Correlation of penetrant transport with polymer free volume: Additional evidence from block copolymers

The transport rates of methanol and water through a series of PEBAX® block copolymers were measured and correlated with the fractional free volume. Excellent agreement between the logarithm of the diffusion coefficient and the inverse of the fractional free volume of the polymer was observed. This provides new evidence of the utility of the free volume theory to describe the transport of highly condensable vapours. Correlation was also quite good when the logarithmic additivity relationship was employed. This relationship has been previously shown to correlate the properties of homogenous blends with copolymer composition. The successful use of this theory for a series of blends that exhibit two glass transition temperature is discussed.     

Experimental determination of interface widths in binary polymer blends from free volume measurements

Interfaces in binary polymer blends play a pivotal role in moulding their physical properties. We observe a diffused interface in immiscible and partially miscible binary polymer blends for which the methods of preparation characterize the interface widths. The interface widths for three binary blends of PVC/PS, PS/PMMA, and PVC/SAN are in the maximum range of 2.15, 5.04 and 6.24 nm respectively. We establish a correlation between hydrodynamic interaction and the Flory–Huggins interaction parameter which is consistent with self-consistent mean field theory and the usual constructed density profile across the interface. Our approach is based on the hydrodynamic interaction which is derived from free volume data measured by positron lifetime spectroscopy.     

Application of the surface free energy concept in polymer processing

The surface characteristics of variously treated carbon and glass fibres have been determined by contact angle measurements (using a capillary rise technique), inverse gas chromatography, and zeta potential measurements. The contact angles of water and methylene iodide were used to calculate the dispersive and non-dispersive components of the fibre surface free energy by applying the geometric mean approach, and the approach by Fowkes to estimate the acid-base term of the thermodynamic work of adhesion. The results obtained correlate with those of inverse gas chromatographic and zeta potential measurements. The non-polar surface character of the carbon fibre can be altered by oxidizing, or finishing the fibres with an epoxy resin. The acid-base term of the thermodynamic work of adhesion, W^ab _a, and the non-dispersive component of the surface free energy, γ^p _s, are increased drastically by these treatments. Treatment of the 'high-energy' glass fibre surface with an aminosilane results in a relatively low surface free energy with basic surface groups. When epoxy dispersions were used for sizing the glass fibres, the surface free energy increased without changing the basic surface character. A direct correlation between the surface-energetic properties of the fibres and the mechanical behaviour of the fibre-reinforced polyamide composites was not generally found.     

Statistical-mechanical theory of the deformation dependence of topological constraints in polymer networks

Summary This paper describes a simple model of topological constraints on polymer network chains. In the frame of this model we calculate the deformation dependence of the constraining potential used in a theory of stress-strain behaviour previously.Presented at the 7th Discussion Conference IUPAC Polymer Networks, Karlovy Vary, CSSR, September 15–19, 1980     

Temperature‐dependence modeling of highly crosslinked polymer networks

The dependence on the temperature of the state of a highly crosslinked polymer network can be modeled as a function of well‐defined molecular‐level network parameters to yield a simple applied model equation. The tightness and strength (modulus of elasticity) of the crosslinked networks formed, as well as any further tightening of the network due to further curing, can easily be compared with the parameters A, M, and α (the coefficient of branching) and the m/E ratio and, therefore, with parameters directly related to molecular‐level characteristics of the system. The crosslinking contribution to the network is represented by A and M, the former representing the frequency of crosslinking and the latter having the dimensions of an energy. The ratio m/E, that is, the ratio of the average number of degrees of freedom of chain segments between crosslinking nodes (m) to the average energy of nonbonded atom interactions between the same segments (E), and α model the noncrosslinked contribution to the characteristics of the network. These are the same parameters that appear in the simple equation modeling the dependence of the characteristics of the network on the temperature within a limited temperature range. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 2416–2426, 2003     

Elastic energy in microscopically phase-separated swollen polymer networks

The paper analyzes a microscopic regime of strain, different from the one conventionally considered, that presumably takes place in swollen polymers showing strong microscopic phase separation, such as ion-exchange resins in water. Such systems show linear dependence of the elastic pressure on swelling in contrast to the Flory-Rehner theory and its modifications. The present work proposes a simple model that predicts this kind of behavior. Swelling is considered as a non-affine ‘inflation’ of the hydrophobic matrix by small aggregates of water molecules (‘droplets’) adsorbed by highly hydrophilic groups, whereas the macroscopic dimensions of the sample change as a result of the compression of the ‘films’ separating the droplets. This compression is then analyzed along the classical lines. In the case of the Dowex resins a partial test of the model based on the reported shear moduli showed reasonable agreement with experiment.     

Excess free energy of nanoparticles in a polymer brush

We present an efficient method for direct determination of the excess free energy ΔF of a nanoparticle inserted into a polymer brush. In contrast to Widom's insertion method, the present approach can be efficiently implemented by Monte Carlo or Molecular Dynamics methods also in a dense environment. In the present investigation the method is used to determine the free energy penalty ΔF(R, D) for placing a spherical particle with an arbitrary radius R at different positions D between the grafting plane and the brush surface. Deep inside the brush, or for dense brushes, one finds ΔF ∝ R³ whereas for shallow nanoclusions ΔF ∝ R², regardless of the particle interaction (attractive/repulsive) with the polymer.The pressure and density fields around spherical nanoinclusions in a polymer brush are also investigated. Extensive Monte Carlo simulations show that the force, exerted on the particle by the surrounding brush, depends essentially on the proximity of the nanocolloid particle to the brush surface not only in strength but also with respect to its angular distribution. For shallow nanoinclusions close to the brush surface this angular distribution is shown to result in a growing buoyant force while deep inside the brush this effect is negligible.     

Epoxy and hyperbranched polymer blends: Morphology and free volume

In this work, the phase separation of an epoxy‐functionalized hyperbranched polymer (HBP) in a blend with a conventional epoxy resin is examined. Morphology development with the advancement of curing reaction was investigated by hot‐stage polarized optical microscope, where it was found that HBP is miscible in epoxy resin solvent at 120°C and undergoes phase separation during the curing reaction, leading to a two‐phase microstructure which maintains a dispersed morphology up to 20 wt % HBP. The degree of phase separation and morphology were also investigated using differential scanning calorimetry, and the resultant microstructure was confirmed by atomic force microscopy. The epoxy/HBP blends were characterized by positron annihilation lifetime spectroscopy for their free volume characteristics where behavior typical of miscible blends was seen, likely due to chemical bonding between the two phases. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Dark reactions of free radicals trapped in densely crosslinked polymer networks after photopolymerization

Difunctional methacrylate monomers containing stiff or flexible spacers were combined with a vinylcyclopropane derivate in a copolymerization to form densely crosslinked networks. The high rate of visible light photoinitiation at 20–22°C was used for starting the polymerization. By switching off the light after 40 s, the long‐lived free radicals, trapped in the polymer network, retain radical processes, however, at substantially retarded rates. The postcuring development of the network structure in the investigated samples lasting at least 12 weeks was proved by the increasing density of the crosslinks, by the increasing amount of the gel fraction, and by the decreasing of the residual unsaturation. The relaxation spectra from dynamic mechanical thermal analyses (DMTA) show curves with two evident maxima. The first one belonged the glass transition (T_g) of original network and increases in the postcuring period. The second one belonged to the final structure to which the crosslinked polymer approaches slowly during aging. The final state develops fast during a DMTA thermal scan to 200°C. All procedures proceeded in the dark, but in the presence of air oxygen. The chemiluminescence (CL) response of the postcured samples proved the accumulation of hydroperoxides. The oxidation chain reaction took place in the postcuring time and competed with the building up of additional crosslinks. The majority of postcuring changes were observed during the first 3 weeks of aging. Nine weeks later, the long‐lived radicals were still present in the network and maintained the sensibility of the crosslinked polymer to free‐radical reactions. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 579–588, 2003     

Nanohole volume dependence on the cure schedule in epoxy thermosetting networks: A PALS study

A systematic study on the dependence of the volumes at nanoscale in epoxy systems cured with two selected aminic hardeners at different pre-cure temperatures is presented. Nanohole volumes were measured by positron annihilation lifetime spectroscopy. Additional information regarding the structure of the thermosets was obtained using dynamic mechanical analysis. Volume results obtained are discussed in terms of the cure schedule applied to the epoxy systems, their characteristic glass transition temperatures and their crosslink density. The pre-cure temperature and the structure of the hardeners govern the packing of the molecular chains of the epoxy network. Using together positron and mechanical experimental techniques allows to conclude that a strong change in the volume and number density of the nanoholes takes place when the pre-cure temperature crosses the glass transition temperature of the systems.     

Experimental measurements on configurational free energy change of the graphite-glassy carbon equilibrium

A precise thermodynamic measurement of the equilibrium: C_graphite = C_{glassy carbon} employing a solid oxide electrolyte in the temperature range 650°–1150°C was carried out to gain structural information on glassy carbons. The measured Gibbs free energy change yields configurational (residual quantities at zero Kelvin) enthalpy and entropy differences, which represent a two parameter measure of the structural differences between a given glassy carbon and graphite, since the above reaction involves vanishingly small differences in composition, specific heat, and hence vibrational contributions. Many of the experimental and commercially available samples of glassy carbons studied exhibited at elevated temperature thermodynamic carbon activities lower than graphite. For various samples studied, the zero point entropy varied from 3.1 to 11.3cal/g-mole-°K. The thermodynamic parameters are correlated with X-ray and density measurements. The configurational enthalpy and entropy changes are interpreted in terms of strain related and atomic disorder parameters, respectively.     

Thermodynamic properties of polymer solutions: effect of free volume fraction of solvent molecules

Knowledge about the thermodynamic properties of a polymer solution is essential to its applications. These properties are derived on the basis of a statistical mechanics approach by modifying the classic Flory–Huggins theory in this study. The analytical result derived is fitted to the available experimental data such as toluene–polystyrene and benzene–silicone polymer solutions in the literature, and its performance is satisfactory. We show that the inconsistency between the Flory–Huggins theory and experimental observations for many polymer solutions might arise from the negligence of the effects of the free volume fractions of solvent and polymer and the change in the disorientation entropy of polymer molecules.     

Reply to comments on the need to reconsider traditional free volume theory for polymer electrolytes

New aspects of the defect diffusion model (DDM) are presented. First, it is shown that if the correlation volume exhibits two dimensional scaling, e.g. grows in two dimensions more rapidly than in a third orthogonal direction, the standard Vogel relation is obtained. Second, it is pointed out that, independent of the dimensionality, ∂ ln σ/∂P should be proportional to ∂ ln σ/∂ ln T where the proportionality constant is −∂ ln T_c/∂P. It is shown that both of these results are consistent with the temperature and pressure variation of the electrical conductivity for 20:1 PPG:LiCF₃SO₃ below about 1.3 times the glass transition temperature, T_g. Finally, the DDM is compared with the free volume theory (FVT) of Dlubek et al. who have reconsidered “traditional” FVT and presented a formalism where the free volume is not proportional to the macroscopic volume. One aspect of the new FVT, which is difficult to understand is that the compressibility of the occupied volume is larger than the compressibility of the free volume.     

Effects of thermodynamic models on the predictions of free volume diffusion theory for concentrated polymer solutions

Three thermodynamic models were used to demonstrate the effects of model choice on solvent–polymer binary diffusion coefficients predicted by free volume theory. Poly(vinyl acetate) and four solvents were used as typical solutions for these calculations. Thermodynamic models affect the predictions the most at high solvent weight fractions and for solutions which exhibit positive enthalpic interactions. For solutions dilute in solvent where Henry's law might describe phase equilibria, diffusion coefficients can be estimated without reference to thermodynamic data.     

Beyond classical theory: Predicting the free energy barrier of bubble nucleation in polymer foaming

Based on the Gibbs‐Tolman‐Koenig formalism, we considered the Tolman correction to the free energy barrier of bubble nucleation in polymer‐gas binary mixtures. For this class of systems, the correction may be estimated with a reasonable accuracy using experimentally accessible macroscopic thermodynamic quantities only. Although the Tolman correction is applicable only in the low supersaturation regime, a simple ansatz regarding the supersaturation dependence of the Tolman length can be made to extend the usefulness of this approach and to yield the free energy barrier that vanishes at the mean‐field spinodal as demanded by thermodynamic considerations. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3042–3053, 2013     

Jarzynski on work and free energy relations: The case of variable volume

Derivations of the Jarzynski equality (JE) appear to be quite general, and applicable to any particle system, whether deterministic or stochastic, under equally general perturbations of an initial equilibrium state at given temperature T. At the same time, the definitions of the quantities appearing in the JE, in particular the work, have been questioned. Answers have been given, but a deeper understanding of the range of phenomena to which the JE applies is necessary, both conceptually and in order to interpret the experiments in which it is used. In fact, domains in which the JE is not applicable have been identified. To clarify the issue, we scrutinize the applicability of the JE to a Hamiltonian particle system in a variable volume. We find that, in this case, the standard interpretation of the terms appearing in the JE is not adequate.     

压裂液从聚合物到无聚合物的转变

阐述了传统聚合物压裂液的组成和突出特点,包括油基压裂液、水基压裂液、泡沫压裂液、乳化压裂液。重点介绍了无聚合物压裂液重大研究成果及需要解决的问题,并对压裂液的发展趋势作了几点展望。     

压裂液从聚合物到无聚合物的转变

阐述了传统聚合物压裂液的组成和突出特点,包括油基压裂液、水基压裂液、泡沫压裂液、乳化压裂液。重点介绍了无聚合物压裂液重大研究成果及需要解决的问题,并对压裂液的发展趋势作了几点展望。     

Temperature dependence of the thermal expansivity in polymer

The effects of temperature on the specific volumes and thermal expansivities for a range of amorphous polymers, above and below the glass transition temperature, are treated on the basis of the physical properties of polymers. The results are found to be in good agreement with observed data. The analysis of the results shows that the temperature derivative of the zeropressure thermal expansivity of the liquid polymer increases with increasing temperature. The change in the thermal expansivity, Δα = α_OL ? α_OG, decreases with increasing temperature.