The identification of small amounts of sugars by means of X-ray diffraction patterns

Summary The identification of small amounts of sugars by their X-ray powder diagrams is suggested as a most simple and practical method in routine analysis.It is especially valuable in working with minute amounts of material, and has proved very useful for the final identification of chromatographically-separated sugars.The characteristics of the powder diagrams of a number of monosaccharides of special interest to the physiological chemist are reported in detail. The substances thus investigated are- and-D-glucose and-glucose monohydrate,- and-D-galactose,- and-D-mannose,D-fructose,D-glucuronolactone,- and-D-glucosamine hydrochloride,- and-D-galactosamine (chondrosamine) hydrochloride,-L-fucose, andD-ribose. For various reasons arabinose, lyxose, and xylose have also been included.It is clear from the powder diagrams of the galactoses that the crystalstructure earlier ascribed to-galactose is that of-galactose.A single-crystal study of-glucosamine hydrochloride was carried out by theWeissenberg technique. The crystal-dimensions obtained agree with those earlier found byCox et al^{5, 7}.The optical rotation of chondrosamine hydrochloride was found to be [] _D ^20° = - 135° - 93° - 39°, the first value being considerably higher than that given for the-form byLevene. A method for the preparation of-mannose is described.

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Zusammenfassung Die Identifizierung kleiner Mengen verschiedener Zuckerarten mit Hilfe ihrer Röntgen-Pulverdiagramme wird als einfache und praktische Routinemethode vorgeschlagen.Diese Methode ist besonders wertvoll, wenn nur kleine Substanzmengen zur Verfügung stehen, und hat sich für die endgültige Identifizierung von chromatographisch getrennten Zuckern als sehr geeignet erwiesen.Die Einzelheiten der Pulverdiagramme folgender physiologisch-chemisch bedeutungsvoller Monosaccharide werden mitgeteilt:- und-D-Glukose und Glukosehydrat,- und-D-Galaktose,- und-D-Mannose,D-Fruktose,D-Glukuronolakton,- und-D-Glukosaminhydrochlorid,- und-D-Galaktosamin-(Chondrosamin)-hydrochlorid,-L-Fukose, dieD-Pentosen Arabinose, Lyxose, Ribose und Xylose.Aus den Pulverdiagrammen der Galaktosen geht deutlich hervor, daß die Krystallstruktur, die früher der-Galaktose zugeschrieben wurde, tatsächlich diejenige der-Form ist.Die Untersuchung eines Einzelkristalles von-Glukosaminhydrochlorid wurde nach derWeissenberg-Technik ausgeführt. Die erhaltenen Werte stimmen mit den früher vonCox und Mitarbeitern gefundenen überein.Die optische Drehung des Chondrosaminhydrochlorids wurde zu [] _D ^20° = + 135° + 93° + 39° gefunden. Der erstgenannte Wert ist größer als der entsprechende, vonLevene angegebene Drehungswert.Eine Methode zur Darstellung von-Mannose wird beschrieben.

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Résumé On propose une méthode de routine simple et pratique pour l'identification de petites quantités de divers sucres au moyen de leur diagramme de poudres aux rayons X. Cette méthode est particulièrement précieuse quand on n'a que de petites quantités de matière à sa disposition et elle s'est montrée très convenable pour l'identification finale de sucres séparés par chromatographie. Des particularités des diagrammes de poudres des monosaccharides suivants intéressent le chimiste physiologiste: et-D-glucose et hydrate de glucose, et-D-galactose, et-D-mannose, D-fructose,D-glucuronolactone, chlorhydrate d' et-D-glucosamine, chlorhydrate d' et-D-galactosamine (chondrosamine), l'-L-fucose, lesD-pentoses, l'arabinose, le lyxose, le ribose, le xylose. Des diagrammes de poudres des galactoses découle clairement le fait que la structure cristalline qui fut attribuée précédemment à l'-galactose est celle de la forme. L'expérience sur un cristal unique de chlorhydrate d'-glucosamine a été effectuée d'après la technique deWeissenberg. Les valeurs obtenues concordent avec celles trouvées précédemment parCox et ses collaborateurs. Le pouvoir rotatoire du chlorhydrate de chondrosamine a été trouvé égal à _D ²⁰ = + 135° + 93° + 39°. La première valeur est plus grande que celle donnée parLevene. On décrit une préparation de l'-mannose.

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With 3 figures.     

Kinetics and mechanism of the hydrolysis of sodium carboxymethylcellulose (Na-CMC) by a cellulase complex

TheSomogyi-Nelson colorimetric method is applied in a new manner more suitable for evaluating the kinetics of the enzyme hydrolysis of sodium carboxymethylcellulose (Na-CMC) catalyzed by the cellulase complex. By means of selective inhibition of a chosen enzyme from the cellulase complex it became possible to trace the effect of the other enzymes included in its composition.

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Kinetik und Mechanismus der Hydrolyse von Natriumcarboxymethylcellulose (Na-CMC) durch einen Cellulase-Komplex

Zusammenfassung Die kolorimetrische Methode nachSomogyi undNelson wird nach einem neuen Verfahren zur Verfolgung der Kinetik der hydrolytischen Spaltung von Natriumcarboxymethylcellulose (Na-CMC), katalysiert durch den Cellulase-Komplex, angewandt. Durch selektive Inhibierung eines bestimmten Enzyms des Cellulase-Komplexes kann man die Wirkung der anderen zu seiner gesamten Zusammensetzung gehörenden Enzyme verfolgen.

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Symbols Used E enzyme (E—cellulase;E—exo-cellobiohydrolase;E—-glucosidase) - [E] _w weight concentration of enzymeE - S substrate (Na-CMC—sodium carboxymethylcellulose) - [S]₀ weight concentration of substrateS - I inhibitor (I—lactose;I—calcium chloride;I—condurrite-B-epoxide) - P product (P—oligosaccharides;P—cellobiose;P—D-glucose) - P end product (K , K , K ) - DP degree of polymerization - DS degree of substitution - ES enzyme-substrate complex (E S, E S, E S) - EP enzyme-product complex (E P, E P) - EI enzyme-inhibitor complex (E I, E I, E I) - M _s molecular mass of substrateS - K _s substrate constant (K _s , K _s , K _s ) - K _I inhibitor constant (K _I , K _I , K _I ) - K _m Michaelis-Menten constant - k ₊₁,k ₊₂ (k ₊₂ ,k ₊₂ ,k ₊₂ ) forward rate constants - k _–1 reverse rate constant - ₀ initial rate of reaction - V maximal reaction rate - A change in absorbance - molar absorption coefficient - wavelength Herrn Prof. Dr.Hans Tuppy zum 60. Geburtstag herzlichst gewidmet.     

Relativistic perturbation theory of molecular structure

Summary The recently developed relativistic double perturbation theory is extended to handle relativistic changes of molecular structure more easily. This is achieved by simple coordinate scalings. Accurate higher order mixed perturbation energies for H ₂ ⁺ are calculated. The relativistic changes of bond energy,DE, of bond length,R _e , and especially of force constant,k, and of anharmonicity,a, are large, up to 100%·(Z/c)². The dominant contributions tok anda are due to the indirect change of the nonrelativistick anda connected with the relativistic change of bond length. Accordingly the relativistic changes obey Badger's and Gordy's rules (–RDEk).Dedicated to Prof. Klaus Ruedenberg in appreciation of his fundamental contributions to both formal theory and physical explanations in quantum chemistry     

Prediction of the non-Newtonian viscosity and shear stability of polymer solutions

The structure-property relationships derived here permit the prediction of both the zero-shear viscosity ₀, as well as the shear rate dependent viscosity . Using this molecular modeling it is now possible to predict over the whole concentration range, independently of the molecular weight, polymer concentration and imposed shear rate. However, the widely accepted concept: dilute — concentrated, is insufficient. Moreover it is necessary to take five distinct states of solution into account if the viscous behavior of polymeric liquids is to be described satisfactorily. For non-homogeneous, semi-dilute (moderately concentrated) solutions the slope in the linear region of the flow curve (= must be standardized against the overlap parameterc · []. As with the ₀-M-c-relationship, a-M -c- relationship can now be formulated for the complete range of concentration and molecular weight. Furthermore, it is possible to predict the onset of shear induced degradation of polymeric liquids subjected to a laminar velocity field on the basis of molecular modeling. These theoretically obtained results lead to the previously made ad hoc conclusion (Kulicke, Porter [32]) that, experimentally, it is not possible to detect the second Newtonian region.Roman and Italian symbols a exponent of the Mark-Houwink relationship - b exponent of the third term of the ₀-M -c relationship - c concentration /g · cm^–3 - E number of entanglements per molecule - F(r) connector tension - f function - G _i ^A shear modulus; A indicates that it /Pa has been evaluated by a transient shear flow experiment; i is the shear rate to whichG ^A refers to - G storage modulus /Pa - G _p plateau modulus /Pa - H() relaxation spectrum /Pa - h shift factor (₀/_r) - K _H Huggins constant - K _b third constant of the ₀-M -c relationship - K constant of the Mark-Houwink relationship - M molecular weight /g · mol^–1 - M _e molecular weight between two /g · mol^–1 entanglement couplings - N number of segments per molecule - n slope in the power-law region of the flow curve - p p-th mode of the relaxation time spectrum - R gas constant /8.314 J·K^–1·mol^–1 - r direction vector - T temperature /K Greek symbols ß reduced shear rate - shear rate /s^–1 - shear viscosity /Pa·s - _s solvent viscosity /Pa·s - _sp specific viscosity - ₀ zero-shear viscosity /Pa·s - apparent viscosity at shear rate - reduced viscosity - viscosity of polymeric liquid in /Pa·s the second Newtonian region - [] intrinsic viscosity/cm³·g^–1 - screening length/m - /g·cm ^–3 density - relaxation time/s - ₀ experimentally derived relaxation time/s - angular frequency of oscillation Indices conc concentrated - corr slope corrected - cr critical - deg degradation - e entanglement - exp experimental - mod moderately concentrated/semi-dilute - n number average - p polymer - R Rouse - rep reptation - s solvent - sp specific - theo theoretical - weight average - relaxation time - o experimental or steady state - * critical - ** transition moderately conc. — conc. - + transition dilute — moderately cone. Paper presented at the 2nd bilateral U.S.-West German Polymer Symposium, Yountville, the 7th–11th September 1987.     

The solid-state structure of (+)-(i)-menthyl 2-formamido-4, 4,4-trifluorobutanoate and the hydrogenation of the 2-butenoate precursor

Hydrogenation ofZ-(–)-(1R, 3R, 4S)-menthyl 2-formamido-4,4,4-trifluoro-2-butenoate catalyzed by Pd/C was performed at atmospheric pressure to yield a mixture of (2R, 1R, 3R, 4S)- and (2S, 1R, 3R, 4S)-menthyl 2-formamido-4,4,4-trifluorobutanoate diastereomers in a 5545 ratio, respectively. Repeated fractional crystallization from ethyl acetate and vapor diffusion of petroleum ether afforded (+)–(2S, 1R, 3R, 4S)-menthyl 2-formamido-4,4,4-trifluorobutanoate as clear colorless, crystalline prisms which were subjected to single-crystal X-ray diffraction analysis. The crystals belong to the orthorhombic system P2₁2₁2₁, and at 213 K:a=5.054(1),b= 10.000(2),c=32.707(1) Å,V=1652.9(4) ų,Z=4,R(F)=0.040, andR _w (F)=0.037. The finding of the (2S)-configuration for the formamido-acid portion of the (+)-ester enabled the configurational assignment of the asymmetric hydrogenation products ofZ-methyl 2-formamido-4, 4,4-trifluoro-2-butenoate catalyzed by chiral diphosphine/rhodium(I) complexes.     

On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Kinetics of photoreduction of 9,10-phenanthrenequinone in the presence of amines and polymethylbenzenes

A study of the kinetics of photoreduction of 9,10-phenanthrenequinone in the presence of hydrogen donors (para-substituted N,N-dimethylanilines and polymethylbenzenes) showed that plots of the quantum yield of photoreduction (_H) and apparent reaction rate constant (k _H) vs. oxidation potential of hydrogen donors are extreme. In the presence of amines, k _H and _H increase, as a whole, whereas they decrease in the presence of polymethylbenzenes. In coordinates _H-G _e (G _e is the change in the free energy of electron transfer) for pairs quinone-H donor, _H increases with G _e approaching to zero. For the amine series, this effect is mainly in the exothermic region of G _e (G _e < 0). For the series of polymethylbenzenes, this increase is observed in the endothermic region (G _e > 0).__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2381–2385, November, 2004.     

Synthesis of tetra- and pentacarbocyanine dyes with alkoxy groups in the β,β′ positions of the polymethine chain

Previously unknown symmetrical and unsymmetrical , '-dialkoxytetracarbocyanine and , '-dialkoxypentacarbocyanine dyes have been synthesized by the condensation of -alkoxy-substituted hexamethine and octamethine hemicyanines with quaternary salts of -alkoxypropenyl derivatives of heterocyclic bases. Tetracarbocyanines with a symmetrical structure have also been obtained by the direct interaction of quaternary salts of -alkoxypropenyl derivatives of heterocyclic bases with malonaldehyde dianil.     

Triterpene Glycosides of Scheffleropsis angkae. IV. Structure of Glycosides L-C2 and L-I2

Two new triterpene glycosides of the -amyrin series, L-C ₂ and L-I ₂ , 27-hydroxyursolic acid 3-O--L-arabinopyranoside and its 28-O--L-rhamnopyranosyl-(14)-O--D-glucopyranosyl-(16)-O--D-glucopyranosyl ester, are isolated from leaves ofScheffleropsis angkae(Araliaceae). The structures of the glycosides are established using chemical methods and NMR techniques ( ¹ H, ¹³ C, ¹³ C-APT, COSY, TOCSY, HSQC, HMBC, and ROESY).     

The electronic structure of molecules by a many-body approach

The vertical valence ionization potentials of cyclopropane, ethylene oxide and ethylene imine are calculated by a many-body Green's function method. For C₃H₆ the ordering of the ionization potentials is 2e(), 1e(), 2a₁(), 1a₂(), 1e(). The assignment of the 2a₁ and the 1a₂ ionization potentials which has been controversial is thus clarified. The ordering is in agreement with the result obtained via Koopmans' theorem. For ethylene oxide and ethylene imine Koopmans' theorem fails in predicting the correct order of ionic states. For C₂H₄O the ordering of the ionization potentials is 2b ₁(), 4a ₁, 1a ₂(), 2b ₂,3a ₁, 1b ₁(), 1b ₂, 2a ₁ and for C₂H₅N 6a, 5a, 3a, 2a, 4a, 3a, 1a, 2a. The agreement of the computed ionization potentials with the experimental values is very satisfactory.     

Some remarks on the periodical change of the stability constants of the lanthanide complexes

The correlations between the values of the lgK (K = stability constant of the lanthanide complex) and the reciprocal of the ionic radius 1/r or the sum of the ionization potentials ₁ ³ I for the lanthanide ions were reviewed for different ligands. A straight-line relationship (lgK – lgK)/lgK vs. (1/r – 1/r)/(1/r) or vs. ( ₁ ³ I – ₁ ³ I)/ ₁ ³ I was found within the tetrads La-Nd, Gd-Ho, and Er-Lu.

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Bemerkungen zum periodischen Wechsel der Stabilitätskonstanten von Lanthaniden-Komplexen

Zusammenfassung Es wurde eine Übersicht der Korrelationen zwischen den Werten von logK (K = Stabilitätskonstante der Lanthanidenkomplexe) und den reziproken Ionenradien 1/r oder der Summe der Ionisierungspotentiale ₁ ³ I für die Lanthanidenionen für verschiedene Liganden gegeben. Dabei wurde eine lineare Korrelation für (lgK – lgK)/lgK gegen (1/r – 1/r)/(1/r) oder gegen ( ₁ ³ I – ₁ ³ I)/_1/3 I innerhalb der Tetraden La-Nd, Gd-Ho und Er-Lu aufgefunden.

     

On the theory of adsorption kinetics of ionic surfactants at fluid interfaces

The kinetic equation to describe the adsorption process of ionic surfactants (derived in part 1) will be solved numerically. The results show the effect of parameters such as ion valencyz, thickness of theDL x ^–1, and surfactant parameters_eq,K, andK _ads on the adsorption process. The results can be used to decide whether the model can explain experimental data on charged surfactant molecules or not.Nomenclature c concentration - c_e bulk concentration in equilibrium - C =c/c _e dimensionless concentration - D diffusion coefficient - e proton charge - F Faraday's constant - f ₀ =e/kTdimensionless potential - k Bolzmann's constant - K _ads rate constant of adsorption - K _des rate constant of desorption - K(f ₀) coefficient of electrostatic deceleration - K = _eq /c _e Henry's constant - R gas law constant - t time - T absolute temperature - z electrovalence - ₀ adsorption of ions - _eq equilibrium value of _o - = ₀/ _eq dimensionless adsorption - , constants - dielectric constants - x Debye-Hückel reciprocal distance - =Dt/K ² dimensionless time - electric potential     

Thermodynamics of Proton Association of Polyacrylates and Polymethacrylates in NaCl(aq)

Enthalpies of protonation of polyacrylates and polymethacrylates with different molecular weights in aqueous NaCl solutions, 0 I 2 mol-L^–1 were determined by titration calorimetry at 25°C. H values are dependent on both the neutralization degree, , and the molecular weight of polyacids. T S of protonation was obtained using pK values already reported and the present H results. Empirical equations for the dependence on I, , and molecular weight are reported for both H and T S.     

Analysis of the Temperature and Composition Dependence of Viscosimetric Properties of 2-Butanone <Emphasis Type="Bold">+</Emphasis> 2-Butanol Solvent Mixtures

Kinematic viscosities were measured for 2-butanone + 2-butanol binary liquid mixtures with a capillary Ubbelohde routine viscometer in the temperature range from 273.15 to 353.15 K at atmospheric pressure, and covering the whole miscibility field (0x_i1). Experimental data have been correlated by means of different empirical or semiempirical relationships, such as =(T), =(x_i), and =(T, x_i). Viscosity deviations, , from ideal behavior are negative at all experimental conditions, confirming that structure breaking effects prevail in the liquids. Furthermore, the thermodynamics of viscous flow and excess Gibbs energy of activation of viscous flow, G*^E, have been calculated. As an alternative and complementary approach to such investigations, the fluidity () of this binary system has been analyzed by the modified—Batschinski theory. The results are discussed in terms of the specific molecular interactions between the mixture components.     

Monte Carlo simulation of a lattice model for ternary polymer mixtures

Monte Carlo studies of symmetrical polymer mixturesAB, modelled by selfavoiding walks withN _A =N _B =N steps on a simple cubic lattice, are presented for arbitrary concentrations of vacancies _v in the range from _v =0.2 to _v =0.8 and chain lengthsN64. We obtained the phase diagrams and the equation of state for three choices of the ratio / _AB ( being the energy between monomers of the same kind, _AB being the energy between different monomers). Flory-Huggins theory provides only a qualitative understanding of these results. If the equation of state is fitted with an effective Flory-Huggins parameter _eff , the latter turns out to be strongly dependent on both concentration and temperature.Contributed paper delivered at the Tagung der Deutschen Physikalischen Gesellschaft, Fachausschuß Polymerphysik, Berlin, March 30–April 3, 1987.     

All-valence-electron and transition density matrix calculations of the electronic spectra of [2.2]paracyclophanequinones

The combined CNDO/S and transition density matrix methods reproduced well the UV-VIS spectra of the intramolecular charge-transfer complexes of double- and triple-layered [2.2]paracyclophanequinones in which benzene and p-benzoquinone represent the donor and acceptor layers: DA, DDA and DAD. Calculations pointed to the already known experimental bathochromic shifts of the longest wavelength absorption band for the DADDADAD transformations. The electronic transitions corresponding to this band are for DA and DDA the CT transitions of the ^* type; however, for DAD the band represents the n ^* transition localized on the acceptor ring.     

Cohesion of crystals and the temperature coefficient of their equilibrium surface pressure

Summary Surface tension _e of mercury in equilibrium with crystals (floating on its surface) of octacosane, 1-hexadecanol, 1-octadecanol, ethyl palmitate, benzophenone and azoxybenzene at 7° is almost equal to that at 23° (measured earlier); also the difference between the surface tension ( ₀) of uncontaminated mercury and _e (i. e., equilibrium surface pressure) is independent of temperature within the limits of the experimental error. This shows that the hypothesis making ₀- _e an analog of the vapor pressure of the solid is incorrect. The relation _e= (=cohesion of the crystal,=thickness of the surface layer of mercury) is in agreement with the negligible temperature coefficient of _e . The calculated is approximately 9 angstroems.

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Zusammenfassung Die Oberflächenspannung _e von Quecksilber im Gleichgewicht mit Kristallen (schwimmend auf der Oberfläche) von Octosane, 1-hexadecanol, 1-octodecanol, Äthylpalmitat, Benzophenon und Azoxylbenzol bei 7 °C ist nahezu gleich der bei23 °C gemessenen. Auch die Differenz der Oberflächenspannung von reinstem Quecksilber ( ₀) und ( _e), d. h. dem Gleichgewichtsobderflächendruck ist unabhängig von der Temperatur innerhalb der experimentellen Fehlergrenze. Dies zeigt, daß die Hypothese, nach der man ₀- _e in Analogie zum Dampfdruck des Festen betrachtet, unkorrekt ist. Die Beziehung _e= (=Kohäsion des Kristalls,=Dicke des Oberflächenfilms auf Quecksilber) ist in Übereinstimmung mit dem vernachlässigbaren Temperaturkoefifzienten von _e. Das berechnete beträgt ungefähr 9 Å.

     

Isomerization of 3β-acetyl-α-3,4-epoxycarane

Conclusions 3-Acetyl--3,4-epoxycarane under the influence of bases is easily rearranged to the,-unsaturated ketol, namely 3-acetyl-4-caren-3-ol, by the E₂ mechanism of the-elimination reaction.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 9, pp. 2084–2086, September, 1971.     

Effects of pressure and solvent on the diffusion of aromatic compounds through polymers

The diffusion of six azo and five anthraquinone derivatives through nylon 6, poly(ethylene terephthalate) and secondary cellulose acetate films were studied under high hydrostatic pressures of up to 3000 bar and at temperatures 80–130 °C, by analyzing the diffusion profiles yielded in a stacked multiple film, placed in the solution of the diffusant. It was found that the diffusion coefficient,D, of the diffusant decreased with increasing pressure, giving a linear relationship between InD and the pressure, the slope of which gave the activation volume for the diffusion,V . It was revealedV increased linearly with increasing intrinsic molecular volume of the diffusant,V _w , the slopes being different between the azo and the anthraquinone derivatives. The ratio ofV toV _w (V /V _w ) ranged from 0.13 to 0.93, depending in a sensitive manner on the degree of swelling of the polymer matrix which in turn was varied by the solvent. The overall results could be explained in accordance with the formulation,V _{f, local} +V =V _w , whereV _{f, local} represents the free volume contribution. It was proposed thatV _w is increased by solvation when the solvent is good for the diffusant.