Search

The importance of diffusional limitations in controlled radical polymerization at laboratory scale and in homogeneous medium is highlighted using different diffusion models. In particular, a coupled 'parallel' encounter pair model is introduced which allows a rigorous description of the influence of diffusional limitations on the activation/deactivation process. Diffusional limitations on termination have a significant influence, whereas those on the activation/deactivation process can disturb the regular growth pattern at high conversion if the mediating agent is a sufficiently bulky species. Diffusional limitations on initiation are only important in case radical initiator is still present at high conversion.

Theories based on free-volume concepts have been developed to characterize the self and mutual-diffusion coefficients of low molecular weight penetrants in rubbery and glassy polymer-solvent systems. These theories are applicable over wide ranges of temperature and concentration. The capability of free-volume theory to describe solvent diffusion in glassy polymers is reviewed in this article. Two alternative free-volume based approaches used to evaluate solvent self-diffusion coefficients in glassy polymer-solvent systems are compared in terms of their differences and applicability. The models can correlate/predict temperature and concentration dependencies of the solvent diffusion coefficient. With the appropriate accompanying thermodynamic factors they can be used to model concentration profiles in mutual diffusion processes that are Fickian such as drying of coatings. The free-volume methodology has been found to be consistent with molecular dynamics simulations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011

Thermodiffusion has an important role in displacements of hydrocarbon reservoir. The ratio of the evaporation energy to the activation energy of viscous flow in pure limits, τpure,k, is of a great importance in estimating the thermodiffusion coefficient for non-associating fluid mixtures. Several methods may be used to estimate τpure,k which causes different values for thermodiffusion coefficients. A fixed value for τpure,k was considered to predict the thermodiffusion coefficient. In this paper, Abbasi et al.'s [J. Non-Equilib. Thermodyn. 2010;35:1–14] model and Shukla and Firoozabadi's model have been applied to predict thermodiffusion coefficients for linear chain hydrocarbon binary mixtures. The results show a very good performance of the simple approach in respect to the previous models in estimating thermodiffusion coefficients. © 2011 Canadian Society for Chemical Engineering

In this paper, polydimethylsiloxane (PDMS) pervaporation membrane was employed to simulate the desulfurization process of gasoline where n-heptane was selected to stand for gasoline. A modified solution–diffusion model is proposed to account for the mass transport of penetrants in the polymer membrane. In the model, the group contribution method (the UNIFAC-ZM model) is applied to calculate the activity of penetrants in the polymer membrane, and the free volume theory with some modifications is employed to describe the diffusion behaviour of the penetrants. The effects of operating temperature and feed concentration on pervaporation properties were investigated to validate the model. It has been shown that the results predicted by the solution–diffusion model are in good agreement with the experimental values. Dans ce document, on a employe une membrane de pervaporation en polydimethylsiloxane (PDMS) pour simuler le processus de desulfuration de l'essence en choisissant de remplacer l'essence par du n-heptane. On a propose un modele de solution–diffusion modifie pour expliquer le transport de masse d'agents mouillants dans la membrane de polymere. Dans le modele, on applique la methode de la contribution de groupe (le modele UNIFAC-ZM) pour calculer l'activite des agents mouillants dans la membrane de polymere et la theorie du volume interstitiel a ete employee, apres lui avoir apporte certaines modifications, pour decrire le comportement de diffusion des agents mouillants. Les effets de la temperature de fonctionnement et de la concentration sur les proprietes de pervaporation ont ete etudies afin de valider le modele. Il a ete demontre que les resultats que predisait le modele de solution–diffusion correspondent bel et bien aux valeurs experimentales.

The fractional free volume values were calculated from the group-contributed equation of state in the case of poly(propylene) and 1-pentene-propylene copolymers. The calculated values were compared to those, which were determined from the zero shear viscosity. The fractional free volume is an excellent parameter to convert pressure-volume-temperature (PVT) data to viscosity and vica versa. Copyright © 2006 John Wiley & Sons, Ltd.

We analysed reported specific volume V from pressure-volume-temperature (PVT) experiments for poly(vinyl acetate) (PVAc) using the Simha-Somcynsky equation of state (S-S eos) and calculated the specific occupied volume, V occ , and hole free volume, V fh We found that V occ shows almost no thermal expansion but is distinctly compressible (T> T g ). Due to this, V fh = V - V occ is not a unique function of Vbut can depend on the specific values of P and T giving rise to the particular value for V. We observed that with decreasing temperature the α-relaxation detected via dielectric measurements slows down faster than the shrinkage of hole free volume V fh would predict on the basis of the free volume theory of Cohen and Tumbull. V fh becomes zero at approximately 65 K below the Vogel temperature To, T 1 0 = T 0 - 65 K. Plots of the α-relaxation frequency logω α versus 1/V fh can be linearised when taking into account this discrepancy by substituting 1/V fh by 1/(V fh - ΔV) with AV = E fh (T 0 - T' 0 ), or by including an energy term of the type exp[-E'/R(T-T 0 )] in the pre-exponential factor of the frequency-volume equation. Our results indicate that the α-relaxation in PVAc operates via the Cohen-Turnbull mechanism only when liquid-like clusters of cells of the S-S lattice appear which contain a hole free volume of three or more empty S-S cells. For regions with a smaller number of empty cells an activation energy is required for allowing segmental motion via the cooperative rearranging of cells. The β-(Johari-Goldstein) relaxation which is a non-cooperative, more local, process follows completely the free volume theory. The same seems to be true for the primitive (uncoupled) relaxation of the coupling model.

Compared with linear polymers, more factors may affect the glass-transition temperature (Tg) of a hyperbranched structure, for instance, the contents of end groups, the chemical properties of end groups, branching junctions, and the compactness of a hyperbranched structure. Tg's decrease with increasing content of end-group free volumes, whereas they increase with increasing polarity of end groups, junction density, or compactness of a hyperbranched structure. However, end-group free volumes are often a prevailing factor according to the literature. In this work, chain-end, free-volume theory was extended for predicting the relations of Tg to conversion (X) and molecular weight (M) in hyperbranched polymers obtained through one-pot approaches of either polycondensation or self-condensing vinyl polymerization. The theoretical relations of polymerization degrees to monomer conversions in developing processes of hyperbranched structures reported in the literature were applied in the extended model, and some interesting results were obtained. Tg's of hyperbranched polymers showed a nonlinear relation to reciprocal molecular weight, which differed from the linear relation observed in linear polymers. Tg values decreased with increasing molecular weight in the low-molecular-weight range; however, they increased with increasing molecular weight in the high-molecular-weight range. Tg values decreased with increasing log M and then turned to a constant value in the high-molecular-weight range. The plot of Tg versus 1/M or log M for hyperbranched polymers may exhibit intersecting straight-line behaviors. The intersection or transition does not result from entanglements that account for such intersections in linear polymers but from a nonlinear feature in hyperbranched polymers according to chain-end, free-volume theory. However, the conclusions obtained in this work cannot be extended to dendrimers because after the third generation, the end-group extents of a dendrimer decrease with molecular weight. Thus, it is very possible for a dendrimer that Tg increases with 1/M before the third generation; however, it decreases with 1/M after the third generation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1235–1242, 2004

New sets of equations have been constructed from the density-pressuretemperature and viscosity-pressure-temperature relationships to determine the rheology of synthetic lubricants at high pressure. A phase diagram was first plotted for the oils up to a pressure of 1.2 GPa and temperatures from 303 to 353 K using high-pressure density experimental results and others. For the oils at temperatures of 313, 333, and 353 K, the high-pressure viscosity experiment was done up to a viscosity of 104 Pa s and up to a pressure of 0.4 GPa. A relationship, based on free volume theory, between pressure and temperature with varying density and viscosity was proposed. It was found that the new equations from these relationships could predict the high-pressure rheology more closely than those of previous researchers. Moreover, it was shown that the Ehrenfest equation or the gradient of the phase diagram is closely related to the expansion coefficient of free volume.

An equation based on the segmental/chain mobility in free volume theory was derived to correlate the gas permeation coefficient and the aging time. An accelerated physical aging of a fluoropolyimide was observed and employed to validate this equation. A strong thickness-dependent aging process was found by employing pure O2 and N2 tests to monitor the change of gas permeation properties as a function of aging time. Experimental results also suggest that chain rigidity and configuration play important roles in physical aging. As a result, the thin 2,2′-bis(3,4′-dicarboxyphenyl) hexafluoropropane dianhydride (6FDA) based polyimide films studied here have different permeability versus time relationship from conventional polyarylate in the early stage of aging, and the experimental data seem to fit the proposed equation well. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 1758–1764, 2004

General characteristics of the free-volume theory of diffusion are discussed, and a recent data-theory comparison involving free-volume theory is critically evaluated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 501–507, 2003

Adopting the quasiharmonic approximation, a newly developed classical mean-field potential (MFP) approach is extended to the quantum case. Two new Debye temperature expressions, which are in accordance with the thermodynamic theory of Dugdale and MacDonald and with the free volume theory, respectively, are derived in addition to the well-known expression of Slater. The Gruneisen law is now implied explicitly in the Debye temperature expression, and therefore no additional conditions for the Gruneisen constant are needed for realistic thermodynamic calculations. The thermal expansion and specific heat of Na, Cu, Mo, Ta, and Th have been calculated from 10 K up to the melting point.

The Vrentas/Duda free-volume diffusion model accurately correlates polymer/solvent diffusion coefficients over wide ranges of concentration and temperature. Currently the model is semipredictive: limited diffusion data are required to estimate model parameters that can then be used to predict diffusion coefficient behavior over sundry conditions. In this work, we present methods for estimating all of the model parameters without any diffusion data and examine the accuracy of the resulting diffusion coefficient predictions. This is the only technique known that predicts polymer/solvent diffusion behavior without any use of any diffusion data.

Un modele representant les proprietes rheologiques de melanges complexes de polymeres a l'etat fondu en fonction de leur composition et des proprietes de leurs composants est propose. Ses predictions sont en accord avec les resultats experimentaux obtenus pour des melanges binaires de polypropene isotactique avec un copolymere sequence styrene/butadiene et un copolymere sequence isoprene/styrene hydrogene

A theoretical model was developed to describe solute transport through moderately swollen networks. The model is an extension of the previous analysis of Peppas and Reinhart (1983), and it describes the normalized effective diffusion coefficient of the solute through the network as a function of the equilibrium degree of swelling, Q, the hydrodynamic radius of the solute, rs, the number average molecular weight between crosslinks, M¯c, and a function f(ξ) of the mesh size ξ, which takes into consideration barriers due to crosslinks, entanglements, etc. For the development of this model, the Cohen–Turnbull (1958) free volume theory was modified to incorporate topological and mobility characteristics from de Gennes' analysis (1979).

The kinetic model given by Cardenas and O'Driscoll, which describes the bulk polymerization of methyl methacrylate (MMA) in the region of the gel effect by the concept of chain entanglements, is extended to the region of the glass effect in accordance with a proposition made by Marten and Hamielec based on the free volume theory. Equations for the calculation of the instantaneous and cumulative molecular weight distributions are derived, too. Dilatometric measurements over the entire conversion range were performed at various temperatures and with three different initiators. For each series of measurements the three adjustable parameters of the extended model were fitted to the time-conversion data. Contrary to the assumptions, it was then found that at least one of the parameters of the model of Cardenas and O'Driscoll (α0) depends both on the concentration and the type of the initiator. The calculated molecular weight distributions are much broader than the experimental ones. Thus the model of Cardenas and O'Driscoll at its present state does not seem to describe adequately the real polymerization behavior of MMA.

The phase behavior at high temperatures of non-polar polymer solutions is discussed in a qualitative way in terms of the free volume theory of liquids developed by Prigogine, Patterson and Flory. This theory is necessary to explain the existence of a Lower Critical Solution Temperature (LCST) in non-polar polymer solutions and the related exothermic heats of mixing. The classical theory of polymer solutions and its limits is first reviewed.

A model has been proposed to correlate the elongational viscosity of blends with the free volume theory so that the elongational viscosity of a blend at any composition can be determined from the elongational viscosity and the weight fractions of the individual components. The predictions of the model are compared with experimental data in four cases and found to give reasonable good agreement. Es wird ein Modell vorgeschlagen, nach dem die Dehnungsviskositat von Blends mit der Theorie des Freien Volumens so korreliert werden kann, das die Dehnungsviskositat eines Blends fur jede Zusammensetzung aus den Dehnungsviskositaten und dem Gewichtsbruch der Komponenten bestimmt werden kann. Die Voraussagen des Modells wurden an experimentellen Daten in vier Fallen uberpruft.

Polar effects on the thermodynamic properties of polymer solutions are treated within the framework of the free volume theory. The Sutherland potential and the dipole-dipole interaction are assumed to represent intermolecular interaction in a polar system, with an approximation concerning the radial distribution function. Application of the treatment to some polar systems shows that the theoretical %-parameters are smaller than the observed ones and than the calculated ones without regard to the polarity. The excess volume ratios are, however, nearer to the observed ones compared with those evaluated without the account of the polarity. Therefore, the present results are fairly good for strong polar solutions.

La dissociation ionique dans les polymeres se produit par interaction des ions avec les groupes polaires des polymeres qui sont lies par liaison covalente. Application dans les appareillages electrochimiques solides

Es wird uber Messungen der Temperaturabhangigkeit des Molvolumens von Glasern und Schmelzen der Zusammensetzung Ge5Se7, Ge2Se3, Ge3Se7, GeSe3 und GeSe5 berichtet. Das aus der gefundenen Abhangigkeit berechnete freie Volumen wird mit Literaturangaben zur Viskositat der Schmelzen zwecks Ermittlung des kritischen Lochvolumens und Abschatzung der Flieseinheit korreliert. Fur die GeSe2−Se-Schmelzen ergibt sich Se als Flieseinheit. Der Mechanismus wird diskutiert. Application of the Free Volume Theory to Glasses and Melts in the System Germanium–Selenium The temperature dependence on the molar volume of glasses and melts was measured for the compositions: Ge5Se7, Ge2Se3, Ge3Se7, GeSe3, GeSe5. Values of the free volume were calculated. Correlating this values according to free volume theory with data from the literature concerning the viscosity of the melts allows the estimation of the minimum required volume of the voids. Se is found as the unit of viscous flow for GeSe2−Se-melts. The mechanism is discussed.

The relation between the relaxation behaviour of photochromic aromatic azo benzenes and spiropyrans in a series of amorphous polymers and the polymer properties has been investigated. The distinctive differences of the rate of thermal isomerization found below and above Tg and also compared to solution can be explained by molecular properties of the polymer matrix, i. e., the overall chain segmental mobility, particular chain segmental motions and free volume effects. — The temperature dependency of the relaxation of the photochromes can be described by a WLF-equation, log aT = -C1(T - Tg)/(C2 + T - Tg). The numerical values of the constants C1 and C2 differ from the „universal” values, but for a given family of polymers a single set of parameters is sufficient for both types of photochromes. The deviations in the constants are ascribed to an unequal distribution of the free volume through the matrix caused by the photochromic foreign molecules. — The anomalies in the thermal cis-trans relaxation of the aromatic azo chromophores in glassy matrices are correlated with restrictions in the fluctuation of the free volume. A temperature T0 is determined at which the contribution of translational motions to the fluctuations in the free volume is widely frozen in. Die Zusammenhange zwischen dem Relaxationsverhalten photochromer aromatischer Azoverbindungen sowie Spiropyranen in einer Reihe amorpher Polymerer und den Polymereigenschaften wurden untersucht. Die deutlichen Unterschiede in der Geschwindigkeit der thermischen Isomerisierung unterhalb und oberhalb der Glastemperatur Tg, und im Vergleich zur Losung, konnen durch bestimmte Eigenschaften der Polymermatrix, d.h. Segmentbeweglichkeit, unterschiedliche Kettenbewegungen und den Anteil an freiem Volumen, erklart werden. — Die Temperaturabhangigkeit der Relaxationszeit der Photochrome last sich durch eine WLF-Gleichung, log aT = -C1(T - Tg)/(C2 + T - Tg), beschreiben. Die numerischen Werte der Konstanten C1 und C2 unterscheiden sich allerdings deutlich von den „universellen” Werten; in Polymeren gleicher Grundstruktur last sich aber das photochrome Verhalten beider Chromophor-Typen durch einen einzigen Satz von Parametern beschreiben. Die Abweichungen der Konstanten werden einer ungleichmasigen Verteilung des freien Volumens zugeschrieben, die durch die photochromen Fremdmolekule verursacht wird. — Die in glasigen Polymeren auftretenden Anomalien bei der thermischen cis-trans-Isomerisierung der aromatischen Azochromophore hangen mit Einschrankungen in der Fluktuation des freien Volumens zusammen. Es kann eine Temperatur T0 bestimmt werden, bei der der Beitrag translatorischer Bewegungsprozesse zur Fluktuation des freien Volumens verschwindet.

In the present work it is shown that the strength, depending on temperature and strain, and durability, depending on temperature and static load, of adhesive joints of polymers with adhesive of elastomer type can be predicted from master curves, drawn according to the principle of temperature–time analogy. Shift factors, determined by the Williams-Landel-Ferry (WLF) equation with universal values of constants, have been used to draw the master curves. It allowed to find relations between reference temperature and glass transition temperature of the adhesive. Their existence can be explained on the basis of free volume theory. Referring to the analogous influence of temperature and the part of the plasticizer inserted into the adhesive, on the strength of adhesive joints the existence of temperature–concentration analogy has been determined on the phenomenological level. Nomograms have been suggested for the calculation of strength and durability values from the master curves. Their application is convenient for repeated usage of master curves.

The free volume theory of Cohen and Turnbull, the results of which are identical with the empirical relationship of Williams, Landel and Ferry (WLF), was compared with the theory of conformational entropy of Adam and Gibbs (AG) using experimental results of measurements of the temperature dependence of the relaxation times of poly(vinyl acetate). In spite of being different in their mathematical form, both theories were found to describe the experiment with similar adequacy. A procedure was also suggested permitting to obtain the AG parameters if the WLF parameters are known. The procedure was applied to 59 compounds, the WLF parameters of which were found in the literature. The results are tabulated.

A prediction technique for gas permeability from polymer structure has been developed on the basis of a specific free volume diffusion theory. In this theory, the free volume available per unit mass in a polymer structure controls the rate of gas diffusion and, hence, its rate of permeation. The smaller this specific free volume is, the more difficult the gas diffusion and, thus, the better its barrier to gases becomes. Specifically, the theory predicts a linear relationship between log (permeability) and (−1/specific volume). A number of existing polymers covering six orders of magnitude in CO2 permeability and O2 permeability were found to follow this correlation. The specific free volume in a polymer was obtained from group contribution calculations. As a result, the gas permeabilities become predictable from the specific volume in a polymer which, in turn, varies with its molecular structure. The advent of this specific free volume theory for gas permeation simplifies greatly the selection of barrier materials for packaging applications. For a given barrier application, a critical specific free volume is first defined from its gas barrier requirement. The polymer structures having specific free volumes smaller than the critical value are then identified. These are the polymers that would have the necessary barrier performance. By this theory, molecular structures, with string polar-to-polar interactions and hydrogen-bonding forces are found to be good barriers to CO2 and O2.

Results of bulk viscosity (η) and local viscosity (ξ) of various molecular weights of polystyrene (PS) have been reported. In this paper the relationship between η and bulk diffusion coefficient (DB), and that between ξ and local diffusion coeffizient (DL) are presented. Data obtained lead to several conclusions. From the results of unperturbed dimensions and a universal constant (Φ), it was found that F. Bueche's equation DB · η = const. is valid for polystyrenes with molecular weights over 600. Temperature and component concentration dependence of bulk diffusion coefficient for the two-component blend system may be interpreted in terms of the free volume theory. At an iso-free volume state, molecular weight dependences of bulk diffusion coefficients for both PS of narrow distribution of molecular weight and blend PS can be composed to a single curve, which is composed of two straight lines in a double logarithmic presentation with intersection at Mw = 1.78 × 104 g/mol. The slopes of these two lines were − 1.0 and − 3.3, respectively. The product DL · ξ was determined to be 1.10 × 10−7 (c.g.s) for n-paraffines from the data of self-diffusion coefficient and ξ. This made it possible to determine DL from ξ. For higher molecular weights of PS, log DB is a linear function of log Mw while log DL stays almost constant. Uber Mesergebnisse der Schmelzviskositat (η) und der lokalen Viskositat (ξ) von Polystyrolen (PS) unterschiedlicher Molmasse ist berichtet worden. In dieser Arbeit wird der Zusammenhang zwischen η und dem Schmelzdiffusionskoeffizienten (DB) sowie ξ und dem lokalen Diffusionskoeffizienten (DL) dargestellt. Die erhaltenen Daten fuhren zu mehreren Schlusfolgerungen. Aus den erhaltenen Werten fur die ungestorten Dimensionen und der universellen Konstante (Φ) wurde gefunden, das die Bueche-Gleichung: DB · η = const. fur Polystyrole mit Molekulargewichten uber 600 g/mol gultig ist. Die Abhangigkeit des Schmelzdiffusionskoeffizienten des Zweikomponenten-Polymergemisches von Temperatur und Komponentenzusammensetzung konnen anhand der Theorie des freien Volumens interpretiert werden. Fur Zustande gleichen freien Volumens kann die Abhangigkeit sowohl von Polystyrol mit enger Molekulargewichtsverteilung als auch vonPolymermischungen in einer einzigen Kurve dargestellt werden, die sich in doppeltlogarithmischer Darstellung aus zwei Geraden mit einem Schnittpunkt bei Mw = 1,78 · 104 g/mol zusammensetzt. Die Steigungen dieser beiden Geraden sind − 1,0 bzw. − 3,3. Das Produkt DL · ξ wurde fur n-Paraffine zu 1,10 · 10−7 (c.g.s.-Einheiten) bestimmt. Dabei wurden Literaturdaten fur die Selbstdiffusionskoeffizienten und ξ zugrunde gelegt. Dies ermoglichte die Bestimmung von DL aus ξ. Fur Polystyrole hoherer Molekulargewichte ist log DB beinahe eine lineare Funktion von log Mw wahrend log DL fast konstant bleibt.

The free-volume theory describing diffusion in polymer–solvent systems is reexamined. Calculation of the specific free volume for such systems is discussed, and equations are presented for the determination of the self-diffusion coefficients of the polymer and the solvent. Conditions under which the mutual diffusion coefficient can be deduced solely from free-volume considerations are clarified, and a more general version of the free-volume diffusion theory proposed by Fujita is presented. The further restrictions needed for the theory of Fujita are discussed, and it is concluded that these additional restrictions are responsible for failures of the Fujita theory.

Viscosities for the binary liquid mixtures of cyclohexanone with n-hexane, n-heptane, 2, 2, 4-trimethylpentane, benzene, toluene and tetrachloromethane have been determined at 298.15 K. The deviation in viscosity from the ideal law is negative in all the systems except in the system, cyclohexanone with tetrachloromethane. In this system excess viscosity exhibits a positive deviation over the entire range of mole fraction. The results have been interpreted in terms of molecular interactions, and of difference in size and shape of components. The theoretical excess viscosities have been calculated from absolute reaction rate theory and free volume theory of flow by making use of the Bloomfield and Dewan relations. Theoretical excess viscosities are in qualitative agreement with experimental results for four out of the six systems examined. Les viscositas pour des malanges liquides binaires de cyclohexanone avec du n-hexane, 2, 2, 4-trimathyl-pentane, benzane, toluane et tatrachloromathane, ont ata daterminaes a 298, 25 K. L'acart de viscosita par rapport au comportement parfait est nagatif dans tous les systames, excepta dans le systame cycIohexanone-tatrachloromathane. Dans ce systame, la viscosita d'excas prasente un aart positif pour toute la gamme de fractions molaires. Les rasultats ont ata interpratas par les intaractions molaculaires et les diffarences de taille et de forme des composants. Les viscositas d'excas thariques ont ata calculaes a partir de la thaorie de la vitesse de raaction absolue et de la thaorie du volume libre de l'acoulement en faisant intervenir les relations de Dewan et de Bloomfield. Les viscositas d'excas thariques montrent un accord qualitatif avec les rasultats exparimentaux pour quatre des six systames atudias.

The view that the glass transition is basically thermodynamic in nature is used to derive an expression for glass temperature depression by plasticizers. The second-order transition temperature is given as that temperature at which the configurational entropy first becomes zero as we cool the polymer–diluent system. The concentration of plasticizer, size of the plasticizing molecule, and its flexibility are found to be the main determinants of glass temperature depression. Available experimental data confirm the predictions of the theory, and it is thereby concluded that the thermodynamic view is sufficient to explain glass temperature depression. It is pointed out that data exist which contradict the free volume theory, as applied to glass temperature depression.

The self-diffusion of ethylbenzene in polystyrene has been measured by means of the NMR field-gradient spin-echo technique. It is shown that the values of the self-diffusion coefficient can be estimated by the modified free-volume theory of Vrentas and Duda. Die Selbstdiffusion von Ethylbenzen in Polystyren wurde mit Hilfe der NMR-Feldgradient-Spinecho-Methode gemessen. Es wird gezeigt, das die Werte des Selbstdiffusionskoeffizienten unter Anwendung einer modifizierten Theorie des freien Volumens von Vrentas und Duda abgeschatzt werden konnen.

High molecular weight plasticizers can be used if they have a low Tg and are miscible with PVC. For example, linear polyesters exhibit miscibility with PVC when their [CH2]/[COO] ratio is intermediate; in that range, as “miscibility window” has been found. However, the degree of miscibility of miscible polymer blends vary with the structure of the polymers involved and thier concentration. The miscibility of these systems is often assessed by the measurement of a single Tg as a function of composition. A careful examination of experimental data of polyester/chlorinated polymer blends, as well as the use of the free volume theory, indicates that several of these systems exhibit a cusp as a function of composition, which is characterized by a critical volume fraction and a critical temperature. Specific examples are given.

The free volume equation for liquid viscosities is generalized to multicomponent mixtures. No experimental mixture data are needed in order to use the correlation. Calculated viscosities for liquid mixtures composed of molecules which approximately obey the Lennard-Jones 6, 12 potential law show very good agreement with experimental data for eight binary systems.

The analysis of the measured temperature dependences of self-diffusion coefficients for prolate ellipsoid type molecules of α,ω-dibromo-methane, -ethane, -octane, -decane and -dodecane performed in the frame of the modified Perrin model enabled to discover anisotropy of translational diffusion in liquids. On the basis of the Eyring theory the effect was confirmed and the jump length of about 7 A for all the molecules was derived. The same jump length for longer molecules was obtained from the Cohen-Turnbull free volume theory.

An investigation of the validity of the free volume theory of liquid has been undertaken on the basis of the theory of correlation functions. A formula for free volume without use of a geometrical model has been proposed and discussed. The magnitude of equivalent free volumes obtained from the formula has been found to be nearly equal to that calculated from the entropy of vaporization by means of the free volume theory. The results give support to the physical reality of the concept of free volumes. The communal entropy deduced agrees with that obtained by an expansion formula to the first order of density. A formula for compressibility has also been derived, which gives satisfactory results in comparison with observed data.