Terms Of Free Volume Research Articles

Application of a new structural theory to polymers. ii. transition states for amorphous polymers and copolymers

Abstract A recently developed nonequilibrium thermodynamic theory of continuum rheology is combined with a generalized definition of thermomechanical transitions, to produce a single equation for interrelating the basic variables (stress o, strain rate ε, pressure p, temperature T, and structure ℊ) at a transition. Specialization of ℊ to represent uncrosslinked polymers leads to incorporation of molecular weight M as a variable. New predictions are thus made for the glass transition [Tg(M), Tg(p), Tg(ε) and others] and compared successfully with data. Particularly remarkable are the results that 1/Tg is a piecewise linear function of In M, and T is piecewise linear with p. Comparable results and confirmation with data arise when applying the theory to the liquid-liquid transition, T ll (M). For random copolymers, application of a single mixing rule to the transition equation leads to a prediction of Tg as a function of composition and the Tgi for the homopolymers (components i). This relationship reduces, in various cases, to several familiar equations in which the parameters were simply empirical, thus providing an interpretation of those parameters and defining restrictions applicable to each case. Finally, an alternative interpretation of ℊ in terms of free volume allows the theory to be extended to other systems, including those with small molecules.

Thermoanalytical study of an aged XLPE-pipe

A high quality pipe made of XLPE (Engel method) for industrial applications was used for the study of the material deterioration process upon accelerated aging. A sample aged at 110°C while submitted to an hydrostatic pressure of 0.53 MPa, giving a hoop stress of 2.66 MPa, was studied by means of Thermal Analysis, Density, and Gel Content measurements. The effects of aging are compared to a reference unexposed sample and the experimental results are discussed in terms of annealing effects, free volume and structural relaxation processes.

UCST and LCST Behavior in Polymer Blends and Its Thermodynamic Interpretation

A pair of dissimilar polymers with high molecular weights, poly(acrylonitrile-co-styrene) poly(acrylonitrile-co-butadiene), was found to exhibit both UCST (upper critical solution temperature) and LCST (lower critical solution temperature) behavior. This phase behavior is interpreted by combining the solubility parameter theory involving the free volume term and the recent idea of “miscibility window” for the polymer blends including random copolymers.

Thermodynamics of polymer miscibility

AbstractThe phase behaviour of polymer blends containing random copolymers is discussed in terms of the PRIGOGINE‐FLORY theory. For a miscible high molecular mass system the interaction parameter XAB has to be negative in polymer/copolymer systems, however, miscibility does not require any specific interactions. Repulsion between the segments comprisiing the copolymer can lead to XAB < 0 and favour miscibility. At elevated temperatures immiscibility occurs due to the unfavourable free volume term depending on the difference in thermal expansion coefficients of the components. The phase diagrams of polymer/copolymer systems calculated by the presented theory agree satisfactorily with the experimental data.

GAS CHROMATOGRAPHIC DETERMINATION AND CORRELATION OF WEIGHT-FRACTION HENRY'S CONSTANTS FOR HYDROCARBON GASES AND VAPORS IN MOLTEN POLYMERS

In the polymer industry, separation equipment is required to separate unreacted monomers and solvents from polymers. In order to design such equipments, solubilities of gases and vapors in molten polymers are needed as fundamental data. It is very helpful if the weight-fraction Henry's constant, which gives solubilities of a solute at concentrated regions of a polymer, can be estimated by a predictive method. In the present study, a new expression for the free volume term has been derived and is coupled with the UNIFAC model. The present UNIFAC-FV model was applied to common polymer systems. The weight-fraction Henry's constants were calculated for several volatile hydrocarbons and the calculated results were compared with the experimental data determined by a gas chromatographic technique. The present UNIFAC-FV model with a new free volume expression was found to be helpful in predicting the weight-fraction Henry's constants of hydrocarbon solutes in molten polystyrene, in polypropylene, and in low-density polyethylene. It is advantageous that our model is applicable both supercritical gases and subcritical vapors with no adjustable parameters.

Upper and lower critical solution temperatures for polystyrene in methyl cyclopentane and in dimethyl cyclohexane

Abstract The demixing of polystyrene in methyl cyclopentane, and in dimethyl cyclohexane has been investigated, and the upper and lower critical solution temperatures established for several polymer molecular weights. In the former solvent both upper and lower θ temperatures can be defined, but not in the latter where cloud point curves for the upper and lower critical temperatures coalesce for high molecular weights. The Patterson theory of polymer solutions has been applied to the data, and the characteristic free volume and exchange energy parameters have been evaluated. The lower critical solution temperatures are nearly the same in cyclopentane and methyl cyclopentane due to a compensation between the free volume and contact interaction terms. Solvent size effects are considered in order to explain the differences in the interaction of solvent with polymer.

Approche du mécanisme de gélification des sols d'agarose III. Comportement rhéologique de divers échantillons et étude énergétique de leur gélification

Investigations of varied agarose samples indicate differences in rheological charactaractics of their sols. An assumption is proposed to explain plastic behavior. The evaluation of the energy of activation for viscous flow depending on samples and concentration of polymer contribute to clarification of the gelling process. Intermolecular forces in every step of the forming network and the influence of polymer concentration are discussed. The results are interpreted in terms of free volume and cooperative motions. Repulsion intermolecular forces become of dominant importance and hinder the gelling process above a particular concentration varying with the rtheological characteristics of agarose samples.

Polymer compatibility with and without a solvent

AbstractA qualitative review of the thermodynamics of polymer systems will be given in terms of three contributions: positional (or combinatorial) entropy, an “international” term and a free volume term. From this one finds that a simple polymer‐solvent system phase separates on lowering T to an Upper Critical Solution Temperature (UCST) or raising it to Lower Critical Solution Temperature (LCST), To achieve miscibility of two polymers of high molecular weight, one requires a “specific” interaction, usually a weak charge‐transfer complex or a hydrogen bond. Phase separation takes place on raising the temperature to an LCST. These various UCST and LCST are predicted semi‐quantitative by the Prigogine‐Flory theory. When a solvent is added to two miscible polymers, a new type of phase separation appears since there is an effect of any difference in the strengths of the two polymer‐solvent interactions. Phase separation may easily occur in the ternary system where there is none in the three binary systems, and examples will be given. In the case of two highly‐attractive polymers in a solvent, a quite different phase separation occurs, sometimes called complex coacervation. A simple Flory‐Huggins type theory predicts these phenomena in ternary systems.

Modified cell theory: Free volume distributions and the equation of state for D-dimensional hard sphere systems

A generalized cell model, using cells of different sizes, is applied to hard rods, disks and spheres. Structures is discussed in terms of free volumes. The derived equation of state is exact for rods. For disks and spheres it provides a good approximation in the dense fluid and solid state.

Empirical relation for diffusion of gases in hydrocarbon polymers: Interpretation in terms of fractional free volume

AbstractAn empirical relationship between the diffusion coefficients of gases in three polyethylenes and their diffusion coefficient in natural rubber is given. The diffusion coefficients are given within a relative error of 4.7%. This relationship is interpreted according to the fractional free volume theory. The ratios of the fractional free volumes in the polyethylenes to the fractional free volume in natural rubber are derived.

Cavities and free volume in hard-disc and hard-sphere systems

The pressure of a hard-sphere system (in 1, 2 and 3 dimensions and at all densities) can be expressed in terms of the surface area 〈si〉 and volume 〈vi〉 of an average cavity. In contrast, the analogous expression for the pressure in terms of free volume requires the average 〈sf/vf〉 over the free volume of each sphere, which is not expressible in terms of an average free volume. We show that 〈si〉/〈vi〉=〈sf/vf〉.Numerical values for the number, size and variance of cavities in the hard-disc fluid and solid are calculated.An incidental finding is that deviations from the ideal gas equation are given to a good approximation by p/ρkT–1 =⅕ exp 5z for discs and by p/ρkT–1 =⅖ exp 5z for spheres, between the low density percolation transition and the freezing density.

Early or late transition states in the Menschutkin reaction. A resolution of the entropy problem

When correctly applied, comparisons of entropies of activation with standard entropies of reaction to the product pair of dissociated ions show that transition states in Menschutkin reactions do not resemble the product dissociated ions, a conclusion that is in agreement with all previous work in terms of free energy, enthalpy, and volume.

Polymer diffusion at intermediate concentrations

AbstractSchlieren optics in conjunction with a modified Claesson cell allows free‐diffusion experiments to be performed over a wide range of polymer concentrations. A data analysis procedure is presented for computation of the mutual diffusion coefficient using this technique. The dependence of the diffusion coefficient on concentration in polymer solutions is satisfactorily explained in terms of free volume, and a relation is proposed for correlating the mutual diffusion coefficient and zero‐shear viscosity.

Diffusion of p‐nitroaniline in poly(tetramethylene oxide)‐poly(tetramethylene terephthalate) block copolymers

AbstractDiffusion coefficients of p‐nitroaniline in poly(tetramethylene ether)glycol terephthalate‐poly(tetramethylene terephthalate) (4GT) block copolymers, containing 4GT wt fraction of 0,345, 0,514, and 0,712, have been determined from sublimative desorption kinetics in the range from 60 to 120°C. The temperature dependence of diffusion coefficients in each diffusion system has been found to be a Williams‐Landel‐Ferry (WLF) type. When the glass transition temperatures (Tg) of the soft segments are selected as reference temperatures, the WLF parameters of C and C in the case of diffusion at temperatures above Tg+100 K can be obtained from a new method, proposed in the present paper, on the basis of Fujita's expression of diffusion coefficient in terms of free volume. Parallel studies of dynamic mechanical properties of these copolymers and the assumption of iso‐free volume state at Tg provide the values of free volume parameters of Bd and expansion coefficients of free volume. Both the quantities so obtained decrease to a small extent with increasing 4GT wt fraction. Alternatively, the temperature dependence of diffusion coefficients in the present study can be expressed exactly by Arrhenius plots. The activation energies of diffusion based on Eyring's rate processes are almost independent of, but the activation entropies decrease significantly with, increasing 4GT wt fraction. An expression of the latter in terms of the free volume parameters is presented.

Fluctuating Free-Volume Analysis of the Soft-Core Model of High-Density Fluid States

The high-density fluid states of the soft core system are analysed in terms of fluctuating free volumes which are defined with use of atomic configurations simulated by a molecular dynamics method. Statistical properties of fluctuating free volumes are examined. They can be classified into extensive and intensive types. The fraction of intensive free volumes increases rather rapidly above ρ * ≃0.7, where ρ * is defined by ρ( e / k T ) 1/4 and ρ= N σ 3 / V . This fact is well correlated with the dynamic as well as the static features of the system found previously. The Helmholtz free energy is derived in terms of mean free volumes under Singer's assumption. It is in a good agreement with the result obtained by computer experiments, but the difference between them is systematic. It is overestimated for stable fluid states, and underestimated for metastable supercooled fluid states.

Dynamic mechanical properties of poly(2‐hydroxyethyl methacrylate) hydrogels

AbstractHomogeneous and heterogeneous poly(2‐hydroxyethyl methacrylate) hydrogels were prepared by copolymerization of 2‐hydroxyethyl methacrylate and small amounts of ethylene glycol dimethacrylate in the presence of water; concentrations of water (V1) in the polymerization mixture and the volume fractions of water (v1) of the gels swollen to equilibrium were 40, 50, 60, 70% by volume, and 0.475, 0.541, 0.669, 0.778, respectively. From the homogeneous (clear) hydrogel (V1 = 40%) preparation, four hydrogels were prepared with v1 = 0.434, 0.418, 0.378, 0.326. Tensile dynamic moduli were measured in the frequency range from 0.006 to 0.6 cps and the temperature range from 0 to 40°C. In these cases, the influence of swelling on the shape of the relaxation spectra and on the monomeric unit friction coefficient was studied. The dependence of the friction coefficient on water concentration was interpreted in terms of free volume. In the heterogeneous (opaque) gel preparations (V1 = 50, 60, 70%), the effect of the aqueous phase in the system on the mechanical behavior was described by a modification of the blending law of Ninomiya. For the systems with V1 = 60% and 70% the shapes of the storage and loss moduli in the main transition region and the friction coefficient were similar to those of the homogeneous gel with V1 = 40%, except for the decrease in absolute value of the storage moduli. For the system with V1 = 50% the shape of the relaxation spectrum changes appreciably and the wedge distribution does not hold.

Heats of mixing of atactic polybutene-1 and of a model molecule with normal alkanes-order in long alkanes

Heats of mixing at infinite dilution of atactic polybutene-1 in the alkanes have been measured at 25° with a Calvet microcalorimeter. Heats for a model molecule, the 3,5-dimethylheptane, in the same alkanes were obtained also. The enthalpy parameter X H was found to be very close for the two sets of systems. Fitting the experimental data with the calculated free volume term of the heats, the parameter X 12 (as expressed in the Flory theory) is found to go through a minimum with chain length. This feature is explained thus: for longer alkanes, the large heat is thought to be due to loss of order in the chain solvent. For the short alkanes, X 12 is found large to compensate an overestimation of the free volume term.

Permeability of solutes through hydrated polymer membranes. Part III. Theoretical background for the selectivity of dialysis membranes

AbstractThe diffusional transport of aqueous solutes through water swollen polymer membranes is examined by the concept of the free volume of the water‐polymer systems, Vf,13. The relative diffusivity (D in membrane/D in water) can be expressed by the product of the probability factor of finding holes of equal or larger cross section, q, than the cross section of solute, q2, (sieve mechanism) and the free volume factor. An analysis of experimental data indicates that within the range of solute size investigated (up to albumin) the sieve mechanism is not yet playing a role in homogeneous cellulosic membranes. The main reduction of permeability of larger solutes is caused by the free volume term which is an exponential function of the negative cross section of the solute, q2, exp (–Bq2/Vf,13). In porous membranes, however, the sieve mechanism alone is responsible for the selectivity.

Formation and quenching of ortho-positronium in molecular materials

A correlation is observed between the lifetime and two-photon annihilation intensity by pick-off process of ortho-positronium in molecular materials. An empirical model, in terms of free volume, is developed to explain this correlation. The variation in lifetime and intensity with change of temperature and pressure, and due to melting of crystals, and glass-transition in polymers is considered, on the basis of this model.