Theoretical aspect

Theoretical understanding is important for the development and analysis of microwave sintering technique. For example, optimization of processing parameters 

The distribution of electromagnetic field within the materials to be processed is determined by various factors, such as effective dielectric and magnetic parameters of the materials that are dependent on temperature and microstracture, dimensions and properties of the applicator, and the degree of matching between the microwave source, transmission line, and applicator. Consequently, the distribution of the electromagnetic field will affect the distribution of temperature within the sintered object. Of course, other factors, such as effective absorption properties, heat capacity, and thermal conductivity of the materials, as well as heat transportation characteristics of the materials and the furnaces, wiU also have their specific effects. Ultimately, all these will be reflected by the properties of the final sintered products. While detailed theoretical elaboration of microwave sintering can be found in Ref. [39], a brief description will be presented in this section. 

the electric field, in the three regions, can be written in the form  

Similarly, expressions for the magnetic field in the three regions are given by  

In Eqs. (6.38-6.40) and (6.41-6.43), A, B, R, and T are unknown coeflftcients, which are determined the boundary conditions that require continuity of the electric and magnetic field components, and Hy, at the front and back surfaces, i.e., z = 0 and z = a. By imposing four boundary conditions and solving four algebraic equations, the coefficients can be obtained as follows  

There have been a number of different theories concerning the theoretical interpretation of the DTA curve. All the theories relate, in some manner, the area of the differential curve peak to lhe various parameters of the sample 

In the theory developed by Speil et al. (2) and modified by Kerr and Kulp (3), the area enclosed by the differential curve is 

Using a sample block constructed from an infinitely-high-thermal-conductivity metal such as nickel, in which the sample holder geometry is a cylinder, Boersma (44) found that the peak area was equal to 

Lastly, for an infinitely large ceramic block, there are no finite solutions for the one- and two-dimensional cases however, there is a solution for a spherical holder  

In the preceding equations as applied to a conventional DTA apparatus, the sample is used for two entirely different purposes (1) as a producer of heat and (2) as a heat measuring resistance in which the flow of heat develops a temperature difference to be measured. To separate these two functions, Boersma (44) recommended the use of metal sample and reference cups in which the temperature difference was measured from outside the sample and reference materials. The peak area then depended on the heat of reaction by 

Large Scale Configuration in Concentrated Systems 2.2.1. Theoretical Aspects 

In unperturbed random coils, the distribution of end-to-end distances for long chains is Gaussian  

For random coils, r2 is directly proportional to the contour length. If n is the number of main chain atoms in the chain, r2 = an. The parameter a is relatively insensitive to environment (21), and has been calculated for a number of polymers from strictly intramolecular considerations using the rotational isomeric model (22). The root-mean-square distance of segments from the center of gravity of the coil is called the radius of gyration S. The quantity S3 is an approximate measure of the pervaded volume of the coil. For Gaussian coils, 

For dilute solutions in good solvents the net excluded volume is positive, and coil dimensions are expanded beyond their unperturbed values. The expansion 

In Fiery s theory of the excluded volume (27), the chains in undiluted polymer systems assume their unperturbed dimensions. The expansion factor in solutions is governed by the parameter (J — x)/v, v being the molar volume of solvent and x the segment-solvent interaction (regular solution) parameter. In undiluted polymers, the solvent for any molecule is simply other polymer molecules. If it is assumed that the excluded volume term in the thermodynamic theory of concentrated systems can be applied directly to the determination of coil dimensions, then x is automatically zero but v is very large, reducing the expansion to zero. 

This Report is divided into three main sections. The first covers theoretical aspects and attempts to update existing reviews by which the topic is already well served. The second deals with methods for obtaining thermodynamic data, a topic largely neglected by review literature for polymer systems. Remarks more appropriate to particular types of polymer system are gathered in the final section. This section concludes with a source table for data on individual polymer solutions and mixtures as culled from the 1977/8 literature. While it is hoped that this tabulation is as complete as possible, omissions are inevitable and this Reporter would be pleased to receive notice of such so that they can be included in future Reports. 

I would like to thank the Science Research Council for support Professor M. Gordon, Professor R. Koningsveld, Dr. L. A. Kleintjens, and Dr. P. Irvine for helpful comments Dr. A. C. Helgeson for assistance with Slavic references and the Staff of University of Essex Library for their considerable help in 

Introduction.—The thermodynamic relationships governing the mixing of polymer systems are no different from those pertaining to any other kind of system. The ratio Q, of partition function for the mixture to that for its separated constituents, is related to the free energy of mixing AG, by  

Other thermodynamic quantities of interest, such as enthalpy AH, entropy AS, of mixing and chemical potential ftf for the /th component of the mixture, follow from either Q or AG by means of classical thermodynamic results. 

The problem has been approached in several ways leading to a variety of statistical mechanical models, some of which survive, in modified form, in present research. No one of these models has yet emerged as entirely satisfactory when assessed in terms of its ability to account for thermodynamic (and other) experimental data. Reviews comparing models in these terms are available cover- 

Two-photon photoemission involves the absorption of two photons, and the two optical transitions can usually be treated as independent consecutive processes. Energy and momentum conservation have been exploited already in Section 3.2.4.2. The matrix elements could be obtained according to the well-deveIop)ed theories for regular photoemission however, the one-step model of photoemission [47] has not yet been applied to two-photon-photoemission spectra. In the following paragraphs, we discuss a few aspects of time-resolved two-photon-photoemission with femtosecond pulses that do not occur in regular photoemission. 

In a time-resolved two-photon-photoemission experiment, the pulse duration can be comparable to the time scale of the temporal quantum-mechanical evolution of the involved states. The lifetime can be measured in the time domain, if it is long compared to the pulse duration. In the energy domain, the intrinsic Unewidth would then be narrow compared to the spectral bandwidth of the laser pulses and could not be resolved. Similarly, states with an energy difference smaller than the spectral bandwidth caimot be separated in spectroscopy, but may be resolved in the time domain. 

The interaction of the laser fields with the electronic states I leads to a superposition 

In the absence of the laser fields, the time dependence Ci(t) would be given by 

The exponential decay is described by the lifetime rj, and the energy Ei determines the quantum-mechanical phase. The term containing l i(t) describes changes of the 

The hydrophobic indices, i., the ratios of hydrophobic to hydrophilic surface areas, of seven monosaccharides have been determined. They were found to correlate well with the partition coefficients of the polystyrene-water system for monosaccharides. The concept of hydrophobic indices is important in the consideration of the hydrophobic interactions of flat molecules in aqueous solution. In an effort to establish quantitative structure-activity relationships for carbohydrates, an experimental data-matrix containing the values of sixteen monosaccharides in thirteen solvent systems was subjected to principal component analysis (PCA). Four PC s (t -t ) were found 

Several calculations have been made of the electronic structure of benzo[c]thiophene.11-15 The earliest calculation11 based on the 

Hartough and S. L. Meisel, in Compounds With Condensed Thiophene Rings (A. Weissberger, ed.), p. 167. Wiley (Interscience), New York, 1954. 

Zahradnik, C. Parkanyi, V. Horak, and J. Koutecky, Collection Czech. Chem. Commun. 28, 776 (1963). 

There has been no systematic study of the spectra (mass, UV, IR, or NMR) of benzo[c]thiophene derivatives, although spectroscopic data have been recorded for individual compounds in the more recent literature. The spectroscopic data for benzo[c]thiophene itself have been recorded,5,6,12,15,16 the IR spectrum of l,3-diphenylbenzo[c]-thiophene has been studied in some detail,17 and the excitation and 

It is noteworthy that HMO calculations have been made of the energy characteristics of the carbonium ion (4).19 

Furthermore, it was found that I I2Si=S is thermodynamically stable compared with H2Si=0. In an attempt to assess the strength of a silicon-sulfur double bond, a comparison was made of the hydrogenation energies released upon addition of H2 

The zero-point corrected MP3/6-31G 76-31G value of 174.7 kcal mol-1 for H2C=0 agrees well with the experimental value of 171.7 kcal mol-1. The proton affinities increase in the order 3 (174.7 kcal mol-1) 1 (190.5 kcal mol-1) 2 (208.3 kcal mol-1). This is explained in terms of the predominance of the electrostatic overcharge transfer interactions, because the charge separations in the double bonds increase in the order H2C+0 2-0-a4 H2Si+0 7-S-0 4 H2Si+1 0-O-a7 while the frontier n orbital levels rise in the order 3 (—11.8 eV) 2 ( — 1 T9 eV) 1 (—9.8 eV). 

As a result of comparing the properties of silanethione with silanone and formaldehyde, Nagase and Kudo obtained an important finding that silicon is much less reluctant to form double bonds with sulfur than with oxygen.12,13 Thus, silanethione is more stable and less reactive than silanone. They concluded that the maj or obstacle to the successful isolation of silanethione is its relatively high reactivity. 

Theoretical Calculation of the Bond Energies and Bond Lengths of Heavy Ketones 

The successful synthesis and isolation of a series of heavy ketones (r r2M = X M = Si, Ge, Sn, Pb X = S, Se, Te) using kinetic stabilization (vide infra) and the remarkable progress in the field of theoretical calculations prompted chemists to perform computational calculations on the a and it bond energies as well as on the single and double bond lengths of H2M=X at the higher level of theory.14 

Until the end of the forties, when the HMO method was first applied to thiazole, most of the experimental results concerning its chemical reactivity remained of a qualitative nature. Papers devoted to the subject 

Most of these theoretical aspects are discussed in the following sections, pointing out the particuliar suitability of the very dissymmetrical molecular frame of thiazole for quantitative study, on the same species, of a large variety of fundamental organic reactions. 

Calculations of31P and 29Si Chemical Shifts of Parent Phosphasilenes 

Rectification effects are due to the asymmetry of a current-voltage curve of an electrode system. The asymmetry of these curves may arise from the intrinsic asymmetry of the charge transfer reaction or from the extraneous asymmetry produced by inequalities in mass 

Devanathan31 obtained the equation for the total rectification current due to mass transfer (JMtr) as 

The total rectification current, JFR, considering charge transfer and mass transfer is given by 

FIGURE 3.31. Reaction of alkyl chlorides with NO as a function of steric hindrance at carbon. Central line reactant state Left-hand lines ET transition and product states. Right-hand lines 5 2 transition and product states. Numbers above and below the lines are the standard free energies (in eV) numbers in parentheses are the entropies in meV/K. The numbers on the structures are bond lengths in A. From MP2/6-31G //UHF/6-31G and COSMO (solvation) calculations. 

ELECTRON TRANSFER, BOND BREAKING, AND BOND FORMATION 

ET transition state is characterized by a looser structure, and accordingly, by a larger entropy than the SN2 transition state. It is interesting to trace the reaction paths from the reactant system to the S 2 and ET products, including the possible bifurcations. 

Nuclei of natural isotopes (atoms of chemical elements differing in the number of neutrons in their nuclei) may possess angular momentum or spin and therefore magnetic moments. One defines spin by the following equation  

The nuclear angular momentum, I, is quantized with magnitude hm, where m = /, /-1, 2. yielding 2 7+1 equally spaced spin states with angular 

The angular momentum and magnetic moment of nuclei act as parallel or antiparallel vectors, and the ratio between these is known as the magnetogyric ratio, y. The magnetogyric ratio is given in terms of equation 3.13  

The low-energy, low-frequency range for NMR transitions corresponds to a small change in energy, AE. This has implications for the population of excited states, the Boltzmann distribution. For a spin-1/2 nuclei with AE= i Bq// and 7=1/2, equation 3.17 applies. Since N N, one can write equation 3.18. 

It is possible to translate these, in three dimensions, as the motion of a magnet of moment p in an applied magnetic field. The magnet axis becomes inclined to the field, precesses around it, and is defined as the Lamour precession. The half-apex angle of the cone equals 0 and the angular velocity is yBo, so that one finds equation 3.16 now rewritten as equation 3.20  

With reference to Fig. 5, the so called quasi Fermi level formalism3 7,1112 is useful for understanding the interfacial energetics at illuminated semiconductor electrolyte interfaces. Thus, in the dark, at equilibrium  

In Eqs. 4a and 4b, x is a position variable since the values of n, p, Etn and Etp are position dependent to varying degrees, Nc and Nv are the densities of states in the conduction and valence bands respectively, k is the Boltzmann constant and T is the absolute temperature. The splitting of the electron and hole quasi-Fermi levels under illumination (Fig. 5b) defines the magnitude of the photovoltage developed, AV (AVm in the specific open-circuit case in Fig. 5b). 

On the basis that the position of Etn at the semiconductor surface is dependent on the photon flux and that Etn has to lie above the HER redox level, a threshold in light intensity has been proposed217 for the sustained photoelectrolysis of water to occur. However, as discussed by other authors,218 no such threshold has been reported in the literature. It has been pointed out218 that the driving force for the photoinduced electron transfer process is related to the difference in standard potentials of the donor (say, an electron at the semiconductor CB edge) and the acceptor (say, protons in solution). This is independent of the carrier concentration and photon flux and thus a light intensity threshold for incipient product formation through photoelectrolysis should not occur.218 

The experimental observations217 of an apparent light intensity threshold for the photocurrent onset have been rationalized218 on the basis that a critical photon flux must be exceeded to counteract the dark current of opposite polarity flowing through the cell. Thus, there appears to be confusion between alternate definitions of a light intensity threshold a threshold for incipient product (say H2) formation and a threshold for product formation in a specific (e.g., standard) state,218 

We consider these materials aspects in the next few Sections. 

Positrons emitted for a radioactive source (such as 22Na) into a polymeric matrix become thermalized and may annihilate with electrons or form positronium (Ps) (a bound state of an electron and positron). The detailed mechanism and models for the formation of positronium in molecular media can be found in Chapters 4 and 5 of this book. The para-positronium (p-Ps), where the positron and electron have opposite spin, decays quickly via self-annihilation. The long-lived ortho positronium (o-Ps), where the positron and electron have parallel spin, undergo so called pick-off annihilation during collisions with molecules. The o-Ps formed in the matrix is localized in the free volume holes within the polymer. Evidence for the localization of o-Ps in the free volume holes has been found from temperature, pressure, and crystallinity-dependent properties [12-14]. In a vacuum o-Ps has a lifetime of 142.1 ns. In the polymer matrix this lifetime is reduced to between 2 - 4 ns by the so-called pick-off annihilation with electrons from the surrounding molecule. The observed lifetime of the o-Ps (zj) depends on the reciprocal of the integral of the positron (p+(rj) and electron (p.(r)) densities at the region where the annihilation takes place  

The analysis of the positron annihilation lifetime spectra is a very important aspect of using the PAL techniques to analyze polymers. Without proper data analysis interpretation of data might be misleading and important scientific information will be lost. In PAL studies of polymers the PAL spectrum can be analyzed in two ways (1) a finite lifetime analysis or (2) continuous lifetime analysis. In the finite lifetime analysis the PAL spectra is resolved into a finite number of negative exponentials decays. The experimental data y(t) is expressed as a convoluted expression (by a symbol ) of the instalment resolution function R(t) and a finite number (n) of negative exponentials  

In continuous lifetime analysis, a PAL spectrum is expressed in a continuous decay form [20]  

In practice the lifetime distributions are usually obtained using a computer program such as the MELT [21] or CONTIN [22, 23] programs. The reliablity of these programs for measurring the o-PS lifetime distribution in polymers was shown by Cao et al [24]. A detailed description of these methods of data analysis is presented in Chapter 4. The advantage of the continuous lifetime analysis is that one can obtain free volume hole distributions rather that the average values obtained in the finite analysis. 

Constitutive equations of the Maxwell-Wiechert tjq)e have received a lot of attention as far as their ability to describe the linear viscoelastic behaviour of pol3maer melts is concerned. From a phenomenological point of view [1-4], these equations can be easily understood and derived using the multiple spring-dashpot mechanical analogy leading to the linear equation  

J = Vu + (Vu) is the rate of strain tensor (u being the fliaid velocity), 

This differential form can be integrated to give the integral form of the model which can also be derived from the Boltzman superposition principle using the concept of fading memory of viscoelastic liquids  

Satisfactory agreement is achieved from these equations for depiction of the main features of linear viscoelastic properties that can be obtained with the experimental tools, either in transient or in oscillatory rheometry. 

These equations are all the more attractive in that similar mathematical forms can also be obtained from molecular considerations for the description of 

The facility of cyclopropanes to react with proton acids and form protonated cyclopropanes—the stability of the complex formed relative to the stability of the cyclopropane—is the basicity of cyclopropane. Protonated cyclopropanes are well established as discrete structural entities and in special circumstances can be generated under conditions where they have a sufficient lifetime to allow spectral investigation. The complex of proton plus cyclopropane can revert to starting species, i.e. cyclopropane and proton, or undergo further reaction, whether rearrangement or addition of a nucleophile. 

The reversion reaction can be probed by isotope labelling experiments and kinetic studies, and rearrangement and nucleophilic attack by labelling studies or, for sufficiently dissymmetric cyclopropanes, by a study of product structure often combined with labelling studies. 

FIGURE 2. Interaction of H Is orbital or C p orbital with the cyclopropane anti-symmetric 3e orbital. 

FIGURE 4. Interaction of Is orbital with the symmetric 3e orbital of cyclopropane 

The X-ray absorption spectrum of Cu,Zn-metallothionein, showing the Cu and Zn K-edges, the demarcation between the X-ray absorption near-edge structure (XANES) and the extended X-ray absorption fine structure (EXAFS), and a pictorial representation of the origin of EXAFS. 

X-ray absorption spectra generally contain two other types of information  

The EXAFS (or XANES) amplitude (k) is defined as the modulation of the absorption coefficient, /u, of a particular atom relative to the smooth background absorption coefficient, fig, normalized by the absorption coefficient that would be observed for a free atom /xq [Eq. (2)]. 

Although EXAFS and XANES are recorded as a function of energy, it is conventional to plot the data as a function of k, the photoelectron wave vector [Eq. (3)] where E is the energy of the X-ray photon, Eq is 

This equation shows the structural basis of EXAFS, in that y(/e) is dependent on the following factors  

In a formal sense, isoindole can be regarded as a IOtt electron system and, as such, complies with the Hiickel (4n + 2) rule for aromatic stabilization, with the usual implicit assumption that the crossing bond (8, 9 in 1) represents a relatively small perturbation of the monocyclic, conjugated system. The question in more explicit terms is whether isoindole possesses aromatic stabilization in excess of that exhibited by pyrrole. 

Several calculations of the electronic structure of isoindoles have been published,and the distribution of charge density around the isoindole nucleus calculated by these methods is summarized in Table I. A common prediction of the calculations, which are based on the LCAO-MO method or the frontier electron concept, is the relatively high electron density to be found at position 1, and the expectation, therefore, is that electrophilic substitution on carbon 

4-position, whereas Longuet-Higgins and Coulson predict the reverse. The semiempirical calculations of Dewar and Polansky and Derflinger estimate a substantial degree of resonance stabilization for isoindole with a value of about 56 kcal/mole. This is significantly larger than the calculated (17-31 kcal/mole ) and experimentally 

Longuet-Higgins andC. A. Coulson, Trans. Faraday Soc. 43, 87 (1947). 

According to a molecular orbital calculation of Veber and Lwowski, isoindole should be favored over its tautomer, isoindolenine, by about 8 kcal/mole. However, the calculated electronic distribution is markedly different in the two cases, particularly at position 1, and it is to be expected that the nature and pattern of substituents will play an important role in determining the position of tautomeric equilibrium between these two species. 

MOMM calculations, have been carried out on H- and 3//-azepine 88MI 90l-0i . The geometries of 1//-azepine are similar to those obtained by ab initio calculations, but with a better defined boat conformation. The MOMM calculations also show that the n-electrons of 3//-azepine are highly localized and that the molecule prefers to exist in a boat conformation, which is predicted to be 4.7 kcal mol more stable than the planar form and 17 kcal mol more stable than l//-azepine. Semiempirical MNDO calculations on a number of methoxy 2,6-alkyl-1//-azepine-1-carboxylates predict that increasing the bulkiness of the alkyl substituent exaggerates the boat conformation 90H(3l)l63 . The angles formed by C —N—Ct and C3—C4—C5—to the plane of the hull are comparable to those obtained by x-ray spectroscopy 81AG(E)699). 

Ab initio calculations at HF, MP2, and CASSCF levels 93JOC6) predict that the singlet nitrenium 

Allinger s MM2 force field has been employed to model the differing stereochemical effects observed in the thermal and anionic Michael addition of compound (1) to acrylates 88JOC3879). Conformational studies have been carried out on 2-amino-6-methyl-4,5,7,8-tetrahydro-6/f-oxazolo[5,4- /]azepine (2) and 2,3,4,5-tetrahydro-l-phenyl-l Af-3-benzazepine (3) using the QCFF/PI method 87JST(37)137 . 

The recyclization of the aza-analogues of benzylium and naphthylmethylium ions to azatropylium ions and their benzylated analogues has been described by a variant of perturbation theory (PPP method) with bond orders on nonbonded atoms used as reactivity indices and the results correlated with the data obtained from mass spectrometry measurements 82KGSI673). 

Molecular dynamics simulation calculations aimed at providing better understanding of the relative sweetness of P-D-glucopyranose, P-D-galactopyranose, and a- and P-D-mannopyranose failed to verify the hydrophobic G site hypothesis proposed by Tinti and Nofre (ACS Symp. Ser., 1991,450, Chapter 15).  

the centrifugal acceleration is a function of the tangential component of the velocity according to the following expression  

The relevant literature on lactose dissolution in water has been reviewed in a paper which describes a mathematical model for this process/ Short time scale molecular dynamics simulations of sucrose in water and DMSO indicated that the conformations in both solvents are similar to that accepted in the crystalline state/ Solid-liquid equilibria for aqueous sucrose have been studied by use of an UNIQUAC model/ A comparison of GROMOS force field and Ha force field in molecular dynamics simulations of glucose crystals indicated superior performance by the latter method/ Predicted crystal structures of P-D-glucose, P-D-galactose, P-D-allose, a-D-glucose, a-D-galactose, and a-D-talose matched or nearly matched the X-ray-derived data in four cases/  

A mathematical description of the retention of ions imder gradient elution conditions was introduced in 1957 by Schwab et al [194]. It is based on parameters that are derived from the normal chromatographic elution process, for which the eluent composition is kept constant during the separation. Hence, the retention of an ion at isocratic elution may be described according to Eq. (3.59), taking into account the definitions for the capacity factor, k, and the selectivity coefficient, K [see Eqs. (3.3) and (3.7)]  

Kjis Gross retention volume Vd Void volume 

Q Ion-exchange capacity of the resin [E] Eluent ion concentration X Charge number of eluent ion y Charge number of solute ion 

With the exception of the eluent ion concentrations, all constants in Eq. (3.59) can be summarized to a general constant, Const,  

A linear relation is obtained by taldng the logarithm on both sides of this equation which is described in a slightly different way in Eq. (3.57)  

This Chaptsr concerns the synthesis, characterisation, reactions, and properties of carbaboranes and their a- and cape-bonded metal derivatives. 

Theoretical Aspects. - Relatively few articles of an original nature have been published. Instead, most concerned the extension of previous work such as Wade s approach to cluster bonding, or the suitability of BH or CH units to cap four-, five-, or slx-membered rings. A hypothetical B H CHICH model was used to analyse the observed C-H bond weakening in the Isolobal analogue [Fe CH] CCD) 

The feasibility of devising localised bond schemes for n-atom borane clusters with eZoso-structures and n, Cn+1], or Cn+2] skeletal electron pairs was examined and compared with results from MO treatments. 

A linear relation is obtained by taking the logarithm on both sides of this equation 

In gradient elution, k changes as a function of the eluant ion concentration, so that it may not be equated with the ratio (Vjns-Vd)/Vd. For a gradient in which the eluant ion concentration increases linearly with time, starting from zero, the momentary eluant ion concentration is calculated by  

V represents the eluant volume delivered since the beginning of the gradient run and R is the slope of the gradient ramp, which is defined as the ratio of the temporal change in the eluant ion concentration and the flow rate. The corresponding momentary capacity factor k for the peak maximum is obtained by inserting Eq. (91) into Eq. (89)  

The compositions of reducing sugars (aldoses, ketoses, mono- and di-saccharides) in solution (76 lefs.) and the hydrophobic behaviour of sugar molecules in aqueous media (33 refs.) have been reviewed. 

The interactions of D-glucopyranose, D-fructopyranose, and sucrose with a proteinaceous receptor have been examined by use of CPK models to validate the steieomolecular inteipretation of sweet taste proposed for these sugars. In continuation of earlier studies (see Vol. 24, Chapter 2, ref. 7) the kinetic effects of 17 free sugars on the hydrolysis of l-benzoyl-3-phenyl-l,2,4-triazole have been measured. Analysis of the results in terms of hydration and stereochemical features led to the conclusion that the relative positions of 2-OH and 4-OH in the sugars are critical.  

The historic development of the understanding of carbohydrate stereochemistry has been briefly reviewed, and a lecture with four references on the energetics and geometry of furanoid tems has been published. Two complementary descriptions of the conformational behaviour of furanose rings have been presented (i) quantum-mechanical energy calculations and (ii) by a geometrical model of pseudorotation in five-membered rings.  

Infrared spectra of adsorbed molecules contain a wealth of information, e.g. 

this information is mostly not directly accessible. Thus for their unravelling, application of theoretical methods like vibrational analysis, group theory and determination of the adsorbent-adsorbate interaction by quantum mechanical or classical means is highly desirable. 

Vibrational analysis has turned out to be an additional valuable tool for giving better insight into details of the changes of molecular properties upon interaction with the zeolite surface. In the case of polyatomics the bonds which are mainly affected by interaction, and to what extent, must be traced out. This is accomplished by comparing the force constants of the free and adsorbed molecules. Furthermore, information on the geometry of the sorption complex may be obtained. Normal coordinate analysis using a harmonic valence force field has been carried out for cyclopropane in faujasites and mordenites, propene in different zeolites A and Y and cis-and /ra/25-but-2-ene in zeolites A [58-61]. 

Examples of the former are studies on small zeolite clusters by Sauer et al. [62], who came to the general conclusion that interaction in zeolites is essentially determined by van der Waals forces [63]. 

Semiempirical calculations of simple molecules on zeolite model clusters were carried out by Beran, Lochmann et al., Kustov et al. and Tasi et al. [64-69]. One of these procedures, the Self Consistent Charge (SCC)-Xa method has been successfully applied also to zeolites [70-76], because of its higher reliability in comparison to other methods in the determination of atomic charges within a reasonable computation time. A combination of semiempirical MO calculations and vibrational analysis supplies detailed information on zeolitic systems when consistently combined with experimental data [77, 78]. 

An essay on the structural representation of sucrose has been published. Following an historical account of the establishment of the constitutional formula and confoimational features of sucrose, the present possibilities for graphics displays of its molecular geometry, contact surfaces, and hydrophobicity potential are given.  

Free energy simulations of the equilibrium between the a- and p-anomers of D-glucopyranose in aqueous solution have been described.  

The hydroxyl acidities of sucrose, assessed through semiempirical calculations of the deprotonation enthalpies, followed the order OH-2g OH-3g OH-3f OH-lf = OH-4g OH-4f OH-6g OH-6f. The molecular electrostatic potential profile of sucrose in polar, aprotic solvents indicated likewise that in the main conformation OH-2g is the most electropositive hydroxyl group the preparations of selectively benzylated and acetylated sucrose derivatives on the basis of these findings are referred to in Chapters 5 and 7, respectively.  

The hydration of a-maltose has been investigated using molecular modelling and thermodynmnic methods. Due to crystallinity, the observed non-freezing water content was lower than that calculated.  

Conformational studies on several free sugars are covered in Chapter 21. 

Calculations of the electronic structures of a series of carbo-hydrates using the CNDO/2 method have produced linear relationships between C-n.m.r. chemical shifts and the atomic charges for the - and /3-D-glucose, u- and d-D-galactose and /3-L-arabinose systems. Model systems, treated by the RHF/ST0-3G method, have been used to evaluate the anomeric -and A effects in simple and 1-0-methylpyrano-sides and hence derive their conformational and anoraeric energies. 

A new kinetic model for the alkaline isomerization and degradation of monosaccharides has been presented. Computer simulations using the model fit the experimental data and allow determination of all relevant rate constants. The rate limiting ste appears to be enolization for both isomerization and degradation. The mechanism of redox reactions between lead hydroxide and 3-0-methyl-D-glucose has been studied by quantum mechanical calculations. The calculations show that there is a redistribution of electron density in both systems which favours the formation of a carboxyl group in the C(1)-G(3) part of the aldose. 

The interactions between the surfaces of some heterogeneous catalysts and mtHiosaccharides, e.g., between gallium(I) and glucose in DMSO, have been described.  

Nuclear transitions involve energies which are orders of magnitude larger than those associated with the excitation of vibrational or electronic states. It thus becomes necessary to account for the effects of mechanical recoil in the emission and absorption of such high-energy radiation in order to interpret the results of resonance-type measurements. 

Daniel A. Scherson Case Center for Electrochemical Sciences and the Department of Chemistry, Case Western Reserve University, Cleveland, Ohio 44106. 

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Cederbaum L S and Domcke W 1977 Theoretical aspects of ionization potentials and photoelectron spectroscopy a Green s function approach Adv. Chem. Phys. 36 205-344 Oddershede J 1987 Propagator methods Adv. Chem. Phys. 69 201-39... 

Tousek J 1985 Theoretical Aspects of the Localized Corrosion of Metals (Rockport, MA TransTech) Boehni H 1987 Corrosion Mechanisms ed F Mansfeld (New York Dekker)... 

Moscowitz A 1962 Theoretical aspects of optical activity Adv. Chem. Rhys. 4 67-112... 

Gascoyne, P.R.C., Pethig, R. Experimental and theoretical aspects of hydration isotherms for biomolecules. J. Chem. Soc. Faradey Trans. 1 (1977) 171-180... 

Further details of the BB, sometimes referred to as Ladyzhenskaya-Babuska-Brezi (LBB) condition and its importance in the numerical solution of incompressible flow equations can be found in textbooks dealing with the theoretical aspects of the finite element method (e.g. see Reddy, 1986), In practice, the instability (or checker-boarding) of pressure in the U-V-P method can be avoided using a variety of strategies. 

Theoretical Aspects and Computer Modelling of the Molecular Solid State A. Gavezotti, Ed., John Wiley Sons, New York (1997). 

One may find many publications in the literature on the theoretical aspects of thiazolium quaternary salts, because of the biological importance of thiamine and their use as catalysts for benzoin condensation. 

The theoretical aspects in eluding pulse sequences that underlie 2D NMR are dis cussed in the May 1990 issue of the Journal of Chemical Education pp A125-A137... 

The study of organic semiconductors and conductors is highly iaterdisciplinary, involving the fields of chemistry, soHd-state physics, engineering, and biology. This article provides a treatment of the theoretical aspects of organic semiconductors as well as an overview of recent advances ia the field and the uses of these materials based on their conductive and optical properties. 

Pyrrole is a colorless, slightly hygroscopic Hquid which, if fresh, emits an odor like that of chloroform. However, it darkens on exposure to air and eventually produces a dark brown resin. It can be preserved by excluding air from the storage container, preferably by displacement with ammonia to prevent acid-catalyzed polymerization. A review of the physical and theoretical aspects of pyrrole is found in Reference 4. Some physical properties of pyrrole are Hsted in Table 1. 

The experimental and theoretical aspects of the radiation and self-induced conversion kinetics and equiUbria between the ortho and para forms of hydrogen, deuterium, and tritium have been correlated (17). In general, the radiation-induced transitions are faster than the self-induced transitions. 

Application of NMR spectroscopy to heterocyclic chemistry has developed very rapidly during the past 15 years, and the technique is now used almost as routinely as H NMR spectroscopy. There are four main areas of application of interest to the heterocyclic chemist (i) elucidation of structure, where the method can be particularly valuable for complex natural products such as alkaloids and carbohydrate antibiotics (ii) stereochemical studies, especially conformational analysis of saturated heterocyclic systems (iii) the correlation of various theoretical aspects of structure and electronic distribution with chemical shifts, coupling constants and other NMR derived parameters and (iv) the unravelling of biosynthetic pathways to natural products, where, in contrast to related studies with " C-labelled precursors, stepwise degradation of the secondary metabolite is usually unnecessary. 

All ctfecis caused by electrostatic or electromagnetic inductions are termed Inductive Interferences. With the use t)f glass optical fibre cables in new installaiioiis. this effect is overcome automatically. Optical fibre cables, as discussed later, have no metal content and cany no electrical signals. Therefore the above discussion is more appropriate for existing installations and also to provide a theoretical aspect and moi c clarity on the phenomena of inductive interferences. These can also be applied to other fields rather than communications alone. 

Stepto, R.F.T., Theoretical aspects of conformation-dependent properties. In Clarson, S.J. and Semiyen, J.A. (Eds.),. Siloxane Polymers, Polymer Science and Technology Series. PTR Prentice Hall, Englewood Cliffs, NJ, 1993, pp. 373-414. 

The basic topic of this chapter is theoretical aspects of air handling units, ductwork design, and the optimization of building energy systems. 

Stephen W. Tsai, Mechanics of Composite Materials, Part It, Theoretical Aspects, Air Force Materials Laboratory Technical Report AFML-TR-66-149, November 1966. 

The existence of a double layer determines the properties of many systems in electrochemistry, in colloidal sciences, in biology, etc. [1-4]. Owing to their importance, electrical double layers have long been and remain a subject of intense research on both experimental and theoretical aspects. This is covered by some recent textbooks and review articles [3,5-10]. 

R. K. Akchurin, D. V. Komarov. Formation of multilayer strained-layer heterostructures by liquid epitaxy. I. Theoretical aspects of the problem and mathematical model. Tech Phys 42 155, 1997. 

S. S. Shark, H. B. Schlegel, and S. Wolfe, Theoretical Aspects of Physical Organic Chemistry The Sf,i2 Mechanism. Wiley, New York, 1992. 

A large number of nucleophilic substitution reactions involving interconversions of pyridopyrimidines have been reported, the majority of which involve substituents in the pyrimidine ring. This subject has been reviewed previously in an earlier volume in this series which dealt with the theoretical aspects of nucleophilic re-activiti in azines, and so only a summary of the nucelophilic displacements of the substituent groups will be given here. In general, nucleophilic substitutions occur most readily at the 4-position of pyrido-... 

The first generalization is illustrated by the behavior of the 2- and 4-vs. the 3-derivatives of pyridine, the second by the reactivity of 4- vs. 2-substituted pyridines, the third by the relation of 4- vs. 2-derivatives of pyrimidine, and the fourth by the appreciable reactivity of 3-substituted pyridines or 5-substituted pyrimidines compared to that of their benzene analogs. Various combinations of azine-nitrogens in other poly-azines supply further examples. Theoretical aspects of (1), (2) and (3) are discussed in Section II, B, 2. The effect involved in (4) is believed to be more the result of the inductive stabilization of an adjacent negative chaise in the transition state (cf. 251) than of the electron deficiency created in the ground state (cf. 252). The quantitative relation between inductive stabihzation and resonance stabilization is not precisely defined by available data. However, a... 

Theoretical aspects of the study of prototropic tautomers by mass spectrometry... 

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