Use of a gee relationship in a diffusion study

Paul and Ebra-Lima⁶ reported on the pressure-induced transport of 12 organic liquids through a highly swollen rubber membrane. Gee¹⁰ examined the capability of a liquid to swell a rubber and the interaction between liquid and rubber from the standpoint of the Hildebrand-Scatchard solubility parameter. In this presentation, the swelling function of Gee was expressed by [V₀(δ₀ ? δ_r)²(1 ? v₀)²]^1/2 where V and δ are the molar volume and solubility parameter of the liquid 0 and the rubber r and (1 ? v) represents the volume fraction of rubber when the rubber is fully swollen by that liquid. The data of Paul and Ebra-Lima are analyzed in terms of the swelling function. It is principally assumed that the flux is a function of the swelling power of the liquid. The analysis indicates that the use of the Gee relationship provides values for the energetics of the various steps in the transport process and a means for differentiating between various types of penetrant liquids.     

Glass transition temperature and critical properties

In a preceding paper it was shown that for high molecular weight polymers, the volume of the repeating unit at T_g is proportional to the total free space defined as V_c?V₀ where V_c is the volume of the repeating unit at the critical temperature and V₀ is the volume of the repeating unit at absolute zero. Here it will be demonstrated that this proportionality is also true for a host of low molecular weight liquids. In addition, an empirical method of estimating T_c for a high molecular weight polymer is proposed which provides values of T_c which are consistent with those for low molecular weight liquids.     

Dynamic moduli for short fiber-CR composites

The dynamic moduli, E′ and E″, and tan δ for nylon–CR and PET–CR composites with unidirectional short fibers were studied as a function of temperature by using a Rheovibron. The temperature dependence of tan δ showed two dispersion peaks for nylon–CR composite. The peak at ?28°C corresponded to the main dispersion of CR and the peak at 100°C to the α-dispersion of nylon 6. For a PET-CR composite, in addition to the individual dispersion of CR and PET, a small and broad peak was observed at about 90°C. The angular dependence of E′ indicated that the short fibers assumed good orientation. The storage modulus for the composites was given by the parallel model as E′ = V_f′E_f + V_mE′_m., where E′_c, E′_f and E′_m were the storage modulus for the composite, fiber, and matrix and V_f and V_m were the volume fraction of fiber and matrix, respectively. In the transverse direction of fiber, the peak values of tan δ at ?28°C were given by the following equation; tan δ_c = tan δ_m ? δV_f, where tan δ_c and tan δ_m are the loss tangent for the composite and matrix, respectively, and α is coefficient depending on fiber type. The results indicated that a region with strong interaction was formed between fibers and CR matrix.     

Effect of molar size and solubility parameter of solvent molecules on swelling of a gel: a fluorescence study

Gels were swollen in various solvents with different molar volume V and solubility parameter δ. In situ steady state fluorescence (SSF) measurements were performed for swelling experiments in gels formed by free radical crosslinking copolymerization (FCC) of methyl methacrylate (MMA) and ethylene glycol dimethacrylate (EGDM). Gels were prepared at 75 °C with pyrene (Py) as a fluorescence probe. After drying these gels, swelling and slow release experiments were performed in various solvents with different V and δ at room temperature by time monitoring of the Py fluorescence intensity. The Li–Tanaka equation was used to produce time constant τ₁ values. Cooperative diffusion coefficients (D_c) were measured and found to be strongly correlated to the molar volume of the solvents used. Solvent uptake and degree of swelling were found to be dependent on the solubility parameter of the solvent. © 2000 Society of Chemical Industry     

Heptane-soluble material from atactic polypropylene. II. Interaction with liquids

Reduced melting point and swelling measurements, involving heptane-soluble material from atactic polypropylene and over thirty liquids of differing chemical type, are reported. A value of 578 ± 40 cal. is obtained for the molar heat of fusion of a crystalline repeat unit which is much lower than values given for isotactic polypropylene. Some reasons for the low value are considered. Values of the polymer-solvent interaction parameter χ₁ for systems involving alkylbenzenes and n-alkanes suggest a solubility parameter of 7.9 ± 0.1 (cal./cc)^1/2 for the polymer. These values of χ₁ decrease with increasing molar volume of liquid. Polar liquids of comparable solubility parameter or molar volume are associated with higher values of χ₁. Intrinsic viscosities and values of the slope constant k′ are given for fractions in the molecular weight range 3,000–25,000 and six solvents at 25°C. The results suggest the following order of solvent power: cyclohexane ≈ cyclohexene > methylcyclohexane > trichloroethylene > decalin > carbon tetrachloride. Intrinsic viscosities are higher than those generally obtained for flexible polymers of comparable molecular weight, and the values of the Mark-Houwink exponent appear to be high. Some reasons for these high values are considered.     

Solubility parameters of poly(4-substituted α-acetoxystyrenes) and alternating copolymers of vinylidene cyanide with substituted styrenes

The δ solubility parameters of three families of polymers have been determined by two calculation methods suggested by Small and Hoy. Hansen's model has also been used to assess δ and its components δ_d0, δ_p0, and δ_h0, so as to obtain more information on the intensity of the forces between the chain segments. Knowing the microstructure, the tacticity, and the thermal behavior of the copolymers has made it possible to explain both the different values of δ and the progression of solubility areas. Using Teas' method has made it possible to visualize on the same map the influence of the forces of interaction. This representation shows that the presence of the vinylidene cyanide unit in styrenic chains implies an increase of δ_p and a decrease of δ_d, whereas δ_h remains roughly constant for the corresponding homopolymer. © 1994 John Wiley & Sons, Inc.     

Diffusion and solubility of n-alkanes in polyolefines

The diffusion and partition coefficients (relative solubility constants) of n-alkanes (from carbon nos. 12–32) have been determined by a permeation method (pouch method) for the polyolefines LDPE, HDPE, and PP–copolymer, and PP–homopolymer at room temperature. The activation energies for the diffusion are interpreted in the meaning of the rate transition theory. Correlations exist between the activation energy δE and the heat of vapourization δ_vH_s as well as between the activation energy δE and the Arrhenius preexponential factors D₀. These correlations are useful for the prediction of the diffusion coefficients of n-alkanes with carbon numbers larger than 32.     

Diffusion and solubility of n-alkanes in polyolefines

The diffusion and partition coefficients (relative solubility constants) of n-alkanes (from carbon nos. 12–32) have been determined by a permeation method (pouch method) for the polyolefines LDPE, HDPE, and PP–copolymer, and PP–homopolymer at room temperature. The activation energies for the diffusion are interpreted in the meaning of the rate transition theory. Correlations exist between the activation energy ΔE and the heat of vapourization Δ_vH_s as well as between the activation energy ΔE and the Arrhenius preexponential factors D₀. These correlations are useful for the prediction of the diffusion coefficients of n-alkanes with carbon numbers larger than 32.     

Free volume of liquids and polymers from internal pressure studies

The free volume, v_f, of liquids is defined in many ways. Comparison of solid and liquid behavior indicates that the definition for free volume in terms of the internal pressure of the liquid (?E/?V)_T, is physically reasonable. Application of the definition of free volume, v_f = RT/(?E/?V)_T, to polymethylenes, coupled with surface energy values, leads to an evaluation of both polymer segmental volume, ?_s, and free volume per segment, (v_f)_s, as a function of temperature. These equilibrium thermodynamic measurements of ?_s and (v_f)_s lead to an energy of activation for viscous flow in good agreement with viscosity studies. Information of this type could be of great use in considering many current problems in polymer flow such as the effect of pressure on viscosity.     

The Solubility Parameter of Cellulose and Alkylketene Dimer (AKD) Determined by Inverse Gas Chromatography

The partial solubility parameters of cellulose and AKD (Alkylketene dimer) treated paper were determined by inverse gas chromatography. The Snyder/Karger-Hansen interaction model was used, where -ΔE^A = Vⁱδ^l _d + δ^l _pδ^j _p + δ^j _h δ^j _h). The adsorption internal energies of a series of n-alkanes and five polar probes were measured. From the ΔE^A values of n-decane, acetone and THF, which give the largest normalized determinant M(n), the partial solubility parameters of the stationary phases were calculated. The partial solubility parameters of cellulose were: δ_d = 8027; δ_p = 8.00; δ_h = 13.88; δ_t = 18.03 cal^½/cm^3/2 AKD treated paper gave δ_d = 8.10, δ_p = 12.35, δ_h = 7.96, and δ_t = 16.78 cal^½/cm^3/2.     

Density,refractive index,excess molar volumes and deviations in molar refraction at 298.15 K for binary and ternary mixtures of DIPE (OR TAME) + 1‐methanol (or 1‐propanol) + trihexyltetra‐decylphosphonium bis (2,4,4‐trimethylpentyl) phosphinate

The excess molar volumes (V^E) and the deviations in molar refraction (ΔR) at 298.15 K were determined for the binary systems {diisopropyl ether (DIPE) + 1‐propanol}, {Tert‐amyl methyl ether (TAME) + methanol}, {DIPE + trihexyltetradecylphosphonium bis(2,4,4‐trimethylpentyl)phosphinate ([P_666,14][TMPP])}, {TAME + [P_666,14][TMPP]}, {methanol + [P_666,14][TMPP]} and {1‐propanol + [P_666,14][TMPP]} using a digital vibrating‐tube densimeter and a precision digital refractometer. The V^E and ΔR were correlated with the Redlich–Kister equation for binary systems. In addition, the ternary V^E and ΔR data at 298.15 K were predicted for the ternary systems {DIPE + 1‐propanol + [P_666,14][TMPP]} and {TAME + methanol + [P_666,14][TMPP]} by using the binary contribution model of Radojkovi? with correlated sub‐binary Redlich–Kister parameters. © 2011 Canadian Society for Chemical Engineering     

Development of a correlation between the non-polar solubility parameter,refractive index and molecular structure. I. Aliphatic hydrocarbons

For non-polar liquids (e.g. the alkanes) the cohesion energy density (λ²) can be shown to be a function of the refractive index (nD ), molal volume (V) and molecular structure according to: where Δ is the non-polar solubility parameter and the increments g_ij are determined from molecular structure. The difference between values of Δ calculated by this formula and experimental data is <0.1% for the C₅–C₁₆ n-alkanes and <0.8% for the C₅–C₈ branched isomers. The main object of this correlation was to provide a method for estimating the London dispersion force contribution to the cohesive energy of branched polar liquids.     

Use of Hildebrand and Lamoreaux's theory to predict solubility and related properties of gas-liquid systems

There is a need in many fields such as chemical engineering, process chemistry and pharmacology for reliable data on the solubility, entropy of solution and partial molar volume of gases in liquids. Experimental data are not available for many systems of practical and academic importance and consequently a reliable theory to predict values for these properties would be of great use. Recent refinements of solubility parameter theory have been successful in predicting such values for several systems and in this paper results obtained from this theory are compared with experimental measurements on a large range of gas-liquid systems. The agreement found is satisfactory in the most part, but for helium, neon, xenon, hydrogen and deuterium, the predicted results deviate consistently from the experimental values. This is to be expected on the basis of some of the earlier results of solubility parameter theory and an empirical modification is proposed that yields significant improvements in the predicted values. This has also been used to predict values for carbon dioxide, tetrafluoromethane and sulphur hexafluoride to which the theory is not directly applicable. Values predicted by solubility parameter theory are compared with those obtained by Battino and co-workers from scaled particle theory. In general, the two theories are equally successful in predicting solubilities, but refined solubility parameter theory yields better values of entropy of solution. It is concluded that the theory provides a useful means of predicting solubility and entropy of solution but that prediction of partial molar volume results is limited because of the paucity of data for the thermal pressure coefficients of the solvents. Attention is drawn to apparent inaccuracies in certain experimental measurements. The interrelationship between the various forms of the entropy of solution used by different workers is clarified. A value of the energy of vaporisation of carbon dioxide, δE₂^v=2.64±0.15 kcal/mol is calculated.     

Predicting solubilities of vinyl polymers

Accurate solubility limits of polymers are best expressed by molecular weight fractionation curves. Individual curves may be obtained for each polymer–solvent (–nonsolvent) system. A method for predicting solubility behavior, based on solubility parameter δ and hydrogen bonding index γ, is proposed here. The correlation is of the form where [η] = intrinsic viscosity of precipitated polymer; T = absolute temperature; (v.f.) = volume fraction of solvent; R = (δ_s ? δ_n) ? 0.3(γ_s ? γ_n); Q = (γ_p ? γ_e)^2.2/(δ_p ? δ_e); p refers to polymer; s refers to solvent; n refers to nonsolvent; e refers to solvent system at theta temperature; and a,b,c, and k are fitted constants. The correlation was derived from data for poly(vinylpyrrolidone) and polyacrylamide. It probably is limited to systems in which the precipitate occurs as a liquid.     

Determination of the glass transition of polymer by the autovibron

The automated Rheovibron (Autovibron) has been useful for determining the glass transition behavior of polymers. The standard (manual Rheovibron viscoelastometer has been used sufficiently small intervals, and so, some accuracy on transition location must be sacrificed when the temperature intervals are taken 5 to 10°C apart. However, the Autovibron can be observed over very small temperature intervals (<1.5°C)), which essentially provide a continous monitoring of the changes in storage modulus, loss modulus, and tan δ. An improved accuracy and sensitivity of the Autovibron are provided by a combination of multiprogrammer, programmable calculator, and lock-in analyzer. The Autovibron are provided by a combination of multiprogrammer, programmable calculator, and lock-in analyzer. The Autovibron shows a good capability for dynamic thermomechanometry. The glass transition bility for dynamic thermomechnometry. The glass transition of polymers can be determined by analyzing the loss tangent peak. The maximum value in loss tangent, peak temperature, and the newly introduced terms, ΔT₁ and ΔT₂ which indicate the widths of tan δ peak, are useful indicators of the glass transition. The ΔT₁ and ΔT₂ show the distribution of the glass transition and are related to order and crystallinity in the structure.     

Solid-liquid phase equilibria,excess molar volume,and molar refraction deviation for the mixtures of ethanoic acid with propanoic,butanoic, and pentanoic acid

The paper reports the solid-liquid phase equilibria (SLE), excess molar volume (V^E), and molar refraction deviation (ΔR) for binary systems of ethanoic acid with the C₃ to C₅ carboxylic acids, propanoic, butanoic, and pentanoic acid, which are the main constituents of bio-butanol fermentation broth. The SLE was determined via a synthetic method using a custom-built glass tube at atmospheric pressure, whereas the thermodynamic mixture properties, V^E and ΔR were obtained from directly measured density and refractive index using a precision densitometer and refractometer, respectively. All of the SLE that were determined for binary mixtures of ethanoic acid+C₃-C₅ carboxylic acids showed a single eutectic point and regressed well with the NRTL activity model within 0.6 K of RMSD. The V^E values for the same binaries were positive for the entire composition ranges of all the systems, whereas the ΔR values were negative for all the systems. The V^E and ΔR were well regressed by polynomial equations, namely Redlich-Kister within 0.006 cm³·mol^?1 of the standard deviation for V^E and 0.02 cm³·mol^?1 for ΔR.     

Dynamic viscoelasticities for short fiber-thermoplastic elastomer composites

Dynamic moduli, E′ and E″, and loss tangent tan δ were investigated for thermoplastic elastomers (TPEs), styrene-isoprene-styrene copolymers (SISs), styrene-butadiene-styrene copolymer (SBS), and Hytrel and composites reinforced by poly(ethylene terephthalate) (PET) short fibers. The styrenic TPEs have a typical rubbery behavior and the Hytrel TPE has medial characteristics between rubber and plastic. Both E′ and E″ of the composites depended on the matrix as well as the fiber loading and fiber length. Based on the viewpoint of different extensibility between the fiber and the matrix elastomer, a triblock model was considered for estimating the storage modulus of the short fiber-TPE composites as follows: E_c = αV_fE_f + β (1 ? V_f) E_m, where α and β are the effective deformation coefficients for the fiber and the matrix elastomer, respectively. They can be quantitatively represented by modulus ratio M (= E_m/E_f) and fiber length L: α = ( Lⁿ + k) M/ ( LⁿM + k), β = (1 ? α V_f)/ (1 ? V_f), where the constants n and k are obtained experimentally. When k = 0.022 and n = 0.45, E_c of the TPE composites agreed well with the prediction of the proposed model. The relaxation spectrum of the composites showed a distinct main peak ascribed to the matrix elastomer, but no peak to the PET fiber. The relative damping of main relaxation, (tan δ_max)_c/(tan δ_max)_m, decreased monotonously with increasing fiber loading and fiber length and with decreasing modulus of matrix elastomer. Thus, the relative damping may be attributed not only to the volume effect of matrix, but also to the unevenness of the strain distribution in the matrix phase, which depends on the fiber length and the matrix's modulus. The findings prove that the different extensibility between fiber and matrix and the uneven distribution of strain in matrix were important for the short-fiber reinforcement of the TPE composites. © 1993 John Wiley & Sons, Inc.     

A novel approach to the interpretation and prediction of solvent effects in the synthesis of macroporous polymers

A trivariate interpolation technique, the modified Shepard's method, was applied for the first time to explain and predict various properties of macroporous polymers from the Hansen solubility parameters of the porogens employed for polymerization. Highly crosslinked polymers and copolymers were prepared from ethylene glycol dimethacrylate and methacrylic acid by free‐radical polymerization with 30 different porogenic solvents. Instead of the spherical model used by Hansen, detailed three‐dimensional maps were computed to represent the measured properties in a δ_d–δ_p–δ_h diagram (where δ_d, δ_p, and δ_h are the Hansen solubility parameters according to the three types of bonding forces: dispersion, polar, and hydrogen‐bonding, respectively). This method was able to detect unapparent correlations between the different polymer properties, thus providing a better understanding of the pore‐formation process. An important finding was the crucial role of the initiator solubility and its partitioning between the solution and the polymer surface, which proved to be key factors for the explanation of many contradictory solvent effects. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Gas permeation of polymer blends. III. Poly(vinyl chloride) (PVC)/chlorinated polyethylene (CPE)

The permeability P, diffusivity D, and activation energy for diffusion, E_D, of He, O₂, N₂, and CO₂ were determined for blends of PVC/chlorinated polyethylene (CPE), where the chlorine content of the CPE components varied: 36 wt-% for CPE-1, 42 wt-% for CPE-2, and 48 wt-% for CPE-3. The difference in thermal expansion coefficients Δα above and below the glass transition temperature T_g of the polymers and the fractional free volume V_g of the polymers at their T_g were determined. Density and crystallinity measurements for the blends were also carried out as in the earlier work (Shur and Rånby, J. Appl. Polym. Sci., 19 , 1337 (1975)). Dynamic mechanical measurements of the blends were made using a torsion pendulum at about 1 Hz. P and D decreased, but E_D increased with increasing CI content of CPE in the blends. P and D for the blends showed no additivity. The permeability indicated phase inversion for blend compositions at about 10% of CPE-1 and CPD-2 by weight. The experimental and the calculated densities were largely the same for PVC/CPE-1 blends; but for PVC/CPE-2 and PVC/CPE-3 blends, the experimental values were higher than the calculated ones. The Δα and V_g values for PVC and the three CPE samples decreased with increasing CI content in the polymers. Dynamic mechanical measurements indicate that PVC/CPE-1 and PVC/CPE-2 blends form largely incompatible blends, while PVC/CPE-3 blends are compatible to some extent. There is some weak interaction between PVC and CPE-3 giving a low level of compatibility. The solubility of gases obtained from time-lag measurements of diffusion for 50/50 blends decreased for He, O₂, and N₂, but increased for CO₂ with increasing Cl content in CPE. The solubility of He, O₂ and N₂ shows a positive correlation with the Lennard-Jones force constant ?/k. However, a deviation from the linear relation between ?/k and In S was observed for CO₂ and the deviation became larger with increasing Cl content in CPE. The abnormally high solubility of CO₂ is probably due to the high polarizability of this gas. The heat of solution ΔH_s indicates that for He the sorption process may be a molecular slip process (endothermic), but for other gases the sorption may proceed by a dissolution process (exothermic). There is a large difference between the calculated solubility for the blends assuming incompatibility and the experimental values from time-lag measurements. This may partly be due to the uncertainty of sorption values obtained from the time-lag method and/or partly to changes of sorption modes by interaction between PVC and CPE in the blends. The resulting transport behavior of the blends is discussed on the basis of the free volume concept and of phase–phase interaction in the blends.     

The solubility parameters of aromatic polyamides

The degrees of swelling of rigid aromatic polyamide networks in various solvents, nonsolvents, and solvent mixtures were used to determine their solubility parameters. This was made possible because of the amorphous nature of the rigid networks and the low levels of intersegmental H-bonding. The solubility parameters are: δ = 23.0 (MPa)^1/2, δ_d = 18.0 (MPa)^1/2, δ_p = 11.9 (MPa)^1/2, and δ_H = 7.9 (MPa)^1/2. The determined values are believed to be good approximations of the solubility parameters of stiff linear aromatic polyamides, because of the essential identity of their structure and the stiff segments in the networks.