent of composition so, according to Eq. (5.6), the diffusivity should be zero. The consolute point for the system n-hexane-nitrobenzene occurs at 20 C at a mole fraction 0.422 of nitrobenzene. The system shows complete miscibility above this temperature and forms two separate phases at lower temperatures. Opposite behavior is shown by the system water-triethylamine, for which the consolute tempera- 

FIGURE 5.1. Variation of Fickian diffusivity with icmpcratiire for liquid mixtures of critical composition, (( ) /i-hexanc-nitrobenzcne (moic fraction nitrobenzene 0.42, consohite temperature, 20 C). h) Water-triclhylaininc (mole fraction triclhylamine - 0.087, consolute temperature. = 18 C. [Reprinted from Chem. En, Set. 30, Turner (ref. 7). Copyright 1975, Pergamon Press, Ltd.] 

There is eertainly strong experimental evidenee for the existenee of radieal-solvent eom-plexes. For instanee, Russelk and eo-workers eolleeted experimental evidenee for radi-eal-eomplex formation in studies of the photoehlorination of 2,3 -dimethylbutane in various solvents. In this work, different produets were obtained in aliphatie and aromatie solvents, and this was attributed to formation of a jr-eomplex between the Cl atom and the aromatie solvent. Complex formation was eonfirmed by flash photolysis. Complex formation was also proposed to explain experimental results for the addition of triehloromethane radieal to 3-phenylpropene and to 4-phenyl-1-butene and for hydrogen abstraetion of the t-butoxy radieal from 2,3-dimethylbutane. Furthermore, eomplexes between nitroxide radieals and a large number of aromatie solvents have been deteeted. Evidenee for eomplexes between polymer radieals and solvent moleeules was eolleeted by Flatada et al., in an analysis of initiator fragments from the polymerization of MMA-d with AIBN and BPO initiators. They diseovered that the ratio of disproportionation to eombination depended on the solvent, and interpreted this as evidenee for the formation of a polymer radieal-solvent eomplex that suppresses the disproportionation reaetion. 

There is also experimental evidenee for the influenee of radieal-solvent eomplexes in small radieal addition reaetions. For instanee, Busfield and eo-workers used radieal-solvent to explain solvent effeets in reaetions involving small radieals, sueh as t-butoxyl radieals towards various eleetron donor-eleetron aeeeptor monomer pairs. The observed solvent effeets were interpreted in terms of eomplex formation between the t-butoxyl radieal and the eleetron-aeeeptor monomer, possibly via a sharing of the lone pair on the t-butoxyl oxy- 

Radical-solvent complexes are expected to be favored in systems containing unstable radical intermediates (such as vinyl acetate) where complexationmay lead to stabilization. In this regard Kamaehi et al have noted that solvent effects on vinyl acetate homopolymerization result in a reduced kp. Kamaehi et al. also measured the absolute rate constants of vinyl benzoate in various aromatic solvents and found that kp increased in the order  

They argued that this trend could not be explained by copolymerization through the solvent or transfer to the solvent because there was no correlation with the solvent dielectric constant or polarity, or with the rate constants for transfer to solvent. However, there was a correlation with the calculated delocalization stabilization energy for complexes between the radieal and the solvent, which suggested that the propagating radical was stabilized by the solvent or monomer, but the solvent did not actually participate in the reaction. 

Given the experimental evidence for the existence of radical-solvent complexes and their influence on free-radieal addition reactions such as homopropagation, it is likely that 

It is evident that even if acetic acid could be demonstrated as an intermediate in fat oxidation, the experimental data are quite preponderant in indicating that it would not be a D-glucose-former. 

Miscellaneous Experimental Evidence that Fat is Converted to Carbohydrate 

Grafe and Wolf123 have also reported exceedingly high D N ratios (exceeding 10 1) in diabetic patients on an exclusive protein-fat diet. Lusk124 suggests that such ratios may be the result of surreptitious in- 

Lusk128 has suggested the following empirical equation for the conversion of palmitic acid to D-glucose. 

The greater the proportion of the total metabolism which is concerned with the change fat — carbohydrate, the more the R. Q. may be expected to be depressed below the fasting non-protein R. Q. of 0.707 which is usually regarded as the minimal normal value. 

These simplifying assumptions are justified on the basis that many step polymerizations have reaction rate constants that are independent of the reaction time or polymer molecular 

TABLE 2-1 Rate Constants for Esterification (25°C) in Homologous Compounds0  

It is evident that, although there is a decrease in reactivity with increased molecular size, the effect is significant only at a very small size. The reaction rate constant very quickly reaches a limiting value at x — 3, which remains constant and independent of molecular size. Analogous results are found for the polyesterification of sebacoyl chloride with oqoalkane diols [Ueberreiter and Engel, 1977]  

The rate constant for esterification is independent of x for the compounds studied (Table 2-2). Examples of similar behavior can be found for other reactions [Rand et al., 1965]. The results for sebacoyl chloride offer direct evidence of the concept of functional group reactivity being independent of molecular size, since the rate constant is independent of n as well as x. 

The independence of functional group reactivity of molecular size is contrary to the general impression that was widely held in the early years of polymer science. There was a general misconception of decreased reactivity with increased molecular size. This was due 

Several papers have been published which report unusual symmetry for small particles. These include atoms in abnormal positions 63 close-packed structures different from the normal bulk structures (e.g., b.c.c. Au, or f.c.c. 

in Catalysis , ed. G. C. Bond and G. Webb (Specialist Periodical Reports), The Royal Society of Chemistry, London, 1982, Vol. 5, p. 172. 

Hernandez, and M.J. Yacaman, Surf. Interface Anal., 1982, 4, 120. 

in Epitaxial Growth , ed. J. W. Mathews, Academic Press, New York, 1975, p. 215. 

Since the 1940s, experiments with additions of nutrients on hundreds of plots in the field have shown a more or less strong N limitation on forest growth in Fennoscandian forests ( I amm, 1991 Binkley and Hogberg, 1997). In such trials, additions of NH4NO3 increase forest production, but they frequently acidify the mineral. soil (Fig. 5 Tamm, 1991 Binkley and Hogberg, 1997). This means that the BC/Al (or Ca/Al) ratio is lowered, while forest production increases, and definitely implies that the N supply has proximal control of forest productivity. 

Furthermore, trees have a low demand for Ca in relation to the supply. Extensive laboratory tests, as well as field evidence, suggest that the demand for N is more than an order of magnitude higher than the demand for Ca in the two major conifer species, Picea abies and Pinns sylvestris (Inge.stad, 1979 Linder, 1993), while in boreal forests, foliar analysis frequently shows that the concentration of N is at most only twice the concentration of Ca (e.g., Ed-fa.stetn/., 1990). 

FIGURE 5 The basic correlation between the. supply of N (and forest 

Any positive effects of Ca on tree gixwth, as suggested by the correlation between Ca supply and forest growth, cannot thus be direct, but can potentially occur in a longer perspective, provided increases in soil pH increase soil N turnover. However, in typical boreal forest soils with a C/N ratio 30 in the inor-layer, the reverse, i.e., increased N immobilization, commonly occurs after liming (Persson and Wiren, 1996) and is most likely the reason why forest growth often declines over a period of several decades after liming (Fig. 5 Derome et ciL, 1986). 

My research has been sponsored by SJFR, NFR, SNV, and the EC. This chapter has benefitted from my introduction to this area of research by C.-O. Timm and many discussions with D. Binkley, R. Giesler, H. Grip, M. Hogberg, H.-O. Nohrstedt, and T. Nasholm. I thank E.-D. Schulze for the kind invitation to write this chapter. 

Very few systems have been studied with a sufficient precision so that we may compare them to our theoretical model. For example no precise data are known for and pjoJkT. On the other hand the systems which have been studied are formed by molecules which axe not spherical and therefore the application of the theorem of corresponding states seems doubtful. Therefore a quantitative test of the theory seems at present impossible and we shall limit ourselves to a qualitative discussion of some mixtures. 

We have selected four systems which have been studied most carefully and are formed by relatively simple molecules 

The first three could reasonably be assumed to obey the law of corresponding states and to interact mainly through dispersion forces. The fourth mixture does certainly not satisfy these conditions. Nevertheless let us compare the signs of jr and t found experimentally with those predicted by the present theory, assuming that 0 = — 5 /8. 

The molecular parameters d and p have been deduced from the critical temperatures, pressures and volumes of pure components (cf. Ch. IX, 2). The signs of t and may then be read at once from Fig. 12.6.1 and 12.6.2. The results are summarized in Table 12.7.1. 

For the first 3 mixtures, there exists a qualitative agreement. For the last one the theoretical sign of r disagrees with the experimental one. As already noticed the application of the present theory to this mixture is probably not very reasonable. Better agreement can be obtained if instead of assuming 6 = — 6 /8 we choose 0 0. 

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Castets V, Dulos E, Boissonade J and De Kepper P 1990 Experimental evidence of a sustained standing Turing-type nonequilibrium structure Rhys. Rev. Lett. 64 2953-6... 

Common experimental evidence shows that the viscosity of polymers varies as they flow. Under certain conditions however, elastic effects in a polymeric flow can be neglected. In these situations the extra stress is again expressed, explicitly, in terms of the rate of deformation as... 

Numerous examples of polymer flow models based on generalized Newtonian behaviour are found in non-Newtonian fluid mechanics literature. Using experimental evidence the time-independent generalized Newtonian fluids are divided into three groups. These are Bingham plastics, pseudoplastic fluids and dilatant fluids. 

The first finite element schemes for differential viscoelastic models that yielded numerically stable results for non-zero Weissenberg numbers appeared less than two decades ago. These schemes were later improved and shown that for some benchmark viscoelastic problems, such as flow through a two-dimensional section with an abrupt contraction (usually a width reduction of four to one), they can generate simulations that were qualitatively comparable with the experimental evidence. A notable example was the coupled scheme developed by Marchal and Crochet (1987) for the solution of Maxwell and Oldroyd constitutive equations. To achieve stability they used element subdivision for the stress approximations and applied inconsistent streamline upwinding to the stress terms in the discretized equations. In another attempt, Luo and Tanner (1989) developed a typical decoupled scheme that started with the solution of the constitutive equation for a fixed-flow field (e.g. obtained by initially assuming non-elastic fluid behaviour). The extra stress found at this step was subsequently inserted into the equation of motion as a pseudo-body force and the flow field was updated. These authors also used inconsistent streamline upwinding to maintain the stability of the scheme. 

The existence of two forms of glucose and of two isomeric methyl glucosides, as well as other experimental evidence, have led to the adoption of the ring structures (I) and (II) ... 

Diels-Alder reactions and other transformations. Unfortunately, experimental evidence for these... 

Because of the mentioned leveling effect of the solvent (or excess acid itself acting as such) the acidity cannot exceed that of its conjugate acid. In the case of water the limiting acidity is that of HsO. Proton-ated water, H30 (hydronium ion), was first postulated in 1907, and its preeminent role in acid-catalyzed reactions in aqueous media was first realized in the acid-base theory of Bronsted and Lowry. Direct experimental evidence for the hydronium ion in solution and in the... 

To date, there have not been any large-scale comparisons of QM/MM methods in which many dilferent techniques were compared against experimental results for a large variety of chemical systems. There does tend to be some preference for the use of link atoms in order to ensure the correct chemical behavior of the QM region. Researchers are advised to consider the physical consequences of the effects that are included or excluded from various methods, as applied to their specific system. It is also prudent to verify results against experimental evidence when possible. 

An alternative approach is to assume, in the light of the experimental evidence just mentioned, that the reactions of cations and neutral molecules have similar values of (or, equivalently, of log ( /l mol and to try to calculate the difference which would arise from the fact that the observed entropy of activation for a minority free base includes a contribution from the acidic dissociation of the conjugate acid in the medium in question (see (5) above). Consider the two following reaction schemes one (primed symbols) represents nitration via the free base, the other the normal nitration of a non-basic majority species (unprimed symbols) ... 

Experimental evidence (523, 524) agrees with the trend suggested by HMO treatment (see the introduction to Part 2 of this volume), which predicts the preference of the amino structure. 

The mechanism includes two single electron transfers (steps 1 and 3) and two proton transfers (steps 2 and 4) Experimental evidence indicates that step 2 is rate determining and it is believed that the observed trans stereochemistry reflects the dis tribution of the two stereoisomeric alkenyl radical intermediates formed in this step... 

From the earliest days, the BET model has been subject to a number of criticisms. The model assumes all the adsorption sites on the surface to be energetically identical, but as was indicated in Section 1.5 (p. 18) homogeneous surfaces of this kind are the exception and energetically heterogeneous surfaces are the rule. Experimental evidence—e.g. in curves of the heat of adsorption as a function of the amount adsorbed (cf. Fig. 2.14)—demonstrates that the degree of heterogeneity can be very considerable. Indeed, Brunauer, Emmett and Teller adduced this nonuniformity as the reason for the failure of their equation to reproduce experimental data in the low-pressure region. 

For other adsorptives the experimental evidence, though less plentiful than with nitrogen, supports the view that at a given temperature the lower closure point is never situated below a critical relative pressure which is characteristic of the adsorptive. Thus, for benzene at 298 K Dubinin noted a value of 017 on active carbons, and on active charcoals Everett and Whitton found 0-19 other values, at 298 K, are 0-20 on alumina xerogel, 0-20-0-22 on titania xerogel and 017-0-20 on ammonium silicomolybdate. Carbon tetrachloride at 298 K gives indication of a minimum closure point at 0-20-0-25 on a number of solids including... 

Temperature rather than frequency is the independent variable. We have previously noted the equivalency of these variables. Figure 3.16 may be taken as experimental evidence for that. 

Other correlations based partially on theoretical considerations but made to fit existing data also exist (71—75). A number of researchers have also attempted to separate from a by measuring the latter, sometimes in terms of the wetted area (76—78). Finally, a number of correlations for the mass transfer coefficient itself exist. These ate based on a mote fundamental theory of mass transfer in packed columns (79—82). Although certain predictions were verified by experimental evidence, these models often cannot serve as design basis because the equations contain the interfacial area as an independent variable. 

The saturation magnetization, J), is the (maximum) magnetic moment per unit of volume. It is easily derived from the spia configuration of the sublattices eight ionic moments and, hence, 40 ]1 per unit cell, which corresponds to = 668 mT at 0 K. This was the first experimental evidence for the Gorter model (66). The temperature dependence of J) (Fig. 7) is remarkable the — T curve is much less rounded than the usual BdUouia function (4). This results ia a relatively low J) value at RT (Table 2) and a relatively high (—0.2%/° C) temperature coefficient of J). By means of Mitssbauer spectroscopy, the temperature dependence of the separate sublattice contributions has been determined (68). It appears that the 12k sublattice is responsible for the unusual temperature dependence of the overall J). 

Physical or chemical vapor-phase mechanisms may be reasonably hypothesized in cases where a phosphoms flame retardant is found to be effective in a noncharring polymer, and especially where the flame retardant or phosphoms-containing breakdown products are capable of being vaporized at the temperature of the pyrolyzing surface. In the engineering of thermoplastic Noryl (General Electric), which consists of a blend of a charrable poly(phenylene oxide) and a poorly charrable polystyrene, experimental evidence indicates that effective flame retardants such as triphenyl phosphate act in the vapor phase to suppress the flammabiUty of the polystyrene pyrolysis products (36). 

Surface Tension. Interfacial surface tension between fluid and filter media is considered to play a role in the adhesion of blood cells to synthetic fibers. Interfacial tension is a result of the interaction between the surface tension of the fluid and the filter media. Direct experimental evidence has shown that varying this interfacial tension influences the adhesion of blood cells to biomaterials. The viscosity of the blood product is important in the shear forces of the fluid to the attached cells viscosity of a red cell concentrate is at least 500 times that of a platelet concentrate. This has a considerable effect on the shear and flow rates through the filter. The surface stickiness plays a role in the critical shear force for detachment of adhered blood cells. 

Hydroxides. The hydrolysis of uranium has been recendy reviewed (154,165,166), yet as noted in these compilations, studies are ongoing to continue identifying all of the numerous solution species and soHd phases. The very hard uranium(IV) ion hydrolyzes even in fairly strong acid (- 0.1 Af) and the hydrolysis is compHcated by the precipitation of insoluble hydroxides or oxides. There is reasonably good experimental evidence for the formation of the initial hydrolysis product, U(OH) " however, there is no direct evidence for other hydrolysis products such as U(OH) " 2> U(OH)" 2> U(OH)4 (or UO2 2H20). There are substantial amounts of data, particulady from solubiUty experiments, which are consistent with the neutral species U(OH)4 (154,167). It is unknown whether this species is monomeric or polymeric. A new study under reducing conditions in NaCl solution confirms its importance and reports that it is monomeric (168). 8olubihty studies indicate that the anionic species U(OH) , if it exists, is only of minor importance (169). There is limited evidence for polymeric species such as Ug(OH) " 25 (1 4). 

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