Experimental data

Data can be derived in several ways, but an experiment is the process we intuitively link with deriving data. Even mental activities are often called mental experiments, especially in quantum mechanics. The better the experiment, the less noisy are the 

More details can be found in Chapter IV, Section 2.2 of the Handbook. 

Prom our data bank, see chapter 8, we selected the following data 

18 structure of cyclohexane, plus selected low frequencies of ethane 

Experimental data have been published for several thousand binary and many multicomponent systems. Virtually all the published experimental data has been collected together in the volumes comprising the DECHEMA vapour-liquid and liquid-liquid data collection, DECHEMA (1977). The books by Chu et al. (1956), Hala et al. (1968, 1973), Hirata et al. (1975) and Ohe (1989, 1990) are also useful sources. 

Thermal analysis data on lamellar crystals of polyethylene over a wide range of thicknesses are plotted in Fig. 2.90. The Gibbs-Thomson equation is a good mathematical description of the observed straight line and can be used to calculate the equilibrium melting temperature by setting C = (t ° = 414.2 K). Also, the ratio of the surface free energy to the heat of fusion can be obtained from the equation. 

Experimental Data for the Melting of Lamellar Crystals of Polyethylene 

In Fig. 1 we display the data of Reference [3]. Notice that the P2 results from NMR, optical and diamagnetic anisotropy, and Raman measurements all agree very well. This is reasonably compelling evidence that all of these techniques, and the Raman technique in particular, are indeed measuring (cos ) . The P data, 

There has been considerable speculation regarding the origin of 

Priestley, P. S. Pershan, R. B. Meyer, and D. H. Dolphin, Raman Scattering from Nematic Liquid Crystals. A Determination of the Degree of Ordering, Vijnana Parishad Anusandhan Patrika, Vol. 14, p. 93 (1971). 

3 Shen Jen, N. A. Clark, P. S. Pershan, and E. B. Priestley, Raman Scattering from a Nematic Liquid Crystal Orientational Statistics, Phys. Rev. Lett., Vol. 31, p. 1552 (1973) E. B. Priestley and P. S. Pershan, Investigation of Nematic Ordering Using Raman Scattering, Mol. CrysL Liquid Cryst., Vol. 23, p. 369 (1973) and E. B. Priestley and A. E. Bell (to be published). 

Wojtowicz, Generalized Mean Field Theory of Nematic Liquid Crystals, Chapter 4. 

A selection of the available data is given in Tables 6.2-6.4. With the exception of 3-methylhex-l-ene, the alk-l-enes higher than but-l-ene give 75 8% trans products (Table 6.2). The lower percentage trans in the product from 3-methylhex-l-ene is attributed to repulsive interactions involving the a-methyl group in the intermediate tran -metallacyclobutane (Kawai 1989). 

In going from Cr to Mo to W in a given type of catalyst system there is some decrease in stereoselectivity with respect to the formation of c/s-MeCH=CHMe from c/5-EtCH=CHMe. Thus the cis content of the but-2-ene decreases as follows (Leconte 1979b, 1980)  

Although, on the whole. Mo-based catalysts tend to be more stereoselective than W-based catalysts, it should nevertheless be noted that some of the highest stereoselectivities are observed with W-based catalysts. 

In the liquid-phase metathesis of linear internal olefins RCH=CHR on Re207/ CSNO3/AI2O3, the trans content of the products increases with the size of R or R. The trans content in the dec-5-ene produced in the metathesis of BuCH=CHR decreases from 71% to 67% to 64% as R is changed from H to Me to Et (Kawai 1988). 

Comparison with Experimental Data 1. Fluidized Beds 

Yamashita and Inoue (1975), Maruyama et al (1981), and Chisti (1989) have measured the values of critical superficial gas velocity for transition. 

The details pertaining to the experiments along with the comparison between model predictions and experimental observations is shown in Table XL It can be seen that the agreement is favorable over a wide range of column widths, hole diameters, and numbers of holes. 

It has been pointed out earlier that the maximum possible hold-up in the homogeneous regime is 42%. This prediction compares favorably with the experimental observations of Maruyama et al (1981) and Koetsier et al (1976). 

Due to experimental difficulties only shielding data for covalent chlorine compounds have been reported. An exception is the 10 ion which will be further discussed in Chapter 9. The experimental diffi- 

In Table 3.3 we have collected most of the experimental halogen shielding data for pure liquids reported in the literature and added some new data recorded in our laboratory. We have also included data for some aqueous solutions. Omitted are a few old shielding values later clearly determined with higher accuracy using modern NMR spectrometers. Practically all chlorine NMR shielding data have been obtained 

Let us now contemplate the shielding data in Table 3.3 and try to find some general patterns. (The following discussion unfortunately has to be somewhat crude and limited in view of the large error in the reported shieldings and the possible importance of medium effects.) 

Shifts equal for central and terminal Cl atom. Determined indirectly from kinetic data. 

VCI4 285 -990 + 50 [230] Compound is paramagnetic and shift temp, dependent. Value of diamagn. shift estimated. 

In this Section we shall discuss experimental data concerning both these pathways. We shall start our discussion with the carrier-mediated mechanisms since it has been studied in more detail. 

For many systems of Table 1 excited molecules are not themselves involved in the stage of the electron transfer across the membrane. They are rather used in the previous stage for the generation of the intermediate radicals which serve as electron carriers. 

Note that equilibrium (34) is shifted to the left. Because of this, with excess dithionite, the measured value of k2 is proportional to the square root of dithionite concentration [171, 172]  

The reoxidation of C16V ut is controlled by its migration to the inner membrane surface  

The direct evidence for the fact that transmembrane electron transfer is provided by the migration of the reduced carrier across the membrane from one aqueous phase to another was obtained also for such water-soluble carriers as methyl-viologen and methylene blue [77, 179]. The corresponding rate constants are 5.3 x 10 2 and 9 x 10 3 s-1. 

The present section is a brief survey of experimental data on electron transfer rate and its theoretical treatment being focused on (a) the Franc-Condon (FC) factor and (b) electronic coupling (resonance integral) V. Role of the media molecular dynamics on ET is discussed in Sections 3.5.1 and 4.1.7 

According to the Marcus (Eqs. 2.9-2.10), the FC value is strongly dependent on medium polarity. For example, for electron transfer between centers with radius about 4 A the following values of the energy reorganization were estimated in eV 0.052 (benzene), 0.12 (acetonitryl) and methanol (0.35). For an aqueous solution a value was estimated within X = 1.0 - 1.3 eV for the centers with radius 3-4 A. Suggesting a dielectric constant of 

Concerning proteins, the X value is strongly dependent on local polarity, which differs in different portions of such a mosaic structure as a protein globule. Positions of the donor and acceptor centers relative to the protein-water interface, chemical nature and mobility of adjacent groups can drastically affect X values. Thus, the precise calculation of real X in biological objects requires special theoretical approaches. 

Ru+2 complexes readily react with surface histidine residues to form stable derivatives. Photochemical methods were used to inject an electron into the Ru3+ site followed by monitoring kinetics of ET from Ru2+to the metalloprotein active site. 

A problem of the experimental measurement of local polarity in the vicinity of donor and acceptor centers incorporated into a protein (bovine serum albumin, BSA) was solved with the use of the dual fluorescence-nitroxide probe (Bystryak et al., 1986 Rubtsova et al., 1993 Fogel et al., 1994 Likhtenshtein, 1993, 1996 Likhtenshtein et al., 2001). In such a hybrid molecule, the photoactive chromophore fragment in the excited singlet state can 

3 Critical Property Isotope Effects 13.3.1 Experimental Data 

13 Reduced Equations of State Critical Property Isotope Effects 

2 Correlations Between Critical Property and Vapor Pressure IE s In(Te /Tc) andln(P fP) 

Correlating ln(Pc /Pc), with vapor pressure data For isotopomer pairs with the vapor pressure and VPIE established near Tc, a thermodynamic consistency test between ln(Tc7Tc) and ln(Pc /Pc), and calculation of ln(Pc7Pc) from ln(Tc7Tc) is possible. The critical pressure of the heavier isotopomer at its critical temperature, Pc(Tc), can be calculated from the lighter, Pc,(Tc7 provided the vapor pressure of the lighter between Tc and Tc, the VPIE, and Tc and Tc are known. For Tc Tc  

The integrals extend over the narrow range, Tc to Tc. Also d ln(P/)/dT is available to sufficient accuracy from vapor pressure data but is not required at high precision because the range of the integration is short. 

Daily exposure of workers (mg/kg body weight) at TLV levels of chemicals (OSHA, 1976) was compared to effective doses of the chemical in experimental animals (see ref. 14). 

It should be emphasized that this kind of comparison is quite theoretical, and it does not provide absolute unsafe exposures, nor does it specify safe levels. However, with the present understanding of the animal experiments it would appear prudent to lower the TLV values for the compounds for which the human exposure may be up to 1/100 of the effective human dose. Even though the extrapolation from animal tests is compounded by uncertainties, the revision of the hygienic standards concerning the pregnant worker appears justifiable in such cases. With ever-increasing female participation in the work force, more emphasis should be placed on reproductive hazards and their prediction, in the absence of adequate epidemiologic data, from experimental results. 

Reproductive hazards in the workplaces can be identified through epidemiologic research, outcomes such as spontaneous abortions and malformations require large sample sizes that cannot usually be collected from single workplaces. Several workplaces need to be pooled and a coordinated effort is required in the execution of the studies. However, a systematic follow-up of the rates of spontaneous abortions and malformations by industrial physicians may offer clues to reproductive hazards. On other outcomes, such as birthweight of children and sperm abnormalities in exposed men, smaller sample sizes are required but many types of confounding factors may exist that impede the interpretation of the results. 

Strobino. J. Kline, and Z. Stein, Chemical and physical exposures of parents Effects on human reproduction and offspring. Early Hum. Dev. 1. 1978, 371. 

Sullivan and S.H. Barlow, Congenital malformations and other reproductive hazards from environmental chemicals. 

In concentrated NaOH solutions, however, the deviations of the experimental data from the Parsons-Zobel plot are quite noticeable.72 These deviations can be used290 to find the derivative of the chemical potential of a single ion with respect to both the concentration of the given ion and the concentration of the ion of opposite sign. However, in concentrated electrolyte solutions, the deviations of the Parsons-Zobel plot can be caused by other effects,126 279 284 e.g., interferences between the solvent structure and the Debye length. Thus various effects may compensate each other for distances of molecular dimensions, and the Parsons-Zobel plot can appear more straight than it could be for an ideally flat interface. 

Mercury in aqueous solutions is undoubtedly the most investigated electrode interface and has been discussed in many reviews.1-1,84,99-109,120,121 There s jittle to add to what is already known. 

A variety of methods have been used to measure Ea=0 in the absence of specific adsorption (essentially, NaF and Na2S04 solutions at c — O). 

A typical set of experimental data290a,290b is shown in Fig. 11. All measurements converge to the value measured by Grahame.286 At present, the of Hg in water can be confidently indicated5 as -0.433 0.001 V (SCE), i.e., -0.192 0.001 V (SHE). The residual uncertainty is related to the unknown liquid junction potential at the boundary with the SCE, which is customarily used as a reference electrode. The temperature coefficient of of the Hg/H20 interface has been measured and its significance discussed.7,106,1 8,291 

The entropy of formation of the Hg/solution interface has been determined for a number of solvents.81,108,291-294,304 It is positive for all 

As described in the Introduction, it is usually possible to consider the modeling of experimental data separately from the scheme actually used to move atoms about. Ideally, the different models should be able to be used in the different minimization or dynamics schemes. Thus, the subsequent sections describe the kind of data offered by NMR and the kinds of penalty functions or pseudo-energy terms that can be used to represent them. For convenience, we use nomenclature common to force field-based approaches where one refers to a distance constraint potential Vdc r) as a function of intemudear distance. 

For each species for which the comparison was done, a page describing the source of the experimental data and the parameters used for each modri preceeds a listing of the calculated and experimental activity coefficients and a plot of these results. 

From H.S. Harned and B.B. Owen, The Physical Chemistry of Electrolytic Solutions, third edition. Reinhold Publishing Corporation, New York (1958) p. 716 

Harned and Owen presented tabulated values for the mean activity coefficients of HCl at temperatures from 0 to 60°C for maximum molalities from 2 to 4. The coefficients are from observed electromotive forces for molalities greater than. 001 the values for molalities less than. 002 were extrapolated from plots. 

From H.P. Snipes. C. Manly and D.D. Ensor. Heats of Dilution of Aqueous 

Snipes et al. measured the heats of dilution of KCl over a concentration range of. 005 to 2 molal for temperatures from 40 to 80°C. They used the data to fit the relative apparent molal heat content to a polynomial equation calculated the relative partial molal heat contents of the solvent and solute from the relative apparent molsil heat content data. They then fit the partial molal heat contents of the solute to a polynomial equation of the form  

Unfortunately, in practice, the application of such approaches is strongly limited by the available experimental data, which in most cases are presented by semi-elfective doses and even by qualitative characteristics active/inactive .  

The determination of biological activity is always associated with some experimental errors, which may be caused by variability of biological objects, inaccuracy of measurements due to the limited precision of the used equipment, inaccuracy of the personnel doing manual and mental work. 

If the experimental measurements have been repeated several times, the resultant data are presented as average values and standard deviations (SDs) of the measurements. In many cases numerical data in the literature and, particularly, in databases are presented without SDs even in cases where such values could be calculated on the basis of primary data. Also, the results of testing in high-throughput assays for inactive compounds typically mean that the compound does not cause the studied effect at a certain threshold, e.g., at 10 [tm, 1 pM, etc.  

Experimental errors associated with human error may be introduced both in experimental procedures (e.g., inaccuracies of sample preparation) and in theoretical analysis of the study results (e.g., errors in data drawing in publications, errors during the input of data into a computer). 

After summarizing our experiences with the quality assurance of chemical data in predictive toxicology, we conclude that the currently available databases and computational chemistry programs are too faulty to be trusted without further inspection. The development of reliable quality control procedures definitely needs more discussion, exchange of experience, and research activity. In this sense, we hope that we will raise some awareness in regard to data quality issues and quality assurance in predictive toxicology. 

The behavior of 3 found in these experiments resembles to the one of a kinetic product of considerably lower stability than the thermodynamic product (2). That is, it disappears from observation as the reaction evolves and gets closer to the equiUb-rium concentrations, where the concentration of 3 is very small. Indeed, this can be observed from the concentration versus time data obtained by monitoring the reaction at 223 K (Fig. 4.3a) the concentration of 2 increases continuously, whereas a small accumulation of 3 is initially produced followed by a decrease in its concentration, so that after 300min it has practically disappeared.  

3 Concentration versus time data obtained by NMR spectroscopy for the reaction of 1 with ZnMeCl in different conditions a ratio 1 20, in THF at T = 223 K. Starting conditions [l]o = 0.01 M [ZnMeClJo = 0.20 M b ratio 1 1, in THF at T = 203 K (in this case 1 is not plotted because its abundance is above the values represented in the ordinate axis). Starting conditions [l]o = 0.056 M [ZnMeCllo = 0.056 M 

Another surprising finding was the fact that despite the transient existence of 3 in the transmetalation reactions, this species prepared by an alternative method was found to be fairly stable. In particular, it took 10 h in THF at 273 K for about half of it to isomerize to 2, whereas at 223 K the 3 to 2 isomerization rate was negligible. On the other hand, the addition of ZnCl2 to a solution of 3 in THF at 223 K, produced the instantaneous and complete transformation of 3 to 1. In the same conditions (i.e. addition of ZnCl2), compound 2 was also transformed into 1 until equilibrium was reached. In other words, the transmetalations between 1 and ZnMeCl to give 2 or 3 are quickly reversible. Hence, these experiments demonstrated that the fast 3 to 2 isomerization observed in Fig. 4.3 is not a direct isomerization, which is slow, but a retrotransmetalation of 3 to 1 followed by transmetalation to 2. 

Finally, the concentration versus time data for the reaction monitored at 223 K (Fig. 4.3a) were fitted to the kinetic model shown in Fig.4.4, thereby allowing the calculation of the transmetalation and retrotransmetalation rates at this temperature. Then, from these rates, the relative Gibbs energies at that temperature (AG223 a ) for 1, 2, 3 and for the transition states that connect these species (TSi 2 and TSi 3) were obtained (Fig. 4.4). The calculated Gibbs energies indicate that the transmetalation from 1 to 3 requires Ikcal mol less than the transmetalation from 1 to 2. This, in terms of reaction rates, means that the transmetalation from 1 to 3 

It is noteworthy to mention that the fact that the experimental results have been 

In most cases of reactions showing a C.E. the relation between A and AE can be represented by the empirical formula 

Examples of the Occurrence of a C.E. if the Composition of the Catalyst or of the Substrate is Changed  

Catalyst (reference) Test reaction Interval of pretreatment, °C. T. A log A 

Arrhenius plot), and the maximuna difference in A (A log A) are given in special columns. 

Systems biology proposes high-level models that attempt to explain a complex series of events that occur at the biochemical level. The derivation and vahdation of such a 

The basic class definitions and other infrastructure are provided in the Biobase package. The base class is the eSet and it has places to store assay data, phenotypic information, and data about the features that were measured and about the experiment that was performed to collect these data. This basic class can then be extended in many different ways, specializing in some of the inputs, and in some cases adding new slots that are relevant to a specific type of experiment. The eSet class has been extended to support expression data, SNP data, and genomic annotation. For expression data the ExpressionSet class has been defined, and it too is quite general. The class can be used for any sort of expression (and is in no way restricted to microarray experiments for mRNA expression, although that is where it is used most). Similar data structures have been used for representing data from experiments in protein mass spectrometry and flow cytometry. 

Experimental datasets are useful for prototyping, testing, and demonstrating statistical methods. There are a number of sources of sample datasets accessible from Bioconductor, including the Bioconductor repository and the GEO database. In the Bioconductor repository, there is a collection of R packages that contain experimental data from different high-throughput experiments and the current set can be found by 

The following code loads the ExpressionSet instance, named fhesc, into R  

SamplelD Sample ID Diff Diff Differentiated or Not featureData 

Hammett and Hammett-Brown Substituent Constants Encouraged by the latter 

NMR chemical shifts (in ppm, 75 MHz, CDCl ), taken from Ref [19]. Potential (in V), taken from Ref. [19]. 

It is evident that BSUs are not identified as coronene or ovalene but are made of a hexagonal core in the size range of 8 to 10 A saturated at its edges not only by hydrogen but also by various functional groups. 

FIGURE 1.25 Geometric arrangements for aromatic molecules (a) coronene trimer (b) part of coronene crystal structure (c) case of four aromatic molecules (basic structural unit limit size). (From E.R. Vorpagel and J.G. Lavin. Most stable configurations of polynuclear aromatic hydrocarbon molecules in pitches via molecular modelling. Carbon 30, 1033-1040 (1992). With permission from Elsevier.) 

Visualization in TEM of single BSUs [32,33] is not possible by using interference images, becanse randomization cannot be avoided due to object thickness. In a 100-A-thick object, whether edge-on or face-on, more than 10 single BSUs are thereby superimposed (see Section 1.1.3.2.1). 

The disordered carbons are made of BSUs that are organized enough to give rise to scattering. In Section 1.3 we discuss the disorder that occurs before and after turbostratic 2D order and that eventually leads to the formation of graphite. 

Q is high which means that diffusion occurs at a high rate for oxide growth at the high temperature range 900 (7 T ISSO C. 

E xample 10.8 Calculate the thickness of AhOz oxide when pure aluminum is exposed to oxygen environment at 600°C and 1 atm for one day. Use the Kw value from Table 10.2 and Pm Os 3-80 glam . 

Both carburizing and nitriding are also oxidizing processes, which are important in industrial applications for enhancing the hardness and strength of steels. Therefore, these methods are out of the scope of this chapter. 

These remarkable differences dictate that carbon and chromium contents control the thickness growth for carbon and stainless steels. 

HTO in hot gases may occur internally or externally, and it is characterized by its quality through the HUing-Bedworth ratio. Thermodynamically, the occurrence of an oxidation reaction at high temperatures may be predicted by the Gibbs free energy of formation if AG 0, which dictates that a M Oy product forms by diffusion. 

It is often tempting to conclude that a crystal structure of a host-guest complex does 

An example of this problem is provided by our work on the interaction of urea and thiourea with crown ethers[23]. Five crystal structures have been carried out on these systems (18-crown-6)(thiourea)2, [24] (18-crown-6)(urea)5, [25], (18-crown-6)(N-methylthiourea) [26], (18-crown-6)(chlorophenylurea)2, [27] and (18-crown-6)(thiourea)4 [28]. In all these structures there are intermolecular hydrogen bonds between the amine hydrogen atoms and the oxygen atoms in the 18-crown-6. The pattern of hydrogen bonds is different in the five structures. 

In order to establish structure-propertj relationships between the molecular com 

There are, however, only a few methods which provide correct absolute order parameters for liquid crystals. The comparison of the absolute anisotropies given in Table 2 may therefore not always 

The influence of a lateral substitution of ring hydrogen atoms in cyanophenyl esters has been studied in detail by Schad and 

The susceptibility curve for E2 can be used to compare the different methods for determining the molar diamagnetic anisotropy The Haller extrapolation gives 

For comparison, we estimated AXq from tensor increments, considering only the aromatic molecular segments. The contributions AXq 0 of the different molecular species i with molar fractions (i) in a mixture are additive  

---

The accuracy of our calculations is strongly dependent on the accuracy of the experimental data used to obtain the necessary parameters. While we cannot make any general quantitative statement about the accuracy of our calculations for multicomponent vapor-liquid equilibria, our experience leads us to believe that the calculated results for ternary or quarternary mixtures have an accuracy only slightly less than that of the binary data upon which the calculations are based. For multicomponent liquid-liquid equilibria, the accuracy of prediction is dependent not only upon the accuracy of the binary data, but also on the method used to obtain binary parameters. While there are always exceptions, in typical cases the technique used for binary-data reduction is of some, but not major, importance for vapor-liquid equilibria. However, for liquid-liquid equilibria, the method of data reduction plays a crucial role, as discussed in Chapters 4 and 6. 

Compilation of binary experimental data reduced with the Wilson equation and, for high pressures, with a modified Redlich-Kwong equation. 

It is important to be consistent in the use of fugacity coefficients. When reducing experimental data to obtain activity coefficients, a particular method for calculating fugacity coefficients must be adopted. That same method must be employed when activity-coefficient correlations are used to generate vapor-liquid equilibria. 

When no experimental data at all are available, activity coefficients can sometimes be estimated using the UNIFAC method (Fredenslund et al., 1977a, b). However, for many real engineering problems it is often necessary to obtain new experimental data. 

Since the accuracy of experimental data is frequently not high, and since experimental data are hardly ever plentiful, it is important to reduce the available data with care using a suitable statistical method and using a model for the excess Gibbs energy which contains only a minimum of binary parameters. Rarely are experimental data of sufficient quality and quantity to justify more than three binary parameters and, all too often, the data justify no more than two such parameters. When data sources (5) or (6) or (7) are used alone, it is not possible to use a three- (or more)-parameter model without making additional arbitrary assumptions. For typical engineering calculations, therefore, it is desirable to use a two-parameter model such as UNIQUAC. 

The most reliable estimates of the parameters are obtained from multiple measurements, usually a series of vapor-liquid equilibrium data (T, P, x and y). Because the number of data points exceeds the number of parameters to be estimated, the equilibrium equations are not exactly satisfied for all experimental measurements. Exact agreement between the model and experiment is not achieved due to random and systematic errors in the data and due to inadequacies of the model. The optimum parameters should, therefore, be found by satisfaction of some selected statistical criterion, as discussed in Chapter 6. However, regardless of statistical sophistication, there is no substitute for reliable experimental data. 

Predictions for the other isobaric systems (experimental data of Sinor, Steinhauser, and Nagata) show good agreement. Excellent agreement is obtained for the system carbon tetrachlor-ide-methanol-benzene, where the binary data are of superior quality. 

In some cases, the temperature of the system may be larger than the critical temperature of one (or more) of the components, i.e., system temperature T may exceed T. . In that event, component i is a supercritical component, one that cannot exist as a pure liquid at temperature T. For this component, it is still possible to use symmetric normalization of the activity coefficient (y - 1 as x - 1) provided that some method of extrapolation is used to evaluate the standard-state fugacity which, in this case, is the fugacity of pure liquid i at system temperature T. For highly supercritical components (T Tj,.), such extrapolation is extremely arbitrary as a result, we have no assurance that when experimental data are reduced, the activity coefficient tends to obey the necessary boundary condition 1... 

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the... 

Figure 4-14. Predicted liquid-liquid equilibria for a typical type-II system shows good agreement with experimental data, using parameters estimated from binary data alone.

The total number of experimental data points is N. Data points 1 through L and L+1 through M refer to VLB measurements (P, T,... 

Enthalpies are referred to the ideal vapor. The enthalpy of the real vapor is found from zero-pressure heat capacities and from the virial equation of state for non-associated species or, for vapors containing highly dimerized vapors (e.g. organic acids), from the chemical theory of vapor imperfections, as discussed in Chapter 3. For pure components, liquid-phase enthalpies (relative to the ideal vapor) are found from differentiation of the zero-pressure standard-state fugacities these, in turn, are determined from vapor-pressure data, from vapor-phase corrections and liquid-phase densities. If good experimental data are used to determine the standard-state fugacity, the derivative gives enthalpies of liquids to nearly the same precision as that obtained with calorimetric data, and provides reliable heats of vaporization. 

In typical situations, we do not have the necessary experimental data to find constants b... To obtain these constants, we need experimental vapor-liquid equilibria (i.e. activity coefficients) as a function of temperature. 

The accuracy of the calculations depends directly on the reliability of the experimental data. The correlated data presented in the Appendices were taken from standard literature sources while these data are probably reliable for most fluids, it is not possible to be certain that they are reliable for all. 

The sum of the squared differences between calculated and measures pressures is minimized as a function of model parameters. This method, often called Barker s method (Barker, 1953), ignores information contained in vapor-phase mole fraction measurements such information is normally only used for consistency tests, as discussed by Van Ness et al. (1973). Nevertheless, when high-quality experimental data are available. Barker s method often gives excellent results (Abbott and Van Ness, 1975). 

The primary purpose for expressing experimental data through model equations is to obtain a representation that can be used confidently for systematic interpolations and extrapolations, especially to multicomponent systems. The confidence placed in the calculations depends on the confidence placed in the data and in the model. Therefore, the method of parameter estimation should also provide measures of reliability for the calculated results. This reliability depends on the uncertainties in the parameters, which, with the statistical method of data reduction used here, are estimated from the parameter variance-covariance matrix. This matrix is obtained as a last step in the iterative calculation of the parameters. 

The maximum-likelihood method, like any statistical tool, is useful for correlating and critically examining experimental information. However, it can never be a substitute for that information. While a statistical tool is useful for minimizing the required experimental effort, reliable calculated phase equilibria can only be obtained if at least some pertinent and reliable experimental data are at hand. 

Convergence is usually accomplished in 2 to 4 iterations. For example, an average of 2.6 iterations was required for 9 bubble-point-temperature calculations over the complete composition range for the azeotropic system ehtanol-ethyl acetate. Standard initial estimates were used. Figure 1 shows results for the incipient vapor-phase compositions together with the experimental data of Murti and van Winkle (1958). For this case, calculated bubble-point temperatures were never more than 0.4 K from observed values. 

Appendix C presents the best set of constants for Equation (2). Also shown are the temperature limits of the real experimental data. Users must exercise caution when using the correlation outside the range of real data such use should, in general, be avoided. 

Appendix C-6 gives parameters for all the condensable binary systems we have here investigated literature references are also given for experimental data. Parameters given are for each set of data analyzed they often reflect in temperature (or pressure) range, number of data points, and experimental accuracy. Best calculated results are usually obtained when the parameters are obtained from experimental data at conditions of temperature, pressure, and composition close to those where the calculations are performed. However, sometimes, if the experimental data at these conditions are of low quality, better calculated results may be obtained with parameters obtained from good experimental data measured at other conditions. 

NOTE - r NG GIl ES THE TENPERArURE RANGE tKl OF THE EXPERIMENTAL DATA USED TO FIT THE CONSTANTS CONSTANTS FOR NCNCONDENSABLES CCOMPONENTS 1-B) MERE DETERMINED FROM A GENERALIZED CORRELATION FOR THE HYPOTHETICAL REFERENCE FUGACITY. 

H. The next cards provide estimates of the standard deviations of the experimental data. At least one card is needed with non-zero values. Units are the same as those of the VLE data. FORMAT(4f10.2,I2). ... 

In spite of considerable development of thermodynamics and molecular theory, most of the methods used today are empirical and their operation requires knowledge of experimental values. However, the rate of accumulation of experimental data seems to be slowing down even though the need for precise values is on the rise. It is then necessary to rely on methods said to be predictive and which are only estimates. 

Characteristics are the experimental data necessary for calculating the physical properties of pure components and their mixtures. We shall distinguish several categories ... 

The viscosity coefficient fjP can also be derived from experimental data. 

The contact fatigue creates independent part of the fatigue tests. As consequence of triaxial state of stress and flexible plastic state in contact area occurrence comes to very considerable scattering of experimental data. From this reason it is necessary to test statistic meaningful number of samples. 

To search for the forms of potentials we are considering here simple mechanical models. Two of them, namely cluster support algorithm (CSA) and plane support algorithm (PSA), were described in details in [6]. Providing the experiments with simulated and experimental data, it was shown that the iteration procedure yields the sweeping of the structures which are not volumetric-like or surface-like, correspondingly. While the number of required projections for the reconstruction is reduced by 10 -100 times, the quality of reconstruction estimated quantitatively remained quite comparative (sometimes even with less artefacts) with that result obtained by classic Computer Tomography (CT). 

Eddy-current non-destructive evaluation is widely used in the aerospace and nuclear power industries for the detection and characterisation of defects in metal components. The ability to predict the probe response to various types of defect is highly valuable since it enables the influence of particular parameters to be studied without recourse to costly and time consuming experiments. The solution of forward problems is also essential in the process of inverting experimental data. 

This paper compares experimental data for aluminium and steel specimens with two methods of solving the forward problem in the thin-skin regime. The first approach is a 3D Finite Element / Boundary Integral Element method (TRIFOU) developed by EDF/RD Division (France). The second approach is specialised for the treatment of surface cracks in the thin-skin regime developed by the University of Surrey (England). In the thin-skin regime, the electromagnetic skin-depth is small compared with the depth of the crack. Such conditions are common in tests on steels and sometimes on aluminium. 

The sampling precision of the measured data depends on the signal amplitude. The difference between simulated and experimental data can be mainly explained by the low numerical precision of the measured data. 

Numerical Modeling of eddy current steam generator inspection Comparison with experimental data, P.O. Gros, Review of Progress in Quantitative Nondestructive Evaluation, Vol 16 A, D.O. Thompson D. Chimenti, Eds (Plenium, New York 1997) pp 257-261. 

Abstract An Eddy current method applying a High Temperature Superconductor ( HTS ) DC SQUID sensor operating at Uquid nitrogen temperature (77K) is presented. The method is developed for the detection of surface or surface near defects. We compare the performance of the SQUID system with the performance gained from a commercial Eddy current system, while using identical probes. The experimental data are obtained on defects in gas turbine blades. The advantage of planar conformable probes for the use with the SQUID is discussed. 

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