A free-volume-based approach to modeling thermoset cure behavior

The free-volume theory for the temperature dependence of transport properties of glass-forming polymers is extended to obtain their relationship to the extent of cure. This treatment centers on the unifying role of molecular mobility and yields a model which connects extent of reaction, viscosity, diffusivity, ionic conductivity and dipole relaxation time. The temporal dependence of these properties is expressed by coupling the extended free-volume model with a relationship for the rate of cure, which included diffusional limitations. Analyses based on this model are applied to the observed behavior of a model epoxy-amine resin system. The intrinsic kinetics of this model system are shown to be first order. It is shown that diffusional limitations strongly affected the progress of the reaction in the final stages of cure. The diffusion-modified rate expression predictions agree with extent of reaction versus time data over the range of experimental temperatures. The temporal dependence of viscous behavior of the curing resin is measured. The extended free-volume model accurately describes the evolution of resin viscosity during cure. The dielectric behavior is similarly characterized and is in close agreement with the predictions of the general free-volume expression. The results of this study indicate that the free-volume theory modified to account for molecular weight effects allows prediction of resin properties with a two-parameter model. The results show that a power-law relationship exists between viscosity and ionic conductivity. This result suggests that electrical properties may be used for on-line measurement of resin viscosity during cure.     

Free-volume theories for self-diffusion in polymer–solvent systems. II. Predictive capabilities

The predictive and correlative capabilities of two recent versions of the free-volume theory for self-diffusion in polymer–solvent systems are examined by comparisons with experimental data. Neither the Vrentas–Duda free-volume theory nor the Paul version generally provides satisfactory predictions for the temperature and concentration variations of solvent self-diffusion coefficients. However, the Vrentas–Duda theory does provide good correlations of solvent self-diffusion data, and, furthermore, this theory can provide good predictions if a small amount of solvent self-diffusion data is used to help estimate the parameters of the theory. New diffusivity and equilibrium data were collected for the toluene-PVAc system to provide a broader database for evaluation of the self-diffusion theories.     

Depolarization thermocurrents in amorphous polymers

The depolarization thermocurrent (DTC) method gives the dependence of the dielectric relaxation time on temperature. It has been used for investigations of relaxations obeying an Arrhenius-like law in crystalline polymers. The analysis of this method shows it is possible to study mechanisms described by the Williams-Landel-Ferry (WLF) equation. The critical temperature appearing in the free-volume theory of Cohen and Turnbull and also in the statistical thermodynamic theory of Adam and Gibbs can then be measured with good accuracy. The thermal coefficient of expansion of the free-volume and the WLF coefficient for any reference temperature can also be obtained. Since analysis of the experimental DTC spectrum is particularly simple, this method seems to be a very useful tool for examination of relaxation transitions in amorphous polymers. As an example, results obtained for poly(methyl methacrylate) are presented; they are consistent with published data.     

Modeling of gamma-ray radiolysis data at moderate and low solute concentrations in aqueous solutions

A radiation chemical model developed for use in pulse radiolysis studies employing high energy electrons has been applied to the calculation of yields in aqueous chemical systems irradiated with ⁶⁰Co γ-rays. The fit between model calculations and experimental data is almost within experimental error in most instances. Trends are accurately predicted where quantitative agreement is not found. Predictions of molecular yields of H₂ and H₂O₂ in the presence of scavengers of precursors of these molecules are in good agreement if an initial molecular yield is assumed for both molecules. Agreement between model predictions and experimental data is reasonable at low solute concentrations where back reactions of spur intermediates are important. The model appears to be useful in modeling steady state γ radiolysis as well as pulse radiolysis data. Implications of the model in predicting possible errors in rate constant determinations are discussed.     

Influence of concentration on the activation energy for diffusion in polymer-solvent systems

The self-diffusion of benzene, toluene, and ethylbenzene in polystyrene have been analyzed using the Vrentas/Duda free-volume diffusion model. Diffusion coefficient predictions suggest an exponential concentration dependence of the activation energy required to overcome attractive forces, E. Without the use of any diffusion data approximating E as zero over the entire concentration range yields self-diffusion coefficient predictions which are in good agreement with experimental data. © 1992 John Wiley & Sons, Inc.     

The diffusion of CO2, CH4, C2H4, and C3H8 in polyethylene at elevated pressures

Diffusion and solubility coefficients have been determined for the CO₂^?, CH₄^?, C₂H₄^?, and C₃H₈-polyethylene systems at temperatures of 5, 20, and 35°C and at gas pressures up to 40 atm. Diffusion coefficients were obtained from rates of gas absorption in polyethylene rods under isothermal-isobaric conditions by means of a new diffusivity apparatus. The concentration dependence of the diffusion coefficients was represented satisfactorily by Fujita's free-volume model, modified for semicrystalline polymers, while the solubility of all the penetrants in polyethylene was within the limit of Henry's law. Semiempirical correlations were found for the free-volume parameters in terms of physicochemical properties of the penetrant gases and the penetrant-polymer systems. These correlations, if confirmed, should permit the prediction of diffusion and permeability coefficients of other gases and of gas mixtures in polyethylene as functions of pressure and temperature.     

Mixtures of charged colloid and neutral polymer: influence of electrostatic interactions on demixing and interfacial tension

The equilibrium phase behavior of a binary mixture of charged colloids and neutral, nonadsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with nonadditive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter-the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion concentration ratios, a free-volume approximation for the free energy is used to compute the fluid phase diagram, which describes demixing into colloid-rich (liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic interactions shifts the demixing binodal toward higher polymer concentration, stabilizing the mixture. The enhanced stability is attributed to a weakening of polymer depletion-induced attraction between electrostatically repelling macroions. Comparison with predictions of density-functional theory reveals a corresponding increase in the liquid-vapor interfacial tension. The predicted trends in phase stability are consistent with observed behavior of protein-polysaccharide mixtures in food colloids.     

A free-volume hole-filling model for the solubility of liquid molecules in glassy polymers 1: Model derivation

The use of hole-filling models is quite common for the sorption of gases into glassy polymers, but these have yet to be explicitly applied to the case of liquid immersion, where extensive use of Flory-Huggins theory dominates. This paper explores how the models based on the idea of sequential filling of a Gaussian distribution of pre-existing free-volume holes within the structure of the glassy polymer can be modified to allow the prediction of the equilibrium solubility of a liquid penetrant. For liquids, the driving force for sorption is more subtle than for gases, with more emphasis on molecular interactions rather than external pressure. For this reason, terms relating to the molecular interactions of a liquid molecule filling a hole were developed, including the effects of elastic constraint for small holes. Consideration of thermal fluctuations show that configurational entropy provides much of the driving force for sorption. Some comparisons with experimental data show a reasonable agreement, and one which is far better than the Flory-Huggins theory.     

氯乙烯在高聚物中的溶解度

本文进行了氯乙烯在氯相/高聚物 (PVC,EVA,EVA-g-VC) 间相平衡的研究。实验数据用三种数学模型作了处理:Flory-Huggins 经典模型、Prigogine-Flory 自由容积模型和本文作者提出的线性模型。氯乙烯在高聚物中的溶解度按三种模型的计算值与实验结果都符合得很好。而且,结果表明,线性模型具有精确易用的优点,Prigogine-Flory 模型完全适用于 VC/PVC体系,VC在EVA-g-VC接枝共聚树脂中的溶解度服从加和性规律。     

Shear and dielectric responses of propylene carbonate, tripropylene glycol, and a mixture of two secondary amides

Propylene carbonate and a mixture of two secondary amides, N-methylformamide and N-ethylacetamide, are investigated by means of broadband dielectric and mechanical shear spectroscopy. The similarities between the rheological and the dielectric responses of these liquids and of the previously investigated tripropylene glycol are discussed within a simple approach that employs an electrical circuit for describing the frequency-dependent behavior of viscous materials. The circuit is equivalent to the Gemant-DiMarzio-Bishop model, but allows for a negative capacitive element. The circuit can be used to calculate the dielectric from the mechanical response and vice versa. Using a single parameter for a given system, good agreement between model calculations and experimental data is achieved for the entire relaxation spectra, including secondary relaxations and the Debye-like dielectric peak in the secondary amides. In addition, the predictions of the shoving model are confirmed for the investigated liquids.     

A simple and generalized model for predicting the density of ionic liquids

A simple and accurate model to predict the density of ionic liquids is presented. The proposed model is based on a generalized correlation that has been conveniently modified and experimental literature data have been used to fit the five model parameters, to finally propose an equation that allows predicting densities of any ionic liquid. The model uses the critical temperature, the critical volume, the normal boiling temperature and the molecular mass to estimate the density at temperatures commonly used in ionic liquid applications (270–360 K). A set of 602 density data for 146 ionic liquids has been used in the study. The results were compared with predictions of ten generalized corresponding states principle correlations available in the literature. These generalized correlations have not been applied to ionic liquids before so the appropriateness and accuracy of these models to ionic liquid density estimation are unknown until now. Results show that the new simple correlation gives low deviations and can be used with confidence in thermodynamic and engineering calculations.     

Scaling analysis of the temperature dependence of intrinsic viscosity

The scaling predictions for the temperature dependence of the intrinsic viscosity of flexible polymers are briefly reviewed. When the predictions are fit to a power law over a fixed range of chain length, a relation between the exponent and prefactor of the Mark–Houwink–Sakurada equation emerges. In comparing with the experimental data compilation of Rai and Rosen, we conclude that real polymer systems are nowhere near the true good solvent limit, even when the exponent matches the good solvent prediction. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1989–1991, 1997     

Theoretical study of two non-Markovian far-infrared spectra of HCl in liquids CCl4 and SF6 using a stochastic model

The far-infrared spectrum of dilute solutions of HCl in liquids SF₆ and CCl₄ are calculated by two non-Markovian formalisms described in ref. 1 using a Gaussian random field to represent the action of the solvent on a HCl molecule. The theoretical absorption coefficients involve two statistical parameters : the mean square interaction λ² and its correlation time t_c. In this paper, numerical values for these parameters are obtained by a fit to the available experimental spectra (refs. 8 and 9). These values are compared with those obtained in ref. 4 using a cell model for the liquid : there is a good agreement for HClSF₆ but not for HClCCl₄.     

On the diffusion of gases in partially crystalline polymers

The diffusion of gases through partially crystalline polymers is studied. The effective diffusion coefficient D^eff is obtained as the result of the averaged superposition of two fundamental mechanisms, namely, diffusion through the crystallites is considered to be zero, and diffusion through the rubbery fraction of the polymer obeys a Fujita-like free-volume theory. The predicted D^eff is compared with experimental data of Kreituss and Frisch. The behavior of the diffusion coefficient in terms of concentration and crystalline fraction is satisfactorily explained through the model.     

Positronium annihilation data and actual free-volume distribution in polymers

Determination of the size distribution of free-volume holes in solids, in particular, polymers, is an important physicochemical problem. The positron annihilation technique has been proposed for this purpose. The central point in this technique is the quantitative interpretation of data, especially, for substances with a high specific surface area. A developed free-volume system in open-pore membrane materials, such as poly(trimethylsilylpropyne) PTMSP and the spirocyclically bound benzodioxane polymer PIM-1, and polymeric sorbents (hypercrosslinked polystyrenes) makes it possible for the first time to compare the sorption characteristics and positron annihilation data on the character of size distribution of nanopores in these polymers. In combination with the results of mathematical simulation of the structure and radiothermoluminescence measurements, the array of data indicate the structural inhomogeneity of the test amorphous materials. It was shown that this inhomogeneity in relation to the positron annihilation technique is expressed in the insufficiency of the representation of the orthopositronium decay curve by one component that takes into account the Gaussian lifetime distribution (symmetrical pore size distribution) and in the necessity of use of several decay components. The feasibility of revealing a nonrandom character of pore size distribution gives the positron annihilation technique an advantage over other approaches (inverse gas chromatography, ¹²⁹Xe NMR) to investigation of nanopores in polymers.     

The effect of trimethylsilyl substituents in the monomer unit on the energy characteristics of surfaces of polynorbornenes obtained via metathesis polymerization

The surface properties of polynorbornenes obtained via metathesis polymerization are investigated via the wetting method. The incorporation of trimethylsilyl groups into the monomer unit causes decreases in the specific free surface energies of the investigated polymers. It is found that the dispersion terms of the specific free surface energies correlate with the free-volume and gas-permeability values of the polymers. As shown through the methods of differential scanning calorimetry and FTIR spectroscopy, during heating in air, the considered polynorbornenes undergo oxidative crosslinking, which increases their specific free surface energies. The interphase energies of crosslinked polynorbornenes are determined at their interfaces with liquids modeling polar and nonpolar phases, and the values of the work of adhesion of the crosslinked polynorbornenes to the model liquids are calculated. It is shown that the work of adhesion of the polymer to the polar phase decreases after introduction of trimethylsilyl groups, while the combination of polar and nonpolar phases give rise to an increase in the work of adhesion.     

Relation of gas-transport parameters of amorphous glassy polymers to their free volume: Positron annihilation study

Correlations of transport parameters (diffusion coefficients D and permeabilities P of gases) and thermodynamic parameters (solubility coefficients S and parameters C′ _H of sorption isotherms) with the sizes of free-volume elements, v _h, as estimated via positron annihilation lifetime spectroscopy are analyzed for the first time on the basis of the data array obtained for glassy polymers. Correlations of logD and logP with 1/v _h that agree with the free-volume model under the condition of a weak change in the concentration of free-volume elements in different polymers are ascertained. Certain deviations from linear correlations with 1/v _h for polymers with high free volumes are interpreted as evidence that the connectivity (openness) of pores increases with the sizes of free-volume elements. For solubility coefficients and Langmuir parameters of sorption capacity C′ _H , good linear correlations with the value of v _h are demonstrated.     

Free-volume theories for self-diffusion in polymer–solvent systems. I. Conceptual differences in theories

Conceptual differences in two recent versions of the free-volume theory for self-diffusion in polymer–solvent systems are identified and discussed. The validity of the assumptions of these two theories is tested using experimental data. In all cases, the experimental evidence favors the Vrentas–Duda free-volume theory over the Paul version of this theory.     

Capillary rise of liquids over a microstructured solid surface

The location of the triple line as a function of time has been recorded for a series of organic liquids, with various surface tension to viscosity ratios, wicking upward a rough Cu(6)Sn(5)/Cu intermetallic (IMC) substrate. The complex topographical features of such an IMC rough surface are characterized by surface porosity and surface roughness. A theoretical model for wicking upward a rough surface has been established by treating the rough IMC surface as a two-dimensional porous medium featuring a network of open microtriangular grooves. The model is verified against experimental data. The study confirms that the kinetics of capillary rise of organic liquids in a nonreactive flow regime over a porous surface having arbitrary but uniformly distributed topographical features involves (i) surface topography metrics (i.e., permeability, tortuosity/porosity, and geometry of the microchannel cross section); (ii) wicking features (i.e., contact angle and filling factor); and (iii) physical properties of liquids (i.e., surface tension and viscosity). An excellent agreement between theoretical predictions and experimentally obtained data proves, for a selected filling factor η, validity of the analytically established model. Scaled data sets show that, for a given rough surface topography, (i) wicking kinetics of considered liquids depend on properties of liquids, that is, surface tension to viscosity ratios and contact angles; (ii) the filling factor for all tested liquids is an invariant, offering good prediction within the range of ~0.9-1.0. The distance of the wicking front versus square root of time relationship was well established throughout the whole considered wicking evolution time.     

A comprehensive kinetic mechanism for CO,CH2O,and CH3OH combustion

New experimental profiles of stable species concentrations are reported for formaldehyde oxidation in a variable pressure flow reactor at initial temperatures of 850–950 K and at constant pressures ranging from 1.5 to 6.0 atm. These data, along with other data published in the literature and a previous comprehensive chemical kinetic model for methanol oxidation, are used to hierarchically develop an updated mechanism for CO/H₂O/H₂/O₂, CH₂O, and CH₃OH oxidation. Important modifications include recent revisions for the hydrogen–oxygen submechanism (Li et al., Int J Chem Kinet 2004, 36, 565), an updated submechanism for methanol reactions, and kinetic and thermochemical parameter modifications based upon recently published information. New rate constant correlations are recommended for CO + OH = CO₂ + H ( R23 ) and HCO + M = H + CO + M ( R24 ), motivated by a new identification of the temperatures over which these rate constants most affect laminar flame speed predictions (Zhao et al., Int J Chem Kinet 2005, 37, 282). The new weighted least‐squares fit of literature experimental data for ( R23 ) yields k₂₃ = 2.23 × 10⁵T^1.89exp(583/T) cm³/mol/s and reflects significantly lower rate constant values at low and intermediate temperatures in comparison to another recently recommended correlation and theoretical predictions. The weighted least‐squares fit of literature results for ( R24 ) yields k₂₄ = 4.75 × 10¹¹T^0.66exp(?7485/T) cm³/mol/s, which predicts values within uncertainties of both prior and new (Friedrichs et al., Phys Chem Chem Phys 2002, 4, 5778; DeSain et al., Chem Phys Lett 2001, 347, 79) measurements. Use of either of the data correlations reported in Friedrichs et al. (2002) and DeSain et al. (2001) for this reaction significantly degrades laminar flame speed predictions for oxygenated fuels as well as for other hydrocarbons. The present C₁/O₂ mechanism compares favorably against a wide range of experimental conditions for laminar premixed flame speed, shock tube ignition delay, and flow reactor species time history data at each level of hierarchical development. Very good agreement of the model predictions with all of the experimental measurements is demonstrated. © 2007 Wiley Periodicals, Inc. 39: 109–136, 2007