Free Volume Approach Research Articles

Thermodynamic properties and stability of grain boundaries in metals based on the universal equation of state at negative pressure

Adopting a free volume approach at negative pressure of the universal equation of state, the thermodynamic properties of unrelaxed grain boundaries are determined for f.c.c., b.c.c. and h.c.p. metals including the excess energy, excess enthalpy, the bulk modulus, the Grüneisen parameter and consequently, the excess entropy and Gibbs free energy. A mechanical instability of a grain boundary is predicted based on the Gibbs stability criteria at an excess volume of about 0.45, corresponding to a scaled atomic separation of 0.7. The calculations suggest that grain boundaries with an excess volume close to this mechanical instability condition are entropy stabilized and can become more stable than boundaries with small excess volume at elevated temperatures. Taking the entropy of sublimation as an upper limit of the grain boundary entropy in order to prevent an entropy catastrophe, this state is separated by the single crystal state at elevated temperatures by an energy barrier on the order of 1 eV.

Intrinsic instability and entropy stabilization of grain boundaries.

A simple method is proposed to describe the thermodynamic properties of disordered grain boundaries in nanocrystalline metals and semiconductors. Based on a free-volume approach at negative pressure of the universal equation of state, the maximum free volume, thermal expansion coefficient, specific-heat capacity, and excess enthalpy, entropy, and free energy of grain boundaries are derived from well-known thermodynamic relationships. The results show good agreement with available experimental data and suggest an intrinsic mechanical instability of a nanograin boundary (Gibbs instability) accompanied by divergences of \ensuremath{\alpha} and ${\mathit{c}}_{\mathit{p}}$, and the possibility of an entropy stabilization of nanograin boundaries.

Thermodynamics of Nano-Grain Boundaries

ABSTRACTA universal, accurate and simple method is developed to describe the thermodynamic properties of disordered grain boundaries in nanocrystalline metals. Based on a free volume approach at negative pressure of the universal equation of state, the maximum free volume, bulk modulus, specific heat at constant pressure, thermal expansion coefficient, excess enthalpy, excess entropy and free energy of grain boundaries are derived from well-known thermodynamic relationships. Describing nanocrystalline metals as a bimodal material with a grain boundary component and a crystalline component, their thermodynamic properties can then be estimated by appropriate scaling of the boundary-to-volume ratio.

Heat capacity of glasslike materials: The free volume approach

The experimental quasi-linear temperature dependence of the heat capacity of glasses is explained in terms of the free volume concept. The state number density n(0) is calculated as a function of microscopic system parameters. It is noted that the proposed model is also suitable for investigation of the dissipation properties of glasses and proteins.

Viscosity of nematic mixtures: A free-volume approach

Abstract The five Leslie viscosities for a mixture of two nematic materials are computed as functions of the temperature, composition and order parameter. It is shown that, for a nematic mixture of A and B, the equations describing the composition and temperature behaviour of the Leslie viscosities have the same form as those for the pure components, provided that composition-averaged values of the parameters are used. For the case where the free volume is additive, the relaxation times for the mixtures can be directly expressed as functions of the parameters for the pure components. These results are compared with the experimental data on λ1 for MBBA/EBBA mixtures, and fairly good agreement is found.

Dielectric properties of polyarylate (PAr) around the glass transition

Dielectric characterization of the α-relaxation in polyarylate (PAr) has been carried out by means of a dielectric spectroscopy technique in a frequency range of 10–30 kHz. Complementary thermally stimulated depolarization currents ( TSDC) and differential scanning calorimetry d.s.c.) measurements have also been performed. The results are interpreted in terms of the standard Cole-Cole plot and Havriliak-Negami distribution for the dielectric relaxation times. Information about the temperature and frequency dependence of a.c. conductivity is also obtained from the experimental curves. However, the behaviour of the main dielectric relaxation time is deduced from the experimental data in a wide range of temperature around the glass transition. This behaviour results in close agreement with the theoretical predictions of a free-volume approach for the dielectric α-relaxation recently proposed by the authors.

Self diffusion of small molecules in aqueous solution of poly(vinylpyrrolidone)

The self-diffusion coefficients of small penetrants were measured in aqueous solutions at varying concentrations of poly(vinylpyrrolidone). Measurements have been performed using the n.m.r. pulsed-gradient spin-echo (PGSE) technique and the classical gradient diffusion (CGD) method, modified for ternary systems. A good agreement was found between the two, confirming the validity of the latter. The results have been quantitatively analysed by a free-volume approach adapted for diffusion of a solute in moderately concentrated polymer solutions. From this model a linear relationship is predicted between ln D D o and ∅ −1, the reciprocal volume fraction of solvent, which was also found experimentally for all diffusants studied. An enhanced concentration dependence of penetrant diffusion with increasing size of the diffusing molecules was observed. These findings are in agreement with predictions from the free-volume theory.

Calculation of impact transition temperature of low density polyethylene from shift factor via a free volume approach

A relationship between the impact transition temperatureTi and the stress concentration factorKs is derived. The relationship involves the temperature shift factoraT; in turn,aT depends on the free volume. In earlier work in this problem Zewi and Corneliussen [6] utilized the W-L-F equation. Here a more direct relationship betweenaT and the free volume is applied. Satisfactory values ofKs corresponding to givenTi are obtained for a wide temperature range; the range also includes temperatures below the glass transition pointTg. The opinion that a free volume exists between 0 K andTg is upheld.

Calculation of impact transition temperature of low density polyethylene from shift factor via a free volume approach

Calculation of impact transition temperature of low density polyethylene from shift factor via a free volume approach

Permeation of water-soluble solutes through poly(2-hydroxyethyl methacrylate) and poly(2-hydroxyethyl methacrylate) crosslinked with ethylene glycol dimethacrylate

A free volume approach has been used to describe the effect of apparent solute molecular size on solute membrane diffusion coefficient in poly(2-hydroxyethyl methacrylate) (pHEMA) and pHEMA crosslinked with 1 mole % ethyleneglycol dimethacrylate (EGDMA). Analysis of experimental results indicates, that for hydrophilic nonelectrolytes and inorganic chloride salts in the molecular weight range 20—500, the membrane diffusion coefficient decreases exponentially with increasing molecular size. p]Solute partition coefficients have been calculated for pHEMA and pHEMA crosslinked with 1 mole % EGDMA using a three-state model for gel water. Comparison of these calculations with experimental partition coefficients indicates that hydrophilic nonelectrolytes and inorganic chloride salts partition primarily into bulk water regions. From this result it may be implied that solute permeation occurs in gel bulk water.

The effects of plasticizer on the electric strength of polystyrene

Measurements made on polystyrene samples indicate that a marked reduction in electric strength occurs at a critical temperature which is indistinguishable from the glass transition temperature determined by differential thermal analysis. Both the electric strength and the critical temperature are shown to be dependent on the presence of plasticizing agent in the polymer. X-ray analysis of both plasticized and unplasticized materials over a range of temperature indicates changes of inter-molecular distance supporting the hypothesis that the action of the plasticizer is to influence the free volume exhibited. The experimental results are discussed and analysed on the basis of a free volume approach.

Liquid-glass transition, a free-volume approach

The free-volume model, which has been useful for describing the behavior of the viscosity $\ensuremath{\eta}$ of dense liquids and glasses, is extended to account for their thermodynamic behavior as well. Experimental results for the heat capacity ${C}_{p}$ and the volume $\overline{v}$ show that the system falls out of complete, metastable thermodynamic equilibrium at the glass transition temperature ${T}_{g}$. As a first step in understanding these universal phenomena, a theory of the underlying metastable phase, the amorphous phase, is developed. Recent molecular-dynamic calculations demonstrating the existence of a cellular structure in liquids and the properties of the local free energy of the molecular cells permit us to formulate more precisely and justify in more detail the standard free-volume model. In particular, it is possible to define the free volume and distinguish solid-like and liquidlike cells. This leads to the introduction of percolation theory, which is used to describe the gradual development of the communal entropy of the amorphous phase. We then determine the probability distribution of the cellular volume as a function of the fraction of liquidlike cells, $p$. The equilibrium liquid-glass transition is associated with the increase of $p$ with temperature. This occurs via a phase transition which is most probably first order. The results of our theory give a generalized equation for the viscosity which agrees accurately with experimental results at all temperatures. Results for ${C}_{p}$ and $\overline{v}$ are also obtained. This equilibrium theory can provide the basis for a relaxation theory of the kinetic effects observed around and below ${T}_{g}$. The relationship between the entropy theory and the free-volume model is also clarified.

Softening temperature of glassy polymers as affected by residual stresses

AbstractHeat deflection temperature and Vicat softening point of polystyrene and polymethylmethacrylate with various thermal histories were measured. Surface residual stresses were characterized by liquid crazing. Residual stress profiles across the sample thickness were also measured. It is suggested that the softening behavior of glassy polymers is affected by the state of the residual stresses in addition to the traditionally accepted free volume approach.

Glass transition temperatures of crosslinked poly ( isobutyl methacrylate)

The correlation between the glass transition temperatures of poly(isobutyl methacrylate) polymers crosslinked to various degrees with ethylene glycol dimethacrylate, tri- and tetraethylene glycol dimethacrylate and the degree of their crosslinking has been investigated. Based on the free volume approach a similar theoretical treatment as for the relation between T g and the length of the polymer side chain in an uncrosslinked polymer can be used. Good agreement is found between the experimental results for the systems investigated and for data in the literature.

Applicability of Free Volume Concept to Relaxation Phenomena in the Glass Transition Range

Abstract Except for discrepancies mentioned with respect to pressure investigations, which need future clarification, we can conclude in a general way, as follows. As far as only average parameters of macroscopic specimens are considered (complex moduli, or dielectric constants, volume or heat content etc...), the free volume concept can relate variations of molecular mobility to changes of an average free volume in a semiquantitative way. This average free volume can no longer fully characterize the wide variety of molecular motions involved in the kinetics of redistribution of holes in the liquid during recovery experiments. These kinetic processes involve a wide distribution of retardation times, which may be associated with local distribution of holes, or with that of cooperating groups of molecules, or molecular segments. On the other hand, free volume is not necessarily the fundamental molecular parameter which controls rate of configurational changes, characterized by variation of entropy of the liquid. Even if this is the case, most of the above discussion may be applied to any other average excess parameter, as far as the Doolittle equation is formally adopted, in which f/b is expressed in terms of the new parameter, rather than that of free volume. However, since relaxational free volume, as determined from the WLF equation, and independently measured volume changes are often in close agreement, this means that variations of excess entropy, or those of configurational free energy, and changes in volume are closely related. This conclusion is in agreement with that of Eisenberg and Saito, who found that the Gibbs—Dimarzio theory, based on configurational entropy, is practically equivalent with the free-volume approach. Thus, the free volume concept remains still a valuable tool for unifying different kinds of rate processes from both a theoretical and an experimental point of view, especially in the glass transition range.

Rayleigh Scattering: Orientational Relaxation in Liquids

A systematic investigation of orientational relaxation in liquids has been initiated employing the technique of Rayleigh scattering. The experimental results are interpreted based on an approximate theory which is developed and justified. Scattering spectra from 15 different liquids, including the homologous alkyl bromides and polyethylene glycols as well as glycerol, 1,3-butanediol, and n-octyl alcohol, were obtained as a function of temperature using a 6328-Å Ne–He laser source and a Fabry–Perot interferometer. All spectra were found to have approximately Lorentzian form symmetric about the source frequency, which implies molecular reorientation is a relaxational process. Also, the width of these Lorentzian lines (which is reciprocally related to the orientational relaxation time) increased with increasing temperature in such a way that an effective orientational activation enthalpy was determined. In both the alkyl bromide and polyethylene glycol series, increased molecular size resulted in increased relaxation time, which is explained using both activation-enthalpy and free-volume approaches. The measured orientational relaxation times which reflect motion of the induced dipole moments are compared with dielectric relaxation times associated with the permanent moments and mechanical relaxation times determined ultrasonically. This comparison provides additional information about the detailed nature of the reorientation mechanism. For example since orientational relaxation is shown to be governed by rotation of ellipsoidal-shaped molecules about their minor axes, it is concluded that mechanical motions are more nearly about major axes. In addition, it is possible to determine whether reorientation is a diffusion, jump, or an intermediate process. Experimental results indicate molecules in n-octyl alcohol and probably in the alkyl bromides reorient by a diffusional process and that glycerol molecules reorient by rather large jumps, while 1,3-butanediol is an intermediate case. These results are in excellent agreement with predictions based upon the McCuffie–Litovitz explanation for the distribution of dielectric relaxation times.

Free Volume Approach to Polysiobutylene melt Viscosity under Pressure

AbstractThe Doolittle melt viscosity expression ν = A eB/f has been applied to published data on polyisobutylene to calculate a parameter aP which is defined as the ratio of relaxation times at any pressure P to those at a reference pressure. To check the results, the parameter aP has also been calculated by the method of reduced variables. The agreement between the theoretical and experimental values of aP is found to be very good. Also the treatment separates melt viscosity of polyisobutylene into two factors, A dependents only on structural parameters, and f, which is determined by the specific volume is a function of temperature and pressure.

Free Volume Approach to Polystyrene Melt Viscosity

The Doolittle approach to Newtonian viscosity assumes η=A expB/f, where A and B are constants independent of temperature and f, the relative free volume, is (v−v0)/v0. Here v is the specific volume and v0 is the occupied volume. Using machine computations, this equation was applied to published data on polystyrene, replacing v by its equivalent vg+(dv/dT)(T−Tg), where vg is the specific volume at the glass temperature Tg. The agreement between calculated and observed viscosities is at least as good, and perhaps better, than that afforded by other existing empirical expressions. The constant B is independent of molecular weight and temperature while v0 depends slightly on molecular weight. A log-log plot of A against molecular weight M produces two straight lines intersecting at M=35 000. At higher values of M, the slope is 3.4; at lower values, it is slightly greater than one. This treatment separates the melt viscosity of polystyrene into two factors, A, dependent only on structural parameters, and f, which is determined by the specific volume and is a function of temperature.